Mind, Consciousness, Body: Hypothetical and Mathematical Description of Mind and Consciousness Emerging from the Nervous System and Body

By Robert G. Howard

Good news at last; here are new and exact descriptions of the mind, consciousness, body, reality, time, nervous system taxonomy.

Feel the stimulation of your curiosity into the ancient questions about the mind-body duality as you plan your research and publication program.
How reality and three time dimensions emerge from the mind and consciousness.
Easy to understand mathematical definitions of otherwise ambiguous terms.
Each of fifty hypotheses will inspire you to publish more than your peers.
Introducing all the recommendations you will need to design an experiment or a research project which will propel you to the credible and prestigious forefront of your field.
Exact scientific answers to the problem of mind-consciousness-body are easily worth 4 hours of reading.
These solutions will kick off your numerous insightful publications.
The price of this book will yield massive funding for years of your research.

The math is reduced to the bare minimum and is explained in detail so the reader can use it is his own publications. The mathematics is treated as an abbreviated language which is translated into natural language.

• Language: English
• Publisher: iUniverse
• Release date: Aug 31, 2012
• ISBN: 9781475940305

Robert G. Howard

Robert Howard has researched computer software, naval machinery, high energy physics, and solar energy. As an engineer, he designed high rise renovations. He founded Sukhavati School in 1997. He earned a BSE in Mechanical Engineering, a Master of Administrative Science, a Ph D. in physics, and a state of mind in Zen Buddhist training.

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As a condition for reading this book, or experimenting with the ideas provided herein, you agree that you are solely responsible for the good or bad results that occur. If you do not agree then you are forbidden to read this book and you will give it to someone else. This book, the author and the publisher do not claim this is valuable advice. Each reader will use this book in a different way which cannot be anticipated. You are liable for the consequences, for the resulting damages, for the excellent experiences, for the bad feelings, and the good feelings. You are responsible for enjoying the excellent results and the distasteful results. You are solely the winner of all the wealth you create. You are solely the loser of any wealth you lose due the risk you take. Your life is separate from, and not connected in any way to the lives of the author and the publisher.

The author and the publisher are not liable for any good or bad consequences whether they are mental, emotional, financial, psychological, bodily, or medical. Each reader will create a different and un-knowable achievement or failure based on reading this book. Each reader will have different expectations and different understanding of the language suggested in this book.

Mind, Consciousness, Body: Hypothetical and Mathematical Description of Mind

and Consciousness Emerging

from the

Nervous System and Body

Robert G. Howard, Ph.D

iUniverse, Inc.

Bloomington

Mind, Consciousness, Body: Hypothetical and Mathematical Description of Mind and Consciousness Emerging from the

Nervous System and Body

Copyright © 2012 by Robert G. Howard, Ph.D.

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Contents

Disclaimer

Acknowledgement

Preface

Introduction

Author Note

Chapter 1      The Probability Laws of Parapsychology

References

Appendix 1.A      Terminology of Probabilities

Appendix 1. B      The changing view of the

scientific meaning of probability

Appendix 1. C      Example of the Power of

Probability Theory

Chapter 2      Synchronicity: A Probabilistic

Time Ordering of Events

References

Chapter 3      The Psychical Experience of Time Described in the Tibetan Book of the Dead: Mathematical Definitions and Practical Examples

References

Glossary

Chapter 4      The Geometry of Precognition

References

Appendix 4.A      Basic Concepts, Geometric Definitions,

and Nomenclature in One to Six Dimensional Levels of Existence

Appendix 4.B      The Equations of Coordinates of the Sense Line and the Sense Plane for Creating Animations and Experimental Models

Chapter 5      Time to Formulate the Laws

and Hypotheses of Psychic Science

References

Appendix 5      A Practical Examples of How We Use the

Second Dimension of Time, t5

Chapter 6      Discovering the Hypotheses

of Psychic Science

References

Appendix 6

Chapter 7      Discovering the Laws of Psychic Science

References

Chapter 8      Can an Ordinary Person Be

Trained to Use the Psychic Senses?

Chapter 9      The Ultimate Ground of

Human Experience

References

Chapter 10      If Paranormal Phenomena Are Information Transmitted by the Consciousness

and Received by the Psyche,

then What Are Consciousness and Psyche?

References

Chapter 11      The Mathematical Theory of

Consciousness, Mind, and Time

References

Appendix 11.A      Elementary applications of

the first theorem

Appendix 11.B      Shannon’s second theorem

is explicitly stated

Appendix 11.C      Example of the probability theory

within the third dimension of time, t6,

the probable connection between events

Chapter 12      Guidance for Experimental Research in Extra Sensory Perception Using the Theories of Diffusion, Probability, Electromagnetism, and Information Science

References

Chapter 13      Derivation of the Conservation Equation for Contents of Non-conscious Mind: the basis of Diffusion Mathematics Describing the Mind

References

Chapter 14      Description of Diffusion of Non-conscious Contents into Conscious Mind

References

Appendix 14      Terminology

Chapter 15      Diffusion of All Factors of Non-conscious Contents and Conscious Contents Based on Entropy Flow and Information Theory

References

Appendix 15. A      Consider the equations of motion of the diffusion processes.

Appendix 15. B      Coupled Diffusion in Non-isothermal Systems

Appendix 15. C      Thermal migration through a barrier between the non-conscious and the conscious minds

Appendix 15. D      Review of entropy production

in physical processes

Appendix 15. E      The Fundamental Hypothesis

of Entropy Generation

Chapter 16      The Remembering Process

References

Appendix 16      Terminology

Chapter 17      The Probability of Forgetting

Reference

Chapter 18      Evolution of Consciousness Levels, Non-consciousness, and Mind Levels

as Emergent States

References

Chapter 19      The Ethical Limits of Science and Materialism and the Moral Responsibility of Scientists

References

Acknowledgement

I acknowledge the patient assistance of Dr. Daniel R. Kelleher, M.D. who tolerated years of discussion. I thank him for the seminars which clarified and steered the formulation of the hypotheses, the direction of research. He gave valuable insight into the consciousness, mind and brain. He was the only person I found who was both interested in the subjects in this book and who also had the relevant knowledge and experience to discuss it.

I acknowledge the permission given by the Academy of Spirituality and Paranormal Studies for allowing the republication of Chapters 1 through 11 which were first published in the Journal of Spirituality and Paranormal Studies, P. O. Box 614, Bloomfield, CT, 06002-0614. http://www.aspsi.org.

Preface

This is the life above all others… in the contemplation of beauty absolute… of divine beauty not clogged by the pollutions… and vanities of human life… bringing into being and teaching true creations of virtue and not idols… . Beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauties, but realities for he has hold not of an image but of a reality… in the attainment of this end love is the best helper.

Plato, Symposium 1925. Francis Birrell, trans., London: Fortune Press.

Each individual human must break the addiction to material possessions. Groups of humans must help each other to stop concentrating on the archetype to war. Groups of humans must make a harmonious effort to stop meditating on the archetype to assist in organizing a totalitarian government. Each individual human must refuse to join the warrior archetype. Each human must stop being absorbed in the will to power archetype, in the conquering archetype, and in the destruction of life instinct. Each individual human must break the addiction to destroy Earth. This is the basic rule of conduct. It cannot be violated because of time, place, or purpose.

The human species is at the crossroad. Either it evolves into the harmony that is possible or it will devolve into extinction taking all life on Earth with it.

The concentration, the meditation, and the absorption in this phenomenon of rising into the harmony of the spiritual and the material world is termed; ‘psychic science’ or ‘parapsychology’ herein. The concepts are too complex to describe in natural language. However, the concepts become simple when expressed in mathematical terms.

Read the last chapter first. It exposes the unworthy pre-occupations of humans that are not fitting when compared to the magnificent gift of harmony which human kind can evolve into. Read it again after you have pondered the hypotheses and after you have made the effort to evolve into the ultimate state of collective human life. Discipline yourself to become a part of the new reality.

Introduction

I observe that technology and science, luxury and material possessions have crowded out the contact with the human spirit and the underlying reality. This book is an attempt to encourage harmony in part of the human kind. If groups use the hypotheses and math tools to rise to highly evolved pursuits of which only humans are capable of realizing, then they will live in harmony. Some few humans will use the hypotheses and suggestions of this book to enter a new reality. They will be free of the pain and suffering inflicted by humans upon all living beings and upon the Earth itself.

Much of the technology described herein is based on communication exclusive of the usual five senses. This extra sensory communication system takes place in the channels called the psychic field, the collective field and the whole life field. The hypotheses, the recommendations for verifying these fields, the math tools, and the examples of communication based on these fields are provided for those who are ready to rise into the higher state of being that humans are capable of.

The incorporation of the psychic field, the collective field and the whole life field into the life of the individual human and into groups of humans is the gateway into the new reality. The few who grasp the reality of the mind and consciousness emerging out of the material Earth, the material body, and the nervous system will begin by integrating the concepts in this book into their world view. They will perceive the fields. They will communicate through the fields so groups of humans can flow together on several levels. They will contribute their physical energy, their chi, and their vast human mental powers to the harmony of the spiritual world integrated into the material world.

This human group behavior is possible because humans can learn to relate to one another in harmony if they apply the hypotheses and the math tools given in this book. This harmony is an archetype which can diffuse into the conscious minds of large groups. This book lists the higher levels of consciousness and mind that humans are capable of achieving in several places such as Chapter 10 If Paranormal Phenomena Are Information Transmitted by the Consciousness and Received by the Psyche, then What Are Consciousness and Psyche?

Humans have the ability to apply material technology to enable a healthy life with leisure time. Many humans have leisure time to rise to higher states of mind and consciousness and to learn to receive the diffusion of the harmony archetype. Humans can use the same ability to concentrate on receiving the diffusion of communication with the psychic fields, to meditate on modes of living in harmony by communicating through the fields, and to become absorbed in the spiritual harmony with large groups. Humans can make the effort to activate this archetype.

Author Note

I persisted in the pursuit of understanding the mind, consciousness and brain for over 40 years. The effort began with the study and practice of the Yoga Aphorisms of Patanjali and Vedanta with Swami Prabhavananda at the Vedanta Society of Southern California. I pursued Zen Buddhism with Shimano Eido Roshi in the New York Zendo Shobo-ji of the Zen Studies Society, Nakagawa Soen Roshi at Dai Bosatsu Zendo in the Catskill Mountains of New York, Suzuki Roshi at Ryutaku-ji, a Rinzai Buddhist Monastery in Mishima, Shizuoka Prefecture, Japan, and Sasaki Joshu Roshi at Mount Baldy Zen Center in California.

For the last 40 years, I have made my home a monastery. The latest is Sukhavati School in Jersey City, New Jersey. Whomever I meet is my student. I do not represent myself as a Buddhist teacher.

Simultaneously, I have been a professional physicist, registered licensed mechanical engineer, and construction manager. With this intellectually demanding background, I have studied the mind, consciousness, body and time from outside the innumerable, fragmented, specialty sciences devoted to these subjects, so I am not obstructed by the dogmas of these disciplines. Nor am I tempted by the professional vanities and achievements which limit research and publication to acceptable subjects. The scientific literature, thousands of publications each year, tends to report incremental explorations into well worn topics. I am curious to discover the facts, laws, and mathematics of the mind, consciousness, body and time. I am neither pursuing promotion in the academic life nor the mental health science field nor the government grant industry. My compensation for this book is the thrill of discovery, the sincere desire to stimulate research in the subjects, providing the tools for humans to rise to higher levels of mind and consciousness by the removing the obstructions which cover the inner light.

The reference books and publications are not just to demonstrate that this book correleates with existing knowledge. The references represent a broad range of knowledge; broader than most readers will have. The quotations and ideas taken from the references are only a brief summation of ten to a thousand pages of exposition in each reference. Therefore, to understand the truth and applicability of this book, Mind, Consciousness, Body, will require reading part or all of each reference. Without such a depth of background education, the tools in this book will not inspire the reader to learn the mental communication skills, to rise to higher levels of mind and consciousness, and to rise into harmony with other humans and with the Earth. Please continue the research briefly summarized herein.

Robert G. Howard, Ph.D. is Chief Executive Officer of Sukhavati School.

Correspondence concerning this book should be addressed to

Robert G. Howard, CEO

Sukhavati School

242 Hancock Ave.

Jersey City, NJ. 07307 [e-mail]

Chapter 1

The Probability Laws of Parapsychology

Introduction

This chapter suggests applying mathematical tools to revive research in psychic science. An example is probability mathematics. Simple examples of probability math are given as well as a limited terminology of probabilities and the changing view of the scientific meaning of probability. Research is recommended into the probability of determining whether one perceives information without the usual five senses. Information is described as entropy associated with disorder. Elementary properties of entropy are given. The probability laws of quantum theory describe some neural processes. Three preliminary hypotheses are proposed about combined physical and psychical concepts based on probability. The first hypothesis is that chi is an element associated with each conscious content and each non-conscious content. The second hypothesis is that equilibrium states exist in the mind and brain. The third hypothesis is that contents of the non-conscious mind diffuse through the body and conscious mind. Entropy in the mind is defined. Entropy tends to increase as the duration of time increases due to non-equilibrium, cause and effect, probability, and chaos. Entropy associated with the mind is described mathematically.

Many scientists are biased to believe that cause yields effect and that a given event was originated from a well determined set of causes. A precise description of cause and effect relationships is required in order to get a solution to the math of differential equations and calculus. The development of these types of math required an exact knowledge of initial conditions and boundary conditions.

About 1760, a few Europeans began to formulate the math of probabilities. This math presumes that there are unknown relations between cause and effect which must be included in the formulation. The math recognizes that there are unpredictable events which must be included in the formulation of the math description. This led to the recognition that there are effects with unknown initial factors, unknown causes, or a limited set of known influences. The evolution of probability concepts is briefly discussed in Appendix 1. B.

Probability mathematics requires the admission that much of humans’ experience is mysterious and even unknowable. The premise of probability laws recognizes that not all causes and effects could be known. So there was the progression of consensus to believe in cause-effect then partially known cause partially known effect, then unknowable cause-unknowable effect. This suggests that there are epistemological processes of knowing or acquiring knowledge that humans do not know or allow themselves to ponder or to believe. In parapsychology research, toleration for the unknown is helpful.

Probability laws were suggested first by Richet and Edgeworth for use in psychical research to detect the effect of volition on extrasensory perception (ESP). ( Richet 1884) (Edgeworth 1885)

Psychic science grew into the more precise and rigorous science of parapsychology when the laws of probability were applied, for example by Rhine at Duke University (Pratt, Rhine, Smith, Stuart,

Greenwood 1966, 22ff). They presented the Mathematical Methods to prove that extrasensory phenomena are reproducible and experimentally controllable due to cause-effect connections and thus are not random events. Rhine was one of the first researchers to use probability mathematics to gain scientific attention to parapsychology. This book suggests many more tools in the mathematics of probabilities. Three preliminary hypotheses are proposed to connect the physical part of parapsychology to the psychical part through probability mathematics.

Rhine and others asked, What would lead to general scientific attention to parapsychology? They gave two answers, Easy application in daily use and a general theory that would harmonize psi communication with the known energetic system of the universe. (Pratt, Rhine, Smith, Stuart, Greenwood 1966, iv) Applications in daily use will be addressed in another chapter. This chapter and later chapters begin to define the general theory that will harmonize ESP communication with unknown psychic systems as Rhine and others requested.

This paper suggests many more tools in the mathematics of probabilities for giving credibility to this science. These heuristics may stimulate other researchers to employ them to analyze psychic data in more depth. This paper also introduces concepts that are the foundation for two more chapters that follow in another issue of this journal; papers on the diffusion of extra sensory data into the conscious psyche, and on the dependence of extra sensory perception on the third dimension of time. The third dimension of time connects realities through probabilities, not cause and effect.

This is the time to discover the mathematical relationships and laws that exist in nature which govern psychic science also called parapsychology. Physical laws were discovered thru observation, intuition and the desire to order nature. The laws of nature encourage falsifiable predictions. Some sciences, like psychic science, do not have well formulated laws. Various mathematical structures are offered below which explain, on general grounds, why observed psychic phenomena occur. They are building blocks for greater mental constructions later. The laws of probability predict quantitative relations between measurements few people would have anticipated. The study of the connection between the physical base of parapsychology and the psychic structure of nature is uncovering a hidden structure of which we humans are a part.

This chapter is addressed to non-scientists, assumes no scientific background but uses high school algebra. One objective is to improve scientific numeracy by teaching how to extend quantitative reasoning about the uses of probability in research into the mind and parapsychology.

The likely the unlikely, and the incomprehensible

The scientific mathematical concept is that the probability of the result, for example, of a dice throw is an objective property associated with dice. The procedure of determining the probabilities of outcomes is to throw the dice many times and note the frequency of each outcome. Then there is a table of outcomes, each assigned a probability of occurring. The table is considered the long view when one can observe the entire million dice throws in a single view. The information in the table is an objective property independent of whether we can predict the result of each individual throw. The significance of the objective property in the long view, is an average of a large number. See Chapter 4 The Geometry of Precognition for an explanation of the second dimension of time, labeled, t5.

The value of the property will be a value close to its probability. This is the conception of probability relevant to statistical problems arising in scientific research and other fields. This concept recognizes that events are connected by both cause and effect and also probabilities. (Bohm, 1961, 27)

A few of the most basic concepts in probability mathematics are briefly listed below to convince the Reader that this is tractable mathematics. See Appendix 1. A. Probability of an event is rated zero for no event and rated one for total probability which is the certainty of the event occurring. The concept of probability requires a repeatable experiment of observation with more than one possible outcome controlled by chance. Which means that before the fact, precisely which outcome will occur is neither known nor deducible. For this experiment, a probability of a given outcome is a numerical estimate, based on experience or theory, of the fractional occurrence of that outcome in a large number of trials. Probability laws do not yield good distributions with a small number of trials. Probabilistic laws will be applied in more penetrating ways below.

How are the probabilities of complicated outcomes deduced from those for elementary ones? This is answered by math rules.

Rule 1)

   The probabilities for all mutually exclusive outcomes add up to one.

   This sum is equal to the probability that an arbitrary element belonging to the set of mutually exclusive outcomes will occur.

Rule 2)

   The probability for two independent events both to occur is the product of the probabilities for the separate events.

Rule 3)

   Even when two events are not independent, the probability of both occurring is the probability of the first event times the probability of the second, subject to the condition that the first has occurred.

Probability of normality and large numbers

An experiment on psychic phenomena with random outcomes performed a large number of times yields a probable fact of nature. The fact is that only a very small number of probable outcomes associated with many trials have a probability of occurring. This mathematical phenomenon leads to near certainty from the chaos of uncertainty in many important cases in physics and in psychic phenomena

The probable binomial distribution

To show how easy it is to use the math tools, there follows more brief summaries of elementary concepts, and terminology, in probability mathematics. The binomial distribution considers an experiment with two outcomes, the desired outcome and not the desired outcome. The math can be expanded to any number of outcomes. To review the missing steps or to use the mathematics, see Reasoning about Luck: Probability and Its Uses in Physics or any elementary probability book. (Ambegaokar 1996, 23ff)

Consider an experiment which consists of N trials of a two outcome experiment (like tossing a six sided die). One outcome is when a six shows on the die. This is success with probability p=success. Another outcome is when a six does not show. This outcome is called a failure with probability (1-p)=failure. The shorthand expression is (N:r) meaning that there are N combinations taken r at a time. What is the probability, P(r) of r successes in N trials? It is based on three factors

1.   The number of ways in which the r successes can occur during the N trials, which is precisely the number of combinations of N things taken r at a time, for example, on a die marked with one to six dots, N=2, either six or not six. One=r since only one side shows at a time.

2.   The probability of r successes, P(r) when a six shows, is the probability of one success multiplied by itself r times

3.   The probability of (N-r) failures (when a six does not show), or equivalently, the probability of one failure multiplied by itself (N-r) times

P(r)=(N:r) pr (1-p)N-r   (1.1)

The collection of numbers P(r) is the probability distribution for

r=1, 2, . . ., N integers

If there are N combinations taken r at a time, this is written

(N:r)={N(N-1) . . . (N-r+1)}/{r(r-1) . . .1}=N!/{r!(N-r)!}   (1.2)

Equation (1.1) is called the binomial distribution. bi means there are two possible outcomes; for example, a die can show a six or not. See below, Figure 1.1 The Binomial and Normal Probability Distribution. Note that equation (1.1) gives the following.

(a.)   When N increases, the lopsided distribution of a plot of P(r) versus N, for small N, become symmetric and looks like a bell.

(b.)   As N increases, the distributions of a plot of P(r) versus N, begin to peak at the same fractional distance along the N axis of the plot. For a die with six sides, the maximum occurs when r=N/6.

(c.)   As N increases, there is a trend toward narrower peaks. This is remarkable: The number of outcomes for which there is an appreciable probability becomes a smaller fraction of all possible outcomes as the number of trials, N increases. So the equation gives a quantitative assessment of likelihood or certainty. Certainty eludes one when one deals with random events. The statistician must construct reasonably sure tests of hypotheses from a fraction of all the potentially available data.

In parapsychology, there is usually extremely large numbers of repetitions of an experiment so one does not test a fraction. One can use these simple rules and formulas of probabilities to show that a psychic reality is not random or is extremely unlikely based on cause and effect. (Ambegaokar 1996, 23ff)

The probable mean and the probable

standard deviation

A complicated random process, such as many trials of a simple random experiment has many possible outcomes. The collection of probabilities is a distribution. If a distribution is peculiar, bumps and wiggles, the only way of conveying the information it contains is to list all its entries one column of a table probabilities and one column of the number of successes. A way to describe the shape of the distribution of successes and number of trials P(r) comes next.

The definition of average is the mean abbreviated as ‘mu’ which can be written

Eqn1.wmf

   (1.3)

The mean square deviation=variance=sigma²

And sigma

Eqn2.wmf

   (1.4)

The connection between standard deviations for trial sizes of N+1 and N and 1 is sigma² N+1=sigma² N+sigma² 1

And the standard deviation is sigma N=√N sigma1

(Ambegaokar 1996, 30ff)

The probable normal distribution

The normal probability distribution is called the Gaussian distribution, a curve depending on a continuous variable, X and 2 numbers called mu and sigma. The curve is bell shaped. The area under it equals 1 unit because the sum of all probabilities of elements of the set of events being pondered is one. The peak is at X=mu and the standard deviation is sigma. A region of 2.6 standard deviations on either side of the mean contains 99.07% of the area under the normal curve. The point is that after a moderate number of trials of a two outcome random experiment, an approximation of the normal distribution emerges with the same mean and standard deviations as the N trial distribution. One standard deviation on either side of the mean contains approximately 68% of the probability. The probable outcomes are distributed in a small range which is more like a near—certainty than a wholly unknown state. Some outcomes are extremely unlikely to occur. The point made here is that the distribution of probabilities changes a wholly unknown process within the mind into one of relative certainty; certainty of the probability. This is demonstrated in a more convincing way in Figure 1.1 The Binomial and Normal Probability Distribution

BookCh1Fig11BinomialProbDist.jpg

Figure 1.1 The Binomial and Normal Probability Distribution

This is a common figure in probability mathematics. In this graph of the coin toss, the mean=mu=40.

Variance=sigma2=80(½)(1-(½))=20

Standard deviation=sigma=4.472. And 2.6 standard deviations on each side of the mean contain 99.07% of all heads observed. Therefore the terminology is: the area under the curve is the 99% level of confidence. And 2 standard deviations on each side of the mean contains 95.45% of the area under the curve. It is the 95 % level of confidence. If a coin were to be tossed 80 times and this were repeated many times , perhaps 100 times, then for any given set of 80, heads would be most probable to be observed 40 times. Some sets of 80, about 25 heads would be observed. In other sets of 80, about 56 heads would be observed. It is extremely improbable that the number of observed heads would be less than about 25 or more than 56.

Description of Entropy associated with disorder

The concept of entropy is essential to understanding communication within the nervous system, the consciousness, and the mind. Let the nervous system be a distribution of neurons and sensors. How to find a number to represent the randomness in a distribution? It is natural to associate decrease in order with the increase in the number of states of motion that are explored. Consider any math function f(II) that increases as the number of states, II, increases. If one follows the practice of information theory, take e=2.7… as the base of a natural logarithm. Then f(II)=ln II so the entropy is ln II. If the equally likely states are labeled with an index i then there are II equally likely states of motion so the normalized probability distribution is

pi=1/II for i=1, 2, 3… II

And the entropy of the collection of neurons or molecules or unconscious entities is ln II. The entropy of a subsystem which is either a molecule or neuron or unconscious content is the natural logarithm of the number of equally likely microstates corresponding to a given ‘macrostate.’ These three types of distributions cannot be mixed together so the explanation is limited to the neurons and sensing cells.

Now assign an entropy to a distribution with unequal entries. Because every state of motion, i is not equally likely. Let S(p1,p2,p3… pII) be the entropy of the distribution.

For the purpose of this explanation, one can simplify this to only two states.

And S(p1, p2)=-[p1 ln p1+p2 ln p2]

for two state molecule or subsystem.   (1.5)

Generalize this to II states.

Using Stirling formula the entropy

Per subsystem

S(p1, p2, p3… pII)=

—[ p1 ln p1+p2 ln p2+ . . . +pII ln pII]=ln II   (1.6)

If all the pi are assumed to be equal to one another and equal to 1/II, then

S(p1, p2 . . . pII)=

ln II=entropy of the system composed of II subsystems.

Properties of entropy

In equation (1.5) consider the math form, s(x)=ln (1/x) which for 0

What is the change in s when x is changed a little?

It is ln(x + dx)=ln[x(1+dx/x)]

= ln x+ln (1+dx/x)=ln x+dx/x+ . . . higher powers of dx   (1.7)

So ds=s(x+dx)-s(x)=-(x+dx) ln(x+dx)-x ln x=

—dx(ln x+1)+ . . . higher powers of dx   (1.8)

The maximum is at ln x=—1 or x=1/e so x=0.367. And s(e-1)=e(-1)

Equation (1.5) is the form of a two state system with probabilities x and 1-x with entropy s(x, 1-x)=s(x)+s(1-x)

Some properties of this limited s(x) are when x=1 or x=0 then s(0,1)=s(1,0)=0; and there is no mixing; there is either one or the other state. Between zero and one entropy rises to the maximum at x=1-x = ½;

This means there is perfect mixing so entropy is ln 2. In general,

(1) for complete mixing between II states, with all pn=1/II, II=2 and the entropy is ln II

(2) entropy=sum of non-negative states, is never negative

(3) When no mixing, when the distribution corresponds to a certainty, that is when all but one of the p=0 and the remaining p=1, the entropy is zero because it is a sum of II-1 terms s(0), each of them zero and a single s(1), also zero.

These are the rules and the mathematical description of entropy and disorder.

This is a simple exposition which can be expanded to study the entire nervous system communication functions. The mathematical theory of information is quantified in terms of entropy. The generation of entropy is part of the description of the diffusion of the contents of the non-conscious mind in Chapter 15 Diffusion of All Factors of Non-conscious Contents and Conscious Contents Based on Entropy Flow and Information Theory.

Maximizing entropy: minimizing order

The following discussion is modeled after the statistical gas theory. One can seek a probability distribution which is a set of numbers 0

Let the gas analogy be the starting point of research. Consider that the neurons and sensing cells or the retained entities in the unconscious mind are a large number of weakly interacting subsystems. Even when the entire system is in equilibrium each entity sub-system is fluctuating by a negligible amount, but the average of the neurons and sensing cells, or total number of unconscious entities is constant over some short duration of time. The assumption is that the system is as mixed as possible. Consider that this model works for a neural matrix. A given sub-system may be changing. Each neuron, or unconscious entity, is a closed subsystem. Assume that it has a theoretical entropy. Under sedation or some types of skillful meditation, the entire neural matrix is a closed system. Assume that theclosed neural matirx has a theoretically calculable entropy based on conservation of energy. Assume there is an entropy even though it is not practical to calculate it based on continuity of physical and psychic entities in a defined volume of brain and mind.

Define chi as the non-physical property that causes the mind to think and the consciousness to communicate. It is often called prana, vitality or elan vital. Define non-conscious contents as all the information systems in the body that are not accessible by the conscious mind. There may be a conservation of chi or non-conscious contents. Conservation will be reported in detail in Chapters below.

The mind, consciousness, the neural system, the nervous system as a whole, and the non-conscious entities are systems with different applicable sets of mathematics.

The restriction of conservation of mass and conservation of energy within the system means that the duration of time must be short enough for these assumptions to be true. This is a severe restriction of the validity of this consideration and the following exposition. Although time is not in the calculation, it enters at the assumption underlying the method. It is assumed that only those states of diffusion which can be reached in the duration of observation are to be included. Consider the example of helium gas in equilibrium in a balloon. Only position vectors within the balloon are allowed to be pondered as the object which is a specific set of atoms. If the equilibrium is question is pondered for several days most of the gas will have diffused through the balloon’s surface leaving a drooping balloon so the math description and equilibrium could not be claimed for the escaped gas. Thus, unstable systems like a disordered non-conscious mind, are not described by the following equations.

Maximum entropy in the mind

Temporarily ignore conservation of physical energy and conservation of chi. Ignoring conservation of