The Geometry of Time

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By Ruth Marion Graf and Taurus Eric Taurus, PhD, Biophysics

©, Ruth Marion Graf, 5/24/15, ruthmariongraf@gmail.com


In days of old the Egyptians developed an extended lexicon of spatial relationships to build the pyramids and restore the borders of annually washed out Nile River farms. It wasn’t until after millennia of practical proof of these spatial rules by successful application that a Greek mathematician, Euclid, came to Egypt and logically stitched them together into the geometry we know and study today. His doing so was an enormous step forward for science.

Now we ask: Can this unification of spatial relationships done by Euclid be repeated for temporal relationships? Can all the different processes in nature - physical, biological and human - be stitched together in a succinct and comprehensive way that parallels Euclidean Geometry?

The answer is: Yes. The last 75 years development of computer science makes this possible. The Cybernetic Age came into existence with the theoretical work done on negative feedback control at MIT in the 1940s. This early cybernetic research soon led to the building of the forerunner machines of modern computers. The science generated by these efforts also led to a much clearer understanding of homeostasis (feedback control) in biological systems. And now cybernetics has evolved into such a firm set of principles that many American universities now have a Dept. of Systems Engineering entirely devoted to feedback control.

We will develop The Geometry of Time around the error function in feedback control systems, epsilon, Ԑ. A familiar system that illustrates the Ԑ epsilon error function is a thermostat controlled heating system. Consider the temperature of a room to be initially at θ = 0oF, very cold. Now you set the thermostat at θS =70oF. That is the set point of this feedback control system. The Ԑ error is just the difference between the desired temperature set on the thermostat, θS, and the actual room temperature on the thermometer, θ.   

301.)            Ԑ = θS−θ 

(The number 301 refers to an equation in Section 17 that can be scrolled down to immediately for greater detail, though the recommended approach to understanding The Geometry of Time is by first reading this introduction.)

The elimination of this Ԑ=θS−θ error is how this cybernetic system works. Specifically the Ԑ= θS−θ error is eliminated by the system responding to it by turning on a furnace to heat the room. This makes the room temperature, θ, increase, eventually to θ=θS, at which point the error is eliminated, Ԑ=θS−θ=0, and the furnace shuts off. Eliminating the error, making Ԑ=(θS−θ)=0 and θ=θS, is how a cybernetic system achieves its θS set point goal.      

Now we want to understand every process in nature – physical, biological or human – as a cybernetic process that works by the elimination of Ԑ error. This perspective clarifies, we will see, some as yet still very confused concepts in science like entropy, evolution, emotion and morality. Because these topics are often heavily debated, emotional and contentious we will talk about them in mathematical language that avoids the spin that ambiguous ordinary language enables in religious, ideological and psychobabble discussions of such important issues.    

Thermostatically controlled heating is one of a wide variety of man-made feedback control systems. Cybernetic theory also explains the organ systems of living creatures whose set points for surviving, reproducing and self-defense avoid death and extinction for them. Our automatically breathing hard when we run fast that draws in oxygen rapidly to eliminate the oxygen deficit or error caused by running fast is a familiar example. 

Beyond these two broad areas of feedback control in engineering and biology lays a spectrum of processes said to operate by passive feedback control. Clarifying it is a prerequisite for making sense of evolution as a passive feedback control process. That is very important because the denial of evolution and other science denials are a major vulnerability for America at this time when it is so beset by violence, domestic and international, that can’t be properly explained or resolved without understanding human nature in terms of evolution.

A simple example of passive feedback control is an RC (resistance-capacitance) electronic circuit. Before we get into it, though, we want to return to our thermostatic heating system for a closer look. A mathematically regular form of thermostatic heating called proportional heating exhibits the 1st order feedback control we need to explain passive feedback control and ultimately evolution. Proportional heating makes for a θ temperature increase in the room that is directly proportional to the Ԑ=θS−θ error. It works by more burners in the furnace being turned on when the Ԑ=θS−θ error is great and the room very cold. And fewer burners stay lit when the θ room temperature increases and the Ԑ=θS−θ error gets smaller and smaller. The θ room temperature increases in this way eventually to θ=θS to eliminate the Ԑ=θS−θ error as seen in the graph below.

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Figure 306. The θ Temp (in green) and Ԑ=θS −θ Error (in blue) in Proportional Heating

The horizontal axis is time passed and the vertical axis numbers (when multiplied by 14) specify the θ room temperature as it increases over time on the green curve. We see this θ room temperature to be θ=00F to start off and then increase gradually towards the θ=θS=70oF thermostat set point (5 multiplied by 14.) And the descending blue curve in the graph represents the decrease in time of the Ԑ=θS −θ error that as it approaches zero and is eliminated causes the furnace to be automatically shut off. We see in this illustration that cybernetics works by an Ԑ=θS −θ error that generates activity aimed at the eventual elimination of that error. An RC circuit works in essentially the same way.

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Figure 307. An RC Circuit

Electric charges, q of them, flow from the battery, VS, on the left to the capacitor on the right whose C capacitance is a measure of the qmax maximum number of charges the capacitor can hold. In that regard qmax as the product of the battery voltage, VS, and the C capacitance, qmax=CVS, is the set point of the charging process, the value of q the system ultimately gets to. The well-known equation that governs this RC charging process, Kirchoff’s Law, has the q charge on the capacitor increase over time to qmax in the same way that the θ temperature increases over time in the green curve of Figure 306 for 1st order feedback control. 

This property identifies the RC circuit as some kind of feedback control system, albeit a “passive” one. This is not that surprising given that Kirchoff’s Law for the RC circuit and the equation for 1st order feedback control for proportional thermostatic heating have the exact same form, the only difference between them that the qmax set point of the RC circuit is a fixed part of circuit while the θS set point desired temperature on the thermostat is a goal actively set by a person. This distinction between passive and active feedback in terms of the origination of the set point is minor relative to the cybernetic properties the RC circuit and the proportional thermostatic heater have in common that are more important than their differences.

The discharge of an RC circuit can also be understood as passive feedback control. When the RC circuit is “open” or disconnected as shown below, whatever qo charge is on the capacitor to begin with dissipates until no charge at all is left, q=0.   

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Figure 309. A Discharging RC Circuit

Now the set point, where the system is headed, is q=0. 

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Figure 310. The q Charge in a Capacitor Over Time in a Discharging RC Circuit

And this understands the error in the system to be Ԑ=0q, which is eliminated and becomes equal to zero when q=0.

We have learned enough now about the basics of passive feedback control to explain evolution in cybernetic terms. The primary components of Darwinian evolution are the natural selection of species from competition and the arrival of new species on the scene from variation which join in the competition between existing species. An equation for natural selection that pinpoints the cybernetic elements of set point and Ԑ error was first worked out by noted population biologists of the 1920s, R.A. Fisher, J.B.S. Haldane and Sewell Wright, and more recently derived in the simplest way by us in Section 14 at Eqs269. The critical term in that equation for determining which of two competing populations wins out is     

274.)                                  F1 = g1−g2= (b1−d1) − (b2−d2) =b1−d1−b2+d2       

The F1 variable is the fitness function for population #1 of two populations that live in the same niche and compete for the space and resources in it that are needed to continue to exist from generation to generation and avoid going extinct in the niche. The b and d terms in F1 are respectively the birth and death rates of population #1 as b1 and d1 and of population #2 as b2 and d2.

And the g=b−d terms are the growth rates of the competing populations. When the g1=b1−d1 growth rate for population #1 is greater than the g2 growth rate for population #2, population #1 in blue below flourishes while population #2 in red dies out or goes extinct in the niche.   

Figure 273. Competitive Population Growth or Natural Selection


The curves in the above that arise from Eqs265,269,271&272 of Section 14 depend strictly on whether the F1 term in them is positive, F1>0, or is negative, F1<0. If F1>0, the equations tell us that the x1 size of population #1 eventually grows to the K=100 carrying capacity of the niche, x1=K=100, and wins out and that the x2 size of population #2 eventually decreases to x2=0 and dies out in the niche.

The set points for the two populations that tell us where they’re heading are quite different. Population #1 has a set point of x1=K and is in error prior to its being reached of Ԑ1=K−x1. And population #2 has a set point of x2=0 and is in error prior to reaching that end point of Ԑ2=0−x2. This take on natural selection of course makes little sense in terms of somebody desiring the θS set point of the temperature set on the thermostat or the qmax set point for a charging RC circuit or the q=0 set point for a discharging one, both of which latter capacitance goals might be desired by a designing electrical engineer for whatever reasons.

Nonetheless an evolving system of two competing populations move to their respective ends in terms of cybernetic set points and Ԑ error functions no differently than the thermostatic and RC circuit control systems, active and passive. Indeed the extreme similarity between the two dynamics despite evolution’s end points not being either desired or selected by any human being is what makes for the mammoth confusion between the quite passive and unintended end point direction of populations naturally selected in evolution and a desired or intended intelligent selection of what succeeds and what goes extinct by some imagined super-human being that we Christians over here call God and the other nuts across the sea call Allah.       

Of course we should ask: If it is not a person of some sort who stipulates the set point choice of the natural selection process, what is it? What determines whether a species (or subset population) survives or goes extinct? Very simple and impossible for any educated person to argue is the chance variation introduced into populations that may be deleterious or beneficial to their g growth rate. By chance here, we mean through random mutation, through sexual gene recombination that is mostly a matter of chance and through chance relocations to novel environments that may affect gene expression in a random deleterious or beneficial way. In that sense it is the fickle hand of fate that controls Darwinian evolution rather than the hand of God or the hand and mind of man, which, as we shall discuss next, does make conscious set point choices that affect not only the destiny of individuals but also where cultural evolution goes.

To unify all processes in nature in The Geometry of Time, we identify them not just as cybernetic but also as evolutionary. Such generality for natural selection becomes clearer when we understands the b birth rates in the F1 = (b1−d1) − (b2−d2) fitness function most generally as the rate of any object (or chunk of matter-energy) coming into existence; and the d death rates in F most generally as the rate of any object going out of existence.

Beyond natural selection for biological populations, it is also readily shown for molecular populations as in the in vitro transformation of amorphous calcium phosphate (ACP) to crystalline calcium phosphate (HA) as mimics bone and tooth maturation in living systems. This is described in detail in Section 18. Both the ACP and HA have a precipitation constant, b, for the rate they come into solid phase existence and a dissolution constant, d, for the rate they go out of existence as solids. In this transformation the HA molecular species, which has the larger growth rate constant, precipitation minus dissolution, increases its number of molecules to eventually become the only calcium phosphate phase in the mix while the ACP with the lower growth rate constant goes completely out of existence. This section is worth reading if no other reason than the strong mathematical recommendation of a leading American mathematician, Dennis Sullivan, the National Medal of Science winner in 2004.

Mon, 27 Feb 2006 23:50: why not publish the part that explains Posner's data in terms of the logistical equating on ...first... then do some of the rest next... etc... then as your acceptance takes hold do the more radical parts...as it is you may be pre-empting any real success by indulging your own deeply felt philosophy... by the way your explanations in the first parts were very clear....you may want to read how Einstein in similar and simple layman's terms dispelled the notion of absolute time in the 1905 paper....and how he did it without being untoward...

good luck  

dennis Sullivan            


(We’ve tried over the last decade to become less “untoward” in our consideration of contentious issues without feigning too much political correctness.)   

While the governing functions for chemical selection of HA over ACP in Eqs411&412 are somewhat different than those of Eqs269&272 for biological natural selection, what is quite the same in both is that the species, chemical or biological, with the greatest growth rate (birth minus death rate) persists while that with the lowest growth rate dies out.    

This difference in growth rates as the fundamental factor in competitive selection is so general that it applies also to every kind of chemical reaction. And note also that every chemical reaction also proceeds in negative feedback control fashion as directed to the position of chemical equilibrium for the reaction as its set point while minimizing an error function based on the set point. Hence we can conclude from this that all biological systems are cybernetic and evolutionarily selective and that all chemical systems are also cybernetic and evolutionarily selective. What of other kinds of processes?     

Sitting at the fringes of chemical and biological systems are thermodynamic and human emotional systems, both of which we treat in full fashion in Section 14 and in Sections 9-13. A thermodynamic system evolves randomly it is shown in Section 14 and its cybernetics is of 2nd order feedback whose set point is an average of a stochastic distribution of energy over molecules.       

I tried to explain all this to the mathematically incompetent Math/Physics Dept. of the Colorado State University at Pueblo (CSU-P), all of nature - physical, biological and human - can be understood in a mathematically unified way in terms of the epsilon error function of cybernetic systems. But these professors led by their Dept. Chairman, Frank Zizza, are a perfect example of the worst that university teachers have become, boneheads incapable of understanding anything other than what they regurgitate from the textbooks they memorized to get their jobs. Worse than that as regards the welfare of the students at CSU-P, as I make clear at the end of Section 17, one of these CSU-P teachers I got into a cute email exchange with is a strong bet to be a Dennis Hastert closet faggot. This crew epitomizes an American academia that truly stinks in caring more about paychecks, position and dominance over students than truth. It’s bad enough that our American media has evolved into hard science deniers, Fox News leading the way. But that the science profession as a whole just sits there with its mouth shut at this critical time for America, domestically and internationally, looking for all practical purposes like the bunch of clowns in The Big Bang Theory is utterly unforgivable. The Geometry of Time is new science that does address our problems in a firm mathematical way and as such deserves a thorough airing. While the bulk of this thesis is the highly technical mathematical analysis starting in Section 1, we begin by laying out some of the main problems the analysis is designed to clarify and solve.

Unkilling the Messenger: the Baltimore Riots and Beyond

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The full message of cybernetic generality and why every effort is made by the ruling class to kill it culminates down in Section 17 the end of which is very funny (as is appropriate after the first 16 sections of mostly very dry mathematics.)

The obvious message in the Baltimore riot photo is that these people are angry about the police murder of Freddie Gray. It’s not just the fellow smashing the window whose anger is plreleased in this act of destruction. It’s the people behind him, too, along with the thousand others who helped tear Baltimore apart. And not just because of the killing of this one man but because they all, as with millions of others across America, black and white, have been the target of police abuse in one form or another. That’s the message the media incessantly kill, that the police are predators on non-professional people effectively making America with its highest lockup rate in the world and in all of human history a police state.

Oh, no its not, say the journalist, politician and clergy mouthpieces of the ruling class who control the media message. The people who trashed Baltimore are thugs, bad people who used Freddy Gray’s death in police cusotody as an excuse to steal and destroy property for no sensibly justifiable reason. These are two very different messages. It matters a lot which of them is understood to correctly represent reality. It matters a lot which one people believe is true.   

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This is Hiroshima, 1945, right after the bomb fell. The utter destruction of that city many years before the Baltimore riots came from the same emotion, the violence from man’s evolutionary heritage intensified by the unhappiness caused by civilization’s inbuilt restrictions and exploitation. Hiroshima’s can happen again and on a scale that terminates the human experiment. For that reason it is important to get the message right. What is the true nature of man, especially as it concerns his [propensity towards violence? What is his predictable fate? Only in getting the message straight can we find the way to prevent more Baltimore’s, more Sandy Hook mass murders, more police murders, by and of them, and more Hiroshima’s.

My noting my co-author’s PhD training is important because we are going to show which message is correct using science. We’re going to prove it with a mathematical argument that is as logical and as trustworthy as 2+3=5. Now there are some out there who think God is above mathematics in being able to make 2+3 be equal to something other than 5 if He wishes. Such people believe whatever anyone in authority tells them, be it God, the media or the police. The violence in the world that threatens to end it will not be quelled with the help of such stupid people who are beyond sensible arguments that even an eleven-year-old can understand. Indeed, let me introduce you to this mathematical take on violence and what to do about it with the help of one such eleven-year-old.        

One day in 2008 down in Acapulco, Mexico, while in retreat there from the Bush regime of 2000-2008, my grandson, the one in the middle below, a dropout in attitude but with a high speed curious mind, asked me: How did they measure distance before rulers and such were invented, Gram?    

They measured distance in feet with their actual feet instead of with one foot rulers, I answered. If you wanted to know how long a road was in ancient times you walked the distance off, one foot pressed in front of the other, while counting the number of feet you walked off.

Champ, the nickname we gave the boy at birth in hopes that fate would be kinder to him than most, quickly replied: But that’s not very exact because unless you had one guy measuring the distance of all the roads in an ancient kingdom with just his feet, the difference in the length of the feet of the different people who might be doing this measuring would lead to inaccuracy in the distances measured. 

Smart kid, a bit lazy like I said, but with a very quick mind. For that is very true and, as we shall see, the basis of an elementary correction in mathematics that configures science differently. That includes not only revising thermodynamics to clarify the centuries old mystery of entropy but also the human sciences to mathematically clarify the emotion of anger and how to tamp down violence and the horror it causes domestically and in war. To see the unarguable connection between extreme violence and tyranny and the inexactness in the count of things unequal in size you have to do the homework needed to follow the mathematical argument.      

A count of things unequal in size, of people’s feet with different lengths or of molecules with different speeds, is inaccurate or inexact. Early humans took care of the inexact distance problem when they replaced people’s anatomical feet as measures of distance with foot long rulers, all of whose feet, unlike people’s feet, are the same size and whose count is, hence, exact. The problem of inexactness in counting things unequal in size goes beyond the distance measure problem, though, and is troublesome even today for a proper understanding of physical nature and of human nature.   

Count the number of objects in (■■■■). There are 4, of course. Now count the number of objects in (■■). There are also 4, you answer quickly. But is that count of 4 for (■■) an exact count? No more than a count of the number of feet an ancient road is long is exact when the feet walked off are of different sizes. This problem of inexactness is why the concept of entropy has remained so difficult to understand for so long. And it’s also why the psuedo-science of psychology is as vague in explaining human nature with its elusive psychobabble as Christian dogma is in explaining the birth of God Jesus with the Virgin Mary’s magical, biologically impossible, no-sex pregnancy. 

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Perhaps it was God, the Father of Jesus, who slipped it in with Mary so fast asleep she didn’t notice? Or perhaps the Devil did the dirty work with Mary not as asleep as she pretended to be? 

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Excuse the blasphemy. The point I’m trying to make with this joke on the Pope and His followers is that super-vague notions like God’s ability to shit without needing to wipe His Ass, Satan’s evil and the ever mysteriously caused disease of “mental illness” don’t give rational cause and effect explanations for the mass dysfunctional behavior, unhappiness and violence we see in modern times. True believers in psychology should question its validity as an authoritative science right from the get-go in psychology giving a pass to all the nutty superstitions of religion as acceptable thinking for well-adjusted people. Psychology’s failure to label praying (talking to a personality nobody can see and asking a favor of it) as delusional, even if emotionally comforting, is quite contrary to how all the other sciences, the ones that make our computers and fly us to the moon, operate. Can people be so blind as to not see that psychology acts consistently like religion, as a moral code whose central preachment is that disobedience to and revolution against the authority of the ruling class is wrong?       

Holding the misleading notions of religion and clinical psychology in one’s mind as firm truth makes impossible a causal explanation of the bad things that happen in life, like today’s epidemic unhappiness from failure in love, and, thus, impossible to correct. Resolving the error in counting inexactness gets science spruced up enough to properly explain not only complex physical phenomena like entropy but also today’s epidemic unhappiness and the violence it brings about and what can be done to eliminate the worst of both the unhappiness and the violence. If this sounds like bullshit at least as doubtful as Mike Huckabee’s promise that an electric bass playing fundamentalist minister in the White House would bring God’s favor upon America, you have the read the God damned mathematics. Before Newton’s mathematical theory of gravitation was accepted, everybody in medieval Europe, rich and poor, educated and peasant, believed as firmly as the sun rising in the East each morning that angels commanded by God pushed the planets around in their observable orbits.          

The problem with resolving today’s contentious issues with mathematics, though, is that the scientists who do understand mathematics fluently are effectively paid off in pay and status to avoid speaking out on matters that cast doubt on the benevolence of the ruling class and that the little people who take the greatest hit from their lowly position on the totem pole see mathematical language as readable as Transylvanian Bulgarian. All use basic math and trust it without question when it comes to adding up the groceries at the checkout counter and computing the dent the grocery bill makes in one’s weekly paycheck. But the article about whether Kim Kardoochian or Taylor Switt’s ass is the cuter is invariably read with more interest than a mathematical explanation of life’s pains, even if the latter can clearly explain their cause and what can be done about them.

To get around such math phobia I’ll start off minus the equations that give the math haters indigestion. That should give them the gist of the argument if not the proof while also encouraging the more educated readers to go on to the Section 1 where we begin the mathematical analysis needed to ail the truth down in an unarguable way.   

Ancient peoples had to develop standard measure devices like twelve inch foot rulers or they would not have been able to make the impressive things they came to construct in centuries past like the pyramids.

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If the building blocks of a pyramid aren’t made exact in size with standard measure, they won’t fit together well enough to make a pyramid. Another thing needed was a lot of people, all guys back then, to do the backbreaking work to make the pyramids the pharaoh used to glorify himself. Was it slaves who made the pyramids? Whatever the spin put on working class life in ancient Egypt, one thing for sure was that there was a lot of slavery around back then, in Egypt and Babylon and Persia and then Rome and Greece and then in the medieval Christian Europe that fueled itself on the labor of its jillions of serfs and slaves and then in the pre-civil-war Southern states of America.            

Not only are people made miserable being under the thumb of a slave-master mentality ruling class, but also, hard truth be told, women, of which I am one, are not impressed by men who are slaves and have the well-adjusted slave mentality. I’m not saying women lack admiration for slaves who have the balls to resist their enslavement by rebellion or flight. Three large cheers for any Django Unchained type who retaliates on his masters with guns blazing. But run of the mill male slaves that suck off their master to avoid a whipping or get a meal, women do not turn on to or fall in love with. With sincere apologies to the sensibilities of my suffering black brethren, Thomas Jefferson’s black slave mistress, Sally Hemings, much preferred screwing President Jefferson by whom she had six kids than the niggers that Jefferson owned as slaves who picked his cotton and cleaned his toilets. 

Excuse the word nigger I use to hammer home the point that slavery, in any and all of its forms, be it plantation or modern wage slavery, makes a nigger out of a guy, black or white, to make a mess out of love. It doesn’t matter if you’re only the boss’s slave for just 40 hours a week. Women just aren’t attracted to men made jerks out of in this way. Not that a woman doesn’t give such men a try, for the female mind says instinctively in the absence of an emotionally healthy fellow, maybe this one will do. But in the end, after a couple of years and a couple of kids, the smell that lingers from hubby’s cleaning the boss’s toilet during the work hours, despite the gewgaws his salary might provide, eventually overwhelms the perfume of love. The initial glow of love she felt turns to contempt and eventually that overpowering urge to reject him unless the prospect of living alone in relative poverty comes to tolerate his noxious smell as the lesser of evils. 

Now not only does slavery, in whatever Christmas paper the slave culture wraps it in, destroy love, but breaking up makes the male slave feel much like a dumb dog out in a pounding rain just happy just to have a bone thrown to him and not very prone to rebel against the subservient state that caused the breakup to begin with. Conversely, few things make a man feel more vigorous and strong than the love of a woman and prone as such to resist the slave state of existence.

The frustration and loss of love, then, is an effective emotional crippling of men that kills the rebel in them. The providence of this for the ruling class, so happy to have slaves who lack the rebel element in them, has made true love taboo. Sexually successful men are much more likely to rebel against control, which slants the culture morally sharply against their kind. On the one hand sexually dominant men are displayed to the girls in the media and in other ruling class controlled information outlets as devils with cruel and abusive horns. The word is out: stay away from this kind of men; they’re going to do nothing but hurt you, rape you, use you, abandon you, make you miserable. And girls who disregard these warnings are made to feel like inferior, stupid fools. What you want, they are told 24/7,  is a nice soft squishy slave type guy who will commit to bringing home the bacon and to not fussing too much when you agree to have sex with him only once every two weeks with him on the bottom and your toy up his ass. It’s hard for the girl to avoid rejecting healthy men and choosing a jerk when every movie, sitcom and news article tells the girls to beware the aggressive male who might have any vigor in him to make things click.                    

And in recent times the “men are bad” campaign that Christianity has fostered for the last millennia has been ramped up by laws across America that make a lingering glance by a man attracted to a pretty girl liable to be taken as “sexual harassment” of some kid that could destroy his life as a “sex offender”, a fate not much worse than being crucified slowly. This broad anti-love strategy imposed by the ruling class through its religious, psychology and politician mouthpieces also turns out to be hell for women in the end. Yes, you get to be a Queen in your teen years and early twenties, the slim girl with a practiced smile who tells the guys to get down on their knees for a sniff of the backside of her jeans. But in the later years it all comes back to haunt the women when they wind up with lives devoid of any intimacy and anybody to love them. Except for the company of other women, which, whatever its glorification these days, has great limits as you can see from the vast ocean of unhappy unattractive women over the age of 30, professional actress bitches on TV and in the movies, who are full of crap in everything they say and do and fake smile about, notwithstanding.

To sum up, wage slavery, along with its associated social controls and restrictions, is the reason for the pained epidemic of frustrated and broken love relationships. Failed lovers make better slaves. And, not incidentally my dears, women wage slaves make better whores for the bosses at work who bleed the last juice from the women in the labor force who lack strong loving men to protect them from asshole bosses emotionally and otherwise.                           

And, wait a minute, that’s not the end of it. For what comes ultimately from the unhappiness of slavery and the failed love it causes in modern civilization is the channeling of that unhappiness into aggression towards others. For passing on one’s unhappiness to others, so often individuals who had nothing to do with causing the unhappiness, is a main way of mitigating your unhappiness, indeed, often the only way in highly controlled societies that don’t let you punch the abusive boss who caused the unhappiness in the face.

Such aggression towards innocent victims to tamp down unhappiness caused by an institutionally protected tyrant is termed redirected aggression. It is so common in life that we take it for granted. And beyond the petty meanness it causes in day to day existence it is the real reason for the mass murders endlessly seen in the news that are persistently touted as having no discernable motive. We just have no idea, say the TV journalists, why the guy killed his wife and his neighbors or the kids at the elementary school or his boss and co-workers. The possibility that the fellow was unhappy enough to crazily kill for the aforesaid reasons of the pain of being a jackass wage slave is never considered though his unhappiness is utterly obvious if one even lightly scratches below the surface of the story. God forbid that his unhappiness and violence might come from the life he’s forced to live in today’s hyper-1984 societies. The fellow who mass murdered the 150 people by driving the airplane into the Alps? The scary looking Adam Lanza who murdered all those second graders at Sandy Hook Elementary? These and the rest of their kind are just the extreme tip of the iceberg of unhappy individuals side-effect manufactured by our highly ordered society. Killing others makes them feel better than doing nothing at all. It reduces the unhappiness in them that comes from the humiliations and restraints of wage slavery and its effect on the possibility of them finding and keeping love.

Redirected aggression emanates not just from an unhappy individual but also from an unhappy group of people. Hate and violence fostered by the unhappiness of civilized life spills across national borders as a significant cause of war. Nothing better than having a foreign enemy with different values and beliefs to hate and kill to distract people from the unhappiness caused them by the rule they live under in their own countries. And these dysfunctional emotions of redirected aggression that make nations prone to war can cause the very worst for mankind when nuclear weapons are in the arsenals of aggressor nations. Doesn’t it make sense that a person as enthralled with mass murder as Adolph Hitler was had to be an unhappy man to begin with, a nut in that sense? And if Hitler had nukes to use, need we question whether or not he would have used them? Can’t we see the dangers in the endless bloodletting in the Middle East and in the Ukraine as to where these might escalate once real weapons of mass destruction come into play? Are people so pacified in their thinking not to see the ease with which a nuclear player backed up against the wall and facing impending defeat by a hated enemy might use his nuclear weapons?   

There is only one sensible solution. The people have to get rid of the weapons before the weapons get rid of the people. Two profoundly good things come out of this. For one, it’s very hard for one person or one group of people to control others significantly without weapons. The ruling class in America ultimately controls the subservient population with police who enforce laws written by legislatures owned through campaign contributions by the wealthy ruling class. The police ultimately keep the people in line with weapons. Get rid of the weapons and you get rid of the tyranny. And, of course, getting rid of the weapons also gets rid of the horrors of war.   

Now you have the gist of the main idea minus the mathematical proof of it. You say you don’t like this picture as too strong a condemnation of the free and fair America you love so much? Or you don’t like the solution of eliminating the weapons as too idealistic or against citizens’ constitutional right to own weapons and use them against bad people who deserve to be shot dead? Or you think this attack on the religious ideas that blur the reality is sinful or on psychology crazy? Well, that’s what the mathematics is for. It makes perfect sense out of these controversial issues to anybody who believes that 2+3=5 provides truth that can’t be denied.

As to actually achieving A World with No Weapons to solve the problem of violence, it’s just a matter of convincing Russia, the world’s other dominant nuclear power, that any war between us two big guys on the block is the end of the game for both of us and for all of us. This is not impossible, for the Russians have produced some of modern history’s top mathematicians and trust in science, whatever our endless vilification of Putin, at least as much as evolution denying America does. Then working with Russia, our two nations can convince the rest of the world, which we two dominate weapons wise, to give up their weapons, or be destroyed by our two nation coalition if they should refuse to give up their weapons. Other nuances of this utterly indispensible Utopia, achievable with great effort and a small miracle or two, are spelled out at the end of the non-mathematical Section 15. And the mathematics that shows how indispensible A World with o Weapons is for mankind’s avoidance of extinction is also indispensible, for people are not about to drop whatever they have felt is so important in their lives to dedicate themselves to a movement for a mass weapons ban without some form of tangible proof that it absolutely must be done to avoid the mass death of themselves and their kids and grandkids.              

We begin such mathematical proof with a discipline called information theory. It will take us back in a formal way to our original the problem of inexactness in the counting of things unequal in size and help to develop a solution to that technical problem. Information theory is the science of the digital, synthetic, information that computers run on as distinct from the meaningful information that the mind runs on. This inability of information theory to develop mathematical specifications of meaningful information is a major shortcoming of it as is made clear in a June, 1995, Scientific American article, From Complexity to Perplexity:   

Created by Claude Shannon in 1948, information theory provided a way to quantify the information content in a message. The hypothesis still serves as the theoretical foundation for information coding, compression, encryption and other aspects of information processing. Efforts to apply information theory to other fields ranging from physics and biology to psychology and even the arts have generally failed – in large part because the theory cannot address the issue of meaning.

It is most important to solve this problem because the greatest impediment to mankind avoiding an annihilating nuclear war is our failure to correctly understand the mind’s information processing operations which include man’s propensity for violence that is so dangerous in this era of nuclear weapons. The solution to this problem shown by the mathematics to be A World with No Weapons must begin in the United States and must have political muscle to succeed. To that end we strongly urge support for Elizabeth Warren in 2016 as the only candidate who is honest and caring enough about people to lean in this direction.

She stands in contrast to Hillary Clinton who merely as an astonishingly good actress pretends to care about people. Further it is important to understand that beyond her genius as a politician during campaign time, Hillary is as stupid a thinker as she is disingenuous. Certainly hubby Bill Clinton gets the Blue Ribbon as the smoothest liar American politics has ever seen. Do you think that this smooth talker’s wife can possibly have a different mindset after four decades of mutual plotting and scheming to hold the public stage?

And it is so important to have an intelligent person in the White House, for the repeated warnings of Vladimir Putin to use nuclear weapons if push comes to shove must be taken seriously in the absence of rapprochement with America. Hillary Clinton calling recently for more military assistance for Ukraine, (4/17/15), makes clear what a stupid she is in this most important issue of our time.

A sensible peace with Russia and movement towards A World with No Weapons will not come about under Hillary. That is for sure. Or under any of the Republican war hawks who might be elected. That pointedly includes current Republican frontrunner, Jeb Bush, whose blood relationship to the pair of assholes in the Bush monarchical dynasty who contrived the War in Iraq strongly suggests a continuation of maximum bloodshed in the Middle East with all that portends for eventual world destruction, anybody who believes Jeb’s campaign denials of it understood to be even stupider than Jeb looks. Once you understand the stakes, given Putin’s determination to never back down to the US, Elizabeth Warren is the only sane choice for president.    
     

Vladimir Putin addressing a rally of supporters at the Luzhniki stadium in Moscow in 2012. Photo: Yuri Kadobnov/AFP/Getty Imageshttp://s3.amazonaws.com/dk-production/images/57279/large/warren_for_president_2016.jpg?1384276624


Those who wish to help start up a movement towards A World with No Weapons with a donation of $20 can do so by
clicking here.  In asking for it we’re either Bernie Madoff in some very mathematically elaborate sheep’s clothing or we’re the real thing. Read the mathematical analysis that follows before you decide which. It provides a most beautiful mathematical explanation of the human emotions and how man’s violent ones can be tamed only by getting rid of weapons that make aggression so horribly bloody. And for the resolute non-math readers, to highlight the underlying social causes of violence, there’s my personal story in Section 15, “Revolution in the Garden of Eden”, that tells of child murders by my cousin, Ed Graf, and my brother, Don Graf, both of them members of the fundamentalist LCMS Christian sect I managed to escape from many years ago.
  

http://www.dallasnews.com/incoming/20141021-convictions_challenged-fire_science_40391987.jpg.ece/BINARY/w620x413/CONVICTIONS_CHALLENGED-FIRE_SCIENCE_40391987.JPGhttp://bloximages.chicago2.vip.townnews.com/wacotrib.com/content/tncms/assets/v3/editorial/e/c3/ec358722-d8b2-5158-8184-51652edde644/5426157fe5d8e.image.jpgDon Graf - Lubbock Texas Commercial and Labor Attorney


That’s cousin, Ed Graf, on the left pleading guilty in court to burning his stepson’s to death to get insurance money, and lawyer brother, Don Graf, on the right. And Section 16, “Waiting for the Bomb”, also provides some non-mathematical material for the reader who wants to pass on the technical analysis that begins below.    

1. Some Basics of Information Theory

The central structure in information theory is the information channel or message channel diagrammed below.

http://www.eaipatterns.com/img/MessageChannelSolution.gif

The set of messages that can be sent through a particular message channel have mathematical representation in terms of their relative probabilities of being sent. Consider a message set consisting of N=4 color messages, red, green, purple or black, that derive from a person blindly picking one object from a set of K=12 objects, (■■■■■, ■■■, ■■■, ), which consists of x1=5 red, x2=3 green, x3=3 purple and x4=1 black object. The probability of the color picked being red and of a message about it being sent to some receiver is p1=x1/K=5/12; that of green, p2=x2/K=3/12=1/4; of purple, p3=x3/K=1/4; and of black, p4=x4/K=1/12. The message set of N=4 color is specified in terms of these probabilities as [pi] = [p1, p2, p3, p4] = [5/12, 3/12, 3/12, 1/12]. 

The amount of information in a message is a function of the probabilities of the N messages, pi, i=1,2,…N. There are two main functions used for information in information theory. The one used most often is the Shannon (information) entropy.

1.)                                                           

The other important information expression in information theory, which is closely related functionally to the Shannon entropy, is the Renyi entropy, in logarithm to the base 2 form,      

2.)                                                          

The key to understanding information as we ordinarily understand that word as information that has meaning for us entails understanding the Renyi entropy rather than the Shannon entropy as the primary function for information as follows. We note from the blurb on it in Wikipedia that the Renyi entropy is important in ecology and statistics as an index or measure of diversity. That is not surprising given that the non-logarithmic part of the Renyi entropy is another longtime used measure of diversity in ecology and sociology, the Simpson’s Reciprocal Diversity Index,

3.)                                                                          

This allows us to specify the Renyi entropy, R, in terms of the Simpson’s diversity index, D, as

4.)                                                            R=log2D

An equiprobable message set for color would derive from a random pick of an object from a balanced set of objects like (■■■, ■■■, ■■■, ■■■), whose N=4 colors have equal probabilities of being picked and sent a message out about of p1= p2= p3= p4=1/N=1/4. Substitution of pi=1/N in Eq3 obtains a simplified D diversity index expression for the balanced case of    

5.)                                                              D = N, balanced

This is intuitively sensible as indicating that the diversity of a set of objects is measured by the N number of different kinds of objects, in (■■■, ■■■, ■■■, ■■■) as D=N=4 differently colored kinds of objects. Note how this also simplifies the Renyi (information) entropy as

6.)                                                            R=log2N   

Clearly R is a function of the number of color messages derived from random picking from the (3, 3, 3, 3) set of objects, (■■■, ■■■, ■■■, ■■■), namely, R=2 bits. In contrast the D diversity index of the (5, 3, 3, 1) unbalanced set of objects, (■■■■■, ■■■, ■■■, ), and the message set derived from it is from Eq3 and its [pi] = [5/12, 3/12, 3/12, 1/12], D=3.273, with a Renyi entropy from Eq4 of R=log2(2.323)=1.71. Now we are not at the moment interested in the meaning of R, but rather that R is for all sets a function of the D diversity of the message set. This includes R=log2N for the equiprobable or balanced case in which N is equal to D from Eq5 and can be considered a diversity measure for the balanced case also. Hence the R Renyi entropy as information is a function of the D diversity of the message set. This gives diversity a central role in information. Why is this? It has to do with the problem of exactness in counting things.


2. Counting

The simplest items in mathematics are the counting numbers: 1, 2, 3, 4, and so on. But counting isn’t as simple as it seems. Count the number of objects in (■■■■). You count 4 objects here, of course. Now count the number of objects in (■■). It is also 4 one says at a glance. But is that count of 4 an exact count?

There is something not quite right with counting the unequal sized objects in (■■) as 4. Counting 4 objects in (■■) should be understood to be inexact as follows. You remember the grade school caveat against adding things together that are different in kind like adding 2 galaxies and 2 kittens together. This caveat also holds for adding things or counting things that are different in size. Consider (■■) as pumpkins of sizes (5, 3, 3, 1) in pounds. Is the count of them of 4 pumpkins exact? A grocer selling the pumpkins would think not, which is why pumpkins are sold not by the pumpkin, but by the pound, all of which pounds being exactly the same in size. Four pounds is an exact enumeration of pounds because all pounds are the same size in weight while four pumpkins is an inexact count of pumpkins when the pumpkins counted are not the same size. This requirement of sameness in size for a count of things to be exact applies to all standard measure whether pounds, fluid ounces or inches. That is why standard measure underpins all commercial transactions unless things bought and sold are the same size, like large eggs, which are sold by a straightforward count of them, as by the dozen.  

We make this point of inexactness in a count of things not the same size in a more rigorous way by next considering our set of K=12 unit objects, all the same size, (■■■■■, ■■■, ■■■, ), divided into N=4 color subsets that are not the same size in having different numbers of unit objects in some of them. The K=12 count of all the objects is exact because the objects are “unit objects” all the same size. But the N=4 count of the subsets, on the other hand, is inexact because the subsets are not the same size in having a different number of unit objects in some of them. To make it analytically clear that there is some sort of error in counting the number of subsets in (■■■■■, ■■■, ■■■, ) as N=4, we first formally specify the set as consisting of x1=5 red, x2=3 green, x3=3 purple and x4=1 black object or in shorthand the (5, 3, 3, 1) natural number set. The sum of the objects in each of the N=4 subsets is the K=12 total number of objects in the set, or generally for any natural number set,    

7.)                               http://matrix-evolutions.com/INDEX_files/image010.png

For the (■■■■■, ■■■, ■■■, ) set, the total number of objects is K = x1+ x2+ x3+ x4 = 5+3+3+1 =12. Now it is a simple matter to show that the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), is inexact or in error with statistical analysis. The basic statistic of a set of numbers like (5, 3, 3, 1), here representing (■■■■■, ■■■, ■■■, ), is the mean or arithmetic average, µ, (mu).

8.)                               http://matrix-evolutions.com/INDEX_files/image003.gif

For the K=12, N=4, set, (5, 3, 3, 1), the arithmetic average is µ=K/N=12/4=3. That the µ arithmetic average is inexact is well made in 47 chapters of myriad examples in the modern classic, The Flaw of Averages by Sam Savage of Stanford. A more immediate register of the inexactness or error in the µ arithmetic average comes from noting that it is always associated with a statistical error measure, explicitly or implicitly, the most common of which is the standard deviation, σ, (sigma),

9.)                               http://matrix-evolutions.com/INDEX_files/image004.gif

For the N=4, µ=3, (5, 3, 3, 1) set, the standard deviation is

10.)                             

Another commonly used statistical error is the relative error or percent error, r,

11.)                               http://matrix-evolutions.com/INDEX_files/image007.gif  

For the µ=3, σ=1.414, (5, 3, 3, 1), set, the relative error is r=σ/µ=1.414/3=.471=47.1%. The statistical error in the µ=K/N=3 arithmetic average of (5, 3, 3, 1), whether expressed as σ=1.414 or r=47.1%, implies a counting error in the N number of subsets parameter in µ=K/N. The K=12 count of the unit objects in (■■■■■, ■■■, ■■■, ) in µ=K/N is exact because its K=12 unit objects are the same size. Hence the statistical error or inexactness in µ=K/N must arise from the inexactness in the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ).

To further make the point of the straight N count of unequal sized subsets being inexact via the statistical error associated with it, we look at the µ, σ and r of the K=4 object, N=4 subset, “balanced” set of objects, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), all of whose subsets are the same size, x1=x2=x3=x4=3. This set also has a µ=K/N=12/4=3 arithmetic average, but from Eq9, it has no statistical error, σ=r=0, which logically implies from what we just said above that there is no error or inaccuracy in µ=K/N for it and, hence, no error or inaccuracy in the K or in the N variables of µ=K/N. And this fits perfectly with our understanding of an exact count coming about when things counted, including the N=4 subsets in (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), are all the same size.

Now while the N=4 count of the number of subsets in (■■■■■, ■■■, ■■■, ) is inexact, its diversity index of D=3.273 is an exact quantification of the subsets in the set. And this holds generally for any set, balanced or unbalanced. To see this, let’s formally define the pi of a set in terms of the K and xi of a set as

12.)                              

The two variables that pi is a function of are exact, both the K count of the total number of same size objects in a set and the xi number of (same sized) unit objects in each subset. From this perspective, D in being entirely a function of the pi of a set in Eq3 is exact. Another way of appreciating the exactness in the D diversity index comes from understanding D as a statistical function. To do that we first express the σ standard deviation of Eq3 as its square, σ2, called the the variance statistical error.   

13.)                                                                 

And then we solve this for the summation term to obtain

14.)                                                               

Now from Eq12, we express the D diversity index as

15.)                                         

And lastly inserting the summation term in Eq14 into D of Eq15 obtains D also via Eqs8&11 as

16.)                                 http://matrix-evolutions.com/INDEX_files/image014.gif

Top of Form

Bottom of Form

This derives an exact D quantification of the subset constituents of a set as a function of their inexact N count effectively made exact by the inclusion of the r relative error measure of the inexactness in N in the function. This understands D as an exact correlate or substitute for inexact N that can be used in place of N as an exact quantification of the constituent subsets of an unbalanced set. And it further understands diversity, in its sense as an exact quantification of balanced or unbalanced subset constituents of a set, as what information is in the most general sense of the word. Let us back up a bit to make what we mean clear here. Earlier we made note that the R Renyi entropy is used in the scientific literature as a measure of diversity, a logarithmic measure of diversity. Now let’s also note that the Shannon information entropy has also been used in the scientific literature of the last 60 years as a measure of ecological and sociological diversity as called the Shannon Diversity Index, it’s configuring as a natural logarithm rather than a base 2 logarithm being irrelevant to the synonymy of information and diversity in the Shannon entropy as well as the Renyi entropy. Furthermore both the logarithmic diversities, Shannon and Renyi, and the linear diversity, D, are exact functions as defined above.

This strongly suggests that the D diversity index is information also. Later we shall prove this rigorously with a bit signal encoding recipe interpretation of D and with a Gödel based rebuttal of the Khinchin argument in its derivation of the Shannon entropy as the only correct form for information (along with the Renyi entropy generalization of the Shannon entropy). These tedious technical proofs, though, are delayed for the moment as too much of a digression from showing rather and first how the D diversity index is readily understandable intuitively as meaningful information.           


3. Diversity as a Measure of Meaningful Information

Information as processed by the human mind has measure in the D diversity index interpreted as the number of significant subsets in a set. The exercise that follows will explain how the mind intuitively distinguishes what is significant in its sense and memory of things from what is insignificant. We illustrate with an item in the recent news about the makeup of the K=53 man Ferguson Police Dept. at the time of the protest over the death of Mike Brown, namely x1=50 White officers and x2=3 Black officers. Few have a problem intuitively understanding the Black contingent of the Ferguson P.D. to be insignificant (quantitatively) even without any mathematical analysis. But D diversity index interpreted as the number of significant subsets in a set makes the understanding of insignificance mathematically precise.    

The Ferguson P.D. as the number set, (50, 3), has from Eq15 a diversity of D=1.12, which rounded off to the nearest integer as D=1 implies that there is only 1 significant subset or subgroup in the department. Were the force made up in a more diverse way of, say, x1=28 Caucasians and x2=25 Blacks, the diversity of its (28, 25) representative number set of D=1.994 rounded off to D=2 would indicate that both subgroups were (quantitatively) significant. Returning to the actual (50, 3) makeup calculated to have a rounded diversity measure of D=1 significant subset, the x1=50 preponderance of the White contingent suggests that it is the significant subgroup and, hence, that the x2=3 Black officer subgroup is insignificant as can also be interpreted as its contributing only token diversity to the police force.  

Before we continue this analysis, given the contentiousness of this issue, it should be made clear that considering the police as the enemy of a hoped for genuinely free and fair society is a mistake. Police are strictly the hired hands of the ruling class business and political leaders of communities that range in size from the small city of Ferguson to the entire USA. Police do not make policy. They simply execute it and do so on threat, like the rest of Americans who work jobs, of being fired and having their lives ruined if they fail to comply with the directives of the upper echelon in the American social hierarchy. There is no good cop, bad cop dichotomy, therefore, only a good leader versus bad leader differentiation. And this current crop of leaders in America are as disgustingly predatory, uncaring of the little people and deceitful as any ruling oligarchy you’ll read about in history. If you want change, that’s where you have to look for change, in the people at the top, not the cops who are the ruling class’s well- controlled ultimate instrument of coercive control of the people.

That important political digression aside, let’s now continue the mathematical analysis of significance versus insignificance by showing how to assign a significance index to each one of the constituent subsets of a set. We will use the K=12, N=3, (■■■■■■, ■■■■■, ), (6, 5, 1), x1=6, x2=5, x3=1, set to introduce significance indices. We calculate from Eq15 a D=2.323 diversity index for this set, which rounded off to D=2 suggests 2 significant subsets, the red and the green, with the purple subset that is represented by only x3=1 object in it understood as insignificant. To specify these attributions of significance and insignificance to each subset in a more direct way, we define next the root mean square average, aka the rms average, of a number set, ξ, (xi) as 

17.)                    https://ci6.googleusercontent.com/proxy/XJw6HNZVHgQIKqADqoiiMN0VtEcQogKRzf60J6hBIlMBjfP6OTuKwMA7bRg2tHWHn1Nt1uWPXBqK_TXjnY5szX-C6QFBLF5o1byq=s0-d-e1-ft#http://matrix-evolutions.com/INDEX_files/image014.png         

The rms average squared, ξ2, is

18.)                   https://ci3.googleusercontent.com/proxy/CYm0SIdBkUWHcG8qiWMAlU10-GutdHXw5J8J_gbcS_qWlhLqlByv1U6uZPy26S2tTTdfQcvpuTSzzwnMYGziweEgukw0rJES4xA0=s0-d-e1-ft#http://matrix-evolutions.com/INDEX_files/image015.png

The ξ rms average of the K=12, N=3, µ=K/N=4, (■■■■■■, ■■■■■, ), (6, 5, 1), unbalanced set is ξ =4.546 with ξ2=62/3=20.667. And the rms average of the K=12, N=3, µ=K/N=4 balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), which we will use for comparison sake, is from the above ξ=µ=4 with ξ22 =16. Next note from Eqs13,8&18 that the D diversity index can be expressed as

19.)                 https://ci6.googleusercontent.com/proxy/dxtA4LjZPiM9XD_oKnSCxO2YT0E8H38z1TsL2dUyElbr3X5Ewz85-baNvTBBGgmUd5xA-V4XidxMbiLEIx6uwRdqqT5Qu9UUhnmQ=s0-d-e1-ft#http://matrix-evolutions.com/INDEX_files/image016.png 

We define the significance index of the ith subset of a set as si, i=1, 2,…N,

20.)                    http://matrix-evolutions.com/INDEX_files/image018.gif

This obtains the D diversity as the sum of its si significance indices as

21.)                http://matrix-evolutions.com/INDEX_files/image019.gif

For sets, balanced and unbalanced, that have N=3 subsets containing a number of objects in each of x1, x2 and x3,

22.)                  D = s1 + s2 + s3

For the N=3, (■■■■, ■■■■, ■■■■), (4, 4, 4), set, x1=4, x2=4 and x3=4, the D=N=3 diversity index of this balanced set from Eq5 alternatively computed from the above is   

23.)                 D = s1 + s2 +s3 = 1 + 1 + 1 = 3 = N

What D=3=1+1+1 tells us is that all N=3 subsets in having significance indices of s1=s2=s3 = 1 are significant. Now consider the unbalanced (■■■■■■, ■■■■■, ) set, whose subset values of x1=6, x2=5 and x3=1 develop its significance indices from Eqs22&23 as    

24.)                  D = s1 + s2 +s3 = 1.161 + .968 + .194 = 2.323

What D= 1.161 + .968 + .194 indicates is that the x1=6 red objects subset in having a significance index of s1=1.161 rounding off to s1=1 is significant; that the x5=5 green objects subset in having a significance index of s2=.968 rounding off to s2=1 is significant; and that the x3=1 purple object subset in having a significance index of s3=.194 rounded to s3=0 is insignificant. This analysis applied to the Ferguson P.D. situation has us interpret from the s1=1.056 index evaluated from the above for the x1=50 White cops and rounded to unity that they are (quantitatively) significant and from the s2=.056 rounded off to s2=0 for the x2=3 Black cops specifies them as (quantitatively) insignificant.   

That the human mind genuinely operates with these significance functions, or some neurobiological facsimile of them, is made clear in the next illustration of significance and insignificance of the three sets of colored objects shown below, each of which has K=21 objects in it in N=3 colors.   
 

Sets of K=21 Objects  

Number Set Values

D, Eq15

Rounded to

Significance Indices, Eq21

(■■■■■■■, ■■■■■■■, ■■■■■■■)

x1=7, x2=7, x3=7

D=3

D=3

s1=1, s2=1, s3=1

(■■■■■■, ■■■■■■, ■■■■■■■■■)

x1=6, x2=6, x3 =9

D= 2.88

D=3

s1=.824, s2=.824, s3=1.24

(■■■■■■■■■■, ■■■■■■■■■■, )

x1=10, x2=10, x3=1

D=2.19

D=2

s1=1.04, s2=1.04, s3=.104

Table 25. Sets of K=21 Objects in N=3 Colors and Their D Diversity and s Significance Indices

The N=3 set, (■■■■■■■■■■, ■■■■■■■■■■, ), (10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 implies D=2 significant subsets, the red and the green from their s1=s2=1.04 significance indices. And that also implies that the one object, purple subset is insignificant as reinforced by its s3=.104 significance index as might also be interpreted as the purple set contributing only token diversity to the set. In contrast, the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set has 3 significant subsets, red, green and purple, s1=1, s2=1, s3=1; as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set whose D=2.88 diversity rounds off to D=3 with s1=.824, s2=.824, s3=1.24.

One gets the most intuitive sense of the mind’s automatic or subconscious evaluation of significance and insignificance by manifesting the K=21, N=3, colored object sets in Table 25 as K=21 threads in N=3 colors in a swath of plaid cloth.   

Description: C:\Users\The Matrix Gang\Dropbox\Documents\Net Files\INDEX_files\image069.jpg

(10, 10, 1), D≈2

(7, 7, 7), D=3

(6, 6, 9), D≈3


Figure 26. The Sets of Colored Objects in Table 27 as Sets of Colored Threads.

A woman who owns a plaid skirt with the (10, 10, 1), D≈2, pattern on the left, as I do, would spontaneously describe it as her red and green plaid skirt, omitting reference to the low density and, hence, relatively insignificant threads of purple in the plaid. She would make this description automatically without any conscious calculation because the human mind just does automatically disregard the insignificant and, indeed, not just in its visual sense of it but also in its not verbalizing things sensed as insignificant. This verbalization of only the significant colors in the plaid swath of red and green should not be surprising given that the word “significant” has as its root, “sign” meaning “word”, which suggests that what is sensed by the mind as significant is signified or verbalized while what is sensed as insignificant and little or not at all sensed or noticed, isn’t signified or assigned a word in discourse or in one’s thoughts.  

Our sensory perceptions are generally quite automatically affected by the magnitude of the sensory input, small inputs being insignificant and disregarded in our sense of them as with our lack of sensing or tasting salt added to a stew when it is just the slightest pinch of salt. This sense of the possibility of insignificant ingredients in a recipe when added in the smallest yet non-zero amounts is what gave me the conceptual germ of A Theory of Epsilon.  

Quantitative significance is not just a characteristic of the size or quantity of things but also of the frequency of our observation of things and events. Consider a game where you guess the color of an object picked blindly from a bag of objects, (■■■■■■■■■■, ■■■■■■■■■■, ). Assume that you don’t at all know the makeup of the objects in the bag ahead of time as you go about guessing and observing which colors get picked and in with what frequency. Then your sense of what colors are significant or insignificant comes only from the frequency the colors are picked from the bag (picked with replacement). And over time, as you see purple picked so infrequently that the purple color will come to seem insignificant in your mind as a possible pick and to also be disregarded as a color you might think likely to be picked. The human mind’s operating automatically to disregard the insignificant is an important factor for behavior because we generally think, talk about, pay attention to and act on what we consider significant while automatically disregarding the insignificant in our thoughts, conversations and behaviors.

From a sociopolitical perspective the development of one’s sense of the significance of some things and insignificance of others via media exposure a central aspect of propaganda and mind control because issues and opinions frequently disseminated through mass media and other ruling class information outlets are subconsciously taken to be significant to some degree and tend, as such, to take up much of one’s thoughts, conversations and behavioral considerations in contrast to issues, observations and opinions infrequently brought up or not at all broadcast, which become regarded, as such, as insignificant and effectively paid little regard if any at all.  

In this way personally immaterial sporting events and entertainments along with political opinions with minimal factual bases come to be subconsciously thought of as significant, crowding out issues and interpretations of news events that are genuinely meaningful for people’s individual welfare, but in being shown infrequently or not at all, such as the daily abuse in workday life people take from all powerful bosses, become insignificant in discourse and in thought for people and in their intentions for future action. This does not come about by chance for people drugged with such an endless stream of misinformation tend to stay in line. To hear a warning to avoid such brain washing set to music, take a few minutes break from the mathematical analysis to listen to Curse That TV Set.

An obvious example of propaganda via frequent repeat of a message is seen in Republican talking point strategy. This political party instrument of the ruling class repeats things as nonsensical as the sky is green and the trees are blue through media controlled by ruling class TV station and newspaper ownership and through advertising with such frequency that the drugged population out there in the audience come to think that such opinions have significance. Hey, maybe there is something to the idea of a green sky and of no evolution and of no climate change and of working people not always living fearfully on the edge of homelessness while the privileged amuse themselves with expensive trivialities purchased at the expense of the misery of the working class. 

A classic illustration of political disingenuousness via a distortion of significance is found in the Republicans getting the public to support the war in Iraq in 2003 by describing our invading force as a “coalition.” It consisted approximately of K=163,700 soldiers from N=32 nations distributed set wise as (145,000, 5000, 2000, 2000, 1000, 1000, 1000, 1000, 500, 500, 500, 500, 500, 500, 500, 200, 200, 200, 200, 100, 100, 100, 100, 100, 50, 50, 50, 50, 50, 50, 50, 50). The invading force set’s number of significant members calculates from Eq15 as D=1.26, which rounded off to D≈1 specifies 1 significant nation in the so-called coalition, the United States, distinctly at odds with the general sense of a coalition as a plural entity rather than a collection of subordinates dominated by on nation, here the modern American empire.

The cleverness of calling it a coalition along with the endlessly repeated WMD talking point as rationalizations for entering this costly and unnecessary bloody war were clear enough to be recognized by the astute back then as raw political hokum without need for the D diversity index to clarify N−1=31 nations in the “coalition” as insignificant, though using D as a measure of the number of significant nations allows us to call out the deceitfulness of the politicians and the media that supported them with mathematical precision.

Manipulation of the intuitive D diversity based operation of the mind to assess significance is a cornerstone foundation of propaganda. It works by repetition of mistruth as evident both in patently totalitarian societies, organized religions and in capitalist pseudo-democracies where almost all politicians are controlled by the big money of corporations and Wall St., an obvious and highly meaningful fact that is made to be insignificant in the minds of people in its seldom being publically voiced. And those who do bring such facts to light, whether about the harsh realities of war or the institutional corruptions and misery of a highly ordered peace, are made to seem significantly bad. 

A case in point is the documentary film maker, Michael Moore, whose primary sin is feeling disgust in both areas and making it known. His calling out Bush’s vanity driven Iraq War that, for no good national purpose and supported by endlessly repeated lies, unnecessarily took the lives of 5000 young American soldiers, crippled 30,000 more and destroyed well a million Iraqi lives, not to speak of the instability it caused that brought cutthroat ISIS to power in the Middle East, all these hard facts made to seem insignificant. Indeed, Moore’s insightful and prophetic castigation of the war at the Oscar nominations in 2003 and later in his documentary, Fahrenheit 9/11, brought about an active encouragement by right wing snake, Glenn Beck, held up in the media as a paragon of virtue, to go out and literally murder Michael Moore.

Those reading this and in despair about finding anything that can be done about it can be given one word of good advice that fits well with their desperation: run. To retain some modicum of self-respect and the possibility of squeezing any real happiness out of life: run. That’s the best you can do in the short term to avoid the powerful if well hidden agencies of control in modern America.  One thing that you can, and must, avoid is the TV set. This is one very important route to maintaining a sane view of life. It is admittedly a limited cure for the bigger problem. To solve that you have to fight back, not just run. And you do that by supporting and placing your hopes in the only true solution to this mess of human existence, helping to bring about A World with No Weapons, not just for bypassing nuclear Armageddon but also in a weapons ban restoring a true balance of power to life, the details to be talked more about in later sections.

To get to A World with No Weapons requires political power, it must be pointed out. Anarchy, everybody doing their own thing, is great if you can get it. But you can’t get it in the real world where the rules forbid it and punish those who break the rules. You have to first get to A World with No Weapons, which has to start with somebody in the White House here in America who actively carries that destiny on their shoulders. As I’m the only suitable candidate for that in 2016, encourage me by dropping a line to ruthmariongraf@gmail.com and sending a $20 donation to join the movement for A World with No Weapons and for the democratic revolution needed to make it happen by clicking here.  

4. A Biased Average

The sense of a Utopia where there is no war or tyranny still must seem to most farfetched. We need more precise mathematical argument to make clear that it’s the only direction we can go in to get out of the hell of debilitating control in our lives and to avoid nuclear annihilation. To that end we next want to consider an adjunct function to the exact specification of the inexact N subsets in an unbalanced set, namely an exact average of the number of objects in each subset. As we made clear earlier, the µ=K/N arithmetic average number of objects per subset in an unbalanced set of K objects distributed over N subsets is inexact. Much as we form the arithmetic average as the ratio of the K objects in a set to the N inexact number of subsets in the set as µ=K/N, we can form an exact average as the ratio of the K objects to the D exact quantification of the subsets as K/D, an exact if biased average, to which we give the symbol, φ, (phi).

27.)                            http://matrix-evolutions.com/INDEX_files/image031.gif  

The φ=K/D biased average is an exact average in being a function of K, which is exact, and of D, which is also exact as was made clear earlier. The K=12, N=4, µ=K/N=4, D=2.323, (■■■■■■, ■■■■■, ), (6, 5, 1) set has a biased average of φ=K/D=12/2.323=5.166. This is greater than this set’s arithmetic average of µ=K/N=4 from the φ biased average being weighted or biased towards the larger xi values in (6, 5, 1). To see the details of the bias in the φ biased average of an unbalanced set towards the larger xi values in the set, let’s develop the µ=K/N arithmetic average in an unusual way from Eqs7&8 as   

28.)                            

This understands the µ mean or arithmetic average as the sum of “slices” of the xi of a set of thickness 1/N.  We can develop a function for the φ biased average with a parallel form from Eqs27,13,8&12 as 

29.)                           

 

This shows φ to be the sum of “slices” of the xi of a set that are pi in thickness to bias the φ average towards the larger xi subsets weighting them with their correspondingly larger pi weight fraction measures. Much as the human mind’s sense of significance is affected in a biased way by the diversity of what it senses, so also is its sense of the average of the constituent subsets of set affected in a biased way towards the greater xi of a set as representing the size of the objects in a set and/or the frequency with which they are sensed. A familiar example is our sense that a dinosaur is generally speaking very, very big. This comes about as a biased average of dinosaur sizes both in terms of the larger ones biasing our sense of the average towards the large sized dinosaurs and also from the fact that people see images of dinosaurs that are very large much more frequently than they see medium sized dinosaurs or small ones.  Note also that the diversity index, D, can be understood as a function of the φ average when Eq27 is solved for D as   

30.)                                      

This expression for D tells us that the K total number of something in a set divided by its φ biased average is its D diversity. This relationship allows us to corroborate this analysis of significance and insignificance for the mind by showing it for physical systems where the concepts of significance and insignificance have measurable, empirical, reality. Specifically we will do it for a thermodynamic system of K energy units distributed over N molecules with a highlight on the concept of entropy, the tight argument presented reinforcing the D diversity based understanding of the highly contentious issue of brain washing propaganda.

5. Entropy

Entropy is a somewhat mysterious concept. Feeling cold in wintertime and hot in summertime comes about from the 2nd Law of Thermodynamics said to be caused by an increase in entropy. But what it is exactly that’s increasing in these processes has been a confusion for science for the last two centuries since the French engineer, Sadi Carnot, first became aware of processes described in terms of entropy. The equation for entropy in terms of measurable quantities is the Clausius macroscopic formulation of entropy   

31.)             

Even though this differential equation tells us that entropy, S, is dimensionally, energy, Q, divided by temperature, T, it still leaves us with a confused mysterious sense of entropy because we lack an intuitive sense of what energy divided by temperature might be. Some light is thrown on the problem by next noting that (absolute) temperature is explained in the standard rubric of physical chemistry as being directly proportional to the µ=K/N arithmetic average of the K energy of a thermodynamic system per its N molecules. But this immediately raises a red flag because we made it very clear earlier that the µ arithmetic average is inexact for an unbalanced set and because the N molecules of a thermodynamic system are an unbalanced set of constituents of a thermodynamic system from the energy units of the system being distributed over them in a skewed or unbalanced way from the empirical Maxwell-Boltzmann energy distribution.  

http://noyesharrigan.cmswiki.wikispaces.net/file/view/MD_distribution.png/250991340/MD_distribution.png

Figure 32. The Maxwell-Boltzmann Energy Distribution


The inexactness in the µ=K/N average energy function that derives from the inexactness in the N number of molecules parameter suggests that it is an error in physical science assuming that systems in nature necessarily operate in an exact way. Or alternatively we might say that this arithmetic average specification of temperature is a poor one in being inexact and is perhaps the reason why the S entropy is so poorly understood and mysterious as a physical quantity.

Following this line of reasoning tell us that temperature might be better understood as a biased average of energy per molecule. That supposition provides us with a very clear and physically sensible interpretation of entropy for as we see from Eqs30&31, K total energy divided by φ as a biased average energy would be the D diversity of the system of molecules which in perfectly fitting dimensionally Q energy divided by T temperature as S entropy pegs S entropy as the energy diversity of the system. As this quite fits the intuitive or qualitative sense of entropy as energy dispersal, just another word for energy diversity, (see entropy as energy dispersal in Wikipedia), it is worth tracking it down further and provide hard core evidence to show if this is truly the case. Doing so will also increase our confidence of the D diversity as a measure of significance and insignificance in cognitive systems and underpinning of a mathematical specification of the human emotions. And it will also provide us with a mathematical template for the generalizations of ideas and thoughts that the human mind also operates on. The evidence we will provide shows a mathematically perfect fit of energy diversity to the Boltzmann formulation of entropy, understood in science to be the most basic expression for entropy as honored by its inscription of Boltzmann’s tombstone in the terminology of 100 years ago as             

33.)                          S = klogW

http://matrix-evolutions.com/INDEX_files/image028.jpg

Ludwig Boltzmann’s 1906 Tombstone

Diversity is a property not only of a set of K objects divided into N color categories, but also of K candies divided between N children and K discrete or whole numbered energy units divided between N molecules. The distribution of K=4 candies to N=2 children takes the form of three natural number sets: (2, 2) for both children getting 2 of the K=4 candies with a diversity from Eqs5&8 of D=2; (4, 0) for one child getting all 4 of the K=4 candies and the other child none with a diversity from Eq5 of D=1; and (3, 1) for one child getting 3 of the K=4 candies and the other child, 1, with a diversity from Eq5 of D=1.6. The (2, 2), (3, 1) and (4, 0) manifestations of the random distribution are also referred to as the configurations of the distribution.  The distribution of K=4 energy units over N=2 molecules has the same diversity values as the distribution of K=4 candies over N=2 children: for (2, 2), both molecules having 2 of the K=4 energy units, a diversity of D=2; for (4, 0), one molecule having all 4 of the K=4 energy units and the other molecule none, a diversity of D=1; and for (3, 1), one molecule having 3 of the K=4 energy units and the other molecule, 1, a diversity of D=1.6.

The candies over kids distribution is easiest to picture and follow, so we begin with it. The random or equiprobable distribution of candies to children as might come from grandma tossing K=4 candies of different color, (), blindly over her shoulder to her N=2 grandkids, Jack and Jill, has a number of ways of occurring, ω,

34.)                            ω = NK

ω (small case omega) is referred to as a combinatorial statistic. Specifically for K=4 candies distributed randomly to N=2 children, the ω number of ways that can occur is

35.)                        ω = NK =24= 16

These ω =16 ways are, with Jack’s candies set to the right of the comma and Jill’s candies to the left,

36.)                                        (■, 0); (, ); (■, ); (■, ); (, ); (, ); (, ); (, )
                                      (
, ); (, ); (■, ); (, ); (, ); (■, ); (, ); (0, )

The probability of each of these permutations or ways or microstates of the random distribution is the same, 

37.)                     1/ω=1/16

If grandma did the tossing of the K=4 candies to the N=2 kids 16 times, on average, Line16 would come about though not necessarily in the sequence depicted. It is possible to compute the average diversity of this random distribution. Here we see that the probability of a (4, 0) permutation is 2/16=1/8; of a (3, 1) configuration, 8/16=1/2; and of a (2. 2) permutation, 6/16=3/8. It is a simple matter to compute the σ2 variances of these permutations from Eq11: for (4, 0), σ2=4; for (3, 1), σ2=1; and for (2, 2), σ2=0. Note that (4, 0), (3, 1) and (2, 2) are also referred to as the configurations of the distribution. The average variance of the ω = 16 permutations, also understandable as the probability weighted average variance of the configurations, is 

38.)                        

The average variance, σ2AV, enables us to calculate the average diversity of the random distribution, DAV, from Eq16 with σ2AV replacing σ2 and DAV replacing D. 

39.)                      

 

Understanding the arithmetic average of the number of energy units per molecule for the K=4 energy unit over N=2 molecule distribution to be µ=K/N=4/2=2, the parameters of σ2AV=1 and N=2 have us calculate the average diversity of the random distribution, DAV, as

40.)                            

 

This dynamic plays out as above - it must be emphasized - even if the candies are all of the same kind, say K=4 red candies, (■■■■). This comes about because the candies, even though all of the same kind, are fundamentally different candies. Let’s back up a minute to explore this in greater depth. The () candies are said to be categorically distinct or distinct in kind. But we don’t just distinguish things as being different kinds, as between a red candy, , and a green candy, . We also distinguish between two of the same kind of thing, as between two red candies, ■■, which though they are categorically indistinguishable or the same kind of thing, are yet distinguishable fundamentally. If you are holding one of these red candies in your hand and the other is on the kitchen table, you definitely distinguish between the two.

This is called fundamental distinction. It is different than categorical distinction, but yet a distinction between things people make as intuitively as they distinguish between different kinds of things. To show the fundamental distinction between K=4 red candies, (■■■■), we can represent them each with a different letter as (abcd). With the fundamental distinction so marked, the number of ways or different permutations of K=4 red candies, (abcd), that come about from their random distribution to N=2 kids is also calculated as ω= NK =24= 16 of Eq35, those permutations being  

41.)                                  (abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
                                         (
bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc}; (0, abcd)

Note that everything we said for the random distribution of () in Eq37 to Eq40 applies also to the random distribution of (■■■■) as is readily understood once we delineate the fundamental distinctions in (■■■■) as (abcd). Now determining the average diversity, DAV, for random distributions gets a bit tedious as the K and N of random distribution get large, indeed, practically impossible for very large K and N values. Fortunately we can develop a shortcut formula for the DAV average diversity of any K energy unit over N molecule random distribution from a shortcut formula for σ2AV that already exists in standard multinomial distribution theory. In general for any multinomial distribution of K objects over N containers,

42.)                           

For an equiprobable multinomial distribution, the Pi term is Pi= 1/N, a relationship that tells us that each of the N containers in a K over N distribution has an equal, 1/N, probability of getting any one of the K objects distributed to it. This Pi=1/N probability for an equiprobable distribution is the P=1/N=1/2 probability of each of grandma’s N=2 kids having an equal, 50%, chance of getting any one candy blindly tossed by grandma. The Pi =1/N probability for a random distribution greatly simplifies the multinomial variance expression of Eq24 for the equiprobable case to

43.)                          

As things turn out this variance of an equiprobable multinomial distribution is the average variance of an equiprobable distribution, σ2AV, of Eq38 we developed for the K=4 over N=2 random distribution. Hence we can write Eq43 as  

 

44.)               

 

That the variance of an equiprobable multinomial distribution is, indeed, the average variance, σ2AV, is demonstrated by calculating the σ2AV=1 average variance of the K=4 over N=2 distribution in Eq41 from the above as  

45.)              

Eq44 can now be used to generate a shortcut formula for the average diversity, DAV, by substituting its σ2AV into Eq39 to obtain   

46.)                                      

 

And we can further demonstrate the validity of the above shortcut formula for DAV by calculating the DAV=1.6 average diversity of the K=4 over N=2 distribution obtained in Eq43 with it. 

47.)                 

These conclusions also hold for a system of K=4 energy units distributed equiprobably over N=2 gas molecules flying about in a container of fixed volume. The equiprobable or random distribution results from collisions between the N=2 molecules that result in random energy transfers of the energy units between molecules. In that case, Line41 represents the microstate permutations that arise on average from the collisions, though not necessarily in that sequence. The average variance, σ2AV, of the microstate permutations and their average diversity, DAV, is the same as for the random distribution of K=4 candies between N=2 children.

With this picture of a thermodynamic system as our template, we can now confirm the dimensional analysis that suggested from the Clausius macroscopic formulation of entropy that entropy is basically energy diversity or energy dispersal. This is done specifically by showing that the average diversity, DAV, has near perfect direct proportionality to the expression for microstate entropy Boltzmann developed that is expressed in modern terminology as

48.)                     S=kBlnΩ 

To demonstrate this we need not explain the meaning of the Ω (capital omega) variable in Boltzmann’s S entropy, held off until later, nor the kB term in the function, a constant, but only show the exceedingly high correlation coefficient between DAV and lnΩ. That is easy to demonstrate because both DAV and Ω are functions solely of the K number of energy units and N molecules in a thermodynamic system, DAV as seen in Eq46 and Ω from a standard formula in mathematical physics.    

49.)                                               

And the lnΩ as a function of K and N is

50.)                           

For large K over N equiprobable distributions it is easiest to calculate lnΩ using Stirling’s Approximation, which approximates the natural logarithm (ln) of the factorial of any number, n, as

51.)                       

Stirling’s approximation works very well for large n values. For example, ln(170!) =706.5731 is very closely approximated as 706.5726. The Stirling’s approximation form of the lnΩ expression of Eq50 is    

52.)     

We can use this formula to compare the lnΩ of randomly chosen large K over N equiprobable distributions to their DAV average diversity of Eq46.     

K

N

lnΩ, Eq52

DAV, Eq46

145

30

75.71

25

500

90

246.86

76.4

800

180

462.07

147.09

1200

300

745.12

240.16

1800

500

1151.2

381.13

2000

800

1673.9

571.63

3000

900

2100.88

692.49

Table 53. The lnΩ and DAV of Large K over N Distributions

The Pierson’s correlation coefficient for the DAV and lnΩ of these distributions is .9995, which indicates a very close direct proportionality between the two as can be appreciated visually from the near straight line of the scatter plot of these DAV versus lnΩ values.   

http://matrix-evolutions.com/INDEX_files/image054.gif

Figure 54. A plot of the DAV versus lnΩ data in Table 33

This high .9995 correlation between lnΩ and DAV becomes greater yet the larger the K and N values of K>N distributions surveyed. For values of K on the order of EXP20 the correlation for K>N distributions is .9999999 indicating effectively a perfect direct proportionality between lnΩ and DAV as fits very large, thermodynamically realistic, K over N equiprobable distributions. As the Boltzmann S=kBlnΩ entropy is judged to be correct ultimately by its fit to laboratory data, given the near perfect correlation of the DAV to it, this diversity entropy formulation must also be correct from that purely empirical perspective. This correlation of diversity entropy to the Boltzmann microstate formulation of entropy powerfully reinforces the dimensional analysis of entropy as energy diversity done from the Clausius macroscopic formulation of entropy.

It must be emphasized, though, that the two microstate formulations of entropy, diversity and Boltzmann, cannot both be correct even though both mathematically fit the data because the assumptions that underpin the two formulations are absolutely mutually contradictory. This requires some explaining. The ω = NK number of ways combinatorial statistic of Eq34 implies from the 16 microstate permutations of Line21 for the K=4 over N=2 distribution that the energy units are all fundamentally distinguishable from each other. Understanding the random distribution in this way is what made possible the foregoing derivation of the average variance, σ2AV, and the average diversity, DAV.

A quite different combinatorial statistic exists for enumerating the number of observably different ways that K categorically indistinguishable objects can be arranged in N containers. It is the Ω variable that we have already seen from Eq49 that sits in Boltzmann’s S=kBlnΩ entropy. 

49.)                                               

Irrespective of Boltzmann’s use of it in his entropy equation, Ω can specify the number of ways that K=4 red candies, (■■■■), which are categorically indistinguishable even if as we made clear they are fundamentally distinguishable, can be arranged over N=2 containers or N=2 children. From Eq49 that is 5 ways

55.)                                                                           http://matrix-evolutions.com/INDEX_files/image009.gif

These Ω=5 ways are as we see below with Jack’s candies to the right of the comma and Jill’s to the left.

55a.)                                                                           (■■■■, 0); (■■■, ); (■■, ■■); (, ■■■); (0, ■■■■)

However the Ω=5 value this has absolutely no meaning as regards the random distribution of K energy units over N molecules because such a distribution is necessarily governed from elementary probability theory by the ω = NK combinatorial statistic of Eq14 that implicitly assumes that the energy units, though they are categorically indistinguishable, are fundamentally distinguishable. This perspective is bolstered by the energy units residing in distinguishable molecules, which themselves reside in different places in space. This suggests that Boltzmann researched a number of mathematical functions associated with the distribution of energy units over molecules until he came to one, lnΩ, which fit the data. In theoretical physics such a fit of a mathematical hypothesis to empirical data is generally taken as strong proof that the hypothesis is correct. In this case, though, it turns out that ln is little more than a fluke fit to another function, DAV, which not only also fits the data, but also makes physical sense out of entropy as energy diversity or energy dispersal  One adds that neither Ω nor lnΩ make any sense out of entropy as a physical quantity, the reason for entropy’s mysteriousness over the last century.   

One readily absolves Boltzmann for this error given that mathematical formulations for diversity did not come into existence until near half a century after his death and we emphasize that without Boltzmann’s breakthrough efforts my clarification of entropy as diversity would have been impossible. The complete acceptance of Boltzmann’s notions for the last hundred years from their perfect fit to data makes his ideas very difficult to overthrow for Boltzmann is as much a revered “saint” of physical science as Newton or Maxwell or Einstein. The task of rectifying our understanding of entropy as energy diversity would be much easier, for that reason, if both interpretations in their both fitting the data empirically, could be accepted. However the two assumptions of energy unit distinguishability and energy unit indistinguishability are totally incompatible and only one can be accepted. Hence Boltzmann is overthrown rather than just refined, difficult to accept for physical scientists who have embraced him as correct in the most foundational way over the last century.

This impediment to a correction of Boltzmann’s error, thus, asks for as much supporting evidence for the diversity entropy proposition as can be mustered. This is doubly important for not only does diversity explain entropy correctly and clearly for the first time in science, but also understanding diversity as a measure of entropy also very much makes clear the underpinning of meaningful information with diversity. That includes not only showing the concept of significance as a marker for what is meaningful in a very firm way in physical systems, but also uncovers a well-defined mathematical structure for the generalizations that the human mind operates on verbally called compressed representation

A very strong supporting argument for diversity based entropy shows that my diversity based statistical mechanics much better explains the Maxwell-Boltzmann energy distribution than Boltzmann statistical mechanics does.   

http://noyesharrigan.cmswiki.wikispaces.net/file/view/MD_distribution.png/250991340/MD_distribution.png

Figure 32.


To show it we next introduce a new structure in mathematics called the Average Configuration of a random distribution. The configurations of the K=4 over N=2 distribution are listed below with their variances and diversity indices.

Configuration

Microstates   

Variance, σ2 

Diversity, D

(4, 0)

[4, 0], [0,4]

4

1

(3, 1)

[3, 1], [1, 3]

1

1.6

(2, 2)

[2, 2]

0

2

Table 56. The Variance, σ2, and Diversity, D, of the Configurations of the K=4 over N=2 Distribution

Recall now the average variance of σ2AV=1 of the K=4 over N=2 distribution from Eq38&45 and its average diversity of DAV=1.6 from Eqs40&47. We see in the above table that the same values of a σ2=1 variance and a D=1.6 diversity are seen for the (3, 1) configuration. On that basis the (3, 1) configuration is understood to be a compressed representation of all of the distribution’s configurations of (4, 0), (3, 1) and (2, 2) and as such is called the Average Configuration of the distribution. The Average Configuration is one configuration that represents all the configurations of a random distribution in compressed form much like the µ arithmetic average is one number that represents all the numbers in a number set in compressed form as, for example, the μ=K/N=4 arithmetic average does for all the numbers in the K=24, N=6, (6, 4, 2, 1, 5, 6), number set.

A configuration includes all of the permutations describable with the same number set, much as the (4, 0) configuration of the K=4 over N=2 distribution includes the permutations, (abcd, 0) and (0, abcd).    Hence the Average Configuration should be understood as a compressed representation not only of all of a distributions configurations but also of all ω=NK of its permutations as develop physically over time as the system’s microstates, each of which exists at any one moment in time. This exceedingly clear microstate picture of a thermodynamic system is worth taking a moment or two to sketch out. Recall the ω=16 permutations or microstates in Line21 for the K=4, N=2 distribution.    

41.)                                  (abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
                                          (
bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc}; (0, abcd)

These should be understood as appearing in this proportion on average though not necessarily in this sequence over 16 moments of time as coming about from the random molecular collisions and transfers of energy in a thermodynamic system. As such, the (3, 1) Average Configuration represents the state of the system as measured over an extended period of time. Now if this microstate picture of a thermodynamic system is correct, the Maxwell-Boltzmann energy distribution should be the average energy distribution of all the microstate configurations as manifest in the energy distribution of the Average Configuration.

The K=4 energy units over N=2 molecules distribution has too few K energy units and N molecules for its Average Configuration of (3, 1) to show any resemblance to the Maxwell-Boltzmann energy distribution of Figure 32. Rather, we need random distributions with higher K and N values. And we will look at some starting with the K=12 energy units over N=6 molecule distribution. To find its Average Configuration we first calculate from Eq44 the σ2AV average variance of this distribution to be  

57.)                                             

The Average Configuration of the K=12 over N=6 distribution is a configuration that has this variance of σ2AV =1.667. The easiest way to find the Average Configuration is with a Microsoft Excel program that generates all the configurations of this distribution and then locates the one/s that has the same variance of σ22AV=1.667. It turns out to be the (4, 3, 2, 2, 1, 0) configuration, taken to be the Average Configuration on the basis of its having as its variance, σ2AV=1.667. A plot of the number of energy units on a molecule vs. the number of its molecules that have that energy for this Average Configuration of (4, 3, 2, 2, 1, 0) is shown below.

 

http://matrix-evolutions.com/INDEX_files/image056.gif

Figure 58. Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=12 over N=6 Distribution

 

Seeing this distribution as the Maxwell-Boltzmann energy distribution of Figure 32 is a bit of a stretch, though it might be characterized generously as an extremely simple choppy form of a Maxwell-Boltzmann. Next let’s consider a larger K over N distribution, one of K=36 energy unit over N=10 molecules. Its σ2AV is from Eq44, σ2AV=3.24. The Microsoft Excel program runs through the configurations of this distribution to find one whose σ2 variance has the same value as σ2AV =3.24, namely, (1, 2, 2, 3, 3, 3, 4, 5, 6, 7). A plot of the energy distribution of this Average Configuration is

 

http://matrix-evolutions.com/INDEX_files/image057.gif

Figure 59. Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=36 over N=10 Distribution

This curve was greeted without prompting by Dr. John Hudson, Professor Emeritus of Materials Engineering at Rensselaer Polytechnic Institute and author of the graduate text, Thermodynamics of Surfaces, with, “It’s an obvious proto-Maxwell-Boltzmann.” Next we look at the K=40 energy unit over N=15 molecule distribution, whose σ2AV average variance is from Eq44, σ2AV =2.489. The Microsoft Excel program finds four configurations that have this diversity including (0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6), which is an Average Configuration of the distribution on the basis of its σ2=2.489 variance. A plot of its energy distribution is

 

http://matrix-evolutions.com/INDEX_files/image058.gif

Figure 60. Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=40 over N=15 Distribution

And next we look at the K=145 energy unit over N=30 molecule distribution whose average diversity is from Eq44, σ2AV =4.672. There are nine configurations with a σ2 =4,672 including this natural number set of (0, 0, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 10), which is an Average Configuration of the distribution on that basis. A plot of its energy distribution is

 

http://matrix-evolutions.com/INDEX_files/image059.gif

Figure 61. Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=145 over N=30 Distribution


At this level we are considering K and N values large enough to display a moderately good resemblance to the classical Maxwell-Boltzmann distribution of Figure 32.

http://noyesharrigan.cmswiki.wikispaces.net/file/view/MD_distribution.png/250991340/MD_distribution.png

Figure 32.

As we progressively increase the K and N values of distributions, the plot of the energy per molecule versus the number of molecules that have that energy more and more approaches and eventually perfectly fits the shape of the above realistic Maxwell-Boltzmann distribution. Now it should be clear that this unorthodox development of the Maxwell-Boltzmann distribution as a property of the Average Configuration comes directly from the mathematics of a random distribution of distinguishable energy units and does not require any additional assumptions, which the Boltzmann derivation of the Maxwell-Boltzmann decidedly does. As only one theory, mine or Boltzmann’s, can be correct because of the mutually contradicting assumptions for the two theories of distinguishable versus indistinguishable energy units, there is a strong argument in favor of mine from the Occam’s razor principle that is used generally in science to decide between two competing explanations on the basis of which has the fewest assumptions, in this case the diversity based explanation.  

The other reinforcing argument for diversity based entropy comes about from the use of a diversity index slightly different than the D diversity index, one whose biased average perfectly fits microstate temperature and so makes the dimensional argument with the Clausius formulation of entropy air tight. We began our consideration of diversity based entropy with the D diversity index because of the mathematical regularities it has that made it easy to work with, but now that we have developed the basic concepts of diversity based entropy from D, we will switch our focus to Square Root Diversity Index, h.

62.)                      http://matrix-evolutions.com/INDEX_files/image029.gif

This h diversity index not only provides a precise dimensional argument for diversity based entropy with the Clausius macroscopic entropy formulation, but also has, like D, a very high Pearson’s correlation to the Boltzmann microscopic entropy. As such it is the proper diversity underpinning of entropy. The pi in h are the weight fraction measures of the xi number of objects in each subset. The K=12 object, N=4 color, (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), set, x1=5, x2=3, x3=3 and x4=1 has pi=xi/K weight fractions of p1=x1/K=5/12, p2=x2/K=3/12=1/4; p3=1/4 and p4 =1/12. This makes for an h square root diversity index of the set of

63.)                   

 

Note that the h diversity index is exact in being solely a function of pi, which we made clear earlier is exact. Note also that the h=3.464 of the (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), set compares well to its D=3.273 index in being, as is D, a reduction from the N=4 of this unbalanced set, though not quite as much as D=3.273 is. The two diversity indices, D and h, have comparable measures for the sets below with h=N=D for balanced sets and h < N for unbalanced sets as is D<N. 

Set of Unit Objects

Subset Values

D, Eq3

h, Eq62

(■■■, ■■■, ■■■, ■■■)

x1=x2= x3=x4=3

4

4

(■■■■■, ■■■, ■■■, )

x1=5, x2= x3=3, x4=1

3.273

3.468

(■■■■■■, ■■■■■■)

x1=x2=6

2

2

(■■■■, ■■■■, ■■■■)

x1=x2= x3=4

3

3

(■■■■■■, ■■■■■■, ■■■■■■■■■)

x1=x2=6,  x3=9

2.882

2.941

(■■■■■■, ■■■■■, )

x1=6, x2=5, x3=1

2.323

2.538

(■■■■■■■■■■, ■■■■■■■■■■, )

x1=x2=10, x3=1

2.194

2.394

Table 64. Various Sets and Their D and h Diversity Indices

Earlier back in Eqs27-29 we developed an exact biased average for the D diversity of φ=K/D. We can also develop an exact biased average for the h square root diversity of Eq42 that we’ll call the Square Root Biased Average. In parallel to K/N=µ and K/D=φ, we define the square root biased average as K/h and give it the symbol, ψ, (psi).

65.)                               

The ψ=K/h biased average is an exact average in being a function of K, which is exact, and of h, which is also exact. The K=12, N=3, µ=K/N=4, h=2.538, (■■■■■■, ■■■■■, ), (6, 5, 1), set has a square root biased average of ψ=K/h=12/2.538=4.72, greater than the arithmetic average of this set, µ=4, in being biased towards the larger xi values in the (6, 5, 1) set. We detail the basis of this bias in the ψ average towards the larger xi in a set by expressing ψ from Eqs3,8&62 as

66.)                          

 

The numerator in the rightmost term shows the ψ square root biased average to be the sum of “slices” of the xi of a set of thickness pi1/2, which biases the average towards the larger xi in the set in their having larger pi1/2. The ∑pi1/2 term in the denominator of the end fraction is a normalizing function used to make all the pi1/2 “slices” in the numerator sum to one, this summing to one of the fractional “slices” being necessary for the construction of any kind of an average of a number set. We next invert Eq60 to express the h square root diversity index as a function of the φ square root biased average as

67.)                            http://matrix-evolutions.com/INDEX_files/image038.gif

Now let’s understand ψ of Eqs65&66 as the microstate temperature of a thermodynamic system of K energy units distributed over N gas molecules. As we said earlier back after Eq31, the microstate temperature is currently understood in the standard physics rubric to be the arithmetic average energy per molecule, µ=K/N. And we made clear that what is wrong with that is that the K energy units of the system being distributed over the N molecules in an unbalanced way as seen in the Maxwell-Boltzmann energy distribution of Figure 32 tells us that the this µ=K/N arithmetic energy average is an inexact specification because the N number of molecules parameter in µ=K/N is inexact. Earlier we suggested a replacement of inexact µ=K/N with the exact biased average, φ=K/D and we saw how doing that quickly developed a dimensional argument from (normalized, absolute) temperature being the φ=K/D exact biased energy average and S entropy being dimensionally from the dS=dQ/T Clausius entropy expression of S entropy deriving from the division of energy by temperature.     

We can make the same dimensional argument for the square root biased average, ψ, as temperature and it is a substantially better one based on how temperature is actually measured physically with a thermometer. Each of the N molecules in the thermodynamic system collides with the thermometer to contribute to its temperature measure in direct proportion to its frequency of collision with the thermometer, which is equal to the velocity of the molecule, which itself is directly proportional to the square root of the xi number of energy units a molecule has. Because of this, the slower moving molecules with the smaller energies in the Maxwell-Boltzmann energy distribution of Figure 32 collide with the thermometer less frequently and have their energies recorded or sensed by the thermometer in its compilation of the temperature measure less frequently to record or sense smaller pi1/2 slices of their energies. And conversely, the faster moving, higher energy molecules, which collide with the thermometer more frequently have their energies recorded or sensed as larger pi1/2 slices of their energy thus biasing the temperature measure towards the energy of the higher energy molecules in an unarguable way. This determines the molecular energy average to be the square root biased average energy per molecule, ψ=K/h.

This first order model is incomplete, however, because it does not take into account the fact that the h energy diversity of a thermodynamic system along with its ψ=K/h biased energy average is changing at every moment in time from one microstate permutation to another as the system’s molecules collide with and transfer energy between themselves, thus continuously altering the distribution of the K energy units over the system’s N molecules. Hence the ψ and h parameters that form the basis respectively of the system’s temperature and entropy must be their average measures, hAV and ψAV, which are properties also of the system’s Average Configuration that represents the system as a whole. This makes it clear by extension from Eq66 that the K total number of energy units divided by the ψAV square root biased energy average as temperature is the hAV square root diversity of the system

68.)           

Now it is only one quick stop at the Clausius macroscopic entropy formulation, dS=dQ/T, to see from a dimensional argument that hAV diversity is the measure of the entropy of the system. As S entropy is dimensionally Q energy divided by T temperature and K energy divided by ψAV temperature is hAV diversity, hAV diversity must be dimensionally entropy.

To conclude that hAV is the proper function for entropy based on its dimensional fit to the Clausius macroscopic entropy, we must also show that hAV has a high correlation to Boltzmann’s S=kBlnΩ entropy (or more simply, to lnΩ.) To demonstrate this, though, is not as straightforward as it was for DAV because hAV is not a simple function of the K energy units and N molecules of a thermodynamic system as DAV was back in Eq46 as DAV=KN/(K+N−1). There is a remedy for this problem, though. Because hAV is the h diversity the Average Configuration much as DAV was the D diversity index of the Average Configuration, we can obtain hAV for the K over N distributions for which we have a specific Average Configuration and its xi and p­i values. Those are the K over N distributions of Figures 58-61. Below we list their hAV values as calculated from Eq62 alongside the lnΩ values of those Average Configurations as calculated from Eq50. And we also include their DAV diversity indices from Eq46 for comparison sake.  

      Figure

K

N

lnW

DAV

hAV

36

12

6

8.73

4.24

4.57

37

36

10

18.3

8

8.85

38

45

15

26.1

11.11

12.33

39

145

30

75.88

25

26.49

Table 69 The lnΩ, DAV and h­AV of the Distributions in Figures 73-76

The Pearson’s correlation coefficient between the lnΩ and hAV values of the above is .995. And between lnΩ and DAV it is .997. Note that though this lnΩ and DAV Pearson’s correlation of .997 is high, it is less than the .9995 correlation between lnΩ and DAV seen in Table 53 for larger K and N distributions. This is attributed to the Pearson’s correlation coefficient being a function of the magnitude of the K and N parameters of the random distributions, those of the distributions in Figures 58-61 used in Table 69 being substantially smaller than the K and N of the distributions in Table 53. Hence the Pearson’s correlation between lnΩ and hAV of .995 for the K over N distributions in Table 69 being little different than the .997 correlation between lnΩ and DAV implies that the lnΩ and hAV correlation is also, as was the .9995 between lnΩ and DAV for larger K and N distributions, understood to be sufficiently great to have hAV accepted as a candidate for entropy from its high correlation with the S=kBlnΩ Boltzmann microstate entropy.  

Now we will show how the hAV diversity index replaces S in the 2nd Law of Thermodynamics. The standard form of the 2nd Law is

70.)               ΔS > 0

This says that entropy, S, always increases in an irreversible or spontaneous process. One such process the 2nd Law applies to is thermal equilibration. In it two bodies at different temperatures both go to some intermediate temperature upon thermal contact. While the mathematics of this is unarguable when entropy is expressed in dS=dQ/T form, any sense of the increase in entropy microscopically or molecularly that can be gleaned from representing entropy with the Boltzmann S entropy is unintuitive and conceptually mysterious. And that, we posit, is not because entropy is inherently difficult to understand or mysterious, but because S=kBln is incorrect and must be replaced with hAV diversity to make any sense out of the process intuitively. 

To show this we will demonstrate the hAV diversity based entropy increasing in a thermal equilibration between two “mini-thermodynamic” subsystems. Subsystem A has KA=12 energy units distributed randomly over NA=3 molecules. And subsystem B has KB=84 energy units distributed randomly over NB =3 molecules. These two subsystems are initially isolated out of thermal contact with each other. From Eq44 the average variance of the KA=12 energy units over NA=3 molecules subsystem is σ2AV =2.667, which calculates an Average Configuration for the subsystem, which has that variance, of (6, 4, 2) along with a normalized microstate temperature of the subsystem from Eq66 of ψAV(A)=4.353. And the KA=84 energy units over NB=3 molecules subsystem B has from its Eq44 average variance of σ2AV=18.667 an Average Configuration of (34, 26, 24) with a normalized microstate temperature from Eq66 of ψAV(B) =28.328.

Upon thermal contact the system, now comprised of the two subsystems as one whole system, consists of N=NA+NB=6 molecules over which are distributed K=KA+KB=96 energy units. At the first moment of contact, we represent the whole system as a composite of their separate Average Configurations, to wit as (6, 4, 2, 34, 26, 24). At this first moment there is no ψAV temperature of the composite system because it is not in thermal equilibrium. But it can be understood to have a square root diversity index of hAV=4.394 from Eq62. This specifying of the composite system not in equilibrium as hAV, as an average diversity, is awkward in (6, 4, 2, 34, 26, 24) being made up of the average h diversities of the two subsystems. But the meaning of hAV is clear here despite the (6, 4, 2, 34, 26, 24) set being made up of the hAV of the subsystems.   

After molecular collisions sufficient to bring about a random distribution of the K=96 energy units over the N=6 molecules, the Average Configuration as obtained from the σ2AV =13.333 average variance of Eq44 is (11, 14, 15, 16, 17, 23). It has a square root diversity index from Eq62 of hAV=5.85 and a normalized microstate temperature from Eq66 of ψAV=16.409.

Note that the usual computation of temperature of the whole system from the 1st Law of Thermodynamics, an energy conservation law, suggests a temperature that is the simple average of the temperature of the two subsystem’s, which would be of the ψAV normalized microstate temperatures, (4.353 + 28.328)/2 =16.341. The discrepancy between this value of 16.341and ψAV=16.409 calculated from Eqs62&66 is not a violation of energy conservation because temperature from our unorthodox diversity based perspective is understood as an average molecular energy biased toward the higher energy molecules.

What is important to demonstrate here is that the hAV energy diversity or energy dispersal understood as entropy increases upon thermal contact from an initial value of hAV=4.39 for (6, 4, 2, 34, 26, 24) to a final value of hAV=5.85 for (11, 14, 15, 16, 17, 23). The change in hAV energy diversity is, hence,   

71.)                         ΔhAV=5.85 – 4.39 = +1.46         

This fits the increase in entropy for thermal equilibration demanded by the 2nd Law of Thermodynamics with entropy now expressed as hAV energy diversity.

72.)                          ΔhAV > 0

There are two things that are different about this unorthodox manifestation of the 2nd Law entropy increase for thermal equilibration. The first is that the entropy increase expressed in terms of ΔhAV =1.46 is measured as a change in the whole system of N=6 molecules. And the second is that what is happening physically in the thermal equilibration process is very clear intuitively when the entropy increase is understood as an increase in energy diversity or dispersal. Indeed, nothing could be clearer intuitively especially by comparison to the standard take on entropy increase as an increase in the Ω microstates of the system, which makes zero sense out of entropy as a physical quantity. This diversity based entropy change quantitatively fits the sense of entropy as energy dispersal, (See Wikipedia), which though taken by most scientists to be the qualitatively sensible interpretation of entropy, has never been given a firm quantitative basis until now.

There are other major improvements in thermodynamics that come about from this diversity based statistical mechanics as in a clearer understanding of free energy and of a real gas law in terms of diversity. We will not detail these and other improvements in thermodynamic theory that a diversity based entropy brings about, leaving that to specialists in the field who have sense enough to expand on our seminal work in the detail it warrants.     


6. Entropy and Information

Two concepts that derive from the development of diversity based entropy have relevance to the information processing operations of the mind. The first is that the h diversity index of Eq62, like the D diversity index of Eq3, is understandable as a measure of the number of significant subsets in a set. In the (■■■■■■■■■■, ■■■■■■■■■■, ), (10, 10, 1), set of Table 25 and Figure 26 it was seen that the D=2.19 diversity index of the set could be interpreted, when rounded off, as the set having D=2 significant subsets, the x1=x2=10 red and the green subsets, with the x3=1 purple subset understood as insignificant. This interpretation of the D=2.19 measure was reinforced with significance indices for it from Eq21 of s1=1.041 for the red subset, s2=1.041 for the green subset and s3=.1040 for the purple subset. The h diversity index of this set, h=2.394 from Eq62, rounded off to h=2, can also be understood as specifying 2 significant subsets in the set.

This has us interpret hAV diversity based entropy as the number of energetically significant molecules in a thermodynamic system, that is, in its Average Configuration or equivalently as the average number of them in the system. For example, consider the K=36 energy units over N=10 molecules random distribution of Figure 59 as its (1, 2, 2, 3, 3, 3, 4, 5, 6, 7) Average Configuration and its hAV from Eq62 of h=8.853≈9. This is readily interpreted as the system having 9 energetically significant molecules, the molecule with just 1 energy unit being insignificant energetically. This sense of the energetic significance versus insignificance of molecules goes a long way to understanding temperature specified as ψAV=K/hAV as coming about from molecular collision with the thermometer that is biased towards the faster moving, more energetically significant molecules. That, in turn, makes clear that the “reality” of a thermodynamic system as manifest in its most basic property of temperature as ψAV=K/hAV depends not just on the molecular energies of the system but also on how the molecular energies are tallied in the temperature measure in a biased way.

This also makes clear by parallel the human mind’s appreciation of significance in its sensory operations as measured by the D diversity index. Ultimately this parallel derives from the commonality between thermodynamic and sensory systems in the measures of both being affected by the magnitude of their subset constituents, be it of the energy of molecules measured in a biased way by a thermometer or of the size of color subsets sensed by the CNS, the central nervous system.

And this helps make clear that our perceptions and the thoughts we developed from them as used to guide our behaviors and communication with others depend not just on what it is that objectively exists out there but also on how they are sensed or measured with our CNS sensing apparatus. Hence understanding entropy as diversity in physical systems as diversity strongly validates the reasonableness of the concept of significance in our sensory apparatus, which tells us that reality for people is what is sensed or measured rather than some totally objective phenomena that lies outside our senses. From a purely epistemological perspective, then, this greatly calls into question transcendental notions like gods and angels and devils that have absolutely no basis in anybody’s sense of them as these items claimed to exist somehow have never been sensed. This is very important to developing a clear picture of what is meaningful in life for plaguing our sense of life with non-sensed imaginations muddies the picture critically.       

Significance is one major determinant of what makes information meaningful. Later we will make it clear that the other determinant of the meaningfulness of things is the association of emotion with them major, something diversity will also present a beautiful picture of by enabling a representation of our basic emotions of fear, hope, excitement, relief, sex, love, warmth, anger and the like with great mathematical precision in a later section.

The other concept basic to the mind’s information processing introduced through diversity based entropy is compressed representation. The µ mean is the most familiar and commonly used compressed representation. Specifying the number of objects in a subset of the K=12, N=4 set of (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), as its µ=K/N=12/4=3 arithmetic average compresses the number of numbers needed to describe the set from N=4 of them, (5, 3,3, 1) to the one number of µ=3. While that constitutes efficiency in description in using less information to describe the set, note that the loss of some information in this compression generates error as seen in the statistical error associated with the arithmetic average of an unbalanced set. This compressed representation of the arithmetic average is also inexact as we made clear earlier.

Another compressed representation of the (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1) is its D=3.273 diversity index. Again, like the arithmetic average, this is a 1 number representation of an N=4 number, number set and an efficient compression in that regard. It also leaves out information about the set but less so than the set’s µ=3 arithmetic average because D includes a measure of the distribution of the K objects over the N=4 subsets as is clear from D=N/(1+r2) of Eq16 inclusion of r2 as a measure of set distribution. And D=3.273 is also an exact compression of the set as is the h=3.468 square root diversity index of the set.     

The hAV average diversity or entropy of a thermodynamic system is a higher level compressed representation in representing the h diversity compressed reductions of all of the microstate permutation of the system as their average. And the ψAV=K/hAV average square root biased average is another higher level compressed representation as the average over time of the square root biased average energy per molecule that changes over time from continuous collisions between molecules.

We can appreciate these mathematically formulated compressed representations as one category of the generalizations we make about the world around us, quantitative generalizations. The usefulness of these compressed representations or quantitative generalizations is obvious enough that we need not enumerate them.

These quantitative compressed representations also shed great light on the non-mathematical generalizations we humans use as compressed representations that range from the common nouns and verbs we use to represent objects and actions with to our generalized knowledge of complex processes of all sorts. In the simpler case of common nouns as compressed representations, note that the word “dog” conjures up a picture in the mind of a person who hears the word that is an average or morph of all the dogs a person has come across including in picture books and movies seen. The mind compresses everything it comes into sensory contact with in its memory of those things. Such compressed information from the past is used in the interplay of emotions and of thought manifest as generalization, which very much affects both the things we decide to do and our communications with others.

This section has been a relatively qualitative discussion of two important information concepts gleaned from our development of diversity based entropy: significance and compressed representation. In the next section we will use the diversity concept to more formally revise information theory.     

  7. Revising Information Theory

To do that, let’s start back with the central function for information in information theory, the Shannon (information) entropy of Eq1. 

1.)               

Information theory was developed in 1948 by Claude Shannon to characterize messages sent from a source to a destination. Consider (■■■, ■■■, ■■■, ■■■) as a set of K=12 colored buttons in a bag in N=4 colors. I’m going to pick one of the buttons blindly and then send a message of the color picked to some destination. The probability of any color of the N=4 colors being picked is the pi weight fraction of the color, for all the colors in this case,   

73.)                   pi = 1/N = 1/4.

So there’s a p1=1/4 probability of my sending a message saying “I picked red.” And a p2=1/4 probability of my message saying, “I picked green,” and so on. Plugging these pi=1/4 probabilities into messy Eq71 obtains the amount of information in the color message sent as  

74.)                               

This tells us that there’s H=2 bits of information in a message sent. What does that mean? The most basic interpretation of the H=2 bits is as the number of binary digits, 0s or 1s, minimally needed to encode the color messages gotten from (■■■, ■■■, ■■■, ■■■) in bit signal form, namely as [00, 01, 10, 11]. Red might be encoded as 00, green as 01, and so on. Then when the receiver of the message gets 00 sent, he decodes it back to red. The H=2 bits measure is considered to be the amount of information in a message as the number of bit symbols in each bit signal. This bit signal information is the synthetic or digital information that computers run on. There is a simpler form of the Shannon information of Eq1 used for balanced or equiprobable sets like (■■■, ■■■, ■■■, ■■■). Because the pi probabilities are all the same for a balanced set as pi=1/N, substituting 1/N for pi in Eq1 derives the simpler form for H of

75.)                              H= log2N

This equation gets us the same H=2 bits result for messages sourced from (■■■, ■■■, ■■■, ■■■) as did Eq74, but in a simpler way as H= log2N = log24 = 2 bits. Now let’s also use Eq75 to calculate the amount of information in a message that derives from a random pick of one of K=16 buttons in N=8 colors, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■). Because this set is balanced, the probability of picking a particular color and sending a message about it is the same for all N=8 colors, pi=1/N=1/8. And the amount of information in a color message from this set can be calculated from the simple, equiprobable, form of the Shannon entropy of Eq75 as H= log2N= log28= 3 bits. This has us encode messages from N=8 color (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) with the N=8 bit signals, [000, 010, 100, 001, 110, 101, 011, 111]. Each bit signal has H=log28=3 bits in it understood as the amount of information in a color message derived from this set.

Now we want to make the case that information and diversity are synonymous with each being a measure of the other. We already tried to make that case before by suggesting that the D diversity interpreted as the number of significant subsets in a set was an instance of meaningful information. The synonymy of diversity and information can also be demonstrated in a more technical way. First of all it is well known that the H Shannon information entropy expressed in natural log terms is the Shannon Diversity Index used over the last 60 years in the scientific literature as a measure of ecological and sociological diversity. Paralleling Eq1 for the Shannon information entropy is the Shannon Diversity Index of

76.)                                       

And for a balanced set, paralleling Eq75, the Shannon Diversity index is H = lnN. The difference between the Shannon entropy as information and the Shannon entropy as diversity is merely the difference in logarithm base, the direct proportionality between the two telling us from measure theory in mathematics that what one function is the measure of, the other must also be a measure of, here both of information and diversity. Another conceptual equivalence between diversity and information that derives from classical information theory comes from Renyi entropy, R, which is taken in information theory to be information in being a parent function or generalization of the Shannon information entropy. Its connection to diversity lies in its being the logarithm of the D Simpson’s Reciprocal Diversity Index as we saw earlier in Eqs2-4.    

4.)                                   R = logD

This also strongly suggests a synonymy between diversity and information. The above two diversity-information associations suggest two kinds of diversity indices that further imply two kinds of information functions. The two kinds of diversity indices are the logarithmic kind, as with H and R; and the linear kind, as with D. To better understand the two kinds of information that the two kinds of diversity indices, logarithmic and linear, imply we next develop the D (linear) diversity index as a bit encoding recipe that parallels H as the bit encoding recipe we introduced it as. The sociopolitical implications of this somewhat tedious exercise are profound and make the following technical considerations worth our time and effort.   

Recall the H=2 bits for (■■■, ■■■, ■■■, ■■■) that specify for its N=4 color messages an encoding of N=4 bit signals, [00, 01, 10, 11], each consisting of H=2 bits or binary digits. We can also use the D=4 diversity index as a bit encoding recipe. The D=4 diversity index of this set translated as the number of bits in a bit signal obtains N=4 bit signals for the N=4 colors of the set of [0001, 0011, 0111, 1111], each of which consists of D=4 bits. And for the N=8 color set of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) whose H=3 bits measure encoded it as [000, 001, 010, 100, 110, 101, 011, 111], the D=8 diversity index used as a coding recipe encodes it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111], with each bit signal consisting of D=8 bits. Note in both D encodings that only one permutation of a given combination of 1s and 0s can be used. This restricts us writing the 2-0s and 6-1s combination of bits in only one permutation of it, as for example as 01111011 or as 00111111, but not both. And also note that the all 0s bit signal is disallowed in this D encoding recipe.  

Anyone familiar with information theory will immediately note that the D bit recipe is inefficient as a practical coding scheme in its requiring significantly more bit symbols for a message than the H Shannon entropy coding recipe. This is not surprising since Claude Shannon devised his H entropy initially strictly as an efficient coding recipe for generating the minimum number of bit symbols needed to encode a message in bit signal form. The D diversity index as a coding recipe fails miserably at that task of bit symbol minimization. But we have developed it not trying to engineer a practical coding system but rather to show how D can be understood in parallel to H as an information function in being understandable as a bit coding recipe, its efficiency for message transmission being quite beside the point. 

We show D to be an information function for a very familiar kind of information, quantitative information, by next looking carefully at the details of the difference between the H and D bit encodings. Recall the (■■■, ■■■, ■■■, ■■■) set, whose N=4 colors are encoded in H encoding with [00, 01, 10, 11] and in D encoding with [0001, 0011, 0111, 1111]. Now look closely to see that these are two very different ways of encoding the N=4 distinguishable color messages derived from (■■■, ■■■, ■■■, ■■■) with N=4 distinguishable bit signals. What is special about the D bit encoding of (■■■, ■■■, ■■■, ■■■) with [0001, 0011, 0111, 1111] is that all of these N=4 bit signals are quantitatively distinguishable from each other with each bit signal having a different number of 0s and 1s in it than the others.

This is not the case for the H encoding of (■■■, ■■■, ■■■, ■■■) with [00, 01, 10, 11]. For with them it is seen that the 01 and 10 signals have the same number of 0s and 1s in them and, hence, are not quantitatively distinct from each other. Rather the distinction between 01 and 10 is positional distinction from the 0 and 1 bit signals being in different positions in 01 and 10. So 01 and 10, we could say, are qualitatively distinct rather than quantitatively distinct.

This quantitative versus qualitative distinction for D and H encoding is even more clear for the N=8 set, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), and its D=8 bit encoding of it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111]. For there we see that every one of the N=8 bit signals is quantitatively distinguished from every other bit signal in each having a different number of 0s and 1s in them. This quantitatively distinguishable bit encoding with D contrasts to the H=3 bit encoding of that color message set as [000, 001, 010, 100, 110, 101, 011, 111] in which we see that the 001, 010 and 100 signals are not quantitatively distinguished, each of them having 2-0s and 1-1, but rather distinguished entirely by the positions of the 1 and 0 bits in them. And that positional or qualitative distinction is also seen between the 011, 101 and 110 signals of its H bit encoding, all of which are quantitatively the same rather than quantitatively distinct.   

The qualitative versus quantitative H versus D encodings corresponds to our everyday sense of information as being either of two broad kinds, qualitative or quantitative. When I tell you General George Washington worked his Virginia planation with slaves rather than hired help, that’s qualitative information for you. But when I tell you that Washington owned 123 slaves at the time of his death, that’s quantitative information. With our example set of (■■■, ■■■, ■■■, ■■■) we see that the color subsets are all qualitatively distinct from each other as is well represented with their [00, 01, 10, 11] H bit encoding. It is also clear, though, that there are N=D=4 color subsets, which is well denoted with [0001, 0011, 0111, 1111], which distinguishes them as the 1st color, the 2nd color, the 3rd color and the 4th color, which effectively counts the number of colors.   

This qualitative versus quantitative differentiation explains why the H, the qualitative coding recipe is logarithmic and why the D quantitative coding recipe is linear. H is logarithmic because it is a coding recipe for information communicated from one person to another. The human mind distinguishes intuitively between the positions of things as between 2-0s and 1-1 arranged as 001 or 010 in different positions. This property of mind allows us to represent distinguishable messages sent from one person to another, like and , encoded with signals distinguished via positional or qualitative distinction like 001 and 010. Because the N number of distinguishable messages that can be constructed from H variously permuted, variously positioned, bit symbols is determined by N=2H, a power function, the information in one of those messages specified as the H number of bits in each bit signal is inherently logarithmic via the inversion of N=2H as H=log2N. 

Compare this to D=4 encoding of the N=4 colors in (■■■, ■■■, ■■■, ■■■) as [0001, 0011, 0111, 1111]. This D encoding recipe encodes the colors via the number of 1s in the bit signals or effectively with ordinal numbers that encode the colors as the 1st color, the 2nd color, the 3rd color and the 4th color, which is most basically just a count of the number of distinguishable colors, clearly quantitative information about them. D is linear because counting is inherently linear as with 1, 2, 3, 4 and so on. While much information transmitted or communicated from one person to another is qualitative in form as suits practical efficiency, information sourced directly from nature is quantitative in form when it is a precise description of nature as every practitioner of physical sciences understands. As such an encoding of such quantitative information from nature should be most basically linear in form rather than logarithmic as is the h diversity encoding of the number of energetically significant molecules in a thermodynamic system.

The above development of quantitative versus qualitative information provides the broadest understanding of information as diversity. That includes logarithmic diversity for information communicated from person to person as the H Shannon information entropy also understandable as the Shannon Diversity Index provides; and linear diversity, linear in form as D or h. Take careful note that quantitative descriptions of items can also be represented and communicated via positional distinctions as seen in the Arabic numerals that write thirteen as 13 rather than 1111111111111 for efficiency sake, with 13 distinct position wise from thirty-one as 31. But that should not take away from the reality of the elemental linear nature of counting and, hence, of science’s distinguishing things quantitatively in the linear rather than logarithmic form the D and h diversity indices have.     

This argument that information can be logarithmic or linear in form runs sharply counter to the notion by many information theorists that that the only proper form of information is from the Khinchin derivation of it, the Shannon information entropy, which is logarithmic. That this rigid perspective, which makes impossible an understanding of meaningful information, is nonsense is easy to show in the Khinchin derivation of information as the Shannon entropy defines information to begin with, in a narrow way that obviates our familiar sense of what information is, and then proceeds to derive information as it specified information must be in its axiom set. This approach is a prime example of the value of Gödel’s incompleteness theorem, which considers all axiomatic schemata invalid for that very reason of any conclusions one wishes to attain being achievable via a biased selection of the axiomatic underpinning of the argument to fit the conclusions.

Recognizing this and allowing the D diversity index to be understood as a measure of quantitative information allows us to understand one cornerstone of meaningful information to be information that is judged significant by the human mind rather than insignificant. In a nutshell: significant information is meaningful information. And D diversity also allows is to develop the other cornerstone of meaningful information and that is information associated with emotion, the central topic of the section following this next one, which deals with significance as it affects people.   

 

8. The Significance of Individuals

Much of what people do and think is affected by their sense of themselves as being significant or insignificant individuals. This is important for our understanding corruption in social institutions as deriving from an individual’s self-interest being greater than his or her commitment to the institution. That is, we can attribute corruption to the great need of an individual to feel significant rather than insignificant, which is generally very difficult to achieve in a hierarchically ordered, exploitive, society. This drive is a determinant not only in the Wall St. corruption that jiggled the mortgage market and caused the 2008 recession that near destroyed many American families, but also in the unspoken judicial, political and medical corruption that abounds in today’s America. And such corruption extends to an academic community whose self-interest in status and position tends to trump considerations of truth. This condemnation of academia is so harsh and so difficult to make stick that we approach this problem of people’s motives to cheat with mathematical analysis.     

Social dominance, malevolent and benevolent, is a universal reality however much the concept is unspoken because it abrades on the hope and promise of freedom and fairness. In general the dominant individual is thought to be significant by himself and others and the subordinate person, insignificant. Dominance in a two person relationship, the simplest to analyze, depends ultimately on the relative probabilities of success in competition between the two whether the competition be explicit as in contact sports or implicit as in the track and field, “I can do this better than you can” type. The characteristics of explicit competition are clearer and, hence, is easiest to consider first.

Consider the random selection of an object from the K=10, N=2 color set, (■■■■■, ■■■■■), xi=5 and x2=5, p1=1/2 and p2=1/2, where the p1 and p2 weight fractions of the set are the probabilities respectively of red and green being picked. If red is picked, the player assigned red gets $100 from the player assigned green, and vice versa. And in contrast to this balanced game, consider it played with the (■■■■■■, ■■■■) set, xi=6 and x2=4, p1=6/10 and p2=4/10, in which the red player has an edge over the green player of

77.)                               Δp = p1−p2 =6/10 – 4/10 = 2/10 = 20% =.2

This Δp=.2 measure is also understandable as the vulnerability of the green player. Assume now that this “unfair game must be played by the green player unless he or she opts out of playing by paying the red player $25. Of course, it makes little sense financially for the green player to pay $25 to avoid the game because the average loss is less than that as Δp=.2($100)=$20 per game.  Now let’s change the game further to one where the color is picked randomly from (■■■■■■■■■, ), xi=9 and x2=1, p1=9/10 and p2=1/10. The edge for the red player has increased now to 

78.)                            Δp = p1−p2 =9/10 – 1/10 = 8/10 = 80% =.8

In this game it makes great sense for the green player to pay $25 to avoid the game because the average loss is greater than $25 at Δp=.8($100)=$80 per game. This doesn’t completely obviate the possibility that the green player might get lucky if he plays and win, thereby getting $100 instead of losing the $25 by forfeit without any attempt to win. But generally speaking in any kind of competition that has this form of two players having very different probabilities of winning, past some critical Δp value the additional cost for losing after playing the game and trying to win gets the inferior player to capitulate to the superior player and accept the lesser penalty without a fight.

If a game with lopsided probabilities were played frequently as part of the ongoing relationship between the two players, this level of control and exploitation would instinctively make the inferior player feel insignificant. This emotional outcome of the lopsided relationship has firm mathematical expression in the D diversity index as expressed as D=N/(1+r2) in Eq16 when its r2 relative error term is given in terms of the weight fraction probabilities as 

79.)                                  

This expression for r2 is easily derived from previous functions we’ve considered but is just simply demonstrated here with an example for expediency sake. Consider the K=9, N=3 natural number set, (4, 4, 1), which from Eqs2,3&4 has a relative error of r=.471 and r2=.222=2/9. With pi = (4/9, 4/9, 1/9), the r2 statistical error of (4, 4, 1) is calculated from Eq79 as

80.)                 

This demonstrates the validity of Eq79 for r2. For an N=2 set of relative probabilities of success of two persons in a competition of p1 and p2, the r2 term is obtained from Eq79 as     

81.)               

This develops the number of significant people in the N=2 person relationship from D=N/(1+r2) as 

82.)                 

When there is perfect balance in the competition and, hence, in the relationship, p1=p21/2 and r2= (Δp)2=0, as brings about D=2, which indicates that there are 2 significant people in the relationship. In such both persons tend to think of themselves and of the other person as significant, a positive or pleasant feeling both in terms of what you think of yourself and what the other person thinks of you. In competitions between N=2 persons where the probabilities of winning are p1=.9 and p2=.1, the D diversity is

83.)              

Rounding off D=1.22 to D=1 indicates that there is but 1 significant person in the relationship, the person with the large p1=.9 probability of winning, the other person, the one with the slight p2=.1 chance of winning, being insignificant in the relationship. That is, the mathematically insignificant person feels insignificant and is also thought to be such by the dominant person. There are other factors in a relationship that mitigate the displeasure of being the insignificant partner in a relationship, it must be stressed. A child inherently thinks of its adult parent as the “big person”, the significant one, and is yet quite happy with a parent who gives love as makes up for this lesser and unequal role in the relationship. But this changes necessarily as the child matures and seeks to develop its own sense of significance. Indeed this mathematical specification of personal significance is a manifestation of a person’s “ego” or sense of self as propounded by Sigmund Freud. The mathematics of the factors of caring for another less able individual, as a child is relative to an adult parent objectively, must wait until we develop functions for the emotions in later sections,  some of which  provide balance for the generally unpleasant feelings of being insignificant or inferior.

Until then we will understand insignificance as a generally unpleasant enough feeling that it causes people to prefer to be significant as an equal or as dominant rather than to be insignificant. Let us repeat for emphasis that there are other factors involved than just competition in relationships and we will get to those in due time. In the meantime we will generalize that people prefer having power than not having power. Nobody who plays an explicit competitive game prefers anything other than winning for this reason.

Tom Brady of football fame from his success in the game feels significant and is thought of as significant, while the fellow on the losing end in games and in scrimmages who soon gets cut from the roster feels insignificant and is thought of as such by others in and out of his profession, (indeed, as insignificant, usually not thought of at all.)  We need not dwell at length on the obvious rewards of being and feeling significant. Hence, the question to be asked is whether Tom Brady would cheat to win and be significant and enjoy the rewards of being significant? Would Tom deflate the footballs to be significant? This is not asking the question of whether or not he actually did. We know Tom Brady personally and can vouch for the fact that he’s not that kind of a guy. But maybe somebody other than Tom Brady would deflate the footballs to achieve Brady’s significance. That’s the point. Would somebody do that or something like that if he or she could get away with it?

The payoff for winning, for having a high p probability of winning, for having the edge in competition and being significant, is so high and the cost of having a low p probability of winning, of being vulnerable to loss and being insignificant, is so great emotionally, that in many situations, people who can get away with corruption, with cheating on the rules, just do it. Moreover it is also the case that such corrupt behavior is never openly confessed to or in any way revealed because doing so kills the “getting away with it” factor in making a deal with the devil.

For that reason, there’s lots of corruption and not much open talking about it. Really does any even half-intelligent person think that no Wall Streeter going to jail, not even for a day, after six years of investigation of this multibillion dollar scam by the Justice Dept. is anything but a manifestation of consummate business, judicial and political corruption? Even though nobody with a public voice ever says, in contradiction to the Orwellian doublespeak reasons why there was no prosecution of this grand theft by Wall Street banks on tens of millions of Americans, that our social system is thoroughly corrupt, is it not apparent on its face? 

Indeed capitalism is corrupt. All civilized social systems are inherently corrupt. The drive to be on top, to be significant, to avoid insignificance, is a powerful incentive to break any code of fairness held up as the moral norm in a society. Even heads of state in a military dictatorship never tell their underling citizens that the game is corrupt and unfair. Be sure that Hosni Mubarak of Egypt, 30 years the military dictator of that vassal state of the USA, a fellow who scuttled billions for himself and his family through systematic corruption, never went on Egyptian TV before the Arab Spring to tell the Egyptian peasants that he was robbing and fucking them blind. 

All power systems work this way including our capitalism, which never buys two hours of airtime on TV to proclaim to the American people that it is robbing them blind. The only difference between military dictatorship and capitalism is how the edge is obtained, not whether it exists and is used for the benefit and privilege of those who have the edge. Buying and selling is inherently corrupt and deceitful. The game is to buy cheap and sell dear. The seller is always out to tell the buyer anything he has to in order to extract the maximum amount of money out of the buyer. In the small, as hagglers over price in a New Delhi marketplace know, it is part of the game of the seller to lie in order to get the maximum cash out of the buyer. Institutional corruption comes in when the political system and the judicial system joins in the game against the rules in order to tolerate the inherent corruption and deceit of the marketplace.

But these instances of corruption get way ahead of the game and require much more analysis for their picture to be drawn our fully. What we want to talk about in this section in detail, rather, is the corruption in the marketplace of analytical ideas, that makes it impossible in the end to honestly talk about and uncover the corruption in the broader society that will soon be taking us all to nuclear hell because of the stupidity and lack of foresight from leaders who attained their power through cleverness in becoming socially significant by maximum capability at corruption and deceit rather than really being smart. Beyond the exceptions like Bill Gates, who is too much of a coward and a pussy to enter the tussle of the political and economic arenas where real people suffer daily, the entrepreneur is nothing but a clever thief.  

In academics, as in all other professions, there is a hierarchy of power and as in all other hierarchies, it is corrupt as long as it can get away with being corrupt as requires centrally hiding the corruption. As in all areas of corruption, people maintain their p probability of being successful by helping to enable other people’s p probability of being successful. That is, in colloquial language, you scratch my back and I scratch yours. The temptation to do this in obviation of the rules is very strong because the penalty for not doing it is frequently that one winds up with little p probability of winning in competition and of being insignificant, while the prize for “playing the game” is attaining some significance, which feels much better than being insignificant.            

In academics, just as in every profession, some people do the hiring and firing, the awarding of cash grants to do research and the editing of journals where research papers are published as enable position and grant support. Most often the people on the top of this game are “experts” in the field. Or better said they are recognized as experts by others in the field, which gets you right back to the “you scratch my back, and I’ll scratch yours” game. Of course, playing that game with the devil is lost if one advertises the fact that one is an academic entrepreneur. One most amusing instance of it in recent times was the Complexity Theory bullshit engineered by Stuart Kauffman whose debunking was the primary focus of the Scientific American article by John Horgan, From Complexity to Perplexity, I brought up at the beginning of A Theory of Epsilon.

Unlike my quip about Tom Brady, we actually do very much know Stuart Kauffman personally. And it is interesting that long before we read Horgan’s article ridiculing complexity theory, we had a sense after an hour’s long lunch with Kauffman from the obvious lack of clarity in his doubletalk mathematics that he was as slick a charlatan as Bernie Madoff. For what Kaufmann did was to spin a mathematical argument so complex about complexity that it was near impossible to take apart, for a while anyway. Before it was taken apart publically and Kaufmann chased off to Canada to talk his nonsense to the more naďve Canuck academics he enjoyed great significance in association with the Santa Fe Institute and even wound up a McArthur grant winner.

The corruption in academics is not as obvious in most cases as Kaufmann’s carny game. In our case at hand it has consisted of “experts” in the field of thermodynamics being unwilling to admit that the material they claim to be experts at is incorrect. Though we have run into a good number of them over the years in various universities, the attitude of Bill Poirier stands out.  Note his comments to us about our revision of microstate entropy.             

In short, though the Gibbs and Boltzmann Shannon-like formulations of entropy have their limitations/issues, there is nothing really mathematically "wrong" about them---they are what they claim to be, within well-known caveats. Conversely, this is not to say that your approach is "wrong" or otherwise without value; as I said in an earlier email, there may well be more than one useful quantity associated with the same general concept. But I would be wary of making claims that classical entropy is "fundamentally incorrect", and that your approach "provides the only correct understanding of microstate entropy."

Poirier is alluding to both the Boltzmann-Shannon take on entropy and our meaningful information derivation of it being mathematically equivalent and both correct in that regard. Yet despite the “limitations/issues” with the standard formulation that Poirier cites, which have interminably confused students and professionals alike for the last 100 years, he still favors the standard, perplexing take on entropy unable to shake the inferior explanation he has grown to accept over the years despite its obvious shortcomings. Proof that Poirier is dead wrong lies in his insistence in Chapter 10 his recent book that entropy can be explained from information theory despite the general understanding in the scientific community conveyed in the above Scientific American quote that information theory, as it presently stands, cannot be applied to explaining physical systems. Our extension and elaboration of information theory to include meaningful or significant information as it is found both in physical and in human nature makes the intimate association between entropy and information clear enough that even a high school chemistry student can understand entropy now.  

We also mention lightly the pettiness and stupidity of today’s scientists in clinging to orthodoxy for the sake of retaining the crown of “expert” and the position, status and pay that go along with it. A perfect example of this is of our front page poster boy, Bill Poirier of Texas Tech in Lubbock. Perusal of Chapter 10 in his recent book, A Conceptual Guide to Thermodynamics shows a frivolous notion of an information theory interpretation of thermodynamic entropy. It can be judged on its merit by anybody who takes the time to pick up the book and read that chapter in it. His frivolous interpretation of entropy as “the amount of information you don’t know about the thermodynamic system” should be damned because it totally misunderstands the mathematical similarities between information and entropy that scientists have been aware of for the last 65 years. The reason for the similar form of the two is that both are inexact measures of sets of things that are generally unbalanced and whose exactness mathematically and as a clear correct understanding of them is provided by the same functional replacement for the N number of constituents in a set, namely diversity be it D or h. He personally should also be damned for not being willing to budge an inch for fear of making a fool of himself in his hypothesis being shown to be wrong, this after a many email exchange with him that laid out the foregoing in a series of first drafts of this material.

He is hardly the only one out there who thinks this way, science having fallen into the same state as all other endeavors in modern day mathematics where people learn to feather their own nests at the expense of the broader needs of society. If such is the case in the natural sciences, that much more is it prevalent in the human sciences, which are thoroughly adulterated by ideology to ascribe people’s unhappiness to the bugaboo of mental illness which is almost as vague, spirit like and intangible as Satan as the cause of evil and unhappiness. Clinical psychology never prescribes rebellion against unfair authority and its humiliations as a remedy for the unhappiness caused by it, but rather “adjustment” to the pain of it and that by any means which includes developing a chronic dependency on psychotropic drugs and delusional belief in religious superstition. God, Heaven, after life and the devil are quite alright with the pseudo-science of clinical psychology.

From a purely logical perspective, one should have great doubt about a supposed science that purports to understand abnormal emotion without giving any clear sense of the normal human emotions, as we will do starting in the next section as the foundation of a new set of mathematics based human sciences.   


9. The Mathematics of Human Emotion

We do not wish to throw the baby out with the bathwater in our revision and expansion of information theory in Section 6. It is in no way a denial of all of its basic principles, a primary one of which we form the foundation of our specification of all of the human emotions in mathematical form. That principle I am talking about is information theory’s alternative interpretation of the H Shannon entropy of Eq71 as the amount of uncertainty that getting a message resolves upon being received. Uncertainty and information are closely related in information coming about as the resolution of uncertainty. If you have no idea of the way Company XYZ you hold stock in is going and I tell you from what my cousin, the president of the company, told me that they are contemplating bankruptcy in two weeks, that message is information for you because you had uncertainty about the company’s situation to begin with. But if I tell you that Osama bin Laden was the mastermind of 9/11, something you certainly knew beforehand, that message would not be information for you because you had no uncertainty about that.   

In a more mathematically treatable way, if you are playing a game where you must guess which of N=4 colors I’ll pick from the set of K=8 colored buttons, (■■, ■■, ■■, ■■), inherently you have uncertainty about what the color is. Keep in mind from our earlier considerations the H=2 bits amount of information associated with this set. That value of H=2 is a measure of the amount of uncertainty you have as the number of yes-no binary questions one needs to ask about the colors in (■■, ■■, ■■, ■■) to determine which color I picked. By a yes-no binary question is meant one that is answered with a “yes” or a “no” and, as binary, cuts the number of possible color answers in half.

One might ask of (■■, ■■, ■■, ■■), “Is the color picked a dark color?” meaning either purple or black? Whatever the answer, a “yes” or a “no”, the number of possible colors picked is cut in half. Assume the answer to the question was “no”, then the next question asked might be, “Is the color green?” If the answer to that next question is also “no”, by process of elimination the color I picked was red. It took H=2 such questions to find that out. So the amount of uncertainty about which color I picked is understood to be H=2. And the amount of information gotten from receiving a message about the color picked is H=2 bits understood as the amount of uncertainty felt beforehand.   

Let’s play that game with (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) now whose H=3 bits Shannon entropy is the amount of uncertainty you feel about which color I picked from that set of buttons because it takes H=3 yes-no binary questions to determine the color. The first question for (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) might be, “Is the color a light color?” meaning red, green, aqua or orange. When “no” is the answer, it halves the field of colors picked to (■■, ■■, ■■, ■■). And two more yes-no binary questions will then reveal the color picked. The amount of uncertainty for the color picked from (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) is then its H Shannon entropy of H=3 bits interpreted as 3 binary questions. And the amount of information you would get if I sent you a message about which color was picked would be H=3 bits of information as the resolution of the H=3 bits of uncertainty felt beforehand.

That information is affected by emotion is obvious from the sense of information underpinned by uncertainty, something people generally feel as an unpleasant emotion. Moreover when uncertainty is resolved, by whatever means, a person tends to feel something akin to relief or elation, a generally pleasant emotion. Now while it is true that the H Shannon entropy provides some measure of uncertainty as discussed above, the human mind really doesn’t work on logarithmic measures for the most part. We tend rather to evaluate uncertainty probabilistically. Let’s go back to guessing the color picked from the N=4 color set, (■■, ■■, ■■, ■■).

The probability of guessing correctly, which we’ll give the symbol, Z, to, is

84.)                http://matrix-evolutions.com/INDEX_files/image062.gif 

And the probability of failing to make the correct guess, understood as the uncertainty in guessing, is

85.)                http://matrix-evolutions.com/INDEX_files/image063.gif

Now let’s recall the D diversity of a balanced set from Eq4 to be D=N. This allows us to understand the U uncertainty as

86.)                 http://matrix-evolutions.com/INDEX_files/image064.gif

Now let’s make a table of sets of buttons that have more and more D diversity and list the U uncertainty in guessing the color picked from them.

Sets of Colored Buttons

D=N

U=(D–1)/D

(■■, ■■)

2

1/2=.5

(■■, ■■, ■■)

3

2/3=.667

(■■, ■■, ■■, ■■)

4

3/4=.75

(■■, ■■, ■■, ■■, ■■)

5

4/5=.8

(■■, ■■, ■■, ■■, ■■, ■■)

6

5/6=.833

(■■, ■■, ■■, ■■, ■■, ■■, ■■)

7

6/7=.857

(■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■)

8

7/8=.875

Figure 87. Various Sets and Their D and U Values


Very obviously the U uncertainty is an increasing function of D diversity. That is, as D increases, U increases. More formally U is an effectively continuous monotonically increasing function of D. This, from measure theory in mathematics, tells us that whatever D is a measure of, U is a measure of. Earlier we made it clear that D diversity was a measure of information. And that would also make the U uncertainty measure understandable as information, which fits with the classical information theory take on information as the resolution of uncertainty.  

This gives us two ways to specify the resolution of uncertainty being information, one as H in a logarithmic way, the other as U in a linear probabilistic way. The breakthrough in psychology that finally makes sense out of human nature is to understand emotion as meaningful information. And to do that we need to specify the uncertainty that precedes information in terms of probability, U, not only because the human mind is geared to sensing uncertainty as probability rather than in bits and bytes, but also because doing so, using U, allows us to connect it up with something meaningful, and that meaningful something is money.

Specifically, configuring uncertainty and information in terms of U probability connects uncertainty up with that meaningful item of money through a game of chance designed to have a cash penalty imposed on you if you fail to win at it. It is a color guessing game that uses the N=3 color set of colored buttons of (■■, ■■, ■■). If you fail to guess the color I pick, you pay a penalty of v=$120. The probability of guessing correctly is

88.)                  

And the probability of failing to guess correctly is

89.)                 

Now the product of the penalty, v, and the uncertainty, U, which is the probability of paying the penalty, is called the expected value of the game

90.)                 E= –Uv

Putting in the values, U=2/3 and v=$120, we calculate the E expected value or expectation to be

91.)               E= –Uv= –(2/3)($120)= –$80

The negative sign specifies E= $80 as a loss of money, the average loss incurred if you are forced to play this game repeatedly. If you play the game three times, for example, on average you will roll a lucky number and escape the v=$120 penalty one time out of three; and you will fail to roll a lucky number and pay the v=$120 penalty two times out of three as adds up to a $240 loss that averaging out over three games is an E= −$240/3= −$80 loss per game.

The E= –Uv term that is the product of the U uncertainty and the v penalty of money, a meaningful item, can also be understood as meaningful uncertainty. A more familiar expression for this E= –Uv meaningful uncertainty is the fear you have of losing money when you are made to play this game.  That E= –Uv is a fitting equation for such fear is clear from three perspectives. The first is that your fear of losing money is a function of the U uncertainty or your probability of failing to guess the color. If we change the game to my randomly picking a colored button from the N=8 color set of buttons of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), then the probability of a successful guess goes down to

92.)                  Z = 1/N =1/8 = .125

And the probability of failing to guess correctly and of your having to pay the v=$120 penalty goes up to

93.)                      U=1–Z=7/8=.875

And the expected value translated as the amount of fear you have in having to play this game is

94.)                 E= –Uv= –(7/8)($120)= –$105

That fear feels unpleasant is manifest in the negative sign of the E= –Uv expectation. And you see that this function also fits the natural sense of fear that would be felt including as a measure of the displeasure in it if we change the v penalty. If we increase it to v=$360, the displeasure of fear felt for this game played with  (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) goes up to

95.)                    E= –Uv= –(7/8)($360)= –$315

We have introduced emotion now in a very straightforward way in terms of understanding meaningful uncertainty as fear. Next now consider what happens if there is a third person involved in this game who sees which color I picked and tells it to you on the quiet. Then you can use it as your guess and avoid paying the penalty. To go along with the basic algorithm that information is the resolution of uncertainty in information theory, we’ll understand the amount of information you got in the color told you, meaningful information from its resolving your meaningful uncertainty, to have the same measure as the meaningful uncertainty, –Uv, except we’ll get rid of the – minus sign understanding the removal of the meaningful uncertainty to be specified as

96.)                T= –(–Uv) = Uv

We’ll explain where the T symbol comes from later on, understanding it now to represent the amount of meaningful information you got from the message told you about color. Now intuitively, you are going to feel an emotion of relief in getting this meaningful information. And the T=Uv function is a very good measure of the amount of relief, how pleasant it is in intensity. For the greater the v penalty, the greater the relief you feel in avoiding it. And the greater the U uncertainty, the greater the relief also. And the implicit (+) positive sign of T=Uv= +Uv, is a reasonable marker for the positive feeling or pleasure you get in relief, that as opposed to the E= –Uv fear, which is unpleasant as it (–) minus sign denotes.

Of course, the amount of fear you feel in expectation of paying the v penalty and the amount of relief you feel in avoiding the penalty are both dependent not only on the U probability of paying the penalty and the v amount of the penalty, but also on how much money, how much wealth, you already have. A millionaire doesn’t really care about losing $80 or get that much pleasure of relief in avoiding the loss as compared to a person who had but $5 in their purse or bank account. This marginality aspect that affects the emotions involved, we’ll obviate by making everybody who plays this game and in every game played have the same amount of wealth.

With that we have the basics down: getting rid of E= –Uv meaningful uncertainty by some activity, here guessing a color randomly chosen, generates T=Uv meaningful information. And this also introduces two primary emotions people feel, fear as E= –Uv and relief as T=Uv. The color guessing game was fine for an introduction to emotion, but next we want to develop the basic emotions, and there are a few more of them, in a more general way. Specifically we want to do it for all goal directed behaviors.

And to do that we are going to switch the game to a dice game called Lucky Numbers. It will develop mathematical functions for a fuller spectrum of our most basic emotions like hope, anxiety, excitement, disappointment, fear, relief, dismay, relief, joy and depression, which we’ll refer to as our operational emotions. And then later we’ll modify the game played to develop functions for our visceral emotions like sex, anger, hunger and the taste pleasures of eating.

We’ll start off playing this Lucky Numbers dice game for a prize, one of V=$120. The lucky numbers in the game are the |2|, |3|, |4|, |10|, |11| and |12|. If you roll any one of them you win a prize of V=$120. The individual probabilities of rolling the numbers |2| through |12| on a pair of dice are:

97.)  p|2|=1/36;  p|3|=2/36;  p|4|=3/36;  p|5|=4/36;  p|6|=5/36;  p|7|=6/36;  p|8|=5/36;  p|9|=4/36;  p|10|=3/36;  p|11|=2/36;  p|12|=1/36

And the probability, Z, of rolling one of these lucky numbers, |2|, |3|, |4|, |10|, |11| and |12|, is just the sum of their individual probabilities.  

98.)              Z = 1/36 + 2/36 + 3/36 + 3/36 + 2/36 + 1/36 =12/36 =1/3

This obtains the probability of rolling a number other than one of these lucky numbers of 

 105.)                   U=1− Z=2/3

(Note: equation numbers 99-104 are not used.) This U=2/3 is the improbability or uncertainty in success of rolling a |2|, |3|, |4|, |10|, |11| or |12| lucky number. The amount of money one can expect to win on average in this V=$120 prize game is

106.)              E = ZV = (1/3)($120) = $40   

E is the expected value of the game, the average amount won per game played. If you played this dice game three times you could expect to win V=$120, on average, one play in three for an average payoff of E=$40 per game played. Eq105 enables us to write the expected value of E=ZV in Eq106 as 

107.)              E = ZV = (1−U)V= V −UV 

The E expected value has three component terms in the above, E=ZV, V and – UV. To understand E=ZV and V in Eq107 in terms of the pleasure associated with them we need to fast forward for the moment to the successful outcome of playing this game of winning the V=$120 prize. We label the prize money gotten or realized with the letter R, hence, R=V=$120. This distinguishes it from the V=$120 in E=V−UV of Eq107, which is most broadly an expectation or anticipation of getting money that is quite different than actually getting or realizing money.

And assumed is that getting money is pleasurable with the intensity of the pleasure greater the more money gotten. Consider a spectrum of prizes offered that can be won by a player. Then R=V=$120 is understood to be more pleasant than R=V=$12 and both less pleasant than R=V=$1200. This assumption is reasonable in being universal in people old enough and sane enough to appreciate money.  The pleasure of the R=V emotion of winning is referred to variously as joy, delight or elation.

For simplicity sake we will take R=V=$120 to provide ten times more pleasure than R=V=$12 and R=V=$1200 to provide ten times more pleasure than R=V=$120. So we will understand the pleasure experienced in getting R=V dollars to be a simple linear function of V. This simplifies the relationships derived for the mathematics of human emotion. One could also assume that the pleasure involved in getting money is marginal, that the more money one gets, the less pleasure felt per unit of money gotten. We could also develop a mathematics of human emotion with functions that model this assumption of marginality, but in the end, the cornerstone relationships of the emotion mathematics derived would be essentially the same as with the linear model, but the computations involved significantly more difficult to develop and to follow.

It is also accepted that the pleasure in getting a certain amount of money is a function of how much money the receiver of some R+V amount already has in her purse or in the bank. Clearly getting R=V=$12 means a lot more and provides more pleasure to a homeless woman with $2 in her purse and no money in the bank than it does to someone like Bill Gates. This is just another manifestation of marginality that we can also omit from consideration by assuming that all recipients of R=V dollars have the same amount of money already in their possession.

The V term in E= V− UV of Eq107 differs from an R=V realization of money in its being the anticipated goal of playing this prize awarding Lucky Numbers game. The V dollar prize in E=V− UV is what the player wants. It is his desire, his wish, his goal in the game, to obtain the V=$120 prize. There is a pleasure in the V wish or desire for obtaining the V dollar prize. Again we will understand the intensity of that pleasure to be directly proportional to or a linear function of V.

We will also understand the pleasure in anticipating V dollars to be equal to the pleasure in realizing R=V dollars. At first this seems incorrect. Surely, one would think, people enjoy greater pleasure in getting R=V dollars than in expecting to get V dollars. That confusion, though, is cleared up by understanding the –UV term in E=V−UV of Eq107 as a measure of the anxiousness or anxiety felt about getting the V dollar prize. The greater the U uncertainty in success, the greater the anxiety in expecting it as also inflated by the V size of the prize expected. That is, the greater the V size of the dollar prize desired or wished for, the greater the −UV anxiousness about getting it. The negative sign in –UV is understood as indicating that the emotion of anxiousness is unpleasant, which is in experience universal for people. 

Note then that the –UV anxiousness reduces the V pleasure of anticipating the prize in E=V−UV of Eq107. This understands the E expected value as a measure of the realistic hope or hopes a person has in getting the as a reduction of the wish for the V prize via the –UV anxiousness the player has about succeeding. That is our realistic hopes take into account both the desire or wish for the V prize and the U probability of not getting it. Indeed, when that U improbability or uncertainty of success is not taken into account, we call it wishful thinking.

Very often, and especially in a game of chance like the prize awarding Lucky Numbers game, there is always some U uncertainty in expectation of the prize.  Hence anticipation of the prize in terms of the E=V−UV measure of realistic hope for it is very often less intense pleasure wise than the R=V pleasure of actually realizing the prize. But that is not always the case as is clear when a person anticipates a paycheck at the end of the week with absolute surety, Z=1, and no uncertainty, U=1−Z=0. In that case E=V−UV=V, and experientially there is no significant difference between surely expecting to get the R=V money on the day before pay day and actually getting it on pay day, E=V=R=V. 

Backing up a bit we see that our hopes are a function of what we hope for, V dollars in this case, and our sense of the likelihood or probability of getting it, Z in this case. The greater the V prize desired and the Z probability supposed of getting it, the “higher” our hopes and greater the pleasure in the E=ZV expectation. Note that we use the word “supposed” in association with Z and the pleasure incumbent in our E=ZV hopes. In this Lucky Numbers game, it is taken that the supposed probability is the true probability of success in rolling a winning lucky number. But generally speaking people may have false hopes, excessive hopes, which actually do feel more pleasant in anticipation of success than if a lesser, more realistic, probability were supposed. Indeed much of the pleasure in believing in religion and the reward of a happy after life derives from a delusional high hope of its actually happening, the reality of the outcome irrelevant to the true believer’s pleasure in anticipating it.   

Backing up again we also should understand that the –UV anxiousness felt also goes in ordinary language by other names like anxiety or fear or concern or worry about getting money wished for. For that reason we also give –UV a technical name, that of meaningful uncertainty as uncertainty, U, made meaningful by its association with V dollars in –UV, money generally being a meaningful or valuable item for people.

Next we want to state a general function for all the emotions involved in this prize awarding Lucky Numbers game, The Law of Emotion. To do that we have to add one more elemental function to the mix. It is what is realized when a lucky number is not rolled. Nothing is gotten or realized as expressed by R=0. The elemental emotions we have considered up to this point now allow us to write the Law of Emotion as 

108.)                             T = R − E  

We are already familiar with two of the three functions in The Law of Emotion. E is the expectation of winning a V dollar prize and R the realization or outcome of the attempt to win by throwing the dice, R=V for a successful attempt and R=0 for an unsuccessful one. The T term is now introduced as a transition emotion that comes about as a combination of what was expected, E, and what was actually realized, R. In a failed attempt where R=0, the transition emotion develops from T=R−E, The Law of Emotion, as

109.)                T = R −E = 0 −ZV = −ZV   

This T= − ZV transition emotion is the disappointment felt when one’s hopes of winning the V prize, E=ZV, are dashed or negated by failure to throw a lucky number. Disappointment is specified as unpleasant from the minus sign in T= − ZV and its displeasure is seen to be greater, the greater is the V size of the prize hoped for but not won and the greater the Z probability the player felt he had to win. In the game for a V=$120 prize that can be won with probability of Z=1/3, the intensity of the disappointment is

110.)                 T = −ZV = −(1/3)($120) = −$40

The T= −$40 cash value of the emotion of disappointment indicates that the intensity of the displeasure in it is equal in magnitude, if not in all its nuances, to losing $40. The T= − ZV disappointment over failing to win a larger, V=$1200, prize hoped for, is greater as 

111.)                T= − ZV= − (1/3)($1200)= − $400

Note that though the realized emotion, R=0, produces no feeling, pleasant or unpleasant in itself, from failure to achieve the goal of obtaining the V dollar prize in the game, failure does produce displeasure in the form of the T= − ZV transition emotion. This transition emotion and the three more basic transition emotions we will consider have a specific function in the emotional machinery of the mind that we will consider in depth once we have generated those three T emotions from The Law of Emotion.

We call attention to the universal emotional experience of T= − ZV disappointment being greater the more V dollars one hoped to get but didn’t. The T= − ZV disappointment is also great when the Z probability of winning is great. Consider this Lucky Numbers dice game where every number except snake eyes, the |3| through|12|, is a lucky number that wins the V=$120 prize. These lucky numbers have a high probability of Z=35/36 of being tossed, so the hopes of winning are great as

112.)        E = ZV = (35/36)($120)= $116.67

And we see that the disappointment from failure when the ZV hopes are dashed or negated to –ZV by rolling the losing |2| is also great as

113.)       T= −ZV = − (35/36)($120)= − $116.67

Compare to T= − ZV = −$40 in Eq10 played for the same V=$120 prize, but when the probability of success was only Z=1/3. This fits the universal emotional experience of people feeling great disappointment when they have a high expectation of success and then fail. And at the other end of the spectrum, as also predicted by T= −ZV, people feel much less disappointment when they have a very low Z expectation of success to begin with. As an example, consider the T=−ZV disappointment in this dice game when to win you must roll the low Z=1/36, probability snake eyes, the |2|, as the only lucky number to win with. Then the disappointment is much less as 

114.)               T= ZV= − (1/36)($120)= −$3.33

Now let’s consider the T transition emotion that arises when one does win the V dollar prize with a successful toss of the dice. With hopeful expectation as E=ZV and realized emotion as R=V, the T transition emotion is from the Law of Emotion of Eq108, T=R−E, via the U=1−Z relationship in Eq105,  

115.)              T = R−E = V −ZV = (1− Z)V = UV

The T= UV transition emotion is the thrill or excitement of winning a V dollar prize under uncertainty. It is a pleasant feeling as denoted by the implied positive sign of UV with the pleasure in the thrill greater the greater is the V size of the prize and the greater is the U uncertainty of winning it felt beforehand. When one is absolutely sure of getting V dollars with no uncertainty, U=0, as in getting a weekly paycheck, while there is still the R=V pleasure of delight in getting the money, the thrill of winning money under uncertainty is lacking. That is, with uncertainty present, U>0, there is an additional thrill or excitement in winning money as in winning the lottery or winning a jackpot in Las Vegas or winning a V=$120 prize in the Lucky Number dice game. In the latter case, with an uncertainty of U=2/3 from Eq105, the intensity of the excitement in winning the V=$120 prize is from Eq115

116.)              T=UV=(2/3)($120)=$80  

That this additional pleasure of T=UV excitement in obtaining V dollars over and above the R=V delight in getting money depends on feeling U uncertainty prior to rolling the dice is made clearer if we look at an attempt to win V=$120 by rolling the dice in a game where only tossing snake eyes, the |2| on the dice, with probability Z=1/36 and uncertainty U=35/36, wins the prize. In that case, if you do win, as with winning in any game of chance where the odds are very much against you, the uncertainty very great, there’s that much more of a thrill or feeling of excitement in the win.       

117.)              T= UV= (35/36)($120)= $116.67

By comparison consider a game that awards the V=$120 prize for rolling any number |3| through |12| with Z=35/36 probability of winning and low uncertainty of U=1−Z=1/36 as makes the player near sure he is going to win the money. While there is still the R=V=$120 delight in getting the money upon rolling one of these many lucky numbers, there is much less thrill because like getting a paycheck, the player was almost completely sure of getting the money in this Z=35/36 dice game to begin with.

118.)              T=UV=(1/36)($120)=$3.33

This relationship between the uncertainty one has about getting something of value and the excitement felt when one does get it is clear in the thrill children feel in unwrapping their presents on Christmas morning. The children’s uncertainty about what they’re going to get in the wrapped presents is what makes them feel that thrill in opening them up. This excitement is an additional pleasure for them on top of the pleasure realized from the gift itself. That special thrill in opening the presents under the Christmas tree is not being felt when the youngsters know ahead of time what’s in the Christmas presents and feel no uncertainty about it.

As is predicted by T=UV, it is seen to be universal for people that winning a V=$1200 prize in a game of chance is more thrilling than winning a V=$120 prize when the U uncertainty (or probability of not winning) is the same in both cases. And we get a fuller picture yet of the T=UV thrill of winning under uncertainty from the T=R−E Law of Emotion of Eq108 when the E expectation term in it is expressed from Eq107 as E=V− UV.   

119.)            T = R− E =V−(V−UV) = − (−UV)=UV           

This derivation of T=UV as the negation –UV anxiousness, T= − (− UV) =UV, derived for the Lucky Numbers dice game is the basis of excitement coming about generally by the negation or elimination of anxiousness via a successful outcome. Adventure movies generate their excitement or thrills for the audience in just that way by being loaded with anxiousness or dramatic tension at the beginning of a drama from the hero’s meaningfully uncertain situation, which the audience feels vicariously. When the hero’s uncertain situation is resolved by success towards the end of the movie, it vicariously brings about thrills and pleasurable excitement for the audience that empathizes with the hero by negating or eliminating the anxiousness they felt about his or her situation to begin with. Though the emotions felt by the audience are vicarious, the essence of the dynamic is essentially the same as spelled out in Eq119.

We have in the above explained excitement as resulting from an outcome of goal directed behavior of success. People are also generally aware of excitement as a feeling that prefaces success. That is also very easy to explain mathematically, as we will in Section 8, but only after a proper workup that makes its understanding instantly simple and clear.  

THE OTHER broad category of goal directed behavior that people engage in is to try to avoid losing something of value, like money. This category is well illustrated with the v= S120 dollar penalty game we introduced earlier in the color guessing game. The player is forced to play this game and the penalty can be avoided with the Z=1/3 probability roll of a |2|, |3|, |4|, 10|, |11| or |12| lucky number. The probability of not rolling one of these lucky numbers as results in paying the v=$120 penalty is U= 1− Z =2/3. And the expected value as Uv=$80 is given below in more proper form with a negative sign as

120.)              E= U(−v)= −Uv= −(2/3)($120)= −$80

The negative sign on –v makes clear that the v dollar value represents a loss of dollars for the player. The E= −Uv= −$80 expected value of this game is the average penalty paid if one were forced to play this game repeatedly. It tells us that if you played three of these penalty games, on average, you will fail to roll a |2|, |3|, |4|, 10|, |11| or |12| lucky number two times out of three to pay the v= −$120 penalty for a total of $240 as averages out over the three games to a penalty per game of E= − $80.

E= –Uv is a measure of the fearful expectation or fear of incurring the penalty. The negative sign prefix of E= −Uv indicates that this fear is an unpleasant emotion with the intensity of the E= −Uv displeasure of the fear greater the greater the U probability of incurring the v penalty and the greater the size of the v penalty, as fits universal emotional experience.

The −Uv fear goes by a number of other names in ordinary language including worry, distress, apprehension and concern. This plethora of names for E= –Uv fear has us give it the technical name also of meaningful uncertainty as puts –Uv fear, as an anticipation of the possibility of losing dollars, in the same general category as −UV anxiety, as an anticipation of the possibility of failing to win V dollars that are hoped for. That both –Uv fear and –UV anxiety are classified together as forms of meaningful uncertainty should not be surprising given that they are very often referred to with the same names of fear, anxiety, concern, worry, distress, apprehension, trepidation, nervousness and so on. Note that we refer in this treatise to –Uv as fear and –UV as anxiety to distinguish between the two however the words are often used interchangeably in ordinary language. We will have more to say about the naming of emotions shortly after we develop a more complete list of them.    

Next we consider the realized emotions of the penalty game. The first is the realized emotion that comes about when the v penalty is realized from the player failing to roll one of the |2|, |3|, |4|, 10|, |11| or |12| lucky numbers, R= −v. This unpleasant emotion is one of the grief or sadness or depression felt from losing money. Again there are many names for it in ordinary language. And when the outcome is of a successful toss of a lucky number the realized emotion is given as R=0 because as no money changes hands when the player is spared the penalty, there is no emotion that comes from the outcome, per se.

That is not to say that there is no emotion felt from avoiding the penalty, but it is a T transition emotion derived from the T= R−E Law of emotion of Eq8 rather than as a form of R realized emotion. When the lucky number is rolled the fearful expectation of E= −Uv is not realized, R=0, and the T transition emotion is from the T=R−E Law of Emotion of Eq108, 

121.)            T = R−E = 0 − (−Uv) = Uv           

This T=Uv measures the intensity of the relief felt from escaping the v dollar penalty when you roll one of the lucky numbers. The positive sign of T=Uv specifies relief as a pleasant emotion with its pleasure greater, the greater is the v loss avoided and the greater is the U improbability of avoiding the loss. The T=Uv relief felt when a |2|, |3|, |4|, 10|, |11| or |12| lucky number is tossed in the v=$120 penalty game with uncertainty U=2/3     

122.)              T= Uv= (2/3)($120) =$80

To make clear how dependent the intensity of Uv relief is dependent on the U uncertainty, note that if one plays a v=$120 penalty game where rolling only the |2| avoids the penalty, with uncertainty U=35/36, there is greater relief in successful avoidance of the penalty by rolling the lucky number because you felt prior to the throw that most likely you would lose. 

123.)              T=Uv=(35/36)($120)=$116.67

This increase in relief with avoidance of a penalty under greater uncertainty is universal. But if you play a v=$120 penalty game that avoids the penalty with any number |3| through |12|, with uncertainty of only U=1/36, there is much less sense of relief because you felt pretty sure you were going to avoid the penalty, with high probability of Z=35/36, to begin with.

124.)              T=Uv=(1/36)($120)=$3.33

Note also that the larger the v penalty at risk, the more intense the relief felt in avoiding it as with a v=$1200 penalty in the game where only rolling the |2| lucky number game with uncertainty, U=35/36, escaped the penalty.

125.)             T=Uv=(35/36)($1200)=$1166.67

Compare to the relief of T=$116.67 in Eq123 when the penalty was only v=$120. The universal fit of mathematically derived Uv relief to the actual emotional experience of feeling relief is remarkable.  We also use the Law of Emotion of Eq108 of T=R−E to obtain the T transition emotion felt when the player does incur the v penalty by failing to roll a lucky number. In that case, with expectation of E=−Uv and a realized emotion of R= − v, the T transition emotion is via Z=1− U   

126.)              T = R − E = −v − (−Uv) = −v+ Uv= −v(1−U)= −Zv

This T= − Zv transition emotion is the dismay or shock felt when a lucky number is not rolled and the v penalty is incurred. The T= −Zv emotion of dismay is an unpleasant feeling as implied by its negative sign and one greater in displeasure, the greater the Z probability of escape one supposed before rolling. Its value for the |2|, |3|, |4|, 10|, |11| or |12| lucky number v=$120 penalty game with Z=1/3 is 

127.)              T= − Zv = − (1/3)($120)= − $40

But if you have a very small Z probability of avoiding a v=$120 dollar loss as in the dice game where only rolling the |2| as the lucky number provides escape from the v penalty to probability, Z=1/36, there is little − Zv dismay when you fail to roll that lucky number and must pay the penalty because you had such a high sense of E= −Uv with U=35/36=.9667 surety that you’d have to pay the penalty to begin with.

128.)              T= − Zv = − (1/36)($120)= − $3.33

One develops a more intuitive feeling for dismay by expressing the E= −Uv fearful expectation via U=1− Z  as   

129.)              E= −Uv = −(1–Z)v = −v + Zv

The − v term in Eq129 is the anticipation of incurring the entire v penalty, which we will call one’s dread of the penalty for want of a better word. The displeasure in the dread of paying the v penalty is marked by the negative sign of − v with the intensity of its displeasure greater, the greater the v dollar penalty that is dreaded. Were the penalty raised to −v= − $1200, the dread and its displeasure would be proportionately greater than the –v= −$120 penalty. This −v dread in E= − v + Zv of Eq129 is partially offset by the +Zv term in it as the (pleasant) hope one has that one will escape the penalty by rolling a lucky number.

This Zv term is understandable emotionally as the sense of security one has that one will avoid the penalty, the greater the Z probability of escaping the penalty in +Zv and the greater the v penalty one is protected from by Z, the greater the sense of security one has when one is forced to play the penalty game that one will be able escape the penalty. The combination of unpleasant –v dread and pleasurable +Zv security produces the realistic fear or fearful expectation of incurring the penalty, E= −v + Zv = −Uv, of Eq129. 

Expressing the E expectation as in Eq129 adds an important nuance to the derivation of dismay from the T=R−E Law of Emotion of Eq108.

130.)              T = R –E = −v −(−v + Zv)= −(Zv)= −Zv

This understands T= –Zv dismay as coming about from the dashing or negation of one’s Zv hopes or expectation of avoiding the v penalty by failure to roll a lucky number. The low dismay that results from failure preceded by low Zv expectation is why some people subconsciously develop a strategy of low expectations in life to avoid the unpleasant feeling of dismay if they do fail. This contrasts to the considerable T= − Zv dismay or shock felt in the v=$120 penalty where the lucky numbers on the dice that are needed to avoid the penalty are the |3| through |12| whose probability of being rolled is Z=35/36.

131.)              T= − Zv = − (35/36)($120)= − $166.67

In short the dismay in this case is high because of the high Zv expectation of not paying the penalty to begin with. Great dismay from failure preceded by a high Z=35/36 probability of escaping failure is also felt and referred to as shock, familiarly as a person’s surprise at failure when what was expected from the preceding high probability was success. Unpleasant unexpected surprise specified here as great −Zv dismay is also the fundamental basis of horror.

The above development of the E fearful expectation as E=− Uv = − v + Zv gives us functions for three more elementary emotions: the − v dread of incurring a penalty; the Zv sense of security one feels in the possibility of escaping the penalty; and the probability tempered E= −Uv fear of incurring a penalty. These add as expectations to the V desire of getting a V prize, the –UV anxiousness about getting it and the E=ZV probability tempered hopes of getting a prize considered earlier to give a complete set of our basic anticipatory emotions.

The −Uv, ZV, V, −v, Zv and –UV symbols are the best representations of our anticipatory emotions rather than the more familiar names for them in ordinary language respectively of fear, hope, desire, dread, security and anxiety. Ludwig Wittgenstein, regarded by many as the greatest philosopher of the 20th Century, made the point well in his masterwork, Philosophical Investigations, of the inadequacy of ordinary language to describe our mental states. Words for externally observable things like a “wallet” are clear in meaning when spoken from one person to another because if any confusion arises in discourse, one can always point to a wallet that both the speaker and the listener can see. “Oh, that’s what you mean by a wallet.” But with emotions, however, as nobody feels the emotions of another person, the words we use for an emotion have no common sensory referent one can point to in order to clarify its meaning.

The mathematical symbol-words of −Uv, ZV, V, −v, Zv and –UV, on the other hand, are at least clear in meaning because they have countable referents of money as V and v and numerical probabilities of Z and U as components. And the fit of these therefore mathematically well-defined word-symbols to emotional experience, pleasant and unpleasant, is universal. That is, all people feel these −Uv, ZV, V, −v, Zv and –UV anticipatory feelings in the same way when playing the V prize and v penalty Lucky Number games assuming all have the same quantitative sense of dollars and of probability. Hence quibbling over the “correct” names to call −Uv, ZV, V, −v, Zv and –UV or any of the other mathematical symbols we will develop for the emotions is not a valid criticism of this analysis.

Our expectations determine our behavioral selections, what we choose or decide to try to do. The basic rules are simple.

Rule #1. If we have a choice between entertaining a hopeful expectation as with E=ZV of the V prize awarding Lucky Numbers game and a fearful expectation as with E= −Uv of the v penalty assessing Lucky numbers game; we act on the behavior that generates hope rather than fear. This is so intuitively obvious that it is almost not worth stating at all other than for the sake of completeness. We can understand Rule #1 as sensible from the standpoint of a V dollar gain being preferred to a –v dollar loss; or, hedonistically, from the pleasure felt in ZV hopes triumphing cognitively over the displeasure of –Uv fear. 

Rule #2. If we have a choice between two hopeful expectations, E1=Z1V1 and E2=Z2V2 with E1>E2, we choose E1 whether E1>E2 comes about via Z1>Z2 or V1>V2 or both. As an example, one would choose to play the standard Z=1/3, V=$120 prize game with E=$40, than a V=$120 game with just |2|, |3| and |4| as the lucky numbers, Z=1/6 and E=$20. We may attribute the underlying cause of greater hopeful expectation triumphing cognitively over less hopeful expectation to the anticipated average gain in E1 being better than in E2; or, hedonistically, to their being greater pleasure in entertaining E1=Z1V1 than in E2=Z2V2. .

Rule #3. If we have a choice between two v penalty games, one with fearful expectation, E1= –U1v1, and the other with E2= –U2v2, one of which games we must play, we choose the game with the smaller expectation (in absolute terms.) Or more exactly, if E1>E2 numerically, we choose to play the E1 game. To clear up any confusion, as between the games in Eqs4&5, we choose to play the E1=–80 game, E1>E2, rather than the E= –$240 game if we have to play one of them. This comes under the colloquial heading of “choosing the lesser of two evils”, also known as a Hobson’s choice.

The nuances and extensions of these three rules are many. The main point is that they show the primary function of our expectations, hopeful and fearful, to be to determine the choices we make. The next section explains the function of the transitional emotions of excitement, relief, disappointment and dismay in our emotional machinery. And then we go on to show how the Law of Emotion derives the Law of Supply and Demand in the most elementary way, something that even the most ardent capitalist hater of our revolutionary ideas cannot deny.  

 

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10. The Function of the Transition Emotions

We continue with our systematic explanation of our emotional machinery by explaining the purpose and function of the transition emotions of T= −ZV disappointment of Eq109, T=UV excitement of Eq115, T=Uv relief of Eq121 and T= −Zv dismay of Eq125. Recall that they all come about from the T=R−E Law of Emotion of Eq108. In it the E expected value depends in a very direct way on the Z and U probabilities: of the E=ZV=V−UV hopeful expectation in the V prize game; and of the E= −Uv= −v+ Zv fearful expectation in the v penalty game.

In our analysis up to this point, the player’s sense of the values of the Z and U probabilities were taken directly and correctly from the mathematics of throwing dice. But that need not be the case. A player may suppose any probabilities of success or failure, which affects the player’s E expectations, and in turn, affects from the T=R−E Law of Emotion, the intensities of the T transition emotions from T=R−E the player experiences upon success or failure. 

As an example of a player supposing incorrect values of Z and U, consider in the V=$120 prize game where rolling a lucky number of
|2|, |3|, |4|, |10|, |11| or |12| has an actual probability of Z=1/3 that a naďve player supposes it is Z’=1/2 for whatever reason. This distorts the hopeful expectation from the player thinking she will win half the time instead of just 1 time in 3 from the correct expected value of E=ZV=(1/3)($120)=$40 of Eq107 to

191.)                E’=Z’V=(1/2)($120)=$60

(Note: Equation numbers 132-190 are not used.) The player has higher hopes of winning than she should and though that cannot affect the actual (average) R outcomes or realizations it does from the T=R−E Law of Emotion of Eq108 affect the T transition emotions that arise. To show this let’s assume the game is played three times as results in the average win-loss record of winning 1 time in 3 with R realizations of (0, 0, $120). And we’ll also assume that the player sticks to her incorrect probability suppositions for all three games played. The transition emotion felt after the first failed attempt of a realization of R=0, labelled T’, is      

192.)                T’=R−E’=0−Z’V= −Z’V= −$60

This T’= −Z’V= −$60 emotion is of disappointment in greater intensity than the disappointment of T= −$40 of Eq10 felt when the correct Z=1/3 probability is supposed. This is because the naďve player thought she had a greater possibility of winning. The 2nd game played is also an R=0 failure and again a T’= −$60 disappointment is felt. On the 3rd play, though, as fits the average % of games won a lucky number is rolled for R=V=$120 and the thrill of winning with E’=Z’V=$60 is from the law of emotion as T’=R−E’

193.)               T’=R−E’=V−Z’V=$120−$60=$60.

This a smaller excitement than the E=ZV=$80 of Eq16 that would have been felt had the player supposed the correct probability of winning of Z=1/3. The player, hence, feels greater disappointment and less excitement over the three games, the sum of the T’ emotions experienced being    

194.)               ∑T’ = −$60 −$60 +$60 = −$60

And the average of these T’ transition emotions per game is 

195.)              ∑T’/3 = T’AV= −$60/3= −$20

Now, though the player retained her incorrect suppositions of probability for the three games, failure to meet her expectations over the three games manifest as an overall unpleasant set of transition emotions of ∑T’ = −$60 and T’AV= −$20 per game lowers her hopeful expectation in the next game she plays and, as we will show below, to the correct E=$40 per game.

Her emotional machinery does this with a T=R−E Law of Emotion inversion that understands T for a game as the T’AV average of prior games, E as E’, the incorrectly supposed expectation and R as what is realized cognitively from T’AV and E’, which is a revised or new expectation, ENEW. Hence, not T=R−E, but 

196.)              TAV =E– E’   

Or solving for ENEW, we arrive at the Law of Emotion Inversion,

197.)              ENEW = E’ + TAV

For the example case developed above, this obtains an ENEW expectation of 

198.)             ENEW = $60 −$20 = $40

Now this revised ENEW=$40 is just the E=ZV=$40 of Eq110 that arises from the correct Z=1/3 probability. So we see that the function of the transition emotions is to correct errors in expectation, and to do it using the ENEW = E’ + TAV variation of the general T=R−E Law of Emotion of our emotional machinery. If this seems too beautifully precise and simple a way for out emotional machinery to act, let’s try another example.

This will be of a fellow who has no confidence at all that he can win at any game, Mr. Unlucky. His sense of probability is hence, Z’=0 and of expectation, E’=Z’V=0. Again we will consider a three game play that realizes R outcomes of the actual average of (0, 0, $120). From the Law of emotion as T’=R−E’, we see that his first two games result in –Z’V disappointments of   

199.)           T’=R−E’=0−Z’V= −Z’V=0

He has no disappointment in the losses because he had absolutely no hopes of a win to begin with. The excitement of winning on the 3rd game, though, is, from R=V=$120, great, as 

200.)         T’=R−E’=$120−0=$120

Note that this is an excitement greater than the T=$80 of Eq116 he would have felt had he supposed correctly a probability of winning of Z=1/3 and an expectation of E=ZV=$40. Now we see that the sum of his T’ transition emotions felt are

201.)          ∑T’ = 0 + 0 + $120 = $120

And the average of these T’ transition emotions per game is 

202.)           ∑T’/3 = T’AV= $120/3 = $60

And from the Law of Emotion Inversion of Eq197 we obtain the correct expectation felt in the next play of the game of

203.)          ENEW = E’ + TAV= 0 + $60 = $60

From the two above examples we see, as fits universal emotional experience, that preponderant disappointment in a goal directed behavior reduces subsequent hopeful expectation or confidence in that behavior and that preponderant excitement from winning increases subsequent confidence. The fit of function to experience is unarguable, quite remarkable, and makes clear that the function of the transition emotions is to keep one’s expectations in line with one’s reality of outcomes. This is reinforced all the more if one repeats the above exercise starting with the correct supposition of E=$40. In this case over the play of three games that realizes outcomes (0, 0, $120), the (correct) transition emotions felt of disappointment and excitement are (−$40, −$40, $80), which sum to 0 as produces no change in expectation from the Law of Emotion Inversion of ENEW = E’ + TAV.

This Law also works in a numerically exact way for the v penalty Lucky Numbers game to show that preponderant relief in repeated play of a penalty game results in subsequent decreased E= −Uv fear of losing; and that preponderant dismay results in a subsequent increase in E= −Uv fearful expectation; as universally fits emotional experience.

While this analysis cannot without neurobiochemical assay say absolutely that the mind uses this exact functional algorithm to keep our expectations in line with the reality of actual experience, the fit of the equations to experience in the broad ways cited above and the exactness of the corrective dynamic they bring about, especially as based on a variation of the Law of Emotion as seen in Eq197 makes clear that the mind’s neurobiochemistry and neurophysiology must operate as controlled by these functions in some way.          

The universality of the fit of the equations for the emotions and of the Laws of Emotion of Eqs108&197 that control the relationships between these basic emotions is very important, for it counters any facile rebuttal of this understanding on the basis of the human emotions not being susceptible to empirical verification. Rather this mathematical explication of the emotions is effectively empirical in being universal.

Our specification of disappointment as the −ZV negation or dashing of ZV hopes, for example, is universal in that all human beings feel disappointment when they fail to achieve a desired goal. Indeed, all of the emotional specifications and dynamic relationships we have considered are universal. Such universal agreement is the fundamental factor in all empirical validation. When ten researchers all read the same data off a laboratory instrument, that data is taken to be empirically valid because all ten agree on what they see. This criterion for empirical validity of universal agreement extends to the emotions of the dice game laid out as what all people would feel if they played it. To deny the validity of the above interlocking, experience reflecting, quantitatively precise emotion specifications and relationships on the basis of an abstract principle of absence of empirical verification is to fail to understand the underlying basis of empirical validity in universality. 

 

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11. Emotions of Partial Success

To further provide observable, empirical proof of the emotion mathematics, we will next consider the emotions that arise from partial success. To that end we alter the Lucky Number V prize awarding game to one where you must roll a lucky number of |2|, |3|, |4|, |10|, |11| or|12| not once but three times to win the prize, one of V=$2700. The excitement gotten from the partial success of rolling the 1st lucky number of the three needed to win the V prize has observable reinforcement in parallel games of chance seen on television. The three rolls of the dice taken to roll three lucky numbers and win the V=$2700 prize may be with three pair of dice rolled simultaneously or with one pair of dice rolled three times in succession. The probability of rolling a |2|, |3|, |4|, |10|, |11| or|12| lucky number on any one roll of dice is from Eq2, Z=1/3. Hence for the 1st roll or with the 1st pair of dice, Z1=Z=1/3; for the 2nd roll or pair of dice, Z2=Z=1/3; and for the 3rd roll or pair of dice, Z3=Z=1/3.

204.)             Z1=Z2=Z3=Z=1/3

And the U uncertainties for each toss are

205.)              U1=(1− Z1)= U2=(1− Z2) =U3=(1− Z3)=(1−Z)=2/3

The probability of rolling a lucky number of |2|, |3|, |4|, |10|, |11| or|12| on all three rolls is the product of the Z1, Z2 and Z3 probabilities, which is given the symbol, z, (lower case z).           

206.)            z = Z1Z2Z3 = Z3 = (1/3)3 = 1/27


And the improbability or uncertainty of making a successful triplet roll successfully is

207.)              u=1–z = 26/27

The expected value of this triplet roll game to win the V=$2700 is in parallel to Eq6, 

208.)              E = zV =V−uv=Z1Z2Z3V = (1/27)($2700) = $100

This is also a measure of the intensity of the player’s pleasant hopes of winning the game. The displeasure of disappointment from failure to make a successful triplet roll is from the T=R−E Law of Emotion of Eq108 with R=0 in parallel to Eq109,

209.)              T=R−E = 0−zV= −zV= −(1/27)($2700)= −$100  

And the pleasure of the excitement or thrill in making the triplet roll, R=V=$2700, is, in parallel to Eq115

210.)              T=R−E = V−zV=(1−z)V= uV= −(−uV)=(26/27)($2700)=$2600  

Next we derive the emotion felt from rolling a lucky number on the 1st throw of three sequential throws on one pair of dice. After a 1st toss that does roll a lucky number, the probability of winning the V=$2700 prize by tossing lucky numbers on the next two rolls increases to 

211.)                Z2Z3 =(1/3)(1/3) = 1/9    

And the hopeful expectation of making the triplet roll after a lucky number is rolled on the 1st toss is, increases from the original E=Z1Z2Z3=$100 to         

212.)               E1 = Z2Z3V = (1/9)($2700) = $300        

Next we want to ask what is realized when the 1st toss is successful. It is not R=V=$2700, for the V prize is not awarded for just getting the 1st lucky number. And it is not R=0, what is realized when the player fails to make the triplet roll and win the V=$2700 prize, for rolling the 1st lucky number successfully quite keeps him on track to roll the next two numbers successfully and win the V=$2700 prize.  Rather what is realized when the 1st roll is of a lucky number is the E1=$300 increased expectation in Eq212. This understanding of the increased E1=$300 expectation as what is realized has us specify E1 as a realization with the R symbol as

213.)               E1=R1=Z2Z3V = $300      

Now we use the Law of Emotion of T= R−E, of Eq108 to obtain the T transition emotion that arises from a successful 1st toss. This specifies the T term in T=R−E as T1; the R term in it as R1=Z2Z3V from Eq213; and the E term in T= R−E as the expectation had prior to the 1st toss being made, E=zV=Z1Z2Z3V of Eq208. And with U1=(1−Z1) from Eq205 we obtain T1 as   

214.)             T1 = R1–E = E1– E= Z2Z3V –Z1Z2Z3V = (1−Z1)Z2Z3V =U1Z2Z3V =(2/3)(1/3)(1/3)($2700) =$200

Now we can ask what kind of emotion this T1=U1Z2Z3V transition emotion is. We answer that by noting that the T=uV excitement of Eq210 from making the triplet toss and winning the V=$2700 prize can be written, given R=V for success, as

215.)               T=uV=uR          

And we also see that we can substitute Z2Z3V=R1=E1 from Eq113 into the T1=U1Z2Z3V term in Eq219 to obtain T1 as   

216.)               T1 =E1−E=U1Z2Z3V =U1E1=U1R1                  

The parallel of this T1=U1R1 to the T=uR excitement of Eq215 identifies T1=U1R1 as the excitement experienced from rolling the 1st lucky number, excitement that is felt even though no money is awarded for rolling just the 1st lucky number. Note that the intensity of this partial success excitement of T1=$200 of Eq214 is much less than the T=$2600 excitement of Eq210 that comes about from making the triplet roll and actually getting the V=$2700 prize.

This development of partial success excitement from the T=R−E Law of Emotion is borne out from observation of situations that go beyond the Lucky Numbers dice game. Excitement from partial success is routinely observed on TV game shows like The Price is Right where a contestant is observed to get visibly excited about entry into the Showcase Showdown at the end of the show, which offers a large prize, by first getting the highest number on the spin-off wheel, which offers no prize in itself. This and other observed examples of the partial success excitement on TV games shows and the like derived as above from the Law of Emotion is a form of empirical validation of the law, even if not a perfectly quantitative validation.    

We can further validate the Law of Emotion with this partial success analysis as follows. We understood that what is realized from getting the 1st lucky number is an increase in expectation from the original E=zV=$100 of Eq108 to E1=Z2Z3V=$300 in Eq212. Now we ask what is realized in rolling the 2nd lucky number after the 1st lucky number is gotten. It is a greater expectation yet of making the full triplet roll and winning the V=$2700 prize,

217.)          R2= E2 =Z3V=(1/3)($2700)=$900

The transition emotion that comes from rolling a 2nd lucky number after having gotten the 1st lucky number is specified as T2 and from the Law of Emotion, T=R−E, with T as T2, R as R2=Z3V from the above and E as the expectation felt after the 1st lucky number was gotten as E1=Z2Z3V in Eq213, is       

218.)        T2 = R2−E1 = E2−E1=Z3V− Z2Z3V =(1−Z2)Z3V = U2Z3V = (2/3)(1/3)($2700) = $600

Expressing T2 = U2Z3V via Z3V=R2 of Eq217 as T2=U2R2 makes it clear from its parallel form to the excitement of T=uR of Eq215 that T2=U2R2 is the excitement felt when the 2nd lucky number is guessed after the 1st lucky number has been rolled. 

And we can also use the Law of Emotion, T=R−E, of Eq108 to derive the excitement felt in getting the 3rd lucky number after getting the first two, which wins the V=$2700 prize. What is realized in that case is the R=V=$2700 prize. Given the expectation that precedes getting the 3rd lucky number of E2=Z3V from Eq217, the Law of Emotion, T=R−E, obtains a T3 transition emotion of  

219.)      T3 = R−E2 = V –Z3V = (1−Z3)V = U3V = (2/3)($2700) = $1800

Now expressing T3 =U3V from R=V as T3=U3R and noting its parallel form to T=uR excitement of Eq215 identifies T3 = U3R as the excitement of rolling the 3nd lucky number after the first two have already been rolled as obtains the V=$2700 prize. Note that the intensity of the T3=$1800 excitement from rolling the 3rd lucky number and getting the V=$2700 prize is significantly more pleasurable than the T1=$200 and T2=$600 excitements for the antecedent partial successes.

Such significantly greater excitement in actually winning the prize than from achieving prefatory partial successes is what is observed in game shows like “The Price is Right” where actually winning the Showcase Showdown has the winner jumping up and down and running around screaming and showing more excitement than the excitement felt and shown from the prefatory partial success of getting into the Showcase Showdown by getting the highest number on the spinning wheel. Again this fit of observed excitement in the approximate relative amounts suggested in the above analysis with the Law of Emotion constitutes an empirical, if not perfectly quantitative, validation of the Law of Emotion.      

Also note that the Law of Emotion, T=R−E, of Eq108 is further validated from the three partial excitements, T1, T2 and T3 of Eqs214,218&219 summing to the T=uV=$2600 excitement of Eq210 that arises from making the triplet roll in one fell swoop as you might from throwing three pair of dice simultaneously.      

220.)              T1 + T2 + T3 = $200 + $600 + $1800 = $2600 = T = uV             

The internal consistency in this equivalence is another validation of the T=R–E Law of emotion. It is also revealing and further validating of the Law of Emotion to calculate what happens when you roll the first two lucky numbers successfully but then miss on the 3rd roll and fail to get the V=$2700 prize, R=0. To evaluate the T3 transition emotion that arises from that we simply use the T3=R−E2 form of the Law of Emotion in Eq119 that applies after the first two lucky numbers are gotten, but with the R realized emotion as R=0 from failure to obtain the V=$2700 prize. 

221.)            T3 = R−E2 = 0 – Z3V = – Z3V = −(1/3)($2700)= −$900

This T­3 = −Z3V= −$900 is the measure of disappointment felt in failing to make the triplet roll after getting the first two lucky numbers and after experiencing the prefatory partial success excitements in getting them. Note that this T3= −Z3V= −$900 disappointment is significantly greater than the T= −zV= −$100 disappointment of Eq209 that arises from failure to roll the lucky numbers in one fell swoop. And note that the −$800 increase relative to the T= −$100 disappointment in the T3= −$900 disappointment felt after partial success is exactly equal to T1+T2=$200+$600=$800 sum of the two partial success excitements of Eqs114&119. This understands the additional −$800 displeasure of disappointment from failure in the 3rd roll to rescind or negate the prefatory $800 pleasure of excitement that was followed by ultimate failure. This fits the universal emotional experience of an increased let down or disappointment when initial partial success is not followed up by ultimate success in achieving a goal as the letdown felt when one counts their chickens before they hatch and they then do not hatch.   

The sequential scenarios that end in success in Eq220 and in ultimate failure in Eq221 universally fit emotional experience and as such are a convincing validation of the Law of Emotion, T=R−E, of Eq108. The linear sums and differences of the transition emotions in these two instances also importantly show that understanding our emotions to reinforce each other positively and negatively in a linear fashion via simple addition and subtraction of the emotion intensity values provides an excellent modeling of our emotional processes regardless of the factor of marginality that affects the linear aspects of emotional intensity.    

In a slight digression, everybody knows that we don’t just feel excitement from winning in a game as T=UV but also in anticipation of a win. The above analysis can be used to derive this sense of prefatory excitement felt by people in anticipation of success. To do that consider the emotional state of a person to whom the opportunity to play this triplet V=$2700 prize game is denied or not offered. For that person the expectation of winning is zero, specified as E0=0. It is only when the game is offered and available to play that there is any expectation of winning, namely or E=zV=$100 of Eq208. Much as we saw that sequential increases in expectation produced a T transition emotion of excitement in Eqs214,218&219, so should we also see that this increase in expectation from E0=0 to E=zV=$100 from being offered the game produces from the T=R−E Law of emotion as it did for other increases in expectation a feeling of excitement. Specifically, with T as T0 and E as E0=0, the original expectation prior to the game being offered, and R=E=R0 as the expectation realized once the game is offered, the T=R−E Law of emotion generates the excitement felt as  

222.)            T0=E−E0=zV−0=zV

As E=R0=zV and as the probability of success prior to game availability is Z=0 and of failure, U=1, then E=R0=zV can also be understood as

223.)         T0= E=R0=zV=UzV=UR0

Again by parallel to T=uR excitement of Eq215, T0=UR0 is excitement, the excitement of getting to play the game to begin with. Note that its value is equal to the expectation or the player’s hopes of winning. Next we see in a successful game that expectation increases as each lucky number in the triplet is tossed. As they are, excitement is also felt as we saw in Eqs214,218&219. The difference between the increasing expectations and the excitement that accompanies their experience is that the excitement is cumulative, it adds to prior excitement or builds with progressive success. This very much fits excitement building in a sequential composite effort to achieve a goal. And it explains the origin of the prefatory excitement that, again, is a universal in emotional experience. All of the transitional emotions, whether excitement, disappointment, relief or dismay, can be shown to have this sense of existence prefatory to the final R outcome of success or failure and in the same entirely exact mathematical way.  

We next consider the transition emotions of partial success in the v penalty Lucky Numbers game. Consider a game one is forced to play that exacts a penalty of v=$2700 unless the player rolls three of the lucky numbers of |2|, |3|, |4|, |10|, |11| or|12|. In parallel to the E= −Uv expectation of Eq120 and with u=26/27 from Eq207 as the improbability of rolling three lucky numbers, the fearful expectation of incurring the v=$2700 penalty is

224.)             E= −uv= −(1−Z1Z2Z3)v= −(26/27)($2700)= −$2600 

The Law of Emotion, T=R−E, of Eq108 generates a uv emotion of relief from avoiding the v penalty, R=0, when one successfully rolls a lucky number on three pair of dice simultaneously as   

225.)           T=R−E=0−(−uv)=uv=$2600

With the game played with three sequential rolls on one pair of dice, the increased expectation of avoiding the v=$2700 penalty after rolling a lucky number on the 1st toss of the dice, E­1, understood as what is realized from the toss, R1, is, with the improbability of escaping the penalty then as 1−Z2Z3    

226.)              E1=R1= −(1−Z2Z3)v= −(1−(1/9))$2700= −(8/9)($2700)= −$2400       

Hence the transition emotion, T1, is, via the T=R−E Law of Emotion expressed as T1=R1−E, and with R1=E1 from the above 

227.)              T1=R1−E= E1−E=−(1−Z2Z3)v−[−(1−Z1Z2Z3)]=(1−Z1)Z2Z3v=U1Z2Z3v=$200

Now recall the parallel forms of the T=UV excitement of Eq115 and the T=Uv relief of Eq121. This understands T1=U1Z2Z3v, in parallel to the partial excitement of U1Z2Z3V of Eq214 for the V prize game, to be the partial relief felt upon rolling the 1st lucky number in the v penalty game. The rest of the analysis for the triplet v penalty game then perfectly parallels that for the triplet V prize game except that the partial emotions felt in sequentially rolling the 1st, 2nd and 3rd lucky numbers are those of relief in escaping a v=$2700 loss of money rather than excitement gotten from a V=$2700 gain of money. The universal fit of this v penalty game analysis to universal emotional experience with sequential behaviors whose goal is escape from a penalty validates the law. And further validating the Law of Emotion and its underlying mathematics is its next deriving the Law of Supply and Demand.    

illustration of two red dice Stock Photo - 13443929

12. The Law of Supply and Demand

The Law of Supply and Demand of Economics 101 states that the price of a commodity is an increasing function of the demand for it and a decreasing function of the supply of it. An alternative expression of the Law of Supply and Demand determines the price as an increasing function of the demand for the commodity and of its scarcity as the inverse of its supply or availability.

Now let’s return to the triplet lucky number V=$2700 prize game with the 1st lucky number in the triplet sequence understood as a commodity that can be purchased. This assumes the existence of an agent who runs the dice game and pays off the V prize money and who will give this commodity of the 1st lucky number to the player for a price. Question: what would be the fair price of the 1st lucky number?

As having the 1st lucky number changes the probability of winning the V=$2700 from z=Z1Z­2Z3=1/27 in Eq106 to Z2Z3=1/9 in Eq211, it is certainly a valuable commodity for the player. But exactly what is its value, what is the fair price of it? It is the difference between the E1=$300 average payoff of Eq213 expected when the 1st lucky number has been gotten and the E=$100 average payoff of Eq108 expected prior to any of the three lucky numbers being attained. Or given the symbol, W1, the fair price for the 1st lucky number is

228.)               W1 = E1−E

This W1 fair price is a function of a number of variables associated with the E1−E term in Eqs214&216.   

229.)                W1 = E1−E = Z2Z3V – zV = U1Z2Z3V = T1 = U1E1 =$200

This W1=$200 is the fair price for the 1st lucky number in the latter increasing the average payoff from E=$100 to E1=$300. From the perspective of economic optimization the player as buyer would want to pay as little as possible for the 1st lucky number and the agent as seller would want to charge as much as possible for it. But W1=$200 is the fair price of the 1st lucky number from that price paid by the player effectively maintaining the initial average payoff of E=$100 for the player.

The fair price expressed in Eq229 as W1=U1E1 is a primitive form of the Law of Supply and Demand given in terms of the emotions that people feel that control the price they’ll pay for a commodity. W1=U1E1 is an increasing function of the scarcity of the 1st lucky number as the uncertainty in rolling it on the dice, U1=2/3, and is an increasing function of the demand for the 1st lucky number as the E1=Z2Z3V=$300 average payoff it provides with its value as such understood as the underlying determinant of the demand for it. This derivation from the emotion mathematics of the Law of Supply and Demand, a firm empirical law of economics universally accepted as correct, is a powerful validation of it. 

There are a number of important nuances in this formulation of the Law of Supply and Demand. Note the equivalence in Eq229 of the W1=$200 fair price for the 1st lucky number and the T1=W1=$200 pleasurable excitement gotten from rolling the 1st lucky number on the dice. This equivalence of T1 excitement and W1 price suggests that the price paid for a commodity is a measure of the pleasurable excitement the commodity generates for the buyer. This fits economic reality quite well as seen from TV commercials for automobiles and vacations and foods that hawk these products by depicting them as exciting.

And, further, the value of the 1st lucky number can be calculated not just in terms of the W1 amount of money one would spend for it but also in terms of the time spent in acquiring the money needed to purchase the 1st lucky number. Given that the time taken to obtain money, risk based investment aside, is directly proportional to the money earned as in a dollars per hour wage, W1 is understandable as a measure of the amount of time spent to get the 1st lucky number. This has the W1=U1E1=T1 Law of Supply and Demand showing that people spend their time to obtain commodities that pleasurably excite them, whether as the time spent working to get the money to spend on the commodity or as time spent directly to obtain pleasurable excitement like watching the Super Bowl for some. 

We can also derive a parallel primitive Law of Supply and Demand from the v penalty game that requires the toss of three lucky numbers to avoid the penalty. The W1 fair price of the 1st lucky number is again W1=E1−E, but with E1−E from Eq227 in the v penalty as  

230.)                W1 = E1−E = U1Z2Z3v = T1 = $200

This form of the primitive Law of Supply and demand tells us that people also spend their money for commodities that provide T1=U1Z2Z3v=W1 relief. This is in addition to commodities that provide T1=U1Z2Z3V=W1 excitement as seen in Eq229. The two forms of the Law of Supply and Demand of Eqs229&230 provide a strong empirical validation of the Law of Emotion of Eq108 that underpin them from the observed fact that people do spend their money and their time to obtain commodities, goods and services, that provide relief and excitement. This is readily seen in the complete spectrum of TV ads, all of whose products are pitched in ads as providing relief, as with insurance and antacids and other medicines, or excitement, as with exciting cars, foods and vacations.  

Next we want to express the primitive Law of Supply and Demand in as simple a form as possible. We do this as preface to our deriving in the next section simple functions for our visceral emotions like the pleasures of feeling warm and of eating food. In Eq229 we saw the equivalence of the W1 fair price with T1 partial success excitement, W1=T1. This implies that the simplest form of T excitement we have seen in Eq115 as T=UV for the one number Lucky Number game should also be a measure of the fair price, W, one would pay for this one lucky number.

231.)              W=T=UV

Now in recalling Eq116 we see the value of the T excitement in getting the V=$120 prize to be T=$80, which allows us to express the fair price of being given the lucky number that gets the V=$120 prize as

232.)              W=T=UV= $80

At first this may seem odd. One may ask what sense there is in paying $80 to win the V=$120 prize. The point is rather that W=$80 is the fair price that you would pay. Consider what happens if you do this for three games, with the total price paid being 3($80)=$240. This wins the player $120 in each game for a total of 3($120)=$360 for the three games. The net winnings for the three games are, thus, $360−$240=$120. And this is what is won on average in three games played strictly from the throw of the dice with no lucky number purchased. That is V=$120 is won one time out of three. Hence W=T=$80 is, indeed, the fair price of the lucky number. And W=T=UV is a most simple form of the Law of Supply and Demand with U as the uncertainty in rolling the lucky number as a measure of its scarcity and V as the cash value of the prize as a measure of the demand for it.

Next we want to write this most simple form of the Law of Supply and Demand with a slight algebraic manipulation as

233.)                W= UV= −(−UV) 

This tells us that people spend W dollars or spend equivalent time both to obtain UV excitement and to negate or eliminate –UV anxiety as very much fits universal emotional experience. And without our going through the details of its derivation or explanation we can write an equivalent simple Law of Supply and Demand pricing law based on T=uV relief of Eq121 with W=T assumed from earlier considerations as

234.)                W= Uv= −(−Uv)    

This tells us that people also spend W dollars or spend equivalent time both to obtain Uv relief and to negate or eliminate their –Uv fears, again as very much fits universal emotional experience. To sum up for emphasis, this mathematics derives people spending their money and time, being motivated to do that, both in the pursuit of the pleasures of excitement and relief and in the avoidance of the displeasures of anxiousness or anxiety and fear. Understanding behavior to be motivated by the pursuit of pleasure and the avoidance of displeasure is the essence of hedonism. It should be made clear that this sense of hedonism is not an encouragement for people to seek pleasure and avoid displeasure, but rather a conclusion drawn from the foregoing mathematical analysis that people just do behave so as to achieve pleasure and avoid displeasure as the essence of human nature. To generalize hedonism you need, of course, to also take into consideration the visceral emotions that motivate our behavior at the most basic levels like hunger and feeling cold and the pleasures of eating and warmth along with the pleasures and displeasures of social and sexual behavior, which we will begin explaining mathematically in the next section. 

illustration of two red dice Stock Photo - 13443929

13. Survival Emotions

Many of our most basic emotions are associated with surviving or staying alive. We derive the pleasant and unpleasant emotions that drive survival behavior from the primitive Law of Supply and Demand in the form of Eq234 of W=Uv= −(−Uv). We do that by applying it not to avoiding the loss of v dollars but to avoiding the loss of one’s v*=1 life. That is, the penalty for failing at a survival behavior like getting food to eat or air to breathe is the loss of one’s own v*=1 life rather than the loss of v dollars. The other terms in W=Uv= −(−Uv) are also asterisked in using it to explain survival behavior to show that they are all associated with avoiding the loss of one’s V*=1 life rather than the loss of v dollars. 

235.)                  W*=T*= U*v*= −(−U*v*)

It is best to introduce this function with specific survival behaviors and save the generalizations of what these variables mean until after we do that. Let’s start with the survival behavior of breathing air whose emotional properties are cut and dried. Consider Eq235 for a situation where air to breathe is lacking whether from a person being underwater and drowning or having a critical asthmatic attack or having a pillow placed forcibly over his face or being water boarded. From Eq235 understood as the Law of Supply and Demand, U* is a measure of the scarcity of air as the uncertainty or improbability of getting air. We can assign a very high value to it in this case of suffocation of, say, U*=.999, also interpretable as the high probability of losing one’s v*=1 life under these circumstances. 

The T*=U*v* transition emotion in Eq235 experienced when a behavior is done to obtain air under this U*=.999 circumstance is, in parallel to T=Uv relief of Eq21, the very pleasurable relief felt in getting air to breathe when one is suffocating. While not all have had the experience of suffocation followed by escape those who have will attest to the great intensity of the pleasurable relief felt. One measure of this great relief is from Eq235 evaluated for the v*=1 life saved and its prior U*=.999 scarcity of air or uncertainty in getting it as  

236.)              T*=U*v*=(.999)(1) =.999  

This .999 fractional measure of relief very close to unity, 1 or 100%, is a good way of indicating an intensely pleasurable level of relief. We can also specify the relief in dollar terms as we did in the Lucky Number games by putting a cash value or price on one’s v*=1 life, the one that one doesn’t want to lose. One measure might be if one was alone in the world, all the money one had, let’s say v*=$100,000. That calculates a cash value for the T*=U*v* relief of

237.)              T*=W*= –(–U*v*)=U*v*=(.999)$100,000=$99,900

This effectively says that one would pay a price of W*=$99,900 or pretty much all of one’s money to escape terminal suffocation, which is true of all with the above assumption of nobody else to worry except the pathological. The –U*v* term in Eqs235&237 that is negated or resolved by the behavior of escaping suffocation to T*= –(–U*v*)=U*v* relief is a measure of the fear instinctively felt upon suffocation, parallel to the E= −Uv fear in Eq120 of losing money in the Lucky Numbers v penalty game. 

The W*=T* equivalence of Eq235 also makes clear that the W*=T*=U*v function that governs the emotional dynamic operates as the Law of Supply and Demand with the demand for some commodity, be it goods or service, object or behavior, that provides escape from suffocation and preservation of one’s v*=1 life measured by the instinctively great value a person places on his or her life; and with the supply of what is needed to preserve that life measured inversely by the scarcity of air to breathe or uncertainty in getting it as U*.    

The fact that we can so simply derive the emotions of breathing under suffocation, the panic fear it causes and the great relief experienced in escape from the suffocation, is a remarkable validation of Eq235, W*=T*­=U*v*= −(− U*v*), and of its derivation from the cash based Lucky Numbers game. It gives confidence that this mathematical understanding of man’s emotional machinery can impact the central problem for mankind of unhappiness from enslavement and the violence that emanates from it that stimulates war and can put the world’s nations into terminal nuclear conflict. And it should give confidence also in the remedy to these problems this mathematical analysis provides of our moving collectively towards A World with No Weapons.

The W* = T*­=U*v*= −(− U*v*) Law of Supply and Demand of Eq235 also holds in the normal situation for people where there is no scarcity of air, no uncertainty in the body’s cells getting oxygen, no probability of losing one’s v*=1 life from lack of oxygen, U*=0. This is made clear by inserting U*=0 into Eq235 to obtain

238.)              W*=T*=U*v*= −(−U*v*)=0

This expression of Eq235 quite perfectly fits normal breathing when there is plenty of air to breath in indicating no unpleasant fearful feeling, −U*v*=0, no noticeable relief in breathing, T*=U*v*=0, and no money a person is willing to pay for air, price W*=$0. The mathematically derived conclusions for U*=.999 suffocation and U*=0 normal breathing universally fit observable human experience.  

And so does the intermediate situation with air in short supply but not critically scarce, as say, U*=.2, as might apply to COPD (Chronic Obstructive Pulmonary Disease.) In this U*=.2 case, the –U*v* displeasure is felt as pulmonary distress but less horribly unpleasant than the panic fear of U*=.999 suffocation. Also significant is the T*= −(−U*v*)=U*v* relief felt when bottled oxygen is supplied to a COPD sufferer. And we also see in this not uncommon ailment for older people that they are willing to pay a W*=U*v* price for relief, a lot if necessary though not every last penny a person has as a person would pay if their life was critically threatened as it is at the U*=.999 level of suffocation.

Temperature regulation as avoidance of the extremes of cold and heat is, like breathing, centrally important for avoiding the loss of one’s v*=1 life. Temperature below 68o puts the heat needed by the body to function well in short supply, makes it scarce with the uncertainty of the body getting the heat needed specifiable as U* >0 in Eq235 whatever the specific value of it we may choose to indicate that scarcity. Generally speaking the colder the skin temperature is, the greater is the U* scarcity of heat and from W*=T*=U*v*= −(−U*v*) of Eq235, the greater is the –U*v* unpleasant feeling of cold.

The –U*v* unpleasant sensation of cold is not quite the feeling of fear as was the –Uv term in Eq120 felt as fear of losing money, but it has the same effect as fear in making one want to do something to avoid the cold as though you did fear it. The range of the displeasure of cold extends to truly freezing cold we would represent as a U*=.999 scarcity of heat, which for those who have felt it approaches the feeling of pain.

Negating the –U*v* displeasure of cold by warming up provides via Eq235 the T*= −(–U*v*)=U*v* relief of warmth and its pleasure that is universally for all people greater in intensity as U*v* the greater is the displeasure of the −U*v* antecedent cold. As further validates this mathematical understanding of temperature regulation, note that a person is quite willing to pay a W*=T*=U*v*= −(−U*v*) price from Eq235 to alleviate the −U*v* displeasure of cold and obtain the U*v* pleasure of warmth, the amount of money willing to be paid being proportional to the U* scarcity of heat in the –U*v* felt as antecedent cold.

And by understanding the W* money spent to get warm when one is cold to be directly proportional to the time spent to make that money, Eq235 also tells us as fits universal experience that a person is willing to spend time to get warm directly as by cutting wood to burn in a fireplace and/or by making clothes to put on to stay warm.

It is also universal experience that when a person is continuously above the optimal 68o temperature of feeling cold to begin with where there is U*=0 no scarcity of heat, the pleasant feeling of warmth is not felt as is mathematically specified by –U*v*=0 (no unpleasant feeling of cold) generating T*= U*v*=0, (no pleasant feeling of warmth.)    

We will also show shortly in other familiar survival behaviors, unpleasant feelings of excessive heat, of hunger from lack of food and of pain from trauma and disease, all of whose pathologies can cause the loss of one’s v*=1 life, how the −U*v* term of Eq235 determines the displeasures of these survival threats and the U*v*term the pleasures of their resolution by appropriate behavior.  But before we do that we want to show how the breathing air and obtaining warmth dynamics considered in detail above are negative feedback control or homeostatic systems. This will take a paragraph or two to do, but it is well worth spending the time on it because it will show how firmly our analysis fits in with existing accepted science.

A typical mechanical negative feedback control system is found in most homes in states that feel the cold of winter, a thermostatic controlled heating system. The idea is quite simple. The thermometer part of the thermostat measures the room temperature, θ, (theta). You set the temperature you want on the thermostat to a set point, θS. The difference between the two is the error, Ԑ, (capital epsilon),

239.)          Ԑ = (θS −θ)         

The existence of an error turns on the furnace, which heats the room up until the room temperature, θ, is equal to the set point, θS, the temperature you set on the thermostat, at which point the ERROR=0, and the furnace shuts off. That is the essence of negative feedback control, the elimination of set point error by appropriate automatic mechanisms.

That’s how the air and heat emotion regulated systems operate. The set point, where the system is set to go, is to have a U*=0 possibility of losing the v*=1 life. And where the system is when the situation is threatening is at a −U*v* value where there is a U*>0 probability of your losing your v*=1 life from lack of air or lack of heat. The error function in either case is

240.)           Ԑ = (0 –(−U*v*) )      

The system is turned on whenever the Ԑ error is not zero. It turns on in our survival situations when the amount of air or heat available is less than adequate and does it by neurologically effecting the feeling of −U*v* suffocation fear or of cold. This motivates the person to act so as to alleviate the situation of suffocation or cold, which brings on the respective pleasure of relief from suffocation or warmth, which shuts off the system when there is no U* probability of the loss of one’s v*=1 life, which takes the error to zero.

Hence the system which operates on the Law of Supply and Demand of Eq238, W*=T*= U*v*= −(−U*v*), which derives ultimately from the T=R−E Law of Emotion as a special form of it, is also a simple negative feedback control system. And as one that operates on the general notion of homeostasis in biological systems as part of the rubric of accepted biological science, both the Law of Emotion and of the primitive Law of Supply and Demand it derives are seen to be also within the rubric of accepted biological science in their confluence with the workings of negative feedback control in biological systems. The three survival behavior systems we’ll consider next also in operating on the Eq235 Law of Supply and Demand are also negative feedback control or homeostatic systems. 

Temperature regulation also demands that body surface temperature be less than about 82oF. Above that we may talk about a “scarcity of coolness” the body needs to operate optimally, hence, U*>0, with the −U*v*>0 displeasure in Eq135 manifest as feeling hot and with the pleasurable alleviation or negation of it by appropriate cooling felt as pleasant relief from the heat, T*= −(−U*v*)=U*v*>0. And it is also clear from Eq235 as fits universal experience that a person is willing to pay for air conditioning to stay cool, W*=T*=U*v*>0. The lack of a pleasant feeling of relief from the heat when one is continuously below 82oF to begin with is also specified by Eq235 to fit universal experience. 

Obtaining food to keep an individual from losing his or her v*=1 life from lack of it also follows Eq235, but not in as simple and direct manner as with breathing and temperature regulation because of the complicating factor of the intermediate storage of the food in various organs of the body, short term in the stomach and long term in fat and the liver. We dodge that problem by minimizing the effect of its storage on the emotions involved for we are only interested in understanding it in the broadest way that it generates the displeasure of lacking food as hunger and the pleasures of eating primarily as the delicious taste of food.   

That said, we consider that when one hasn’t eaten for some time, the glucose or blood sugar in the blood vessels of the body becomes in short supply or scarce for the body’s cells, U*>0. Then the emotion of feeling hungry arises as −U*v*>0 of Eq235 or when U*>0 is small as the disquiet of appetite. This −U*v* feeling of being hungry, quite unpleasant as hunger in high intensity, is negated or relieved to the T*= −(−U*v*)=U*v* pleasure of eating that includes both the deliciousness of food taste and the pleasant relief felt from the filling of the stomach. 

The T*= −(−U*v*)= U*v* equivalence in Eq235 tells us that the intensity of the pleasure of eating, T*=U*v*, is greater, the greater the antecedent −U*v* hunger. This is readily validated by those who have had genuine hunger and experienced marked pleasure in eating to relieve the hunger even with eating just a piece of stale bread or cracker, which tastes very delicious under that circumstance. Almost all of us have experienced the fact that feeling hungry before eating makes the food taste better or be more pleasant as fits Eq235. And Eq235 also tells us that people are willing to spend W* dollars to obtain food and also to spend time for that end whether time to earn the money needed to purchase food or, as our primitive hunter-gatherer ancestors did by gathering plants and hunting animals, time spent directly to get food. 

When blood sugar levels are high and the stomach full, U*=0, that is, there is no scarcity of food chemicals for the body’s cells and under normal circumstances, hence, no feeling to eat, −U*v*=0. Under these circumstances, eating food pretty much lacks the T*=U*v*>0 pleasure produced when one does have a −U*v*>0 appetite. In such a state, absent the abnormal, constantly present hunger that is pathologically responsible for modern man’s epidemic obesity, there is neither a pleasure nor displeasure motivation to eat.

Lastly as a survival behavior we want to consider physical trauma like a fracture that causes pain. Pain is signified as –U*v* with U*>0 the uncertainty or scarcity or lack of a healthy mechanical condition that threatens losing one’s v*=1 life. In this way pain is in obvious parallel to the scarcity of air, warmth or food, all unhealthy circumstances that threaten the loss of one’s v*=1 life,. Behavior that eliminates or negates the −U*v* pain as with not putting mechanical pressure on the fracture as −(−U*v*)=U*v*>0 produces U*v*>0 relief from the pain, which is felt as pleasant in proportion to the antecedent pain that pampering the fracture relieves.      

Now let us make it clear that the unpleasant emotions of suffocation, hunger, cold, excessive heat and physical trauma and the pleasant emotions of their alleviation, all of which derive from W*=T*= U*v*= −(−U*v*) of Eq235, are different from the emotions of behaviors utilized to get the commodities that satisfy these survival needs when they are not immediately available.  

When one is hungry, for example, eating may proceed in a very direct and immediate fashion when food is readily available, as when a roast beef sandwich is there in the refrigerator to satisfy the −U*v* hunger of a starving person who just woke up after being passed out for two days from a drinking binge. But one must have food first before one can eat it. Explaining the relationship between the emotions for getting food to those for eating it is best done with an example of food procurement that is mathematically well-defined like playing a Lucky Number dice game where food is the prize for the rolling of a lucky number by a hungry player.     

Eating this food prize alleviates a hunger of –U*v* to produce the eating pleasure of T*= −(−U*v*)=U*v*. This behavior to get food has in the standard game a Z=1/3 probability of success and an improbability of U=(1−Z)=2/3. One’s expectations in this game are not via E=ZV the prize of V dollars but rather of getting the W*=T*=U*v* pleasure of eating the food. Because this T* pleasant emotion gotten has an explicit dollar value from W*=T*=W*v* of Eq235 we can substitute W* for the V dollar term in E=ZV to obtain our hopes of pleasure as

241.)              E=ZW*=ZT*=ZU*v*=(1−U)U*v*=U*v*−UU*v*

This E=ZU*v*=U*v*−UU*v*expectation or hopes of obtaining T*=U*v* food pleasure nominally worth W*=T* dollars to probability Z stands in comparison to E=ZV=V−UV of Eq107 as the hopes of getting V dollars. In the latter, the pleasurable desire is for V dollars while in the former of Eq241 the desire is for U*v* food pleasure. Then much as the pleasant desire for V dollars is reduced by the –UV meaningful uncertainty about winning the money to one’s uncertainty tempered hopes of E=ZV, so is the U*v* pleasant thought of eating the food reduced by −UU*v* meaningful uncertainty in getting the food to the uncertainty tempered expectation of ZU*v*. This latter term is the intensity of pleasure felt in one’s hopes of satisfying one’s hunger by a particular behavior of getting food, here by playing the dice game to get food to eat. And this is exactly how the mind works in seeking pleasure by a particular behavior characterized by some Z probability of success in achieving that pleasure.

We can also develop a T transition emotion felt when one rolls a lucky number and gets the food. From the Eq8, Law of Emotion, T=R−E, what is realized following a successful throw of the dice is the R=U*v* pleasure of eating the food gotten as the prize. But also because there is U uncertainty in getting the food, there is an additional pleasure in the thrill or excitement in getting the food to eat,  

242.)              T=R−E= U*v*− (U*v*−UU*v*) =UU*v*   

When there is no uncertainty in getting the food as in reaching into the refrigerator to pull out a ham sandwich, there is no excitement involved in the act of getting the food to eat. Contrast this to a hunt for food for people who have no immediate food store or to a search to gather berries to eat under the same circumstances of otherwise having nothing to eat. Then upon making the kill for meat or the finding of berry bush, there is great excitement.

In that sense UU* in UU*v in the above is a compound improbability, the U* improbability of your body’s cells getting what they need in food chemicals because your blood stream is low on blood sugar and the U uncertainty or improbability of your getting the food to eat in order to replenish your blood stream with the blood sugar it needs to provide the body’s cellular needs.

The T=UU*v* excitement in getting the food, hence, is a function of the U=2/3 uncertainty in getting the food and of the T*=U*v* pleasure in eating the food, itself a function of the –U*v* antecedent hunger via T*=U*v*= −(−U*v*) of Eq235. One gets both the R=U*V* pleasure of eating the food and the T=UU*v* thrill of obtaining it under uncertainty, which is what our hunter gatherer ancestors surely felt when searching for vegetative food or hunting for animal food with uncertainty, U. One can picture such a group having an exciting feast following a successful hunt or search. In contrast if there is no U uncertainty in getting food, from T=UU*v*=0, there is no excitement or thrill in getting the food despite the R=U*v* pleasure in eating it, much as when one needs but to open the door of one’s refrigerator to grab a ham sandwich or an apple to eat if one is hungry.

Note also in the food prize dice game the disappointment that is felt, assuming the game can be played only one time, when the lucky number is not rolled and food is not obtained under a condition of –U*v* hunger. In that case with E*=ZU*v* and R=0 for no prize realized, from the Law of Emotion, T=R−E,  

243.)             T=R−E*= 0−ZU*v*= −ZU*v*

This tells us that beyond the factor of one’s Z confidence in getting the food, the more –U*v* hungry you are and the more U*v* pleasure you anticipated in getting the food, the greater is the T= –ZU*v* disappointment in failing to get the food.

Now we have developed a good mathematical understanding of the emotions associated with our basic survival behaviors. The nuances and ramifications of this analysis are manifold and we will consider many of them in subsequent sections. We also want to develop the emotions for two other centrally important classes of human activity, violent behavior and sexual behavior. A mathematically clear explanation of the emotions of violence and sex based on Eq235 and similar Law of Supply and Demand functions can be very controversial, though, because sex and violence are heavily laden with morality injunction, which itself provides a group of emotions that must also be independently explained. Hence, we need to be very careful in approaching those topics and will begin prior to applying the Law of Supply and Demand to them by first considering natural selection in evolution and how it affects our understanding of violence and sex.   

 

 

illustration of two red dice Stock Photo - 13443929

14. Natural Selection

 

We take great pains to explain natural selection mathematically because of the controversial issue that evolution has become in America. The mathematics moves up to a slightly higher level, but we’ll do our best to keep it as simple as possible. We will start with a formula from the banking industry for interest in a savings account that nobody sane disagrees with. It is found in all junior high math texts.
 

244.)               

 

The x0 term is the initial deposit in the savings account; x is the amount of money in the account after t years assuming no more money was deposited; and g is the annual interest or growth rate of the money. If in a savings account that has an annual interest rate of g=5%=.05 you start with x0=$100 and keep that money in the bank for t=2 years, the initial x0=$100 will grow according to

 

245.)                    

 

You could also get a savings account with a quarterly or daily compounding of the interest. This modifies the interest formula in Eq245 a touch to

 

246.)             

 

The m term is the number of times a year the interest is compounded or paid. So with the same initial deposit of x0=$100 and same interest rate of g=5%=.05, if the savings account had quarterly interest paid, which is m=4 times a year, the money in the account would grow in t=2 years to

 

247.)                   

 

And if a savings account had interest compounded daily, or m=365 times a year, the $100 you originally started the account with would grow over t=2 years to 

 

248.)             

 

An alternative formula for the daily compounding case is

 

249.)              

 

The letter, e, is Euler’s number, e=2.7183. So with x0=$100, g=5%=.05 and t=2 years we calculate from it the x=$110.52 for daily compounding we saw in Eq248 but as 

  

250.)             

 

Eq249 is the formula for exponential growth, which means the growth of something at a rate that depends on how many of that something there already are. This fits the growth of money in a daily compounded savings account, which depends on how much money you already have in the account. Often, indeed usually, the formula for exponential growth is written in a different form than Eq249, in differential form as

 

251.)                

 

The dx/dt symbol is the rate of growth of the money and this differential equation tells us that it depends on the x amount of money in the account and the g annual interest or growth rate. Eqs249&250 apply not only to the exponential growth of money in a daily compounded savings account but also to the exponential growth of a population of x organisms that also depend on the number of organisms that already exist and which generate additional organisms by reproducing themselves. For biological exponential growth, the annual growth rate, g, assumed like the annual interest rate for money to be constant as a reasonable simplifying assumption, depends not just on the birth rate of new organisms, b, but also on the death rate of existing organisms, d.

 

252.)               g = b − d

 

Also this formula only applies when, like dollars in a daily compounded savings account that have just come into existence immediately “giving birth” to more new dollars on the same day, biological organisms just produced are themselves able to reproduce more newborn organisms the same day they come into existence. This happens with bacteria and other single celled organisms, but not with multicellular organisms such as man unless the “birth” of an organism is taken to be the coming into existence of a sexually mature organism, puberty or adolescence for humans, which itself, like a bacterium, is immediately able to biologically reproduce, whatever the cultural taboos against it. That important consideration fits the exponential growth formula of Eqs249&251, to be kept in mind for the later discussion of the emotions experienced by the parents of human offspring.

 

For now we want to get back to the basics of population growth in order to understand the nuts and bolts of natural selection. Pure exponential growth has a population grow without limit. In Eq149, as t, time, increases generation after generation, the x population size just grows and grows and never stops growing. In a population that starts with x0=10 organisms, the population grows by g=1.1 organisms per existing organism per year, Eq249 tells us that after t=10 years, there will be x=598,785 organisms in the population and in another 10 years, upwards of 358 billion. 

 

In reality, though, there is a limit to how many organisms a particular environment or niche can sustain called the carrying capacity of the niche, K. Back in the 19th Century a Belgian mathematician, named Pierre Verhulst, came out with a modification of exponential growth in Eq251 that takes the reality of limited growth into account. It is, with K as the carrying capacity,

 

253.)           

 

 This Verhulst equation or logistic equation spells out growth over time in differential form is expressed as a time equation as 

 

254.)              

 

Eq253 and Eq254 translate into each other much as do Eq249 and Eq251, the details of the operation omitted. Now let’s consider the growth of the same population of x0=10 organisms with a g=1.1 organisms per existing organism growth rate, but with the limit of growth or the carrying capacity, K=1000 organisms.  

 

 

Figure 255.
Limited Growth of a Population of x0=10 Organisms with a g=1.1 Growth Rate over t=10 years

 

A second impediment to the unlimited growth of a population is the presence of a competing population. To see how competition affects growth, consider two populations of organisms, #1 and #2, which both grow exponentially in unlimited circumstances according to Eq249 as    

 

256.)                   

 

256a.)                  g1 = b1 – d1

 

257.)                   

 

257a.)                   g2 = b2 – d2

 

The x10 and x20 terms are the initial sizes respectively of the #1 and #2 populations; g1 and g2 are their annual growth rates; and x1 and x2 are their sizes at any time over time, t, in years.  The sum of the x1 and x2 sizes of these populations, x1+x2, at any time t is calculated from the above to be

   

258.)                         


We calculated this x1+x2 sum because it allows us to track the fractional size of each population over time, t, that is, the x1 and x2 sizes of each population relative to the x1+ x2 sum of the populations.   

 

259.)                      


260.)                     

 

Now consider these two populations existing and growing together in the same niche that has a carrying capacity, K, limit to the total number of organisms that the niche can support. When that limit is reached, the sum of the two population sizes must equal the K carrying capacity.

 

261.)                      


If the g growth rates of the two populations are unequal, g1 ≠ g2, the population sizes of the two populations will still continue to change even at the K carrying capacity of their mutual niche.

 

262.)                  

 

263.)                  

 

This x1+x2=K condition of the niche we assumed will also be understood as applying to the initial population sizes of x10 and x20.

 

264.)                         

This expresses Eq252 via x20=K−x10 as     

 

265.)                  

This expression for x1 is further simplified by dividing the numerator and denominator of the right hand term by to get 
 

266.)          

 

We can simplify Eq256 further by expressing the difference in growth rates, g1−g2, as F1, the competitive fitness, or more simply, the fitness of the #1 population

267.)            F1 = g1 – g2

 

268.)           

 

Noting the sameness in form of the above to the Verhulst time equation of Eq254 tells us that we can write it in a differential form that has the same form as the Verhulst differential function of Eq253.

 

269.)          

 

Next we define the fitness of the #2 population, F2 to be 

270.)             F2 = g2 – g1 = –F1

This allows us in parallel to Eqs268&269 for x1 to write for the x2 size of population #2,

 

271.)         

 

272.)         

 

A graph of Eqs268&271 makes clear the fate of these two competing populations. Consider the niche they live in together to have a carrying capacity of K=100 organisms with an initial size of x10=1 for the #1 population (asexual reproduction assumed for simplicity) and x20=99 for the #2 population and with growth rates of g1=2 and g2=1 as shows x1 in blue and x2 in red over time.
 

Figure 273. Competitive Population Growth or Natural Selection

 

The #1 population in blue, which has the higher growth rate of g1 =2, is seen to flourish over time while the #2 population in red, which has the smaller growth rate of g2 =1, dies out or goes extinct in the niche. For these and for any two competing populations, the one with the greater g growth rate or positive F fitness, here population #1 with F1=g1−g2=1 >0, eventually takes over the entire niche, x1=K=100, and the one with the lesser g growth rate or negative F fitness, here population #2 with F2=g2 − g1 = −1 <0 decreases in size and eventually dies out or goes extinct in the niche, x2=0. We get a better sense of this natural selection dynamic by expressing the F fitness functions of the two populations with Eqs267&270 expanded with Eqs256a&257a.  

274.)                    F1 = g1 − g2 = (b1−d1) − (b2−d2)

 

275.)                F2 = g2 − g1 = (b2−d2) − (b1−d1)

This mathematical description of natural selection perfectly fits its description in non-mathematical language as given by the Harvard grandmaster evolutionist, Ernst Mayr,

“.....it must be pointed out that two kinds of qualities are at a premium in selection. What Darwin called natural selection refers to any attribute that favors survival, such as better use of resources, a better adaptation to weather and climate, superior resistance to diseases, and a greater ability to escape enemies. However, an individual may make a higher genetic contribution to the next generation not by having superior survival attributes but merely by being more successful in reproduction.” (Mayr, Ernst; One Long Argument: Charles Darwin and Modern Evolutionary Thought; Harvard Univ. Press, 1991, p.88).


(We also point out that the defining functions for the natural selection dynamic of Eqs268-272 are not new and can also be derived from the pre-WW1 work of the classical population biologists, R.A. Fisher and J.B.S. Haldane, though done here in a much simpler way.)

 

The advantage of having a mathematical formulation for natural selection is not only in showing the underlying mechanism of the dynamic but also in providing a clear understanding via the F fitness function of where the primary behaviors of humans of survival, reproduction and combat come from as seen in the expansion of the F1 fitness of Eq253 to    

 

276.)          F1=b1−d1−b2+d2    

 

Population #1’s chances of its F1 fitness being positive, F1 >0, and of its surviving from generation to generation and flourishing are greatest when its members behave in such a way as to maximize its F1 fitness. This optimization of F1 mathematically entails in part minimizing the d1 death rate in F1=b1−d1−b2+d2 through survival behaviors like eating and staying warm that keep the organisms of population #1 alive and maximize their life span, for when the life spans of member organisms are great, the d1 death rate of their population is small. This minimization of the d1 term in F1=b1−d1−b2+d2 comes about as we saw by the homeostatic survival behaviors that operate on the emotional machinery described earlier that derive from Eq235. The negative feedback control systems that regulate behavior and motivate it through our emotions have as their implicit goal the evolutionary success of a population over time from generation to generation. This is clear from the simplest logic of surviving populations necessarily having competent, emotion driven survival behaviors. Those that don’t do not survive in evolutionary time and go extinct.   

It is also clear from F1=b1−d1−b2+d2 that F1 fitness and the possibility of evolutionary success is optimized by maximizing the b1 birth rate and the d2 death rate of a rival population in the niche. On the face of it, this suggests in the maximization of b1 that biological organisms including humans should have been programmed emotionally by evolution to maximize the number of offspring they produce. It also suggests from the nature of the foundation function of exponential growth for natural selection laid out in Eqs249,251&252 that humans should be programmed emotionally to raise their children to adolescence. And in regard to maximizing d2, the death rate of rivals, in order to optimize F1 that there be emotional programming to kill off rivals in the niche or drive them out of the niche as produces the same outcome prescribed by the mathematics of lowering the population size of rivals in the niche.   

Another alternative conclusion to combat is one group conquering another and taking them as slaves. As slave labor by definition results in greater wealth for the conquerors, it necessarily improves the life span of individuals and lowers the death rate, −d1, of the dominant population of slave masters.  Keeping people in chains physically or economically also effectively removes them from the competing competition, kills them as competing individuals and in doing so increases d2. As both a decrease in −d1 and an increase in d2 helps to maximize the evolutionary fitness of a group, the behavior of slave taking and the economic control of others generally is favored in evolution. This is hardly to say that the positive emotions involved in being a slave master are actively advertised because doing so would run contrary to having a maximally efficient control. The lion does not advertise the fact as he stalks the wildebeest that he is about to kill and eat it. And, indeed, this behavioral deception that is general in just about all predators is matched by varieties of passive signal deception such as the lion’s coat being the color of savannah grass so as to hide its approach to its prey. In short if we all did live in a slave society, the last thing it would do is advertise the fact of it.

And in conjunction with this comes the hiding of the consequences of being controlled in an exploitive way, religion blaming the devil or the person himself or herself for their pains and clinical psychology the equally vague evil spirit of mental illness and/or the person, himself or herself. Most unhappiness comes from one’s loss of true freedom along with much of violence we see in the news, domestically and internationally. To clarify these issues takes further mathematical analysis based on the foundation ideas we have developed up to this point.          

But talking about the emotions related to sex, love (parental and romantic) and violence, however, and what the mathematically prescribed behavioral outcomes of these emotions are or are not is fraught with problems because sex, love and violence are very much tied up with values and morality. And these considerations get all the more confused and contentious, on the one hand, when moral restrictions are used to control people and their behaviors in a servile society, one that depends on the enslavement of its people for its strength and survival; and on the other hand, when the morality of behaviors are broadcast with fiction that utterly distorts the reality of life and with supposed non-fiction news  programming that is at heart as non-representational of real life as the fictional programming in television series and in movies. 

For the above reasons, before we dive into these problems with considering violence and sex, epistemologically and morally, we are required to first present a template for reality in the form of true life stories that are more representative of not just what happens to people but in the emotions that people feel generally. For that reason, despite the fact that I would prefer to keep my failures and humiliations to myself, as people generally do which keeps the harsher truths of life all the more hidden, I tell my story in the following section.  Then we will continue with the mathematical analysis in the sections after that. 


15. Revolution in the Garden in Eden

http://www.dallasnews.com/incoming/20141021-convictions_challenged-fire_science_40391987.jpg.ece/BINARY/w620x413/CONVICTIONS_CHALLENGED-FIRE_SCIENCE_40391987.JPGhttp://bloximages.chicago2.vip.townnews.com/wacotrib.com/content/tncms/assets/v3/editorial/e/c3/ec358722-d8b2-5158-8184-51652edde644/5426157fe5d8e.image.jpgDon Graf - Lubbock Texas Commercial and Labor Attorney

Ed Graf Pleading Guilty to Murdering His Two Stepson’s for Insurance Money and Ed’s cousin, my brother, Don Graf

The prosecution said at his first trial in Waco in 1988 that Ed Graf left work early on Aug. 26, 1986 and picked up his two sons from daycare. He told his wife to stay at work late. He and the kids got home about 4:40 in the afternoon. Ed Graf then rendered the boys unconscious, dragged them from the house to this small wood shed in the backyard, poured gasoline around near the door, closed the door, locked it and went back to the house. By 4:55 p.m., flames engulfed the shed and burned it to almost nothing in minutes. One of the most damning pieces of evidence in the case that found him guilty and had him serve 25 years in prison before he was granted a retrial in 2014 was the fact that Ed had taken out insurance policies on the eight and nine year old boys about a month before the fire.  

Bail was set for his retrial at a million dollars. But Ed’s brother, Craig, was only able to raise $100,000 so Ed remained in jail during the retrial. It was nearing its end when I first came across the story of how my cousin had burned his kids alive. I was in shock because though I’m Ed’s cousin too and was close enough to the family in my younger days to be brother, Craig’s, baptismal sponsor, the first I heard of the murders was when I came across the story entirely by chance while browsing the Internet during the retrial. I was in the dark about the killings for the last thirty years because I was the one lucky Graf who escaped from this fundamentalist clan as a young woman, never to be told by anybody in my estranged family about this hideous skeleton in the closet that makes an evidenced case of why I ran away from them all those years ago.

Toward the end of Ed’s retrial, with the jury polled to be leaning in favor of conviction, 10-2, which would have locked him up for life with no chance of parole, he suddenly pleaded guilty to the murders as part of a most unusual last minute plea bargain that released him on parole a few days later. A letter to the editor that appeared on the front page of the Waco Tribune shortly after makes clear the outrage caused by his being freed. It read in part: “I would venture to say in the opinion of 99.9 percent of the public who have followed the Edward Graf murder retrial, the handling of this case, including its outcome, is a travesty of the judicial system. It is an enormous injustice to those two boys’ lives that he took and to the family of those two boys who have had to relive their nightmare not once but twice. And now this man, if you want to call him that, is going to be able to walk the streets of society again.”

I’ll speak to these twin evils of Ed’s child murders and the judicial corruption that released him from my own experience as a former member of the Graf extended family. I was the one who rebelled against its control and abuse and threw the pain of my suffering back in the face of those who caused it while Ed absorbed the worst of it without resistance and passed his lunatic unhappiness from it onto the two youngsters he burned alive. This release of unhappiness as violence on innocent victims who weren’t its cause is utterly common from the petty meanness people daily endure from those who have some power over them to the mass murders so familiar in the news to the butchery of war, the grand release of one nation’s unhappiness from the control imposed on its people on another. And that will reach its maximum horror in the mega-death of nuclear conflict. This true view of adult life as highly controlled ultimately by those at the top of the social hierarchy for their benefit runs counter to the American Dream picture presented to young people in ruling class controlled media.

To expose the reality of life, one calls on the one picture of it that one is sure of, the reality of one’s own life. Nothing, though, is as difficult as revealing the truth about, especially the bad things that happened to you. For whatever feels bad inside when you think about it brings greater humiliation yet in the public confessing of it. But the cost of keeping private matters hidden from others is also great if making life clear is important to you, for only the raw truth spat out is able to show that the society we live in has problems, significant institutional problems that must be spelled out clearly if there is to be any chance of doing anything about them. And after I finish my story I’ll talk about the important issues in precise mathematical language.    

I was born four months before America entered WWII as part of the last wave of women whom fundamentalist tradition was set up to control them as tightly and painfully as the foot bound women of imperial China. My father was a minister in rural parishes in Cullman, Alabama, where I was born, and later in Serbin, Texas, north of Austin, where his superior ability to extort tithes from parishioners elevated him to a position at Lutheran seminary where he taught Stewardship, a fancy name for extracting cash from the congregation.

My mother was a shrewd bulldog faced woman right out of Stephen King's, Carrie, crazy enough to think and tell us kids that Jesus talked to her every day and that the fossils in Dinosaur National Monument were plaster fakes secretly buried in the ground by people who hated God. This gave her cover for raising her children with the switch, including this little girl, me, with near weekly humiliating and painful britches pulled down whippings. If she didn't get off sexually with this game, for she had a way of twisting truth in all matters, I wouldn't believe it. Mildred Graf was 50 Shades of Grey with a halo.

Fear ruled my life, fear of punishment for taking a cookie without permission, fear of my mother whenever I approached my house coming home from school, fear of the dark, fear of dogs and a fear of the moon at night that stretched into my early thirties, at which time I was miraculously able to escape from this idiotic pointless terror of disobeying and everything else conditioned in me by childhood brutality disguised and blessed by my minister father as a proper Christian upbringing.

Some of the worst of my early years was my role as ego fodder for my brother, Don, older than me by two years. He was the recipient of the same sort of corporal punishment I got until he firmed into the role of my mother's toad and henchman over me. My hearing her spank Don used to bring on tears in me for him, but a waste of emotional energy in that my mother's iron rule could never be softened with tears and in Don's passing on a good amount of the pain he got from her to his younger sister, me. If my recall of his punching me in the shoulder at least once a day is an exaggerated memory, it is not by much. And once you are scared of somebody physically, even suggestions to stupid things potentially frightening become effective like being told there was a wolf upstairs in my bedroom that brought on a kind of terror I showed outwardly that he delighted in.   

I was lucky, though. I was not so destroyed as to be unable to hate my mother, for she and my minister father left enough in dumbbell me by pampering on the margins to make me a pretty if frightfully awkward girl child, for the minister's daughter is a public figure and if thought pretty by the congregation, a valuable status symbol helpful for stewardship and for the minister’s promotion in the pastoral ranks.

Alone in a piously brutal regime, all that mattered to me growing up was the thought and hope of love and rescue. The most daring books in our home library in those days were the Zane Grey novels. My imagination translated the cowboy heroes in them into would be lovers scooping me up on their horses and taking me far away from my family while squirting me in my pre-teen private parts with some warm liquid of unknown composition.

Beyond this seeping in of instinctive sexual feeling under the repression my attitude towards men was also shaped my father, a classic ever smiling father knows best type minister who is both an extreme asshole and an extreme bastard underneath the smile. And also by my brother, Don, who sustained his imperious position over me with constant disdain and disapproval even as I grew beyond the punch in the arm years. I was the model he practiced on in learning to control and humiliate people successfully as a lawyer in later life.

My early romances once I reached adolescence were the typical failures of young Christian girls. The boy I came to love most, the one who loved me the most, my parents hated and never stopped talking him down. Unfortunately the poor fellow, only seventeen like me, lacked the vigor and toughness of a Zane Grey hero even if his fondling was enough to kindle a strong flame of desire and affection in me for him. It takes more weapons and courage to be the knight in shining armor that rescues a damsel as much in distress as I was than any seventeen year old boy could possibly have mustered. My tears from the inevitable breakup were doubly painful with my mother reveling in soothing me over what I took emotionally to be a personal failure and shortcoming on top of the loss of love.

I remember the humiliation of being seventeen and dragged along by my parents on Sunday family trips devoid of any male attention or admiration. It was on one of these family jaunts to Wichita Falls in Texas that I first have a memory of Edward E. Graf Jr. This photo of his parents suggest a childhood for Ed Jr. little different than mine if the ugliness of parents is any indication of the way they treat their offspring as it was with my also strikingly ugly mother and father.

Uncle Ed and Aunt Sue, the Killer’s Parents


That Sunday visit, Ed Jr. was six-years-old, eleven years my junior. My memory of him back then was that he was puny, though glossed with a reputation for being smart, perhaps what you might expected for a first born boy raised in a corporal punishment believing family. I don’t want to make too strong a comparison to my brother, Don, as a way of cutely suggesting that Don would have burned children to death for insurance money, but in fact he was also puny as a young man, my corporal punishing mother constantly haranguing him to “walk with your shoulders back” and glossing him as a very smart boy. They were both standard middle class momma’s boys. As were Ed and Sue and my parents, in personality and looks, your standard fundamentalist ugly looking piously mean parents.       

A few years later, shortly after I got married, I ran into Ed Jr. again after we went back to Wichita Falls for a visit with Aunt Sue and Uncle Ed right after Don’s wedding down in Galveston. I remember Ed Jr. more critically then when he was about ten as being awkward to the point of what southern girls called back then, punky, and his mother, Sue, as your typically unattractive Christian mother who talked to Ed Jr. like some school teachers do to their students, in a continuously controlling tone. He definitely did not strike me as a “killer” at that time, but you learn as you age in these circles that whatever sinfulness resides in a fundamentalist person, hint of killer? In this case, they don’t show their feelings. Indeed one piece of advice my fundamentalist mother gave me, likely a commonplace tip in Missouri Synod Lutheran families, was “never say what you think.”

But killer aside, what you do see here is the makings of an injured soul of a little boy who is over-dominated by his less than empathetic mother. Two decades later I ran into him again a few years just before he killed his stepsons and then the results of his less than perfect childhood began to show an adult level pathology. But that is getting way ahead in my story.

The fellow my wounded heart connected with in marriage, or better, was connected to me by my parents, was a seminary student in my father's class at Concordia Theological Seminary in Springfield, Illinois. What I soon found out about him, that he was a toady type who filtered all his thoughts before he spoke them, I had absolutely no way of appreciating when I met him, for my father, like ministers generally, behaved this way as an integral part of being a minister, a job that is 95% acting. After two years of college at age twenty I married this Len Schoppa, a classic Texas phony. The error in it was inadvertently forewarned by my brother Don’s not bothering to attend my wedding whether he really did need to study for an important law school exam or from the utter disdain he had for me on this supposed most important day in a woman’s life. It was a fairy tale omen of worse things to come with Len and, indeed, with brother Don, too,

To speak of myself as gullible as Len and I headed off two years later to Japan as Lutheran missionaries is as much an understatement as calling a blind person gullible. I came equipped for my role as wife only with a thoroughly ingrained sense of duties to be performed, cook and wash the dishes and prepare the Sunday communion wafers and such, along with a few primitive feelings that escaped my mother's guillotine like my continued strong longing for love including sex not satisfied in this very emotionally empty Christian marriage. Further, the usually subtle misery of this loveless, effectively arranged marriage manifested itself in the less than subtle daily migraine headaches I'd had since early grade school that worsened as the anniversaries piled up.  

Can I make a light joke of the preposterousness of the goal of converting the Japanese to Christianity? For my minister husband it was all dominance games aimed mostly at the young Japanese guys who came to our mission church in search of escape from the empty life that awaited that generation of losers to America in World War II. For me it was being unwittingly being used as the pretty young wife of the missionary pastor, my vacant, submissive personality a fine fit to docility expected of Japanese women. I was a very efficient window dressing for his game. Many young men fell in love with me in this part I blindly played like Elizabeth Taylor in Suddenly Last Summer with Len beating the boys into subordination to him as the guy who had the woman they were all falling in love with. And down they went to him, all these poor bastards, one of them committing suicide as a result of this love triangle game Len played that I was completely unaware of. This story you won’t find in the Bible or preached about on televangelist TV.

I hesitate to say anything about my relationship to the three kids I bore for this haloed predator, they being the only love this inadequate mother ever had in her life. If they got anything good it was because they were everything in my life, but my failure was so clearly revealed in the end by the lack of any sparkle in their eyes as they approached adolescence. That makes you wish you were dead if you’re unable to rationalize such things, as I was not. For as bad as what is done to you in life and what you become as a result of it, worse is what you pass on to others, intended or not, especially to the innocents. On the other hand, my leaving Len in a dramatic way (as I’ll get into in a moment) smack in the middle of the kids’ pre-adolescence turned out to be an intended amelioration of the worst of me that I have always been grateful for in retrospect. They all turned out to be rather good looking creatures in their adult lives.  

As a pastor's wife in mildly idiot type rather like Sandy Dennis in Whose Afraid of Virginia Wolf I would have been totally devoured by the older women in any American congregation. But in Japan I was protected from the lady’s groups by my semi-worship by a vast gaggle of Japanese men that extended out beyond our mission church boys to the classes of college age guys I taught English to at Hokkaido University. This support that nature gives free of charge to girls who manage, by care or luck, to keep their waist slim was raised to a better level when fate, most miraculously, handed me a side role in life as a commercial model on Japanese TV. One of our social contacts through the mission church was a television producer who signed me on to pitch canned bean soup on Japanese television, the equivalent of Campbell’s soups. For six years I was known all over Japan in this guise, stopped by strangers on the street and at restaurants when I dined out and asked, "Aren't you the Koiten Soup Girl?!!"

A sort of Zane Grey hero soon came into my life in the form of a Japanese college boy, a ski bum sort of fellow who took the missionary's wife bait that the Reverend Schoppa dangled in front of all the young men, too her off to bed. This happened on church sponsored ski trips up on the slopes of Hokkaido that Len didn't come to because he didn't ski. It was real love as close as I'd ever been to it. He liked me a lot and I loved him for him for loving me that much and loved him too. The affair, whenever I could get it, was a great relief from the empty life I’d had with my mom and dad appointed missionary husband. Physical love that works for a woman in her twenties is fairly close to Heaven when you’re in the middle of it as much as not having it is quite hell.

Perhaps affairs like this are easy to hide for the smart women on the Real Housewives of New Jersey TV shows, but in a crowd of 30 fellow LCMS missionary couples we were but one of, some of whom also went on these Christian Fellowship ski trips, once the slightest suspicion arose about Mrs. Schoppa and her ski partner, the gossip fell like rain from the sky on the doorstep of the Rev. Schoppa. The climax of the confrontation between him and I was funny in its surprising twists and turns only in distant recollection of it.


I didn't hesitate to confess once he accused. I was much too dumb to tell a good lie and, to tell the truth, I had no good reason for wanting to hide it from him for by this time, I hated him for plaguing my life with his presence and instinctive female intuition must have primed me to unload with the truth with both barrels once he popped the question. What surprised me was his falling smack on the floor when I told him, yes, yes, I did it, and then writhing on the rug like a big piece of bacon frying in a pan turned up high; and while twisting all about like that confessing in a series of blurts to having had sex with farm animals, sheep, pigs and even the large dog his parents named, "Lassie." Even at this, though, I was sure later that he was lying, for he was the quintessential toady type who had to lie about everything in his toady life. What his preferring to fuck geese better than me had to do with my having had an affair the last six months with one of our converts did not, could not, register in my head at the moment of his deep confession and only in retrospect a few days later did I realize that the rumor that he had had sex with his retarded cousin, Larry, that a few of the good old boys in Harrold, Texas, had lightly joked about must have been true. 

Once you have a sense of that, parallax with pastor personalities generally so similar to his and my father’s makes it clear that they're all closet fags of one kind or another. Sense would tell you that the Protestant Christian clerics couldn’t be that much different than the Catholic Christian clerics, however seldom you see one get his trousers pulled down in public like Ted Haggard and Jim Bakker. It quite fit my own father, who though he likely sinned only in his heart in this regard I would guess, had to be perverse sexually in marrying anyone as bearishly ugly as my mother. Indeed, the truest truth ever spoken on TV had to be about queer conservatives as the norm by Joel McHale at the 2014 White House Correspondent’s Dinner. I mean, the brief titter and then drop dead silence tells it all. I mean, who looks prissier and weirder and queerer than pretty boys Ted Cruz and Marco Rubio and slippery ugly boys Rush Limbaugh and Karl Rove.

And back closer to home, it would take a very kind woman not to see my brother, Don, quintessentially conservative in his outward religious and political behavior, as faggy. That’s not to say he never married, did twice. But on the other hand both divorced him. And a wealthy lawyer has to be a pretty something off the norm to be left behind when he’s got that much status and that much money in the bank, and by two women no less. That’s just an educated guess, mind you, though the extent of his hating women, which I know a lot about as you’ll see, (I am not labelling him as a murderer for nothing), is a bit of a tip off on what he does on his frequent weekend trips out of town.  

Anyway, angry gossip aside and back to the main story, the headline of Missionary’s Wife Has Affair with College Boy Convert in Japan quickly spread beyond our Lutheran missionary circle in Japan to all the Christian missionaries in Japan and shortly, in less than a year, all but one of our 30 LCMS (Lutheran Church Missouri Synod) missionary couples were recalled back to America. Sounds like a very funny movie, but that actually did happen, I’m proud to say. The scandal hit home state-side, too, for my father was way up there in the LCMS church hierarchy and seeking just at this inopportune time to be elected Bishop of the Texas District of our church. Indeed, he lost not long after Len and I crawled home. You also have to understand that the Graf clan’s primary occupations were in the church as ministers or teachers in LCMS parochial schools. So I was not exactly welcomed back with smiles and flowers. So, I mean that as, as a result of this, the word was put out by my immediate family who were all, including my brother Don, directly affected by the scandal, that I was mentally ill. For why else would a girl from such a good Christian family do something so horribly sinful and to such a wonderful fellow minister (and son-in-law) as Len, as seeking another man’s carnal companionship.

Mentally ill, though, was not how I began feeling shortly after the plane touched down in Dallas. Scared rather to see my family siding with the now villainous poisonous snake of a husband I had that I was longing to make my ex-snake. They all became snakes at this point, and snakes with a mind to bite down hard on me as punishment for my sin and to get me back with Len, the thought of whom at this point, animal-fucker and so on, made me feel like vomiting any time I came into visual contact with him. Ted Haggard's wife remained “loyal” to her homosexual fundamentalist minister husband after his Tuesday night affairs with the muscular ass fucking prostitute was made public by the latter, but she knew what she and he was getting into to begin with and hung around wither fake brave smile as a heavily invested business partner. That kind is her own kind of Christian perversity that God fortunately did not curse me with too.     

Ah, the silver lining to the story I will now backtrack to. It came in the form of a Japanese baby girl Len and I adopted at Len’s insistence to make us look like the spitting image of Holy Family to the Japanese around us. Ba-chan, the nickname I gave her shortly after I fell in love with this most darling baby child, was the product of a young, very pretty prostitute from Yokohama, whom I met before she gave the baby up, and of her Norwegian seaman few weeks lover, so she said. Ba-chan was strikingly adorable with her unusual mix of Asiatic and Nordic features.

Ba-chan was special also in my being able to love her as other than a co-offspring of the snake. My ski fellow lover was also in love with her, always brought her on the ski trips, so she also provided bonding in that way. And Ba-chan also provided a splendid excuse for my avoiding Len at night for the last three years of the marriage by needing to sleep on the couch near Ba-chan to keep her from crying. This avoided his touch, a special dispensation for me under the circumstances and one packed with plausible deniability for my loathing of him, a face saver for him.  I loved her in a special way that had no poison in it.

Anyway, whatever hell was there for me back in the States if I didn't go back with Len to please my father and the hundred minsters pressuring me to do so, it was impossible to do that, on par with my being forced to amputate one of my fingers with a kitchen knife. So I ran away in my mind even if not in physical reality. But a lot of good that did as they all ran after me, calling me on the phone incessantly with preachments and ringing the doorbell to talk Jesus and God’s love to me. Actually I was going mad because I couldn't leave the kids behind, I knew that, and the whole deal just frightened the hell out of me. The most I could do was spend a few hours a day curled up in a ball fantasizing impossible Zane Gray level solutions to this impossible problem.  Even thought some about my boyfriend back in Japan at times, who wrote to beg me to come back to Japan. But he was no Zane Grey hero because he was just a college kid who lacked the high caliber punch this quite dangerous situation I was in required.  Len pushed and pushed for reconciliation to save his reputation and as he did it got brutal, emotionally and at times, physically, for there was none of this rape or violence on a wife stuff for a husband back in those days. 

Oddly, as luck would have it or I wouldn’t be writing this, my fantasies did come true. This was in the guise of a fellow appearing on the scene just in the nick of time. I had insisted to Len upon our being booted out of Japan that we go to Berkeley where I'd read in an issue of International Time Magazine that things were happening, new things that gave hope in a general way, just what I needed in my personal life at that time of despair. I insisted we go to Berkeley.

Len enrolled at this school, a Presbyterian seminary just north of San Francisco, to get a Master’s Degree in something called pastoral counseling so he could become a marriage counselor or drug counselor, his sense of being a minister having taken a good beating. We got set up in an apartment in student housing at this seminary in San Anselmo in Marin County barely speaking to each other.

It was like being locked up in a cage. I avoided the other minister's wives, all sweetly phony kinds I couldn’t stand beyond my situation with Len that was not the norm on campus. This was not at all what I had come to the Bay Area hoping for. So a great relief it was to go 40 miles away to a youth hostel at Point Reyes National Seashore for a weekend of environmental education with my oldest boy's seventh grade class. It was an especially great relief because I was due on that Monday following the weekend to go with Len to see two psychiatrists who were teachers of his as some sort of marriage therapy he said he had set up to patch us back together again. Like a doll with a broken arm stuffed with sawdust in the head I agreed to this, perhaps as evidence of just how stupid I was. For Len had already dragged me to one marriage counselor back in Japan and the eighth grade suggestions made by this toad who was almost as low as Len could have only worked if the wife wanted to stay with a husband for material reasons despite despising him.

The collection of people who were out at this youth hostel included not only all the other kids in my son, Lenny's, classroom and some of their parents but also what you’d have to call genuine users of a youth hostel just north of San Francisco in the early 70s, many of them guys with long hair and girls with torn jeans and actual flowers in their hair, the kind that favored organically produced cheese. They were mostly a sweet kind of looking people, not that strong, but all trying to be, all except for one who wasn't particularly sweet looking.


Pete was coming from New York, a dropout from graduate school at Rensselaer Polytechnic, one credit shy of a PhD in biophysics. And he was different than the others in being very tough looking, more what you’d think a Hell’s Angel would look like than scientist. It was easy to see that he was not afraid of anybody or possibly anything. Later he would tell me that a dream he had while sleeping in a campground in Spain across from the coast of Africa got him to prefer death, actually, to losing his freedom. Of the many creatures who inhabited the interesting world of the late sixties in America, a lot of them following the style of the day, he was very, very real, a real give me liberty or give me death character.  

Later he would also tell me that on first seeing me that he thought I looked like a model in a Woman’s Day magazine, which wasn't far from the truth as I had been a TV model in Japan. We talked for six hours that evening I first met him, his eyes that rather glowed never leaving mine. He said the self-help psychology book I had brought with me was nonsense, that they all were all nonsense, and that the true cause of unhappiness was abuse and the cure for it, rebellion against abusive people and situations, period. He couldn’t have found a more receptive audience for his politics, for without knowing my situation, he spelled it out for me perfectly. When I told him about my husband as the night went on and my being about to go to a therapy session with Len's two psychiatrist professors, he said not to go. “I wouldn’t trust the bastard. It's possibly a trap. Two psychiatrists can commit a person involuntarily. Don’t go.” He was smart, tough and careful. 

The next morning at breakfast in the communal kitchen of the youth hostel, he got to talking with two Australian fellows in my presence who were arguing that you had to compromise in life to survive and that anybody who didn’t was a fool. Pete, not liking the implication and likely especially not in front of me,   retorted that he thought it cowardly if you compromised with people who were abusive or insulting towards you, which could have included the two of them at this moment. Both of these Australians were big guys. But when it became clear that their differences were irreconcilable and the remarks going back and forth picked up steam, Pete just raised his eyebrows and lowered his tone and stopped smiling and they both more or less ran out of the kitchen. He was not somebody who made you afraid of him, never me, but it was also clear that he would not back down in a fight, not even against two, not unlike my heroes in the Zane Grey novels.

We separated during a group tour of the seashore later that afternoon and when we met again I opened up to him. When he asked why I seemed so sad, I said, "Look at my son, look at his eyes." To me, anyone could tell that Lenny Jr. hadn't turned out as well as he might have. And that killed me, for I did love the boy. Pete talked to reassure me, saying that Lenny didn't look that bad, “looks better than a lot of other kids his age.” He meant it, too, you could tell, and that made me feel better. Our conversations went on and on that night too, Saturday night, touching a lot on politics for Pete was heavily into the idea of actual revolution for he said that the hierarchy you had to submit to in order to survive was deadly to self-respect and with that lost, you might as well be dead.    

We parents and our kids were all due to leave the next morning on Sunday. At some point during our last exchange before I left, he touched my upper arm in a firm way as I was about to go, something I could feel down to my knees. As my son and I were about to get into our blue Toyota, I suddenly turned and asked him on impulse, stupidly in retrospect, if he wanted to come over to the house and have dinner with the family. Given my situation with Len, I don't know why those words came out of my mouth. I suppose I wanted to see him again, but didn't know how to say it in a socially acceptable way.

He smiled and shook his head and said, "Three doesn't work." And we parted. That night after Lenny and I got back home I told Len I wasn't going to the therapy session he'd set up. And the next morning after Len went off to class for the day I called the youth hostel and told Pete I wanted to make the 40 mile drive back to see him and talk some more.

He was very forward when I got there, aggressive at the level of putting his hands down my jeans without saying a word a minute after I arrived and we were alone. The thought came into my head that he was some sort of a sex maniac you hear about and that women are told, of course, to avoid. As it turned out I suppose he was sort of a sex maniac, but what he was doing was something so instantly pleasurable that you can't help but want him to keep doing it. It was a little more aggressive and forceful than you might think a honeymoon encounter should be. But like a new great flavor of pizza you’d never heard of before shoved down your throat to begin with, once you've tried one slice, it's hard to not want more. And he quite felt the same way about me, maybe even doubly judging from the second and third slices he wanted right away.

I stayed overnight and by the time morning came and I knew I had to get back to the kids, Pete was telling me that he had never seen a girl as beautiful as I looked that morning, not in a movie, not in a magazine, not in real life, not ever. As I've been with him 41 years now, I know he meant it at that moment, though some credit to him because all that physical attention does make a girl feel and look really good. He also said that first intimate day, "I'd die for you. I'd kill for you." As such, given my circumstances, he was "just what I needed" as things would turn out.

Whatever the nonsense in pop psych books about guys “needing to make a commitment”, Darwin says it all much better than Freud or the Pope. When the sex clicks, you just are committed. And when it doesn't, there's no future in the relationship. Either the guy's got the testosterone and heart capable of love required or he doesn't. There's little love in America today, it’s all breakups and divorce and loneliness, even in marriages that hold together for money sake, because all the guys but the bravest ones who resist critical compromise, have been gelded, castrated, made cute little boys out of at best and those worth little in the long run.  

What was truly amazing and unarguable as to the power of love was that starting after that morning up at the youth hostel, my migraine headaches went away. I don’t mean that they were less painful, but that they just completely went away, never to come back again for the rest of my life. That’s physical proof of the power of love. It also tells you something about where migraines come from. And it tells you one way to get rid of them, though it’s obviously not something you can buy over the counter or get a prescription for.

Len knew what was up the minute I got back home late that morning. "I can tell by your eyes," he said, but better he could tell by the fact that I had been out all night. Pete said to tell him the minute I got back home to get out of the house. I did. He refused at first until I told him angrily that I'd run screaming out onto the seminary campus if he didn't. It helps to be furious at critical moments. He left.  

The pious fraud I'd had the misfortune to live with for the previous ten years came back the next day, though, and tried to rape me. I ran from the apartment with bruises on my shoulders and arms. Len went out the door and took the car keys with him. Pete was furious when he heard about what he’d done when I hitchhiked out to the youth hostel the following day. "I'll kill the bastard," he made clear.

He didn't have to wait long to have the opportunity. Len drove out to the youth hostel to ask questions and confront him a couple of days later. Pete's best war story was how he backed down a gang of ten Puerto Ricans on East 11th St. in Manhattan where he lived by beating the leader of the gang in front of them. This was just before he came to California and met me. By the time he left New York City he had picked up a couple of knife scars and four bullet holes and had never backed down in a fight even when confronted with the gun.

He’s told me the story of the fight with Len that day often over the years and without going into all the words said between them and the punches thrown, Pete in the end got Len down in a position where he could have ripped Len's eyes out and felt angry enough to do it but didn't because he knew that would go over the line and surely get him locked up. He didn't have to do anything that hash, though, because whatever the details of their fight, Len got the point and was scared enough of Pete after that to never come over and bother me again.

But that was hardly the end of the pain Len could cause. Immediately after my filing for divorce a few days later, Len got visitation rights and it was impossible not to see how he loved coming over to take a bite out of me with the courts backing him up, something 50 million women in America in the same situation have to have experienced. It was so obvious in my case because Len never cared anything about the kids any more than he did about me - until I filed for divorce. Before that we were little more than window dressing for the creep. Now he was their loving father doing more with them in the next couple of months than he’d done in the previous ten years. I should make it clear that through all this, Len wanted me back, both to please my parents and to not look like the biggest loser in the world to everybody else as the minister whose wife ran off and left him. So endless intrusions in every way he was licensed by the law to make them through the kids. Even Pete had to swallow his urge to crack Len’s skull when he came round, which caused him noticeable if not unbearable discomfort when Len came for the kids every other weekend. 

All of these maneuvers by Len during the divorce were calculated to get me back, not to produce a livable divorce. Len made no bones about it. Neither did my parents or my brother, Don, who called from Texas and talked to me endlessly like I was a disobedient eight year old. As this phase dragged on it became clear that much of Len's legal strategizing was engineered by Don.  Pete and I felt sure of this because Len's actual lawyer in California was a cheapo prematurely balding grease head who mostly wanted me to like him when we had contact and who seemed half in the dark about the maneuvers Len was making on his own.  

Like I said a good part of the endless harassment to get me to leave the evil Pete and go back to worthy Len was near daily phone calls and house calls from a dozen or so Lutheran ministers in the area. I felt a jolt every time I heard the front door bell ring. One ring, though, produced not a dark robed minister but my mother in an unannounced fly up from Texas. She brought along a large roast beef.  Fortunately Pete happened to be right there in the living room two feet from the front door when the bell rang.

The interaction between the three of us was relatively brief and to the point. My mother, whom Pete once described as looking remarkably like the "basilisk", a mythical lizard-like monster, threatened us both with punishment from God and told Pete more than a few times the hour she was there what she had told me when I was young, that Jesus spoke to her directly on a daily basis. What Pete suggested God could do, shouted back in her face, is exactly what you might imagine a politically radical, physically confident lover fed up with the crap that had been rained down on me since the day I filed the divorce would say, namely that God and she could both go fuck themselves and for her to get the hell out of the house. When she hesitated, Pete more or less pushed her out the front door and to make his point even more emphatically, he tossed her roast beef in the garbage can sitting on the porch next to the front door.

"Seemed to me more like a squabble with a dyke over their mutual girlfriend,” he said the minute she cleared the driveway with her luggage in her hand. “Your mother really is weird. No wonder you hated her so much when you were young." My memory of some of her more invasive, hygienic sort of, punishments my mother abused me with made that picture of her a fairly accurate one. She was disgusting on top of being cruel and overbearing.

I'm positive, though I don't know how I'd go about proving it, that maternal rape of children has to be common and the most hidden crime. I'm sure even though I don’t know how to prove it that Adam Lanza’s mother screwed his ass into the painful hell his life became because of her that drove him to take all those kids there to hell with him as some twisted revenge on his pious fraud mother. Forget the happy kids’ faces on the cereal commercials on TV. Go take a look at real kids in real daycare facilities and in real schools in America and be shocked at the obvious unhappiness and fear that sits on their obedient faces.

One thing for sure is that Columbine and the Virginia Tech and Newtown mass murders were all perpetrated by unhappy kids. And it’s hard to dismiss the fact that a lot of the unhappiness in unhappy kids has to come from the mothers, whether from their predation or neglect. I am sure fathers too, but whatever the psychobabble nonsense of parental equality drummed up by the propaganda chorus to insure that capitalism has a willing female labor force, bad mothering in an especially big way is the problem because we women are what we are as mothers in a very basic instinctively way whatever the myth. Pity the children.

When my mother saw how forceful Pete was during that brief time and got a quick but telling picture of how much my kids liked and respected him, she and Len and Don changed strategy with respect to custody of the kids. First Len said that, of course, I'd get the kids, the strategy in that being that he'd get to keep his feet in the game with every visitation and that eventually the kids would influence me to go back to being Mrs. Ruth Schoppa. But after my mother's visit, the legal papers changed abruptly to Len asking for custody of our three biological kids, this to take the kids away from me and break my heart, which it did, as a means to get me back with Len so I could be back with them. With both sets of their grandparents on Len’s side, the kids’ tone quickly became, “We're going with daddy; and you should come back with him, too.” Nothing more to be said. 

This thing of losing custody of your children is portrayed if at all in the media as something as casual as going for an annual check-up at the doctor, no big deal.  But it's damn not like that at all. It killed me. Almost. At that point nearly turning me into the crazy person they said I was because of the kids deciding under the influence of all the “good” adults in the game to leave me. Still I refused to go back to him and reunite with this bunch of bastards. That wasn't going to work, fuck you all and your horrible games, I thought.

In the end in tough times your heart weighs all the options and tells you what to do. As pained as I was about the kids, I never once had the slightest impulse to go back to the Graf clan. Soon after the kids went off with Len and out of the house, Pete and I bought an $800 trailer to live in with three-year-old Ba-chan whom I still had custody of. They left her behind, not fighting for custody, to keep up Len's connection to me, for the theme was relentlessly, come back, Ruth, come back.

Len still had legal visitation rights with little Ba every other weekend. After the other kids left, his comings and goings to get her were very difficult. Almost too sad to talk about was the third or fourth one of these weekend visitations. When he brought Ba-chan back this time, she wouldn't speak. She was completely unresponsive. Wouldn't talk, wouldn't smile, wouldn't do anything but crawl around on the floor after a while making sounds like a kitty cat. Whatever had been my baby Ba seemed dead, just not there anymore and replaced with something truly out of a horror story, but one you’re a part of instead of one you’re reading.

After a half an hour of this nightmare scene in the living room of the trailer, I called Len on the phone and screamed out, "What did you do to her!?" Only to hear him immediately reply in a clearly faked, contrived manner, "What did you do to her?" This doubled the scariness of what had happened by making it clear that something had been done by them that they were aware of, for his tone was not at all terrified for what might have happened to her, but accusatory towards me. Whatever they had done to produce this horror, they wanted to use it on me, on us, to destroy me and us by destroying the baby while blaming it on us, which made it clear that they had intentionally done something to destroy this poor little three year old.

What did we do? We ran the next day, terrified. Pete remarked that he was usually prepared for anything, but not this. That while he despised Len, he found it impossible to believe that anybody could do something this horrible. We just picked up stakes and hitched the trailer to the pick-up truck and drove away, up the highway not sure where we were going, but to someplace unknown to them, just out of there where Len knew our location. Screw the legality of it, rather be locked up for violating court ordered visitation than ever let him get his hands on her again, we quickly agreed without debate.

Soon we crossed from California into Oregon. Leaving the state upping the potential charges for violating visitation to the felony level. We didn't care. Threatening letters from Len and his lawyer and the authorities came to the Post Office Box we kept on the California side of the border. We didn't care. We worried constantly that they'd track us down, every sight of a car in Oregon with California or Texas plates producing a feeling of sharp fear and violent anger. Pete said if he ever came across Len after what had happened, he'd literally kill him. And he would have. I was so sad and crazy after that, I don't know how we made it through the days. Pete never quit. All the love available between the three of us went to Ba-chan after that. We spoiled her with anything and everything she wanted just to get her to keep her smile. And that worked. We became like her slaves, tiring and often humiliating for she developed a bit of a mean streak like you might think a frightened individual might do if it had power over you. But this kind of treatment kept her looking beautiful, no matter the cost in time and energy and however much it made her one very self-interested child.

Pete never quit. I was half crazy over the loss of the three kids and what they’d done to Ba-chan and she was a load to handle every minute she was awake. He was a real fighter, to the death against the viciousness of life under the control of those who had the power. I should talk about that to make it clear why he had this extremely dedicated disposition that is so rare in this post 9/11 era. When Pete was in graduate school, his thesis advisor, a fellow high up in science by the name of Dr. Posner, stole his research, publishing what Pete had done on his own without Pete's name on it. Pete said at first he couldn't believe it. Then Posner told Pete that he wouldn't sign his thesis to get him his PhD degree unless Pete kissed his ass, figuratively, of course, but in such a blatant way that it was almost a literal demand. In a way this was just part of who Posner was, for he had a reputation, Pete found out after the fact, of being the worst kind of bastard, an academic manipulator supreme. But also his mega-extreme treatment of Pete was in no small way because Pete was and very much looked like a 60s rebel, anti-Vietnam war radical, long hair, anti-authoritarian attitude and the rest.

Posner’s game was pure power play, teaching Pete who was the boss, a kind of rape of a young man that’s not that uncommon in the academic community if you read the last chapters of the book by Desmond Morris, The Human Zoo. So what did Pete do in response to all this? He told Posner along with the rest of his thesis committee, some in on the gang rape, others too cowardly to challenge big science Posner, to go fuck themselves. All five of them were sent telegrams in high style telling them this.

And from that experience of resisting abusive authority, he said he experienced a genuine miracle, an unexpected major uptick in his life, reborn with a new level of confidence in his heart. He joked that his sex life, which wasn't the worst even before this, (he lived with a lingerie model his junior and senior year in college) took off to new heights where women started near fighting to see who could sit on his lap in the watering holes on 1st Avenue in Manhattan. And on his way from New York to California shortly before we met, he'd had sex with three different girls on the Greyhound bus ride cross country. He said it was a new life impossible to turn back from even though he gave up his PhD as the price paid to get it. And he got that back, too, ten years later when his biophysical research on bone growth was validated by a research team in Czechoslovakia who gave him credit for the discovery.

Anyway, he was a fighter in all things he believed in and that led to his fighting every day to bring Ba-chan back to life, always propping me up and telling me to never lose hope. This was a hard task because      Ba-chan hardly ever spoke a word over the next three years. But what she did do was draw all the time. She was a precociously gifted artist almost as a compensation for her not communicating by talking. And when she was about six years old, she started drawing cartoon frames like I was doing at the time, hers about strange looking creatures with large threatening eyes that Pete guessed might have a connection to whoever had hurt her on that visitation. He got this idea because many of these cartoon frames had a background of rain storms in them and of a child sad n being stuck in endless rain.  

Right about at this time Pete took a special course in the Montessori Method of teaching reading to deaf children and he used it to teach Ba-chan how to read and all the talk back and forth from the reading lessons loosened Ba-chan’s tongue until it gradually got her talking again. Not only did her talking seem a miracle in itself but it also got to make sense out of what had been done to her.

As a critical part of this story I must introduce the fact now that Ba-chan never used a pillow when she went to bed. She just didn't like a pillow. Unusual we thought, but no big deal. Eventually, though, Ba-chan told us that they had beaten her up with the excuse that she wouldn't be quiet in church on that weekend when they took her on visitation. They took her home after church and beat her up. And then, horror of horrors revealed, they put a pillow over her face, so she said, and partially suffocated her and then told her if she ever told anybody, they'd smother her. And that put that level of fear in her that made her act that way that day Len brought her back to us. I'm not exaggerating.

She also talked about things done to her that seemed sexual, but Pete never took that part too seriously because once you start thinking and talking in that way about somebody that you hate, especially from the recall memory of a six year old talking about when she was three, nobody would believe you. It was horrible enough that they beat her dumb without accusing them of anything more than that. Though I thought it odd that this young child was putting things in her vagina like pieces of foam rubber from her mattress. Was this possibly evidence that some of the bizarre tales she started telling about what they made her do sexually were actually true? 

What was amazing was that after two weeks of intense focus and her talking about what had happened to her, her lightening up was marked and, lo and behold, on one of these remarkable days she started playfully throwing a pillow on our bed up in the air again and again. And however much it may seem too much made up to fit the story as one might like to tell it, she started using a pillow to sleep with ever after that.

The cartoons June drew she got the basics of from a comic book I was doing at that time about my life. I can’t overstate how much the combination of losing three of my kids and Ba-chan being turned into an incubus by the beating shattered me. Frequent sex, believe it or not, and constant comforting reassurance from Pete helped. But he said again and again, “You’ve got to fight back.” And suggested I write up the story of my life as a way of sorting things out in my head. This was back near 40 years ago and try as I may I couldn’t put sentences together in any readable way. I was no writer.

He asked then, “Can you draw?” Underground comics, as they were called back in the 60s, were big in those days. “Can you draw?” Well I couldn’t. And neither could Pete. But like I said, he was stubborn about everything and said, “It can’t be that hard, you just follow the lines you see and put them down on paper as you see them.” He tried that doing a drawing of Ba-chan’s pretty face, and it came out startlingly well. And he said: “If I can draw and I always hated drawing, you can draw. Just follow the lines and tell the story of your life in drawings, your childhood and your marriage exactly as they happened.”     

And I did. I entitled it Minister’s Daughter, Missionary’s Wife. Parts were very raw and real. I talked in comics frames openly about the abuse I’d gotten from my parents, some of it from my mother interpretable as sexual abuse. He said what mattered was to be completely honest, so I talked in a few frames about an incident I had with one of my own children. I might as well repeat it here. It’s the truth and it does shed some light on the emotional grip I was in all my life. When my first born came along, he’s now the head of a Dept. of Political Science in a university whose name I won’t mention, I was utterly devoted to him, at least as well as someone like me could be. He was really the focus of everything minute I had available in my life beyond the household and minor mission chores I was responsible for.

When the second child came along, a girl, I don’t know, maybe it was harder to give attention to her because I was so bound like a Siamese twin to the first born. Whatever the reason, she had a hard time going to bed at night and she’d cry. And her crying would drive me crazy because some nights I couldn’t soothe it. One night it drove me so crazy, I started hitting her, “Shut up! Shut up!” I can’t remember if that got her to shut up. What I do remember, and this feels twice as difficult to tell now as it was to put it in a cartoon frame, which was still very difficult to do back then, it turned me on sexually, hitting her did.

This was in about the third year of my marriage to Len. It was horrifying. You don’t try to analyze something like that. You just feel revulsion for yourself, full of self-loathing, so much you don’t ever want to think about it. It happened twice and then never again because I never came a mile near to hitting any of my kids for anything after that. But years alter and now that I’m talking about to again here, obviously there was something wrong with me. And since something like that can’t possibly be genetic, the connection had to be with my upbringing, the regular whippings and invasiveness my mother laid on me, which is the really the whole point of my telling this story, how horrible all that stuff done in the name of raising a child to be obedient is. For if something like that was possible for me, forget that I totally resisted it once it came out like that and eventually ran away from this nutty bunch of people, what wasn’t possible with others who were all raised the same way, with beatings and minutely rigid rules about everything, rules that hid the sadism and freakishly dominating nature of the people doing this to children. And, of course, I think of Ed Graf Jr. burning those children to death, not all that strange in the context of the way he was also raised as a Graf. And what about a lot of the violence out there that hits the headlines. You are telling me that all these young people’s unprovoked mass murders don’t have some origin in their own childhoods, that their parents aren’t to blame or that the control placed on the parents in our authoritarian society, even if well disguised as such, isn’t the ultimate cause of crazy violence like this?     

The truth is hard to tell, which is why nobody really tells it, or even sees it in their own lives, prefers to accept the fluff show on TV and in the movies as the reality out there, and the reality of their own lives. My book turned out very well in two respects. Years after I sent out copies of it around to 1000 people connected with my family and Len, including neighbors and lots of Lutheran ministers, I sent a copy to a fellow named Robert Crumb. He was the premier commix artist of the 60s, hands down in just about everybody’s opinion back then. He wrote back that he loved it, “a masterpiece of sorts” he said in a postcard he wrote me. But he didn’t like the ending, the very last page of the 20 page comic book that showed me poisoning my mother to death with black widow spiders. He didn’t like that because he was a pacifist, against violence generally. But in reality, that was more or less what I did do sending around the comic book like that, poison her reputation and Len’s too.  

Because the story was believable from my telling the truth about my own “sins”, the book caused my jerk of a minister father to be near instantly retired from the ministry, fired pretty much as the pastor of a Lutheran congregation in Waco, TX. He became a real estate salesman after that, interestingly, which should tell you what the profession of minister is really all about, both being most basically inflated sell jobs on people. And the book also caused Len to come down with throat cancer six weeks after I sent the book around to anybody he ever knew. Maybe my cause and effect supposition between emotional travail and cancer is less than provable, but it made me very happy to hear he had cancer even if by odd coincidence after I sent the book out with the intent of hurting him.

The last frame on the very last page of the comic book said it all: “Revenge gives a person a second life.” That’s an Old Italian saying, you know. And it works. At least it did for me. For I felt a thousand times better after writing the book up and sending it out and hearing from this or that channel the harm it did to these people who had done so much over so many years to make my life miserable. Fighting back, getting revenge, does matter. You don’t complain. You don’t take your pain out on other people who did nothing to hurt you. You give it back to the bastards who caused it. That’s what revolution is, fighting back.

Things changed course in our life shortly after this, which will soon take us back to child murderer, Ed Graf.  As we entered the year, 1979, almost ten years after Pete had dropped out of graduate school, he found out that certain research work he had done on bone growth but kept out of the plagiarizer’s hands had been validated by the then newly invented SCM or scanning electron microscope and that he had been credit for the initial discovery in the scientific journal, Calcified Tissue Research.

This had Pete head back to Rensselaer Polytechnic in Troy, New York, (RPI), with me and a New Ba-chan in tow. There the news that Pete’s theoretical work had been validated observationally with the SCM got Posner removed from his PhD committee and Pete, now regarded as sort of a prodigal son genius, not only his PhD but also a position on faculty in the Dept. of Biomedical Engineering at RPI. This sudden leap in status for the family from cliff dwellers up in an abandoned gold mine in Northern California where we had hid from Len after running off with Ba-chan to Professor Calabria and his beautiful wife and daughter enabled us to travel down to Texas to see my three kids after six long years away from them. Pete with his once long and scraggly 60s hair now cut and trim looked as socially acceptable as Robert McNamara for the occasion. 

 

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Neatened up on the way to the in-laws.

 

Our first stop was Vernon, TX, where Len and my two oldest were living. Then we were off to Waco where the youngest, Nathan, was at some religious indoctrination get together for young people at Baylor and where my parents were still living. Uncle Ed and Aunt Sue looking a touch younger but no less ugly than in that photo of them were also living in Waco as were their kids, now grown Ed Jr. and Craig. Because I was doing my best to make nice on this Texas trip for the sake of my three kids, we went along with my mother’s suggestion for us, now respectable what with Pete’s doctorate and faculty position in hand, to visit Uncle Ed and Aunt Sue. And we even brought a wedding present to then recently married Craig Graf, my godson, and his wife.

Ed Graf Jr., the future murderer, stood out sharply on this occasion for a couple of reasons. For one thing he was still living with his parents in his thirties. And this was with no recession at hand in the country to rationalize this not usual living situation. Another was that he was, immediately upon introduction to us, afraid and apprehensive about me and Pete, really you’d have to say in a general state of fear and apprehension, because despite Pete’s moderately imposing presence, Pete was charismatic enough that almost everybody liked him on first sight, not feared him. Most odd was that right in the middle of a make nice, hi, how’re you doing, exchange, Ed Jr. suddenly did an about face and ran out the back door into Sue and Ed’s lushly gardened back yard. Also odd is that neither Uncle Ed or Aunt Sue breathed a word, made a sound, stirred the slightest, about this odd action from Ed Jr. that was totally misfit to the occasion of our long belated family visit to the family. 

I doubt Ed was seeing a psychiatrist or getting any professional help because LCMS Lutherans just don’t do that. It wasn’t just that they just resolved such things by prayer and similar, but also that our kind of people in the Graf clan, who were so professionally connected with the church, avoided scandal like a model avoids chocolate cake. This attitude no doubt was instrumental in the suicide of Pastor Rick Warren’s son. All the fundamentalist Christians must be ostensibly at all times and in all ways as close to perfect as God wants them and blesses them to be, until they turn out on the front page to be homosexuals like the Rev. Ted Haggard or suicides or child murderers.         

Anyway, it was clear that Ed Jr. had problems back then, eight years before the murders, significant enough to call our attention to them. We thought little about it afterward because without my going through the full menagerie of my Graf relatives, most of them ostensibly had observable quirks if not problems like patent ugliness or obesity on a grand scale as showed in Uncle Ed and Aunt Sue possibly as a marker for their more perverse undercoat that produced their first born offspring, Ed, the Child Murderer. I knew the reality of the deviations from emotionally healthy for my own parents, but could only guess at those for the parents that created Ed, the Child Murderer.           

The last person on the menu for this trip to Texas trip was my brother, Don Graf. He was over in Lubbock. It was something we weren’t keen on doing but did so on repeated cajoling from my parents, whom, like I said, I was inclined to placate in minor ways because of the influence they had on my kids whom I still had great affection for and wanted to maintain contact with. As things would turn out, though, the trip to Lubbock wasn’t a minor item. The visit with my parents for a few days had an undercurrent of intense if fairly well concealed hate that stemmed at this point in time not just from my leaving Len and the church back then, but also from the devastating effect the comic book had had on them. One might have expected worse to come through their forced politeness and formal hospitality. And it did come, over in Lubbock.   

We bought a box of chocolate doughnuts to bring over to Don’s house for breakfast, a little nosh to share with him and his then wife, Ruby. Good thing we brought a full dozen because, lo and behold, also invited to this family reunion sort of breakfast was, surprise, surprise, Ruby’s father, a large sized Texas pig farmer, and Ruby’s sister and her husband, an enormous Texas speedway owner with the classic back of the neck fat roll and the hard beady eyes of a movie cast Southern bully boy.  

What a coincidence! Don’s in-laws showed up just at the same time that sister, Ruth, is coming home to see the family for the first time in seven years! The few conversational bites that came from the supersized father-in-law and brother-in-law made it clear that they would intimidate Pete if they could. But it was equally clear that Pete was not pressed in that direction in the slightest for his winning record in street violence, one with a touch of blood spattered on it, made Pete think, correctly or not, sane or crazy, that if he stepped into the ring with Muhammad Ali, he’d beat his ass in. So he gamely engaged in light conversation with the “boys” just like they were all a bunch of good old boys.

Attorney Don Graf’s trophy wife, Ruby, was all smiles and asking friendly flirty Southern gal questions of Pete at the breakfast table as though everything was “jus’ fine.” Her gab was friendly enough to make me wonder how much of it was tinsel and how much personal stimulation by Pete. Brother Don, despite being a senior partner in the oldest and largest law firm in West Texas did not strike Pete or me as impressive in appearance or demeanor as noted to each other after we left Lubbock. Though it’s hard to tell if that was an objectively fair impression by me given how much I disliked this pansy ass creep who wore cowboy boots to Sunday breakfast to keep up his pretense of mother blessed manhood.  

The participants on their team seemed eager to hurry through breakfast and I saw why when Pete and I were suddenly invited at the second cup of coffee to check out Don’s newly purchased winery out on the outskirts of Lubbock. Participants on this tour will include Ruth and Peter and Don and his two large sized male in-laws, but not Ruby or her mousy sister. Despite a sharp chill brought back no doubt from earlier times of punches in the shoulder, with Pete leading the way as recklessly brave as a teenage matador and I still as naďve as a newborn rabbit, we all jumped into our respective vehicles and off we went.  

That picture worth a thousand words would do better at this point, but we have to settle for the verbal snapshot of my brother, Don, standing on one side of the table at the winery where corks are put in the wine bottles with a cork hammer. He is banging one such hammer on the table surface as his insulting voice starts to throw emotional punches at me, then again and again. This, as planned by him, but of course, is making me progressively more and more uncomfortable and starting to feel shaky as in my victimized days of old. Don knows me well, which buttons to push. And next to me on my side of the table, getting progressively more irritated while naively trying to disguise his bubbling up fury for the sake of maintaining some semblance of family civility, is Pete. To complete the picture worth a thousand words, the two henchmen in-laws are standing about fifteen feet away, waiting for the real action to begin that will call them on stage too.

As the tempo of Don’s bangs with the hammer and bangs with his voice at me increases in tandem with Pete’s less and less well disguised look of violence about to come out of him, I suddenly got a sense of full security. Pete’s supremely excessive physical confidence from ghetto living on the Lower East Side after he dropped out of school blocked out any feelings of fear as his faced welled up in a twist of violent hatred towards Don for what he was trying to do to me. He looked as though he were about to leap on Don and strangle him to death, which kept me sane and intact. And at this point in the upward spiraling drama, Don dropped the hammer, his face fell and he slunk away from the table and from the two of us. 

The tour of the winery was then as suddenly declared over as the invitation to it at Don’s house at breakfast was suddenly tendered. Out in our car on a dirt road that circled this winery muddied from rain the night before, I took a good look at Pete’s face and told him to look in the rear view mirror to see what he looked like. ”Christ,” he said, “I look like some kind of killer you might see in the movies.” He said he hoped he hadn’t made a bad impression. I wondered for ten seconds if he really meant that. Another ten seconds after that, though, Pete said, as I realized also before he spoke us, “Punk faggot piece of shit couldn’t pull the trigger,” meaning that Don was supposed to provoke Pete into a fight that the other two would join in on to either beat Pete up, three on one, and/or to call the sheriff in on it to have Pete locked up for assault or such and be destroyed in that way. No wonder my mother pushed so hard and so smoothly to get us to come to Lubbock. 

Don and his in-laws at this point are in a car in front of us on this puddle drenched road. And as we slowly meander down its muddy path, their car comes to an abrupt stop. And, of course, as we are right behind them, so does ours. We wait tensed. It is a long minute and a half until Donald Lee Graf jumps out of their car and runs over to Pete’s driver’s side window, sputtering nervously, “We got stuck in the mud, honestly!” He seemed like he was afraid that Pete really was about to kill him, whatever the specific motive for his saying that. I wasn’t thinking that at the time, though, but rather blurted out to Don from my passenger side spontaneously, surely this aggressive only because I sensed such fear in his face, “Were you in California with Len the summer of 1974?” At that the fear on his face turned to a look of terror and half bobbing his head up and down twice in affirmation, he ran back to his car, jumped in and drove away.

At that I knew he was the bastard who did it, the one who killed my baby Ba-chan’s soul or gave the order or suggestion to do it or was seriously in on it somehow, likely carrying out a plan that had originated in my mother’s dark heart. And beyond that and being a conservative closet gay, a pedophile too?   

Less than a year later back up in New York we received a letter out of the blue from Don’s wife, Ruby, telling us that she had just divorced Don. It was filled with bitter spiteful words obviously designed to hurt Don as much as she could by telling us about his humiliation of being left by her. Understand that this was to two prime enemies he had at this point in his life. We guessed that Ruby’s male relatives seeing what a coward punk her meal ticket lawyer husband was must have taken her beyond the critical point of putting up with the bad small of a subpar husband, well off lawyer or no. I recently read a piece from a 40s issue of The New Yorker about the Nuremberg Trial that talked about Goebbels escape from execution by taking cyanide indicating that Goebbels was the exception to the rule that all bullies are cowards. Whether Goebbels was or not, Don wasn’t such an exception.    

Pete’s stay at the university in the early 80s didn’t last long. He was a favorite of his students, being the only professor I have ever heard of who received a standing ovation at a final exam, this from three classes he taught engineering thermodynamics to. And he had the highest student evaluations in the School of Engineering at RPI for the ten years they were conducted. But he found his position in the hierarchy and the degree of control over him not that much improved from his days as a graduate student. Ten years of pretty much complete freedom made him a poor candidate for the upper middle class role of a university professor.

So after gleaning considerable pleasure in paying back the four professors who had fucked with him in his graduate school days in various ways, revenge actually improving one’s life and mood considerably as one finds out when one takes it, we went back to a life of anarchy, no rule over you, with all that implies for survival being a true, and somewhat dangerous, adventure.

After two years at the university we devoted all of our attention, outside of survival and the kids who came along, to solving the problem of hierarchical control and the unhappiness it generated, and the problem of violence enhanced by weapons, especially nuclear weapons. From his personal experiences as a street fighter in his younger days, he understood that once a fight starts with punches thrown, the fellow leaning towards the losing side will do ANYTHING to keep from losing, no care as to the consequences since losing is near the equivalent of death.

The translation of this scenario to the world stage is simple and straightforward. If Russia was losing in a war with the United States, would it use nuclear weapons? It has already said it would a dozen times in a dozen ways over the last few years. And if we were on the losing end, truly losing, would we use nuclear weapons to keep that from happening? Whatever a moralist lacking in actual fighting experience might conclude, those who have felt the emotions involved know better. And as to the start of such a fight, where do you think this proxy conflict in the Ukraine between America and Russia is heading?  Certainly not to a settlement at the peace table as ongoing events make eminently clear.  

The culmination of this conclusion unavoidable for anybody who understands violent aggression from a personal sense of it is that only getting rid of the weapons that cause the horrendous deaths and crippling of war can solve the problem. You can’t get rid of violence without castrating all the male members of the human race. We’re already getting close to doing that in America psychology and with not very palatable results other than for the erectile dysfunction medication manufacturers. You have to get rid of weapons to get rid of the mayhem of major violence.   

And in its bringing about a much more equable balance of power between individuals, the total elimination of all weapons in a society most definitely ameliorates the problem of the loss of freedom from excessive social control because, while one man with a gun can control ten others without one, when all are denied the use of weapons, the level of control possible in a society greatly decreases to produce a concomitant increase in personal freedom, which is the most important enabler of success in the pursuit of happiness in life. No freedom, no happiness, as is obvious in this joyous world mankind currently inhabits. To these ends we worked hard to write up and then publish the following newspaper article that directs all men and women to achieving A World with No Weapons.

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Knickerbocker News, Albany, NY, May 1986

 

What would a world with no weapons be like? The blueprint we have in mind is a rough sketch, for details in building a realistic Utopia have to be open to progressive refinement. But this is our first take on it. A world with No Weapons would have to be divided into two sectors, the biggest sector consisting of a large number of city states of about a quarter to a half million people, none of whom would have any weapons at all. This banning of all weapons is not just for the individuals living in it, but for the city state as a whole, including the police, who must in A World with No Weapons enforce any rules a city state wishes to impose on its citizens without the use of weapons. This proviso gives maximum freedom for the citizens of the city state, for as we see again and again in the world today, the wishes of the people in popular uprisings against tyranny are inevitably brought down and the people defeated by police power that relies first and foremost on the weapons that police have and that the people don’t have. This is not to say that rules decided by each city state can’t exist along with punishment of some sort for breaking the rules. But such enforcement and punishment must occur without weapons. There are no guns and no jails in the city states of A World with No Weapons as makes for the true balance in power needed to keep individual freedom at a maximum.

This is freedom in the real sense even if obtained at a loss of order and efficiency. The next broad question is how the ban on weapons would be enforced. It would be done by the second sector in A World with No Weapons, the Guardians of Freedom. Anyone holding a weapon whose sole use is for resolving conflict is put to death. This rule also extends for anybody who uses a tool like a knife in fighting with another person. The maximum weapons allowed in a conflict that can only be settled by force is one’s fists. Any use of a weapon results in a sentence of death executed by the Guardians of Freedom.

Mercy would be shown. And that would be especially to the young. This mercy would be in the form of a reprieve is possible by the rolling of a lucky number in a dice game to be considered in the mathematics section of this work. In it the lucky numbers assigned and the probability of escaping the death penalty that accrues from rolling one of them would be a function of the circumstances involved in breaking of the no weapons law. Invasion of another city state is also punishable by death. Those are the two principle rules enforced by the Guardians of Freedom. The city states decide on all other rules they wish to impose on their citizens, few, it should be obvious, given that the only way to enforce them would be through the muscle power of police who have no weapons themselves.

There is obviously a lot of uncertainly in an existence without rules enforceable by weapons, lots of excitement in it for each person or family or clan or wider group must protect themselves for the most part. But there is also lots of freedom and from our own experience in living the life of rebels, the intoxicating pleasure of freedom greatly outweighs the lack of protection by armed police, too much of whose actions nowadays are unjust and excessive in force as part of their daily routines.

Another great question is: How do you get to this World with No Weapons? For most who hold the advantage of power will necessarily be reluctant to give it up. It is only the consequence of continuing down the deadly path we are currently on that can convince a critical mass of people currently in power to join in this quest. Mankind is heading inevitably for nuclear war, the math that follows this essay and story section will show in an unarguable way. That is why we will be spelling out that fate for man with mathematical precision. If the inevitability of the nations of the world going to that most undesirable place of mega-death without a banning of weapons is not understood, no effort will be made in that direction. Read the math that follows.

This effort must be led by the United States because only it has the moral authority and the military power to make it happen. We have the carrot to offer sensible nations to get them to lay down their weapons with the reward of getting us all to A World with No Weapons and peace that will ensure that mankind continues to live on. And we have the stick to hit reluctant nations with in terms of our military might. Accomplishing this task of saving the world from nuclear annihilation effectively requires a coalition of the leaders of sensible nations who will be the future Guardian of Freedom to come together to effectively conquer the world against all of those unwilling to join in this effort. Winning such a war for worldwide peace absolutely requires the carrot of peace that our mathematics say will come from nations laying down their weapons. If that diplomatic weapon didn’t exist, pure military might could never work to conquer the world for the sake of peace and freedom.  

But, it must also be stressed that military might matters because some nations will not want to give up their weapons and will only do it when there is a gun to their heads or when the trigger is pulled to eliminate them from obstruction of the goal entirely. If this effort must kill a billion to save the other 6 billion, that’s much better than all of us going down in Nuclear Armageddon. My guess is that Russia will join with us once Putin sees that this path is the only alternative to the end of the world; and possibly China, too, though, less certain than Russia. Personally I have absolutely nothing against the Chinese. It’s just that there’s less cultural cohesion between them and us than between us and quasi-western Russia. And frightening were Chinese plans revealed on May 26 in The Global Times - a newspaper regarded as the mouthpiece of the Chinese government. It said: “If the United States’ bottom line is that China has to halt its activities, then a US-China war is inevitable in the South China Sea.” The article added that Beijing does not want a conflict with the US - “but if it were to come, we have to accept it”. This sounds more like a harbinger for war with this nuclear armed country than peace and if anything a further strong piece of evidence for why A World with No Weapons is necessary.  

In that regard the question comes up as to the Guardians of Freedom in the weapons free Utopia having all he weapons and the city states having none. That is unavoidable. History shows a repeated control of territory within grasp by one empire particular empire. There are two dangers that an existing empire must concern itself with. The first is being overthrown by outside nations or empires. And the other problem that concerns the rulers of an empire is revolution from within. In a world that is entirely dominated by one empire or ruling group, the concern about invasion from the outside that is the primary worry of the ruling states of today, like the USA and Russia, does not exist in A World with No Weapons.

This makes a major difference in two ways. It very much lessens the need to enslave the people in the city states under it, very much unlike today where inter-nation stability requires that nations or empires control their people to a significant degree in order to maintain the military and associated economic power needed to protect themselves from conquest by competing nations or empires. The only problem is for the Guardians of Freedom, who are admittedly the rulers of this new social matrix, to retain control over the city states. And that is quite easy given that the Guardians of Freedom have all the weapons and the city states absolutely none. As to those who see this as a scam given that there will still be rulers and the ruled, the circumstances of this social set up make for a singularly novel world situation, whose factors for continued survival are so significantly changed as to make for significant changes in the lives of people. 

To those who want Heaven on earth, it no more exists than Heaven after death. A common sense understanding that we will reinforce with precise mathematical analysis makes clear that the above solution to man’s problems of war and tyranny is the best social matrix that can be devised. Once that is realized, if people are not already so stupidly inculcated with ideology that fails to appreciate the realistic fearful expectations we should all have and understand the limits of hopeful expectation in terms of delusions about the future that distort realistic foresight, they will join together to do their best, all of us, to make this one long shot for the survival of the human race become a reality.  

In the above regard it must be stressed that a major impediment to the clear thinking needed to pull this off is religious delusions about our future. On the one hand, God isn’t going to save the world from nuclear annihilation because there isn’t any God except in people’s infantile hopes that there’s something “up there” who loves us like some all-powerful parent that loves a desperate child. That thought is a near total impediment to we the people doing something real to stop nuclear annihilation. The thought of just wishing it will happen and praying to something that’s not there is not going to save us.

And the second religious delusion as impediment to saving the world is that even if the world does go to hell, all the “good” people are going to Heaven, so who cares if God destroys the world in a nuclear war for whatever Divine Reason He might have. This is banana brained idiocy that lies beyond further comment. If there is nuclear salvation, we the people are going to have to make it happen. For these reasons we make it a point in the mathematical sections that follow to make it clear that the thought of God and the emotional feelings people have about him arise only as an odd fuck up in human nature taken advantage of by the exploiting class over the centuries to maintain their privilege and abuse of the people under them by promising some impossible recompense for it “after death”. This is so stupid that religion should be ridiculed in every guise it manifests itself in. Besides the horror that hides wearing the halo of religion, saving the world unavoidably requires clear rather than childish superstitious thinking  

It is impossible to condemn religion too much. No matter the nonsense by some that bloodthirsty cruel ISIS is not religious extremism, none of those murdering bastards would have done what they did, whether ending 3000 lives and destroying the happiness of 3000 families with the 9/11 attack or beheading young Americans if they were not surged up to do it with the notion that some superior being up there in the sky would make them exquisitely happy after they gave their lives in martyrdom. That this includes the notion of the Allah God giving his butchers each 20 virgins to jump into the hay with does not minimize the monstrous idiocy of Christian belief and the respect it is given despite 10,000 priests and ministers screwing 10,000 nine-year-old boys in the ass and getting away with it. If any other group committed crimes that heinous and that broad a level, the group would be rightly decried as a group of disgusting monsters, and not allowed to continue to exist. The reason that they are allowed to get away with it is because these slimy assholes preach obedience to authority as the centerpiece of the Ten Commandments, aka, the ruling class whose lives are filled with sex parties and other privileges that are equally as disgusting when viewed through the prism of the suffering of families and their children whose poverty in the face of the wealth of our ruling class is a true horror. Religion for all its moralizing turns a blind eye to the true miseries of life and offers the beaten in spirit a recompense of an existence after death that only a madman or a three year old could possibly accept as practically tenable. Short of suggesting that all clerics are deserving of corporal punishment and elimination from the human race, whether Muslim or Christian, all religion should be forcibly flushed down the toilet once and for all. 

I should end this now with a word or two about how things ended up with our Ba-chan. The picture of me with her with the youngest of her three kids up the top says it all. Love, perseverance and knowing who the enemy is make all the difference. 

 

 

 

Now let’s fast forward to the present down in Las Vegas where much of this last edition of this website was written up. This lunatic city is valuable as a microcosm of America in a number of ways. First of all are the casinos. Nobody wins in them, yet everybody plays thinking they’re going to win. Is the inability of anybody to win my idea? No. One owner of a very flashy and successful casino on The Strip said it all on CBS Sixty Minutes. To paraphrase Steve Wynn, never saw anybody come out a winner. Eventually everybody loses.

The reason for this is, first of all, raw mathematics. The odds in every form of casino gambling are in the house’s favor. And the law of large numbers, not argued about in mathematics, says that over time, the casino has to win and you have to lose. That’s not to say you can’t win in the short run. And some people do. But human nature specified in terms of the mathematics of human emotion on this website tell it clearly. If you win with something, the instructions to that brain of yours, quite inadequate to cope with the statistical nature of gambling, tells you to go back and play again. And the law of large numbers takes over. And you lose. You just do, and even more what you first one because your stupid brain has to be taught the lesson of a significant loss before it gets the picture.

Assisting in this clockwork fleecing is a generalized form of propaganda that we’ll get into later mathematically that is the other leg of brain washing. The first was how insignificant things could be made to be significant by outsizing and repetition, like the possibility of winning in a casino as paraded with the big wins that happens every once and a blue moon. The other has to do with associating positive emotion with casino play in a general way. That emotion is excitement. Normally, if you win at something difficult or uncertain, it is exciting and as made clear in Section to on the function of the transition emotions, excitement leads to confidence in winning in future efforts of the same kind.

But excitement can also come about in an indirect way via communication with others. Nature set you up this way because if someone close to you wins at something and shows excitement, by smiling, by dancing about as TV contestants do instinctively on game shows, by singing, you get excited too. And alcohol gets you artificially excited, which is why they give it away for free in casinos. And music gets you excited. And girls with their skirts hiked up close to their privates get the males who make up the bulk of gamblers excited. All of this artificial excitement tells your stupid brain, which then conveys the message to your stupid mind, that good things are about to happen.

Made insignificant and in sharp contradiction to all the smiles and laughter and such seen in every form of publicity for casinos are the frowns of the losers, and the incessant run of suicides by jumping off the roof of the Golden Nugget Casino’s parking lot, and the like. Information in, behavior out. Bad information in, bullshit propaganda, bad behavior out.

And you have to see the people who play to understand why they play. These are not James Bond and Ms. Pussywhistle playing at the slot machines. These are unattractive people, who play and hope to win as part of their general spectrum of delusional expectations in life. If they don’t have the delusions, they feel as bad as they look. And you don’t have the delusion of winning at casino gambling unless you do it. It’s a con game, pure and simple. And the biggest losers in a con game are those who are desperate for some kind of success in their loser’s life. Religious delusions of happiness after you’re in the casket are very similar in kind to gambler’s delusions. And their promulgated in the same way, by making meaningless things appear to be meaningful with the usual bag of propaganda techniques, the ones we’ve just gone over. The choir in the church balcony is singing to you the message that all here is happy and bright, have confidence in the promise of God. It’s really no different than the function and consequences of the upbeat never ending music in casinos. Hey this is a happy place. Put your money down and win the equivalent of happiness for eternity, enough money by fortuitous gambling to never have to worry about it again.

And this is exactly what life in capitalism is about. Great promise, and no discovery of the promise as a false promise until you’re too damn old to do anything about it. Which is why all the casino players, the youngest crop of adults who play from natural youthful enthusiasm tricked excluded, look so damn ugly. And why adult Americans past the glow of youth look so damn ugly in reality. The entirety of TV programming is a con game. The endless excitement; the endless old “song and dance” to make you think, hey you really are in the Garden of Eden. Just be a good boy or girl and you’ll wind up with a smile as bright as the plaster smiles placed on the professional actors and actresses who make up the news corps and the characters in all those dramas that have little to nothing to do with the dramas that murder people’s spirits clockwork in workaday reality life.  And make them look very ugly by the time the beginning of middle age sets in.

Anyway it’s all clear in Las Vegas, not just how you’re robbed of your life and its potential for happiness with tricks and games, but also the end consequences of the false promises and the delusional behavior it drives. That’s easy to see if you ride the city bus in Lubbock, the one that the working people, not the tourists ride on. All you see, accent on the word, “all”, are miserable people. They’re miserable in the way they look. And they’re miserable in the way they feel. Oh, and yes, this shows so much in the way much of this misery is expiated through redirected aggression, meaning that the misery flows rapidly wherever and whenever it can from one miserable person to whomever is vulnerable to its reception.

Black on white is clear as a bell down in the lower echelons. Black people, real black people, basically hate white people because it’s white people who basically are the ones that fuck them over in the broader institutional power structures in America. The association of “my source of pain” for a black person with a white face is simple Pavlov conditioning. Now you think that I’m a bleeding heart in all I’ve said so far against the conservative assholes. But reality is what’s important, the pain and the hate out there. And I’ll make that clear in two very real, very personal stories that happened to us when we were in Las Vegas. The first was an episode of what happened on the bus, the Las Vegas RTC, to Pete. I’ll let the note he emailed to the RTC, which was never answered, speak for itself.  It’s a bit tongue in cheek here and there as any letter to an uncaring institution has to be, but the crux of it is 100% true.

Dear RTC: I flew down to Las Vegas from New York on business and have reason to frequent UNLV up on Maryland Parkway. After minor shock at the daily taxi fare to UNLV from and back to Fremont St. where I’m staying, I had the pleasure of making acquaintance with your transit system, as things turned out not very pleasant at all. The inconvenience of the crowds is one thing, something a New Yorker is used to, but to have the potentially dangerous experience I had this morning on one of your busses, another thing entirely. I’m going to spell it out in the detail it deserves. Please bear with any seeming intermediate trivialities.

I found out I qualified for reduced fare as a senior citizen and always show my ID by holding it very visibly with my thumb above the RTC card when I swipe it. Drivers can’t and haven’t ever missed it, until this morning. When I got on the BHX bus (# 845) today at 6:55AM at Fremont a couple of miles from the Casino section, the driver, a black fellow, that fact not incidental to the what happened, was in the middle of a chat with a passenger, another black fellow, and took no notice of my reduced fare ID, which as I said was unmistakably obvious had he been looking at me swipe my card instead of talking to the passenger. So he stopped me as I walked past him by shouting out for me to show him my reduced fare card. I turned back and said as I held up the RTC card and the ID together, “It was on my thumb.” Couldn’t be missed. “I didn’t see it,” he replied. No problem here. People make mistakes, this one totally minor.

But the black fellow he was talking to me touched my shoulder as I walked back to my seat on the bus and said something to the effect that I better be cool. My reply as I went back to get a seat was, “Don’t touch me.” I’m old enough to know that sticks and stones can break my bones but words alone can never hurt me. But touching is in the category of sticks and stones, and potentially dangerous, a forewarning of worse possibly coming, which is why battery or touching is a crime. This fellows’ response to my resistance to his touching was to race back towards the rear of the bus where I was seated and standing over me six inches away shouting, “My daddy just died two days ago, and I’ll kill you, motherfucker, if you give me any trouble.”

Now it is important to make clear that I am generally cognizant of and sympathetic with blacks in their underdog position in society. Had your RTC contact format allowed for it, I would have included newspaper articles that make it clear that I have been a civil rights and peace activist all of my life. Indeed I was a primary speaker at a rally for Trayvon Martin in Las Vegas a few years back, videoed on YouTube. And one of the OP pieces that shows my liberal bent is on our mathematical sociopolitical website.

So I was able to reckon that this fellow, whatever his level of violence, considerable, was quite nuts at the moment, and maybe with understandable reason. And I gave out a sentence or two of sympathy to cool things down, though adding as I took out my cell phone, “If you touch me again, I’ll call 911 and have you locked up.” That was enough to get him to back off and return to the front of the bus next to the driver. But amazing is what he did next, turning his fury deflected from me to this old man white passenger sitting in the seat closest to the front of the bus and the bus driver, all of which was impossible for the driver to miss. The black fellow’s words to the old man were unmistakably racist, hateful and violent. But, as I said, who cares about words, especially in nut town Las Vegas (at least my estimate of your fair city that circumstances have forced me to be in again.) What was horrible to watch, though, was that this black guy started grabbing the old white man by his nose and his ear as he cursed him repeatedly.

Now my complaint to you isn’t about this unfortunate black fellow, whatever misery in life, present and past, drove him to his dangerous behavior – also dangerous for him given his shouting out in the middle of his ranting that he was on probation and didn’t “give a fuck” about what anybody might do to him in that regard. My complaint is rather about the driver, a coward it certainly seemed, or even something worse for not respecting the plight of the poor white bastard or the four or five onlooker passengers who were shouting to him at this point to get the guy off the bus. No effort was made to that end. All the driver had to do was stop the bus and tell the guy, “I’m not going anywhere until you get off the bus and if not, I’ll call in security. Nothing was done anywhere close to that. Let me emphasize that that the level of curses, threats and mayhem was such that the situation would have been apprised by any objective observe of this real life movie scene as potentially very dangerous.

Recognizing this, I jumped off at the next bus stop in the Casino area instead of proceeding directly to the UNLV Law Library via the Bonneville Transit Center and the #109 bus. By chance walking through the intersection of Fremont and Las Vegas Blvd. I encountered an RTC cop I quickly told the story to. He pulled out his phone and said he’d call the Transit Center to notify them of what happened and possibly do something about it if he made contact on time. I then cooled my heels with a cup of coffee in one of the casinos for an hour or so and got back on the bus to get to my originally intended destination. While back on the bus, I ran into another RTC cop who was also sympathetic and who directed me to a supervisor at the Transit Center to file a complaint.

I was hoping to hear and thought reasonable that the driver would have immediately told one of the handful of RTC cops you usually see at the Transit Center about the incident, which was clearly criminal, and minimally had the perpetrator, who was quite off his head and possibly on drugs, to cool it down. That was not the case. And the supervisor I spoke to, also black if that matters, bordered on curt in his reaction in telling me that he had heard about the incident and already reprimanded the driver, not interested in what happened to me including the death threat, as though there was really nothing to it and what was I making such a fuss about.

The rest of the note and the lack of any reply by the RTC transit system is irrelevant. What is relevant is the degree of hate between people that sits on the end of a hair trigger. Well, you say, big deal, who cares what could have happened. All that id happen was some non-fatal slapping of one guy in the face by another on the bus and a black driver doing nothing to prevent it or punish it. And maybe that’s cool, the real point being the enormous amount of random violence going about that is impossible to even guess at it from the endlessly smiling faces on TV who endlessly make out that life is nothing but a bowl of cherries, past, present and future. Ok, let’s try the next story, which was not incidental and at a distance from us. Well, again, it wound up in a letter written by Pete about it, this time sent to the Las Vegas PD, that I’ll let speak for itself.  

Dear Las Vegas Metro Police,

My wife and I are on our way out of Las Vegas as I drop this note in a mail box, happy to be leaving. If my interpretation of the events I’ll relate is emotionally excessive, please excuse. But it is better to err on the side of caution.  These are strange and dangerous times.

We have been down here for the last five weeks, not for gambling but interacting with academic types including Dr. Kathy Robins up at UNLV.  We wound up staying at the Siegel’s Suites on Fremont and 15th, not because I’m poor or like “slumming it” but because I’m severely asthmatic, doubly dangerous at age 71, and this Siegel’s place has tile floors rather than the rugs that every other hotel in Las Vegas has that I can be super sensitive to asthmatically.

The very nice woman who manages the place, Sharon, will corroborate any of the odd parts of what I’m saying concerning my asthma if you ask her. She went out of her way to set us up when we first got here with a room easy to breathe in. We ran into her and this place by chance a year or so back during an asthmatic episode on me that came out of the blue when I was staying at one of the casino hotels. 

Off to the side of my having a PhD in Biophysics, I am also a lifelong political activist. If you check out these two Op-Ed pieces I wrote in years past, it will be clear that I am anti-violence and also pro civil rights and against police brutality against minorities. As to why I am giving you this background, the studio apt. at Siegel’s next to ours, Room 216, had a class of people in it I was not familiar with and that nobody would want to be. Lots of noise, swearing, loud music late at night and so on. If they weren’t using drugs regularly (though to be honest I never caught any smell of marijuana) they must have had a special instinct for whoops and hollers come the late hours.

I tolerated it because asthma at its worst feels little different than suffocating from waterboarding and this room was health-wise pain and stress free. Staying there I did not use my asthma medicine at all the entire five weeks we were in Las Vegas. As Sharon will tell you if you ask, the window in Room 217, our place, was missing, not the screen, just the glass window. The only room available in the place the day we got into town was this one, no window in it. But we took it because the fresh air flowing in constantly is positive for my condition. The point of my bringing it up is that the missing window had me hearing just about everything from next door when their door was open, which was often, and when they were outside, which was very often.

I should mention that the principal person in this room, possibly the leader of a gang (?), is a very large black guy always dressed almost in a uniform consisting of a totally white pullover and a distinctive kind of cap he wore even when the weather got warmish.

Anyway it was the night after the news broke out about the two police officers shot in Ferguson. These guys (some of them we heard often might just have been frequent visitors to the room rather than residents) went nuts over the shootings. There was no doubt about this from what they were shouting out to each other about feeling great over what happened. But this was also likely with a million other black guys of this type around the country, so nothing special about it. What got to me sharply, though, was a phrase that popped out unmistakably no less than three times during the evening - “gonna get one of these motherfuckers myself.”   

Now I want to make it clear at this point that I heard nothing of any plans to do anything tangible. So there was a good chance that those words came out only to impress each other. I should make clear that I have as little prejudice towards blacks as any white in the country. I just don’t. I spoke at a Trayvon Martin rally right here in Las Vegas a few years back. In fact it was hosted on the business property of a black woman Metro Police detective, also a hairdresser, who said she was the daughter-in-law of the first big city black mayor in America, Carl Stokes of Cleveland. I think her name was Dorothy, Dorothy Stokes, but it was a while back and I’m not entirely sure of the first name. I’m sure she must remember me and how much I was on the side of oppressed blacks. I talked with her head to head for more than a few minutes and then spoke publically to all the blacks there about the need for a political process to get justice for Trayvon Martin.

That is to say that there is no way I’d exaggerate what I’m saying, and perhaps when you check things out with the black guy in Room 216, you might find out that he was, in fact, just a loud mouth punk with no real intentions. But to hear people talking about murder, whatever the level of real intention, sent real chills up my spine. Actually did. This is just a few days back. Talking it over with my wife I didn’t think I could live with myself if I saw on the evening news in a week or two that cops were murdered in Las Vegas in an ambush or something, and possibly because I said nothing. Whatever happens next, at least, with this note, my conscience is clear.

Sincerely,

What precipitated this letter in all honestly just wasn’t the hard facts of what we heard. Pete actually did think that it was all bluff and bravado mainly because he sensed the main guy in the story as a genuine punk, a faker, a faggot of the predatory kind, a bully and too much of a loser in life to ever try anything like killing a cop other than shout out words about it to his buddies. When we first moved into the place, the thug was right on the scene parading in front of our window and shouting out motherfucker this and motherfucker that to this friend up on our second floor tier or down to the street below. Was he doing it on purpose to get to us well groomed white people whom he thought he could screw over?  Or was this just life in the ghetto that everyplace in Las Vegas not part of the tourist casino scene more or less is? Well, having more important things to do like try to save the world from nuclear annihilation and with hairy mathematics no less and also trying to convince small minded scientists up at UNLV of the correctness of our science, we opted for an intermediate disposition that while the jerk could have been trying to intentionally get on our nerves, it was better to pay him no attention and just stay at a non-responding distance from him.

Then as fate would have it, avoiding came to an end by chance when Pete came back from UNLV walking through a narrow corridor at the same time this Porky Pig fellow was coming in the opposite direction. Pete gave a polite “pardon me” and moved to the side as they closed in while Porky addressing Pete as “sir” made little effort to do the same. Cute. This was a cute bastard. And that was followed up by Porky walking past our window not two minutes later, with a string of loud screeching motherfucker this and that. And at that point he began to get on Pete’s nerves, be worrisome, in his life, in our lives. The evening hours certified the problem as real as the music post 11PM was too loud to get to sleep by and Porky’s walking back and forth in front of our window repeatedly with the music blaring was as unsubtle a subtle threat as could be constructed by a cute bastard.

Now despite Pete being 71 and Porky somewhere around 31 and at least 100 pounds bigger and five or six inches taller, Pete put on his pants and opened the door intercepting Porky in his walk back from our place to his. While he didn’t say it with excessive politeness, for the situation didn’t call for a Miss Manners approach, Pete’s request/demand that Porky turn the music down wasn’t all that impolite. Porky thought otherwise.

Porky: “You disrespecting me, talking to me like that!”

Pete: “You’re disrespecting me and my wife playing the music like that.”

Porky: “I’ll fix your ass soon enough.”

Pete: “You make the next two plays and I’ll make the final play.”

And with that Pete shut the door. The next two hours were rough, at least from a noise and threat perspective. Whether they came from his room or from the neighborhood, every quickly there were four or five thuggish voices and the insults and threats were anything but subtle. I wasn’t sure what Pete’s “final play” would be and neither was Pete. The words just came out of his mouth that way, in a spontaneous way, for he was a spontaneous person, with a kind of like a talking animal personality. But you could never tell with Pete. Many years before that, we had a problem with a landlord who eventually brought a new tenant into the building who was extremely aggressive. Dickie Yadoo started parking his porch chair right out in front of our bathroom window, getting right into our life not unlike what Porky was doing. Dickie was muscular and looked very thuggish, so Pete just twisted in the wind for a couple of days all tightened up like a ball of string with a tangle of knots in it. Then Dickie brought in some relative and his 11 year old kid who went into the backyard and made our two year old still in diapers start crying. Pete went bananas and picked up a red magic marker and went up to Dickie’s 2nd floor porch and wrote FAGGOT on the vinyl covering on the chair in big letters. 

Sure enough Dickie Yadoo came down and they met on the porch, Pete rushing him and almost throwing him over the railing. By the time the fight ended, Dickie conceding, Pete had pretty much ripped his eyes out, for Dickie had two streams of blood rolling out of his eyes, something I never saw or heard of before. When the cops came, they reassured us that we didn’t have a problem with them. They told us that they just wanted to know who had whipped Dickie Yadoo, a known thug for hire in town, so bad that he’d even think of calling them.

So you never know what Pete might do. And neither did he. The next day was bad for him, he told me when he got home, because Porky was on his mind all day. Then just before he got on the bus to return home, he said he started worrying about me. And that got him to go a bit mad with anger. He said he started clenching his fists and biting down hard on his teeth and shaking uncontrollably on the bus like when he was a kid and angry. And the thought came through his mind that he could take Porky despite their age, weight and health differences, that he got determined to kill him if it came to it. By the time he came inside he looked not unlike that time with my brother, Don, out at the winery, like a murderer set on murdering somebody. But instead of doing the next step physically, he went for Porky’s throat by writing out that letter to the Las Vegas police. And that calmed him way down.

Now the point of this story, at least one that’s meaningful in the context of the larger problem the world has in terms of its near universal unhappiness and violence, is that when men are pushed far enough in the wrong direction, they don’t care about consequences. Pete would have thrown the punch, whatever the consequences, if that’s all that remained that could be done. He didn’t care about consequences. And you see that a lot in the world today if you care to look closely enough not to dress it away with psychobabble. Past some point angry people just don’t care about consequences, including those with nuclear weapons in their hands. Man has to rid the world of weapons before the weapons rid the world of man.  Lousy fag bastard, hope the cops break every bone in your body.

 

16. Waiting for the Bomb

It’s near impossible to interest people in the coming of the end of the world, let alone trying to do something about it. For us the frustrations are also personal. In our seventies now, this has been the focus of our life’s efforts. The hypothesis is simple and quite precise even when expressed in non-mathematical terms. Human aggression, particularly in males, is an ineradicable instinct dictated by the evolutionary demand to optimize survival from generation to generation. This propensity to aggression is obvious in history’s never ending warring, in the daily domestic violence and murders seen in the news and even in the endless attention given to sports aggression. And whatever aggression comes about naturally from evolutionary factors, it’s made all the worse from the unhappiness of man that arises from social control expiated by violence on innocent vulnerable others as redirected aggression. And that is made worse yet by mankind’s development of super-lethal weapons up to an including nuclear weapons.

But our shout for the last thirty years as peace activists that our worst fearful expectation of nuclear war is eventually going to be realized unless weapons are expunged from the planet has been ignored. This is also part of human nature for people pretty much instinctively ignore impending disasters they don’t think they can do anything at all about. And this blind man’s attitude toward coming nuclear catastrophe is made all the worse by its being made to seem insignificant from its near absence from main stream media considerations.  

We recognized this back 30 years ago when we stated in our Weapons Ban newspaper article that nothing would be done until the first world leader with access to a nuke went emotionally over the brink to use it. Of course we hoped for better, hoped that somehow the message of the need for a weapons ban might be received so well wrapped in a firm mathematical analysis that some initial nuclear detonation would not be needed to wake people up to the need to rid the world of weapons before the weapons come to rid the world of all its people. So while our work developing the mathematics that explains man’s emotional nature at the heart of the problem has been very satisfying as pure science, reaching people with it to make clear the more meaningful problem of potential nuclear annihilation has been nothing but decades’ long frustration as we enter our seventies now. Quite exhausted from the lack of response to our efforts, hence, we are just sitting back and waiting for the bomb. We’ll spend the rest of our writing time dotting a few i’s and crossing a few t’s we might have missed. 

The media does well hiding the visceral horror of our endless domestic mass murders and of the world’s endless wars by hiding images of the blood and body parts of victims including our own soldiers, their torn apart bodies never being shown to the public. But a nuke dropped and a million killed in a flash will not be able to be hidden by the media. And then people will understand that if A World with No Weapons is no achieved there will be no world left for any people to live in.

This thought was paramount as we fled Las Vegas and landed in a relative paradise far from Hate City where we are just nursing the normal wounds of aging and passing time waiting for the bomb. It is an odd strategy, effectively betting what’s left of our lives on our hope of a nuclear detonation that will happen before Election Day, 2016. The lead players in this statistical prediction are Israel dropping a nuke on Iran or Putin one in an open field in the Ukraine to let the West know that Russia will not put up with encroachment this close to its borders. And let’s not forget bit player North Korea as the pit bull on a leash of ever increasingly militaristic China. And one never knows what nuclear armed Pakistan and India will do in their endless strife that without fail comes to murder a few dozen citizens on each side every year.

Something should also be said about our newfound fear and dislike for black people. Our bad experiences in Las Vegas just grabbed hold of us emotionally. It is a distinctly uncomfortable state for people who have been mega pro civil-rights all our lives, impossible for us to not empathize with the ugly oppression and travail of blacks in America. Indeed, we actually were primary speakers at a Las Vegas Trayvon Martin rally, the only whites that day. But effectively threatened with destruction in an obviously hateful way intuitively makes you very wary of blacks who harbor a generalized hatred of whites from the generations of oppression put on them up to and including the current cluster of unwarranted police killings of them.

People have to come together to understand what their common oppressor is, the current power structure up at the top. And they have to understand the ultimate common problem we all have, the possibility of nuclear annihilation if we don’t get together and act together. It’s so important that we all tamp down our instinctively driven petty hatreds of each other. Whites, other than the wealthy powerful ones who gain from everybody else’s pain, are not the enemies of blacks, nor are blacks the enemies of white working people, though both realizations can be emotionally difficult especially for people on either side of the game who have felt the sharp bite of the other. We hope this impediment to collective action is overcome once both races realize the common problems and enemies they have. Our Las Vegas story and the feelings we experienced in it are laid out exactly as we experienced them to make clear just how powerful these racial antagonisms can be from bad personal experiences. We hope that as time passes, a few months, the worst of our bad feelings will pass and that we’ll be able to take our own advice, for any possibility for common salvation lies in the many victims of mass aggression shaking the antagonisms the ruling class sets up between us and loves to see keeping us separate and at odds with each other.     

I’d also like to make clear my attitude towards homosexuals. Certainly there is no way that depriving them of their basic civil rights should be excused or tolerated. But it is equally absurd to fail to see homosexuality as what it is most basically, a consequence of reproductive failure that comes about primarily not by genetic aberration but developmentally from the excess social control I’ve been talking about from the start. This, of course, will be argued against by critics of A Theory of Epsilon as being unscientific, but the so-called data used to argue homosexuality as inescapably genetic is as mythical and misleading as the data that shows lower black IQ to irremediably arise as a cause of inherent black stupidity from the genetic makeup of blacks.

To argue this I’ll report and explain some very firm mathematical data about homosexuality whose conclusions are impossible to avoid. Younger brothers in a family have on average, as measured from a statistically significant sample population, a one third greater frequency of homosexuality. This is an unarguable fact. A second born brother has a one-third greater chance of becoming homosexual than the eldest brother; a third born brother has a one-third greater chance than a second born brother; and so on down the line. These numbers cannot be spun or dismissed as irrelevant.

Any male who has brothers, be he an older or a younger brother, understands the obvious that older brother/s are generally dominant to the younger one/s. And conversely younger males in a family strongly tend to be subordinate to the older ones. The Boston Bombing case, which has nothing to do with gay men, illustrates this characteristic of older brother dominance in a clear way. Nobody who thinks objectively can fail to see that of Tamar and Dzhokhar Tsarnaev, the older brother was dominant to the younger. And that is utterly obvious even if one chooses to excuse in any way the behavior of the younger brother. That is but one of a million examples of older brothers being dominant to younger ones quite independent of the issue of sexual orientation.  

Dominance and sexual behavior, however, are, generally speaking, not independent of each other. This is clear between men and women. In the arena of heterosexual sex, personal experience overrides silly exhortations of the ideological notion of perfect equality between the sexes as it relates to women in the labor force. A woman not at least somewhat impressed or dominated by the élan and vigor of a guy suitor does not turn on to him sexually. The evolutionary argument for this is obvious and observed in all mammals where the males are larger and stronger. There is always some form of at least ritual struggle between the female and the male; and the male who loses in it is shooed away by the female. And this fact of male dominance as a propitiator of sexual arousal should also be obvious in the absolutely bestselling erotic book of all time, “Fifty Shades of Grey” making it clear that women being dominated to a significant degree is an instinctive  prompt for sexual acquiescence.

Taking this clutch of ideas together, the dominance of older brothers, the undeniably higher incidence of homosexually in the dominated younger ones and the notion of sexual arousal from social dominance as a significant factor leads to the conclusion not, it must be stressed, that older males make homosexuals out of their younger brothers, but that male dominance generally is a significant factor in the making of a male homosexual. That is, that sexual seduction of a male by another male goes hand in hand with dominating behavior by the former, this as opposed to same sex relationships somehow coming about strictly from some mutant thread of DNA.     

And add to that another undeniable fact of the generally excessive subordination of males in our Goebbels society that develops American men now more and more with subordinate female personalities and you are quick to catch the primary cause of male homosexuality in such female-type men both being unable to woo females successfully and in their being susceptible to sexual dominance by other men.

In agreement with this perspective is the firm fact that every professional biologist knows about, namely that expression of a gene is generally very much dependent on the environment of the developing organism. A most telling illustration of this lies in the formation of feathers on the legs of baby chicks as grow in a chicken egg. People with enough brains to accept evolution as scientific fact understand that all birds including chickens descended from dinosaurs, their lizard-like evolutionary ancestors.

The egg the chick develops in has a certain concentration of calcium ions. With the normal concentration of calcium, the growing chick develops feathers on its legs normally. But if you increase the egg’s concentration of calcium ions with an injection of calcium chloride, the chick develops lizard-like scales on its legs from its dinosaur ancestry instead of chicken feathers. This is only one of a million illustrations of genetic expression being dependent on the environment of the gene that can be cited. And, generally speaking, the more complex the anatomical, biochemical, physiological and/or neurobiological characteristics of the organism that come about from a gene, the greater the weight of the environmental effect on the expression of the gene.

The conclusion of a purely genetic causation for a trait as socially complex as homosexuality is poppycock, such a perspective being useful only for hiding the true origin of homosexuality as a substitute for reproductive sex by those males in a population inclined to fail at such because of the position of males as wage slaves and/or by their parents, obedient wage slaves themselves, raising the boys in an over-obedient emotionally unhealthy way.

This is not to say that homosexuality is a “choice” that a gay man can make either way as the religious goofballs insist on. But rather that it is, once firmly developed in a male, an emotionally unavoidable behavioral propensity that is as difficult to choose not to do as the pleasurable gross overeating of the millions of obese people who die fat whatever might be their inclination or “choice” to do otherwise.

The worst in all of this are homosexuals who have power over weaker males and can effectively seduce or emotionally rape them. There’s neither sense nor fairness in denying homosexuals basic civil rights. But incaution on the part of young men from this current American culture denying the cause of the lesser sociosexual achievement of homosexual union as the result of exploitive subordination is equally without sense and fairness to young men who, from an evolutionary perspective should be willing to fight, indeed to the death if necessary, to preserve their honor and reproductive competency. Be wary, my boys, whom you submit to and for what reasons as you approach adult life. The oft used phrase, “protect your ass,” should be taken literally.

Now let’s start to work our way through a number of mathematical explanations of various aspect of human nature to fill in the big picture as completely as possible. To show that our emotions are information for us in the sense of their being described mathematically by diversity functions we made clear earlier were measures of information, we next want to develop the probability component of the emotions as with the Z of E=ZV of Eq106 and the U of E= –Uv of Eq90 as a function of diversity indices. We do that by developing a matrix basis for the D diversity index. This exercise also provides a super-clear explanation of the most basic foundation of how the mind works by making distinctions between some things and sensing others as being the same. 

The D Simpson’s diversity index of Eqs3&16 is an excellent measure of the diversity in a set in terms of the N distinguishable subsets counted in the set as the prime variables for diversity, the N more of subsets there are in the set, the greater the diversity of the set. It is seen, though, that the D diversity index has one shortcoming in this regard and that is in its specifying the diversity of a uniform set, like the all red, N=1 subset, uniform set, (■■■■■■■■■■■■), as having from Eqs3,13&5 a Simpson’s diversity of D=N=1, which does not fit our intuitive sense of there being no diversity or zero diversity in this (■■■■■■■■■■■■) uniform set or in any other uniform set. This problem is readily resolved, though, with a simple variation of D that we will call the Exact Diversity Index, L,

277.)                                 L = D – 1       

The L Exact Diversity Index, also called Number Information, has an immediate advantage over D in its specification of the diversity of uniform sets like (■■■■■■■■■■■■) as L=D–1=0 as fits the zero diversity of a uniform set. And L has a couple of other very fundamental properties that make it special as we’ll see. Consider L for balanced sets like the N=3, (■■■■, ■■■■, ■■■■), set whose L value is from Eqs277&5, L=D1=N1=2; and the (■■, ■■, ■■, ■■), N=4 balanced set with  L=D1=N–1=3; and the N=8, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), balanced set with L=D1=N1=7. In general, for any balanced set, from Eqs277&5,

278.)                             L = N – 1 

Now we will see that L for balanced sets is not only a measure of their diversity but also of distinction. In the N=4, L=3 set, (■■, ■■, ■■, ■■), we intuitively distinguish any one of its N=4 subsets from the L=N–1=3 other subsets in the set. Hence L=3 for the (■■, ■■, ■■, ■■) set is the number of distinctions that any one subset has in the set from all the other subsets. And we see the same for the other balanced sets, (■■■■, ■■■■, ■■■■) and (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), in their L diversity index being a measure of the number of subsets that any one subset in the set is distinguishable from.

Next we’ll make the point that L diversity, aka L number information, is truly a measure of information from the perspective that it is a measure of the distinctions between subsets in a set, which are commonly understood as information for us. Consider 4 apples on a table, which when seen at a distance are sensed to be all the same variety of apple, but as they are approached more closely they come to be seen and distinguished as 2 Macintosh apples and 2 Delicious apples. This distinction in kind or variety of apple that comes from closer inspection of the apples is readily understood intuitively as information for the observer about the apples. In that way we understand L diversity to be as a measure of distinction a measure of information. This perspective also bolsters the synonymy between diversity and information we developed in a number of sections in the foregoing.

The sense of L as distinction and, hence, as information is further bolstered by showing L to be a measure not only of the distinctions between the N subsets of a set but also of the distinction between objects in a set such as between the different colored objects in the K=6 object, N=3 color set, (■■, ■■, ■■), (2, 2, 2). As this set, (■■, ■■, ■■), is a balanced set, L=N–1=2. We can show its L=2 to be a measure of distinctions between the different colored objects in the set by comparing all K=6 objects in the set to each other in a systematic way with a comparison matrix as shown below.

 

 ■

 ■

 ■

 ■

 ■

 ■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 279. The Comparison Matrix of (■■, ■■, ■■)

 

Note that out of K2=36 comparison pairs in the matrix, we count Y=24 distinctions or pairs of objects with different color like . And we count ε=12 samenesses or pairs of objects with the same color like ■■. The symbol, ε, is the small case epsilon. For this comparison matrix and for those of all sets of K unit objects divided into N subsets, because a comparison pair of two objects must be either a distinction or sameness,   

280.)                                 Y + ε = K2  

Next note that the ratio of Y distinctions to ε samenesses, Y/ ε, obtains the (■■, ■■, ■■) set’s L=2 diversity index. 

281.)                                     

This relationship is valid for all sets, balanced or imbalanced, and can be written via Eq280 as

282.)                                 

This makes it clear that L diversity is a monotonically increasing function of the Y number of object distinctions for constant K and, hence, is a measure of object distinction as reinforces our understanding of L diversity as information given the synonymy of distinction and information illustrated with our Macintosh and Delicious apples example. It is worthwhile to show that Eq282 also holds for the general case that includes unbalanced sets. For the K=6, N=3, (3, 2, 1) unbalanced set, (■■■, ■■, ), that has x1=3, x2=2 and x3=1 we see from Eq16 that its D diversity index is D=18/7=2.571 and from Eq277 that L=D–1=11/7=1.571. The comparison matrix of (■■■, ■■, ) is displayed below.

 

 ■

 ■

 ■

 ■

 ■

 ■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 283. The Comparison Matrix of (■■■, ■■, )

Out of K2=36 comparison pairs, we count Y=22 object distinctions and ε=14 object samenesses as obtains L=Y/ε=22/14=11/7=1.571. The proof of L as the number of subset distinctions is also straightforward but a bit more tedious and too off the track from our main considerations to detail here, that proof left to the mathematically savvy reader.

Note next that the D diversity index is also a simple function of the matrix variables K, Y and ε from Eqs277,280&282.

284.)               

Two related matrix functions are important to understanding emotion as information. These are the fractional or density measures of the Y distinctions and ε samenesses in the matrix. To the former we give the symbol, U.    

285.)                 

The distinction density, U, is also referred to as the uncertainty from a matrix perspective that will be clear shortly. For the balanced (■■, ■■, ■■) set, whose matrix in Figure 279 counts Y=24 distinctions out of K2=36 comparisons, U=Y/K2=24/36=2/3=.667. And the sameness density of a set is

286.)                                          

For the balanced (■■, ■■, ■■) set whose matrix in Figure 279 counts ε =12 samenesses out of K2=36 comparisons, Z= ε /K2=12/36=1/3=.333. The reader will recognize U and Z as the probabilities used in the extended emotion analyses of Eqs84-241. How they come to be such from a matrix perspective is seen in the following interpretation of the comparison matrix of (■■, ■■, ■■) of Figure 279.

  

 

 ■

 ■

 ■

 ■

 ■

 ■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 279. The Comparison Matrix of (■■, ■■, ■■)

 

This comparison matrix provides a measure of the guesses of which color of object is randomly picked from a bag of K=6 objects, (■■, ■■, ■■), and a measure of the color of the object that is actually picked. It provides this by understanding the (■■, ■■, ■■) set on the horizontal axis of the matrix to be the average color outcome of picks for every six picks taken, two picks of each color; and by understanding the (■■, ■■, ■■) set on the vertical axis of the matrix to be the average of six guesses of color when the guesses of color are equiprobable, that is, with no one color preferred to be guessed over any other color because of the equiprobability of the color outcomes as displayed by the (■■, ■■, ■■) set on the horizontal axis. 

This interprets the Y=24 object distinctions in the matrix as incorrect guesses, as with the distinction taken to be green guessed, red picked. And it interprets the ε=12 samenesses in the matrix to be correct guesses, as with the ■■ sameness taken to be green guessed, green picked. Now we see that the fraction of correct guesses in the matrix, Z=ε/K2=1/3=.333, is when projected to future guessing the probability of making a correct guess; and that the fraction of incorrect guesses, U=Y/K2=2/3=.667, is when projected to future guessing the probability of making an incorrect guess, or, equivalently, the uncertainty in making a correct guess.   

There are a number of insights to be developed from this. One is that the human mind operates in many of its modes in terms of the distinctions it makes between things (or doesn’t make as its sense of sameness.) Such distinctions and samenesses are not limited to the colors of things or other markers of things that make them out to be different kinds, but also includes, as developed above, the distinction we intuitively make between a guess about an outcome and an actual outcome different than the guess, as defines an incorrect guess. And similarly the mind meaningfully recognizes sameness not only between things in our sensory field but also as between a guess about an outcome and an actual outcome in agreement as a correct guess.

This most elementary cerebral determination of incorrect guess via distinction and correct guess via sameness is extremely general and extends also to our sense of success in a goal directed effort. When the outcome of an activity is the same as the intended goal, the activity is successful; and when the outcome of an activity is distinct or different than the goal intended, the activity is chalked off by the mind as a failure. In that vein all of the emotions we developed from rolling a pair of dice with the intended goal of getting a lucky number applies to all goal directed behaviors, which  including but is not limited to guessing a right answer as one’s goal.      

This insight further suggests that the emotions we developed for goal directed behavior from the Lucky Numbers game are in being most essentially probability functions like the expectations, E=ZV and E= –Uv, information, for the probabilities associated with the emotions are simple functions of diversity as we just showed above. More specifically, note carefully that the Z probability of guessing the color picked from the N=3 color balanced set of objects, (■■, ■■, ■■), is from Eqs284&286, the inverse of D.

287.)              

 

This gives the sense that as D is an information function as diversity, which we have argued in the foregoing, so also is Z probability as this simple Z=1/D function of diversity. Indeed those familiar with Edward Hugh Simpson’s three diversity indexes he introduced in the late 40s will recall that Z=1/D was also specified by him as a measure of diversity. Indeed Simpson’s Z diversity index was the first one developed by him as diversity. And it will also be recalled that U=1–Z was the third of Simpson’s trio of diversity measures, which suggests that U uncertainty is information also, something we made quite clear from basic information theory considerations back in Section 9 prior to Eq84. 

This dependence on diversity of Z and U=1–Z probability and of the (probability based) human emotion, which specifies them as information, is entirely general and extends also to the unbalanced case as in guessing a color picked from an unbalanced set like the K=6, N=3, (■■■, ■■, ) set whose matrix of Figure 283 is redisplayed below.   

 

 

 ■

 ■

 ■

 ■

 ■

 ■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

■■

Figure 283. The Comparison Matrix of (■■■, ■■, )

From the ε =14 samenesses and K2=36 comparisons of the matrix we calculate its sameness density of Z=ε/K2=14/36=.389 as the probability of making a correct guess when, and this “when” is very important, the probability of guessing a particular color is the same as the probability of that color being picked from the set of objects, (■■■, ■■, ). This guessing strategy is called rational guessing because the guesses made have the same probability or frequency as the ratio of color outcomes as is developed from the (■■■, ■■, ) vertical axis in the above matrix understood as guesses having the same probability distribution as the color outcomes specified on the horizontal axis as (■■■, ■■, ).  

Do people actually guess that way, using the rational guessing strategy? Just about every species in the animal kingdom guesses or selects rationally in all the selections made. This is shown in myriad Skinner box selection experiments. Humans also select or guess rationally about half the time. In the color guessing game we are playing, however, with an object picked blindly being replaced in the bag before any subsequent pick, rational guessing does not make for the highest probability of success.

It would, though, if the objects picked were not replaced in the bag, the relatively simple proof of this left to the reader. The reason that animals select rationally is because what they are usually picking are objects to eat, which are not replaced as we do in a game or in an experiment. But that’s why animal instinct developed in the animal mind to select rationally and why the instinct remains sufficiently strong in humans for them to select rationally half the time even though there is a way to select when in repeated games and situations where there is a replacement.

What makes for the highest probability of success in that case is the best bet strategy. In the color guessing game played with replacement of the object picked after every pick, a person has the highest probability of success with the best bet strategy. In guessing the color picked from (■■■, ■■, ), the best bet is to guess red all the time. As red comes out ˝ or .5 of the time, the probability of success in making the best bet guess is ˝ or .5. This is better than the Z=.389 probability of success in guessing a color picked from (■■■, ■■, ) with rationally selection. As most modern casino games have the element of replacement in them, a savvy gambler always takes the best bet strategy.

The important point for our consideration of the emotions is that the Z selection probability is always the inverse of some diversity index. This is obvious in guessing from a balanced set like the N=3 (■■, ■■, ■■) set where the Z=1/3 probability of guessing correctly is Z=1/3=1/N=1/D. And it is also clearly the case when guessing from an unbalanced set like (■■■, ■■, ) with the rational guessing strategy where Z=.389=1/D=1/2.571.

Next we want to show that the probability of success in best bet guessing, as from an unbalanced set, also takes the form of the inverse of a diversity index. Showing this develops diversity as a very general community of diversity indices, one of which underpins the best bet strategy. Recall the h Square Root Diversity Index of Eq62. We can express h in an alternative way using a β (beta) index as

288.)        

 

We can also express the D diversity with a β index. Understanding the sum of the weight fractions of any set to necessarily be unity, pi=1, we write the D diversity of Eq3 as a function of the β index as    

 

289.)             

 

 

The h and D diversities are then understandable as two diversity indices that exist in a continuum or community of diversity indices expressed in terms of the β index as

290.)             



This general Dβ diversity form expresses D of Eq3 as D=Dβ=D1 and h of Eq62 as h=Dβ=D1/2. Of particular of interest from the perspective of specifying the emotions in connection with the best bet strategy of guessing is the β=∞ form of Eq289, which is D.  For the case of picking blindly from the K=8, N=3, (■■■■■, ■■■, ), (5, 3, 1), set of objects whose weight fractions are p1=5/9, p2=1/3 and p3=1/9, we evaluate D from Eq289 with β=100, a large enough number to approximate β=∞ well.   

 

290.)              



From elementary probability theory, if we guess red all the time from (■■■■■, ■■■, ) with the best bet strategy, the probability of success is 5/9=.555. This perfectly fits a probability of success as the inverse of the set’s D=9/5 calculated above, Z=1/D=5/9=.555. Or generally for best bet guessing from any set of objects, 

291.)             

Are rational guessing and best bet guessing the only ways a person would guess from an unbalanced set? No. A person might also guess from an unbalanced set like (■■■■■, ■■■, ), (5, 3, 1), in a purely random way, that is, guessing each color, red, green and purple, with equal frequency or probability. The probability of success in guessing color randomly no matter the unbalance in the set picked from can also be expressed in terms of a β diversity index, specifically Dβ of Eq290 with β=0, the value of which is, for any set of objects with N distinguishable subsets, balanced or unbalanced, 

292.)               

 

This random diversity measure, D0=N, develops a Z0 probability of success for random guessing as the inverse of the D0 random diversity index,   

293.)                

For the N=3, (■■■■■, ■■■, ), set, this obtains a probability of success of Z0=1/N=1/3=.333. The D diversity of (■■■■■, ■■■, ) is from Eq3, D=2.314. Hence the probability of guessing with the rational guessing strategy from it is Z=Z1=1/D=1/D1=.432. And with the best bet strategy as we saw from Eqs290&291, Z=1/D=.555.

This comparison of the three guessing strategies, random, rational and best set, makes it clear why a “smart” person, one who had some sense of mathematics or casino gambling, would choose the best bet strategy for it provides the highest probability of success. As we said above some people would guess according to the rational guessing strategy when human instinct dominates calculated best bet guessing, even when the color guessing game played is with replacement. Guessing randomly even from an unbalanced set like (■■■■■, ■■■, ), the worst strategy with the lowest probability of success, is generally something only a young child might do.

So we see that selecting from an unbalanced set of possibilities tends to lean selection towards the most probable outcome to a varying degree, β, that ranges from β=0 for completely random guessing to βŕ∞ for best bet guessing. This understands the probability of success in guessing or selecting what to do as some function of diversity generally.  

294.)              

The probability of success in selection from unbalanced sets is a function of probability, Zβ, based on diversity, Dβ, as the simple inverse of it in Eq294. In the sense that we have developed D diversity index as information, this makes it clear that the Z probabilities associated with emotion are information and further that the emotions formed from Z probability functionally associated with something meaningful like money as in E=ZV hope, are meaningful information for us. This should make it clear that the mind operates according to rules that are entirely mathematical in nature; and as we shall discuss next that these operating rules of the mind can be taken advantage of to influence people as to what is meaningful or not by disingenuously associating things with emotions to make them seem meaningful. That is, indeed the general strategy of television commercials. And it is also an important part of political and cultural propaganda, newscasters beholding to a political ideology, as all of them are, tilting the news reported by associating emotion with the report in their tone of voice, etc.        

To see this more clearly yet, understand that the emotions we feel about things can come about not just from mathematical analysis but from experience. If one is playing the Lucky Numbers game for a prize of V dollars and has a choice between playing it with lucky numbers, |4|, |7| and |10| and its Z=1/3=.333 probability of winning or with lucky numbers of just |7| and |10| and its probability of winning of Z=1/4=.25, one can get a sense of the probabilities of winning for both not just from elementary probability theory but also by watching these games being played repeatedly and evaluating their probabilities from the frequency of success observed. For those entirely ignorant of mathematics, this is the way such evaluations of likelihood are often made.    

But also because humans are advanced social animals, one can get a sense of the probability of success of this or that activity from other people. This comes about not just from one person giving another the Z numerical value of the probabilities associated with an activity as would affect their emotional feeling about it, but also by communicating emotions about an activity directly. For example for one person to be smiling and show excitement about an activity is to cause the recipient of such a display to feel similarly, that the activity is a “good” thing to do, has a high probability of success. But such information from a source that affects the emotions of the recipient or audience for the information can also be faked, as it done easily by professional actors and by politicians and by anybody who is an effective liar. There are so many instances of a source of a message trying to affect the emotions of a recipient that to discuss them all would easily require one or more volumes of an encyclopedia. The bubbly enthusiasm of a paid actor in a TV commercial for a car, super-wonderful toilet paper or life insurance is, of course, faked and should be suspected of producing an emotionally positive sense of the value of the product advertised that is overblown (and in more cases than the business community that cares little how it makes its money would care to admit, entirely bogus.)

As which behaviors we choose to do depend very much on the emotions or meaningful information associated with those behaviors, the emotions aroused by professional fakers or actors go a long way to arousing bogus emotion in people to make them do what is not in their interest and avoid behaviors which are in their interest. We have already talked at length about (quantitative) significance as a basis of meaningfulness in information. Now we see that the emotions associated with things and events very directly affect their meaningfulness. And we see that both markers for meaningfulness, quantitative significance and emotion, can be jiggled by mass media and other ruling class controlled information outlets to control what people think are meaningful, which controls their behaviors given that people act on meaningful information. The extent of such mind manipulation is staggering with such mass disingenuousness affecting every aspect of people’s lives in ways profitable to the interests of the ruling class and detrimental to the interests of the fools on the down end of this endless con game that utterly confuses reality with Pollyanna fiction in people’s minds. 

It is difficult to understand social control without understanding hierarchy. To speak even lightly of hierarchical control as of big bosses controlling middle managers controlling foremen controlling workers or billionaires controlling politicians through campaign money determining the laws (in favor of billionaires) that control the behaviors of people is to make public and clear the nature of institutional social control in modern civilizations. Hence it’s a concept that, though utterly general as we’ll see, is seldom talked about and if it were would prove to be a highly contentious topic whose meaningfulness as regards exploitation and the unhappiness it causes would be swept as quickly as possible back under the rug.

For that reason we will define and describe hierarchy with mathematical precision before discussing its social downside for people. Let’s start, indeed, with a qualitative description of hierarchy. Hierarchy is a very general phenomenon in nature. Corporations in America are hierarchies as is the military. The Catholic Church and the Hindu caste system are patently hierarchical. Indeed, all organized institutions are hierarchical though most at the national level say otherwise. And though we are less interested in abstract forms of hierarchy, knowledge is inherently hierarchical as exemplified in the Linnaean Classification of living organisms and the standard Thesaurus of word forms. Also scientific concepts are inherently hierarchical as is most obvious for science expressed in mathematical form where one or a few equations can describe systems nature in a general form that apply hierarchically to many specific situations. The food chain in ecologies is also patently hierarchical and is paralleled by exploitive human hierarchies that extract energy for those on the upper levels of the hierarchy, labor energy, from those on the lower levels.

 

To discuss hierarchy in a precise way, we need to define a regular hierarchy. One should recall that the basic set upon which all of the foregoing analysis was based was a regular set, one with mathematical regularity, in all the objects in the set, as with (■■■■■, ■■■, ), being unit objects having the same size. It was from such a regular mathematical structure that we were able to develop the basic properties of a set including diversity. Having done so, we could if we wished to, gone back to consider sets of objects that are unequal quantitatively. We did not do this because it has little relevance to our main topics of interest. But the mathematically savvy reader will understand immediately that doing that is not very difficult to do.

 

In a parallel way we want to define and develop a regular hierarchy, one that has equivalences in its structure that make understanding the basic properties of a hierarchy a relatively simple matter. We develop it by first listing side by side for some example sets the H Shannon entropy of Eq1 and the log2h form of the Square Root Diversity Index, h, of Eq62.  

 

295.)            



Sets of Objects   

K

(xi)

H

log2h

(■■■■, ■■, , ■, , )

10

(4, 2, 1, 1, 1, 1)

2.585

2.585

(■■, ■■, ■■, ■■)

8

(2, 2, 2, 2)

2

2

(■■■, , ■■■, )

8

(3, 1, 3, 1)

1.811

1.819

(■■■■■, , , )

8

(5, 1, 1, 1)

1.549

1.563

(■■■■, ■■■■, ■■■■)

12

(4, 4, 4)

1.585

1.585

(■■■■■■, ■■■■■, )

12

(6, 5, 1)

1.325

1.344

(■■■■■■, ■■■■■■)

12

(6, 6)

1

1

(■■■■■■■■■■■, )

12

(11, 1)

0.414

0.467

Table 296. H and log2h of Various Sets


Note carefully that only one set other than the balanced sets in the list has H=log2h, the (4 2, 1, 1, 1, 1) set at the top of the list. That equivalence is a marker for a regular hierarchy.

 

297.)                       H=log2h

 

A geometric representative of the (4 2, 1, 1, 1, 1) regular hierarchy is very helpful for introducing the basic properties of a hierarchy. 

 


Figure 298. A Geometric Hierarchy



The (4 2, 1, 1, 1, 1) hierarchical set has subsets of x1=4, x2=2, x3=2, x4=1, x5=1, x6=1 and x7=1. In its geometric manifestation of the square of Figure 298, the side of the square is specified as 2 inches. Hence the N=7 numbers in the (4, 2, 2, 1, 1, 1, 1) natural number set represent the area in square inches of the N=7 polygons that make up the hierarchy of polygons at three levels of the hierarchy. These levels are the large square at the 1st level in the hierarchy that has an area of x1=4 square inches; the pair of large, two-toned triangles at the 2nd level in the hierarchy, one two-toned blue and the other two-toned brown, each of which has an area of x2=x3=2 square inches; and the four small triangles, brown, tan, blue and azure at the 3rd level in the hierarchy, each of which has an area of x4=x5=x6=x7=1 square inches.  This understands the square of Figure 298 interpreted as a hierarchy of the N=7 polygons seen in the figure below.


Figure 299. The Geometric Hierarchy of Figure 298 in terms of its N=7 Constituent Polygons
 

The (4, 2, 2, 1, 1, 1, 1) set of the areas of the N=7 polygon members of the hierarchy sum to K=x1+x2+x3+x4+x5+x6+x7=12 square inches. This is an unusual mathematical specification of the figure given that the Euclidian area of the dissected square is x1=x2+x3=x4+x5+x6+x7=4 square inches. This defines this number set of (4, 2, 2, 1, 1, 1, 1) not as a quantitative description of the square itself but of the hierarchy of polygons in the figure, each of which is understood to have an independent existence despite the larger polygon of the square being made up in normal Euclidian fashion of the smaller polygons. Indeed, a hierarchy is a perfect example of a whole that is more than the sum of its parts.          

There are 3 levels of polygons in this regular hierarchy: the square; the two larger triangles; and the four smaller triangles. These three levels are implicitly specified in the (4, 2, 2, 1, 1, 1, 1) number set representation of the hierarchy, for all polygons with the same area are understood to be at the same level in the hierarchy. We could also have explicitly specified the 3 levels in the hierarchy by separating the polygon subsets at different level with semicolons in the number set as (4; 2, 2; 1, 1, 1, 1). The use of semicolons is not necessary for the perfect hierarchy that has the H=log2h equality because the equal areas of some polygons at one level clearly separates them from other polygons of different area without the need for semi-colons.  

 

The regular hierarchy with H=log2h clearly displays the three central features of a hierarchy. The first, expressed in terms of the geometric hierarchy in Figure 299, is that polygons at the same level have the same area as with x2=x3=2 and x4=x5=x6=x7=2. The second feature is that the sum of the areas of the polygons at every level are equal as with the 4=2+2=1+1+1+1 equality of the 3 levels of polygons in the (4, 2, 2, 1, 1, 1, 1) hierarchy. And the third feature is that the ratio of polygon area between adjacent levels are equal as with the 4/2=2/1=2 ratios in the (4, 2, 2, 1, 1, 1, 1) regular hierarchy. This ratio is called the degree of dominance in a hierarchy, given the symbol. The dd degree of dominance for the (4, 2, 2, 1, 1, 1, 1) hierarchy is dd=2.

 

Let’s go over these three features with another hierarchy, (27, 9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1). It is marked as a regular hierarchy from its H=log2h=4.377 equivalence. This hierarchy has 4 levels in it. The polygons at each level have the same area. The sum of the polygons ate each level are the same, namely 27. And the degree of dominance for this hierarchy is dd=27/9=9/3=3/1=3.       

 

These properties of a regular hierarchy help explain why the level of control over individuals below the top level in a social hierarchy is large enough to be crushing of freedom, human spirit and happiness. That is made clear from the weight fractions of a hierarchical number set, which for (4, 2, 2, 1, 1, 1, 1) are (1/3, 1/6, 16, 1/12, 1/12, 1/12, 1/12). A polygon in Figure 298 is readily understood as an individual and the polygon area as a measure of his or her strength and competitive capability as probability of success in competition with other “polygon individuals.” This allows for an understanding of the competitive power of an individual at any level in the hierarchy as deriving from the polygon individuals under it at lower levels. For example the square taken as an individual is understood in this interpretation as deriving its p1=1/3 relative probability of success in competition from its having control over and access to the strength and power of the two large two-tone triangle individuals it, the square, is made up of. Such power of those at the top levels in a hierarchy, as in a corporation or the military, is understood as coming about from their control over the people under them at the next lower level in the hierarchy; and so on for those at subsequent lower levels in the hierarchy as colloquially representing an extended chain or totem pole of power.

  

To illustrate hierarchical competition and control consider an actual or anticipated battle between the square as individual with probability of winning of p1=1/3 and the two-toned blue triangle as individual with p2=1/6. These two pi weight fractions are normalized to sum to 1 as the p1=2/3 and p2=1/3 probabilities of each beating the other in competition. This gives a large Δp edge to the square individual over the two-toned blue triangle of 

 

300.)                        

 

From our analysis of potential competition outcomes back in Eqs77-83, the possibility of the lower level individual submitting to the control of the upper level individual is considerable. Note that the Δp edge is greater yet in a contest between the square at the top level with p1=1/3 and the little brown triangle at the bottom level of p4=1/12. The normalized probabilities of success in competition for them are respectively p1=4/5 and p4=1/5 as brings about a Δp edge for the square individual at the top of the hierarchy of  

 

301.)                           

 

If the Δp=.333 edge of the top dog is sufficient to dominate the fellow at the next lower level, that is all the more the case for his dominating and controlling the fellow at the third level with this Δp=.6 edge. And the higher the dd degree of dominance in the hierarchy, the greater yet is the likelihood of submission without a fight.

 

It is helpful to be more specific as to what it is that might bring about an individual in the hierarchy’s pi relative probability of success in competition. In the above examples, it was the “size” of the individual manifest as the size or area of the polygons in the geometric figure of Figure 298. We can also understand the pi weight fraction measures to derive from the financial wealth of the individuals, money at one’s reach being an obvious measure of one’s power in competition, this so obvious in election campaigns where money spent enables the votes needed to win and in war where money buys the weapons needed to win.

 

Let’s use the (27, 9, 9, 9, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) regular hierarchy to illustrate. Without needing to spell the math out in detail, we see those at the higher levels in the hierarchy clearly dominating those at the lower levels. There can be no arguing that money power rules and that those at the lower levels submit to and are controlled by those at the higher levels.

 

For comparison sake, we can look at other possible distributions of financial power in a society. If the K=108 money values in our example set were distributed over the N=40 individuals equally as provides for a perfect balance of power, at least money power, each would have an amount of wealth equal to xi=108/40=2.7. The number of significant individuals in the society would then be for this balanced or perfectly fair set, given r2=0, D=N=40.

 

Next let’s consider what would happen if the money were distributed “fairly” from a different perspective, with each person having an equal probability of winding up with each unit of money in the system. To evaluate such an equiprobable distribution that takes into account the vagaries of chance non-equal distribution, let’s return to Eqs44&11, which tell us that the average equiprobable distribution of money has an r2 statistical error of    

        

302.)             

 

This has r2AV for our example set as r2AV=.361, which develops from Eq16 a D diversity index as the number of significant individuals in the society as D=29.4. While this is still less than the N=40 individuals in the group, most of them are yet significant. Compare now the perfectly fair society with r2=0 and D=N=40 significant individuals and the equiprobably fair society with r2=.361 and from Eq16, D=29 significant individuals out of N=40 to the hierarchical society with N=40 individuals that has an r2AV=2.704 and from Eq16, D=10 significant individuals. Mapping these out as the topmost 10 individuals in the hierarchy of our example set, (27, 9, 9, 9, 3, 3, 3, 3, 3, 3) suggests that the significant individuals power-wise are the ruler (or ruling class), x1=27, the upper level managers, x2= x3= x4=9 and some of the midlevel managers, x5= x6=x7= x8= x9= x10=3, with all of the lowest levels in society, the workers and foot soldiers, insignificant. Yes, if we haven’t made it clear before, soldiers, most who join up out of economic necessity to lose their lives and limbs, are a miserable lot, too (See: Front Page, USA Today, 4/17/15.)  

 

As long as the power of money to control people is accepted as fact, something impossible to deny other than by a right wing double talker like Rush Limbaugh or any of the Republican candidates for president in 2016, the idea of a “fair” society, fair mathematically defined as above is ridiculous. So is the notion of a “free” society once one understands the position of the lower classes as that of being controlled by the money power of the upper classes. This should destroy the silly notion of a free society via democratic elections given the extent to which elections are “bought” with the money of the significant upper class members of the hierarchy. As we made clear in the earlier section on the significance of individuals, low man on the totem pole makes for a considerable lack of self-esteem and self-love and the unhappiness associated with that.                

 

The trouble with rectifying this problem is unfortunately near impossible to fix. That is because another central characteristic of social hierarchies is that they are efficient as a whole and as such they win out, don’t go extinct, in evolutionary competition, like war. It is unarguable that the American Indians the Europeans found in the New World lacked the highly hierarchical organization of advanced civilizations for the most part. It is also unarguable that there societies had a much greater balance of power and were fairer and freer then the invading Europeans and as such, inherently provided a significantly happier living experience for its individuals, that the case for all primitive societies.

 

The problem, though, is that the more loosely organized, much less hierarchical, primitive societies that once existed on the planet in non-insignificant numbers have all been effectively wiped out by the more efficient, more likely to win in competition, hierarchical societies. This problem, really the problem of unhappiness in peacetime caused by excessive dominance is not totally intractable in A World with No Weapons. As made clear in the previous section, A World with No Weapons is only achieved by the entire world coming under the control of one power. Note that even if that power consists of people from different nations, it would yet be one governing power.

 

Under such a system there is no competing power on planet Earth to be wary of or to need a highly controlled efficient hierarchical society to compete successfully against. This is a bonus with A World with No Weapons. Not only is the horror and misery of war eliminated, but also the otherwise inevitable destruction of the human spirit and happiness that happens lockstep for all civilized people as they pass through the eventually crushing adult stage of life, the propaganda of ruling class information outlets notwithstanding.

 

Of course, the central mission of our movement to establish A World with No Weapons is to eliminate an annihilating nuclear war. The misery of peacetime tyranny and of non-nuclear weapons war is statistical. Some are affected in both and to varying extent over the time of their lives. But nuclear war is the sure end of it all and something all human beings should rally to avoid however much the more hopeful and healthily egoistic hopeful may reject the notion that their lives are or will be irrevocably damned by either great hierarchical control or the bloody mayhem of war. Hence we want next to explain why nuclear war is eventually inevitable as the years pass.

 

The key to that explanation lies in two drives to aggression. One is the “natural” combat competition for territory and resources effectively mandated by the fitness function of Eq276, F1=b1−d1−b2+d2, with its drive to increase the d2 death rate of rivals as by killing them. And the other is the development of redirected aggression in civilized people from their condition of servitude. We will consider both in detail after first painting a broad objective picture of reality in set form as background for our close up examination of human violence and the extinction of mankind it is about to take the world to. 

 

There are three generalizations we can make about what we see in nature. The first is that objects are distinguished by their positions in space. The second is that things are seen to change over time both in terms of the positions they occupy in space and transformations they undergo as to what kind of objects they are. And third is that the dynamic behavior of objects is itself seen to change over time.

 

In number set parlance, we specify the first generalization in terms of K objects distinguished by location in N extended locations in space; the second generation as N objects over which K energy units, what makes the objects move or change, are distributed. And lastly we see ω=NK permutations of K energy units distributed over N objects that are contained in time. This gives a simple general view of everything that is observed, objects contained in space, energy units contained in objects, and the latter dynamic sets as changing events contained in time.

 

It is quite impossible to see nature in any other way no matter the complexity of the dynamics or their evolution or change in this dynamics over time. This simple view is very important in explaining what evolution is in the clearest and most general way. First of all it makes clear that the change in energy unit distribution over time whose average is the Average Configuration of a thermodynamic system is an evolution of the system. It is indeed a random evolution whose diversity from the reformulated 2nd Law of Thermodynamics of Eq72 takes on a maximum value, ΔhAV>0. This is in contrast to biological evolution, yet a change in the dynamics of objects when seen as a change in the behavior of organisms, the correct way to understand biological and cultural evolution, where competition produces one winner eventually and a minimum value of diversity, D=N=1 of the population that did not go extinct from the competition.

 

Newtonian mechanical reality as one broad instance of this simple picture is telling. The positions of objects in space set in a three dimensional coordinate system are well specified as (x, y, z). And the motion from the inclusion of energy or energy units on these objects is well specified with the velocities, (dx/dt, dy/dt, dz/dt). Changes in the distribution of energy from the perspective of the objects as with the N molecules in a thermodynamic system bring about increasing or decreasing accelerations of these objects. In biological evolution, on the other hand, the changes in the dynamic behavior of objects as organisms tend to be too complex to be efficiently characterized as simple accelerations of the objects, though in effect that is what happens mechanically whenever we change our behavior.

 

It should be clear that the above characterizations of objects and their dynamics and changes in these dynamics over time derive from observation of them. That is not the only conscious sense of things we have, though, for a primary function of the mind is to project to future possibilities of objects in space, energy distribution over objects and in the evolution of such dynamic behavior. Such future prediction of behavior and planning of one’s own behavior is not limited to a repeat of what was observed in the past, however, but rather can be additionally colored by imagination’s develop of variations or permutations of past structures and dynamics and evolution.

 

Those are two primary operations of the mind, recollecting the past to package it in compressed representations and using those generalizations of past experience to project, sometimes with imaginative variation of past experience to future possibility in prediction and planning. Indeed, to repeat for emphasis, thinking consists basically of those two mental operations, recalling and compressing past experiences into generalizations, on the one hand, and using recollections and generalizations of the past, sometimes imaginatively, on the other hand, to develop predictions and plans.

 

The human mind does not make a sufficient enough distinction between these two primary operations to avoid using elements of the one in the other by accident and in error. To wit, imaginative explanations of the past that deviate from observational description are a misuse of imagination. It is one thing, for example, to place hope in an impossible situation in some imaginative rescue that might be performed by a powerful agency to save oneself in the nick of time. But it is another thing all together to explain past events with imaginative causation never observed in past experience. The difference between the two applications of imaginative construction is subtle but very meaningful.

 

Prior to Galileo and Newton explaining the motion of physical bodies with mathematical precision, the cause of such motion was attributed to a spirit that existed within the bodies, the vis-visa. Such an explanation had no basis in “fact”, for no spirit form was ever observed, the rebuttal to such a rebuttal, of course, being that spirits aren’t observed and don’t have to be to exist. Now to posit the “existence” of something that isn’t observed is to thoroughly misunderstand what is meant by existence for things absolutely do not exist but rather are sensed to exist. That is, if we sense something, we say that it exists. But nothing exists outside of its being sensed to exist, the word “exist” being a shorthand verbalization for what is sensed.

 

This may seem to be some sort of sneak attack designed especially to put down religion and “spiritual” notions, but rather it is a clear spelling out of how the human mind designed to provide a framework for any objectively sensible consideration of reality. That is, once you admit to imaginative explanations of things seen to occur, you can always conjure up a spirit or superstitious causation from your imagination to describe “reality” in any way you like.

This understanding of what is allowed as an explanation of life and nature in terms of what is actually experienced, be it mental or perceptual, makes it possible to argue the details of life and nature in a “sensible” way, that is, through the senses. And it allows us to castigate those who insist of pulling babble out of the pie to explain things as being without sense in their considerations, stupid or nuts. And that’s what we have in the world today as has developed not just through error developed from good intentions, but also from the endless deception that we have made clear arises to control populations in the most efficient way by misinformation and mind control. 

 

This has us return now back to the topic of violence to explain it and the unpleasant things that happen to people because of it not in terms of “evil” coming from of the Devil, an imaginative character nobody has ever, ever, ever, ever seen and not in terms of mental illness, again an imaginative concept nobody has ever seen that predicates its validity as an explanation by metaphorical parallels to physical illness, which has an obvious observational basis in microscopically observable microbial invasiveness and cellular deterioration. 

 

This means in any thinking about reality that we toss out as imaginative bullshit religious dogma and psychobabble that suffers from the same downside of having no foundation in anything observable. Depression, for example, is not a “disease”, but rather a natural response to loss or a frustrated inability to gain what is desired, that train of thought being what is observed in contrast to the ever unseen and vaguely described “mental illness” etiology of depression.

 

Now back to the topic of aggression. The cause of somebody being violent cannot be that they are bad. That doesn’t explain violence in any way other than your saying that if somebody is violent towards you or somebody that you have empathy for, you don’t like them and would like to see them destroyed or otherwise stopped. Note that this “bad” characterization of a violent person is not a cause of his violence because it is subject to the perspective of the person making the characterization. If I am about to be robbed or raped by a violent individual and violently defend myself against him by whatever means, my violence is now not “bad” or immoral, which should be a strong clue that violence cannot be explained with a moral attribution because that depends much on whether the one making the attribution is doing the violence or having it done to her or him.

 

This is very important to understanding violence sufficient to bolster the argument that weapons must be gotten rid of to save the world from man’s violence. That is, when we see the group ISIS slaughtering 1700 Iraqi soldiers and we want to ask why they would do such a thing like that or beheading Christians, we should not explain their actions by calling them terrorists. There are actually real reasons for things that go beyond name calling and they are very important to understand as a basis for motivating people to make a great effort to rid the world of weapons.

 

Once we toss out the vague and imaginative explanations for violence, we have two routes to properly explaining it. One is very broad and looks back to the evolutionary fitness function of Eq276, F1=b1−d1−b2+d2. It is quite impossible to deny this fitness function as a compressed representation of what must be done by populations of organisms to avoid extinction. The individuals of a population must survive as minimizes the population’s d1 death rate. And they must reproduce to persevere from generation to generation because all living organisms do eventually die - the superstition of the life after death delusion notwithstanding. In that regard, minimally the b1 birth rate term in F1 must be positive, b1>0, and best must be maximal to have a maximal F1 fitness.  And the individuals of one population must best their rivals in combat for the territory and resources of a niche as maximized the d2 death rate of the rival population.

 

Such behavior may include driving rivals from contested territory. In both killing rivals and driving them off territory, destructive behavior is called for. Killing somebody is inherently destructive and potential destruction is what works to scare rivals off of territory and from the resources needed to survive and reproduce. This is hardly “pure theory” derived from a hypothetical mathematical equation. War, violent behavior in the extreme, for territory and for resources (including the acquisition of slave labor) has been going on for ten millennia. This is observed and cannot be denied. To posit the cause of the violence observed in these wars in the need to maximize evolutionary fitness and avoid extinction is really quite inarguable, for those genetic groups who lost in such competition, like the Neanderthals wiped out by early Homo sapiens, went extinct because they were not as proficient in murdering their Home sapiens rivals as their rivals were in murdering them. And this war between different strands of genetic information extends to wars between fairly identical genetic information groups who are distinguished by significant differences in the cultural information that also affects their behavior. For remember as we said above that what evolves and matters are the behaviors of individuals and groups of individuals.

 

And we should not lightly pass over reproductive violence, also mandated for maximum evolutionary fitness. Everyone should read the classic by Nobel Prize winner, Konrad Lorentz, On Aggression, in which the point is well developed that not only is their violent competition between males for reproductive mates in just about every species in the biosphere, but also that such reproductive violence is almost invariably the greatest violence undertaken.

 

These two sources of violence are ingrained in just about living organisms. Furthermore violence is that much more mandated by evolution in predator animal species who obtain their food energy by killing and eating other animals. This is a very general observation that is hard to walk past. Lions and tigers just are more violent than non-predator vegetable eating species like rabbits and cows. And, guess what, man is a predator as a large part of where it gets its food energy. It kills other organisms to feed itself and survive, to minimize the d1 death rate of the F1 fitness function of Eq276, F1=b1−d1−b2+d2.

 

So we have in the above three very strong reasons why humans, especially human males, are inherently violent creatures. That is the cause of their violence. It is not the Devil and it is not mental illness and it is not “badness.” And this drive to winning in competition by aggressive behavior is impossible to eradicate. That can be argued, on the one hand, from the ubiquity of aggressive competition in sports, which includes some very violent forms as in football and hockey and boxing and mixed marital arts and so on. People not only like to engage in such aggressive sports but also take great pleasure in just watching them.

 

Of course it can be argued that violence can be tamped down by punishing people for it and conditioning them out of aggression. Indeed, that has been a principle mode of controlling violent insurrections against exploitive control over the years. That it has been done in obvious in the culture in modern America and much of the West in raising males as behavioral females. But no matter the repression of the violent instinct that can start at a very early age, aggression tends strongly to find a way to seep out of even the most passive person when the violence done to them to make them that way produces an unhappiness that ultimately finds respite and release in being in some manner violent or mean or bullying to another person who happens for whatever reason to be vulnerable to them.

 

Let’s go through that again for it is the basis of an add-on to violent aggression that is particularly troubling and dangerous in our civilized world. You don’t have the order and efficiency of a civilized nation without having substantial control over the behaviors of people, especially the behaviors that intrinsically resist frustration of their emotional drives to optimize their evolutionary fitness via competition with those who would frustrate those emotionally favored drives, notably the ruling class of said civilizations. The first impulse to humiliating submission is to fight back, but such emotions to retaliate against tyrants quickly fades out as we have made clear when more punishment and pain yet is in store for those who try it.

 

What to do with the displeasure of being beat down below the optimal point of self-interested fitness optimization? If you can’t get rid of it by retaliating against the individual in the hierarchy who caused your pain, attack somebody else down below you in the power ranking even if that person had nothing to do with causing you pain to begin with. This “redirected aggression” or “misdirected aggression” is utterly common in man and stems from a very primitive mechanisms man has for satisfying his evolutionary needs. If you can’t do it in the most optimal way that evolved, do it any way you can and get as much as you can if not all. Starving soldiers like those at Valley Forge during the American Revolutionary War ate tree bark and the leather of their boots as this at least provided some relief from the pains of starvation. The principle followed is: A half full stomach is better than totally empty; and half full of tree bark is better than and feels better than half full of nothing.

 

This mechanism extends quite beyond raw survival behavior to reproductive behavior, a sexual drive frustrated by cultural restrictions and/or relatedly the psychological castration of males undertaken to subordinate them to rule and exploitation make successful reproductive behavior difficult to impossible as brings about substitute behaviors that are little different in underlying principle to starving soldiers making do with boots and bark to eat. It is not only a major factor in the homosexualizing of a population but also very likely in the epidemic of child sex up to and including men getting off incessantly and irresistibly on child pornography.

 

And going one step further, not only are frustrated survival drives partially assuaged by eating boot leather and frustrated reproductive drives partially assuaged by sexual substitute behaviors of homosexuality and pedophilia, but also the repressed rage that sits unsatisfied in victims of abuse from great power finds partial outlet in aggression, often violent in some manner, on an individual other than the one who inflicted the damage to begin with. And just as eating bark or boots does little to nothing to keep a person alive and non-reproductive sex does nothing to produce an offspring, so also does redirected aggression do nothing to resolve the emotional displeasure caused by the original perpetrator of the offenses done. That is, though these substitute behaviors reduce the displeasure of the unsatisfied need and provide some pleasure, often of relief of some sort, in doing that, the real outcome that nature expects from its evolved instincts in these matters is not attained. Indeed such substitute behaviors represent an error in reckoning what actions resolve what needs much as the drinking of sugar-free soda provides no caloric insurance of survival whatever the pleasure involve in ingesting such sugar-free foods. 

 

And not only does redirected aggression on an incidental if vulnerable victim not resolve the pain of the wound inflicted by the actual perpetrator, but also it emotionally motivates the victim of such redirected aggression to do the same to any new victim in the chain of aggression that it can get hold of. In this way redirected or misdirected aggression increases over time in a population. And when it reaches some critical marker in the development of epidemic redirected aggression, it tends, often through unconscious mechanisms, to spill across national borders to relieve the pain caused by it in a nation by aggression on other groups, very often in human history on those of different cultures, ideologies and religions.

 

Now let’s put weapons into the equation. The fellow sitting on the wrongs side of the shooting gallery cares little about what kind of weapon he needs to pick up to defend himself. A comprehensive clarification of the emotional circuits of desperate defense is not necessary to understand that it is simply the way it operates that is important to understand that it is better to fight and take the chance of having both of you die in a fight than just to sit there and not defend yourself with any weapon available and die all by your lonesome. So the idea that nuclear weapons are too nasty to be used is utterly ridiculous and is the kind of thinking that delusional people, religious and ideological, use to avoid the hard thinking necessary to actually do something about the catastrophically threatening reality.                 

            

 Of course this quite sound idea is completely obfuscated not just by the reality of it not being broadcast from ruling class information outlets, but also by people’s heads being clogged with misinformation generally from the significance versus insignificance mode and emotion association mode of propaganda that makes the meaningful in life seem meaningless and the meaningless, March Madness and the Super Bowl two good examples, meaningful.

 

And for that reason there is little choice but to wait until the first nuclear weapon is detonated and a few million die to get people, stupid people, deluded people, the nutty people of the 3rd Millennium AD, to do anything about the problem of having our species eradicated by Weapons of Mass Destruction by getting those weapons ahead of time before the worst happens to us all and to our children and to our grandchildren.

 

At this point let me advertise the two of us as champions for this effort and ask those this makes some sense to join with us by sending a token donation of $20 by clicking here. This identifies you to yourself and hopefully to the others you’ll communicate with about it as a formal member in the movement to make A World with No Weapons. What exactly we’ll do with the money when we get it, I’m not sure at the moment other than to tell you that however much we get or if we don’t get a penny, we will continue to dedicate our existence to making A World with No Weapons in the hopes that we’ll manage to be successful, somehow, in making this necessary Utopia for mankind a reality. 

 

As I begin writing this morning, 4/8/15, while waiting for the bomb to fall I see that the cop who shot the black guy in the back in Charleston, a horrible town as we know from personal experience, is indicted for murder. As I said earlier, cops are just the weapons of the ruling class on a leash, subject to their direction. In this case, they’re pulling the leash a bit tighter. Be interesting to see the details of how this plays out but America wakes up to the reality of abusive control by corporations and police only after they locate the cause of excessive force in the wealthy ruling class in each community, small and large, who has hold of the leash.

 

Now I want to go back to the concept of redirected aggression to make it clear that such meanness and violence develops in a person from unhappiness caused them not just from the person being aggressed upon, but also from reproductive frustration or the failure to achieve love. This subject is so intensely moralized and contentious that we approach it only from a rigidly scientific perspective.

 

Maximization of the fitness function of Eq276, F1=b1−d1−b2+d2, a must for evolutionary survival from generation to generation, comes about, of course, from minimizing the d1 death rate, which for the individuals of a population, maximizing one’s life span, something we are all emotionally imbued by instinct to do. It also comes about, mathematically, by maximizing the b1 birth rate as translates to individuals having as many kids as they can that can, as we made clear earlier, be raised up to functional, competent sexual maturity at adolescence.

 

This was not a problem needing any consideration for the female of our species for prior to effective conception. For 99.9% of the 100,000 year existence of anatomically modern humans physiologically healthy women had about a dozen or so children in their lifetime as provided the more or less maximum number that could be raised to a healthy adolescence. To be blunt, women need but a drop of semen to have a child and there are plenty of such drops available.

 

For males it is entirely a different game. It can be a major problem to find a mate to reproduce with and to keep, for reproduction by the male consists not only in producing an infant but also in staying with her to help raise the child successfully to adolescent sexual maturity. You will notice how difficult it can be for couples to stay together these days as a marker for the existence of a real problem in this area. Success for the male in this area is no small thing. To fail is to fail at the one thing that all living organisms are not allowed by the evolutionary rules to fail at, procreating. For that reason the principle preoccupation of male animals of all sorts is to get the female mate/s.

 

This hard core aspect of animal reality is well laid out in a recently published book, Animal Weapons: The Evolution of Battle, by Douglas J. Emlen, a biologist at the Univ. of Montana. His research makes it clear that male animals readily risk death and destruction to win the reproductive battles with other males and the prize of winning of a female to bear offspring with. The drive to maximize the b1 birth rate of F1 manifest in the intense emotions associated with it for human males arises from the inarguable fact that failure in this effort is the ultimate failure of one’s genetic lineage going extinct.

 

Because of this, much as evolutionary success generally is marked by a reward of pleasure, there is enormous pleasure in success for male humans in the reproductive area. Pete recalled a college friend of his philosophizing back then on what made a guy happy: “If you got a girlfriend, you’re happy; if not, you’re not.” And the unhappiness that derives from such failure is also considerable. The song “Heartbreak Hotel” hints at this in a relatively light way, but other tunes tell of losers in this are doing the true to life thing of jumping of a bridge. However much humming one of the ten thousand tunes about breaking up may help the pain of losing in a courtship effort, the displeasure involved rightly deserves to be qualified as pain.

 

How this comes about is important to understand. While the fact of breakup is culturally aired as being just one of those things, causes can be cited. For one thing today’s crop of males is increasingly less attractive to women socially and sexually. This is a big mouthful of explanation, though, because it sits astride the extremely contentious issue of what it is that women find attractive in males. The observed fact that the biggest bestselling erotic book of all time is Fifty Shades of Grey strongly suggests that women are sexually aroused and, hence, attracted to dominant male behavior. This, of course, runs entirely counter to today’s advertised zeitgeist of sexually equality and the subtle but persistent moralizing of sexually dominant men as first cousins of Satan himself.

 

The sense of dominant males being attractive to women, though, makes considerable sense from the perspective of men having evolved to be physically larger and tougher than women and able as such, at least during the hundred millennia of mankind’s primitive existence before police enforced restrictive policy on men “taking” women by force came into existence, able to win in the game of which males get to generate offspring and avoid local genetic extinction. Also from an evolutionary perspective, dominant males would be favored by women in both giving more vigorous genes to their kids and in being more able to protect the family from would be male interlopers looking to stay alive in the evolutionary procreation contest themselves. And certainly instinctive male dominance in humans is strongly suggested by the large wash of male sexual dominance seen in the vast majority of mammals, especially those in which the males, as with human males, are significantly larger and stronger than the females.

 

So the question must be asked: Why is the dominant approach in males so put down? Could it possibly be that males who fail in love are weaker in spirit and more likely to submit to control in civilized societies and less likely to angrily rebel agai8nst that control? A sharp examination of sexual morality concerning adolescents strongly suggests that possibility. Keep in mind as preface to the more analytical considerations that will follow three songs from yesteryear. One is “Down by the Old Mill Stream,” which proclaims of the apple of the singer’s eye, “You were 16, the village queen, down by the old mill stream.” Another is Chuck Berry’s “Sweet Little Sixteen,” which makes no bones about the desirability of a legally underage girl. And a third is the Beatle’s classic, “She was just Seventeen (you know what I mean).” To harbor these thoughts towards female “children” these days is to be an evil criminal and/or a deviant psychologically. And we can top this off by noting that the most beautiful and desirable female of the last millennium, the Mona Lisa, was but 12 years old, a not uncommon age for marriage and copulation back just back 500 years ago.

 

Let’s argue the reasonableness of a female engaging in sexual behavior upon puberty from a physiological perspective. That is to say, nature enabled them to procreate. Why is it bad? And not only are post-puberty females physiologically able to have sex and bear children, they are also extremely prone to having the sexual feelings that emotionally motivate sexual behavior. If anyone doubts these latter two facts, one needs only to note the high frequency of teen pregnancies that occur despite the enormous social disapprobation that hangs over it. One also notes that females in every other mammalian species procreate starting pretty much immediately after they are physiologically sexually mature at puberty. And that all primitive societies encourage or minimally tolerate sexual union for females at puberty. And that at least one major, billion strong, modern civilized culture allows it, the Moslems.

 

All of this suggests that the sexual prohibitions for female adolescents and the extreme punishments awaiting those who violate these restrictions, particularly any grown men involved, are culturally driven and that however much modern clinical psychology spouts that such inclinations are deviant. Indeed to the extent that the male is aroused sexually by a sexually mature female from her anatomical attributes as a matter of inborn instinct, so also would he be by any post puberty teenage girl, all of whom have, in case you haven’t looked lately, quite developed breasts, etc.

 

Now as a female myself who has borne four biological children and helped raise a total of eight, I can tell you that the crux of what I am saying in the above is entirely true and correct. Teen girls are easily turned on, especially by manly or “cool” men, (as with Zane Grey novel heroes), and easily fall in love. They don’t resist it as is subtly counseled in near every piece of information, fiction or distorted factual, broadcast to us over ruling class information outlets. But that changes as the girl grows up and there is no love connection made. One might say, should say as it is so obvious in a way, that the adolescent years in being the ones in which young people do fall in love and are sexually aroused so easily, are the time designed by nature to fall in love and get a mate. To the extent that all of that sounds reasonable, we must ask the question of why it is that such connecting with younger females is so totally taboo.

 

The answer is quite simple. Couples who actually do fall in love to enjoy and treasure the heavenly joys of sexual intimacy and the spectrum of enabling pleasures it produces make lousy wage slaves. The converse of this fact may make more sense. That is, individuals who fail to find romantic love and/or keep it, feel like the evolutionary losers they are in fact and are much more likely, in deservedly thinking less of themselves as reproductive losers, to submit to regimen of obedience demanded of well-adjusted citizens in capitalist societies. Or to put in another way, solitary assholes are more compliantly agreeable and, hence, better workers than lovers. And this disparagement of worker losers is also justified for male homosexual couples, who are much less prone to overthrowing the capitalist system from the very fact of their submissive nature than heterosexual lovers, of which there are but few these days.

 

This analysis should also take into account the very modern reality of women as a stock part of the labor force. In that situation women are very much under the control of bosses who are intrinsically dominant to them by dint of the ability to not hire, retain or promote them, the reasons for such things being subtle enough to insure that the workday dominance that exists can be very extensive if the boss desires it to be such. And that is very powerful on the female worker, for as seen with Fifty Shades of Grey, women strongly tend to turn on sexually to persistent dominance. And once the boss gets into the woman’s underpants psychologically sufficient to turn her on, a very common experience truth be told (which as embarrassment it seldom is), that’s pretty much the end of her marital relationship, even if she does stick with the jerk husband out of survival need for her and/or her kids. To recap in brief, today’s women are nothing but members of a vast brothel for the bosses up there in the social hierarchy, no matter the delusions put into girls minds in their younger days that working a job and having a career will be such an uplifting and satisfying life experience.

 

The solution to this mass that produces so much unhappiness for both men and women? Well, it’s nothing that can be done piecemeal for it is the big picture of the enormous imbalance of power that exists between the social classes that is the cause of the problem. And either it takes us all to hell by being a major cause of the unhappiness in people that fuels the redirected aggression that causes so much violence, domestically and internationally in war. Or we all work towards A World with No Weapons in which some true balance of power is restored for the human species. And people get to do what their natural instincts, rather than rules and propaganda, tell them is right to do. In contradiction to promises of a joyful life after death, you only have the miracle of life bestowed on you by nature once. And you best make the best of it for yourself rather than trading the monumentally important reproductive satisfactions in life for the delusions of a happy retirement or life eternal in a heaven that cannot possibly exist other than in the mind of a total jackass fool.

 

All of this takes us back to a thorough examination of the broadest aspects of human nature as it has developed in modern times. At every moment, consciously or subconsciously, we are in the grasp of, under the control of, our expectations, be they fearful or hopeful and almost always both. The centrally of your expectations in your life is in their directing your behavior. This perspective dichotomizes behavior in a very broad way. Whatever your expectations are positive about, are pleasant about, you want to get, keep or do, have as positive attitude towards. And what your expectations are negative about, fearful, you want to get rid of or avoid, whether and action or an object. Well, those are the only thing you can do with and object or an action, embrace it or reject it. So this dichotomy by nature shouldn’t be surprising.

 

Or that your emotions, in telling you which of the two alternatives to take, are the information for these behaviors much as genetic information, DNA, directs chemical behaviors to be done or not. Emotions are directions for physiological behavior just like DNA contains the directions for biochemical behavior. In that sense both are information. Indeed the parallels between DNA and information are extensive. General speaking, the physiology including observable behavior one actually sees in organisms that are completely controlled by DNA, plants and invertebrate animals, is directed by their DNA, but yet as expressed in a specific environment that very much affects the phenotypic expression of the gene. We went over this in some detail with the chick with dinosaur scales on its legs instead of feathers example.  Emotions work the same way. How they are expressed in behavior including being repressed or not acted on at all depends much on their environment, which indeed can generate competing emotions that may repress others. This is in close parallel to gene repression. This should elevate emotion to the level of importance of DNA in human science considerations instead of treating it strictly as some sort of thing we would rather do without as good human robots for the workplace and that become salient in consideration only when dysfunctional.      

 

Many situations conjure up mixed emotions, mixed expectations, positive and negative, hopeful and fearful. Indeed it is not an oversimplification to say that at any moment you are capable of having a mix of a spectrum of expectations,

 

303.)                                        E=∑(ZV) − ∑(Uv)

 

In modern humans the fearful expectations dominate for much of what we do conforms to rules and the wishes of authority, which if not paid attention to bring about punishment of one kind or another including economic, prison and social punishments like disapproval. That’s how civilization works. People don’t surrender their own inclinations to do this or not in favor of rules unless these rules bring about a great deal of pleasure, even more than what was given up or the displeasure of punishment. People are afraid these days, afraid of authority and afraid of other people generally.

 

They have lots more fearful expectation than hopeful expectation. And unable to anything about this tangibly, they tend to minimize their fearful expectations, deny them, not think about them, not talk about them; and inflate whatever hopeful expectations they can conjure up, wishful thinking, delusions. And that’s what you have out there in America, obedient robots who suffer in silence while they distract themselves with televised entertainments they reinforce their delusions and minimize or make insignificant their fears.

 

And this makes for stupid people, unaware, blind factory robots who pass their delusions on to their children while they hide their fears for fear of being made to feel even worse than telling the truth to others about their experience, including to their kids whom they are being controlled to raise as the next generation of fearful, obedient, deluded (and what more than with the magical power of religion) factory, office and service robots.

 

Nobody might or should care, least of all me, about this nutty state of affairs. Except that all the hidden fear and the past failures and frustrations that made for unpleasant negative realizations in the psyches of this vast loser crowd, is what also caused the redirected, misdirected, random aggression and violence I talked about earlier that, in building up at an exponential autocatalytic rate, will soon come to fruition in nuclear Armageddon.

 

I could shout “wake up” ten thousand times to all you robots out there, WAKE UP damn it, but the delusions and the entertaining distractions and the timidity that all wage slaves have deep down after a couple of years in the labor force makes that impossible. So I won’t strain, just waiting for the bomb. And hoping that we will be lucky enough to just get one on the first salvo, just enough to warn, not so many as to be terminal.           

        

I’ll try again, sigh. Today NATO kicked 20 Russians out of its contact group. The reason given was utterly fabricated. NATO said that they were reducing EVERYBODY’S contingent size to 30 at a maximum. The trick was that Russia was the only entity that had over 30 and that this “general rule” applied to. What is obvious is that this sort of disingenuousness is part of a warring attitude toward another nation. It says that WWIII is on, this sort of “diplomatic” maneuvering being the stuff of Von Clausewitz’s “war by other means.” And Russia has lots and lots of nuclear weapons, which Putin has said now about 25 times it will not hesitate to use.      

 

And China this morning retorted to the US telling it that it, China, is destabilizing the Far East by being a bully by saying that the US is the overpowering bully on the block. And they alone have more than enough nuclear weapons to end all vertebrate life on earth. And let’s not walk past the possibility of Israel nuking Iran to end its nuclear program. They’d love to and if they and their American allies get to screw up the lift the sanctions on Iran deal, who knows what Iran will do or say to provoke them.   

 

These words of warning are big enough to be highlighted on the TV new shows that spend all their time on sensational crime and bad weather around the nation (a good ten minutes of natural disasters on every news program.) But they’re not giving you a clear picture of what should dominate your meaningful fearful expectations. Indeed, on TV people are not afraid of each other at all. They’re always smiling like each is having a silent orgasm or just taken a toke from a pipe before coming on stage. Everything’s fine in TV land.

 

But not in reality, as you’ll see once the bomb drops. Shame can’t wake you robots up until one of your kids dies screaming in your arms from radiation poisoning? Anybody out there who wants to help avoid this now, send in your donation of $20 by clicking here. Be the first kid on your block to understand that if we don’t come up with A World with No Weapons before the increasingly stupid and violent leaders of the world start throwing the big punches, we won’t have any world to live in at all.                                                        


17. The Message: Everything Operates as Feedback Control

Everything includes not only a robot whose behavior is programmed by negative feedback control to do what the owner of the robot wants it to do, but also natural systems like electronic circuits and like evolving societies whose goals are achieved by feedback control. Understanding everything in this way unifies science making everything in the universe much easier to make sense out of. For that reason it is important to understand the very basics of negative feedback control even though that gets a bit technical. 

A robot’s control apparatus is much too complex to illustrate the basics of negative feedback control with. Rather we introduce the components of negative feedback control using the simple system of thermostat controlled heating. The thermometer in it measures the temperature, θ, of a room to be heated. One sets the desired temperature on the thermostat. That temperature is the set point of the feedback control system, θS, where you want the temperature of the room to do be, say θS=70o F. The difference between the actual room temperature, θ, and the desired room temperature, θS, is the error component in feedback control, Ԑ, (capital epsilon).     

303.)          Ԑ=(θS−θ)         

Feedback control works by eliminating the Ԑ error sensed by the system. A heating system eliminates the Ԑ=(θS−θ) by turning on a heater like a furnace. The heater, once turned on by the presence of an error then warms up the room until the room temperature, θ, is equal to the set point temperature, θS, on the thermostat, θ=θS, at which point the Ԑ error is eliminated, Ԑ=S −θ)=0, and the furnace shuts off. That is the essence of how negative feedback control works by eliminating the Ԑ=S −θ) error to achieve the desired goal of θ=θS.  

Textbook 1st order feedback control entails a response to the sensed Ԑ=S −θ) error that is directly proportional to the Ԑ=S −θ) error. Specifically the rate of increase in the variable of interest, θ, in 1st order feedback control, dθ/dt in calculus terminology, is directly proportional to the Ԑ error as 

304.)          dθ/dt=kԐ=kS −θ)

The k term in the above is a constant that depends on the details of the response needed to eliminate the error. We see from Eq304 that the greater the Ԑ=S −θ) error, the faster the dθ/dt response of the negative feedback control system to eliminate the error. The algebraic solution to the differential equation for 1st order feedback control is

305.)            

This tells us how fast the θ temperature increases over time as shown in the green curve below.

http://expeyes.in/sites/default/files/eyes-jun/rc-plot.png

Figure 306. Typical Changes over Time in the θ Variable and Ԑ=S −θ) Error in 1st Order Feedback Control.


The numbers on the horizontal axis are units of time. And the numbers on the vertical axis of the graph (multiplied by 14) specify the Fahrenheit temperature of the room, θ. We see the θS set point temperature on the thermostat of 70o (the number, 5, on the vertical axis multiplied by 14) approached over time on the green curve, while the descending blue curve represents the decrease in the error, Ԑ=S −θ), over time to zero. This well illustrates the central characteristic of a negative feedback control system of the θS set point desired goal of the owner of the system, the  pleasant room temperature of θS=70o being achieved automatically over time. Many naturally evolved biological processes operate in this same way, the basis of biological homeostasis. Organisms with a cold surface temperature, for example, will shiver and shake automatically to generate heat for themselves by mechanical action.    

There is also a dynamic called passive negative feedback control. Its set point is just the end point of the process, not something that a human being necessary would want as a desired goal. A simple example of this that has the exact same mathematical form as the 1st order feedback control we described above for thermostatic heating in Eq304 is an RC electronic circuit (RC meaning resistance-capacitance.) With q as the number of charges that flow in a circuit to a capacitor, R the resistance of the circuit in ohms, C the capacitance of the capacitor in farads and E the voltage of the battery of the circuit in volts, the rate, dq/dt, at which the capacitor fills up with charge is 

308.)                          dq/dt=(1/RC)(ECq)=(1/RC)(qmaxq)

The similar form of the above to the equation for 1st order feedback control in Eq304 is obvious. Specifically we see qmax as the maximum number of charges the capacitor can hold and, hence, the end point of the process filling it up with charge. Once enough q charges flow through the circuit into the capacitor to make q=qmax and qmaxq=0, the equation tells us that dq/dt=0 as the end of the charging process. That qmax as the endpoint of the dynamic is understandable as the set point of the system or goal of the charging process is obvious for when qmax is reached, much as with the θS set point temperature in a feedback control heating system, the effective “error” in the RC circuit, Ԑ=(qmaxq) is eliminated as stops the charging process.

Biological and cultural evolution works in the same way except that the set point or end goal of an evolving system is to make itself continue to exist over time and avoid extinction. The behaviors of organisms including human beings that accomplish this are specified in the evolutionary fitness function, F1=b1−d1–b2+d2, of Eq276 to include maximization of the d2 death rate of rivals in a niche of common resources. What is notable here is the conflux of the dynamic of evolution as passive feedback control brought about by the elimination of rivals demanded by the F1 fitness function and the emotional drives of human beings towards the violent elimination of their rivals readily understandable as the active feedback control that was thoroughly discussed back in Section 13 following Eq235.   

Further human beings also use mortal combat to acquire slaves through which the conqueror’s fitness is enhanced economically by the minimization of the −d1 death rate that slave labor brings about. In this we see the tyranny for the loser taken away as slaves, very unpleasant, in contrast to the joy of conquest for the winner and the attendant economic plusses of slavery for the slave masters, very pleasant. For both, prior to the outcome of the deciding battle, the goal of winning in is the set point of the governing negative feedback control systems of the two combatants. Both set point goals are not achievable, the success by one of the combatants being the failure to achieve the goal of winning of the other.

This is to say that aggression, as emotion and activity, is very much an evolved natural phenomenon. Wars have been fought (aggressively) and won repeatedly in human history by one side in the wars, a natural occurrence if not pleasant for the losers in the wars. Now one aspect of war that makes it particularly bloody and horrible are the means to success in mortal combat. Much as the furnace in a thermostatic negative feedback control system is a primary instrument in achieving the end point goal of the system, so the primary instruments that make this possible victory in battle are the weapons used. Again and again it is seen that weapons are the dominant deciding factor for victory in this very natural phenomenon of war.

Weapons not only make it possible to win in battle, but also to induce submission in the losers in battle as to make slaves out of them. Hence we must see the extremely high value of weapons in both slaughtering rivals bloodily and in inducing obedience in them as slaves. Hence we see inarguably that weapons are the central instrumentalities for bloodletting and for sustaining tyranny following conquest in battle. As long as weapons exist, then, the net result of evolutionary driven and culturally aroused aggression inescapably must be the bloody mayhem of war and the miserable institution of slavery. As to the latter and its relevancy to our modern era read of wage slavery as the major cause of unhappiness in the Internet article: Our jobs just make us sad: How the1 percent crushed America’s spirit and drained our souls.

As one side or another always wins in competition sooner or later, it should be clear that the horrible job that aggression does on people, in war and as threatened insuring slavery, cannot be eliminated until weapons are eliminated. That is the point of this entire thesis read section by section from the top. Aggression is an innate emotion and activity evolved for fitness optimization that has changed markedly from the days for primitive people because of weapons. Back 50,000 years ago, long before the discovery of agriculture that made slavery efficient, a battle between two groups of primitive humans most often resulted in the losers running away from superior warriors, a dynamic central to the dissemination of people around the globe in nearly every kind of environment the Earth offers. But as weapons became more powerful through the invention of metal swords and then gunpowder arms and bombs, escape was increasingly impossible and that not just from the power of the weapons used in battle but also from all the viable places on earth already being settled. At that point weapons enhanced very bloody wars and weapons enforced slavery became inevitable. 

The invention of very powerful weapons compounds the potential horror of war and the misery of servitude and the possession by a fair number of nuclear armed rivals in the world threatens us all now with total annihilation. The only solution to this problem that wishful thinking including hope in the mercy of a god will not resolve is to get rid of the weapons and to do it before the weapons get rid of us by developing A World with No Weapons. There’s a thorough non-mathematical discussion of this indispensible Utopia we must strive toward at the end of Section 15 in the personal story of my life, Revolution in the Garden of Eden

Now, honestly, getting rid of the weapons that make not only for bloody war but also slavery is not in the interests of the ruling class in the inherently tyrannical slave states of the world that range from North Korea to the USA who live off the misery of those they dominate, (the differences between these states being much less significant than the similarities between them in the hard fact that in each there is a ruling class which dines on caviar while the workers and their families often go hungry and homeless.

You don’t think that happens here, too, as wage slavery? The proper take on workday life in America is well summed up in a recent Dilbert comic (5/20/15) where the boss says to him: “As you head to your horrible job, remember these inspirational words…in the long run, we’re all dead.” To which Dilbert replies: “That seems like an over-simplification.” To which the boss replies: “I skipped the part where you suffer for 90 years.”        

This is a laudable spelling out of the truth of life with humor. But it is only part truth, for in reality the end result of a life saturated with the suffering implied in that comic strip is very much not funny at all, but truly unhappiness producing and enough so that the unfunny picture one should hold in their mind of life under capitalism should prompt smart folks to risk any and all punishment for rebelling against the ruling class and the weapons they use to subjugate workers, the elimination of which is central to the peace and freedom that comes with A World with No Weapons. 

For those for whom the tyranny of 40 hour a week slavery is not enough to overcome the punishment that rebellion against the ruling class promises, consider the horror of mass death from nuclear radiation sickness whose attack on the body is the digestion of one’s innards by one’s own stomach acid spilled out through ruptures in the stomach lining caused by the nuclear radiation. How about seeing that happening to your kids?

Does anybody care enough to make the attempt to do something about it? How about the old farts out there, who on entering the boring retirement years have nothing better to do with their lives than fart in each other’s faces and lie to each other about the stench. One can’t help despising the old folks so settled in their delusions and ritual imitations of a happy life by that time like Valentine’s Day, Mother’s Day and Christmas. Help change the world for the better, all of you, or hurry up and die and go to hell and get it over with. 

And let’s not limit the despising and ridicule of people who will not join this effort to make a World with No Weapons to just the old.  Anybody who refuses to help in this fight against tyranny and approaching nuclear annihilation should be kicked in the ass and spit on. Damn the notion of innocent bystanders. There are none in this effort. You are either a friend of this revolution or an enemy of this revolution, the latter consisting not just of the active enemies of the ruling class who will ever resist anything that reduces their power over the working class, but also of the asshole morons in the working class who use their money mostly past some point to buy the convincing delusions they need to avoid the realization of their meaningless lives that would drive them to suicide.  

If the imaginary Man upstairs was evaluating modern society with the same scrutiny He did Sodom and Gomorrah, bet He’d have a harder time finding one good person over the age of 30 to save the town for than back then. For in this era when the men are clockwork castrated psychologically and the women clockwork raped, psychologically and otherwise, by people with direct power over them like their bosses at work, there’s nothing left in town worth saving.

Oh, you submissive fool! Don’t you understand that past some point of continuously choosing the lesser of two evils what happens is your getting an enormous dose of that seemingly lesser evil. And that eventually turns you into an evil sneaky jerk yourself, the female variety included, or your just being out and out destroyed by the evil done you that you obediently put up no resistance to because you were told by the ruling class controlled media that being an asshole slave was a good thing that would eventually deliver substantial rewards as with a happy retirement and/or an eternity of happiness in a Heaven that doesn’t exist and/or that your kids would be better off because of your suffering, the biggest lie of all.   

It’s a terribly bad scene because accepting all the crap that brings you down in spirit also generates a great deal of resentment in you, not only towards those who beat you up but also in being unable to retaliate on the perpetrators towards people who never did anything to you. This latter dynamic that arises from a life of rationalized slavery is called misdirected aggression and well treated in the earlier sections of this work. It is in modern times a dominant reason why there is so much violence both domestically in our endless mass murders and internationally in the ever escalating wars we see in the Middle East and in the Ukraine today. Can’t you see that it is weapons that have brought this about and only their elimination can make these problems go away?  

We have always thought over the years of our trying to solve these problems that spelling out the truth with scientific firmness would expose the 24/7 lies of the ruling class that so fog people’s minds and make it near impossible for them to understand what makes for their unhappiness and what can be done in rebellion against the ruling class to get rid of it.  But we found over the years, a bit to our naďve surprise, that you have to first get this weighty science past the science censors before the public would consider it as scientific truth. This means past the PhDs who teach at an accredited university that effectively rule on what new discoveries constitute valid science by their openly saying that it is valid. And if they rule against it, as the Roman Catholic Church and their university level monks did against the early astronomical science of Copernicus and Galileo, there’s not much you can do about it.

Where the church held total power on the continent of Europe during the medieval era emerging scientists were burned at the stake. Few people realize that the Law of Gravity of Isaac Newton would never have taken root if did not develop in England, which through Henry VIII for personal reasons was a powerful enough enemy of the Pope to nurture these new ideas.      

In modern times, again we have the ruling class vetoing science where its implications conflict with their ownership of the people. Evolution? Forget that the biomedical science that keeps even ruling class assholes healthy makes no sense without Darwinian evolution as its indispensible theoretical foundation. But almost as bad as that level of censorship is the strangling of new ideas that comes from the competitive game of academia itself. In reality having other scientists give a “thumbs up” to your research work means a lot for obtaining status, your paycheck and financial grants, most of which come from government agencies that are effectively controlled by the ruling class who own our legislators through campaign contributions. As thick and unavoidable as banks who collude as cartels to jiggle currency markets and rob small investors is the collusion of scientists to achieve success by any means in the time honored strategy of “you scratch my back and I’ll scratch yours.” As such modern science, in practice outside of practical result driven technology, winds up a cartel that cares less about scientific truth than personal success.         

And from this overriding strategy of human nature operating at less than its ethical best, outsiders to the game who aren’t back scratchers, who can’t repay a scratch because they have no institutional power, have their ideas dismissed in this environment of academic information corruption. A form of this is seen in science experts who cling to invalid hypotheses rather than questioning them to the point that would take away their expert status, for one is only an expert when the information one possesses is valid. Our problem with revising microstate thermodynamics laid out in Section 5 is a case in point. 

And there are the homosexual types in academia that amusingly (to us) believing in whatever is in the textbook with a level of zeal as though they’d developed the ideas themselves as in those who specialize in Newtonian mechanics feeling that they’re as smart as Isaac Newton himself. 

One such of our recent acquaintance is Jonathan Poritz of Colorado State University at Pueblo (CSU-P), a PhD mathematician who fears his mommy might find out there’s someone out there who’s smarter than Jonathan. This type of small time megalomania is so important for gay professionals for balancing their less desirable attributes. Is this guy gay? Have no idea what he does behind a locked door, nor care to know, but the mode of his bait and switch ploy seems very familiar. Let me try to paint of picture of Dr. Poritz in terms of someone I recall from a long time ago.

The year I went off to high school, 1956, we had just moved to one of the better middle class neighborhoods in Revere, MA, better in the sense that the City Manager lived two doors down from us on this street. Directly across the street from us lived the Belgiorno’s. They were noticeable to a teenage boy like me because the father in the Belgiorno family, Al Belgiorno, always had a brand new Ford in his driveway. Every year a new one would pop up. Teenage boys crazy about cars as all were back in those days, and maybe now too, notice such things. 

While this thing about Al Belgiorno gave him and by extension the entire Belgiorno family a few status points, the overall image of Al from his physical appearance and unimposing demeanor intuitively took away a significant number of status points for he was noticeably slack jawed, balding and kind of grey looking. As to the flux of ever new automobiles, that happened because Al was a salesman for the Gerber Baby Food Corporation. He kept up the stock of Gerber baby food on the shelves of the grocery stores in the area and they gave him a new Ford every year to do this.

Get to the point, my cerebral monitor is telling me. Now the Belgiorno’s had a nice bunch of shrubbery on their front lawn and my mother as an aspiring upper middle class jerk had her put lots of shrubbery on the front lawn of our new house, possibly to keep up with or even to outdo our neighbors across the street.  Such a stupid rivalry with people who were obvious mediocre nobodies was apparent from her proclaiming to me at some point in my high school years, “We’re better than the Belgiorno’s.” I don’t remember her ever saying anything like that about anybody else.

Though she was right. Not so much because our shrubbery was better than theirs or our house was newer than the Belgiorno’s even if they had a new car in their driveway every year. But because Marge Belgiorno, the mother of the Belgiorno family, (who can’t possibly be yet alive at this time to be offended), was a worse typical 50s mother than my own mother, who was bad enough in her own right as I hope I’ve made subtly clear.

How so? The salient indicator of the lesser worth of Marge Belgiorno relative to my mother was not in their shrubbery, which I always thought was neither better nor worse than ours whatever my mother’s estimate of it, but the existence of Stephen Belgiorno, the one son they had. This kid was about ten years younger than me so I really seldom even noticed his existence. But Victor, a high school chum of mine who lived a couple of doors up and was a good enough rock and roll pianist to play with a group at teen dances just about every weekend, used to call Stephen Belgiorno by the name, Mary Belgiorno. He would address the kid when occasion arose to say something to him as Mary. 

Now I would never have done that, knocking a little kid like that. And to be honest, I had zero idea of the connotations of calling Stephen Mary as to his leaning towards or being destined to be homosexual, though in retrospect Stephen kind of did act a bit more like a Mary Belgiorno than a Stephen Belgiorno. Further description of this boy as to his personality being feminine and such even if objective would only mark me as a homophobic monster.

And for all I know Stephen, aka Mary, Belgiorno didn’t turn out to be actually gay. His older sister, Paula Belgiorno, married a milky puppet of a guy that the Belgiorno mother possessed and controlled with her strings fully attached to him. And after they had a kid, Paula and her puppet like husband became the perfect 50s family in the neighborhood, increasing the Belgiorno’s family status with this just like with Al’s new car in the driveway every year. The point is that the mother, very clever as I hope I made clear with her maintaining a pretty good bright plastic frontage, might also have wangled some kind of wife for Stephen (Mary) Belgiorno that would not have made him a candidate today for same sex marriage. 

Anyway that’s our impression of the persona that Jonathan Poritz has, near enough to a faggot to behave like the few out and out faggot mathematicians Ruth and I have ran into in our careers of having to deal with popinjay scientists in our quest to save the world from nuclear annihilation. And I’m sure the rest of the science faculty at CSU-P, who were no more helpful to us than Jonathan, knows this about Jonathan Poritz, too, as they weren’t that much different than him, emails with seven of them available upon request to make it clear why we feel this way. 

So that’s what we’re up against in trying to get us all to A World with No Weapons, the enslaved 99% of America who can’t get beyond their religious and ideological delusions to see the firm mathematical truth of their unhappy situations and that nuclear nightmare is on the horizon, the triple asshole ruling class 1% who have no problem killing the message and the messenger to retain their lives of privileged decadence and the plethora of momma’s boy scientists content to live in their well feathered nests, no more worthy of respect than the gay comedian who stars in the Big Bang Theory comedy about preposterously pretentious scientists.                                                         

  Section 18. Molecular Evolution

This work was done some years back. It was kindly reviewed for me by Dennis Sullivan, a National Medal of Science recipient in 2004. His comments should make it worth reading for the professional scientist.  

Mon, 27 Feb 2006 23:50: why not publish the part that explains Posner's data in terms of the logistical equation ...first... then do some of the rest  next... etc... then as your acceptance takes hold do the more radical parts...as it is you may be pre-empting any real success by indulging your own deeply felt philosophy... by the way your explanations in the first parts were very clear....you may want to read how Einstein in similar and simple layman's terms dispelled the notion of absolute time in the 1905 paper....and how he did it without being untoward...

good luck  

dennis Sullivan            


(Note that equation numbers 309-395 are not used. Also note in the N=2 molecular population evolution to be discussed that the variables in the F1 fitness function of Eq274 are replaced as follows: F1 by F; b1 by b; d2 by d; and F2, b2 and d2 by FR, bR and dR. And note also that the growth rate is specified by capital G rather than small case g.)


The molecular evolution used to prove the generality of the natural selection aspect evolution is the evolution or phase change of an
amorphous calcium phosphate “population” of molecules, ACP, to a crystalline calcium phosphate called hydroxyapatite, HA. This molecular evolution or phase change has been well studied and thoroughly quantified in the biophysics literature because it is an in vitro analog of the transformation of immature hard tissue, bone and teeth, to mature bone and teeth. Its parallel to biological evolution lies in the self-seeding, exponential nature of molecular replication. In the experiments done, a precipitation of solid phase calcium phosphate results from the mixing of calcium and phosphate solutions at high concentrations. The first precipitate obtained is the amorphous calcium phosphate, ACP, with formula, Ca3(PO4)2(H20)n, where n is a variable number of hydrating water molecules. This initial calcium phosphate precipitate is said to be amorphous because of its diffuse X-ray diffraction pattern, which is more like that of amorphous liquids than of crystalline solids. The ACP molecules clump together in large spherical agglomerates dispersed in a suspension of dilute calcium and phosphate ion mother liquor. This ACP transforms over time to a crystalline calcium phosphate called hydroxyapatite, HA, formula, Ca10(PO4)6(OH)2. The transformation of the ACP amorphous solid to the HA crystalline solid is represented below. (We use the non-subscripted fitness variables for the molecular population variables, a minor screw up in the symbol reference, but still clear.) 

(396)                                                                  ACP ŕ HA

The ACP and HA molecules may be understood to transform into one another in a way that is mathematically the same as individuals of one biological population transforming into those of another to another during Darwinian natural selection, that is, by solid molecules of ACP and HA being born and dying via precipitation and dissolution events. Both ACP and HA have a birth rate or precipitation rate constant, that of HA represented as b and that of its rival molecular population, ACP, as bR. And both ACP and HA have a death rate or dissolution rate constant, that of HA represented as d and that of ACP as dR.

The mechanism of the ACP ŕ HA transformation was quantitatively investigated over an extended period in kinetic studies done mostly in the laboratory of Aaron S. Posner, then Director of the Research Division of the New York Hospital for Special Surgery, Cornell Medical School, with findings relevant to our analysis published as:

Study I: (Eanes, E. D. and Posner, A.S.: Kinetics and Mechanism of the Conversion of Noncrystalline Calcium Phosphate & to Crystalline Hydroxyapatite) Transactions of the New York Academy of Sciences, 28, p. 233, 1965);

Study II: (Boskey, A. L. and Posner, A. S.: Conversion of Amorphous Calcium Phosphate to Microcrystalline Hydroxyapatite, Journal of Physical Chemistry, 77, 2313, 1973);

Study III: (Boskey, A. L. and Posner, A. S.: Formation of Hydroxyapatite at Low Supersaturation, Journal of Physical Chemistry, 80, 40, 1976)

In Study I, X-ray diffraction methods were used to obtain kinetic data for the ACP ŕ HA transformation. Plots from study I of the amount of HA formed in the reaction vessel vs. the time of reaction are shown below.

                                                                 Other%20S%20Curve

      Figure 397. Concentration of HA vs. time in reaction system under condition of constant stirring. Concentration is expressed as percent crystallinity.

                                                                  S%20Curve

           Figure 398. Concentration of HA vs. time in reaction system under static conditions. Concentration is expressed as percent crystallinity.

The sigmoid shape of HA growth in the linear plots of Figure 397 and Figure 398 is clear and is also seen in another half dozen HA growth curves done in the Study II.  Also given in Study I is a logarithmic plot of the HA growth data of Figure 397.

 

                                                                   Log%20Plot

                                            Figure 399. Logarithm of percent crystallinity vs. time for same data in Figure 398.

Study I derived a function for the ascending portion of the above plot, called the proliferation period of HA growth. From simple observation of the straight line seen in the plot, the authors took the functional relationship to be

(400)             

In the above C is the concentration of HA and k is an unspecified constant. From the above they obtained the differential equation 

(401)                   

This is the governing kinetic expression for HA growth in the proliferation period. This expression indicates that the  speed of formation of HA at any time is proportional to the C concentration of HA already present in the reaction vessel. Such a mechanism of growth in which the rate of formation of a substance is proportional to the amount already formed is called autocatalytic. This means that the growth of new HA derives from existing HA which acts as a seed or template for further HA growth. This mechanism for HA growth is operationally identical to biological population growth, whereby the rate of growth of new organisms, , as seen in Eq1, , depends on the x number of existing organisms that act as seeds or templates for further production of the organisms.

This conclusion from Study I was important in its physiological implications that bone, which is essentially HA, matures by an autocatalytic process that is biologically passive rather than active. However their understanding of the ACP ŕ HA transformation as represented by Eq400&401 is chemically naive and a bit misleading. We show next the ACPŕHA transformation they studied must take the form, rather, of the natural selection equations of Eqs269&272 and that the phase change process is just a kind of competitive growth or molecular natural selection no different mechanistically than what occurs for competing biological populations. Note that Eqs269&272 should be read for this phase change molecular evolution with the unscripted symbols as 

(269a)                      

 

(272a)                     

 

Their understanding of the HA growth process as governed by Eq401 is an oversimplification because it takes into account only the proliferation period of HA growth, ignoring the final period of growth, the horizontal line part in the graph of Figure 399, which also needs to be considered to understand the true nature of the ACPŕHA transformation. That their Eq401 does not describe the complete process is clear when we consider a plot of (x vs. t) for the solution to Eq201, not specified in any of the studies, which is

(402)                                                       

In the above, Co is initial or seed concentration of HA, the source of which shall be clarified shortly. For present purposes, we want to note that a plot of x vs. t for the above function is a simple exponential curve that increases without limit rather than the sigmoid curve of the experimental data on the ACP ŕ HA transformation in Figures 397&398. Also the ascending straight line that would be produced by a logarithmic plot of the C and t variables in Eq202, that is, logC vs. t, would rise without limit rather than flattening out as the experimental data of Figure 399 shows at t=6.5 hours. Hence their kinetic equation of Eq202 does not describe the process properly, that expression distorting the true mechanism of the growth of HA from ACP, which, as we shall next make clear, is properly described by the natural selection equations, Eqs269a&272a.

The similarity of the sigmoid curve of the experimental HA growth curves of Figures 397&398 to the sigmoid curve of logistical growth in Figure 255 and to the ascending (blue) sigmoid curve of competitive growth in Figure 273 suggests that HA growth from ACP might be either a kind of logistical growth or a kind of competitive growth. We decide between these two possibilities from the following argument. Chemical analysis in these studies shows the total amount or mass of solid phase calcium phosphate precipitate, whether as ACP or HA, to remain essentially constant during the ACP ŕ HA transformation. Hence as the amount of solid phase HA increases over time as seen in Figures 397,398&399, the concentration of ACP must decrease concomitantly in what is essentially a zero sum game between the HA and ACP phases. Thus the ascending HA growth sigmoid curve in Figures 397&398 must be matched by a mirror image descending ACP sigmoid curve as penciled in our minds eye, one that would look very much like the descending (red) sigmoid curve in the competitive growth plot in Figure 273. This similarity in the experimental data of Figures 397&398 to Figure 273 points to a competitive growth explanation for the ACP ŕ HA transformation because the kinetic data fit the functions of competitive growth or natural selection of biological organisms. This has us understanding HA growth to fit the evolution equation of Eq269a.

(403)                                     

And it has a time solution parallel to Eq266 of

(404)                                            


And we assume the ACP molecular population to grow, from Eq272a, as

(272b)                                     

And its time solution is in parallel to the time solution of Eq271 as

(205)                                 

To test these equations derived for biological population growth for generating the ACP ŕ HA transformation, we must consider that chemical transformation from a population perspective, that is, consider HA as a population of HA molecules and HA growth as an increase in the number of HA molecules over time; and consider the ACP decrease as that of a population of ACP molecules which decrease in number over time. To understand the changes in HA over time from this population perspective, we need to convert the C concentration of HA obtained as % HA crystallinity in the X-ray studies into some number of HA molecules which we shall designate as x. This conversion of variables from C concentration or % crystallinity measure to an x number of HA molecules understands the 100% crystallinity of HA value in the experimental plots of Figures 397&398 as the maximum number of HA molecules found at the end of the reaction.

Taking for numerical ease the maximum concentration of HA at 100% HA crystallinity to be approximately 1/6 of a mole of HA and understanding there to be an Avogadro’s Number of 6.023x1023 molecules in a mole, we take the maximum number of HA molecules at 100% HA crystallinity to be 1023 HA molecules. In parallel to the K maximum number of focus population organisms in competitive population growth, we will understand this 1023 maximum number of HA molecules to be K in the above equations when they are taken to represent the ACPŕ HA transformation as a competitive growth, K=1023.

We will also take the K=1023 value to be the maximum number of ACP molecules. To do that, given the divergent stoichiometry of HA and ACP as Ca10(PO)4(OH)2 and Ca3(PO4)2(H20)n respectively, we must consider the ACP molecules three at time, that is, as a triplet ACP form with formula written as [Ca3(PO4)2(H20)n]3. Note that this triplet ACP, [Ca3(PO4)2(H20)n]3, has no reality other than to provide a stoichiometric equivalent form to HA, Ca10(PO)6(OH)2. Note that this ACP form and HA have the same number of six PO4--- , phosphate ions, but that the ACP form is deficient by one Ca++, calcium ion relative to HA.

Given our earlier stated understanding that the amount of solid phase calcium phosphate, be it ACP or HA, remains appreciably constant in the reaction, the above triplet representation of ACP allows us to understand the maximum number of ACP molecules as K=1023 given that the ACP and HA have the same number of PO---, phosphate, ions in them, if we can make the case that the Ca++ ion deficit in ACP relative to HA is corrected or made up by an uptake of Ca++ ions from the mother liquor as the ACP ŕ HA transformation proceeds. This is exactly what happens as shown in Study II wherein mother liquor Ca++ ion concentration at the beginning of the ACP ŕ HA transformation, at 0% HA crystallinity, is seen to decrease progressively as ACP is transformed to HA, which indicates such a progressive uptake of Ca++ ions into the solid phase during the transformation.

This stoichiometric simplification of ACP not only allows for K to represent both the maximum number of ACP molecules and the maximum number of HA molecules, but also, with the number of triplet ACP molecules given as xR, understands the total number ACP and HA molecules at any time to be is K.

(406)                                                  x  +  x= K

This relationship between the number of triplet ACP and HA at any time is the same as x1 + x2 =K function of Eq261 for biological competitive growth, which facilitates our efforts to understand the ACP ŕ HA transformation as competitive growth or natural selection. To further test the fit of these equations to the ACP ŕ HA transformation data, we next make a logarithmic plot for HA growth as it would be generated by Eq404 

(407)             

Using the parameters of K=1023, x0=1, (this x0=1 representing a first HA molecule whose origins we shall make clear shortly) and F=.8 in the above, we obtain the logarithmic plot of x in the above vs. time as shown below.

                                                        

                                                                Figure 408. Theoretical Logarithmic Plot of HA Formation 

 

The remarkable similarity in the shape of this logarithmic curve of HA growth, as obtained from the log plot of Eq404, to that of the experimental logarithmic curve of HA growth of Figure 399 indicates that the form of the log plot of Eq404 has a perfect fit to the data and, on that basis, that it and its parent differential equation, Eq403, may be understood to derive HA growth and by extension Eqs272b&405, the ACP decay part of the ACPŕHA transformation. We consider the fit of this representation of the process further by writing out the Eqs203&188b differential equations with F and FR expanded via Eqs269a&272b so as to be able to key in on the details of the expanded molecular birth and death rate terms to see if they fit the chemistry of the ACP ŕ HA transformation. 

 

(409)             

 

(410)                


We have already clarified x in the above as the number of HA molecules, xR as the number of (triplet) ACP molecules and K=1023 as the total number of solid phase molecules, HA or ACP, at any time. What is required now to justify the above equations as determining the kinetics of the ACP
ŕ HA transformation is our explaining, from standard physical chemical theory and/or from specific empirical evidence, the reasonableness of the  and   terms in Eq409 as determinants of the  rate of formation of HA; and the reasonableness of the  and terms in Eq210 as determinants of the  rate of decay of ACP.

The b parameter in the term in Eq109 is readily interpreted as the birth rate or precipitation rate constant of HA molecules. It is the rate constant of the precipitation process, which is a standard factor in the  rate of formation of HA. The x variable in affects  because the  rate of growth of HA is necessarily proportional to the x number of existing HA molecules as fits the self-seeding autocatalytic mechanism of HA growth concluded in the laboratory studies. The xR variable in affects  because the rate of formation of HA depends on the xR amount of ACP, this relationship most obvious when all the ACP needed to make HA is used up, xR=0, and the reaction ceases with =0 as seen from the laboratory data.


Note importantly that b as the precipitation constant, a chemical parameter, does not change over time as b does as the birth rate in biological evolution, thus explaining, in part, why there is such a tight fit of the ACP
ŕHA kinetics to the natural selection equations. Another reason for the tight fit is that the number of moieties in the chemical phase change is K=1023, a large enough number, to be sure, to remove all stochastic irregularity from the evolving system.

The d parameter in the  term in Eq109 is the death rate or dissolution rate constant of HA molecules. Its proportional relationship to –(dx/dt) is readily understandable in a dissolution process whose rate is also proportional to the x number of HA molecules that can dissolve.

The bR parameter in the  term of Eq410 may be understood as a birth rate or precipitation rate constant for the ACP molecules. The relationship of  to  in Eq410 suggests that the rate of precipitation of ACP may be proportional to the xR number of existing ACP molecules and that its precipitation is, thus, self-seeding or autocatalytic as the growth process for HA is. But that is not the case. Rather the precipitation rate of ACP is proportional to , this, though, sufficiently close to xR quantitatively to fit the natural selection equations and for the process to be understood as such.


We show this by providing clear evidence that ACP precipitation is proportional to the surface area of the large ACP agglomerates suspended in the mother liquor. The evidence for such a surface mediated ACP precipitation is obtained indirectly from an understanding of the rate of formation of the initial HA crystals in the ACP
ŕ HA transformation being proportional to the surface area of the ACP agglomerates as was shown in a thermodynamic analysis done by Peter Calabria.

(Calabria, P. V., A Kinetic Study of the Heterogeneous Nucleation of Hydroxyapatite on Amorphous Calcium Phosphate Particles, PhD Thesis, Rensselaer Polytechnic Institute, Troy, NY, 1980)

(Calabria, P. V. and Katz, J. L.: The Kinetics and Mechanism of Heterogeneous Hydroxyapatite Nucleation, International Association of Dental research Abstracts, Abstract # 448, 1970).</