Hiroshima, 1945                                              Washington, DC, 2025


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 Burning His Two Stepsons Alive and Ed’s Cousin, Don Graf.
I’ll give their stories and how I managed to escape their fundamentalist LCMS clan
in Section 4 between mathematics that precisely clarifies
the violence priming
unhappiness of workday enslavement whose reality is hidden from us
in the lies of the media and our politicians, one of the cleverest of


Whom is wife of “I did not have sexual relations with that woman” mega-liar Bill Clinton.
Think twice before trusting the caring tone of this well groomed, self-interested snake.
Hillary is also dangerously stupid as seen in her ego-driven takedown of the Gadhafi
regime that totally destabilized Libya and gave bloodthirsty ISIS a foothold there. 

endless lies in today’s hyper-Orwellian America are significantly sustained by an
academic community devoted to position and paycheck rather than truth as seen
in their dogmatic commitment to the incorrect entropy function inscribed on


Ludwig Boltzmann’s Tombstone

Nobody is a greater devotee of Boltzmann’s Balderdash than Bill Poirier


He is the author of A Conceptual Guide to Thermodynamics whose mangling of information
theory confounds not only a proper understanding of entropy but also of the thought
and emotional machinery of the human mind needed to be understood well to
make sense of the terrible predicament the human race has gotten itself into. 

By Ruth Marion Graf and Dr. Peter V. Calabria, PhD, Biophysics

© Ruth Marion Graf, 2/21/15                                   contact: ruthmariongraf@gmail.com

An unvarnished understanding of human nature predicts that man’s ineradicable instinct for violence combined with modern weapons will lead in the next decade to the annihilation of the human race unless we get ourselves to A World with No Weapons before the international conflict seen daily on our front pages goes critical. The problem with explaining this mess clearly enough to generate confidence in this prediction sufficient to rally people to do something about it is that our sense of human nature is majorly confused not just from the unexplained complexity of the human emotions that human nature depends on but also from the misleading ideologies, religious dogmas, wishful thinking and competitive disingenuousness that further confound our understanding of what makes us tick.

Understanding human nature correctly is not a totally intractable problem, though, if approached mathematically for math has an excellent track record of unravelling mysteries of nature once thought incomprehensible like planetary motion, magnetism and genetics. We explain human nature mathematically by elaborating information theory with a function for diversity developed in 1949 by the British statistician and WWII code cracker, Edward Hugh Simpson. His Simpson’s Reciprocal Diversity Index enables a thorough expansion of information theory that remedies the shortcomings in it talked about in the June, 1995, john Horgan, 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.

A revision of information theory using Simpson’s diversity measure explains clearly for the first time how the mind processes meaningful information in terms of its significance and insignificance and its association with emotion. This approach enables us mathematically describe our basic emotions like fear, hope, excitement, relief, dismay, anxiousness, depression, joy, hunger, sex, love and the anger that sits bottled up in man from social control that is at the root of our worst problems. And it shows modern human nature to be a perversion of primitive human nature brought about by millennia of civilized socialization that has brought about a peculiar form of violence called redirected aggression that is particularly dangerous in this era of advanced modern weapons.

Russia’s effective invasion of the Ukraine that includes Putin’s repeated waving of Russia’s 8000 strong arsenal of nuclear weapons in the face of the United States and the West should not be dismissed lightly. The international headlines make it clear that nuclear war is a distinctly real possibility. And we should not be blaming just the enemies of America for being the cause of the violence in the world that threatens to destroy it for we are not the nation of George Washington and Abraham Lincoln anymore, but a world empire that puts the value of its control of people way ahead of their welfare, whatever the endless moralizing about our goodness used to cover the worst of what money run democratic capitalism does to individuals at home and abroad. Our precise mathematical analysis of the worst side of human nature, the violent side, makes it clear that nuclear war is eventually inevitable unless weapons are eliminated by a mass movement of all the world’s people before World War III irreversibly begins.        

That the human race will go extinct if weapons are not banned internationally is inescapable if one is rational enough to trust in the truth of 2+3=5 mathematics. Our argument is lost, though, on those who believe that God’s omnipotence supersedes mathematics in being able to make 2+3 be something other than 5 if He wishes. These worshippers of magical beings who also believe God will be there to save us from the end of the world or if it does comes, that it is God’s will are worthless in the fight that man must take up himself to rid the world of weapons. Those who want to support this can become a member of the World with No Weapons movement by sending a $20 donation. We will use the bulk of the money donated to support candidates in the 2016 election, perhaps also including myself, a woman mathematician, who understands the need to change the planet into A World with No Weapons. For those who understand the dire need for this and for those who yet need some convincing we begin meaningful information theory with a careful consideration of the most basic operation in mathematics, counting.  

1. Counting

The simplest thing in mathematics are the counting numbers: 1, 2, 3, 4, and so on. But even counting isn’t as simple as it seems. Count the number of objects in (■■■■). There are 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 exact?

There’s something not quite right with counting the unequal sized objects in (■■) as 4. Counting 4 objects in (■■) is inexact. You remember the grade school caveat against adding things together that are different in kind like adding 2 galaxies up with 2 kittens. This restriction also holds for adding or counting things together 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 are exactly the same in size. Four pounds is an exact count of pounds because all pounds are the same size 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 of pounds or fluid ounces or inches, which is why standard measure underpins all commercial transactions, other than when things sold are the same size, like large eggs, which are then sold by dozen number of eggs. 

We make this point of counting objects not the same size being inexact in a more rigorous way by considering a set of K=12 objects all the same size, (■■■■■, ■■■, ■■■, ), divided into N=4 color subsets that are not the same size. The K=12 count of the objects is exact because the objects are “unit objects” all the same size. 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 them. To make it analytically clear that there is an error in counting the number of subsets in (■■■■■, ■■■, ■■■, ) as N=4, we need to first formally describe the set as consisting of x1=5 red objects, x2=3 green objects, x3=3 purple objects and x4=1 black object, in shorthand the (5, 3, 3, 1) natural number set, (one that consists only of positive integers and zeroes.) 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,    

1.)                               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 an easy 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).

2.)                               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 fleshed out in 47 chapters of myriad examples in the modern classic, The Flaw of Averages. A very direct way of understanding the inexactness or error in the µ arithmetic average is to note that the mean or arithmetic average is always associated with a statistical error measure, explicitly or implicitly. The most common statistical error used is the standard deviation, σ, (sigma),

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

For the N=4, µ=3, (5, 3, 3, 1) set,

3a.)                             http://matrix-evolutions.com/INDEX_files/image005.gif=http://matrix-evolutions.com/INDEX_files/image006.gif=1.414

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

4.)                               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 of σ=1.414 or r=47.1%, can also be understood as a counting error in the N number of subsets variable that appears in µ=K/N. The K=12 count of the unit objects in (■■■■■, ■■■, ■■■, ) in µ=K/N is exact because all K=12 objects are the same size. Hence the statistical error or inexactness in µ=K/N, whether as σ=1.414 or r=.471, arises from the inexactness in the N=4 count of the unequal sized subsets in the (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1) set.

To further make the point of the counting of unequal sized subsets being inexact from the statistical error inherently associated with them, let’s 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 Eq3, its statistical error is σ=r=0, which suggests from what we have said above no error or inaccuracy in µ and, hence, no error or inaccuracy in either the K or the N variables that make up µ=K/N. And that 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.

Since many systems of things in the natural world have constituents of different size, the inexactness in counting those constituents straight up with a simple 1, 2, 3, 4, count poses a genuine problem in understanding those systems correctly. This is decidedly the case for the N number of sensory and/or verbal messages of different kinds the human mind receives as information from moment to moment that are generally unequal in size both in terms of the frequencies of the messages received and the sizes of the objects in them. And it is also the case for the N number of molecules in a chemical system unequal in size in terms of their molecular energy as is clear from their Maxwell-Boltzmann energy distribution.


The latter problem affects a proper understanding of entropy, the solution to which using an exact quantification of the N number of molecules very much impinges upon a correct understanding of information, which in turn provides for a clear and correct understanding of the thought and emotional machinery of the human mind, totally central for understanding the violent side of human nature and why weapons must be gotten rid of as the only solution to avoiding an annihilating nuclear war. The exact quantification of the N number of any set of things that solves the twin problems of entropy and information is the diversity of the set. 

2. Diversity

Diversity is a concept with such broad application that we might guess it to have been part of science for a long time. But it is relatively new in mathematical form, having arisen only after WWII in the work of the British statistician, Edward Hugh Simpson. We will focus to begin with on one of the Simpson diversity indices to show how diversity solves the problem of the inexact counting of unbalanced subsets like (■■■■■, ■■■, ■■■, ). We see intuitively that N=4 color set of objects, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), is greater in color diversity than the N=2 color set, (■■■■■■, ■■■■■■), (6, 6), from the former having a greater N number of colors in it than the latter. A measure for diversity that fits this intuitive sense is the Simpson’s Reciprocal Diversity Index. It can be defined in terms of the K and xi parameters of the set as


For the N=4, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), set, the D Simpson’s Reciprocal Diversity Index is

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

And for the N=2, (■■■■■■, ■■■■■■), (6, 6), set, it is       

7.)                                       Dhttp://matrix-evolutions.com/INDEX_files/image010.gif  

This fits our intuitive sense of color diversity being greater the greater the N number of colors in a set. For both of these balanced sets and for all balanced sets we see   

8.)                                           D = N      (balanced)

For the N=4 color unbalanced set, (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), the diversity is from Eq5,

9.)                               http://matrix-evolutions.com/INDEX_files/image011.gif                                                   

The smaller subsets of a unbalanced set contribute less to its diversity so as to generally make for

10.)                               D < N      (unbalanced)

Indeed we might think of the x4=1 object in the black subset of (■■■■■, ■■■, ■■■, ) contributing only token diversity to the diversity of the set. What is important is to see that D is an exact quantification of the subsets in a set, be it balanced or unbalanced, because, as we see from Eq5, D is a function of the exact K count of the total number of objects in a set and also of the exact count of the xi number of (same sized) unit objects in each subset, i=1, 2,…N. Hence D is understandable as an exact correlate of the N inexact number of subsets in an unbalanced set.

Another way of appreciating the exactness in the D diversity index comes from understanding it as a statistical function. To do that we first express the σ standard deviation of Eq3 as its square, σ2, called the variance statistical error of statistics.  


Solving the above for the summation term obtains,


Now inserting this summation term into D of Eq5 obtains D via µ of Eq2 and r of Eq4 as

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

Bottom of Form

This shows exact D developed from inexact N via the inclusion of the r relative error measure of inexactness in N. This reinforces D as an exact correlate of inexact N that can be used in place of N as an exact quantification of the constituents that make up an unbalanced set. This has important ramifications for properly understanding information and entropy. We choose to explain the entropy of a thermodynamic system in terms of diversity because understanding diversity as an exact corrective of physical system first gives a firm basis for using it to explain the less concrete phenomenon of information as the human mind processes it in the clearest way. The mathematics of it takes us some distance from our primary topics of interest, but the additional homework needed to follow the (yet clear) argument is worth it because we need a firm foundation for talking about aspects of information and mind that can be contentious and only be resolved by precise argument.  

3. Entropy

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 of K discrete (or whole numbered) energy units divided or distributed over 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 distribution of K=4 energy units over N=2 molecules has the same diversity measures: (2, 2) for both molecules having 2 of the K=4 energy units with a diversity of D=2; (4, 0) for one molecule having all 4 of the K=4 energy units and the other molecule none with a diversity of D=1; and (3, 1) for one molecule having 3 of the K=4 energy units and the other molecule, 1, with a diversity of D=1.6.

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, that derive from the combinatorial statistic,

14.)                            ω = NK

Specifically for K=4 candies distributed randomly to N=2 children, the ω number of ways that can occur is

15.)                        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,

16.)                                        (■, 0); (, ); (■, ); (■, ); (, ); (, ); (, ); (, )
, ); (, ); (■, ); (, ); (, ); (■, ); (, ); (0, )

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

17.)                     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 


The average variance, σ2AV, enables us to calculate the average diversity of the random distribution, DAV, from Eq13 with σ2AV replacing σ2 and DAV replacing D. 



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




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 Eq15, those permutations being  

21.)                                  (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 Eq17 to Eq20 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,


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


As things turn out this variance of an equiprobable multinomial distribution is the average variance of an equiprobable distribution, σ2AV, of Eq18 we developed for the K=4 over N=2 random distribution. Hence we can write Eq23 as  




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 Eq21 from the above as  


Eq24 can now be used to generate a shortcut formula for the average diversity, DAV, by substituting its σ2AV into Eq19 to obtain   



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 Eq23 with it. 


These conclusions also hold for the equiprobable distribution of K=4 energy units over N=2 molecules.  Such in a system of N=2 gas molecules in a container of fixed volume via collision between the molecules that results in a transfer of the K=4 energy units between molecules that results in an equiprobable distribution of the energy units over the molecules. In that case Line21 represent represents the average collision to collision change in the microstate permutations of Line21 though not necessarily in that sequence with the sense of the average variance, σ2AV, and the average diversity, DAV, the same as above. Now it becomes clear that the average diversity, DAV, is a measure of entropy on the basis of its near perfect direct proportionality to the famous expression for microstate entropy Boltzmann developed that is inscribed on his 1906 tombstone, in modern terminology,

28.)            S=kBlnΩ 

That is, S=kBlnΩ and DAV are directly proportional within a very small limit of error little different than are the Fahrenheit and Centigrade measures of temperature. To demonstrate this we need not even explain the meaning of the Ω (capital omega) variable in Boltzmann’s S entropy nor its kB term, which is a constant, but only have to show the exceedingly high correlation that exists between DAV and lnΩ. That is easy to show because both DAV and Ω are solely functions of the K number of energy units and N molecules of a thermodynamic system, DAV as seen in Eq26 and Ω along with lnΩ via standard formulae in mathematical physics.    




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


It works excellently for large n values. For example, it is seen that ln(170!) =706.5731is well approximated from Stirling’s approximation as ln170! ≈706.5726. The Stirling’s approximation form of the lnΩ expression of Eq30 is    


Now let’s use this formula to compare the lnΩ of randomly chosen large K over N equiprobable distributions to their DAV average diversity of Eq26.     

































Table 33. The lnΩ and DAV of Large K over N Distributions

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


Figure 34. 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 the distribution, K>N. 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 for 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 empirical perspective. However the two cannot both be correct even though both mathematically fit the data because the assumptions that underpin the two functions are mutually contradictory.

This requires some explaining. The ω = NK number of ways combinatorial statistic of Eq14 implies from the 16 microstate permutations of Line21 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. Another combinatorial statistic exists for enumerating the number of observably different ways that K categorically distinguishable objects can be arranged over N containers. It is


It clearly enumerates the number of ways that the K=4 red candies, (■■■■), which are categorically indistinguishable even if, as we also made clear, they are fundamentally distinguishable, can be arranged over N=2 containers or N=2 children. It is from Eq29,

34a.)                                                                           http://matrix-evolutions.com/INDEX_files/image009.gif

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

35a.)                                                                           (■■■■, 0); (■■■, ); (■■, ■■); (, ■■■); (0, ■■■■)

However 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 necessarily fundamentally distinguishable, unavoidably so in being able to be randomly distributed over different molecules that themselves reside in different places in space, as, hence, necessarily do the energy units the molecules contain. And if the Ω statistic makes absolutely no sense in describing the random description quantitatively, the lnΩ makes even less sense. What rather does make sense out of entropy as a physical quantity, and quite intuitively, is that entropy is a measure of the energy diversity or energy dispersal in thermodynamic system. See entropy as energy dispersal in Wikipedia.          

While the above argument tells us is that Boltzmann played with 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 this mathematical fit of hypothesis to data is usually strong empirical proof that the hypothesis is correct. In this case, though, it would seem that ln turns out to be no more than a fluke fit to the another function, DAV, that not only fits the data, but also makes physical sense out of entropy.

However the pretty much complete acceptance of Boltzmann’s ideas for the last hundred years as the only numerical fit to data for all that time makes it a very difficult notion to overthrow, Boltzmann being as much a revered saint of physical science as Newton and Maxwell and Einstein. This impediment to a correction of Boltzmann’s error demands further supporting evidence for the diversity entropy proposition. There are two very strong supporting arguments that exist, the next leg of our argument showing that diversity based entropy much better explains the empirical Maxwell-Boltzmann energy distribution than Boltzmann’s S entropy.  


Figure 35.

To do that we next introduce a new mathematical structure called the Average Configuration of a distribution. The configurations of the K=4 over N=2 distribution are listed below with their variances and diversity indices.



Variance, σ2 

Diversity, D

(4, 0)

[4, 0], [0,4]



(3, 1)

[3, 1], [1, 3]



(2, 2)

[2, 2]



Table 36. 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 Eq18&25 its average diversity of DAV=1.6 from Eqs20&27. We see by perusing 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 of the distribution. On that basis the (3, 1) configuration is understood to be a compressed representation 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 is a compressed representation of all the configurations of a random distribution much like the µ arithmetic average is one number that is a compressed representation of all the numbers in a number set, as the μ=K/N=4 arithmetic average is 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 that have its number set form, 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, which should be physically understood as the system’s microstates that exist at any one moment in time. The 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.    

21.)                                  (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 though not necessarily in this sequence, on average, over 16 instances of time via the random collisions and transfers of energy that come about for a thermodynamic system of N gas molecules flying about in a container of fixed volume. The (3, 1) Average Configuration represents the state of the system as measured over a time period greater than the individual instances that produce each microstate permutation of the system. If this microstate sense 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 distribution of Figure 35. 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 Eq24 the σ2AV average variance of this distribution to be  


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.



Figure 38. 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 35 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 Eq24, 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



Figure 39. 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 Eq24, 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



Figure 40. 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 Eq24, 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



Figure 41. 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

We are at this level considering K and N values large enough to show a moderately good resemblance to the classical Maxwell-Boltzmann distribution of Figure 35.


Figure 35.

As we progressively increase the K and N values of distributions, the plot of their energy per molecule versus the number of molecules with 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 the distribution with distinguishable energy units assumed. It does not require any additional assumptions, which the Boltzmann derivation of it decidedly does. As only one theory can be correct because of the mutually contradicting assumptions for the two of energy units being distinguishable or indistinguishable, this is a strong argument in favor of our unorthodox theory via the Occam’s razor principle that is used in science in an entirely general way for deciding between two explanations that both lead to correct conclusions on the basis of which has the fewest assumptions. In this case it is the unorthodox diversity underpinned explanation as suggests its being correct from the Occam’s razor principle.  

Another argument for the unorthodox view requires a refinement of diversity that will get us into a consideration of microstate temperature that strongly supports diversity based entropy in terms of a perfect fit of it not just to the Boltzmann microstate entropy but also, dimensionally, to Clausius macroscopic entropy. The correct diversity index measure for entropy, which also has an exceedingly high correlation to Boltzmann’s S entropy, is a close cousin of the D Simpson’s Reciprocal Diversity Index called the Square Root Diversity Index. We initially developed the argument for diversity based entropy using D because it has mathematical regularities like its simple relationship to the variance that make it easy to work with. Now that we have familiarized ourselves with some of the basic concepts of diversity based entropy using D, we introduce the square root entropy, h.

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

The pi variable in h is easy to understand as the weight fraction measure of the xi of a number set. Recall the K=12 object, N=4 color, (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), set that has x1=5 red objects, x2=3 green objects, x3=3 purple objects and x4=1 black object. The pi term in Eq42 is just the fractional measures of the colored objects formally defined as 


For the K=12, (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), set, the pi weight fractions are p1=x1/K=5/12, p2=x2/K=3/12=1/4; p3=1/4 and p4 =1/12. The p3=1/4, for example, just says that the purple objects represent 1/4 of all the objects in the set. The pi weight fractions are a convenient measure of the subsets of a set. The pi=xi/K weight fractions are exact in being a function of K, which is exact, and of the xi of a set, which are exact. Note from Eqs5&43 we could also have defined the D diversity index in terms of pi as



That h is a reasonable measure of diversity is seen when we evaluate it for the (■■■■■, ■■■, ■■■, ), (5, 3, 3, 1), set as



This compares to D=3.273 as a measure of the diversity of the (5, 3, 3, 1) set.  We see that h=3.464 is also a reduction from N=4 for this unbalanced set, just not quite as much as D=3.273. The two diversity indices, D and h, have comparable measures for diversity over a range of sets as seen below with h=N for balanced sets and h < N for unbalanced sets if not as much as D is.

Set of Unit Objects

Subset Values

D, Eq5

h, Eq42

(■■■, ■■■, ■■■, ■■■)

x1=x2= x3=x4=3



(■■■■■, ■■■, ■■■, )

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



(■■■■■■, ■■■■■■)




(■■■■, ■■■■, ■■■■)

x1=x2= x3=4



(■■■■■■, ■■■■■■, ■■■■■■■■■)

x1=x2=6,  x3=9



(■■■■■■, ■■■■■, )

x1=6, x2=5, x3=1



(■■■■■■■■■■, ■■■■■■■■■■, )

x1=x2=10, x3=1







Table 46. Various Sets and Their D and h Diversity Indices

Now we want to return to the topic of inexactness in the arithmetic average, µ, first discussed following Eq2 to ask if there is there an exact average for an unbalanced set. Yes, there are and we will consider two of them, one based on the D diversity and the other based on the h diversity. Much as we form the arithmetic average as the ratio of K to N with K/N=µ, we can form an average as the ratio of K to D to form the biased average, K/D, to which we give the symbol, φ, (phi).

47.)                            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 D, which is also exact as discussed 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. It is greater than this set’s arithmetic average of µ=K/N=4 in the φ biased average being weighted or biased towards the larger xi values in (6, 5, 1). We detail the origin of the bias in the φ average towards the larger xi values in the set by expressing φ via Eqs5,2&43 as

48.)                           http://matrix-evolutions.com/INDEX_files/image032.gif= http://matrix-evolutions.com/INDEX_files/image033.gif= http://matrix-evolutions.com/INDEX_files/image034.gif

This shows φ to be the sum of fractional “slices” of the xi of a set, slices that are pi in thickness, which biases the average towards the larger xi in the set by weighting them with their paired larger pi weight fractions. Now note that we can invert Eq47 to define the D diversity index from the φ biased average as

49.)                        http://matrix-evolutions.com/INDEX_files/image035.gif

We can also develop an exact average from the h square root diversity of Eq42 called the square root biased average. In parallel to K/N= µ and K/D= φ, we develop the square root biased average as K/h, to which we give the symbol, ψ, (psi).


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 in its being solely a function of the pi of a set. 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 origin of the bias in the ψ average towards the larger xi in a set by expressing ψ via Eqs5,2&43 as

51.)                           ψhttp://matrix-evolutions.com/INDEX_files/image037.gif

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, with each slice pi1/2 in thickness as biases this average towards the larger xi in the set. The ∑pi1/2 term in the denominator of the end term is a normalizing function that makes the pi1/2  slices” in the numerator sum to one, this summing to one of the fractional “slices” necessary for the construction of any kind of an average of a number set. We can invert Eq50 to express the h square root diversity index as a function of the φ square root biased average as

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

Now let’s apply the above analyses to a thermodynamic system of N gas molecules over which are distributed K discrete energy units. In it the microstate absolute temperature is understood in the standard physics rubric as the arithmetic average per molecule of the system’s kinetic energy. This implies, via the equipartition of energy theorem, a normalized microstate temperature of an arithmetic average per molecule of the K total energy, µ=K/N.    

There is something wrong or inexact with that, though, for we earlier learned that the K energy units of the system are distributed over its N molecules in an unbalanced way as seen in the Maxwell-Boltzmann energy distribution of Figure 35. Hence though the count of K discrete energy units in the system is exact because they all have the same value of 1 energy unit, the N number of molecules is inexact because the N molecules are not all the “same size” energetically in not all containing the same number of energy units, as the Maxwell-Boltzmann distribution of Figure 35 makes clear. Hence the arithmetic average molecular energy of the N molecules as µ=K/N must also be inexact in being a function of inexact N. This suggests its replacement with one of the exact biased averages we have developed, φ or ψ.

We need not equivocate between the two because the specification of the square root biased average, ψ, as normalized microstate temperature quickly becomes clear from how temperature is physically measured with a thermometer. Each of the N molecules in the system collides with the thermometer wall to contribute to the temperature measure at a frequency of collision equal to the velocity of the molecule, which is itself proportional to the square root of the xi number of energy units on the molecule. Hence the smaller energies of the slower moving molecules in the Maxwell-Boltzmann energy distribution of Figure 35 collide with the thermometer less frequently and have their energies “recorded” by the thermometer less frequently, with smaller pi1/2 slices of their energies, and in this way contributing less to the temperature measure than the energies of the faster moving molecules which collide with the thermometer more frequently, thus contributing to the temperature measure their energies with a larger pi1/2 slice in an obviously biased way.  

As the velocities and, hence, collision rates of the molecules are directly proportional to the square root of the xi energy of the molecules, the true average molecular energy that is temperature is the weighting of the xi molecular energies by their square-root-of-the-energy velocities, which fractional weightings are the pi1/2 slices as determines the biased energy average to be the square root biased average energy per molecule, ψ. This is the inarguable physical end of temperature measure. 

Now we see the K energy divided by ψ biased energy average, K/ψ, to be the h square root diversity, h= K/ψ. In parallel the Clausius formulation of entropy as dS=dQ/T tells us that dimensionally S entropy is Q energy divided by T temperature. With normalized microstate temperature understood as the ψ square root biased average, the division of dQ energy by T temperature as ψ leads dimensionally to dS entropy being some measure of the h square root diversity index. This understanding of entropy as energy diversity or energy dispersal in terms of h diversity understands it as h as the number of energetically significant molecules in the system. But the h=K/ψ Square Root Diversity Index of Eqs45&52 has a distinct property that makes it the actual diversity that is entropy. And that is its ψ Square Root Biased Average is the correct form for normalized microstate temperature as explained above.   

But to accept it as such we must also show that hAV also has a very high correlation to the lnΩ variable in S=kBlnΩ before we can consider it as a valid replacement for Boltzmann’s S entropy. To demonstrate this, though, is not as straightforward as was done between DAV and lnΩ earlier because hAV is not a simple function of the K energy units and N molecules of a thermodynamic system as DAV was in Eq26 as DAV=KN/(K+N−1). 

Because hAV is the h square root diversity index of the Average Configuration much as DAV was its D diversity index, we can obtain hAV for the K over N distributions for which we know the specific Average Configurations and their xi and p­i values, which are those in Figures 73-76. We list their hAV values as calculated from Eq42 below alongside the lnΩ values of those Average Configurations as calculated from Eq65. And we also include their DAV diversity indices from Eq26 for comparison sake.  
































Table 53. The lnΩ, DAV and AV of the Distributions in Figures 73-76

The correlation between the lnΩ and DAV of the above random distributions is .997. Though quite high, this is less than the .9995 correlation between lnΩ and DAV seen in Table 33 for large K and N distributions. This difference in correlation coefficients is attributable to the fact that the Pearson’s correlation coefficient is a function of the magnitude of the K and N parameters, those of the distributions in Figures 38-41 and in Table 53 definitely being smaller than those in Table 33. However we see that the Pearson’s correlation between lnΩ and hAV of .995 for the K over N distributions in Table 53is not much different than the .997 correlation between lnΩ and DAV for them, which implies that generally the lnΩ and hAV correlation
is, as it was between l and DAV, very high for all distributions, high enough to be accepted as entropy in being a replacement for lnΩ based entropy on that basis.

To repeat now, while the DAV and hAV average diversities would both be candidates for diversity based entropy in both having a very high correlation to lnΩ and in both fitting the Average Configuration manifest as the Maxwell-Boltzmann energy distribution, we take hAV as the proper diversity based entropy on the basis of the relationship of the hAV average square root diversity index to ψAV that parallels the h=K/ψ relationship of Eq50.  

54.)               http://matrix-evolutions.com/INDEX_files/image060.gif

The ψAV function in the above is the average square root biased average energy per molecule. We earlier introduced ψ as a function that represented normalized microstate temperature dimensionally. But ψ, in itself, is not temperature because each permuted state of a thermodynamic system has a ψ measure as the square root average energy of all of the molecules in that permuted state. Rather it is the average of ψ of all the permuted states, ψAV, which is also the ψ of the Average Configuration as the normalized microstate temperature of a thermodynamic system. As such we understand ψAV as a double average of molecular energy, first as the ψ biased average of the energy of all of the N molecules of the system in a specific permuted state that exists physically at a specific time in the random sequence of permuted states that is a thermodynamic system. And with ψ then averaged over all the ω permuted states of the system to form ψAV, which is also the ψ of the Average Configuration that is a compressed representation of the entire thermodynamic system.  This has us understand entropy as the average square root diversity index, hAV,        

55.)               http://matrix-evolutions.com/INDEX_files/image061.gif

Now let us demonstrate how this diversity index replaces S in the 2nd Law of Thermodynamics. The usual form of the 2nd Law is

56.)               ΔS > 0

Now let us demonstrate how this diversity index replaces S in the 2nd Law of Thermodynamics. The usual form of the 2nd Law is

57.)               ΔS > 0

We replace it with diversity as

58.)              Δh > 0

The reason we use h for diversity based entropy rather than hAV in the above diversity based rendition of the 2nd Law will become apparent in a moment. A mini-thermodynamic system we use to illustrate the 2nd Law of Thermodynamics with a thermal equilibration process is comprised of two 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 from each other out of thermal contact. From Eq24 we see the average variance of the KA=12 energy units over NA=3 molecules subsystem to be σ2AV =2.667 with an Average Configuration that has that variance of (6, 4, 2). Its normalized microstate temperature is from 50, ψAV-A=4.353. And for the KB=84 energy units over NB=3 molecules subsystem, from its Eq24 average variance is σ2AV=18.667, the Average Configuration is (34, 26, 24). And its normalized microstate temperature is from Eq50, ψAV-B=28.328.

Upon thermal contact the system as a whole has K=KA+KB=96 energy units and N=NA+NB=6 molecules. At the first moment of contact the K=96 energy units of the system are distributed over the N=6 molecules as (6, 4, 2, 34, 26, 24). At this moment there is no ψAV temperature of the system because it is not in thermal equilibrium. But it does have a square root diversity index of h=4.394 from Eq42.

After molecular collision sufficient to achieve an equilibrium random distribution of the K=96 energy units over the N=6 molecules, the Average Configuration from a σ2AV =13.333 variance of Eq24 is (11, 14, 15, 16, 17, 23) with a h diversity index from Eq42 of hAV=5.85 and a normalized microstate temperature from Eq50 of ψAV=16.409. This is the whole system’s temperature at equilibrium. Note that standard computation of what the temperature should be from the 1st Law of Thermodynamics, an energy conservation law, suggests rather a temperature that is the simple average of the subsystem temperatures   

59.)                        (ψAV-A + ψAV-B)/2 = (4.353 + 28.328)/2 = 16.341

The discrepancy between the above value of 16.341 and ψAV=16.409 from Eq46 as temperature does not indicate a violation of energy conservation for temperature here is the average molecular energy biased toward the high energy molecules. This discrepancy is all but undetectable from temperature measure in realistic large K and N thermodynamic systems with K>>N. 

Important is that we see the energy diversity of the system as the entropy increasing from an initial value of hi=4.39 for (6, 4, 2, 34, 26, 24) to a final value of hAV=hf =5.85 for (11, 14, 15, 16, 17, 23). The change in energy diversity is, hence,   

60.)           Δh = hf – hi = 5.85 – 4.39 = +1.46         

We see that Δh>0, as fits a 2nd Law increase in entropy for thermal equilibration with entropy expressed as h energy diversity. There are two things different about this unorthodox formulation of 2nd Law entropy increase in thermal equilibration. The first is that it is a change of the whole system of N=6 molecules that we are considering. And the second is that what happens physically is very clear intuitively, the entropy increase being understood as greater energy diversity or energy dispersal coming about from the random mixing of the total K=KA+KB=96 energy units of the initially isolated two subsystems over all N=NA+NB=6 molecules of the whole system. Nothing could be clearer. That is especially so in comparison to the standard take on microstate entropy increase from thermal equilibration as an increase in the Ω microstates of the system, which makes no sense whatever out of entropy physically. The diversity based entropy change quantitatively fits the sense of entropy as energy dispersal, (See Wikipedia), which though taken by many scientists to, indeed, be the qualitatively sensible interpretation of entropy, has never before been given a firm mathematical underpinning until now. This is a much more sensible understanding of the 2nd Law of Thermodynamics. 

In the next mathematical section we will use two important aspects of entropy as based on diversity to explain the most important properties of meaningful information mathematically with information understood generally to take the form of diversity. One of these is the sense of the h diversity measure representing the number of energetically significant molecules in a system. We will go over that in depth in that section both as it refers to energetically significant molecules and to significant information. And the other is an extension of the notion of compressed representation that we introduced in this section in terms of the Average Configuration and the common arithmetic average that makes clear mathematically the nature of the mind’s generalized thoughts or ideas.

This analysis of basics will then lead us to developing mathematical formulations for the human emotions underpinned by a mathematical formulation of natural selection that will guide us to a clear understanding of both biological and cultural evolution with focus on the evolution of violence in homo sapiens and the perverse forms that it took for post-agricultural civilized man back 10 millennia ago. But before we undertake to explain human behavior mathematically, we need to have a sense of the reality of the behavior we want to explain. It is not the misleading fluff spouted in the media and from other ruling class information outlets, it must be emphasized. I am writing this at this moment from Las Vegas where I take the city bus from one public computer venue to another for a few hours writing here and there, Its advantage is the window it offers onto the people one observes and interacts with, their tone, their looks and the reality of the difficulty in their lives that is impossible to misinterpret. The contrast between this and what I see on TV back in our motel room is so great as to be truly startling. Our opinion of the endless disingenuousness on TV is made clear in a song Pete wrote about it back 20 years ago, Curse That TV Set. I would prefer to wait until we develop a mathematical underpinning for emotion and behavior in later sections to talk about why TV and the movies are this way, rather now just laying out my own personal experiences, which though difficult to talk about are much closer to the reality of life that most adults come to know. 

4. 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 my mother's iron rule that 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 Kioten 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, took 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 labeling 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. 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. 


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. 

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.

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.  

Of course the question comes up as to the Guardians of Freedom 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.       

Of course, religion and most of the other things we’ve been talking about are highly contentious. For that reason we want to start talking in the next section in mathematical language to develop a firm foundation for our ideas of what is wrong and what can be done to make them right. I should end this section with a word or two about how things ended up with our Ba-chan. Well, here she is in 2008 with the youngest of her three kids. The picture says it all. Love, perseverance and knowing who the enemy is makes all the difference. 

Grandma Ruth, young genius grandson and his mom in Acapulco in 2008 as refugees from the Bush police state. Photo taken just before returning to America to campaign for Obama, who turned out to be somewhat of a disappointment.    



Ba-chan and my grandson at the Las Vegas Occupy March on The Strip in 2011 before the Occupy protest against corporate control of America was erased from the public view with 6000 slam-to-the-ground wrist breaking arrests. To join A World with No Weapons with a donation of $20 and encourage me to run for president to bring an end to war and to America’s NSA run police state, click here


5. Information

As to information as it is processed by the human mind, the D diversity is readily interpreted as the number of significant subsets in a set, which explains how the mind intuitively distinguishes what is significant from what is insignificant. We illustrate this with an item in the news about the makeup of the K=53 man Ferguson Police Dept. at the time of the protest there, there being x1=50 Caucasian officers and x2=3 Blacks officers. While a mathematical understanding is not entirely necessary for people to understand the Black contingent of the force to be insignificant (quantitatively), the D diversity index as the number of significant subsets in a set makes it mathematically clear.   

The Ferguson PD number set of (50, 3) has from Eq5 a diversity index of D=1.12, which rounded off to the nearest integer as D=1 implies that there is only 1 significant subset in it. Were the force made up in a more diverse way of, say, x1=28 Caucasians and x2=25 Blacks, the diversity for its (28, 25) number set of D=1.994 rounded off to D=2 would indicate 2 significant subsets, that both racial contingents 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 Caucasian contingent suggests that it is the significant subset or subgroup in the force and, hence, that the x2=3 Black officer subgroup is insignificant, which might also be interpreted as its contributing only token diversity to the force.  

The parallel of the D diversity index as a measure of the number of significant subsets in a set perfectly parallels the h square root diversity index measure as a measure of the number of energetically significant molecules in a thermodynamic system.

It is also possible to assign a significance index to each subset in a set as a more direct way to specify the subsets that are significant and those that are insignificant. 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 Eq5 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 has only x3=1 object in it understood as insignificant. To specify these attributions of significant and insignificant in a more direct way, we first introduce the root mean square (rms) average, ξ, (xi), 

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

And the rms average squared, ξ2, is

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

The rms average of the K=12, N=3, (■■■■■■, ■■■■■, ), (6, 5, 1), unbalanced set is ξ =4.546 with ξ2=20.667=62/3. The rms average of the K=12, N=3, balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), which we will use for comparison sake, is ξ =µ=4 with ξ22 =16. Next note from Eqs5,2&62 that the D diversity index can be given as

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

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

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

Obtains the D diversity index as the sum of its si significance indices.

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

For sets, balanced and unbalanced, that have N=3 subsets, x1, x2 and x3,

66.)                 D = s1 + s2 + s3

For the balanced, N=3, (■■■■, ■■■■, ■■■■), (4, 4, 4), set, x1=4, x2=4 and x3=4, D computed from the above is   

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

What D=1+1+1 means is that all N=3 subsets, in having the value of unity or one, are significant. The D diversity of the unbalanced (■■■■■■, ■■■■■, ), which has subsets, x1=6, x2=5 and x3=1, is  

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

What D= 1.161 + .968 + .194 means is that the subset with x1=6 red objects in it, in having a significance index of s1=1.161, is significant in rounding off to s1=1; that the subset with x5=5 green objects in it, in having a significance index of s2=.968, is significant in rounding off to s2=1; and that the purple subset with x3=1 object in it, in having a significance index of s3=.194, is insignificant in in rounding off s3=0.

Now returning to the Ferguson Police Dept. we see that s1=1.056 rounded off to s1=1 indicates that the x =50 Caucasian cops are significant and with s2=.056 rounded off to s2=0, that the x2=3 Black cops are insignificant.   

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

Sets of K=21 Objects  

Number Set Values

D, Eq5

Rounded to

Significance Indices

(■■■■■■■, ■■■■■■■, ■■■■■■■)

x1=7, x2=7, x3=7



s1=1, s2=1, s3=1

(■■■■■■, ■■■■■■, ■■■■■■■■■)

x1=6, x2=6, x3 =9

D= 2.88


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

(■■■■■■■■■■, ■■■■■■■■■■, )

x1=10, x2=10, x3=1



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

Table 69. 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 via their s1=s2=1.04 significance indices, with the one object purple subset insignificant via its s3=.104 significance index, which also might 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, s1=.824, s2=.824, s3=1.24.

One can get a better sense of how automatically the human mind evaluates significance and insignificance by manifesting the K=21, N=3, colored object sets in Table 22 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 70. The Sets of Colored Objects in Table 69 as Sets of Colored Threads.

A woman with a plaid skirt with the (10, 10, 1), D≈2, pattern on the left would spontaneously describe it as a red and green plaid, omitting reference to the insignificant thread of purple. She would do this automatically or subconsciously without any conscious calculation of her sense of it because the human mind automatically disregards the insignificant both in its sense and verbalizing of things in tis visual field. This verbalization of only the significant colors in the plaid swath, 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 insignificant isn’t signified or verbalized or given a word in discourse or in thought.  

Quantitative significance is not just a characteristic of the size or quantity of objects observed but also of the frequency of our observing objects or events. Consider as an illustration of this a game where you guess the color of an object picked blindly from a bag of objects, (■■■■■■■■■■, ■■■■■■■■■■, ). Assume that you don’t know the makeup of the objects in the bag. Then your sense of what colors are significant or insignificant come only from the frequency the colors are picked from the bag (with replacement). And over time, as you see purple picked infrequently, that color will come to seem insignificant in your mind and to also be disregarded as the color you 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 to be significant while automatically disregarding the insignificant in our thoughts, conversations and behavior. This is an important aspect of propaganda and mind control for issues and opinions frequently disseminated through mass media and other ruling class information outlets subconsciously or automatically are sensed as significant and tend to take up the bulk of one’s thoughts, conversations and behavioral considerations; while issues, observations and opinions infrequently or not at all transmitted are appraised as insignificant and disregarded. In this way sports, entertainment and vacuous political opinions are made to seem significant, crowding out issues genuinely meaningful to people shown infrequently or not at all, like the abuse in workday life from bosses, which then tend to become insignificant in discourse and thought or less significant than they should be. This does not come about by chance, for people drugged with misinformation tend to stay in line. To hear this set to music, take a few minutes break from the math and listen to Curse That TV Set.

The application of the D diversity index to explaining the mind’s sense of significance and insignificance is a proper understanding of information as the human mind process it because D is an exact function that shows how the mind actually views and automatically compares sets of things balanced and unbalanced. To make this clearer we next will look at what information is from the broadest perspective. And in the section following the next one we will reformulate entropy correctly, which will not only explain this heretofore mystery phenomenon clearly, but also in locating significance in physical systems by showing entropy to be the number of energetically significant molecules in a thermodynamic system, reinforce the above explanation of the mind’s sense of significance and insignificance, which is central to understanding how we think and feel about things and how it is affected by ideological propaganda.      

The best case for D diversity based significance from insignificance as an intrinsic part of mental information is made with a revised elaboration of information theory. It has major limitations it stands. The inability of information theory to address the problem of meaning, which includes the meaning of things in terms of their significance, is made clear in a Scientific American article, From Complexity to Perplexity, (John Horgan, June, 1995.)  

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.

This shortcoming of information theory is remedied by understanding the prime information functions in information theory as diversity. This not only develops quantitative significance as one of the two primary factors for meaningfulness in information but also develops the association of emotion with objects and events as the other primary factor for meaningfulness. This revision of information theory also aids in clarifying thermodynamic entropy as a physical manifestation of diversity based significance, which further reinforces the reality of the mind’s diversity based sense of significance and insignificance. The central function for information in information theory is the Shannon information entropy. 


This is an exceedingly messy looking thing, to be introduced in the simplest way possible. The sole variable in H is the pi term. The simplest way to understand it is with a set of colored objects. Recall the K=12 object, N=4 color, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), set that has x1=3 red, x2=3 green, x3=3 purple and x4=3 black objects. The pi term in Eq24 is most basically just the fractional measures of the colored objects. Formally we define pi in this way as 


For (■■■, ■■■, ■■■, ■■■), the pi weight fractions of the set are p1=x1/K=3/12=1/4, p2=x2/K=1/4; p3=1/4 and p4 =1/4. The p3=1/4, for example, just says that the green objects in the set are 1/4 of all the objects in the set. Note that pi is an exact property of a set as the ratio of two exact functions, K and xi. Also note that the pi weight fractions of a set must sum to one.


Information theory was developed in 1948 by Claude Shannon, then a communications engineer with Bell Labs, to characterize messages sent from a source to some 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 without looking and then send a message of the color I picked to some destination. The probability of any color of the N=4 colors being picked is just their pi weight fraction.  

74.)                   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.  


That tells us that there’s H=2 bits of information in a message sent. What does that mean? This H=2 bits is the number of binary digits, 0s or 1s, minimally used to encode the color messages derived from the N=4 color set, (■■■, ■■■, ■■■, ■■■), as bits signals, namely as [00, 01, 10, 00]. Red might be encoded as 00, green, 01, and so on. So when the receiver gets 00 as the message, he decodes it back to red. The H=2 bits in each bit signal are considered to be the amount of information in a message. This kind of bit signal information is the synthetic or digital information that computers run on. All of this may seem quite out of the way from our primary goal of understanding violence, war and the need to rid the world of weapons, but be patient, for eventually this exercise will develop precise mathematical functions for all of the emotions including excitement, sex, fear, love and anger that are quite relevant.    

To continue on technically, there is a simpler form of the Shannon entropy of Eq71 for balanced or equiprobable sets like (■■■, ■■■, ■■■, ■■■). Because the pi probabilities for them are all alike as pi=1/N, substitution of 1/N for pi in Eq71 gets us a much simpler form for H for them of

76.)                            H= log2N

This simpler equation gets us the same result as Eq75 in a faster way as    

77.)                                      H= log2N = log24 = 2 bits

Now let’s evaluate the amount of information in a message that derives from a random pick from another set of buttons, K=16 of them 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 Eq76 as   

78.)                                H= log2N= log28= 3 bits

It tells us to encode messages derived from N=8 color (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) with the N=8 bit signals, [000, 010, 100, 001, 110, 101, 011, 111]. Each of them has H=log28=3 bits in it as the amount of information in a message from this set. Now we want to make the case that information can be understood as diversity and conversely that diversity is a measure of information. A very direct corroboration of a synonymy between diversity and information lies in the H Shannon entropy expressed in natural log terms as the Shannon Diversity Index that is found over the last 60 years as a measure of ecological and sociological diversity in the scientific literature. Paralleling Eqs71&76 for the Shannon information entropy is the Shannon Diversity Index of

79.)                               H=http://matrix-evolutions.com/INDEX_files/image025.gif     (general);                   H=ln(N)       (equiprobable)

The difference between the Shannon entropy as information and the Shannon entropy as diversity derives merely from the difference in logarithm base used in the two as no way affects the perfect mathematical equivalence of H as information and as diversity. We can also generate a linear measure of H as

80.)                            M = 2H

Termed the number of messages (in Pierce, Introduction to Information Theory), it is readily understood as a linear measure of diversity akin to the D Simpson’s Reciprocal Diversity Index as seen in the list of sets below.


Number Set Values

D, Eq5 or Eq8

M, Eqs24&33

(■■■, ■■■, ■■■, ■■■)

x1=x2= x3=x4=3



(■■■■■, ■■■, ■■■, )

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



(■■■■■■, ■■■■■■)




(■■■■, ■■■■, ■■■■)

x1=x2= x3=4



(■■■■■■, ■■■■■■, ■■■■■■■■■)

x1=x2=6,  x3=9



(■■■■■■, ■■■■■, )

x1=6, x2=5, x3=1



(■■■■■■■■■■, ■■■■■■■■■■, )

x1=x2=10, x3=1



(■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■)

All x­i=2



Table 81. Various Sets and Their D and M Biased Diversity Indices

We see in the above that M=2H functions as a measure of diversity much like D in having the same value as it, M=D=N, for the balanced sets and being less than N in imbalanced sets as D is, even if not quite by the same amount, which does not make it less a measure of diversity for the specific reduction from N in the unbalanced case is inherently arbitrary given that our intuitive sense of diversity is the only guide we have to the functions for diversity being correct.

And another connection of the D diversity index with accepted information functions lies in D being the non-logarithmic term in the Renyi entropy of information theory.   

82.)                                R = logD

The Renyi entropy, R, is considered in information theory a bona fide information function as a generalization of the H Shannon entropy, details of the close relationship between R and H omitted here. The important thing to be pointed out is the intimate relationship between D as diversity sitting in R as information, which makes the R Renyi entropy a logarithmic form of diversity and suggests that D is information in some way in being the variable part of R

The above diversity, information connections suggest two kinds of diversity indices that fit two kinds of information. The two kinds of diversity indices are the logarithmic kind, as with H and R; and the linear kind, as with D and M. To better understand the two kinds of information that the two kinds of diversity, logarithmic and linear, represent, we next develop the D diversity index as a bit encoding recipe that parallels H as we showed it to be when we first introduced it.  

Recall the H=2 bits measure for (■■■, ■■■, ■■■, ■■■) specify a bit encoding of the N=4 color messages derived from it of N=4 bit signals, [00, 01, 10, 11], each consisting of H=2 bits. We can also use the D=4 diversity index of this set as a bit encoding recipe for bit  signals, each of which have D=4 bits: [0001, 0011, 0111, 1111]. 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 is used. This restricts us writing the 2-0s and 6-1s combination of bits in any one permutation of it, as 01111011 or 00111111 and so on, but not more than one permutation of the 2-0S and 6-1s combination. Also note that the all 0s bit signal is disallowed in this D encoding recipe.  

Now anyone familiar with information theory will immediately note that the D bit recipe is quite 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 in any way but rather to show how D can be understood in parallel to H as an information function, the efficiency of D for message transmission being quite beside the point.

We show that for D by next looking carefully at the details of the difference in the H and D bit encodings. Recall the (■■■, ■■■, ■■■, ■■■) set, whose N=4 colors are encoded in H coding with [00, 01, 10, 11] and in D coding 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 from (■■■, ■■■, ■■■, ■■■) with N=4 distinguishable bit signals. What is special about the D bit encoding of (■■■, ■■■, ■■■, ■■■) with [0001, 0011, 0111, 1111] is that these N=4 bit signals are all quantitatively distinguishable with each bit signal distinct numerically from the other bit signals in having a different number of 0s and 1s in each bit signal.

This is not the case for the H encoding of (■■■, ■■■, ■■■, ■■■) with [00, 01, 10, 11], for there it is seen that the 01 and 10 signals have the exact same number of 0s and 1s in them and are, thus, not quantitatively distinguished from each other. Rather the 01 and 10 bit signals are positionally distinct from each other in the 0 and 1 bit signals being in different positions in 01 and 10. They are, we might say, qualitatively distinct, different, but in kind from position rather than in amounts of 1 and 0 bits.   

This quantitative versus qualitative distinction between D versus H encoding is also 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, each having a different number of 0s and 1s in them. This quantitatively distinguishable bit encoding with D=8 is in contrast 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 those bit signals. And that positional or qualitative distinction in bit signals is also seen between the 011, 101 and 110 signals, all of which are quantitatively the same rather than quantitatively distinguishable.  

This qualitative versus quantitative difference between these two kinds of bit information, H and D, corresponds to our everyday sense of information as being either 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. While if I tell you that he owned 123 slaves at the time of his death, that’s quantitative information. Nearer at hand with our example set, it is clear in (■■■, ■■■, ■■■, ■■■) that the color subsets are all qualitatively distinct from each other as is well denoted with their [00, 01, 10, 11] bit encoding. It is also, though, clear that there are N=D=4 color subsets, which is well denoted with [0001, 0011, 0111, 1111], which effectively counts them.   

This explains why the H (qualitative) coding recipe is logarithmic in form and why the D (quantitative) coding recipe is linear in form. 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 and clearly represents quantitative information about them. Information that comes to us from nature, in contrast to information communicated between one person and another, is, when it is a precise description of nature, quantitative information as every serious practitioner of physical sciences knows. As such an encoding in bit form of such quantitative information whose source is nature, must be, in contrast to information communicated from person to person, of the D encoded linear type because the fundamental operation for quantification, counting, is inherently linear as 1, 2, 3, and so on.

Hence the most general understanding of information is as diversity. That includes logarithmic diversity for communicated information, as H most basically is as we see unarguably when it is understood as the Shannon Diversity Index; and linear diversity, which is linear in form as specified with the counting numbers, 1, 2, 3, and so on. It is not that such quantitative descriptions of items cannot be conveyed in communication via positional distinctions as seen in the Arabic numerals that write thirteen as 13, distinct from 31 positionally, rather than as 1111111111111; and in binary numbers that write thirteen with positional distinctions as 1101, distinct from 1110 positionally. 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 form that the D diversity exists in.    

Further, as is clear from our introductory take on the inexactness in counting things unequal in size, the quantitative information that comes to us from nature when the things to be counted in a natural system are unequal in size, must come in the form of the exact D diversity rather than inexact N. And in that case, as we also have made clear, D must be understood as the number of significant things or subsets in a set.  It was important to show this convincingly in a physical system in order to show that the human mind works this way as a matter of course in obeying physical laws or better said, biophysical laws, that are as inviolate and compelling in controlling human nature and the behavior that flows from it as the law of gravitation is in controlling planetary behavior and the 2nd Law of Thermodynamics. 

6. The Mathematics of Human Emotion

We develop the human emotions mathematically with information theory expanded and revised using the D diversity measure.

Another interpretation of the H Shannon entropy of Eq24 in information theory is as the amount of uncertainty a message resolves in 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



(■■, ■■)



(■■, ■■, ■■)



(■■, ■■, ■■, ■■)



(■■, ■■, ■■, ■■, ■■)



(■■, ■■, ■■, ■■, ■■, ■■)



(■■, ■■, ■■, ■■, ■■, ■■, ■■)



(■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■)



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 being the resolution of information. 

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 can connect U 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


And the probability of failing to guess correctly is


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 repeatedly you could expect to win V=$120, on average, one play in three for an average payoff of E=$40 per game played. Eqs3&6 enable us to write the expected value of E=ZV in Eq6 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 Eq7 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. That is, 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 felling 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 consider 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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7. 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 principal of absence of empirical verification is to fail to understand the underlying basis of empirical validity in universality. 


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8. The 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 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

9. 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 this commodity of the 1st lucky number to the player. Question: what is 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. 

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10. 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,

239.)          ERROR = (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.

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.)           ERROR = (0 –(−U*v*) )      

The system is turned on whenever the 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 skin the 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 relived 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 supply 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 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

11. 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.



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




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




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




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 




An alternative formula for the daily compounding case is




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 




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




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 also 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 keep 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 organism 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,




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




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    




256a.)                  g1 = b1 – d1




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



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.   





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.



If the g grow 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.






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.



This expresses Eq252 via x20=K−x10 as     



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



We can simply 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




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.




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,






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.   

Talking about the emotions related to sex, love (parental and romantic) and violence, however, and what the mathematically prescribed outcomes of these emotions should or shouldn’t be is fraught with problems because sex, love and violence are very much tied up with values and morality. And these consideration can get all the more confused and contentious 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.

For the above reasons, before we dive into these problems with considering violence and sex, epistemologically and morally, we are required to first consider in depth and with precise mathematical argument the nature of information, both how it is used by the human mind to determine behavior and also how as misinformation it can be used to produce behavior influencing notions about reality that are entirely off the mark and yet are believed as correct by so many.

This also has us delay discussion of many important nuances and ramifications of evolution not considered in this section. Rather we will leave them for later sections as we proceed by the most direct path to get to the heart of matters most meaningful to take up: of enslavement; of the religious dogma that essentially support it; of the violence that enslavement indirectly causes; of the worst aspects of such redirected aggression in being a significant cause of war; of the worst incarnation of that dynamic in the possibility of the coming of nuclear war; and of what can be done to avoid man’s extinction from a nuclear Armageddon. All of that begins with a clear understanding of information in the next section and propaganda in the section after that.   



illustration of two red dice Stock Photo - 13443929

12. Propaganda


Some of this material is a repeat of earlier material. Our sense of significance versus insignificance is automatic or subconscious as made clearer yet with the three sets of colored objects below, each of which have K=21 objects in them. 

Sets of K=21 Objects  

Number Set

D from Eq37

D, rounded off

(■■■■■■■, ■■■■■■■, ■■■■■■■)

(7, 7, 7);  x1=7, x2=7, x3=7



(■■■■■■, ■■■■■■, ■■■■■■■■■)

(6, 6, 9);  x1=6, x2 =6, x3 =9

D= 2.88


(■■■■■■■■■■, ■■■■■■■■■■, )

(10, 10, 1);  x1=10, x2=10, x3=1



Table 285. Sets of K=21 Objects in N=3 Colors and Their D Diversity Indices

(Note: Equation and Table nos. 277-284 are not used.) The N=3 set, (
■■■■■■■■■■, ■■■■■■■■■■, ), (10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 specifies D=2 significant subsets of color, the red and the green, with the x3=1 object purple subset sensed as insignificant, as might also be understood from its contributing only token diversity to the set. By contrast the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set has 3 significant subsets, red, green and purple, as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set whose D=2.88 diversity rounds off to D=3. One can get a stronger intuitive feel for how the human mind determines significance and insignificance intuitively by represented the sets in Table 185 as K=21 threads in N=3 colors in a swath of plaid cloth.  


(10, 10, 1), D≈2

(7, 7, 7), D=3

(6, 6, 9), D≈3

Figure 286. The Sets of Colored Objects in Table 184 as Sets of Colored Threads.

A woman with a plaid skirt with the (10, 10, 1), D≈2, pattern on the left would spontaneously describe it as a red and green plaid, omitting reference to the insignificant thread of purple. She would do this intuitively and automatically without any conscious calculation because that is how the human mind automatically registers what is significant and what is insignificant. The rounded off D≈2 diversity specifies the 2 significant colors in the plaid, red and green, that the mind intuitively senses and also intuitively verbalizes as such. Note how the insignificance of the purple thread specified in the D=2 measure is manifest linguistically in purple being disregarded in the description of the cloth as a red and green plaid. 

This verbalization of only the significant colors in the plaid, red and green, should not be surprising given that the word “significance” 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 insignificant isn’t signified or verbalized or given a word. The human mind operating in this way to barely notice and not verbalize what is insignificant is an important factor in human behavior because we generally think, talk about, pay attention to and act on what we sense to be significant while automatically disregarding the insignificant in thought, conversation and behavior.

The sense of significance versus insignificance as spelled out by the D diversity index is also clear in the Ferguson Police Dept. having x1=50 of its K=53 officers White and only x2=3 of them Black. This is described colloquially as “no diversity” and the few blacks on the force as insignificant as quite perfectly fits the D diversity index measure of the number of significant ethnic groups here to be from Eq36, D=1.12 as rounds off to tell us there is only D=1 significant ethnic group on the force.    

The significance of something we see as affected by its size or quantity is not the only thing affected by magnitude. Our sense of significance also extends to our frequency of observing an object or event. Consider as illustration a game where you guess the color of a button picked blindly from a bag of buttons, (■■■■■■■■■■, ■■■■■■■■■■, ). Now let’s assume that you don’t know the color or number of buttons in the bag, but only what you see over time in watching the buttons be picked (with replacement), namely that some picks are red, some green and some purple.  Over time, as you see purple picked infrequently, purple will come to be insignificant in your mind and so much so that you will not even think about guessing it as the color picked when your turn comes to play this guessing game. This sense of significance versus insignificance determined from the frequency of the sensing of an event as measured by the D diversity index perfectly parallels what occurs with the GAV square root biased diversity entropy measure of Eq89 interpreted as the number of energetically significant molecules in a thermodynamic system in a given state.

The mind’s automatic mechanism of sensing quantitative significance and insignificance enables the ruling class in a modern society to use the mass media they control to make the realistically significant seem insignificant and the realistically insignificant seem significant via the politicians, journalists, ministers, actors and other media they pay to perform. The ruling class does this to control the thoughts of those on lower rungs of the social hierarchy, which we’ll explain mathematically in a later section. The purpose of bamboozling of what the American people feel is significant and what it dismisses as insignificant is to get them to accept their abuse and exploitation in the social hierarchy most expedient way, that is, through mind control rather than through out and out economic or penal coercion.

To that end common life situations of workplace control and degradation are seldom broadcast on TV in fiction or factual form including news reports while people are bombarded instead with feel items and frivolous entertainment including sports broadcasting, which takes up a large fraction of TV fare. What affects the public’s subconscious acceptance of this often subtle misinformation on the realities of life is how often bogus points of view are repeated in the media to be made to seem significant and thus take up a significant portion of a person’s thoughts, conversation and feelings, all of which affect a person’s behavior.

To understand the inculcation of bogus significance by the repetition of disingenuous talking points and the relative absence of any correction of them, consider the N=2 (■■■■■■■■■■■■■■■, ), (15, 1), set as representing N=2 polar opposite interpretations of an issue with the number of objects in each subset representing the relative frequency of broadcast of each interpretation. We will assume the red interpretation to be ruling class misinformation on a situation and the green interpretation to be the reality of the situation. The broadcast of the interpretations with relative frequencies of 15:1 makes for a D diversity measure of D=1.132, which rounded off to D=1, imprints on the minds of the audience that the misinformation is significant and the hard truth of the matter insignificant.     

From an analytical perspective, then, we see that the significance determining mechanism of the mind functions off both the relative number and size of objects in a situation and on the relative frequency with which situations, real and contrived, are projected into the mind. 

A combined illustration of both kinds of insignificance and significance deception is found in the Republicans getting the public to support the war in Iraq in 2003 by describing the invading force in that war as a “coalition.” The invading force consisted approximately of K=163,700 soldiers from N=32 nations distributed 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). This set’s D number of significant contributors to the invading force is D=1.26, which rounds off to D≈1 significant nation in the so-called coalition, the United States, which is at odds with the general sense of a coalition as a genuine plural entity rather than a collection of subordinates dominated by one nation.

The deceit in calling it a coalition as one of the rationalizations for entering this costly, bloody, unnecessary war is clear enough to be recognized by the astute as raw political deceit without the need for the D Simpson’s Reciprocal Diversity Index to clarify the contributions of N−1=31 of the N=32 nations as insignificant, though using D as a measure of significance allows us to call the politicians and those who supported them in entering the war liars with mathematical precision. Very much also affecting the public’s acceptance of this clever propaganda was how often the above spin on entering war was repeated over and over again to the public to make the lies about the coalition and the supposed WMD’s seem significant and reasonable.

The D diversity index understood as the number of significant objects or events is one of the cornerstones of propaganda. It works by repetition of mistruth and is evident as such in obvious totalitarian governments, religious dogmatists and talking points blabbering Fox News conservatives who repeat “black is white” assertions in a concerted way so often as to make the possibility of their being some truth in them seem significant and reasonable.

In the propagation of religious doctrine the need for near complete unanimity in talking point assertions to make observably insignificant divine characters like angels and God and unseen divine places like Heaven seem significant is why heretics with opposing views have always been anathema to those who have been made to believe in such nonsense and those in such circles who know better but preach the nonsense for reasons of personal benefit. While heretics against ideological thinking are not quite burned at the stake, their ideas are generally ridiculed or denied outlet in the media and made to seem insignificant.

A case in point is the documentary film maker, Michael Moore, whose primary sin was disgust with the mayhem and slaughter of schoolyard mass murder and George Bush’s vanity driven war in Iraq that, for no good national purpose and as driven with repeated out and out lies reinforced by most major media outlets back in 2003, unnecessarily took the lives of 5000 mostly young American soldiers and crippled 30,000 more, not to speak of the horror it wreaked on a million Iraqis to this day from the instability asshole Bush’s invasion of the country caused, itself totally downplayed and swept under the rug in happy, smiley media land. Indeed as regards Moore’s insightful and prophetic castigation of the war in public at the Oscar nominations in 2003 and later in his documentary, Fahrenheit 9/11, this went as far as active encouragement (as by the likes of right wing snake, Glenn Beck, who is held up as a paragon of righteousness and allowed to have endless radio and TV access), for people to out and out kill Moore. Nor are the billions of dollars wasted in our Middle East wars much of which goes into the pockets of ruling class owned and run companies like Halliburton and their local and foreign cronies, which is a primary reason our economy has been so gutted to the personal destruction of so many millions of American families, a hard fact never mentioned.

The question should arise for anybody who has read this far of what to do about this situation in America of near complete physical control via the police, near complete economic control via Wall Street and near complete information control via our Wall Street controlled mainstream media? In the short term the answer is: Run. To keep your self-respect and the possibility of any happiness in life alive: Run. The best you can do in the short run is to avoid all of the above agencies of control, including avoiding the media drubbing anybody who watches TV and enjoys it gets unavoidably.

Throw the TV set out, out, out. This singular path to maintaining sanity is limited, though. On its own, it takes you down in the end too. You have to fight back somehow. And you do that with the only true solution to the mess human existence has culturally evolved into by shooting for A World with No Weapons, not just for eliminating war and nuclear Armageddon but also for reviving a balance of power that takes personal relationships back to relatively uncontrolled pre-civilized days.

Keep in mind, as I made clear in the middle of my story in Section 4 that this can only be accomplished by the USA effectively conquering the world in alliance with other sane nations whose leaders also see that A World with No Weapons is the only solution to mankind’s subjugation and the mass murder of war. And understand that this can only happen with somebody in the White House who carries that destiny for the country on their shoulders actively. Other than in the event that somebody other than me, who I don’t know about, has come up with the idea of A World with No Weapons independent of us, I’m the only suitable candidate in 2016.

True the protestors for the Mike Brown and Eric Garner horrors, bravo to them, and old line Occupy guys and gals would prefer a world where we don’t need politics and don’t need leaders of any kind, the joys of individual anarchy cannot be achieved in any tangible way with the present humanoids at the top in charge. And the only way to displace them in our media glossed capitalist police state is to try to change things with the ballot box. It’s hardly guaranteed even if we could come up with majority vote, but it’s the only real path to any salvation, excepting the always chancy panacea of Heaven after death. 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 the democratic revolution needed to make it happen by clicking here.   

13. The Mind’s Compression of Information

The E expected value can be understood as a compression of information on events perceived in the past. Consider that you play the Lucky Numbers game twelve times with penalties incurred of (−$120, 0, −$120, −$120, −$120, −$120, 0, 0, −$120, −$120, −$120, 0). You could either remember them as twelve individual pieces of information or compress them as the average penalty, that is, the E=−$80 expected value. Of course knowing the probabilities of rolling dice is a short cut to obtaining the E expected value of the game and what to expect in the game when you play it in the future. But the more primitive dynamic of compressing information gotten from the past to get the expected value and use it for future expectation is the more general way that the mind stores information and process it for the future. Knowing this is a principle key to understanding how the mind stores information from experience as our thoughts and our emotions and uses it for the future.  

A non-mathematical example makes sense of this compression of information process a bit more intuitively. The word “dog” conjures up a picture of what to expect when one encounters a dog as a pictorial average or morph of all the dogs one has ever come across in the past including in books and movies. The mind does this quantitatively also, the size of a dog in our minds being a rough average of the sizes of all the dogs we have ever come across. The averaging of all dogs sensed over all times is roughly what we intuitively expect a dog’s size to be in future encounters with a dog. 

Of course, it is not as simple as that, but working out the important nuances of information compression that are a major part of our mental machinery requires an understanding of quantitative information compression that goes beyond the arithmetic average. We obtain that from our development of entropy as a compression of information in Section 5, which we then will use in Section 6 to explain compression as it applies to and explains the totality of cognition in subsequent sections. We will put this most important topic of information compression on the back burner until then. 

In the last section we developed the concept of compressed information in terms of the µ mean, the D diversity index and the Average Configuration. Now let’s consider information compression in terms of two of the main properties of the Average Configuration, the hAV average square root energy diversity and the ψAV average of the ψ square root biased average energy per molecule. The latter property, ψAV, derives from the ψ the square root biased average energy per molecule of a system of N molecules. This is an average of the thermodynamic system at a particular moment in time when the system is in a particular one of its Ω states. This ψ biased average is a compression of xi energies of all of the N molecules, of the discrete energy units on all the molecules, though as the square root biased average rather than the simple µ arithmetic average. Then this ψ average is itself as ψAV averaged over all the W states of the system as weighted by the probability of each state. Hence ψAV is a double average of molecular energy, first over every one of the N molecules at a particular moment in time and then over every state of the system over time

What is remarkable about this ψAV double average is that it is a measure of temperature not only as taken by a Mercury in glass thermometer but also as sensed by the human body, which collectively measures the energies of all of the environment’s molecules that impinge upon the skin’s surface and senses them as temperature by averaging the energies over all N molecules at any moment in time and then also over time assuming (reasonably) that the collisions of the molecules on the skin are rapid relative to the brain’s integrating sensory impression of them. This is noteworthy because it understands the mind’s sense of temperature as a compression of information.

The mind compresses everything it senses in its memory of it. Consider a human observer who could see every dog in the world at every moment in time. Then the person’s sense of a dog upon recall would be akin to the ψAV sense of temperature in averaging all the world’s dogs at any one moment and then averaging this at time average over time as time passed. This sense of what a dog is, though, would be tempered by recency, that is, with the set of dogs in the world most recently observed having greater weight in the average than those observed in the more distant past.

This is not only how we think about objects observed that are common nouns for us, but also for particular dogs, like the family pet, Fido. Our sense of what Fido is, is a compression of all of his various characteristics or properties over time, some of which change quickly and some slowly, again with recency coming into play in our temporal averaging of Fido’s characteristics.

This sense of compressed information is necessary for understanding the interplay between our emotions and our thoughts, both of which take the form of compressed information. We should make it clear that the E expected value of a Lucky Numbers Game, such as E= −$80 of Eq91 in the penalty incurring game and E=$40 in Eq106 in the prize awarding game, are most basically compressions of information from past experience. Now when we expressed the E expectation for the prize awarding game as E=V−UV, we specified V as our wish or desire for the V amount of dollars. In the quantitatively couched goal directed behavior of rolling the dice to obtain the goal desired or wished for, the “thought” of receiving the V prize is a very precise picture in one’s mind, varying little in image as receiving money generally has little variation in it. But that is not the case for many of our desires whose goals are qualitative rather than quantitative and lie beyond getting money. In those cases where variation is the norm, what is wished for is formed by our imagination as a compression of information that impinges on the mind from the past.

That is to say, that we think, especially about the future, in terms of ideas and concepts that are inherently statistical in nature as compressed information. When these ideas, thoughts, concepts are expressed in quantitative form, there is greater clarity in what they mean and in predictions about the future that stem from them. Freedom and enslavement, the one desirable and desired, the other dreaded, are two examples of immediate interest, both of which are information compressions whose meaning can be quite fuzzy unless they are couched in precise mathematical terms. As both freedom and enslavement are highly emotional terms, this will become more clearly as we continue.