Systematic Political Science


The YHWH Axiom and the Effect of (Thermodynamic) Information Entropy
on Counter-Intuitive Processes such as Randomness etc. 

Dallas F. Bell, Jr. 

1. The YHWH Axiom

The works of Archimedes of Syracuse (c. 287 BC--212 BC) were made available to a wide audience based largely on the commentaries written by Eutocius in the 6th century.  Eudoxus of Cnidus (c. 410 to 408 BC--355 to 347 BC) wrote a mathematical statement used by Archimedes that has come to be known as the Archimedes axiom.  It can be stated as follows. 

Let x be any real number.  Then there exists a natural number n such that n > x

Since the statement is a consequence of the completeness of real numbers, it may be called an Archimedean property instead of an axiom.  The axiom concept from Archimedes pointed out that if there are two different sized lines the shorter line could be laid end to end a finite number of times to create a distance that exceeds the longer line.  This property has no non-trivial infinitesimals (i.e. no infinitely large or infinitely small elements.) 

In decision making, if a utility for general understanding is to be assigned to all (earthly) consequences, the Archimedean axiom that there is no (earthly) consequence that is infinitely worse than any other could be required. Of course, there are eternal consequences which can be construed as infinitely worse or infinitely better especially regarding the decision of eternal salvation. 

At times it seems that two people with the same theological beliefs behave differently.  Either they are self-deceived about their theology or they are dishonest about their true beliefs.  People can claim to be whatever they choose.  Even if a person is honest they are finite and can fail to behave as they desire due to ignorance or temporarily yielding to temptation.  To avoid fuzzy or relativist analysis of behavior, behavior should be compared to compliance with or noncompliance with Natural Law of Freewill (NLF).  That can produce a result that can be objectively compared to other behavior when comparisons are in order, such as for employment considerations etc. 

If a Christian church denomination has a convention and some of its members support a government action and some members do not support that government action, their opposing views can be compared to NLF.  That does not mean that all Christians inherently have different views but that there are different levels of abilities and experience regarding implementing NLF. 

The omniscient bracket of game theory leads to Yahweh or YHWH and the subsequent axiom.  A YHWH axiom could be stated as follows: 

Let x be any behavior.  Then there exists a Natural Law of Freewill, NLF, such that

NLF > x

A simplified proof could be thought of as either of the two following statements. 

(i)  Given any behavioral choice, there always is a controlling NLF.

(ii)  Given any NLF, there always is a behavioral choice that is a subset of that NLF. 

It is often logically concluded that (i) and (ii) are intuitive. 

2. Counter-Intuitive Processes

Intuition is considered to be direct knowledge that is seemingly without preliminary cognition or thinking.  Most people do not want to be murdered or stolen from and intuitively accept those two NLF.  Counter-intuitiveness is something real or perceived that is counter to beliefs, derived from experience, which may be either true or false as determined by proofs.  An example of a truth is the belief that the earth orbits the sun when it was previously believed that the sun orbited the earth.  An example of a falsehood is the belief that there is no God which is counter-intuitive to all evidence that proves the necessity of the existence of the God of the first cause of all effects--YHWH. 

Those examples demonstrate the subjective nature of intuition and limits what is referred to as counter-intuitiveness because there are different chosen beliefs.  The recent writings of noted Darwinian evolutionists support the murdering of babies for research and decry the stupidity of the notion of human dignity contrary to NLF.  In June 2008, the U.S. Supreme Court overruled state laws that allowed for the death penalty to be justly included for consideration in cases for child rapists.  It is epistemologically rational, for Darwinian evolutionist theology, to reason that if children can be legally murdered then raping them should not carry the possibility of being punished by death.  

Despite not having any Divine authority or standard, the former atheist, Antony Flew (now a theist) chose to value some NLF he called norms while other atheists choose to value a specific NLF such as peace.  (The value of peace was confirmed to be held by Eric Schechter in an email exchange between Schechter and Dallas F. Bell Jr. in June, 2008.) 

The truth, includes philosophy and science, will always be generally opposed by those that reject truth and by necessity embrace untruth expressed in vain philosophy and so-called science within the arena of information. 

3. (Thermodynamic) Information Entropy

Claude Shannon (1916-2001) is considered to be the father of information theory.  Information theory qualifies information in the academic branches of mathematics and engineering with applications in statistics, linguistics, cryptography, neurobiology and computing etc.   

Shannon entropy or information entropy is a key measure of information for information theory.  Information is defined as a measure of the amount of knowledge and not the knowledge itself.  The amount of information does not reveal anything about itself, its location or its form.  This idea could be juxtaposed with bundle theory where something is described as consisting of its properties. 

Entropy is defined as the information one person does not have for a situation which may or may not reflect the information another person does not have for that situation.  Thus, information is subjective even where entropy is small as between two educated physicists observing the same situation.  Information is measured in bits.  With large numbers, Joules per degree Kelvin may be used.  In that instance of entropy, when using the chain rule, entropy is not increased by additional input.  In mutual information, entropy is concave and mutual information can be both concave and convex. 

On the other hand, thermodynamic information entropy defines information and entropy differently than does information theory.  Information is the object that holds the information and is not the nonphysical information itself.  For example, a book, a computer, a piece of art, a musical composition, DNA/RNA in biochemistry etc.  Entropy is the amount of physical degrading of the object of information measured in bits or Joules. Entropy rates vary due to the potential of the object and its environment.  Entropy or loss to the object will occur unless there is an infusion from outside the object's system. 

An object of information, such as a computer program, cannot become more complex than its potential and in time will degrade beyond the point of providing useful information unless it is infused from an outside source.  To say otherwise is to not just promote the notion of self-perpetuation but to imply a form of self-creation.  Those two ideas are provably false and are counter-intuitive to most people. 

Unfortunately, there are highly capable atheists like Stephen Wolfram who reject their intuition.  Wolfram's recent writings and book of 1,000 plus pages explains how he used a computer to run his Cellular Automata (CA) program in an attempt to disprove the existence of God by serving to disprove laws of thermodynamics.  He had to first ignore that he himself existed from DNA/RNA biochemistry which is subject to entropy to a future certain date of physical death.  Second, Wolfram had to reject the reality that the computer was made by other humans and will eventually deteriorate.  Third, he had to reject that his finite CA program only achieved the potential of what he himself had dictated by his input.   

An observer could deduce that a higher energy or intelligent designer created Wolfram's DNA/RNA, other humans intelligently created his computer, and Wolfram intelligently created his program.  From Wolfram to his program, entropy is shown by energy being lost.  An intelligent design of overall creation complexity could be condensed into the following three logical steps. 

  1. The universe has both order and complexity or ordered complexity.
  2. Ordered complexity could not be without a designer.
  3. A designer created the universe.

All sane people agree with (1), and (3) cannot be disproved.  Wolfram inadvertently proved (2) to be true and the reality of freewill contrary to section 12.7 of his book.

(In an email exchange between Catherine Boucher, at Wolfram research, and Dallas F. Bell Jr. during June, 2008, that section was recommended concerning the subject of freewill.)  Wolfram wrote that he believed that freewill is an illusion because all the controlling details are not known.  This means that his CA program behaved only as he programmed it and could not have witnessed complexity coming from non complexity without his input.  If he had incorrectly argued for freewill, his CA program would then have had to have self-analysis or consciousness as humans with freewill have within the bounds of NLF.  Either choice proved that there was a designer of his CA program's ordered complexity as perceived by him. 

Thereby, efforts in information entropy, such as Wolfram's, end up demonstrating the reality of truth and NLF.  They also provide a vehicle to address related effects that are often described with names like randomness. 

4. Randomness etc.

Probability is the study of coincidence, arbitrariness and chance or randomness.  Coincidence is the alignment of two or more seemingly unrelated events that are perceived as having a non causal origin.  The perceiver(s) of that occurrence usually places more importance on that event than those not directly affected by it.  Arbitrariness (Latin from arbitrarius meaning someone that must judge a matter) is considered to be choices made without underlying logic.  Chance or randomness is used to describe a seeming lack of order from cause to effect.  (That is a view of randomness held by Louis Anthony Cox Jr. expressed in an email exchange with Dallas F. Bell Jr. in November, 2007.

In a Newtonian sense, there are no probabilities if all the variables are known.  If all the numerous conditions are known for a person shooting an arrow with a bow, then it would be perfectly obvious where the arrow would strike.  The notion of randomness proposes that there is a state where no law exists and where everything is possible, such as an apple becoming an airplane. 

Randomness describes lawless variance in change.  A randomness proof would need to consider both the physical realm (e.g. electrons etc.) and the nonphysical realm (e.g. numbers etc.)  Likewise, disproving randomness would need to address those same issues.  Disproving randomness could be as follows: 

*Observe the variables of a situation:

-Something in state A changed to state B.

*Observe the known laws:

-Something cannot not be something.  It is, if not the sum of its parts.

-Cause is necessary for state A to change to state B.

-The cause is not without causal parameters.

-The change is entropic unless inputted by energy from outside the process/system.

*Then, something is caused to change from state A to state B within causal parameters.  So whether all variables are known or not, true randomness cannot occur on any known level.  That proof of no randomness would be applied to quantum phenomena and other unknowns. 

The Axiom of Choice (AC) was formally created around 1904 by Ernst Zermelo.  It described the mechanism of arbitrary choice.  A simple AC form may be the choice from a group of nonempty sets.  A choice can be made from a member of each set in the group.  A choice function exists for each set even if there are no rules.  If a choice is to pick an apple from each set of a group of baskets full of the same type of red apples, picking the apple on the top of each basket could require using AC.  However, if the baskets contain only one green apple and only one red apple each, an algorithm of always choosing the green apple first could be used. 

The AC could be applied to infinite untruth such as randomness where untruth is defined as the group of sets of all possibilities that are not truth.  It would not be applied for truth such as eternal salvation where formal logic could be applied. 

5. Conclusion

The YHWH axiom demonstrates the intuitive link between NLF and behavior.  Information entropy in thermodynamics is shown to be as useful a definition as is found in information theory.  The disproval of randomness shows how its counter-intuitiveness is indeed false.  The choice is then axiomatic of whether to accept, by freewill, the truth of the God of the first cause of all effects or by necessity reject Him and suffer the present and eternal consequences. 

---------------ALL RIGHTS RESERVED © 2008 DALLAS F. BELL, JR.---------------