MEANINGFUL
INFORMATION THEORY
by
Ruth Marion Graf
©
March 21, 2015, contact: ruthmariongraf@gmail.com
Information theory is a science of synthetic information, of the digital information computers run on, not the meaningful information the mind runs on to determine people’s behaviors. This shortcoming of information theory was made clear in the June, 1995, Scientific American article, From Complexity to Perplexity:
Created by Claude Shannon in 1948, information theory provided a way to quantify the information content in a message. The hypothesis still serves as the theoretical foundation for information coding, compression, encryption and other aspects of information processing. Efforts to apply information theory to other fields ranging from physics and biology to psychology and even the arts have generally failed – in large part because the theory cannot address the issue of meaning.
It is most important to solve this problem because the greatest impediment to mankind avoiding an annihilating nuclear war is our failure to understand the mind’s information processing, which includes our instinct for violence that makes nuclear war inevitable unless A World with No Weapons is brought about before nuclear Armageddon begins.
We can avoid Hiroshima on a worldwide scale by developing a no weapons Utopia, which however it may seem a fantasy, is shown with our upgrading of information theory to be absolutely necessary for the man to survive and also possible to make happen with the collective political will of all the people of the world. Such a movement must begin in the United States and must have political muscle to succeed. To that end we strongly urge support for Elizabeth Warren in 2016 as the only candidate who is honest and cares about people, this in contrast to Hillary who merely pretends to care. It is so important to have an intelligent person in the White House, for the repeated warnings of Vladimir Putin to use nuclear weapons if push comes to shove must be taken seriously.
Those who wish to help jump start A World with No Weapons can join the movement with a donation of $20 by clicking here. The source of today’s hyper level of violence, domestic and international, in redirected aggression sourced in worldwide unhappiness causing exploitive social control including in con game “free and fair” America will be spelled out, on the one hand, with Meaningful Information Theory that enables a precise mathematical specification of the human emotions including hate and how differentiate significance and insignificance. And on the other in the true personal story in Section 15 it tells of child murders by my cousin, Ed Graf, on the left shown pleading guilty in court to burning his two stepsons to death, and by my brother, Don Graf, both of them members of the fundamentalist LCMS sect I managed to escape from many years ago. It also includes (actually) coming across a plot to murder policemen in Las Vegas.
1. Some Basics of Information Theory
The central structure in information theory is the information channel or message channel diagrammed below.
The set of messages that can be sent through a particular message channel have mathematical representation in terms of their relative probabilities of being sent. Consider a message set consisting of N=4 color messages, red, green, purple or black, that derive from a person blindly picking one object from a set of K=12 objects, (■■■■■, ■■■, ■■■, ■), which consists of x_{1}=5 red, x_{2}=3 green, x_{3}=3 purple and x_{4}=1 black object. The probability of the color picked being red and of a message about it being sent to some receiver is p_{1}=x_{1}/K=5/12; that of green, p_{2}=x_{2}/K=3/12=1/4; of purple, p_{3}=x_{3}/K=1/4; and of black, p_{4}=x_{4}/K=1/12. The message set of N=4 color is specified in terms of these probabilities as [p_{i}] = [p_{1}, p_{2}, p_{3}, p_{4}] = [5/12, 3/12, 3/12, 1/12].
The amount of information in a message
is a function of the probabilities of the N messages, p_{i}, i=1,2,…N. There
are two main functions used for information in information theory. The one used
most often is the Shannon (information) entropy.
1.)
The other important information expression in information theory, which is closely related functionally to the Shannon entropy, is the Renyi entropy, in logarithm to the base 2 form,
2.)
The key to understanding information as we ordinarily understand that word as information that has meaning for us entails understanding the Renyi entropy rather than the Shannon entropy as the primary function for information as follows. We note from the blurb on it in Wikipedia that the Renyi entropy is important in ecology and statistics as an index or measure of diversity. That is not surprising given that the nonlogarithmic part of the Renyi entropy is another longtime used measure of diversity in ecology and sociology, the Simpson’s Reciprocal Diversity Index,
3.)
This allows us to specify the Renyi entropy, R, in terms of the Simpson’s diversity index, D, as
4.) R=log_{2}D
An equiprobable message set for color would derive from a random pick of an object from a balanced set of objects like (■■■, ■■■, ■■■, ■■■), whose N=4 colors have equal probabilities of being picked and sent a message out about of p_{1}= p_{2}= p_{3}= p_{4}=1/N=1/4. Substitution of p_{i}=1/N in Eq3 obtains a simplified D diversity index expression for the balanced case of
5.) D = N
This is intuitively sensible as indicating that the diversity of a set of objects is measured by the N number of different kinds of objects, in (■■■, ■■■, ■■■, ■■■) as D=N=4 differently colored kinds of objects. Note how this also simplifies the Renyi (information) entropy as
6.) R=log_{2}N
Clearly R is a function of the number of color messages derived from random picking from the (3, 3, 3, 3) set of objects, (■■■, ■■■, ■■■, ■■■), namely, R=2 bits. In contrast the D diversity index of the (5, 3, 3, 1) unbalanced set of objects, (■■■■■, ■■■, ■■■, ■), and the message set derived from it is from Eq3 and its [p_{i}] = [5/12, 3/12, 3/12, 1/12], D=3.273, with a Renyi entropy from Eq4 of R=log_{2}(2.323)=1.71. Now we are not at the moment interested in the meaning of R, but rather that R is for all sets a function of the D diversity of the message set. This includes R=log_{2}N for the equiprobable or balanced case in which N is equal to D from Eq5 and can be consider a diversity measure for the balanced case also. Hence the R Renyi entropy as information is a function of the D diversity of the message set. This gives diversity a central role in information. Why is this? It has to do with the problem of exactness in counting things.
2. Counting
The simplest items in mathematics are the counting numbers: 1, 2, 3, 4, and so on. But counting isn’t as simple as it seems. Count the number of objects in (■■■■). You count 4 objects here, of course. Now count the number of objects in (■■■■). It is also 4 one says at a glance. But is that count of 4 an exact count.
There’s something not quite right with counting the unequal sized objects in (■■■■) as 4. Counting 4 objects in (■■■■) should be understood to be inexact as follows. You remember the grade school caveat against adding things together that are different in kind like adding 2 galaxies and 2 kittens together. This caveat also holds for adding things or counting things that are different in size. Consider (■■■■) as pumpkins of sizes (5, 3, 3, 1) in pounds. Is the count of them of 4 pumpkins exact? A grocer selling the pumpkins would think not, which is why pumpkins are sold not by the pumpkin, but by the pound, all of which pounds being exactly the same in size. Four pounds is an exact enumeration of pounds because all pounds are the same size in weight while four pumpkins is an inexact count of pumpkins when the pumpkins counted are not the same size. This requirement of sameness in size for a count of things to be exact applies to all standard measure whether pounds, fluid ounces or inches. That is why standard measure underpins all commercial transactions unless things bought and sold are the same size, like large eggs, which are sold by a straightforward count of them, as by the dozen.
We make this point of inexactness in a count of things not the same size in a more rigorous way by next considering our set of K=12 unit objects, all the same size, (■■■■■, ■■■, ■■■, ■), divided into N=4 color subsets that are not the same size in having different numbers of unit objects in some of them. The K=12 count of all the objects is exact because the objects are “unit objects” all the same size. But the N=4 count of the subsets, on the other hand, is inexact because the subsets are not the same size in having a different number of unit objects in some of them. To make it analytically clear that there is some sort of error in counting the number of subsets in (■■■■■, ■■■, ■■■, ■) as N=4, we first formally specify the set as consisting of x_{1}=5 red, x_{2}=3 green, x_{3}=3 purple and x_{4}=1 black object or in shorthand the (5, 3, 3, 1) natural number set. The sum of the objects in each of the N=4 subsets is the K=12 total number of objects in the set, or generally for any natural number set,
7.)
For the (■■■■■, ■■■, ■■■, ■) set, the total number of objects is K = x_{1}+ x_{2}+ x_{3}+ x_{4 }= 5+3+3+1 =12. Now it is a simple matter to show that the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), is inexact or in error with statistical analysis. The basic statistic of a set of numbers like (5, 3, 3, 1), here representing (■■■■■, ■■■, ■■■, ■), is the mean or arithmetic average, µ, (mu).
8.)
For the K=12, N=4, set, (5, 3, 3, 1), the arithmetic average is µ=K/N=12/4=3. That the µ arithmetic average is inexact is well made in 47 chapters of myriad examples in the modern classic, The Flaw of Averages by Sam Savage of Stanford. A more immediate register of the inexactness or error in the µ arithmetic average comes from noting that it is always associated with a statistical error measure, explicitly or implicitly, the most common of which is the standard deviation, σ, (sigma),
9.)
For the N=4, µ=3, (5, 3, 3, 1) set, the standard deviation is
10.)
Another commonly used statistical error is the relative error or percent error, r,
11.)
For the µ=3, σ=1.414, (5, 3, 3, 1), set, the relative error is r=σ/µ=1.414/3=.471=47.1%. The statistical error in the µ=K/N=3 arithmetic average of (5, 3, 3, 1), whether expressed as σ=1.414 or r=47.1%, implies a counting error in the N number of subsets parameter in µ=K/N. The K=12 count of the unit objects in (■■■■■, ■■■, ■■■, ■) in µ=K/N is exact because its K=12 unit objects are the same size. Hence the statistical error or inexactness in µ=K/N must arise from the inexactness in the N=4 count of the unequal sized subsets in (■■■■■, ■■■, ■■■, ■).
To further make the point of the straight N count of unequal sized subsets being inexact via the statistical error associated with it, we look at the µ, σ and r of the K=4 object, N=4 subset, “balanced” set of objects, (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), all of whose subsets are the same size, x_{1}=x_{2}=x_{3}=x_{4}=3. This set also has a µ=K/N=12/4=3 arithmetic average, but from Eq9, it has no statistical error, σ=r=0, which logically implies from what we just said above that there is no error or inaccuracy in µ=K/N for it and, hence, no error or inaccuracy in the K or in the N variables of µ=K/N. And this fits perfectly with our understanding of an exact count coming about when things counted, including the N=4 subsets in (■■■, ■■■, ■■■, ■■■), (3, 3, 3, 3), are all the same size.
Now while the N=4 count of the number of subsets in (■■■■■, ■■■, ■■■, ■) is inexact, its diversity index of D=3.273 is an exact quantification of the subsets in the set. And this holds generally for any set, balanced or unbalanced. To see this, let’s formally define the p_{i} of a set in terms of the K and x_{i} of a set as
12.)
The two variables that p_{i} is a function of are exact, both the K count of the total number of same size objects in a set and the x_{i} number of (same sized) unit objects in each subset. From this perspective, D in being entirely a function of the p_{i} of a set in Eq3 is exact. Another way of appreciating the exactness in the D diversity index comes from understanding D as a statistical function. To do that we first express the σ standard deviation of Eq3 as its square, σ^{2}, called the the variance statistical error.
13.)
And then we solve this for the summation term to obtain
14.)
Now from Eq12, we express the D diversity index as
15.)
And lastly inserting the summation term in Eq14 into D of Eq15 obtains D also via Eqs8&11 as
16.)
This derives an exact D quantification of the subset constituents of a set as a function of their inexact N count effectively made exact by the inclusion of the r relative error measure of the inexactness in N in the function. This understand D as an exact correlate or substitute for inexact N that can be used in place of N as an exact quantification of the constituent subsets of an unbalanced set. And it further understands diversity, in its sense as an exact quantification of balanced or unbalanced subset constituents of a set, as what information is in the most general sense of the word. Let us back up a bit to make what we mean clear here. Earlier we made note that the R Renyi entropy is used in the scientific literature as a measure of diversity, a logarithmic measure of diversity. Now let’s also note that the Shannon information entropy has also been used in the scientific literature of the last 60 years as a measure of ecological and sociological diversity as called the Shannon Diversity Index, it’s configuring as a natural logarithm rather than a base 2 logarithm being irrelevant to the synonymy of information and diversity in the Shannon entropy as well as the Renyi entropy. Furthermore both the logarithmic diversities, Shannon and Renyi, and the linear diversity, D, are exact functions as defined above.
This strongly suggests that the D diversity index is an information also. Later we shall prove this rigorously with a bit signal encoding recipe interpretation of D and with a Gödel based rebuttal of the Khinchin argument in its derivation of the Shannon entropy as the only correct form for information (along with the Renyi entropy generalization of the Shannon entropy). These tedious technical proofs, though, are delayed for the moment as too much of a digression from showing rather and first how the D diversity index is readily understandable intuitively as meaningful information.
3. Diversity as a Measure of Meaningful Information
Information as processed by the human mind has measure in the D diversity index interpreted as the number of significant subsets in a set. The exercise that follows will explain how the mind intuitively distinguishes what is significant in its sense and memory of things from what is insignificant. We illustrate with an item in the recent news about the makeup of the K=53 man Ferguson Police Dept. at the time of the protest over the death of Mike Brown, namely x_{1}=50 White officers and x_{2}=3 Black officers. Few have a problem intuitively understanding the Black contingent of the Ferguson P.D. to be insignificant (quantitatively) even without any mathematical analysis. But D diversity index interpreted as the number of significant subsets in a set makes the understanding of insignificance mathematically precise.
The Ferguson P.D. as the number set, (50, 3), has from Eq15 a diversity of D=1.12, which rounded off to the nearest integer as D=1 implies that there is only 1 significant subset or subgroup in the department. Were the force made up in a more diverse way of, say, x_{1}=28 Caucasians and x_{2}=25 Blacks, the diversity of its (28, 25) representative number set of D=1.994 rounded off to D=2 would indicate that both subgroups were (quantitatively) significant. Returning to the actual (50, 3) makeup calculated to have a rounded diversity measure of D=1 significant subset, the x_{1}=50 preponderance of the White contingent suggests that it is the significant subgroup and, hence, that the x_{2}=3 Black officer subgroup is insignificant as can also be interpreted as its contributing only token diversity to the police force.
Before we continue this analysis, given the contentiousness of this issue, it should be made clear that considering the police as the enemy of a hoped for genuinely free and fair society is a mistake. Police are strictly the hired hands of the ruling class business and political leaders of communities that range in size from the small city of Ferguson to the entire USA. Police do not make policy. They simply execute it and do so on threat, like the rest of Americans who work jobs, of being fired and having their lives ruined if they fail to comply with the directives of the upper echelon in the American social hierarchy. There is no good cop, bad cop dichotomy, therefore, only a good leader versus bad leader differentiation. And this current crop of leaders in America are as disgustingly predatory, uncaring of the little people and deceitful as any ruling oligarchy you’ll read about in history. If you want change, that’s where you have to look for change, in the people at the top, not the cops who are the ruling class’s well controlled ultimate instrument of coercive control of the people.
That important political digression aside, let’s now continue the mathematical analysis of significance versus insignificance by showing how to assign a significance index to each one of the constituent subsets of a set. We will use the K=12, N=3, (■■■■■■, ■■■■■, ■), (6, 5, 1), x_{1}=6, x_{2}=5, x_{3}=1, set to introduce significance indices. We calculate from Eq15 a D=2.323 diversity index for this set, which rounded off to D=2 suggests 2 significant subsets, the red and the green, with the purple subset that is represented by only x_{3}=1 object in it understood as insignificant. To specify these attributions of significance and insignificance to each subset in a more direct way, we define next the root mean square average, aka the rms average, of a number set, ξ, (xi) as
17.)
The rms average squared, ξ^{2}, is
18.)
The ξ rms average of the K=12, N=3, µ=K/N=4, (■■■■■■, ■■■■■, ■), (6, 5, 1), unbalanced set is ξ =4.546 with ξ^{2}=20.667=62/3. And the rms average of the K=12, N=3, µ=K/N=4 balanced set, (■■■■, ■■■■, ■■■■), (4, 4, 4), which we will use for comparison sake, is from the above ξ=µ=4 with ξ^{2} =µ^{2} =16. Next note from Eqs13,8&18 that the D diversity index can be expressed as
19.)
We define the significance index of the i^{th} subset of a set as s_{i}, i=1, 2,…N,
20.)
This obtains the D diversity as the sum of its s_{i} significance indices as
21.)
For sets, balanced and unbalanced, that have N=3 subsets containing a number of objects in each of x_{1}, x_{2} and x_{3},
22.) D = s_{1} + s_{2} + s_{3}
For the N=3, (■■■■, ■■■■, ■■■■), (4, 4, 4), set, x_{1}=4, x_{2}=4 and x_{3}=4, the D=N=3 diversity index of this balanced set from Eq5 alternatively computed from the above is
23.) D = s_{1} + s_{2} +s_{3 }= 1 + 1 + 1 = 3 = N
What D=3=1+1+1 tells us is that all N=3 subsets in having significance indices of s_{1}=s_{2}=s_{3 }= 1 are significant. Now consider the unbalanced (■■■■■■, ■■■■■, ■) set, whose subset values of x_{1}=6, x_{2}=5 and x_{3}=1 develop its significance indices from Eqs22&23 as
24.) D = s_{1} + s_{2} +s_{3 }= 1.161 + .968 + .194 = 2.323
What D= 1.161 + .968 + .194 indicates is that the x_{1}=6 red objects subset in having a significance index of s_{1}=1.161 rounding off to s_{1}=1 is significant; that the x_{5}=5 green objects subset in having a significance index of s_{2}=.968 rounding off to s_{2}=1 is significant; and that the x_{3}=1 purple object subset in having a significance index of s_{3}=.194 rounded to s_{3}=0 is insignificant. This analysis applied to the Ferguson P.D. situation has us interpret from the s_{1}=1.056 index evaluated from the above for the x_{1}=50 White cops and rounded to unity that they are (quantitatively) significant and from the s_{2}=.056 rounded off to s_{2}=0 for the x_{2}=3 Black cops specifies them as (quantitatively) insignificant.
That
the human mind genuinely operates with these significance functions, or some
neurobiological facsimile of them, is made clear in the next illustration of
significance and insignificance of the three sets of colored objects shown below,
each of which has K=21 objects in it in N=3 colors.
Sets of K=21 Objects 
Number Set Values 
D, Eq15 
Rounded to 
Significance Indices, Eq21 
(■■■■■■■, ■■■■■■■, ■■■■■■■) 
x_{1}=7, x_{2}=7, x_{3}=7 
D=3 
D=3 
s_{1}=1, s_{2}=1, s_{3}=1 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
x_{1}=6, x_{2}=6, x_{3} =9 
D= 2.88 
D=3 
s_{1}=.824, s_{2}=.824, s_{3}=1.24 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
x_{1}=10, x_{2}=10, x_{3}=1 
D=2.19 
D=2 
s_{1}=1.04, s_{2}=1.04, s_{3}=.104 
Table 25. Sets of K=21 Objects in N=3 Colors and Their D Diversity and s Significance Indices
The N=3 set, (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), has a diversity index of D=2.19, which rounded off to D=2 implies D=2 significant subsets, the red and the green from their s_{1}=s_{2}=1.04 significance indices. And that also implies that the one object, purple subset is insignificant as reinforced by its s_{3}=.104 significance index as might also be interpreted as the purple set contributing only token diversity to the set. In contrast, the D=3, (■■■■■■■, ■■■■■■■, ■■■■■■■), (7, 7, 7), set has 3 significant subsets, red, green and purple, s_{1}=1, s_{2}=1, s_{3}=1; as does the (■■■■■■, ■■■■■■, ■■■■■■■■■), (6, 6, 9), set whose D=2.88 diversity rounds off to D=3 with s_{1}=.824, s_{2}=.824, s_{3}=1.24.
One gets the nest intuitive sense of the mind’s automatic or subconscious evaluation of significance and insignificance by manifesting the K=21, N=3, colored object sets in Table 25 as K=21 threads in N=3 colors in a swath of plaid cloth.


(10, 10, 1), D≈2 
(7, 7, 7), D=3 
(6, 6, 9), D≈3 

A woman who owns a plaid skirt with the (10, 10, 1), D≈2, pattern on the left, as I do, would spontaneously describe it as her red and green plaid skirt, omitting reference to the low density and, hence, relatively insignificant threads of purple in the plaid. She would make this description automatically without any conscious calculation because the human mind just does automatically disregard the insignificant and, indeed, not just in its visual sense of it but also in its not verbalizing things sensed as insignificant. This verbalization of only the significant colors in the plaid swath of red and green should not be surprising given that the word “significant” has as its root, “sign” meaning “word”, which suggests that what is sensed by the mind as significant is signified or verbalized while what is sensed as insignificant and little or not at all sensed or noticed, isn’t signified or assigned a word in discourse or in one’s thoughts.
Our sensory perceptions are generally quite automatically affected by the magnitude of the sensory input, small inputs being insignificant and disregarded in our sense of them as with our lack of sensing or tasting salt added to a stew when it is just the slightest pinch of salt. This sense of the possibility of insignificant ingredients in a recipe when added in the smallest yet nonzero amounts is the what gave me the conceptual germ of Meaningful Information Theory.
Quantitative significance is not just a characteristic of the size or quantity of things but also of the frequency of our observation of things and events. Consider a game where you guess the color of an object picked blindly from a bag of objects, (■■■■■■■■■■, ■■■■■■■■■■, ■). Assume that you don’t at all know the makeup of the objects in the bag ahead of time as you go about guessing and observing which colors get picked and in with what frequency. Then your sense of what colors are significant or insignificant comes only from the frequency the colors are picked from the bag (picked with replacement). And over time, as you see purple picked so infrequently that the purple color will come to seem insignificant in your mind as a possible pick and to also be disregarded as a color you might think likely to be picked. The human mind’s operating automatically to disregard the insignificant is an important factor for behavior because we generally think, talk about, pay attention to and act on what we consider significant while automatically disregarding the insignificant in our thoughts, conversations and behaviors.
From a sociopolitical perspective the development of one’s sense of the significance of some things and insignificance of others via media exposure a central aspect of propaganda and mind control because issues and opinions frequently disseminated through mass media and other ruling class information outlets are subconsciously taken to be significant to some degree and tend, as such, to take up much of one’s thoughts, conversations and behavioral considerations in contrast to issues, observations and opinions infrequently brought up or not at all broadcast, which become regarded, as such, as insignificant and effectively paid little regarded if any at all.
In this way personally immaterial sporting events and entertainments along with political opinions with minimal factual bases come to be subconsciously thought of as significant, crowding out issues and interpretations of news events that are genuinely meaningful for people’s individual welfare, but in being shown infrequently or not at all, such as the daily abuse in workday life people take from all powerful bosses, become insignificant in discourse and in thought for people and in their intensions for future action. This does not come about by chance for people drugged with such an endless stream of misinformation tend to stay in line. To hear a warning to avoid such brain washing set to music, take a few minutes break from the mathematical analysis to listen to Curse That TV Set.
An obvious example of propaganda via frequent repeat of a message is seen in Republican talking point strategy. This political party instrument of the ruling class repeats things as nonsensical as the sky is green and the trees are blue through media controlled by ruling class TV station and newspaper ownership and through advertising with such frequency that the drugged population out there in the audience come to think that such opinions have significance. Hey, maybe there is something to the idea of a green sky and of no evolution and of no climate change and of working people not always living fearfully on the edge of homelessness while the privileged amuse themselves with expensive trivialities purchased at the expense of the misery of the working class.
A classic illustration of political disingenuousness via a distortion of significance is found in the Republicans getting the public to support the war in Iraq in 2003 by describing our invading force as a “coalition.” It consisted approximately of K=163,700 soldiers from N=32 nations distributed set wise as (145,000, 5000, 2000, 2000, 1000, 1000, 1000, 1000, 500, 500, 500, 500, 500, 500, 500, 200, 200, 200, 200, 100, 100, 100, 100, 100, 50, 50, 50, 50, 50, 50, 50, 50). The invading force set’s number of significant members calculates from Eq15 as D=1.26, which rounded off to D≈1 specifies 1 significant nation in the socalled coalition, the United States, distinctly at odds with the general sense of a coalition as a plural entity rather than a collection of subordinates dominated by on nation, here the modern American empire.
The cleverness of calling it a coalition along with the endlessly repeated WMD talking point as rationalizations for entering this costly and unnecessary bloody war were clear enough to be recognized by the astute back then as raw political hokum without need for the D diversity index to clarify N−1=31 nations in the “coalition” as insignificant, though using D as a measure of the number of significant nations allows us to call out the deceitfulness of the politicians and the media that supported them with mathematical precision.
Manipulation of the intuitive D diversity based operation of the mind to assess significance is a cornerstone foundation of propaganda. It works by repetition of mistruth as evident both in patently totalitarian societies, organized religions and in capitalist pseudodemocracies where almost all politicians are controlled by the big money of corporations and Wall St., an obvious and highly meaningful fact that is made to be insignificant in the minds of people in its seldom being publically voiced. And those who do bring such facts to light, whether about the harsh realities of war or the institutional corruptions and misery of a highly ordered peace, are made to seem significantly bad.
A case in point is the documentary film maker, Michael Moore, whose primary sin is feeling disgust in both areas and making it known. His calling out Bush’s vanity driven Iraq War that, for no good national purpose and supported by endlessly repeated lies, unnecessarily took the lives of 5000 young American soldiers, crippled 30,000 more and destroyed well a million Iraqi lives, not to speak of the instability it caused that brought cutthroat ISIS to power in the Middle East, all these hard facts made to seem insignificant. Indeed, Moore’s insightful and prophetic castigation of the war at the Oscar nominations in 2003 and later in his documentary, Fahrenheit 9/11, brought about an active encouragement by right wing snake, Glenn Beck, held up in the media as a paragon of virtue, to go out and literally murder Michael Moore.
Those reading this and in despair about finding anything that can be done about it can be given one word of good advice that fits well with their desperation: run. To retain some modicum of selfrespect and the possibility of squeezing any real happiness out of life: run. That’s the best you can do in the short term to avoid the powerful if well hidden agencies of control in modern America. One thing that you can, and must, avoid is the TV set. This is one very important route to maintaining a sane view of life. It is admittedly a limited cure for the bigger problem. To solve that you have to fight back, not just run. And you do that by supporting and placing your hopes in the only true solution to this mess of human existence, helping to bring about A World with No Weapons, not just for bypassing nuclear Armageddon but also in a weapons ban restoring a true balance of power to life, the details to be talked more about in later sections.
To get to A World with No Weapons requires political power, it must be pointed out. Anarchy, everybody doing their own thing, is great if you can get it. But you can’t get it in the real world where the rules forbid it and punish those who break the rules. You have to first get to A World with No Weapons, which has to start with somebody in the White House here who actively carries that destiny on their shoulders. As I’m the only suitable candidate for that in 2016, encourage me by dropping a line to ruthmariongraf@gmail.com and sending a $20 donation to join the movement for A World with No Weapons and for the democratic revolution needed to make it happen by clicking here.
4. A Biased Average
The sense of a Utopia where there is no war or tyranny still must seem to most farfetched. We need more precise mathematical argument to make clear that it’s the only direction we can go in to get out of the hell of debilitating control in our lives and to avoid nuclear annihilation. To that end we next want to consider an adjunct function to the exact specification of the inexact N subsets in an unbalanced set, namely an exact average of the number of objects in each subset. As we made clear earlier, the µ=K/N arithmetic average number of objects per subset in an unbalanced set of K objects distributed over N subsets is inexact. Much as we form the arithmetic average as the ratio of the K objects in a set to the N inexact number of subsets in the set as µ=K/N, we can form an exact average as the ratio of the K objects to the D exact quantification of the subsets as K/D, an exact if biased average, to which we give the symbol, φ, (phi).
27.)
The φ=K/D biased average is an exact average in being a function of K, which is exact, and of D, which is also exact as was made clear earlier. The K=12, N=4, µ=K/N=4, D=2.323, (■■■■■■, ■■■■■, ■), (6, 5, 1) set has a biased average of φ=K/D=12/2.323=5.166. This is greater than this set’s arithmetic average of µ=K/N=4 from the φ biased average being weighted or biased towards the larger x_{i} values in (6, 5, 1). To see the details of the bias in the φ biased average of an unbalanced set towards the larger x_{i} values in the set, let’s develop the µ=K/N arithmetic average in an unusual way from Eqs7&8 as
28.)
This understands the µ mean or arithmetic average as the sum of “slices” of the x_{i} of a set of thickness 1/N. We can develop a function for the φ biased average with a parallel form from Eqs27,13,8&12 as
29.)
This shows φ to be the sum of “slices” of the x_{i} of a set that are p_{i} in thickness to bias the φ average towards the larger x_{i} subsets weighting them with their correspondingly larger p_{i} weight fraction measures. Much as the human mind’s sense of significance is affected in a biased way by the diversity of what it senses, so also is its sense of the average of the constituent subsets of set affected in a biased way towards the greater x_{i} of a set as representing the size of the objects in a set and/or the frequency with which they are sensed. A familiar example is our sense that a dinosaur is generally speaking very, very big. This comes about as a biased average of dinosaur sizes both in terms of the larger ones biasing our sense of the average towards the large sized dinosaurs and also from the fact that people see images of dinosaurs that are very large much more frequently than they see medium sized dinosaurs or small ones. Note also that the diversity index, D, can be understood as a function of the φ average when Eq27 is solved for D as
30.)
This expression for D tells us that the K total number of something in a set divided by its φ biased average is its D diversity. This relationship allows us to corroborate this analysis of significance and insignificance for the mind by showing it for physical systems where the concepts of significance and insignificance have measurable, empirical, reality. Specifically we will do it for a thermodynamic system of K energy units distributed over N molecules with a highlight on the concept of entropy, the tight argument presented reinforcing the D diversity based understanding of the highly contentious issue of brain washing propaganda.
5. Entropy
Entropy is somewhat mysterious concept. Feeling cold in wintertime and hot in summertime comes about from the 2^{nd} Law of Thermodynamics said to be caused by an increase in entropy. The equation for entropy in terms of measurable quantities is the Clausius macroscopic formulation of entropy
31.)
Even though this differential equation tells us that entropy, S, is dimensionally, energy, Q, divided by temperature, T, it still leaves us with a confused mysterious sense of entropy because we lack an intuitive sense of what energy divided by temperature might be. Some light is thrown on the problem by next noting that (absolute) temperature is explained in the standard rubric of physical chemistry as being directly proportional to the µ=K/N arithmetic average of the K energy of a thermodynamic system per its N molecules. But this immediately raises a red flag because we made it very clear earlier that the µ arithmetic average is inexact for an unbalanced set and because the N molecules of a thermodynamic system are an unbalanced set of constituents of a thermodynamic system from the energy units of the system being distributed over them in a skewed or unbalanced way from the empirical MaxwellBoltzmann energy distribution.
Figure 32. The MaxwellBoltzmann Energy Distribution
The inexactness in the µ=K/N average energy function that derives from the
inexactness in the N number of molecules parameter suggests that it is an error
in physical science assuming that systems in nature necessarily operate in an
exact way. Or alternatively we might say that this arithmetic average
specification of temperature is a poor one in being inexact and is perhaps the
reason why the S entropy is so poorly understood and mysterious as a physical
quantity.
Following this line of reasoning tell us that temperature might be better understood as a biased average of energy per molecule. That supposition providing us with a very clear and physically sensible interpretation of entropy for as we see from Eqs30&31, K total energy divided by φ as a biased average energy would be the D diversity of the system of molecules which in perfectly fitting dimensionally Q energy divided by T temperature as S entropy pegs S entropy as the energy diversity of the system. As this quite fits the intuitive or qualitative sense of entropy as energy dispersal, just another word for energy diversity, (see entropy as energy dispersal in Wikipedia), it is worth tracking it down further and provide hard core evidence to show if this is truly the case. Doing so will also increase our confidence of the D diversity as a measure of significance and insignificance in cognitive systems and underpinning of a mathematical specification of the human emotions. And it will also provide us with a mathematical template for the generalizations of ideas and thoughts that the human mind also operates on. The evidence we will provide shows a mathematically perfect fit of energy diversity to the Boltzmann formulation of entropy, understood in science to be the most basic expression for entropy as honored by its inscription of Boltzmann’s tombstone in the terminology of 100 years ago as
33.) S = klogW

Ludwig Boltzmann’s 1906 Tombstone
Diversity is a property not only of a set of K objects divided into N color categories, but also of K candies divided between N children and K discrete or whole numbered energy units divided between N molecules. The distribution of K=4 candies to N=2 children takes the form of three natural number sets: (2, 2) for both children getting 2 of the K=4 candies with a diversity from Eqs5&8 of D=2; (4, 0) for one child getting all 4 of the K=4 candies and the other child none with a diversity from Eq5 of D=1; and (3, 1) for one child getting 3 of the K=4 candies and the other child, 1, with a diversity from Eq5 of D=1.6. The (2, 2), (3, 1) and (4, 0) manifestations of the random distribution are also referred to as the configurations of the distribution. The distribution of K=4 energy units over N=2 molecules has the same diversity values as the distribution of K=4 candies over N=2 children: for (2, 2), both molecules having 2 of the K=4 energy units, a diversity of D=2; for (4, 0), one molecule having all 4 of the K=4 energy units and the other molecule none, a diversity of D=1; and for (3, 1), one molecule having 3 of the K=4 energy units and the other molecule, 1, a diversity of D=1.6.
The candies over kids distribution is easiest to picture and follow, so we begin with it. The random or equiprobable distribution of candies to children as might come from grandma tossing K=4 candies of different color, (■■■■), blindly over her shoulder to her N=2 grandkids, Jack and Jill, has a number of ways of occurring, ω, that derive from the combinatorial statistic,
34.) ω = N^{K}
Specifically for K=4 candies distributed randomly to N=2 children, the ω number of ways that can occur is
35.) ω = N^{K} =2^{4}= 16
These ω =16 ways are, with Jack’s candies set to the right of the comma and Jill’s candies to the left,
36.)
(■■■■,
0); (■■■, ■); (■■■, ■); (■■■, ■); (■■■, ■); (■■, ■■); (■■, ■■);
(■■, ■■)
(■■, ■■);
(■■, ■■); (■■,
■■); (■■■, ■); (■■■, ■); (■■■, ■); (■■■, ■); (0, ■■■■)
The probability of each of these permutations or ways or microstates of the random distribution is the same,
37.) 1/ω=1/16
If grandma did the tossing of the K=4 candies to the N=2 kids 16 times, on average, Line16 would come about though not necessarily in the sequence depicted. It is possible to compute the average diversity of this random distribution. Here we see that the probability of a (4, 0) permutation is 2/16=1/8; of a (3, 1) configuration, 8/16=1/2; and of a (2. 2) permutation, 6/16=3/8. It is a simple matter to compute the σ^{2 }variances of these permutations from Eq11: for (4, 0), σ^{2}=4; for (3, 1), σ^{2}=1; and for (2, 2), σ^{2}=0. Note that (4, 0), (3, 1) and (2, 2) are also referred to as the configurations of the distribution. The average variance of the ω = 16 permutations, also understandable as the probability weighted average variance of the configurations, is
38.)
The average variance, σ^{2}_{AV}, enables us to calculate the average diversity of the random distribution, D_{AV}, from Eq16 with σ^{2}_{AV} replacing σ^{2} and D_{AV} replacing D.
39.)
Understanding the arithmetic average of the number of energy units per molecule for the K=4 energy unit over N=2 molecule distribution to be µ=K/N=4/2=2, the parameters of σ^{2}_{AV}=1 and N=2 have us calculate the average diversity of the random distribution, D_{AV}, as
40.)
This dynamic plays out as above  it must be emphasized  even if the candies are all of the same kind, say K=4 red candies, (■■■■). This comes about because the candies, even though all of the same kind, are fundamentally different candies. Let’s back up a minute to explore this in greater depth. The (■■■■) candies are said to be categorically distinct or distinct in kind. But we don’t just distinguish things as being different kinds, as between a red candy, ■, and a green candy, ■. We also distinguish between two of the same kind of thing, as between two red candies, ■■, which though they are categorically indistinguishable or the same kind of thing, are yet distinguishable fundamentally. If you are holding one of these red candies in your hand and the other is on the kitchen table, you definitely distinguish between the two.
This is called fundamental distinction. It is different than categorical distinction, but yet a distinction between things people make as intuitively as they distinguish between different kinds of things. To show the fundamental distinction between K=4 red candies, (■■■■), we can represent them each with a different letter as (abcd). With the fundamental distinction so marked, the number of ways or different permutations of K=4 red candies, (abcd), that come about from their random distribution to N=2 kids is also calculated as ω= N^{K} =2^{4}= 16 of Eq35, those permutations being
41.)
(abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
(bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc}; (0, abcd)
Note that everything we said for the random distribution of (■■■■) in Eq37 to Eq40 applies also to the random distribution of (■■■■) as is readily understood once we delineate the fundamental distinctions in (■■■■) as (abcd). Now determining the average diversity, D_{AV}, 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 D_{AV} average diversity of any K energy unit over N molecule random distribution from a shortcut formula for σ^{2}_{AV} that already exists in standard multinomial distribution theory. In general for any multinomial distribution of K objects over N containers,
42.)
For an equiprobable multinomial distribution, the P_{i} term is P_{i}= 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 P_{i}=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 P_{i} =1/N probability for a random distribution greatly simplifies the multinomial variance expression of Eq24 for the equiprobable case to
43.)
As things turn out this variance of an equiprobable multinomial distribution is the average variance of an equiprobable distribution, σ^{2}_{AV}, of Eq38 we developed for the K=4 over N=2 random distribution. Hence we can write Eq43 as
44.)
That the variance of an equiprobable multinomial distribution is, indeed, the average variance, σ^{2}_{AV}, is demonstrated by calculating the σ^{2}_{AV}=1 average variance of the K=4 over N=2 distribution in Eq41 from the above as
45.)
Eq44 can now be used to generate a shortcut formula for the average diversity, D_{AV}, by substituting its σ^{2}_{AV} into Eq39 to obtain
46.)
And we can further demonstrate the validity of the above shortcut formula for D_{AV} by calculating the D_{AV}=1.6 average diversity of the K=4 over N=2 distribution obtained in Eq43 with it.
47.)
These conclusions also hold for a system of K=4 energy units distributed equiprobably over N=2 gas molecules flying about in a container of fixed volume. The equiprobable or random distribution results from collisions between the N=2 molecules that result in random energy transfers of the energy units between molecules. In that case, Line41 represent represents the microstate permutations that arise on average from the collisions, though not necessarily in that sequence. The average variance, σ^{2}_{AV}, of the microstate permutations and their average diversity, D_{AV}, is the same as for the random distribution of K=4 candies between N=2 children.
With this picture of a thermodynamic system as our template, we can now confirm the dimensional analysis that suggested from the Clausius macroscopic formulation of entropy that entropy is basically energy diversity or energy dispersal. This is done specifically by showing that the average diversity, D_{AV}, has near perfect direct proportionality to the expression for microstate entropy Boltzmann developed that is expressed in modern terminology as
48.) S=k_{B}lnΩ
To demonstrate this we need not explain the meaning of the Ω (capital omega) variable in Boltzmann’s S entropy, held off until later, nor the k_{B} term in the function, a constant, but only show the exceedingly high correlation coefficient between D_{AV} and lnΩ. That is easy to demonstrate because both D_{AV} and Ω are functions solely of the K number of energy units and N molecules in a thermodynamic system, D_{AV} as seen in Eq46 and Ω from a standard formula in mathematical physics.
49.)
And the lnΩ as a function of K and N is
50.)
For large K over N equiprobable distributions it is easiest to calculate lnΩ using Stirling’s Approximation, which approximates the natural logarithm (ln) of the factorial of any number, n, as
51.)
Stirling’s approximation works very well for large n values. For example, ln(170!) =706.5731 is very closely approximated as 706.5726. The Stirling’s approximation form of the lnΩ expression of Eq50 is
52.)
We can use this formula to compare the lnΩ of randomly chosen large K over N equiprobable distributions to their D_{AV} average diversity of Eq46.
K 
N 
lnΩ, Eq52 
D_{AV}, Eq46 
145 
30 
75.71 
25 
500 
90 
246.86 
76.4 
800 
180 
462.07 
147.09 
1200 
300 
745.12 
240.16 
1800 
500 
1151.2 
381.13 
2000 
800 
1673.9 
571.63 
3000 
900 
2100.88 
692.49 
Table 53. The lnΩ and D_{AV} of Large K over N Distributions
The Pierson’s correlation coefficient for the D_{AV} and lnΩ of these distributions is .9995, which indicates a very close direct proportionality between the two as can be appreciated visually from the near straight line of the scatter plot of these D_{AV} versus lnΩ values.
Figure 54. A plot of the D_{AV} versus lnΩ data in Table 33
This high .9995 correlation between lnΩ and D_{AV} becomes greater yet the larger the K and N values of K>N distributions surveyed. For values of K on the order of EXP20 the correlation for K>N distributions is .9999999 indicating effectively a perfect direct proportionality between lnΩ and D_{AV} as fits very large, thermodynamically realistic, K over N equiprobable distributions. As the Boltzmann S=k_{B}lnΩ entropy is judged to be correct ultimately by its fit to laboratory data, given the near perfect correlation of the D_{AV} to it, this diversity entropy formulation must also be correct from that purely empirical perspective. This correlation of diversity entropy to the Boltzmann microstate formulation of entropy powerfully reinforces the dimensional analysis of entropy as energy diversity done from the Clausius macroscopic formulation of entropy.
It must be emphasized, though, that the two microstate formulations of entropy, diversity and Boltzmann, cannot both be correct even though both mathematically fit the data because the assumptions that underpin the two formulations are absolutely mutually contradictory. This requires some explaining. The ω = N^{K} number of ways combinatorial statistic of Eq34 implies from the 16 microstate permutations of Line21 for the K=4 over N=2 distribution that the energy units are all fundamentally distinguishable from each other. Understanding the random distribution in this way is what made possible the foregoing derivation of the average variance, σ^{2}_{AV}, and the average diversity, D_{AV}.
A quite different combinatorial statistic exists for enumerating the number of observably different ways that K categorically indistinguishable objects can be arranged in N containers. It is the Ω variable that we have already seen from Eq49 that sits in Boltzmann’s S=k_{B}lnΩ entropy.
49.)
Irrespective of Boltzmann’s use of it in his entropy equation, Ω can specify the number of ways that K=4 red candies, (■■■■), which are categorically indistinguishable even if as we made clear they are fundamentally distinguishable, can be arranged over N=2 containers or N=2 children. From Eq49 that is 5 ways
55.)
These Ω=5 ways are as we see below with Jack’s candies to the right of the comma and Jill’s to the left.
55a.) (■■■■, 0); (■■■, ■); (■■, ■■); (■, ■■■); (0, ■■■■)
However the Ω=5 value this has absolutely no meaning as regards the random distribution of K energy units over N molecules because such a distribution is necessarily governed from elementary probability theory by the ω = N^{K} combinatorial statistic of Eq14 that implicitly assumes that the energy units, though they are categorically indistinguishable, are fundamentally distinguishable. This perspective is bolstered by the energy units residing in distinguishable molecules, which themselves reside in different places in space. This suggests that Boltzmann researched a number of mathematical functions associated with the distribution of energy units over molecules until he came to one, lnΩ, which fit the data. In theoretical physics such a fit of a mathematical hypothesis to empirical data is generally taken as strong proof that the hypothesis is correct. In this case, though, it turns out that lnΩ is little more than a fluke fit to another function, D_{AV}, which not only also fits the data, but also makes physical sense out of entropy as energy diversity or energy dispersal One adds that neither Ω nor lnΩ make any sense out of entropy as a physical quantity, the reason for entropy’s mysteriousness over the last century.
One readily absolves Boltzmann for this error given that mathematical formulations for diversity did not come into existence until near half a century after his death and we emphasize that without Boltzmann’s breakthrough efforts my clarification of entropy as diversity would have been impossible. The complete acceptance of Boltzmann’s notions for the last hundred years from their perfect fit to data makes his ideas very difficult to overthrow for Boltzmann is as much a revered “saint” of physical science as Newton or Maxwell or Einstein. The task of rectifying our understanding of entropy as energy diversity would be much easier, for that reason, if both interpretations in their both fitting the data empirically, could be accepted. However the two assumptions of energy unit distinguishability and energy unit indistinguishability are totally incompatible and only one can be accepted. Hence Boltzmann is overthrown rather than just refined, difficult to accept for physical scientists who have embraced him as correct in the most foundational way over the last century.
This impediment to a correction of Boltzmann’s error, thus, asks for as much supporting evidence for the diversity entropy proposition as can be mustered. This doubly important for not only does diversity explain entropy correctly and clearly for the first time in science, but also understanding diversity as a measure of entropy also very much makes clear the underpinning of meaningful information with diversity. That includes not only showing the concept of significance as a marker for what is meaningful in a very firm way in physical systems, but also uncovering a welldefined mathematical structure for the generalizations that the human mind operates on verbally called compressed representation.
A very strong supporting argument for diversity based entropy shows that my diversity based statistical mechanics much better explains the MaxwellBoltzmann energy distribution than Boltzmann statistical mechanics.
Figure 32.
To show it we next introduce a new structure in mathematics called the Average
Configuration of a random distribution. The configurations of the K=4 over
N=2 distribution are listed below with their variances and diversity indices.
Configuration 
Microstates 
Variance, σ^{2} 
Diversity, D 
(4, 0) 
[4, 0], [0,4] 
4 
1 
(3, 1) 
[3, 1], [1, 3] 
1 
1.6 
(2, 2) 
[2, 2] 
0 
2 
Table 56. The Variance, σ^{2}, and Diversity, D, of the Configurations of the K=4 over N=2 Distribution
Recall now the average variance of σ^{2}_{AV}=1 of the K=4 over N=2 distribution from Eq38&45 and its average diversity of D_{AV}=1.6 from Eqs40&47. We see in the above table that the same values of a σ^{2}=1 variance and a D=1.6 diversity are seen for the (3, 1) configuration. On that basis the (3, 1) configuration is understood to be a compressed representation of all of the distribution’s configurations of (4, 0), (3, 1) and (2, 2) and as such is called the Average Configuration of the distribution. The Average Configuration is one configuration that represents all the configurations of a random distribution in compressed form much like the µ arithmetic average is one number that represents all the numbers in a number set in compressed form as, for example, the μ=K/N=4 arithmetic average does for all the numbers in the K=24, N=6, (6, 4, 2, 1, 5, 6), number set.
A configuration includes all of the permutations that have its number set form much as the (4, 0) configuration of the K=4 over N=2 distribution includes the permutations, (abcd, 0) and (0, abcd). Hence the Average Configuration should be understood as a compressed representation not only of all of a distributions configurations but also of all ω=N^{K }of its permutations as develop physically over time as the system’s microstates, each of which exists at any one moment in time. This exceedingly clear microstate picture of a thermodynamic system is worth taking a moment or two to sketch out. Recall the ω=16 permutations or microstates in Line21 for the K=4, N=2 distribution.
41.)
(abcd, 0); (abc, d); (abd, c); (adc, b); (bcd, a}; (ab, cd); (ac, bd); (ad, bc)
(bd, ac); (bc, ad); (cd, ab); (a, bcd); (b, acd}; (c, abd}; (d, abc}; (0, abcd)
These should be understood as appearing in this proportion on average though not necessarily in this sequence over 16 moments of time as coming about from the random molecular collisions and transfers of energy in a thermodynamic system. As such, the (3, 1) Average Configuration represents the state of the system as measured over an extended period of time. Now if this microstate picture of a thermodynamic system is correct, the MaxwellBoltzmann 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 MaxwellBoltzmann energy distribution of Figure 32. Rather, we need random distributions with higher K and N values. And we will look at some starting with the K=12 energy units over N=6 molecule distribution. To find its Average Configuration we first calculate from Eq44 the σ^{2}_{AV} average variance of this distribution to be
57.)
The Average Configuration of the K=12 over N=6 distribution is a configuration that has this variance of σ^{2}_{AV} =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 σ^{2}=σ^{2}_{AV}=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, σ^{2}_{AV}=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 58.
Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=12 over N=6
Distribution
Seeing this distribution as the MaxwellBoltzmann energy distribution of Figure 32 is a bit of a stretch, though it might be characterized generously as an extremely simple choppy form of a MaxwellBoltzmann. Next let’s consider a larger K over N distribution, one of K=36 energy unit over N=10 molecules. Its σ^{2}_{AV} is from Eq44, σ^{2}_{AV}=3.24. The Microsoft Excel program runs through the configurations of this distribution to find one whose σ^{2} variance has the same value as σ^{2}_{AV} =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 59.
Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=36 over N=10
Distribution
This curve was greeted without prompting by Dr. John Hudson, Professor Emeritus of Materials Engineering at Rensselaer Polytechnic Institute and author of the graduate text, Thermodynamics of Surfaces, with, “It’s an obvious protoMaxwellBoltzmann.” Next we look at the K=40 energy unit over N=15 molecule distribution, whose σ^{2}_{AV} average variance is from Eq44, σ^{2}_{AV} =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 σ^{2}=2.489 variance. A plot of its energy distribution is
Figure 60.
Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=40 over N=15
Distribution
And next we look at the K=145 energy unit over N=30 molecule distribution whose average diversity is from Eq44, σ^{2}_{AV} =4.672. There are nine configurations with a σ^{2 }=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 61.
Number of Energy Units per Molecule vs. the Number of Molecules Which
Have That Energy for the Average Configuration of the K=145 over N=30
Distribution
At this level we are considering K and N values large enough to display a moderately
good resemblance to the classical MaxwellBoltzmann distribution of Figure 32.
Figure 32.
As we progressively increase the K and N values of distributions, the plot of the energy per molecule versus the number of molecules that have that energy more and more approaches and eventually perfectly fits the shape of the above realistic MaxwellBoltzmann distribution. Now it should be clear that this unorthodox development of the MaxwellBoltzmann distribution as a property of the Average Configuration comes directly from the mathematics of a random distribution of distinguishable energy units and does not require any additional assumptions, which the Boltzmann derivation of the MaxwellBoltzmann decidedly does. As only one theory, mine or Boltzmann’s, can be correct because of the mutually contradicting assumptions for the two theories of distinguishable versus indistinguishable energy units, there is a strong argument in favor of mine from the Occam’s razor principle that is used generally in science to decide between two competing explanations on the basis of which has the fewest assumptions, in this case the diversity based explanation.
The other reinforcing argument for diversity based entropy comes about from the use of a diversity index slightly different than the D diversity index, one whose biased average perfectly fits microstate temperature and so makes the dimensional argument with the Clausius formulation of entropy air tight. We began our consideration of diversity based entropy with the D diversity index because of the mathematical regularities it has that made it easy to work with, but now that we have developed the basic concepts of diversity based entropy from D, we will switch our focus to Square Root Diversity Index, h.
62.)
This h diversity index not only provides a precise dimensional argument for diversity based entropy with the Clausius macroscopic entropy formulation, but also has like D a very high Pearson’s correlation to the Boltzmann microscopic entropy. As such it is the proper diversity underpinning of entropy. The p_{i }in h are the weight fraction measures of the x_{i} number of objects in each subset. The K=12 object, N=4 color, (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), set, x_{1}=5, x_{2}=3, x_{3}=3 and x_{4}=1 has p_{i}=x_{i}/K weight fractions of p_{1}=x_{1}/K=5/12, p_{2}=x_{2}/K=3/12=1/4; p_{3}=1/4 and p_{4 }=1/12. This makes for and h diversity index of the set6 of
63.)
Note that the h diversity index is exact in being solely a function of p_{i}, which we made clear earlier is exact. Note also that the h=3.464 of the (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), set compares well to its D=3.273 index in being, as is D, a reduction from the N=4 of this unbalanced set, though not quite as much as D=3.273 is. The two diversity indices, D and h, have comparable measures for the sets below with h=N=D for balanced sets and h < N for unbalanced sets as is D<N.
Set of Unit Objects 
Subset Values 
D, Eq3 
h, Eq62 
(■■■, ■■■, ■■■, ■■■) 
x_{1}=x_{2}=_{ }x_{3}=x_{4}=3 
4 
4 
(■■■■■, ■■■, ■■■, ■) 
x_{1}=5, x_{2}=_{ }x_{3}=3, x_{4}=1 
3.273 
3.468 
(■■■■■■, ■■■■■■) 
x_{1}=x_{2}=6 
2 
2 
(■■■■, ■■■■, ■■■■) 
x_{1}=x_{2}=_{ }x_{3}=4 
3 
3 
(■■■■■■, ■■■■■■, ■■■■■■■■■) 
x_{1}=x_{2}=6, _{ }x_{3}=9 
2.882 
2.941 
(■■■■■■, ■■■■■, ■) 
x_{1}=6, x_{2}=5,_{ }x_{3}=1 
2.323 
2.538 
(■■■■■■■■■■, ■■■■■■■■■■, ■) 
x_{1}=x_{2}=10,_{ }x_{3}=1 
2.194 
2.394 
Table 64. Various Sets and Their D and h Diversity Indices
Earlier back in Eqs2729 we developed an exact biased average for the D diversity of φ=K/D. We can also develop an exact biased average for the h square root diversity of Eq42 that we’ll call the Square Root Biased Average. In parallel to K/N=µ and K/D=φ, we define the square root biased average as K/h and give it the symbol, ψ, (psi).
65.)
The ψ=K/h biased average is an exact average in being a function of K, which is exact, and of h, which is also exact. The K=12, N=3, µ=K/N=4, h=2.538, (■■■■■■, ■■■■■, ■), (6, 5, 1), set has a square root biased average of ψ=K/h=12/2.538=4.72, greater than the arithmetic average of this set, µ=4, in being biased towards the larger x_{i} values in the (6, 5, 1) set. We detail the basis of this bias in the ψ average towards the larger x_{i} in a set by expressing ψ from Eqs3,8&62 as
66.)
The numerator in the rightmost term shows the ψ square root biased average to be the sum of “slices” of the x_{i} of a set of thickness p_{i}^{1/2}, which biases the average towards the larger x_{i} in the set in their having larger p_{i}^{1/2}. The ∑p_{i}^{1/2} term in the denominator of the end fraction is a normalizing function used to make all the p_{i}^{1/2 }“slices” in the numerator sum to one, this summing to one of the fractional “slices” being necessary for the construction of any kind of an average of a number set. We next invert Eq60 to express the h square root diversity index as a function of the φ square root biased average as
67.)
Now let’s understand ψ of Eqs65&66 as the microstate temperature of a thermodynamic system of K energy units distributed over N gas molecules. As we said earlier back after Eq31, the microstate temperature is currently understood in the standard physics rubric to be the arithmetic average energy per molecule, µ=K/N. And we made clear that what is wrong with that is that the K energy units of the system being distributed over the N molecules in an unbalanced way as seen in the MaxwellBoltzmann energy distribution of Figure 32 tells us that the this µ=K/N arithmetic energy average is an inexact specification because the N number of molecules parameter in µ=K/N is inexact. Earlier we suggested a replacement of inexact µ=K/N with the exact biased average, φ=K/D and we saw how doing that quickly developed a dimensional argument from (normalized, absolute) temperature being the φ=K/D exact biased energy average and S entropy being dimensionally from the dS=dQ/T Clausius entropy expression of S entropy deriving from the division of energy by temperatur4e.
We can make the same dimensional argument for the square root biased average, ψ, as temperature and it is a substantially better one based on how temperature is actually measured physically with a thermometer. Each of the N molecules in the thermodynamic system collides with the thermometer to contribute to its temperature measure in direct proportion to its frequency of collision with the thermometer, which is equal to the velocity of the molecule, which itself is directly proportional to the square root of the x_{i} number of energy units a molecule has. Because of this, the slower moving molecules with the smaller energies in the MaxwellBoltzmann energy distribution of Figure 32 collide with the thermometer less frequently and have their energies recorded or sensed by the thermometer in its compilation of the temperature measure less frequently to record or sense smaller p_{i}^{1/2} slices of their energies. And conversely, the faster moving, higher energy molecules, which collide with the thermometer more frequently have their energies recorded or sensed as larger p_{i}^{1/2} slices of their energy thus biasing the temperature measure towards the energy of the higher energy molecules in an unarguable way. This determines the molecular energy average to be the square root biased average energy per molecule, ψ=K/h.
This first order model is incomplete, however, because it does not take into account the fact that the h energy diversity of a thermodynamic system along with its ψ=K/h biased energy average is changing at every moment in time from one microstate permutation to another as the system’s molecules collide with and transfer energy between themselves, thus continuously altering the distribution of the K energy units over the system’s N molecules. Hence the ψ and h parameters that form the basis respectively of the system’s temperature and entropy must be their average measures, h_{AV} and ψ_{AV}, which are properties also of the system’s Average Configuration that represents the system as a whole. This makes it clear by extension from Eq66 that the K total number of energy units divided by the ψ_{AV} square root biased energy average as temperature is the h_{AV} square root diversity of the system
68.)
Now it is only one quick stop at the Clausius macroscopic entropy formulation, dS=dQ/T, to see from a dimensional argument that h_{AV} diversity is the measure of the entropy of the system. As S entropy is dimensionally Q energy divided by T temperature and K energy divided by ψ_{AV} temperature is h_{AV} diversity, h_{AV} diversity must be dimensionally entropy.
To conclude that h_{AV} is the proper function for entropy based on its dimensional fit to the Clausius macroscopic entropy, we must also show that h_{AV} has a high correlation to Boltzmann’s S=k_{B}lnΩ entropy (or more simply, to lnΩ.) To demonstrate this, though, is not as straightforward as it was for D_{AV} because h_{AV} is not a simple function of the K energy units and N molecules of a thermodynamic system as D_{AV }was back in Eq46 as D_{AV}=KN/(K+N−1). There is a remedy for this problem, though. Because h_{AV} is the h diversity the Average Configuration much as D_{AV} was the D diversity index of the Average Configuration, we can obtain h_{AV} for the K over N distributions for which we have a specific Average Configuration and its x_{i }and p_{i} values. Those are the K over N distributions of Figures 5861. Below we list their h_{AV} values as calculated from Eq62 alongside the lnΩ values of those Average Configurations as calculated from Eq50. And we also include their D_{AV} diversity indices from Eq46 for comparison sake.
Figure 
K 
N 
lnW 
D_{AV} 
h_{AV} 
36 
12 
6 
8.73 
4.24 
4.57 
37 
36 
10 
18.3 
8 
8.85 
38 
45 
15 
26.1 
11.11 
12.33 
39 
145 
30 
75.88 
25 
26.49 
Table 69 The lnΩ, D_{AV} and h_{AV} of the Distributions in Figures 7376
The Pearson’s correlation coefficient between the lnΩ and h_{AV} values of the above is .995 and between lnΩ and D_{AV} it is .997. Note that though this lnΩ and D_{AV} Pearson’s correlation of .997 is high, it is less than the .9995 correlation between lnΩ and D_{AV} seen in Table 53 for larger K and N distributions. This is attributed to the Pearson’s correlation coefficient being a function of the magnitude of the K and N parameters of the random distributions, those of the distributions in Figures 5861 used in Table 69 being substantially smaller than those in Table 53. So the Pearson’s correlation between lnΩ and h_{AV }of .995 for the K over N distributions in Table 69 being little different than the .997 correlation between lnΩ and D_{AV} implies that the lnΩ and h_{AV }correlation is also, as with the .9995 between lnΩ and D_{AV }very high for larger K and N distributions suffici9ent to be accepted as entropy from its correlation with the S=k_{B}lnΩ Boltzmann microstate entropy.
Now let’s see how the h_{AV} diversity index replaces S in the 2^{nd} Law of Thermodynamics. The usual form of the 2^{nd} Law is
70.) ΔS > 0
This says that entropy, S, increases in an irreversible or spontaneous process. One such process is thermal equilibration in which two bodies at different temperatures both go to some intermediate temperature upon thermal contact. While the mathematics of this is unarguable when entropy is expressed in dS=dQ/T form, any sense of the increase in entropy microscopically or molecularly that can be gleaned from representing entropy with the Boltzmann S entropy is nonintuitive and conceptually mysterious. And that, we posit is not because entropy is inherently difficult to understand to the point of seeming mysterious, but because S=k_{B}lnΩ is flat out incorrect and must be replaced with h_{AV} diversity to make any sense out of the process.
To show this we will show the h_{AV} diversity based entropy to increase in a thermal equilibration between two minithermodynamic subsystems. Subsystem A has K_{A}=12 energy units distributed randomly over N_{A}=3 molecules. And subsystem B has K_{B}=84 energy units distributed randomly over N_{B} =3 molecules. These two subsystems are initially isolated out of thermal contact. From Eq44 the average variance of the K_{A}=12 energy units over N_{A}=3 molecules subsystem is σ^{2}_{AV }=2.667 calculating an Average Configuration that has that variance of (6, 4, 2) with a normalized microstate temperature from Eq66 of ψ_{AV}(A)=4.353. And the K_{A}=84 energy units over N_{B}=3 molecules subsystem B has from its Eq44 average variance of σ^{2}_{AV}=18.667 an Average Configuration of (34, 26, 24) with a normalized microstate temperature from Eq66 of ψ_{AV}(B)_{ }=28.328.
Upon thermal contact the system comprised now of the two subsystems as one whole system consists of N=N_{A}+N_{B}=6 molecules over which are distributed K=K_{A}+K_{B}=96 energy units. At the first moment of contact, we represent the system in terms of the energies of the molecules in their separate Average Configurations as (6, 4, 2, 34, 26, 24). At this first moment there is no ψ_{AV} temperature of the composite system because it is not in thermal equilibrium. But the system can be understood to have a square root diversity index of h_{AV}=4.394 from Eq62. The specification of the system not in equilibrium as h_{AV}, as an average diversity, is a bit awkward in its actually consisting of the average diversities of the two subsystems, but the meaning is clear.
After molecular collision sufficient to bring about a true random distribution of the K=96 energy units over the N=6 molecules, the Average Configuration as obtained from the σ^{2}_{AV }=13.333 average variance function of of Eq44 is (11, 14, 15, 16, 17, 23) with a square root diversity index from Eq62 of h_{AV}=5.85 and a normalized microstate temperature from Eq66 of ψ_{AV}=16.409. Note that the usual computation of temperature of the whole system from the 1^{st} Law of Thermodynamics, an energy conservation law, suggests rather a temperature that is the simple average of the two subsystem’s temperatures of (4.353 + 28.328)/2 = 16.341. The discrepancy between this value and ψ_{AV}=16.409 calculated from Eqs62&66 is not a violation of energy conservation because temperature here is understood as an average molecular energy biased toward the higher energy molecules. Such a discrepancy would be all but undetectable in realistic very large K and N thermodynamic systems.
What is important to note is that the h_{AV} energy diversity or energy dispersal of the system seen as entropy increases from an initial value of h_{AV}=4.39 for (6, 4, 2, 34, 26, 24) to a final value of h_{AV}=5.85 for (11, 14, 15, 16, 17, 23). The change in h_{AV} energy diversity is, hence,
71.) Δh_{AV}=5.85 – 4.39 = +1.46
And we see that this fits the increase in entropy for thermal equilibration demanded by The 2^{nd} Law of Thermodynamics with entropy expressed now as h_{AV} energy diversity.
72.) Δh_{AV} > 0
There are two things that are different about this unorthodox formulation of the 2^{nd} Law entropy increase for thermal equilibration. The first is that the entropy increase expressed in terms of h_{AV} diversity is measured as a change in the whole system of N=6 molecules. And the second is that what is happening physically in the thermal equilibration process is clear intuitively when the entropy increase is understood as an increase in energy diversity or energy dispersal. Nothing could be clearer intuitively especially in comparison to the standard take on microstate entropy increase as an increase in the Ω microstates of the system, which makes zero sense out of entropy as a physical quantity. This diversity based entropy change quantitatively fits the sense of entropy as energy dispersal, (See Wikipedia), which though taken by most physical scientists to be the qualitatively sensible interpretation of entropy, has never been given a firm mathematical basis until now.
There are other quite major improvements in thermodynamics that come about from this diversity based statistical mechanics, for example, in understanding free energy and the real gas law. We will not detail these and other improvements in theory that a diversity based entropy understanding brings about leaving that to those specialists in the field who have sense enough to expand on our seminal work in the detail it deserves.
6. Entropy Concepts and Information
Two concepts that derive from the development of diversity based entropy have relevance to the information processing operations of the mind. The first is that ≈the h diversity index of Eq62 like the D diversity index of Eq3 is understandable as a measure of the number of significant subsets in a set. In the (■■■■■■■■■■, ■■■■■■■■■■, ■), (10, 10, 1), set Table 25 and Figure 26 it was seen that the D=2.19 diversity index of the set could be interpreted, when rounded off, as indicating that the set has D=2 significant subsets, the red and the green, the purple subset understood as insignificant. This interpretation of the D=2.19 measure was reinforced with significance indices for it from Eq21 of s_{1}=1.04≈1 for red, s_{2}=1.04≈1 for green and s_{3}=.104≈0 for purple. It is also possible to calculate from Eq62 an h diversity index for this set, h=2.394, which rounded off to h=2, specifies 2 significant subsets for the set.
Applied to a thermodynamic system, this has us interprets the h_{AV} diversity based entropy as the number of energetically significant molecules in the system’s Average Configuration, equivalently as the average number of energetically significant molecules in the system. As an example, consider the K=36 energy units over N=10 random distribution in Figure 59 as represented by its (1, 2, 2, 3, 3, 3, 4, 5, 6, 7) Average Configuration. Its h, the h_{AV} of the system, is, from Eq62, h=8.853≈9. This is readily interpreted as specifying 9 energetically significant molecules in the system, the one molecule associated with just 1 energy unit being understood as insignificant. Of course, this sense of energetic insignificance is relative, but the overall sense of the energetic significance versus insignificance of molecules goes a long way to understanding temperature specified as ψ_{AV}=K/h_{AV} as coming about from collisions of molecules with the thermometric temperature measuring device biased towards the faster moving, energetically significant molecules. This in turn makes clear that the “reality” of a thermodynamic system as manifest in its most basic property of temperature, ψ_{AV}=K/h_{AV} in normalized microstate form, depends not just on the molecular energies displayed in the MaxwellBoltzmann energy distribution of Figure 32, but also on how the molecular energies are sensed or measured in a biased way.
This shows a clear parallel between h_{AV} diversity based entropy in physical systems as the number of energetically significance molecules and the human mind’s appreciation of significance in sensory systems as measured by the D diversity index. Ultimately this parallel derives from the commonality between thermodynamic systems and sensory systems both being affected in the measure of their subset constituents by the magnitude of those constituents, small things, be they molecules energywise or subsets of colored objects with few representatives deliver less energy to their sensing device, be it the human brain or a thermometer.
This should make clear our perceptions and thoughts and how they are used in our behaviors and communication with others ultimately depend not just on what in the external objective world is sensed, but on how they are sensed with the sensing apparatus. Hence the locating of a significance measure in physical systems as diversity based entropy not only reinforces the concepts of significance and insignificance in our sensory apparatus, indeed, very much so in the measure of significance in each system being diversity, but also tells us, in a nutshell, that reality for people is what is sensed rather than some objective reality that lies outside our senses. And from a purely epistemological perspective this very much calls into question transcendental notions like the gods of various religions along with angels and devils and other “spirits” that have no basis in anybody’s sense of them. This is very important to our fleshing out a clear picture of what is meaningful in life and the best way to deal with life for plaguing our sense of life with nonsensed imaginations muddies the picture critically.
Accepting significance now as one major determinant of what makes information meaningful, we make it clear that the other determinant of which things are meaningful are those that have emotion associated with them major, something that the D diversity will also clarify with great mathematical precision in a later section.
The other concept basic to the mind’s information processing that was introduced through diversity entropy is compressed representation. The µ mean is the most familiar and commonly used compressed representation. Specifying the number of objects in a subset of the K=12, N=4 set of (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1), as its µ=K/N=12/4=3 arithmetic average compresses the number of numbers needed to describe the set from N=4 of them, (5, 3,3, 1) to the one number of µ=3. While that constitutes efficiency in description in using less information to describe the set, note that the loss of some information in this compression generates error as seen in the statistical error associated with the arithmetic average of an unbalanced set. This compressed representation of the arithmetic average is also inexact as we made clear earlier.
Another compressed representation of the (■■■■■, ■■■, ■■■, ■), (5, 3, 3, 1) is its D=3.273 diversity index. Again, like the arithmetic average, this is a 1 number representation of an N=4 number, number set and an efficient compression in that regard. It also leaves out information about the set but less so than the set’s µ=3 arithmetic average because D includes a measure of the distribution of the K objects over the N=4 subsets as is clear from D=N/(1+r^{2}) of Eq16 inclusion of r^{2} as a measure of set distribution. And D=3.273 is also an exact compression of the set as is the h=3.468 square root diversity index of the set.
The h_{AV} average diversity or entropy of a thermodynamic system is a higher level compressed representation in representing the h diversity compressed reductions of all of the microstate permutation of the system as their average. And the ψ_{AV}=K/h_{AV} average square root biased average is another higher level compressed representation as the average over time of the square root biased average energy per molecule that changes over time from continuous collisions between molecules.
We can appreciate these mathematically formulated compressed representations as one category of the generalizations we make about the world around us, quantitative generalizations. The usefulness of these compressed representations or quantitative generalizations is obvious enough that we need not enumerate them.
These quantitative compressed representations also shed great light on the nonmathematical generalizations we humans use as compressed representations that range from the common nouns and verbs we use to represent objects and actions with to our generalized knowledge of complex processes of all sorts. In the simpler case of common nouns as compressed representations, not that the word “dog” conjures up a picture in the mind of a person who hears the word that is an average or morph of all the dogs a person has come across including in picture books and movies seen. The mind compresses everything it comes into sensory contact with in its memory of those things. Such compressed information from the past is used in the interplay of emotions and of thought manifest as generalization, which very much affects both the things we decide to do and our communications with others.
This section has been a relatively qualitative discussion of two important information concepts gleaned from our development of diversity based entropy: significance and compressed representation. In the next section we will use the diversity concept to more formally revise information theory.
7. Revising Information Theory
To do that, let’s start back with the central function for information in information theory, the Shannon (information) entropy of Eq1.
1.)
Information theory was developed in 1948 by Claude Shannon to characterize messages sent from a source to a destination. Consider (■■■, ■■■, ■■■, ■■■) as a set of K=12 colored buttons in a bag in N=4 colors. I’m going to pick one of the buttons blindly and then send a message of the color picked to some destination. The probability of any color of the N=4 colors being picked is the p_{i} weight fraction of the color, for all the colors in this case,
73.) p_{i }= 1/N = 1/4.
So there’s a p_{1}=1/4 probability of my sending a message saying “I picked red.” And a p_{2}=1/4 probability of my message saying, “I picked green,” and so on. Plugging these p_{i}=1/4 probabilities into messy Eq71 obtains the amount of information in the color message sent as
74.)
This tells us that there’s H=2 bits of information in a message sent. What does that mean? The most basic interpretation of the H=2 bits is as the number of binary digits, 0s or 1s, minimally needed to encode the color messages gotten from (■■■, ■■■, ■■■, ■■■) in bit signal form, namely as [00, 01, 10, 11]. Red might be encoded as 00, green as 01, and so on. Then when the receiver of the message gets 00 sent, he decodes it back to red. The H=2 bits measure is considered to be the amount of information in a message as the number of bit symbols in each bit signal. This bit signal information is the synthetic or digital information that computers run on. There is a simpler form of the Shannon information of Eq1 used for balanced or equiprobable sets like (■■■, ■■■, ■■■, ■■■). Because the p_{i} probabilities are all the same for a balanced set as p_{i}=1/N, substituting 1/N for p_{i} in Eq1 derives the simpler form for H of
75.) H= log_{2}N
This equation gets us the same H=2 bits result for messages sourced from (■■■, ■■■, ■■■, ■■■) as did Eq74, but in a simpler way as H= log_{2}N = log_{2}4 = 2 bits. Now let’s also use Eq75 to calculate the amount of information in a message that derives from a random pick a K=16 buttons in N=8 colors, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■). Because this set is balanced, the probability of picking a particular color and sending a message about it is the same for all N=8 colors, p_{i}=1/N=1/8. And the amount of information in a color message from this set can be calculated from the simple, equiprobable, form of the Shannon entropy of Eq75 as H= log_{2}N= log_{2}8= 3 bits. This has us encode messages from N=8 color (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) with the N=8 bit signals, [000, 010, 100, 001, 110, 101, 011, 111]. Each bit signal has H=log_{2}8=3 bits in it understood as the amount of information in a color message derived from this set.
Now we want to make the case that information and diversity are synonymous with each being a measure of the other. We already tried to make that case before by suggesting that the D diversity interpreted as the number of significant subsets in a set was an instance of meaningful. The synonymy of diversity and information can also be demonstrated in a more technical way. First of all it is well known that the H Shannon information entropy expressed in natural log terms is the Shannon Diversity Index used over the last 60 years in the scientific literature as a measure of ecological and sociological diversity. Paralleling Eq1 for the Shannon information entropy is the Shannon Diversity Index of
76.)
And for a balanced set, paralleling Eq75, the Shannon Diversity index is H = lnN. The difference between the Shannon entropy as information and the Shannon entropy as diversity is merely the difference in logarithm base, the direct proportionality between the two telling us from measure theory in mathematics that what one function is the measure of, the other must also be a measure of, here both of information and diversity. Another conceptual equivalence between diversity and information that derives from classical information theory comes from Renyi entropy, R, which is taken in information theory to be information in being a parent function or generalization of the Shannon information entropy. Its connection to diversity lies in its being the logarithm of the D Simpson’s Reciprocal Diversity Index as we saw earlier in Eqs24.
4.) R = logD
This also strongly suggests a synonymy between diversity and information. The above two diversityinformation associations suggest two kinds of diversity indices that further imply two kinds of information functions. The two kinds of diversity indices are the logarithmic kind, as with H and R; and the linear kind, as with D. To better understand the two kinds of information that the two kinds of diversity indices, logarithmic and linear, imply we next develop the D (linear) diversity index as a bit encoding recipe that parallels H as the bit encoding recipe we introduced it as. The sociopolitical implications of this somewhat tedious exercise are profound and make the following technical considerations worth our time and effort.
Recall the H=2 bits for (■■■, ■■■, ■■■, ■■■) that specify for its N=4 color messages an encoding of N=4 bit signals, [00, 01, 10, 11], each consisting of H=2 bits or binary digits. We can also use the D=4 diversity index as a bit encoding recipe. The D=4 diversity index of this set translated as the number of bits in a bit signal obtains N=4 bit signals for the N=4 colors of the set of [0001, 0011, 0111, 1111], each of which consists of D=4 bits. And for the N=8 color set of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) whose H=3 bits measure encoded it as [000, 001, 010, 100, 110, 101, 011, 111], the D=8 diversity index used as a coding recipe encodes it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111], with each bit signal consisting of D=8 bits. Note in both D encodings that only one permutation of a given combination of 1s and 0s can be used. This restricts us writing the 20s and 61s combination of bits in only one permutation of it, as for example as 01111011 or as 00111111, but not both. And also note that the all 0s bit signal is disallowed in this D encoding recipe.
Anyone familiar with information theory will immediately note that the D bit recipe is inefficient as a practical coding scheme in its requiring significantly more bit symbols for a message than the H Shannon entropy coding recipe. This is not surprising since Claude Shannon devised his H entropy initially strictly as an efficient coding recipe for generating the minimum number of bit symbols needed to encode a message in bit signal form. The D diversity index as a coding recipe fails miserably at that task of bit symbol minimization. But we have developed it not trying to engineer a practical coding system but rather to show how D can be understood in parallel to H as an information function in being understandable as a bit coding recipe, its efficiency for message transmission being quite beside the point.
We show D to be an information function for a very familiar kind of information, quantitative information, by next looking carefully at the details of the difference between the H and D bit encodings. Recall the (■■■, ■■■, ■■■, ■■■) set, whose N=4 colors are encoded in H encoding with [00, 01, 10, 11] and in D encoding with [0001, 0011, 0111, 1111]. Now look closely to see that these are two very different ways of encoding the N=4 distinguishable color messages derived from (■■■, ■■■, ■■■, ■■■) with N=4 distinguishable bit signals. What is special about the D bit encoding of (■■■, ■■■, ■■■, ■■■) with [0001, 0011, 0111, 1111] is that all of these N=4 bit signals are quantitatively distinguishable from each other with each bit signal having a different number of 0s and 1s in it than the others.
This is not the case for the H encoding of (■■■, ■■■, ■■■, ■■■) with [00, 01, 10, 11]. For with them it is seen that the 01 and 10 signals have the same number of 0s and 1s in them and, hence, are not quantitatively distinct from each other. Rather the distinction between 01 and 10 is positional distinction from the 0 and 1 bit signals being in different positions in 01 and 10. So 01 and 10, we could say, are qualitatively distinct rather than quantitatively distinct.
This quantitative versus qualitative distinction for D and H encoding is even more clear for the N=8 set, (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), and its D=8 bit encoding of it as [00000001, 00000011, 00000111, 00001111, 00011111, 00111111, 01111111, 11111111]. For there we see that every one of the N=8 bit signals is quantitatively distinguished from every other bit signal in each having a different number of 0s and 1s in them. This quantitatively distinguishable bit encoding with D contrasts to the H=3 bit encoding of that color message set as [000, 001, 010, 100, 110, 101, 011, 111] in which we see that the 001, 010 and 100 signals are not quantitatively distinguished, each of them having 20s and 11, but rather distinguished entirely by the positions of the 1 and 0 bits in them. And that positional or qualitative distinction is also seen between the 011, 101 and 110 signals of its H bit encoding, all of which are quantitatively the same rather than quantitatively distinct.
The qualitative versus quantitative H versus D encodings corresponds to our everyday sense of information as being either of two broad kinds, qualitative or quantitative. When I tell you General George Washington worked his Virginia planation with slaves rather than hired help, that’s qualitative information for you. But when I tell you that Washington owned 123 slaves at the time of his death, that’s quantitative information. With our example set of (■■■, ■■■, ■■■, ■■■) we see that the color subsets are all qualitatively distinct from each other as is well represented with their [00, 01, 10, 11] H bit encoding. It is also clear, though, that there are N=D=4 color subsets, which is well denoted with [0001, 0011, 0111, 1111], which distinguishes them as the 1^{st} color, the 2^{nd} color, the 3^{rd} color and the 4^{th} color, which effectively counts the number of colors.
This qualitative versus quantitative differentiation explains why the H, the qualitative coding recipe is logarithmic and why the D quantitative coding recipe is linear. H is logarithmic because it is a coding recipe for information communicated from one person to another. The human mind distinguishes intuitively between the positions of things as between 20s and 11 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=2^{H}, 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=2^{H} as H=log_{2}N.
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 1^{st} color, the 2^{nd} color, the 3^{rd} color and the 4^{th} color, which is most basically just a count of the number of distinguishable colors, clearly quantitative information about them. D is linear because counting is inherently linear as with 1, 2, 3, 4 and so on. While much information transmitted or communicated from one person to another is qualitative in form as suits practical efficiency, information sourced directly from nature is quantitative in form when it is a precise description of nature as every practitioner of physical sciences understands. As such an encoding of such quantitative information from nature should be most basically linear in form rather than logarithmic as is the h diversity encoding of the number of energetically significant molecules in a thermodynamic system.
The above development of quantitative versus qualitative information provides the broadest understanding of information as diversity. That includes logarithmic diversity for information communicated from person to person as the H Shannon informatio9n entropy also understandable as the Shannon Diversity Index provides; and linear diversity, linear in form as D or h. Tale careful note that quantitative descriptions of items can also be represented and communicated via positional distinctions as seen in the Arabic numerals that write thirteen as 13 rather than 1111111111111 for efficiency sake, with 13 distinct position wise from thirtyone as 31. But that should not take away from the reality of the elemental linear nature of counting and, hence, of science’s distinguishing things quantitatively in the linear rather than logarithmic form the D and h diversity indices have.
This argument that information can be logarithmic or linear in form runs sharply counter to the notion by many information theorists that that the only proper form of information is from the Khinchin derivation of it, the Shannon information entropy, which is logarithmic. That this rigid perspective, which makes impossible an understanding of meaningful information, is nonsense is easy to show in the Khinchin derivation of information as the Shannon entropy defines information to begin with, in a narrow way that obviates our familiar sense of what information is, and then proceeds to derive information as it specified information must be in its axiom set. This approach is a prime example of the value of Gödel’s incompleteness theorem, which considers all axiomatic schemata invalid for that very reason of any conclusions one wishes to be attain being achievable via a biased selection of the axiomatic underpinning of an argument.
Recognizing this and allowing the D diversity index to be understood as a measure of quantitative information allows us to understanding one cornerstone of meaningful information to be information that is judged significant by the human mind rather than insignificant. In a nutshell: significant information is meaningful information. And D diversity also allows is to develop the other cornerstone of meaningful information and that is information associated with emotion, the central topic of the section following this next one, which deals with significance as it affects people.
8. The Significance of Individuals
Much of what people do and think is affected by their sense of themselves as significant or insignificant. This is so important that we can locate corruption in social institutions in it as the selfinterest in an individual overcoming commitment to group success, that is attribute corruption to the great need of an individual to feel significant rather than insignificant, which is generally very difficult in a hierarchically ordered, often exploitive society. This drive is a determinant not only in the Wall St. corruption that jiggled the mortgage market and caused the 2008 recession that near destroyed many American families, but also in the unspoken judicial, political and medical corruption that abounds in today’s America. And such corruption extends to an academic community whose individual interests of status and position have a strong tendency trump concerns about truth, especially as might run contrary to the propagandistic nonsense that hides the reality of rampant corruption in our major institutions. This condemnation of academia is so harsh and so difficult to make stick that we approach the problem of people’s motives to cheat mathematically.
Social dominance, malevolent and benevolent, is a universal reality however much the concept is unspoken because it abrades on the hope for and promise of freedom and fairness. In general the dominant individual is thought to be significant by himself and others and the subordinate person, insignificant. Dominance in a two person relationship, the simplest to analyze, depends ultimately on the relative probabilities of success in competition between the two whether the competition be explicit as in contact sports or implicit as in the track and field, “I can do this better than you can” type. The characteristics of explicit competition are clearer and, hence, is easiest to consider first.
Consider the random selection of an object from the K=10, N=2 color set, (■■■■■, ■■■■■), x_{i}=5 and x_{2}=5, p_{1}=1/2 and p_{2}=1/2, where the p_{1} and p_{2 }weight fractions of the set are the probabilities respectively of red and green being picked. If red is picked, the player assigned red gets $100 from the player assigned green, and vice versa. And in contrast to this balanced game, consider it played with the (■■■■■■, ■■■■) set, x_{i}=6 and x_{2}=4, p_{1}=6/10 and p_{2}=4/10, in which the red player has an edge over the green player of
77.) Δp = p_{1}−p_{2 }=6/10 – 4/10 = 2/10 = 20% =.2
This Δp=.2 measure is also understandable as the vulnerability of the green player. Assume now that this “unfair game must be played by the green player unless he or she opts out of playing by paying the red player $25. Of course, it makes little sense financially for the green player to pay $25 to avoid the game because the average loss is less than that as Δp=.2($100)=$20 per game. Now let’s change the game further to one where the color is picked randomly from (■■■■■■■■■, ■), x_{i}=9 and x_{2}=1, p_{1}=9/10 and p_{2}=1/10. The edge for the red player has increased now to
78.) Δp = p_{1}−p_{2 }=9/10 – 1/10 = 8/10 = 80% =.8
In this game it makes great sense for the green player to pay $25 to avoid the game because the average loss is greater than $25 at Δp=.8($100)=$80 per game. This doesn’t completely obviate the possibility that the green player might get lucky if he plays and win, thereby getting $100 instead of losing the $25 by forfeit without any attempt to win. But generally speaking in any kind of competition that has this form of two players having very different probabilities of winning, past some critical Δp value the additional cost for losing after playing the game and trying to win gets the inferior player to capitulate to the superior player and accept the lesser penalty without a fight.
If a game with lopsided probabilities were played frequently as part of the ongoing relationship between the two players, this level of control and exploitation would instinctively make the inferior player feel insignificant. This emotional outcome of the lopsided relationship has firm mathematical expression in the D diversity index as expressed as D=N/(1+r^{2}) in Eq16 when its r^{2} relative error term is given in terms of the weight fraction probabilities as
79.)
This
expression for r^{2} is easily derived from previous functions we’ve
considered but is just simply demonstrated here with an example for expediency
sake. Consider the K=9, N=3 natural number set, (4, 4, 1), which from
Eqs2,3&4 has a relative error of r=.471 and r^{2}=.222=2/9. With p_{i}
= (4/9, 4/9, 1/9), the r^{2} statistical error of (4, 4, 1) is
calculated from Eq79 as
80.)
This demonstrates the validity of Eq79 for r^{2}. For an N=2 set of relative probabilities of success of two persons in a competition of p_{1} and p_{2}, the r^{2} term is obtained from Eq79 as
81.)
This develops the number of significant people in the N=2 person relationship from D=N/(1+r^{2}) as
82.)
When there is perfect balance in the competition and, hence, in the relationship, p_{1}=p_{2}1/2 and r^{2}= (Δp)^{2}=0 effecting D=2 which indicates that there are 2 significant people in the relationship. And, indeed, both tend to think in such of themselves and of the other person as significant, a positive or pleasant feeling. In competitions between N=2 persons where the probabilities of winning are p_{1}=.9 and p_{2}=.1, the D diversity is
83.)
Rounding off D=1.22 to D=1 indicates that there is but 1 significant person in the relationship, the person with the large p_{1}=.9 probability of winning, the other person, the one with the slight p_{2}=.1 chance of winning, being insignificant in the relationship. That is, the mathematically insignificant person feels insignificant and is also thought to be such by the dominant person. There are other factors in a relationship that mitigate the displeasure of being the insignificant partner in a relationship, it must be stressed. A child inherently thinks of its adult parent as the “big person”, the significant one, and is yet quite happy with a parent who gives love as makes up for this lesser and unequal role in the relationship. But this changes necessary as the child matures and seeks to develop its own sense of significance. Indeed this mathematical specification of personal significance is a manifestation of a person’s “ego” or sense of self as propounded by Sigmund Freud. The mathematics of the factors of caring for another less able individual, as a child is relative to an adult parent objectively, must wait until we develop functions for the emotions in later sections, some of which provide balance for the generally unpleasant feelings of being insignificant or inferior.
Until then we will understand insignificance as a generally unpleasant enough feeling that it causes people to prefer to be significant as an equal or as dominant rather than to be insignificant. Let us repeat for emphasis that there are other factors involved than just competition in relationships and we will get to those in due time. In the meantime we will generalize that from people prefer having power than not. Nobody who plays an explicit competitive game prefers anything other than winning for this reason.
Tom Brady of football fame from his success in the game feels significant and is thought of as significant, while the fellow on the losing end in games and in scrimmages who soon gets cut from the roster feels insignificant and is thought of as such by others in and out of his profession, (indeed, as insignificant, usually not thought of at all.) We need not dwell at length on the obvious rewards of being and feeling significant. Hence, the question to be asked is whether Tom Brady would cheat to win and be significant and enjoy the rewards of being significant? Would Tom deflate the footballs to be significant? This is not asking the question of whether or not he actually did. We know Tom Brady personally and can vouch for the fact that he’s not that kind of a guy. But maybe somebody other than Tom Brady would deflate the footballs to achieve Brady’s significance. That’s the point. Would somebody do that or something like that if he or she could get away with it?
The payoff for winning, for having a high p probability of winning, for having the edge in competition and being significant, is so high and the cost of having a low p probability of winning, of being vulnerable to loss and being insignificant, is so great emotionally, that in many situations, people who can get away with corruption, with cheating on the rules, just do it. Moreover it is also the case that such corrupt behavior is never openly confessed to or in any way revealed because doing so kills the “getting away with it” factor in making a deal with the devil.
For that reason, there’s lots of corruption and not much open talking about it. Really does any even halfintelligent person think that no Wall Streeter going to jail, not even for a day, after six years of investigation of this multibillion dollar scam by the Justice Dept. is anything but a manifestation of consummate business, judicial and political corruption? Even though nobody with a public voice ever says, in contradiction to the Orwellian doublespeak reasons why there was no prosecution of this grand theft by Wall Street banks on tens of millions of Americans, that our social system is thoroughly corrupt, is it not apparent on its face?
Indeed capitalism is corrupt. All civilized social systems are inherently corrupt. The drive to be on top, to be significant, to avoid insignificance, is a powerful incentive to break any code of fairness held up as the moral norm in a society. Even heads of state in a military dictatorship never tell their underling citizens that the game is corrupt and unfair. Be sure that Hosni Mubarak of Egypt, 30 years the military dictator of that vassal state of the USA, a fellow who scuttled billions for himself and his family through systematic corruption, never went on Egyptian TV before the Arab Spring to tell the Egyptian peasants that he was robbing and fucking them blind.
All power systems work this way including our capitalism, which never buys two hours of airtime on TV to proclaim to the American people that it is robbing them blind. The only difference between military dictatorship and capitalism is how the edge is obtained, not whether it exists and is used for the benefit and privilege of those who have the edge. Buying and selling is inherently corrupt and deceitful. The game is to buy cheap and sell dear. The seller is always out to tell the buyer anything he has to in order to extract the maximum amount of money out of the buyer. In the small, as hagglers over price in a New Delhi marketplace know, it is part of the game of the seller to lie in order to get the maximum cash out of the buyer. Institutional corruption comes in when the political system and the judicial system joins in the game against the rules in order to tolerate the inherent corruption and deceit of the marketplace.
But these instances of corruption get way ahead of the game and require much more analysis for their picture to be drawn our fully. What we want to talk about in this section in detail, rather, is the corruption in the marketplace of analytical ideas, that makes it impossible in the end to honestly talk about and uncover the corruption in the broader society that will soon be taking us all to nuclear hell because of the stupidity and lack of foresight from leaders who attained their power through cleverness in becoming socially significant by maximum capability at corruption and deceit rather than really being smart. Beyond the exceptions like Bill Gates, who is too much of a coward and a pussy to enter the tussle of the political and economic arenas where real people suffer daily, the entrepreneur is nothing but a clever thief.
In academics, as in all other professions, there is a hierarchy of power and as in all other hierarchies, it is corrupt as long as it can get away with being corrupt as requires centrally hiding the corruption. As in all areas of corruption, people maintain their p probability of being successful by helping to enable other people’s p probability of being successful. That is, in colloquial language, you scratch my back and I scratch yours. The temptation to do this in obviation of the rules is very strong because the penalty for not doing it is extremely frequently that one winds up with little p probability of winning and being insignificant. And because the payoff for “playing the game” is relative significance, which feels extremely much better than being insignificant. Right Tom?
In academics, just as in every profession, some people do the hiring and firing, the awarding of cash grants to do research and the editing of journals where research papers are published as enable position and grant support. Most often the people on the top of this game are “experts” in the field. Or better said they are recognized as experts by others in the field, which gets you right back to the “you scratch my back, and I’ll scratch yours” game. Of course, playing that game with the devil is lost if one advertises the fact that one is an academic entrepreneur. One most amusing instance of it in recent times was the Complexity Theory bullshit engineered by Stuart Kauffman whose debunking was the primary focus of the Scientific American article by John Horgan, From Complexity to Perplexity, I brought up at the beginning of Meaningful Information Theory.
Unlike my quip about Tom Brady, we actually do very much know Stuart Kauffman personally. And it is interesting that long before we read Horgan’s article ridiculing complexity theory, we had a sense after an hour’s long lunch with Kauffman from the obvious lack of clarity in his doubletalk mathematics that he was as slick a charlatan as Bernie Madoff. For what Kaufmann did was to spin a mathematical argument so complex about complexity that it was near impossible to take apart, for a while anyway. Before it was taken apart publically and Kaufmann chased off to Canada to talk his nonsense to the more naïve Canuck academics he enjoyed great significance in association with the Santa Fe Institute and even wound up a McArthur grant winner.
The corruption in academics is not as obvious in most cases as Kaufmann’s carny game. In our case at hand it has consisted of “experts” in the field of thermodynamics being unwilling to admit that the material they claim to be experts at is incorrect. Though we have run into a good number of them over the years in various universities, the attitude of Bill Poirier stands out. Note his comments to us about our revision of microstate entropy.
In short, though the Gibbs and Boltzmann Shannonlike formulations of entropy have their limitations/issues, there is nothing really mathematically "wrong" about themthey are what they claim to be, within wellknown caveats. Conversely, this is not to say that your approach is "wrong" or otherwise without value; as I said in an earlier email, there may well be more than one useful quantity associated with the same general concept. But I would be wary of making claims that classical entropy is "fundamentally incorrect", and that your approach "provides the only correct understanding of microstate entropy."
Poirier is alluding to both the BoltzmannShannon take on entropy and our meaningful information derivation of it being mathematically equivalent and both correct in that regard. Yet despite the “limitations/issues” with the standard formulation that Poirier cites, which have interminably confused students and professionals alike for the last 100 years, he still favors the standard, perplexing take on entropy unable to shake the inferior explanation he has grown to accept over the years despite its obvious shortcomings. Proof that Poirier is dead wrong lies in his insistence in Chapter his recent book that entropy can be explained from information theory despite the general understanding in the scientific community conveyed in the above Scientific American quote that information theory, as it presently stands, cannot be applied to explaining physical systems. Our extension and elaboration of information theory to include meaningful or significant information as it is found both in physical and in human nature makes the intimate association between entropy and information clear enough that even a high school chemistry student can understand entropy now.
We also mention lightly the pettiness and stupidity of today’s scientists in clinging to orthodoxy for the sake of retaining the crown of “expert” and the position, status and pay that go along with it. A perfect example of this is of our front page poster boy, Bill Poirier of Texas Tech in Lubbock. Perusal of Chapter 10 in his recent book, A Conceptual Guide to Thermodynamics shows a frivolous notion of an information theory interpretation of thermodynamic entropy. It can be judged on its merit by anybody who takes the time to pick up the book and read that chapter in it. His frivolous interpretation of entropy as “the amount of information you don’t know about the thermodynamic system” should be damned because it totally misunderstands the mathematical similarities between information and entropy that scientists have been aw3are of for the last 65 years. The reason for the similar form of the two is that both are inexact measures of sets of things that are generally unbalanced and whose exactness mathematically and as a clear correct understanding of them is provided by the same functional replacement for the N number of constituents in a set, namely diversity be it D or h. He personally should also be damned for not being willing to budge an inch for fear of making a fool of himself in his hypothesis being shown to be wrong, this after a many emai9l exchange with him that laid out the foregoing in a series of first drafts of this material.
He is hardly the only one out there who thinks this way, science having fallen into the same state as all other endeavors in modern day mathematics where people learn to feather their own nests at the expense of the broader needs of society. If such is the case in the natural sciences, that much more is it prevalent in the human sciences, which are thoroughly adulterated by ideology to ascribe people’s unhappiness to the bugaboo of mental illness which is almost as vague, spirit like and intangible as Satan as the cause of evil and unhappiness. Clinical psychology never prescribes rebellion against unfair authority and its humiliations as a remedy for the unhappiness caused by it, but rather “adjustment” to the pain of it and that by any means which includes developing a chronic dependency on psychotropic drugs and delusional belief in religious superstition. God, Heaven after life and the devil are quite alright with the pseudoscience of clinical psychology.
From a purely logical perspective, one should have great doubt about a supposed science that purports to understand abnormal emotion without giving any clear sense of the normal human emotions, as we will do starting in the next section as the foundation of a new set of mathematics based human sciences.
9. The Mathematics of Human Emotion
We do not wish to throw the baby out with the bathwater in our revision and expansion of information theory in Section 6. It is in no way a denial of all of its basic principles, a primary one of which we form the foundation of our specification of all of the human emotions in mathematical form. That principle I am talking about is information theory’s alternative interpretation of the H Shannon entropy of Eq71 as the amount of uncertainty that getting a message resolves upon being received. Uncertainty and information are closely related in information coming about as the resolution of uncertainty. If you have no idea of the way Company XYZ you hold stock in is going and I tell you from what my cousin, the president of the company, told me that they are contemplating bankruptcy in two weeks, that message is information for you because you had uncertainty about the company’s situation to begin with. But if I tell you that Osama bin Laden was the mastermind of 9/11, something you certainly knew beforehand, that message would not be information for you because you had no uncertainty about that.
In a more mathematically treatable way, if you are playing a game where you must guess which of N=4 colors I’ll pick from the set of K=8 colored buttons, (■■, ■■, ■■, ■■), inherently you have uncertainty about what the color is. Keep in mind from our earlier considerations the H=2 bits amount of information associated with this set. That value of H=2 is a measure of the amount of uncertainty you have as the number of yesno binary questions one needs to ask about the colors in (■■, ■■, ■■, ■■) to determine which color I picked. By a yesno 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 yesno 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 yesno 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.)
And the probability of failing to make the correct guess, understood as the uncertainty in guessing, is
85.)
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.)
Now let’s make a table of sets of buttons that have more and more D diversity and list the U uncertainty in guessing the color picked from them.
Sets of Colored Buttons 
D=N 
U=(D–1)/D 
(■■, ■■) 
2 
1/2=.5 
(■■, ■■, ■■) 
3 
2/3=.667 
(■■, ■■, ■■, ■■) 
4 
3/4=.75 
(■■, ■■, ■■, ■■, ■■) 
5 
4/5=.8 
(■■, ■■, ■■, ■■, ■■, ■■) 
6 
5/6=.833 
(■■, ■■, ■■, ■■, ■■, ■■, ■■) 
7 
6/7=.857 
(■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) 
8 
7/8=.875 
Figure 87. Various Sets and Their D and U Values
Very obviously the U uncertainty is an increasing function of D diversity. That
is, as D increases, U increases. More formally U is an effectively continuous
monotonically increasing function of D. This, from measure theory in
mathematics, tells us that whatever D is a measure of, U is a measure of.
Earlier we made it clear that D diversity was a measure of information. And
that would also make the U uncertainty measure understandable as information,
which fits with the classical information theory take on information 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
88.)
And the probability of failing to guess correctly is
89.)
Now the product of the penalty, v, and the uncertainty, U, which is the probability of paying the penalty, is called the expected value of the game
90.) E= –Uv
Putting in the values, U=2/3 and v=$120, we calculate the E expected value or expectation to be
91.) E= –Uv= –(2/3)($120)= –$80
The negative sign specifies E= −$80 as a loss of money, the average loss incurred if you are forced to play this game repeatedly. If you play the game three times, for example, on average you will roll a lucky number and escape the v=$120 penalty one time out of three; and you will fail to roll a lucky number and pay the v=$120 penalty two times out of three as adds up to a $240 loss that averaging out over three games is an E= −$240/3= −$80 loss per game.
The E= –Uv term that is the product of the U uncertainty and the v penalty of money, a meaningful item, can also be understood as meaningful uncertainty. A more familiar expression for this E= –Uv meaningful uncertainty is the fear you have of losing money when you are made to play this game. That E= –Uv is a fitting equation for such fear is clear from three perspectives. The first is that your fear of losing money is a function of the U uncertainty or your probability of failing to guess the color. If we change the game to my randomly picking a colored button from the N=8 color set of buttons of (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■), then the probability of a successful guess goes down to
92.) Z = 1/N =1/8 = .125
And the probability of failing to guess correctly and of your having to pay the v=$120 penalty goes up to
93.) U=1–Z=7/8=.875
And the expected value translated as the amount of fear you have in having to play this game is
94.) E= –Uv= –(7/8)($120)= –$105
That fear feels unpleasant is manifest in the negative sign of the E= –Uv expectation. And you see that this function also fits the natural sense of fear that would be felt including as a measure of the displeasure in it if we change the v penalty. If we increase it to v=$360, the displeasure of fear felt for this game played with (■■, ■■, ■■, ■■, ■■, ■■, ■■, ■■) goes up to
95.) E= –Uv= –(7/8)($360)= –$315
We have introduced emotion now in a very straightforward way in terms of understanding meaningful uncertainty as fear. Next now consider what happens if there is a third person involved in this game who sees which color I picked and tells it to you on the quiet. Then you can use it as your guess and avoid paying the penalty. To go along with the basic algorithm that information is the resolution of uncertainty in information theory, we’ll understand the amount of information you got in the color told you, meaningful information from its resolving your meaningful uncertainty, to have the same measure as the meaningful uncertainty, –Uv, except we’ll get rid of the – minus sign understanding the removal of the meaningful uncertainty to be specified as
96.) T= –(–Uv) = Uv
We’ll explain where the T symbol comes from later on, understanding it now to represent the amount of meaningful information you got from the message told you about color. Now intuitively, you are going to feel an emotion of relief in getting this meaningful information. And the T=Uv function is a very good measure of the amount of relief, how pleasant it is in intensity. For the greater the v penalty, the greater the relief you feel in avoiding it. And the greater the U uncertainty, the greater the relief also. And the implicit (+) positive sign of T=Uv= +Uv, is a reasonable marker for the positive feeling or pleasure you get in relief, that as opposed to the E= –Uv fear, which is unpleasant as it (–) minus sign denotes.
Of course, the amount of fear you feel in expectation of paying the v penalty and the amount of relief you feel in avoiding the penalty are both dependent not only on the U probability of paying the penalty and the v amount of the penalty, but also on how much money, how much wealth, you already have. A millionaire doesn’t really care about losing $80 or get that much pleasure of relief in avoiding the loss as compared to a person who had but $5 in their purse or bank account. This marginality aspect that affects the emotions involved, we’ll obviate by making everybody who plays this game and in every game played have the same amount of wealth.
With that we have the basics down: getting rid of E= –Uv meaningful uncertainty by some activity, here guessing a color randomly chosen, generates T=Uv meaningful information. And this also introduces two primary emotions people feel, fear as E= –Uv and relief as T=Uv. The color guessing game was fine for an introduction to emotion, but next we want to develop the basic emotions, and there are a few more of them, in a more general way. Specifically we want to do it for all goal directed behaviors.
And to do that we are going to switch the game to a dice game called Lucky Numbers. It will develop mathematical functions for a fuller spectrum of our most basic emotions like hope, anxiety, excitement, disappointment, fear, relief, dismay, relief, joy and depression, which we’ll refer to as our operational emotions. And then later we’ll modify the game played to develop functions for our visceral emotions like sex, anger, hunger and the taste pleasures of eating.
We’ll start off playing this Lucky Numbers dice game for a prize, one of V=$120. The lucky numbers in the game are the 2, 3, 4, 10, 11 and 12. If you roll any one of them you win a prize of V=$120. The individual probabilities of rolling the numbers 2 through 12 on a pair of dice are:
97.) p2=1/36; p3=2/36; p4=3/36; p5=4/36; p6=5/36; p7=6/36; p8=5/36; p9=4/36; p10=3/36; p11=2/36; p12=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 99104 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 through12, 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 20^{th} 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 symbolwords 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 welldefined wordsymbols 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, E_{1}=Z_{1}V_{1} and E_{2}=Z_{2}V_{2} with E_{1}>E_{2}, we choose E_{1} whether E_{1}>E_{2} comes about via Z_{1}>Z_{2} or V_{1}>V_{2} 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 E_{1} being better than in E_{2}; or, hedonistically, to their being greater pleasure in entertaining E_{1}=Z_{1}V_{1 }than in E_{2}=Z_{2}V_{2}. _{. }
Rule #3. If we have a choice between two v penalty games, one with fearful expectation, E_{1}= –U_{1}v_{1}, and the other with E_{2}= –U_{2}v_{2}, one of which games we must play, we choose the game with the smaller expectation (in absolute terms.) Or more exactly, if E_{1}>E_{2 }numerically, we choose to play the E_{1} game. To clear up any confusion, as between the games in Eqs4&5, we choose to play the E_{1}=–80 game, E_{1}>E_{2}, 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.
10. The Function of the Transition Emotions
We continue with our systematic explanation of our emotional machinery by explaining the purpose and function of the transition emotions of T= −ZV disappointment of Eq109, T=UV excitement of Eq115, T=Uv relief of Eq121 and T= −Zv dismay of Eq125. Recall that they all come about from the T=R−E Law of Emotion of Eq108. In it the E expected value depends in a very direct way on the Z and U probabilities: of the E=ZV=V−UV hopeful expectation in the V prize game; and of the E= −Uv= −v+ Zv fearful expectation in the v penalty game.
In our
analysis up to this point, the player’s sense of the values of the Z and U
probabilities were taken directly and correctly from the mathematics of
throwing dice. But that need not be the case. A player may suppose any
probabilities of success or failure, which affects the player’s E expectations,
and in turn, affects from the T=R−E Law of Emotion, the intensities of
the T transition emotions from T=R−E the player experiences upon success
or failure.
As an example of a player supposing incorrect values of Z and U, consider in
the V=$120 prize game where rolling a lucky number of 2, 3, 4, 10, 11 or 12 has
an actual probability of Z=1/3 that a naïve 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 132190 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 winloss 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 naïve player thought she had a greater possibility of winning. The 2^{nd} game played is also an R=0 failure and again a T’= −$60 disappointment is felt. On the 3^{rd} 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, E_{NEW}. Hence, not T=R−E, but
196.) T_{AV} =E– E’
Or solving for E_{NEW}, we arrive at the Law of Emotion Inversion,
197.) E_{NEW} = E’ + T_{AV}
For the example case developed above, this obtains an E_{NEW} expectation of
198.) E_{NEW }= $60 −$20 = $40
Now this revised E_{NEW}=$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 E_{NEW} = E’ + T_{AV} 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 3^{rd} 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.) E_{NEW} = E’ + T_{AV}= 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 E_{NEW} = E’ + T_{AV}.
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.
11. Emotions of Partial Success
To further provide observable, empirical proof of the emotion mathematics, we will next consider the emotions that arise from partial success. To that end we alter the Lucky Number V prize awarding game to one where you must roll a lucky number of 2, 3, 4, 10, 11 or12 not once but three times to win the prize, one of V=$2700. The excitement gotten from the partial success of rolling the 1^{st} 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 or12 lucky number on any one roll of dice is from Eq2, Z=1/3. Hence for the 1^{st} roll or with the 1^{st} pair of dice, Z_{1}=Z=1/3; for the 2^{nd} roll or pair of dice, Z_{2}=Z=1/3; and for the 3^{rd} roll or pair of dice, Z_{3}=Z=1/3.
204.) Z_{1}=Z_{2}=Z_{3}=Z=1/3
And the U uncertainties for each toss are
205.) U_{1}=(1− Z_{1})=_{ }U_{2}=(1− Z_{2})_{ }=U_{3}=(1− Z_{3})=(1−Z)=2/3
The probability of rolling a lucky number of 2, 3, 4, 10, 11 or12 on all three rolls is the product of the Z_{1}, Z_{2} and Z_{3} probabilities, which is given the symbol, z, (lower case z).
206.) z = Z_{1}Z_{2}Z_{3 }= Z^{3 }= (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=Z_{1}Z_{2}Z_{3}V_{ }= (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 1^{st} throw of three sequential throws on one pair of dice. After a 1^{st} 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.) Z_{2}Z_{3 }=(1/3)(1/3) = 1/9
And the hopeful expectation of making the triplet roll after a lucky number is rolled on the 1^{st} toss is, increases from the original E=Z_{1}Z_{2}Z_{3}=$100 to
212.) E_{1 }= Z_{2}Z_{3}V = (1/9)($2700) = $300
Next we want to ask what is realized when the 1^{st} toss is successful. It is not R=V=$2700, for the V prize is not awarded for just getting the 1^{st} 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 1^{st} 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 1^{st} roll is of a lucky number is the E_{1}=$300 increased expectation in Eq212. This understanding of the increased E_{1}=$300 expectation as what is realized has us specify E_{1} as a realization with the R symbol as
213.) E_{1}=R_{1}=Z_{2}Z_{3}V = $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 1^{st} toss. This specifies the T term in T=R−E as T_{1}; the R term in it as R_{1}=Z_{2}Z_{3}V from Eq213; and the E term in T= R−E as the expectation had prior to the 1^{st} toss being made, E=zV=Z_{1}Z_{2}Z_{3}V of Eq208. And with U_{1}=(1−Z_{1}) from Eq205 we obtain T_{1} as
214.) T_{1 }= R_{1}–E = E_{1}– E= Z_{2}Z_{3}V –Z_{1}Z_{2}Z_{3}V = (1−Z_{1})Z_{2}Z_{3}V =U_{1}Z_{2}Z_{3}V =(2/3)(1/3)(1/3)($2700) =$200
Now we can ask what kind of emotion this T_{1}=U_{1}Z_{2}Z_{3}V 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 Z_{2}Z_{3}V=R_{1}=E_{1} from Eq113 into the T_{1}=U_{1}Z_{2}Z_{3}V term in Eq219 to obtain T_{1} as
216.) T_{1 }=E_{1}−E=U_{1}Z_{2}Z_{3}V =U_{1}E_{1}=U_{1}R_{1}
The parallel of this T_{1}=U_{1}R_{1} to the T=uR excitement of Eq215 identifies T_{1}=U_{1}R_{1} as the excitement experienced from rolling the 1^{st} lucky number, excitement that is felt even though no money is awarded for rolling just the 1^{st} lucky number. Note that the intensity of this partial success excitement of T_{1}=$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 spinoff 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 1^{st} lucky number is an increase in expectation from the original E=zV=$100 of Eq108 to E_{1}=Z_{2}Z_{3}V=$300 in Eq212. Now we ask what is realized in rolling the 2^{nd} lucky number after the 1^{st} lucky number is gotten. It is a greater expectation yet of making the full triplet roll and winning the V=$2700 prize,
217.) R_{2}= E_{2 }=Z_{3}V=(1/3)($2700)=$900
The transition emotion that comes from rolling 2^{nd} lucky number after having gotten the 1^{st} lucky number is specified as T_{2 }and from the Law of Emotion, T=R−E, with T as T_{2}, R as R_{2}=Z_{3}V from the above and E as the expectation felt after the 1^{st} lucky number was gotten as E_{1}=Z_{2}Z_{3}V in Eq213, is
218.) T_{2} = R_{2}−E_{1
}= E_{2}−E_{1}=Z_{3}V− Z_{2}Z_{3}V
=(1−Z_{2})Z_{3}V = U_{2}Z_{3}V =
(2/3)(1/3)($2700) = $600
Expressing T_{2 }= U_{2}Z_{3}V via Z_{3}V=R_{2}
of Eq217 as T_{2}=U_{2}R_{2} makes it clear from its
parallel form to the excitement of T=uR of Eq215 that T_{2}=U_{2}R_{2}
is the excitement felt when the 2^{nd} lucky number is guessed after
the 1^{st} 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 3^{rd} 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 3^{rd} lucky number of E_{2}=Z_{3}V from Eq217, the
Law of Emotion, T=R−E, obtains a T_{3 }transition emotion of
219.) T_{3 }= R−E_{2 }= V –Z_{3}V
= (1−Z_{3})V = U_{3}V = (2/3)($2700) = $1800
Now expressing T_{3 }=U_{3}V from R=V as T_{3}=U_{3}R and noting its parallel form to T=uR excitement of Eq215 identifies T_{3 }= U_{3}R as the excitement of rolling the 3^{nd} lucky number after the first two have already been rolled as obtains the V=$2700 prize. Note that the intensity of the T_{3}=$1800 excitement from rolling the 3^{rd} lucky number and getting the V=$2700 prize is significantly more pleasurable than the T_{1}=$200 and T_{2}=$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, T_{1}, T_{2} and T_{3} 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.) T_{1 }+ T_{2 }+ T_{3 }= $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 3^{rd} roll and fail to get the V=$2700 prize, R=0. To evaluate the T_{3} transition emotion that arises from that we simply use the T_{3}=R−E_{2} 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.) T_{3 }= R−E_{2 }= 0 – Z_{3}V = – Z_{3}V = −(1/3)($2700)= −$900
This T_{3 }= −Z_{3}V= −$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 T_{3}= −Z_{3}V= −$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 T_{3}= −$900 disappointment felt after partial success is exactly equal to T_{1}+T_{2}=$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 3^{rd} 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 E_{0}=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 E_{0}=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 T_{0} and E as E_{0}=0, the original expectation prior to the game being offered, and R=E=R_{0} as the expectation realized once the game is offered, the T=R−E Law of emotion generates the excitement felt as
222.) T_{0}=E−E_{0}=zV−0=zV
As E=R_{0}=zV and as the probability of success prior to game availability is Z=0 and of failure, U=1, then E=R_{0}=zV can also be understood as
223.) T_{0}= E=R_{0}=zV=UzV=UR_{0}
Again by parallel to T=uR excitement of Eq215, T_{0}=UR_{0} 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 or12. 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−Z_{1}Z_{2}Z_{3})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 1^{st} toss of the dice, E_{1}, understood as what is realized from the toss, R_{1}, is, with the improbability of escaping the penalty then as 1−Z_{2}Z_{3}
226.) E_{1}=R_{1}= −(1−Z_{2}Z_{3})v= −(1−(1/9))$2700= −(8/9)($2700)= −$2400
Hence the transition emotion, T_{1}, is, via the T=R−E Law of Emotion expressed as T_{1}=R_{1}−E, and with R_{1}=E_{1} from the above
227.) T_{1}=R_{1}−E= E_{1}−E=−(1−Z_{2}Z_{3})v−[−(1−Z_{1}Z_{2}Z_{3})]=(1−Z_{1})Z_{2}Z_{3}v=U_{1}Z_{2}Z_{3}v=$200
Now recall the parallel forms of the T=UV excitement of Eq115 and the T=Uv relief of Eq121. This understands T_{1}=U_{1}Z_{2}Z_{3}v, in parallel to the partial excitement of U_{1}Z_{2}Z_{3}V of Eq214 for the V prize game, to be the partial relief felt upon rolling the 1^{st} 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 1^{st}, 2^{nd} and 3^{rd} 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.
12. The Law of Supply and Deman
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 1^{st} 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 1^{st} lucky number to the player. Question: what is the fair price of the 1^{st} lucky number?
As having the 1^{st} lucky number changes the probability of winning the V=$2700 from z=Z_{1}Z_{2}Z_{3}=1/27 in Eq106 to Z_{2}Z_{3}=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 E_{1}=$300 average payoff of Eq213 expected when the 1^{st} 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, W_{1}, the fair price for the 1^{st} lucky number is
228.) W_{1 }= E_{1}−E
This W_{1} fair price is a function of a number of variables associated with the E_{1}−E term in Eqs214&216.
229.) W_{1 }= E_{1}−E = Z_{2}Z_{3}V – zV = U_{1}Z_{2}Z_{3}V = T_{1} = U_{1}E_{1 }=$200
This W_{1}=$200 is the fair price for the 1^{st} lucky number in the latter increasing the average payoff from E=$100 to E_{1}=$300. From the perspective of economic optimization the player as buyer would want to pay as little as possible for the 1^{st} lucky number and the agent as seller would want to charge as much as possible for it. But W_{1}=$200 is the fair price of the 1^{st} 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 W_{1}=U_{1}E_{1 }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. W_{1}=U_{1}E_{1} is an increasing function of the scarcity of the 1^{st} lucky number as the uncertainty in rolling it on the dice, U_{1}=2/3, and is an increasing function of the demand for the 1^{st} lucky number as the E_{1}=Z_{2}Z_{3}V=$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 W_{1}=$200 fair price for the 1^{st} lucky number and the T_{1}=W_{1}=$200 pleasurable excitement gotten from rolling the 1^{st} lucky number on the dice. This equivalence of T_{1} excitement and W_{1} 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 1^{st} lucky number can be calculated not just in terms of the W_{1} amount of money one would spend for it but also in terms of the time spent in acquiring the money needed to purchase the 1^{st} 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, W_{1} is understandable as a measure of the amount of time spent to get the 1^{st} lucky number. This has the W_{1}=U_{1}E_{1}=T_{1} 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 W_{1} fair price of the 1^{st} lucky number is again W_{1}=E_{1}−E, but with E_{1}−E from Eq227 in the v penalty as
230.) W_{1 }= E_{1}−E = U_{1}Z_{2}Z_{3}v = T_{1} = $200
This form of the primitive Law of Supply and demand tells us that people also spend their money for commodities that provide T_{1}=U_{1}Z_{2}Z_{3}v=W_{1} relief. This is in addition to commodities that provide T_{1}=U_{1}Z_{2}Z_{3}V=W_{1} 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 W_{1} fair price with T_{1} partial success excitement, W_{1}=T_{1}. 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.
13. Survival Emotions
Many of our most basic emotions are associated with surviving or staying alive. We derive the pleasant and unpleasant emotions that drive survival behavior from the primitive Law of Supply and Demand in the form of Eq234 of W=Uv= −(−Uv). We do that by applying it not to avoiding the loss of v dollars but to avoiding the loss of one’s v*=1 life. That is, the penalty for failing at a survival behavior like getting food to eat or air to breathe is the loss of one’s own v*=1 life rather than the loss of v dollars. The other terms in W=Uv= −(−Uv) are also asterisked in using it to explain survival behavior to show that they are all associated with avoiding the loss of one’s V*=1 life rather than the loss of v dollars.
235.) W*=T*= U*v*= −(−U*v*)
It is best to introduce this function with specific survival behaviors and save the generalizations of what these variables mean until after we do that. Let’s start with the survival behavior of breathing air whose emotional properties are cut and dried. Consider Eq235 for a situation where air to breathe is lacking whether from a person being underwater and drowning or having a critical asthmatic attack or having a pillow placed forcibly over his face or being water boarded. From Eq235 understood as the Law of Supply and Demand, U* is a measure of the scarcity of air as the uncertainty or improbability of getting air. We can assign a very high value to it in this case of suffocation of, say, U*=.999, also interpretable as the high probability of losing one’s v*=1 life under these circumstances.
The T*=U*v* transition emotion in Eq235 experienced when a behavior is done to obtain air under this U*=.999 circumstance is, in parallel to T=Uv relief of Eq21, the very pleasurable relief felt in getting air to breathe when one is suffocating. While not all have had the experience of suffocation followed by escape those who have will attest to the great intensity of the pleasurable relief felt. One measure of this great relief is from Eq235 evaluated for the v*=1 life saved and its prior U*=.999 scarcity of air or uncertainty in getting it as
236.) T*=U*v*=(.999)(1) =.999
This .999 fractional measure of relief very close to unity, 1 or 100%, is a good way of indicating an intensely pleasurable level of relief. We can also specify the relief in dollar terms as we did in the Lucky Number games by putting a cash value or price on one’s v*=1 life, the one that one doesn’t want to lose. One measure might be if one was alone in the world, all the money one had, let’s say v*=$100,000. That calculates a cash value for the T*=U*v* relief of
237.) T*=W*= –(–U*v*)=U*v*=(.999)$100,000=$99,900
This effectively says that one would pay a price of W*=$99,900 or pretty much all of one’s money to escape terminal suffocation, which is true of all with the above assumption of nobody else to worry except the pathological. The –U*v* term in Eqs235&237 that is negated or resolved by the behavior of escaping suffocation to T*= –(–U*v*)=U*v* relief is a measure of the fear instinctively felt upon suffocation, parallel to the E= −Uv fear in Eq120 of losing money in the Lucky Numbers v penalty game.
The W*=T* equivalence of Eq235 also makes clear that the W*=T*=U*v function that governs the emotional dynamic operates as the Law of Supply and Demand with the demand for some commodity, be it goods or service, object or behavior, that provides escape from suffocation and preservation of one’s v*=1 life measured by the instinctively great value a person places on his or her life; and with the supply of what is needed to preserve that life measured inversely by the scarcity of air to breathe or uncertainty in getting it as U*.
The fact that we can so simply derive the emotions of breathing under suffocation, the panic fear it causes and the great relief experienced in escape from the suffocation, is a remarkable validation of Eq235, W*=T*_{}=U*v*= −(− U*v*), and of its derivation from the cash based Lucky Numbers game. It gives confidence that this mathematical understanding of man’s emotional machinery can impact the central problem for mankind of unhappiness from enslavement and the violence that emanates from it that stimulates war and can put the world’s nations into terminal nuclear conflict. And it should give confidence also in the remedy to these problems this mathematical analysis provides of our moving collectively towards A World with No Weapons.
The W*_{ }= T*_{}=U*v*= −(− U*v*) Law of Supply and Demand of Eq235 also holds in the normal situation for people where there is no scarcity of air, no uncertainty in the body’s cells getting oxygen, no probability of losing one’s v*=1 life from lack of oxygen, U*=0. This is made clear by inserting U*=0 into Eq235 to obtain
238.) W*=T*=U*v*= −(−U*v*)=0
This expression of Eq235 quite perfectly fits normal breathing when there is plenty of air to breath in indicating no unpleasant fearful feeling, −U*v*=0, no noticeable relief in breathing, T*=U*v*=0, and no money a person is willing to pay for air, price W*=$0. The mathematically derived conclusions for U*=.999 suffocation and U*=0 normal breathing universally fit observable human experience.
And so does the intermediate situation with air in short supply but not critically scarce, as say, U*=.2, as might apply to COPD (Chronic Obstructive Pulmonary Disease.) In this U*=.2 case, the –U*v* displeasure is felt as pulmonary distress but less horribly unpleasant than the panic fear of U*=.999 suffocation. Also significant is the T*= −(−U*v*)=U*v* relief felt when bottled oxygen is supplied to a COPD sufferer. And we also see in this not uncommon ailment for older people that they are willing to pay a W*=U*v* price for relief, a lot if necessary though not every last penny a person has as a person would pay if their life was critically threatened as it is at the U*=.999 level of suffocation.
Temperature regulation as avoidance of the extremes of cold and heat is, like breathing, centrally important for avoiding the loss of one’s v*=1 life. Temperature below 68^{o} 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 68^{o }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, θ_{S}. The difference between the two is the error,
239.) ERROR = (θ_{S }−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, θ_{S}, 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 82^{o}F. 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 82^{o}F 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 huntergatherer 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 welldefined 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.
14. Natural Selection
We take
great pains to explain natural selection mathematically because of the
controversial issue that evolution has become in America. The mathematics moves
up to a slightly higher level, but we’ll do our best to keep it as simple as
possible. We will start with a formula from the banking industry for interest
in a savings account that nobody sane disagrees with. It is found in all junior
high math texts.
244.)
The x_{0} 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 x_{0}=$100 and keep that money in the bank for t=2 years, the initial x_{0}=$100 will grow according to
245.)
You could also get a savings account with a quarterly or daily compounding of the interest. This modifies the interest formula in Eq245 a touch to
246.)
The m term is the number of times a year the interest is compounded or paid. So with the same initial deposit of x_{0}=$100 and same interest rate of g=5%=.05, if the savings account had quarterly interest paid, which is m=4 times a year, the money in the account would grow in t=2 years to
247.)
And if a savings account had interest compounded daily, or m=365 times a year, the $100 you originally started the account with would grow over t=2 years to
248.)
An alternative formula for the daily compounding case is
249.)
The letter, e, is Euler’s number, e=2.7183. So with x_{0}=$100, g=5%=.05 and t=2 years we calculate from it the x=$110.52 for daily compounding we saw in Eq248 but as
250.)
Eq249 is the formula for exponential growth, which means the growth of something at a rate that depends on how many of that something there already are. This fits the growth of money in a daily compounded savings account, which depends on how much money you already have in the account. Often, indeed usually, the formula for exponential growth is written in a different form than Eq249, in differential form as
251.)
The dx/dt symbol is the rate of growth of the money and this differential equation tells us that it depends on the x amount of money in the account and the g annual interest or growth rate. Eqs249&250 apply not only to the exponential growth of money in a daily compounded savings account 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 x_{0}=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 19^{th} Century a Belgian mathematician, named Pierre Verhulst, came out with a modification of exponential growth in Eq251 that takes the reality of limited growth into account. It is, with K as the carrying capacity,
253.)
This Verhulst equation or logistic equation spells out growth over time in differential form is expressed as a time equation as
254.)
Eq253 and Eq254 translate into each other much as do Eq249 and Eq251, the details of the operation omitted. Now let’s consider the growth of the same population of x_{0}=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 x_{0}=10 Organisms with a g=1.1
Growth Rate over t=10 years
A second impediment to the unlimited growth of a population is the presence of a competing population. To see how competition affects growth, consider two populations of organisms, #1 and #2, which both grow exponentially in unlimited circumstances according to Eq249 as
256.)
256a.) g_{1} = b_{1} – d_{1}
257.)
257a.) g_{2} = b_{2} – d_{2}
The x_{10} and x_{20} terms are the initial sizes respectively of the #1 and #2 populations; g_{1} and g_{2} are their annual growth rates; and x_{1} and x_{2} are their sizes at any time over time, t, in years. The sum of the x_{1} and x_{2} sizes of these populations, x_{1}+x_{2}, at any time t is calculated from the above to be
258.)
We calculated this x_{1}+x_{2} sum because it allows us to
track the fractional size of each population over time, t, that is, the
x_{1} and x_{2} sizes of each population relative to the x_{1}+
x_{2} 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.
261.)
If the g grow rates of the two populations are unequal, g_{1} ≠ g_{2},
the population sizes of the two populations will still continue to change even
at the K carrying capacity of their mutual niche.
262.)
263.)
This x_{1}+x_{2}=K condition of the niche we assumed will also be understood as applying to the initial population sizes of x_{10} and x_{20}.
264.)
This expresses Eq252 via x_{20}=K−x_{10} as
265.)
This expression for x_{1} is further simplified by
dividing the numerator and denominator of the right hand term by to get
266.)
We can simply Eq256 further by expressing the difference in growth rates, g_{1}−g_{2}, as F_{1}, the competitive fitness, or more simply, the fitness of the #1 population
267.) F_{1} = g_{1} – g_{2}
268.)
Noting the sameness in form of the above to the Verhulst time equation of Eq254 tells us that we can write it in a differential form that has the same form as the Verhulst differential function of Eq253.
269.)
Next we define the fitness of the #2 population, F_{2} to be
270.) F_{2 }= g_{2} – g_{1 }= –F_{1}
This allows us in parallel to Eqs268&269 for x_{1} to write for the x_{2} size of population #2,
271.)
272.)
A graph of
Eqs268&271 makes clear the fate of these two competing populations.
Consider the niche they live in together to have a carrying capacity of K=100
organisms with an initial size of x_{10}=1 for the #1 population (asexual
reproduction assumed for simplicity) and x_{20}=99 for the #2
population and with growth rates of g_{1}=2 and g_{2}=1 as
shows x_{1} in blue and x_{2} in red over time.
Figure 273. Competitive Population Growth or Natural Selection
The #1 population in blue, which has the higher growth rate of g_{1} =2, is seen to flourish over time while the #2 population in red, which has the smaller growth rate of g_{2} =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 F_{1}=g_{1}−g_{2}=1_{ }>0, eventually takes over the entire niche, x_{1}=K=100, and the one with the lesser g growth rate or negative F fitness, here population #2 with F_{2}=g_{2 }− g_{1 }= −1_{ }<0 decreases in size and eventually dies out or goes extinct in the niche, x_{2}=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.) F_{1 }= g_{1 }− g_{2 }= (b_{1}−d_{1}) − (b_{2}−d_{2})
275.)
F_{2 }= g_{2 − }g_{1} = (b_{2}−d_{2})
− (b_{1}−d_{1})
This
mathematical description of natural selection perfectly fits its description in
nonmathematical 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 Eqs268272 are not
new and can also be derived from the preWW1 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 F_{1} fitness of Eq253 to
276.) F_{1}=b_{1}−d_{1}−b_{2}+d_{2}
Population #1’s chances of its F_{1} fitness being positive, F_{1 }>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 F_{1} fitness. This optimization of F_{1} mathematically entails in part minimizing the d_{1} death rate in F_{1}=b_{1}−d_{1}−b_{2}+d_{2 }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 d_{1} death rate of their population is small. This minimization of the d_{1} term in F_{1}=b_{1}−d_{1}−b_{2}+d_{2} 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 F_{1}=b_{1}−d_{1}−b_{2}+d_{2} that F_{1} fitness and the possibility of evolutionary success is optimized by maximizing the b_{1} birth rate and the d_{2} death rate of a rival population in the niche. On the face of it, this suggests in the maximization of b_{1} 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 d_{2}, the death rate of rivals, in order to optimize F_{1} that there be emotional programming to kill off rivals in the niche or drive them out of the niche as produces the same outcome prescribed by the mathematics of lowering the population size of rivals in the niche.
Another alternative conclusion to combat is one group conquering another and taking them as slaves. As slave labor by definition results in greater wealth for the conquerors, it necessarily improves the life span of individuals and lowers the death rate, −d_{1}, of dominant population of slave masters. Keeping people in chains physically or economically also effectively removes them the competing competition, kills them as competing individuals and in doing so increases d_{2}. As both a decrease in −d_{1} and an increase in d_{2} helps to maximize the evolutionary fitness of a group, the behavior of slave taking and the economic control of others generally is favored in evolution. This is hardly to say that the positive emotions involved in being a slave master are actively advertised because doing so would run contrary to having a maximally efficient control. The lion does not advertise the fact as he stalks the wildebeest that he is about to kill and eat it. And, indeed, this behavioral deception that is general in just about all predators is matched by varieties of passive signal deception such as the lion’s coat being the color of savannah grass so as to hide its approach to its prey. In short if we all did live in a slave society, the last thing it would do is advertise the fact of it.
And in conjunction with this comes the hiding of the consequences of being controlled in an exploitive way, religion blaming the devil or the person himself or herself for their pains and clinical psychology the equally vague evil spirit of mental illness and/or the person, himself or herself. Most unhappiness comes one’s loss of true freedom, that and much of violence that we see relentlessly in the news, domestically and internationally. To clarify these issues takes further mathematical analysis based on the foundation ideas we have developed up to this point.
But talking about the emotions related to sex, love (parental and romantic) and violence, however, and what the mathematically prescribed behavioral outcomes of these emotions are or are not is fraught with problems because sex, love and violence are very much tied up with values and morality. And these consideration get all the more confused and contentious, on the one hand, when moral restrictions are used to control people and their behaviors in a servile society, one that depends on the enslavement of its people for its strength and survival; and on the other hand, when the morality of behaviors are broadcast with fiction that utterly distorts the reality of life and with supposed nonfiction news programming that is at heart as nonrepresentational of real life as the fictional programming in television series and in movies.
For the above reasons, before we dive into these problems with considering violence and sex, epistemologically and morally, we are required to first present a template for reality in the form of true life stories that are more representative of not just what happens to people but in the emotions that people feel generally. For that reason, despite the fact that I would prefer to keep my failures and humiliations to myself, as people generally do which keeps the harsher truths of life all the more hidden, I tell my story in the following section. Then we will continue with the mathematical analysis in the sections after that.
15. Revolution in the Garden in Eden
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, 102, 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 megadeath of nuclear conflict. This true view of adult life as highly controlled ultimately by those at the top of the social hierarchy for their benefit runs counter to the American Dream picture presented to young people in ruling class controlled media.
To expose the reality of life, one calls on the one picture of it that one is sure of, the reality of one’s own life. Nothing, though, is as difficult as revealing the truth about, especially the bad things that happened to you. For whatever feels bad inside when you think about it brings greater humiliation yet in the public confessing of it. But the cost of keeping private matters hidden from others is also great if making life clear is important to you, for only the raw truth spat out is able to show that the society we live in has problems, significant institutional problems that must be spelled out clearly if there is to be any chance of doing anything about them. And after I finish my story I’ll talk about the important issues in precise mathematical language.
I was born
four months before America entered WWII as part of the last wave of women whom
fundamentalist tradition was set up to control them as tightly and painfully as
the foot bound women of imperial China. My father was a minister in rural parishes
in Cullman, Alabama, where I was born, and later in Serbin, Texas, north of
Austin, where his superior ability to extort tithes from parishioners elevated
him to a position at Lutheran seminary where he taught Stewardship, a fancy
name for extracting cash from the congregation.
My mother was a shrewd bulldog faced woman right out of Stephen King's, Carrie,
crazy enough to think and tell us kids that Jesus talked to her every day and
that the fossils in Dinosaur National Monument were plaster fakes secretly
buried in the ground by people who hated God. This gave her cover for raising her
children with the switch, including this little girl, me, with near weekly
humiliating and painful britches pulled down whippings. If she didn't get off
sexually with this game, for she had a way of twisting truth in all matters, I
wouldn't believe it. Mildred Graf was 50 Shades of Grey with a halo.
Fear ruled my life, fear of punishment for taking a cookie without permission,
fear of my mother whenever I approached my house coming home from school, fear
of the dark, fear of dogs and a fear of the moon at night that stretched into
my early thirties, at which time I was miraculously able to escape from this
idiotic pointless terror of disobeying and everything else conditioned in me by
childhood brutality disguised and blessed by my minister father as a proper
Christian upbringing.
Some of the worst of my early years was my role as ego fodder for my brother, Don, older than me by two years. He was the recipient of the same sort of corporal punishment I got until he firmed into the role of my mother's toad and henchman over me. My hearing her spank Don used to bring on tears in me for him, but a waste of emotional energy in that my mother's iron rule could never be softened with tears and in Don's passing on a good amount of the pain he got from her to his younger sister, me. If my recall of his punching me in the shoulder at least once a day is an exaggerated memory, it is not by much. And once you are scared of somebody physically, even suggestions to stupid things potentially frightening become effective like being told there was a wolf upstairs in my bedroom that brought on a kind of terror I showed outwardly that he delighted in.
I was lucky, though. I was not so destroyed as to be unable to hate my mother, for she and my minister father left enough in dumbbell me by pampering on the margins to make me a pretty if frightfully awkward girl child, for the minister's daughter is a public figure and if thought pretty by the congregation, a valuable status symbol helpful for stewardship and for the minister’s promotion in the pastoral ranks.
Alone in a
piously brutal regime, all that mattered to me growing up was the thought and
hope of love and rescue. The most daring books in our home library in those
days were the Zane Grey novels. My imagination translated the cowboy heroes in
them into would be lovers scooping me up on their horses and taking me far away
from my family while squirting me in my preteen 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 sixyearsold, 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 overdominated 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’ preadolescence 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 semiworship by a vast gaggle of Japanese men that extended out beyond our
mission church boys to the classes of college age guys I taught English to at
Hokkaido University. This support that nature gives free of charge to girls who
manage, by care or luck, to keep their waist slim was raised to a better level when
fate, most miraculously, handed me a side role in life as a commercial model on
Japanese TV. One of our social contacts through the mission church was a television
producer who signed me on to pitch canned bean soup on Japanese television, the
equivalent of Campbell’s soups. For six years I was known all over Japan in
this guise, stopped by strangers on the street and at restaurants when I dined
out and asked, "Aren't you the Koiten Soup Girl?!!"
A sort of Zane Grey hero soon came into my life in the form of a Japanese
college boy, a ski bum sort of fellow who took the missionary's wife bait that
the Reverend Schoppa dangled in front of all the young men, too her off to bed.
This happened on church sponsored ski trips up on the slopes of Hokkaido that
Len didn't come to because he didn't ski. It was real love as close as I'd ever
been to it. He liked me a lot and I loved him for him for loving me that much and
loved him too. The affair, whenever I could get it, was a great relief from the
empty life I’d had with my mom and dad appointed missionary husband. Physical
love that works for a woman in her twenties is fairly close to Heaven when
you’re in the middle of it as much as not having it is quite hell.
Perhaps affairs like this are easy to hide for the smart women on the Real Housewives
of New Jersey TV shows, but in a crowd of 30 fellow LCMS missionary couples
we were but one of, some of whom also went on these Christian Fellowship ski
trips, once the slightest suspicion arose about Mrs. Schoppa and her ski
partner, the gossip fell like rain from the sky on the doorstep of the Rev.
Schoppa. The climax of the confrontation between him and I was funny in its surprising
twists and turns only in distant recollection of it.
I didn't hesitate to confess once he accused. I was much too dumb to tell a
good lie and, to tell the truth, I had no good reason for wanting to hide it
from him for by this time, I hated him for plaguing my life with his presence
and instinctive female intuition must have primed me to unload with the truth
with both barrels once he popped the question. What surprised me was his
falling smack on the floor when I told him, yes, yes, I did it, and then writhing
on the rug like a big piece of bacon frying in a pan turned up high; and while
twisting all about like that confessing in a series of blurts to having had sex
with farm animals, sheep, pigs and even the large dog his parents named,
"Lassie." Even at this, though, I was sure later that he was lying,
for he was the quintessential toady type who had to lie about everything in his
toady life. What his preferring to fuck geese better than me had to do with my
having had an affair the last six months with one of our converts did not,
could not, register in my head at the moment of his deep confession and only in
retrospect a few days later did I realize that the rumor that he had had sex
with his retarded cousin, Larry, that a few of the good old boys in Harrold,
Texas, had lightly joked about must have been true.
Once you have a sense of that, parallax with pastor personalities generally so
similar to his and my father’s makes it clear that they're all closet fags of
one kind or another. Sense would tell you that the Protestant Christian clerics
couldn’t be that much different than the Catholic Christian clerics, however
seldom you see one get his trousers pulled down in public like Ted Haggard and
Jim Bakker. It quite fit my own father, who though he likely sinned only in his
heart in this regard I would guess, had to be perverse sexually in marrying
anyone as bearishly ugly as my mother. Indeed, the truest truth ever spoken on
TV had to be about queer conservatives as the norm by Joel McHale at the 2014
White House Correspondent’s Dinner. I mean, the brief titter and then drop dead
silence tells it all. I mean, who looks prissier and weirder and queerer than
pretty boys Ted Cruz and Marco Rubio and slippery ugly boys Rush Limbaugh and
Karl Rove.
And back
closer to home, it would take a very kind woman not to see my brother, Don,
quintessentially conservative in his outward religious and political behavior, as
faggy. That’s not to say he never married, did twice. But on the other hand
both divorced him. And a wealthy lawyer has to be a pretty something off the
norm to be left behind when he’s got that much status and that much money in
the bank, and by two women no less. That’s just an educated guess, mind you,
though the extent of his hating women, which I know a lot about as you’ll see,
(I am not labelling him as a murderer for nothing), is a bit of a tip off on
what he does on his frequent weekend trips out of town.
Anyway, angry gossip aside and back to the main story, the headline of Missionary’s
Wife Has Affair with College Boy Convert in Japan quickly spread beyond our
Lutheran missionary circle in Japan to all the Christian missionaries in Japan
and shortly, in less than a year, all but one of our 30 LCMS (Lutheran Church
Missouri Synod) missionary couples were recalled back to America. Sounds like a
very funny movie, but that actually did happen, I’m proud to say. The scandal
hit home stateside, 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 soninlaw) 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 exsnake. 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, animalfucker 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. Bachan, 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. Bachan was strikingly adorable with her unusual mix of Asiatic
and Nordic features.
Bachan was special also in my being able to love her as other than a cooffspring 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 Bachan 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 Bachan 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 selfhelp
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 selfrespect 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 lizardlike 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 checkup 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 threeyearold Bachan 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 Bachan 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 pickup 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 Bachan 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 selfinterested
child.
Pete never quit. I was half crazy over the loss of the three kids and what
they’d done to Bachan 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 megaextreme treatment of Pete was in no small way because Pete was
and very much looked like a 60s rebel, antiVietnam war radical, long hair,
antiauthoritarian 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 1^{st} 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 Bachan back to life, always propping me up and telling me to never lose hope. This was a hard task because Bachan 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 Bachan how to read and all the talk back and forth from the reading lessons loosened Bachan’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 Bachan 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, Bachan told us that they had beaten her up with the excuse that she wouldn't be quiet in church on that weekend when they took her on visitation. They took her home after church and beat her up. And then, horror of horrors revealed, they put a pillow over her face, so she said, and partially suffocated her and then told her if she ever told anybody, they'd smother her. And that put that level of fear in her that made her act that way that day Len brought her back to us. I'm not exaggerating.
She also talked about things done to her that seemed sexual, but Pete never took that part too seriously because once you start thinking and talking in that way about somebody that you hate, especially from the recall memory of a six year old talking about when she was three, nobody would believe you. It was horrible enough that they beat her dumb without accusing them of anything more than that. Though I thought it odd that this young child was putting things in her vagina like pieces of foam rubber from her mattress. Was this possibly evidence that some of the bizarre tales she started telling about what they made her do sexually were actually true?
What was amazing was that after two weeks of intense focus and her talking about what had happened to her, her lightening up was marked and, lo and behold, on one of these remarkable days she started playfully throwing a pillow on our bed up in the air again and again. And however much it may seem too much made up to fit the story as one might like to tell it, she started using a pillow to sleep with ever after that.
The cartoons June drew she got the basics of from a comic book I was doing at that time about my life. I can’t overstate how much the combination of losing three of my kids and Bachan 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 Bachan’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 selfloathing, 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 Bachan 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 Bachan 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 inlaws.
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 inlaws 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 fatherinlaw and brotherinlaw 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 inlaws, 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 naïve 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 inlaws 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 inlaws 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 Bachan’s soul or gave the order or suggestion to do it or was seriously in on it somehow, likely carrying out a plan that had originated in my mother’s dark heart. And beyond that and being a conservative closet gay, a pedophile too?
Less than a year later back up in New York we received a letter out of the blue from Don’s wife, Ruby, telling us that she had just divorced Don. It was filled with bitter spiteful words obviously designed to hurt Don as much as she could by telling us about his humiliation of being left by her. Understand that this was to two prime enemies he had at this point in his life. We guessed that Ruby’s male relatives seeing what a coward punk her meal ticket lawyer husband was must have taken her beyond the critical point of putting up with the bad small of a subpar husband, well off lawyer or no. I recently read a piece from a 40s issue of The New Yorker about the Nuremberg Trial that talked about Goebbels escape from execution by taking cyanide indicating that Goebbels was the exception to the rule that all bullies are cowards. Whether Goebbels was or not, Don wasn’t such an exception.
Pete’s stay at the university in the early 80s didn’t last long. He was a favorite of his students, being the only professor I have ever heard of who received a standing ovation at a final exam, this from three classes he taught engineering thermodynamics to. And he had the highest student evaluations in the School of Engineering at RPI for the ten years they were conducted. But he found his position in the hierarchy and the degree of control over him not that much improved from his days as a graduate student. Ten years of pretty much complete freedom made him a poor candidate for the upper middle class role of a university professor.
So after gleaning considerable pleasure in paying back the four professors who had fucked with him in his graduate school days in various ways, revenge actually improving one’s life and mood considerably as one finds out when one takes it, we went back to a life of anarchy, no rule over you, with all that implies for survival being a true, and somewhat dangerous, adventure.
After two years at the university we devoted all of our attention, outside of survival and the kids who came along, to solving the problem of hierarchical control and the unhappiness it generated, and the problem of violence enhanced by weapons, especially nuclear weapons. From his personal experiences as a street fighter in his younger days, he understood that once a fight starts with punches thrown, the fellow leaning towards the losing side will do ANYTHING to keep from losing, no care as to the consequences since losing is near the equivalent of death.
The translation of this scenario to the world stage is simple and straightforward. If Russia was losing in a war with the United States, would it use nuclear weapons? It has already said it would a dozen times in a dozen ways over the last few years. And if we were on the losing end, truly losing, would we use nuclear weapons to keep that from happening? Whatever a moralist lacking in actual fighting experience might conclude, those who have felt the emotions involved know better. And as to the start of such a fight, where do you think this proxy conflict in the Ukraine between America and Russia is heading? Certainly not to a settlement at the peace table as ongoing events make eminently clear.
The culmination of this conclusion unavoidable for anybody who understands violent aggression from a personal sense of it is that only getting rid of the weapons that cause the horrendous deaths and crippling of war can solve the problem. You can’t get rid of violence without castrating all the male members of the human race. We’re already getting close to doing that in America psychology and with not very palatable results other than for the erectile dysfunction medication manufacturers. You have to get rid of weapons to get rid of the mayhem of major violence.
And in its
bringing about a much more equable balance of power between individuals, the
total elimination of all weapons in a society most definitely ameliorates the
problem of the loss of freedom from excessive social control because, while one
man with a gun can control ten others without one, when all are denied the use
of weapons, the level of control possible in a society greatly decreases to
produce a concomitant increase in personal freedom, which is the most important
enabler of success in the pursuit of happiness in life. No freedom, no
happiness, as is obvious in this joyous world mankind currently inhabits. To
these ends we worked hard to write up and then publish the following newspaper
article that directs all men and women to achieving A World with No Weapons.
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 megadeath 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 quasiwestern 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 internation 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 allpowerful 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 nineyearold 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 Bachan. 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. 

Bachan 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 slamtotheground wrist breaking arrests. To join A World with No Weapons with a donation of $20 and encourage me to help bring an end to war and to America’s NSA run police state, click here.

Now let’s fast forward to the present down in Las Vegas where much of this last edition of this website was written up. This lunatic city is valuable as a microcosm of America in a number of ways. First of all are the casinos. Nobody wins in them, yet everybody plays thinking they’re going to win. Is the inability of anybody to win my idea? No. One owner of a very flashy and successful casino on The Strip said it all on CBS Sixty Minutes. To paraphrase Steve Wynn, never saw anybody come out a winner. Eventually everybody loses.
The reason for this is, first of all, raw mathematics. The odds in every form of casino gambling are in the house’s favor. And the law of large numbers, not argued about in mathematics, says that over time, the casino has to win and you have to lose. That’s not to say you can’t win in the short run. And some people do. But human nature specified in terms of the mathematics of human emotion on this website tell it clearly. If you win with something, the instructions to that brain of yours, quite inadequate to cope with the statistical nature of gambling, tells you to go back and play again. And the law of large numbers takes over. And you lose. You just do, and even more what you first one because your stupid brain has to be taught the lesson of a significant loss before it gets the picture.
Assisting in this clockwork fleecing is a generalized form of propaganda that we’ll get into later mathematically that is the other leg of brain washing. The first was how insignificant things could be made to be significant by outsizing and repetition, like the possibility of winning in a casino as paraded with the big wins that happens every once and a blue moon. The other has to do with associating positive emotion with casino play in a general way. That emotion is excitement. Normally, if you win at something difficult or uncertain, it is exciting and as made clear in Section to on the function of the transition emotions, excitement leads to confidence in winning in future efforts of the same kind.
But excitement can also come about in an indirect way via communication with others. Nature set you up this way because if someone close to you wins at something and shows excitement, by smiling, by dancing about as TV contestants do instinctively on game shows, by singing, you get excited too. And alcohol gets you artificially excited, which is why they give it away for free in casinos. And music gets you excited. And girls with their skirts hiked up close to their privates get the males who make up the bulk of gamblers excited. All of this artificial excitement tells your stupid brain, which then conveys the message to your stupid mind, that good things are about to happen.
Made insignificant and in sharp contradiction to all the smiles and laughter and such seen in every form of publicity for casinos are the frowns of the losers, and the incessant run of suicides by jumping off the roof of the Golden Nugget Casino’s parking lot, and the like. Information in, behavior out. Bad information in, bullshit propaganda, bad behavior out.
And you have to see the people who play to understand why they play. These are not James Bond and Ms. Pussywhistle playing at the slot machines. These are unattractive people, who play and hope to win as part of their general spectrum of delusional expectations in life. If they don’t have the delusions, they feel as bad as they look. And you don’t have the delusion of winning at casino gambling unless you do it. It’s a con game, pure and simple. And the biggest losers in a con game are those who are desperate for some kind of success in their loser’s life. Religious delusions of happiness after you’re in the casket are very similar in kind to gambler’s delusions. And their promulgated in the same way, by making meaningless things appear to be meaningful with the usual bag of propaganda techniques, the ones we’ve just gone over. The choir in the church balcony is singing to you the message that all here is happy and bright, have confidence in the promise of God. It’s really no different than the function and consequences of the upbeat never ending music in casinos. Hey this is a happy place. Put your money down and win the equivalent of happiness for eternity, enough money by fortuitous gambling to never have to worry about it again.
And this is exactly what life in capitalism is about. Great promise, and no discovery of the promise as a false promise until you’re too damn old to do anything about it. Which is why all the casino players, the youngest crop of adults who play from natural youthful enthusiasm tricked excluded, look so damn ugly. And why adult Americans past the glow of youth look so damn ugly in reality. The entirety of TV programming is a con game. The endless excitement; the endless old “song and dance” to make you think, hey you really are in the Garden of Eden. Just be a good boy or girl and you’ll wind up with a smile as bright as the plaster smiles placed on the professional actors and actresses who make up the news corps and the characters in all those dramas that have little to nothing to do with the dramas that murder people’s spirits clockwork in workaday reality life. And make them look very ugly by the time the beginning of middle age sets in.
Anyway it’s all clear in Las Vegas, not just how you’re robbed of your life and its potential for happiness with tricks and games, but also the end consequences of the false promises and the delusional behavior it drives. That’s easy to see if you ride the city bus in Lubbock, the one that the working people, not the tourists ride on. All you see, accent on the word, “all”, are miserable people. They’re miserable in the way they look. And they’re miserable in the way they feel. Oh, and yes, this shows so much in the way much of this misery is expiated through redirected aggression, meaning that the misery flows rapidly wherever and whenever it can from one miserable person to whomever is vulnerable to its reception.
Black on white is clear as a bell down in the lower echelons. Black people, real black people, basically hate white people because it’s white people who basically are the ones that fuck them over in the broader institutional power structures in America. The association of “my source of pain” for a black person with a white face is simple Pavlov conditioning. Now you think that I’m a bleeding heart in all I’ve said so far against the conservative assholes. But reality is what’s important, the pain and the hate out there. And I’ll make that clear in two very real, very personal stories that happened to us when we were in Las Vegas. The first was an episode of what happened on the bus, the Las Vegas RTC, to Pete. I’ll let the note he emailed to the RTC, which was never answered, speak for itself. It’s a bit tongue in cheek here and there as any letter to an uncaring institution has to be, but the crux of it is 100% true.
Dear RTC: I flew down to Las Vegas from New York on business and have reason to frequent UNLV up on Maryland Parkway. After minor shock at the daily taxi fare to UNLV from and back to Fremont St. where I’m staying, I had the pleasure of making acquaintance with your transit system, as things turned out not very pleasant at all. The inconvenience of the crowds is one thing, something a New Yorker is used to, but to have the potentially dangerous experience I had this morning on one of your busses, another thing entirely. I’m going to spell it out in the detail it deserves. Please bear with any seeming intermediate trivialities.
I found out I qualified for reduced fare as a senior citizen and always show my ID by holding it very visibly with my thumb above the RTC card when I swipe it. Drivers can’t and haven’t ever missed it, until this morning. When I got on the BHX bus (# 845) today at 6:55AM at Fremont a couple of miles from the Casino section, the driver, a black fellow, that fact not incidental to the what happened, was in the middle of a chat with a passenger, another black fellow, and took no notice of my reduced fare ID, which as I said was unmistakably obvious had he been looking at me swipe my card instead of talking to the passenger. So he stopped me as I walked past him by shouting out for me to show him my reduced fare card. I turned back and said as I held up the RTC card and the ID together, “It was on my thumb.” Couldn’t be missed. “I didn’t see it,” he replied. No problem here. People make mistakes, this one totally minor.
But the black fellow he was talking to me touched my shoulder as I walked back to my seat on the bus and said something to the effect that I better be cool. My reply as I went back to get a seat was, “Don’t touch me.” I’m old enough to know that sticks and stones can break my bones but words alone can never hurt me. But touching is in the category of sticks and stones, and potentially dangerous, a forewarning of worse possibly coming, which is why battery or touching is a crime. This fellows’ response to my resistance to his touching was to race back towards the rear of the bus where I was seated and standing over me six inches away shouting, “My daddy just died two days ago, and I’ll kill you, motherfucker, if you give me any trouble.”
Now it is important to make clear that I am generally cognizant of and sympathetic with blacks in their underdog position in society. Had your RTC contact format allowed for it, I would have included newspaper articles that make it clear that I have been a civil rights and peace activist all of my life. Indeed I was a primary speaker at a rally for Trayvon Martin in Las Vegas a few years back, videoed on YouTube. And one of the OP pieces that shows my liberal bent is on our mathematical sociopolitical website.
So I was able to reckon that this fellow, whatever his level of violence, considerable, was quite nuts at the moment, and maybe with understandable reason. And I gave out a sentence or two of sympathy to cool things down, though adding as I took out my cell phone, “If you touch me again, I’ll call 911 and have you locked up.” That was enough to get him to back off and return to the front of the bus next to the driver. But amazing is what he did next, turning his fury deflected from me to this old man white passenger sitting in the seat closest to the front of the bus and the bus driver, all of which was impossible for the driver to miss. The black fellow’s words to the old man were unmistakably racist, hateful and violent. But, as I said, who cares about words, especially in nut town Las Vegas (at least my estimate of your fair city that circumstances have forced me to be in again.) What was horrible to watch, though, was that this black guy started grabbing the old white man by his nose and his ear as he cursed him repeatedly.
Now my complaint to you isn’t about this unfortunate black fellow, whatever misery in life, present and past, drove him to his dangerous behavior – also dangerous for him given his shouting out in the middle of his ranting that he was on probation and didn’t “give a fuck” about what anybody might do to him in that regard. My complaint is rather about the driver, a coward it certainly seemed, or even something worse for not respecting the plight of the poor white bastard or the four or five onlooker passengers who were shouting to him at this point to get the guy off the bus. No effort was made to that end. All the driver had to do was stop the bus and tell the guy, “I’m not going anywhere until you get off the bus and if not, I’ll call in security. Nothing was done anywhere close to that. Let me emphasize that that the level of curses, threats and mayhem was such that the situation would have been apprised by any objective observe of this real life movie scene as potentially very dangerous.
Recognizing this, I jumped off at the next bus stop in the Casino area instead of proceeding directly to the UNLV Law Library via the Bonneville Transit Center and the #109 bus. By chance walking through the intersection of Fremont and Las Vegas Blvd. I encountered an RTC cop I quickly told the story to. He pulled out his phone and said he’d call the Transit Center to notify them of what happened and possibly do something about it if he made contact on time. I then cooled my heels with a cup of coffee in one of the casinos for an hour or so and got back on the bus to get to my originally intended destination. While back on the bus, I ran into another RTC cop who was also sympathetic and who directed me to a supervisor at the Transit Center to file a complaint.
I was hoping to hear and thought reasonable that the driver would have immediately told one of the handful of RTC cops you usually see at the Transit Center about the incident, which was clearly criminal, and minimally had the perpetrator, who was quite off his head and possibly on drugs, to cool it down. That was not the case. And the supervisor I spoke to, also black if that matters, bordered on curt in his reaction in telling me that he had heard about the incident and already reprimanded the driver, not interested in what happened to me including the death threat, as though there was really nothing to it and what was I making such a fuss about.
The rest of the note and the lack of any reply by the RTC transit system is irrelevant. What is relevant is the degree of hate between people that sits on the end of a hair trigger. Well, you say, big deal, who cares what could have happened. All that id happen was some nonfatal slapping of one guy in the face by another on the bus and a black driver doing nothing to prevent it or punish it. And maybe that’s cool, the real point being the enormous amount of random violence going about that is impossible to even guess at it from the endlessly smiling faces on TV who endlessly make out that life is nothing but a bowl of cherries, past, present and future. Ok, let’s try the next story, which was not incidental and at a distance from us. Well, again, it wound up in a letter written by Pete about it, this time sent to the Las Vegas PD, that I’ll let speak for itself.
Dear Las Vegas Metro Police,
My wife and I are on our way out of Las Vegas as I drop this note in a mail box, happy to be leaving. If my interpretation of the events I’ll relate is emotionally excessive, please excuse. But it is better to err on the side of caution. These are strange and dangerous times.
We have been down here for the last five weeks, not for gambling but interacting with academic types including Dr. Kathy Robins up at UNLV. We wound up staying at the Siegel’s Suites on Fremont and 15^{th}, not because I’m poor or like “slumming it” but because I’m severely asthmatic, doubly dangerous at age 71, and this Siegel’s place has tile floors rather than the rugs that every other hotel in Las Vegas has that I can be super sensitive to asthmatically.
The very nice woman who manages the place, Sharon, will corroborate any of the odd parts of what I’m saying concerning my asthma if you ask her. She went out of her way to set us up when we first got here with a room easy to breathe in. We ran into her and this place by chance a year or so back during an asthmatic episode on me that came out of the blue when I was staying at one of the casino hotels.
Off to the side of my having a PhD in Biophysics, I am also a lifelong political activist. If you check out these two OpEd pieces I wrote in years past, it will be clear that I am antiviolence and also pro civil rights and against police brutality against minorities. As to why I am giving you this background, the studio apt. at Siegel’s next to ours, Room 216, had a class of people in it I was not familiar with and that nobody would want to be. Lots of noise, swearing, loud music late at night and so on. If they weren’t using drugs regularly (though to be honest I never caught any smell of marijuana) they must have had a special instinct for whoops and hollers come the late hours.
I tolerated it because asthma at its worst feels little different than suffocating from waterboarding and this room was healthwise pain and stress free. Staying there I did not use my asthma medicine at all the entire five weeks we were in Las Vegas. As Sharon will tell you if you ask, the window in Room 217, our place, was missing, not the screen, just the glass window. The only room available in the place the day we got into town was this one, no window in it. But we took it because the fresh air flowing in constantly is positive for my condition. The point of my bringing it up is that the missing window had me hearing just about everything from next door when their door was open, which was often, and when they were outside, which was very often.
I should mention that the principal person in this room, possibly the leader of a gang (?), is a very large black guy always dressed almost in a uniform consisting of a totally white pullover and a distinctive kind of cap he wore even when the weather got warmish.
Anyway it was the night after the news broke out about the two police officers shot in Ferguson. These guys (some of them we heard often might just have been frequent visitors to the room rather than residents) went nuts over the shootings. There was no doubt about this from what they were shouting out to each other about feeling great over what happened. But this was also likely with a million other black guys of this type around the country, so nothing special about it. What got to me sharply, though, was a phrase that popped out unmistakably no less than three times during the evening  “gonna get one of these motherfuckers myself.”
Now I want to make it clear at this point that I heard nothing of any plans to do anything tangible. So there was a good chance that those words came out only to impress each other. I should make clear that I have as little prejudice towards blacks as any white in the country. I just don’t. I spoke at a Trayvon Martin rally right here in Las Vegas a few years back. In fact it was hosted on the business property of a black woman Metro Police detective, also a hairdresser, who said she was the daughterinlaw of the first big city black mayor in America, Carl Stokes of Cleveland. I think her name was Dorothy, Dorothy Stokes, but it was a while back and I’m not entirely sure of the first name. I’m sure she must remember me and how much I was on the side of oppressed blacks. I talked with her head to head for more than a few minutes and then spoke publically to all the blacks there about the need for a political process to get justice for Trayvon Martin.
That is to say that there is no way I’d exaggerate what I’m saying, and perhaps when you check things out with the black guy in Room 216, you might find out that he was, in fact, just a loud mouth punk with no real intentions. But to hear people talking about murder, whatever the level of real intention, sent real chills up my spine. Actually did. This is just a few days back. Talking it over with my wife I didn’t think I could live with myself if I saw on the evening news in a week or two that cops were murdered in Las Vegas in an ambush or something, and possibly because I said nothing. Whatever happens next, at least, with this note, my conscience is clear.
Sincerely,
What precipitated this letter in all honestly just wasn’t the hard facts of what we heard. Pete actually did think that it was all bluff and bravado mainly because he sensed the main guy in the story as a genuine punk, a faker, a faggot of the predatory kind, a bully and too much of a loser in life to ever try anything like killing a cop other than shout out words about it to his buddies. When we first moved into the place, the thug was right on the scene parading in front of our window and shouting out motherfucker this and motherfucker that to this friend up on our second floor tier or down to the street below. Was he doing it on purpose to get to us well groomed white people whom he thought he could screw over? Or was this just life in the ghetto that everyplace in Las Vegas not part of the tourist casino scene more or less is? Well, having more important things to do like try to save the world from nuclear annihilation and with hairy mathematics no less and also trying to convince small minded scientists up at UNLV of the correctness of our science, we opted for an intermediate disposition that while the jerk could have been trying to intentionally get on our nerves, it was better to pay him no attention and just stay at a nonresponding distance from him.
Then as fate would have it, avoiding came to an end by chance when Pete came back from UNLV walking through a narrow corridor at the same time this Porky Pig fellow was coming in the opposite direction. Pete gave a polite “pardon me” and moved to the side as they closed in while Porky addressing Pete as “sir” made little effort to do the same. Cute. This was a cute bastard. And that was followed up by Porky walking past our window not two minutes later, with a string of loud screeching motherfucker this and that. And at that point he began to get on Pete’s nerves, be worrisome, in his life, in our lives. The evening hours certified the problem as real as the music post 11PM was too loud to get to sleep by and Porky’s walking back and forth in front of our window repeatedly with the music blaring was as unsubtle a subtle threat as could be constructed by a cute bastard.
Now despite Pete being 71 and Porky somewhere around 31 and at least 100 pounds bigger and five or six inches taller, Pete put on his pants and opened the door intercepting Porky in his walk back from our place to his. While he didn’t say it with excessive politeness, for the situation didn’t call for a Miss Manners approach, Pete’s request/demand that Porky turn the music down wasn’t all that impolite. Porky thought otherwise.
Porky: “You disrespecting me talking to me like that!”
Pete: “You’re disrespecting me and my wife playi8ng the music like that.”
Porky: “I’ll fix your ass soon enough.”
Pete: “You make the next two plays and I’ll make the final play.”
And with that Pete shut the door. The next two hours were rough, at least from a noise and threat perspective. Whether they came from his room or from the neighborhood, every quickly there were four or five thuggish voices and the insults and threats were anything but subtle. I wasn’t sure what Pete’s “final play” would be and neither was Pete. The words just came out of his mouth that way, in a spontaneous way, for he was a spontaneous person, with a kind of like a talking animal personality. But you could never tell with Pete. Many years before that, we had a problem with a landlord who eventually brought a new tenant into the building who was extremely aggressive. Dickie Yadoo started parking his porch chair right out in front of our bathroom window, getting right into our life not unlike what Porky was doing. Dickie was muscular and looked very thuggish, so Pete just twisted in the wind for a couple of days all tightened up like a ball of string with a tangle of knots in it. Then Dickie brought in some relative and his 11 year old kid who went into the backyard and made our two year old still in diapers start crying. Pete went bananas and picked up a red magic marker and went up to Dickie’s 2^{nd} floor porch and wrote FAGGOT on the vinyl covering on the chair in big letters.
Sure enough Dickie Yadoo came down and they met on the porch, Pete rushing him and almost throwing him over the railing. By the time the fight ended, Dickie conceding, Pete had pretty much ripped his eyes out, for Dickie had two streams of blood rolling out of his eyes, something I never saw or heard of before. When the cops came, they reassured us that we didn’t have a problem with them. They told us that they just wanted to know who had whipped Dickie Yadoo, a known thug for hire in town, so bad that he’d even think of calling them.
So you never know what Pete might do. And neither did he. The next day was bad for him, he told me when he got home, because Porky was on his mind all day. Then just before he got on the bus to return home, he said he started worrying about me. And that got him to go a bit mad with anger. He said he started clenching his fists and biting down hard on his teeth and shaking uncontrollably on the bus like when he was a kid and angry. And the thought came through his mind that he could take Porky despite their age, weight and health differences, that he got determined to kill him if it came to it. By the time he came inside he looked not unlike that time with my brother, Don, out at the winery, like a murderer set on murdering somebody. But instead of doing the next step physically, he went for Porky’s throat by writing out that letter to the Las Vegas police. And that calmed him way down.
Now the point of this story, at least one that’s meaningful in the context of the larger problem the world has in terms of its near universal unhappiness and violence, is that when men are pushed far enough in the wrong direction, they don’t care about consequences. Pete would have thrown the punch, whatever the consequences, if that’s all that remained that could be done. He didn’t care about consequences. And you see that a lot in the world today if you care to look closely enough not to dress it away with psychobabble. Past some point angry people just don’t care about consequences, including those with nuclear weapons in their hands. Man has to rid the world of weapons before the weapons rid the world of man. Lousy fag bastard, hope the cops break every bone in your body.
MATHEMATICS TO BE CONTINUED