NEW APPROACH PART EIGHTEEN

 

WHAT IS THE TRUTH?

© Copyright 2022, Edward R. Close, PhD

Introduction

I have a friend who is a certified member of more than 30 high-IQ societies, with very high-level entry requirements. Even most of the members of MENSA would not be able to qualify for membership in them. No one would doubt that my friend is an exceptionally gifted person. But he is not very happy. Why would he feel the need to join so many high-IQ societies? What is he trying to prove? What should he do with his life? Is his life worth living? These are serious questions that I will not try to discuss further in a public forum because I respect my friend’s privacy, and because the academic subject of intelligence is only peripherally related to the subject I want to discuss in this post. I do, however, want to make a point that I think is relevant:

A person’s intelligence quotient (IQ) is nothing more than a measure of his or her relative intellectual potential. That number alone is not very important. What the individual does with that potential IS important.

When I was a junior in High School in Houston Missouri, my classmates, and I were given a battery of aptitude tests and the standard Stanford-Benet IQ test. Most of us didn’t take the tests very seriously. They were administered by Mrs. Roberts, the school’s guidance counselor, for the purpose of helping us know what we might be able to do with our lives. We were shown our scores on the aptitude tests but were not told our IQ scores - for obvious reasons. The guidance counselor, who also taught English, knew that I was interested in science and mathematics, and she also knew that I had very little interest in other subjects. What Mrs. Roberts said during my private counselling session, changed my life forever. She said: “You scored in the 99 percentiles on all of the aptitude tests, and your IQ is good enough that you should be successful in science, engineering, or anything you might choose to do.”

Students were being told at that time that people going into professional careers should have IQs in the 120 to 125 range. So, I assumed that I had probably scored somewhere in that range. I was curious about how I had done on the IQ test, but when I asked, she said: “Your score on the IQ test is unimportant. It’s just a measure of potential. What IS important, is what you do with that potential.” She paused to let me think about what she had said, and then continued: “If you become the greatest scientist who ever lived, but can’t communicate what you learn to others, it is meaningless!" I knew that what Mrs. Roberts had said was true, and from that moment on, I began to take my education more seriously.

Looking back, I realize that none of us lives in a vacuum. While success in life depends primarily on our own thinking and actions, what we have, the raw material of mental resources that we have to deal with life, is what God and our ancestors gave us. I know that some of my ancestors, including a great grandfather on one side, and a great uncle on the other, were well-educated professionals, but beyond that, I know very little about them. My ancestors immigrated from Europe, England, Scotland, and Ireland to America from about 1720 to 1850 and eventually to the Midwest. My grandparents on both sides came to the St. François Mountains before Missouri was a state. It was still part of the Louisiana Territory on the frontier of a new nation. They came here seeking the freedom to live their lives as they saw fit.

The two small villages, where my parents were born, about 20 miles apart, were basically mining camps, several days’ journey by horse and wagon south of St. Louis. Life was hard, and they worked hard to help support their families. Education beyond the eighth grade was not an option for either of my parents. My mother dreamed of being a dancer, but she never had the opportunity to fulfill that dream. Because she was one of the eldest in a family of ten children, she had to help care for her younger siblings, and she married my father at the age of 19 and became a mother and a housewife. My father had some natural skills and the ability to build things, so he became a carpenter, later a small business owner, and after World War II, a police officer.

I was born in the relatively peaceful time period between World War I and World War II. When I began talking at the age of nine months, my mother realized that I had a better than average ability to learn, so she began teaching me to read and write and basic math before I was old enough to go to school. School was easy for me, and my parents encouraged me, telling me that I could be anything I wanted to be. My maternal grandmother and paternal grandfather were of German descent, and my best friend was from a family of German descent, so I learned German at an early age, and because I found languages interesting, I started learning Spanish and French at the age of eleven or twelve. Algebra and geometry were easy for me, and I discovered Einstein’s special theory of relativity the summer I was fourteen. It opened a fascinating new world for me, and I decided that I wanted to be a physicist.

I was blessed to have the ancestors and parents I had, to be born when and where I was, and to grow up close to nature in peaceful times, and finally, to have the opportunity to apply myself in ways that might benefit my family and maybe even humanity in general. When the tests indicated that I had the potential to succeed at whatever I wanted to do, it simply verified what my parents had been telling me from day one: I could be whatever I chose to be. Unlike my friend who is obsessed with IQ, I knew that IQ was not nearly as important as motivation, so I applied myself in order to try to achieve whatever my potential might be. I never knew or cared what my score was on that high school IQ test, until I was 72 years old – technically a senior citizen. Why and how I came to know my IQ is not important, but I learned that I had scored above 165 on that high school test. Later, my scores on the graduate record exam, the Army General Classification Test (AGCT), actuarial systems analysis tests, and a High-IQ society test, taken when I was 25, 28, 50, and 72, respectively, indicated that my IQ was higher than 165. But the rarity of IQ scores above 165 makes assigning an exact IQ number meaningless, and as Mrs. Roberts the guidance counselor said, what my IQ may or may not be, is really unimportant. What I do with whatever potential I may have, is what’s important, and that brings us back to TDVP.

My only reason for revealing the fact that I have an IQ in the same range as people like Einstein, Planck, Bohr, Pauli, and Gödel, scientists who have discovered some of the deepest secrets of reality, is to lend credibility to the claim that TDVP is the long-awaited paradigm of the future that expands science to include non-physical reality. Dr. Vernon Neppe and I have certainly made this claim - because we believe it - and it has also been made in writing by others too, namely some of the 200-plus scientists world-wide who have reviewed our work. Those whose statements lauding TDVP are quoted in many of our papers and books, include some very accomplished individuals with PhDs in physics, geophysics, astrophysics, and other sciences.

Having an exceptionally high IQ does not necessarily give one an advantage in life or make one happier than most. In fact, a person with an IQ above 175, lacking other positive human qualities like emotional maturity and social skills, may become a very unhappy, lonely, antisocial individual who will never fit into normal human society. In this regard, IQ is not unlike other relative measures of human existence and abilities. Physical size is a good example. In America, the average height of adult women is 5 feet 4 inches (2.63 meters), and the average height of men is 5 feet 9 inches (1.75 meters). A few inches more in either case can be an advantage. But the advantage goes away when it becomes extreme. Excessive height becomes a negative for women quicker than it does for men. A woman who is 6 feet to 6 feet 2 or 3 inches tall may be good at sports, but the extra height will be a social disadvantage. A man who is 6 to 7 feet tall may be good at sports, and still be considered normal otherwise. But a woman who is 7 feet tall or more, and a man who is 8 feet tall or more is likely to be disadvantaged in many ways.

In IQ scores, anyone with a score within one standard deviation (15 points) on either side of the average score of 100, which includes 68% of the population, should not have much trouble fitting in. Those in the 115 to 130 range will, like good athletes, be capable of being successful easily, and those in the 130 to 145 range (the MENSA entry level is 132) should be able to excel and still fit into society quite well. This would be comparable to 6-to-7-foot athletes. Those with scores from 145 to 160 should be exceptional at whatever they do, like the top echelon of athletes who often become celebrities, but just as often have problems fitting into society; and those with IQs much above that will, like people who are 9 or 10 feet tall, not fit in anywhere very well. All they can hope to do is to use their special gift in some marginally beneficial way.

What does IQ have to do with truth? Not nearly as much as people with above average IQs like to think it does. Successful people, especially those in the 130 to 160 IQ range, because of their exceptional ability to reason, often believe that whatever they reason to be true, is true. More often than not, however, they are wrong. Some highly intelligent people, despite their potential to do good, actually do great harm. Because they know they are very intelligent, they convince themselves that they are superior to everyone else and believe that that gives them the right to tell everyone else what to do. There are many historical examples, pharaohs, kings, tyrants, and dictators, people who essentially believe that they can replace God. Unfortunately, as the world population increases, there are more of these psychopaths.

The reason that people sometimes outsmart themselves in this way, is because they fail to examine their own a priori assumptions. That is to say, their own brilliance blinds them to the fact that the logical system they believe in is based on some assumptions that have been accepted without proof because they cannot be proved using the logical system within which they arise. This self-referential fact about all consistent logical systems was proved by the brilliant mathematician Kurt Gödel in 1933. The logic proving this fact is called the incompleteness theorem. (Note that a mathematical theorem is not a theory. It is a hypothesis that has been proved.)

Before we go on to discuss what truth is, I want to be sure that you get three very specific things from this introduction: 1) You shouldn’t accept what any human being says as truth on face value, because conclusions produced by even the most intelligent person who ever lived, no matter how brilliant and no matter how logically rigorous the reasoning may be, may still be wrong if even one assumption behind the system of logic being used is wrong. 2) Be aware that the most impeccable logical reasoning, perfectly applied, may not be able to prove the truth or falsity of a given statement, in the context of the logical system within which it is stated, however  true or false it may sound. 3) These two pitfalls in the search for truth can only be avoided by in-depth critical examination of basic assumptions. In the first case, wrong assumptions must be identified based on direct evidence, and removed or replaced. In the second case, basic assumptions may have to be expanded or augmented, based on direct evidence, before the statement can be proved to be true or false.

Practical Application of TDVP in Today’s Reality

We have a very serious situation in the world today, with several groups of intelligent people espousing conflicting beliefs about what the truth is. These conflicting beliefs have already caused a lot of violence and will probably lead to more violence if the truth isn’t revealed and recognized. Is there a way to determine what the truth really is? Yes, there is, and it involves the critical examination of basic assumptions as discussed above, followed by comparison of the conflicting belief systems with existing truth, and correction.

In the last post, we answered the first of the three questions posed at the end of post number sixteen. We uncovered the truth about who you are. You are not a name, you are not what you do, and you are not a physical body. You are a quantized bit of pure consciousness. This totally refutes the basis of identity politics so prevalent today. As pure consciousness, you are immortal and forever part of Primary Consciousness, the reality behind all things. The reality that is Primary Consciousness has been detected by physical science as the Zero-Point field within which all objects in the physical universe exist as temporary continuity perturbations.

Understanding these truths brings about the realization that violence with evil intent harms everyone, including the perpetrator, and ultimately, it is the perpetrator who will pay the most. This raises the concepts of good and evil, which also have to be related to truth and falsehood, existence, and non-existence. while exploring these relationships, I will address the remaining two question from post number sixteen. Questions two and three were: 2) How can you recognize what can help or hinder your physical, mental, and spiritual progress? And 3) how can you find the path leading to the ultimate goal? To answer number two, we begin by examining the basic assumptions behind the concepts of truth and reality.

Truth and Reality

Historically, mathematicians and logicians have chosen to separate truth from existence in the basic assumptions of logic and the primitive equations of mathematics, in order to make the proofs they produce as general as possible, so that resulting theorems and syllogisms can describe the universal principles and laws of the natural sciences. This approach served us very well until Max Planck discovered that physical reality is quantized. Recall that in earlier posts, we saw that in order to develop a consistent system of quantized mathematical logic, reality had to be defined as everything that exists. Thus, in the quantum calculus of TDVP, truth is equivalent to existence, and existence is reality, but in the mathematics of contemporary mainstream science, this equivalence is not recognized except in special cases where the equivalence is obvious.

An in-depth examination of basic assumptions has revealed a paradox in contemporary science, providing us with a basis for making some progress. Revising this basic assumption of reason by restoring the equality of reality and truth, as required for a logically consistent quantum calculus, resolves the paradox, and the process of infinite descent leads to the discovery that the non-physical aspect of reality that we call gimmel, and the discovery that we exist as quantized non-physical consciousness are two aspects of the same thing. That thing, which I am calling Primary Consciousness, is the fabric of the universe and the only reality. With the truth that the existence of a stable physical universe is only made possible by the existence of quanta of non-physical reality in atomic structure as well as in consciousness, we can proceed in future posts, to answer questions two and three.

ERC – April 2, 2022

NEW APPROACH PART SEVENTEEN: WHO WE REALLY ARE

SEVENTEEN: DETERMINING WHO WE REALLY ARE

© Copyright 2022, Edward R. Close, PhD

“That whereof we cannot speak, thereof we must remain silent.” - Ludwig Wittgenstein

This is one of my favorite quotes from Wittgenstein’s Tractatus. There certainly are a variety of reasons why there are many things of which one cannot speak, but that doesn’t mean that those things are not important. On the contrary, often they are very important. And I think it is appropriate to begin this post by paraphrasing Wittgenstein’s famous quote in this way:

Things of which we cannot speak, because words are completely  inadequate, thereof we must remain silent. But, conscious of their truth, we must point to their existence with the best analogy we can muster.

I think the reader will understand why and how this paraphrase is appropriate in the context of this post.

A prerequisite for solving the problems of spiritual awakening mentioned in the last post is knowing exactly who you are. “Who are you?” is not a trivial question in the context of these discussions, and answering it properly is not a trivial task. Most people, when asked who they are, provide an answer like “I am a teacher, a writer, a computer programmer, a sales person, a mother, a senior citizen, … whatever that person’s current occupation or role in this life may be. This kind of answer is encouraged more than ever in today’s toxic culture of “identity politics”, where those who want to control you think they can do so by demanding that you conform to the standards of a specific group that they define so that they can either control you, or in some way eliminate you. This kind of shallow identification is not what we are talking about here.

Determining who you really are is done by a consciousness focusing process that I have referred to in earlier posts as “Self-Inquiry”. The logic of Self-Inquiry is a process of sequential elimination of non-essential identifications, allowing you to move deeper and deeper into the heart of consciousness, until only one thing is left: the essence of your existence. The process is analogous to the mathematical process of infinite descent, a method of proof developed by the French mathematician Pierre de Fermat. It shouldn’t be too surprising that the process of Self-Inquiry is analogous to the mathematical process of the quantum calculus of transcendental physics and TDVP, that led to the discovery of gimmel, because the nature of the end result in both cases, is the same: Discovery of the non-physical essence of reality.

In the quantum calculus of dimensional distinctions, expressions describing quantum phenomena, are nine-dimensional Diophantine equations (equations whose real-world solutions are quantal). They are called Diophantine equations in honor of Diophantus of Alexandria, who introduced the concept around 255 AD. The method of infinite descent was developed in modern times by Pierre de Fermat about 1635 for the purpose of identifying solvable Diophantine equations. And the application of the method to analyze the combination of quarks to form protons resulted in the discovery of the non-physical essence of reality present in every stable atom was first accomplished by this author in 2011 and amplified in co-authored works with Dr. V.M. Neppe during the next few years. In this post, we shall see that application of the method of infinite descent in the form of Self-Inquiry results in the discovery of the non-physical essence of consciousness.

Diophantus and Fermat are just two of many evolved souls who reincarnated from past periods of higher mental virtue from time to time, specifically to help humanity survive the dark ages of materialism. As we go on in this series of posts, we will see how all things are intimately and ultimately connected by the all-encompassing field of the non-physical essence of reality, revealed in the logical process of infinite descent, the analytical method of the last apex of conscious reality in the cycles of solar time, in 12,501 BC. More about this later. For now, let’s get back to the process of determining who we really are.

Let’s suppose that you are a carpenter. Have you always been a carpenter? No. After you retire from a lifetime of building things, are you still a carpenter? No. The point is that the word carpenter is inadequate to describe the real you. You existed before you were a carpenter, and you still exist when you are no longer a carpenter. The word “carpenter” is not you, it’s only a useful role you play for a certain period of time. Replace the descriptor carpenter with butcher, baker, or candlestick maker, - anything – and the result is the same: remove the name and the activity, and you still exist.

Now let’s move a little deeper. Each of us identifies intimately with our own physical body and its relationship to a certain line of souls reaching all the way back into the completely forgotten past. Your body consists of a combination of complex interacting semi-autonomous organic structures, formed and stabilized by gimmel in the same way that Primary Consciousness forms and stabilizes all atomic structures including organic lifeforms. At this point in time, most people believe that they are the physical body, no more and no less. But is this true, or just a belief arising from life-long identification, similar to the identification with a profession or any other group of sentient beings, like a profession or a family?

There is a growing body of empirical evidence strongly suggesting that individualized consciousness survives the physical destruction of the body it inhabits. In fact, there is a wealth of very convincing observations and data, from both scientific experiment and personal experience that I have gathered and written about, proving that individualized consciousness is immortal, existing before physical birth and after the death of the physical body. However, I am not going to take up valuable time and space here repeating details of that evidence because most of you who are likely to read this, already know about this evidence. For further information on this subject, see the works of Dr. Ian Stevenson of the University of Virginia, Dr. Vernon Neppe of the Pacific Neuropsychiatric Institute, Dr. Gary E. Schwartz of the University of Arizona, Dr. Jeffrey Mishlove of New Thinking Allowed, Dr. Alan Ross Hugenot, Publications of the Academy for the Advancement of Postmaterialist Sciences. and many more.

The purpose of this blogpost is not to convince anyone that consciousness exists independent of the physical bodies it temporarily occupies. That is simply a fact that everyone will eventually experience. The purpose of this post is to present a cogent picture of the comprehensive model of reality we call TDVP and suggest practical applications within the context of TDVP that can help those who are ready to expand their own individual consciousness beyond material identification, and farther, for those who have already experienced OBEs or NDEs. To that end, let’s continue this exploration of Self-Inquiry.

Because of intense identification with the ephemeral physical bodies that we inhabit during this lifetime, and the trauma of birth, physical life, and death, we almost completely forget who and what we really are. To regain that lost memory, we have to reverse our attention and abandon our hypnotic fascination with physical stimuli. We must turn the spotlight of our mental focus around from the distracting events in the world, events that are beyond our control, to the ever-existing multi-dimensional field of consciousness to discover who we really are. This is a lot easier to say than it is to do! This deliberate turning around from the singular focus on our involvement with the material world, to focus on the pure consciousness of the spiritual world, is identical from an objective point of view, with repenting in the Biblical sense. See Revelation 2:3–5:

And you have perseverance and have endured for My name’s sake and have not grown weary. But I have this against you, that you have left your first love. Therefore, remember from where you have fallen, and repent …

While you may not remember it, every one of us now alive has actually asked to be born. We choose to brave the temporary pains of birth and death again and again, in order to experience physical existence, and we forget that our “first love” was the Infinite Love we experienced in Pure Consciousness, the place from whence we fell.

The proper frame of mind for effective Self-Inquiry is one of alert attention, free of imaginary expectations and random thoughts. Most of the prayerful meditation techniques taught in the various spiritual traditions are designed for calming the mind so that we may connect with the transcendental reality of Pure Consciousness, so prayerful meditation is the best way to prepare for Self-Inquiry. But for anyone who does not already have a well-established meditation practice, I would like to suggest the following: Start by making yourself as comfortable as you possibly can, avoiding the position you habitually assume for sleep. As you probably know, distracting localized physical discomforts are sure to arise, but they can be mitigated by alternately tensing and relaxing the muscle or muscle group involved.

The next two steps are very important. They are simple and easy to describe, but difficult to accomplish: First, withdraw your attention completely from everything outside of your skin, especially including sensations on the surface of your skin. Difficult? Yes, but absolutely achievable. You already know it is achievable because it happens every time you go to sleep. You just have to learn to do it without going to sleep. Second: Focus with increasing intensity on feeling the reality of your existence within the world encompassed by your skin, from head to foot, in all your body’s cells. It is helpful to study anatomy and learn where every organ, bone, and muscle is located in your body. This is not absolutely necessary for successful Self-Inquiry but will make the process easier to master.

It is likely, when first attempting this, that as you try to intensify the feeling of conscious existence within the boundaries of you own skin, you will find yourself tensing certain muscles in your hands, feet, jaws, neck, and stomach as part of the effort. Avoid this. It will block your progress into Self-Inquiry. As soon as you realize that you are tensing up as part of attempting to increase the intensity of your awareness, back off, relax those muscles, and refocus on the simple awareness of  existence. In this way, as you intensify your focus on the existence of consciousness, you will be able to disconnect mental effort from physical effort.

When you are fully focused on the reality of your conscious existence, in this relaxed, alert state, you are ready to initiate conscious Self-Inquiry. Notice that the rhythmic movements of air in and out of your lungs, and of blood circulating throughout your body, will begin to slow down and become more natural and regular. Notice also, that your body, a complex combination of symbiotic living organisms with which you were identified, continues to function very well without your conscious involvement.

When you have successfully completed the steps of infinite descent described above, you will have moved beyond shallow identification with the temporary roles and titles of earthly life, including name, family, profession, position in society, etc., and you will have repented of your love affair with the external world by withdrawing the energies of your conscious attention from it and focusing them on the conscious life existing within your physical body. And finally, you will have realized that you are not actually part of the complex of organisms that make up the physical body.

At this juncture, it may seem that you are left with only two options, both of which appear to end badly. You can continue the descent, in a very real sense, into the bowels of the physical body, descending from the largest organ to the smallest organ, to the largest complex molecule, to the smallest molecule, to the largest cell, to the smallest cell, to the most complex stable atom to the simplest atom, and on to nothingness, without ever finding out who or what you are. Or you can just return to the vicinity of the surface of your skin, where “the wages of sin is death.” – Romans 6:23.

The conclusion in either case is that there is no such thing as consciousness. But consciousness is the only that thing we experience directly. How can it not exist? So, we have reached a Reductio ad absurdum, and I can hear Niels Bohr saying: “Hvor vidunderligt! Vi har et paradoks! Nu kan vi måske gøre nogle fremskridt!” How wonderful! We have a paradox! Now perhaps we can make some progress! And I agree! In fact, I am happy to report that the paradox has already been resolved. To understand how, we must go back to the next-to-last step of the descent traced through the organs, cells, molecules, and atoms above. That smallest atom happens to be the simplest atom, the ionized hydrogen atom, also known as the proton.

The proton, composed of two up-quarks and one down quark, is the most stable object in the physical universe. In 2011, I applied the dimensional quantum calculus I had developed in 1986 to the quark combination to determine why it takes three quarks to form a proton, and why the result is so stable. To my surprise, I discovered that the proton could not be stable, and wouldn’t have the mass it has, unless there were several quanta of something non-physical present in each of the quarks. This became the basis of the mathematical-physics proof of the existence of gimmel, the non-physical third quantized essence of reality. The paradox is resolved when we realize that consciousness is non-physical and non-physical gimmel is the logical end result of Self-Inquiry.

Here, at last, we see that the infinite descent to gimmel, the non-physical essence of reality that makes the stable proton and the physical world possible, and the infinite descent into the essence of what you and I really are, is actually the same journey! The first is a description of the journey in symbols of mathematical logic, while the latter is a description of the actual direct experience of making a personal journey into the essence of consciousness.

I am very much aware of the fact that understanding something intellectually after hearing or reading about it, and actually experiencing it for yourself, are two entirely different things. I have written about the discovery of gimmel and the process of Self-Inquiry before, both on this blogsite and in peer-reviewed papers and other publications. Both Dr. Neppe and I have speculated that gimmel must be related to consciousness for a variety of reasons, but in this post, I am saying something quite different:

In this post, I am saying that the quantum-physics infinite-descent demonstration that proves that gimmel exists, is actually a mathematical analog of the first-person infinite-descent process of Self-Inquiry that proves that consciousness exists. Gimmel and individual awareness exist as finite quantized forms of the essence of consciousness embedded in the infinitely continuous field of Primary Consciousness, and you have access to that field. Everything that exists is immersed in it, and you become aware of it through the process of Self-Inquiry.

The structural forms that make up physical reality are finite logical patterns that exist in the infinitely continuous field of Primary Consciousness, and the laws of form that govern those patterns to be discovered by sentient beings like us, are the natural laws of science.

In future posts, I plan to discuss questions 2 and 3 listed at the end of Part Sixteen.

ERC – 3/25/2022
 

NEW APPROACH PART EIGHT

 

EIGHT: DIMENSIONS OF THE KNOWN AND UNKNOWN

“It requires a very unusual mind to undertake the analysis of the obvious.”- Alfred North Whitehead

Dear reader, in these blogposts, I am asking you to awaken your innate potential as someone with “a very unusual mind”. Everyone knows what a dimension is, right? We all think we know what dimensions are. The dimensions of reality are so obvious to us that the vast majority of us talk about dimensions all the time, and thus see no need to undertake an “analysis of the obvious”. But that’s exactly what I propose we do in this discussion. I think there is a great need for just such an analysis. Like the paradoxes we have been analyzing in this series of discussions, dimensions reach all the way from the patently familiar world of everyday life to the wildest regions of the vast unknown.

So, what are dimensions? No one can ship a package, build a home, or plan a trip without dealing with dimensions. Dimensions are the basic measurements of extent needed for use in the calculations that solve many of the practical problems of our lives. Measurements of the dimensions of space and time are the raw data for calculations of distances, areas, volumes, and velocities, and even more challenging rates of motion like the speed of light. Such practical uses of the data obtained from accurate observations and precise measurements of dimensions are the first steps on the path that led to the development of that currently dreaded public educational headache called mathematics.

If you have come with me this far, you know that when I use the term mathematics in these blogposts, I am referring to something far different than what the average person thinks of when seeing that word. As a writer, I was told by publishers and other writers many times that with every use of that word, many readers are lost. And the appearance of an equation is even worse, they say. Why is this? In my opinion, based on years of experience teaching mathematics, it is because of a general “dumbing down” of public education. For many people, that horrible word brings back memories of  painful experiences of a high school or university math instructor yelling at them, like a frustrated pedagogue, finding fault with the students, rather than with his teaching methods, lack of proper preparation, or poor understanding of the subject.

We are constantly told that education has progressed, and that there is so much more to learn today than when our grandparents were young. But when I look at the course material in public education, what I see is more and more detail that is utterly useless except in very narrow areas of specialization. I see that today’s math classes are more about how to use a computer than how to think. Critical reasoning doesn’t seem to have any place in public education. My mother, father, and grandparents, who were born and grew up in the backwoods of the Missouri Ozarks, with no formal education beyond the eighth grade, were far better at critical thinking and problem solving than many people today with BS, MS, and PhD after their names. Why is this? The dumbing down and narrow specialization of public and now, even private education in this country. When everyone who pays the proscribed fee is given a diploma or degree whether they master the material or not, and an advanced degree means a cluttered mind with more and more narrow detail with less and less substance, you have a recipe for disaster.

While on the path to my chosen profession in theoretical physics, one of the degrees I earned was a Batchelor’s degree in mathematics. I enjoyed the subject so much that I decided to teach math and took some education courses and got a job as a public high school math teacher in 1962. The first two years of teaching gave me some of the most rewarding experiences of my life. They were not monetarily rewarding experiences, but I maintain that there is nothing more satisfying or exciting, than seeing the light come on in a student’s eyes when she, or he, understands, for the first time, the elegant proof of a theorem, or the beautiful symmetry of a polynomial expansion. But, after teaching at the high school and university levels for a few years, I left the teaching profession. I left mainly for two reasons: 1) The obvious dumbing down of public education, and 2) at that time, teachers were being paid less than garbage collectors. I decided to get a PhD in environmental engineering.

OK, enough complaining  about the disappointing state of public education, which, sorry to say, is worsening as we speak. Back to the subject at hand.

The concept of dimension leads to some things far more interesting than the mundane tasks of calculating distances, areas, volumes, and velocities. What do theoretical physicists mean when they talk about ten dimensions of string theory, or curved space and dilated time? What do UFO theorists mean when they say that alien spacecrafts may come here by traveling through “another dimension”? What do spiritual mystics mean when they speak of experiencing other planes of existence? Are they all referring to the same thing when they use the word dimension? Obviously not, but what are dimensions, anyway?

“...the only simplicity to be trusted is the simplicity to be found on the far side of complexity.” ― Alfred North Whitehead

In the end, truth is always simple. But sometimes the complexity that must be endured to arrive at a simple truth is tedious and time-consuming. Grasping the importance of multi-dimensional analysis is a case in point. Because our physical senses are so limited and focused primarily on physical survival, visualization of more than three dimensions is difficult. Even the idea that time is the fourth dimension is difficult to grasp.

Prior to the introduction of time as a fourth dimension in general relativity, it was usually only abstract mathematicians who talked about n-dimensional space, where n could be any number from one to infinity. Professionals in advanced mathematics don’t like to limit their explorations of number theory by tying mathematics to things that actually exist in reality, and most physicists and other scientists look at math as nothing more than a source of tools they can use to solve problems. As a result, one of the most persistent misconceptions about dimensionality is that there is, was, or could be more than three dimensions of space.

Applications of the calculus of dimensional distinctions (CoDD) however, show that, when related to the physical universe and its reflection in pure mathematics, natural dimensions beyond three are not spatial. Their scope and meaning are more complex than simple length, width, and depth, and the pattern of reality reflected in sub-atomic reality, mathematics, and consciousness, is not singular, linear, or binary, but triadic. As I developed dimensionometry to identify and explore the invariant relationships between the dimensional domains of the TDVP model of reality, the analysis revealed that three dimensions of space, three dimensions of time, and three dimensions of consciousness are necessary to model the structure of the human experiences of reality.

It took several years of study and several experiences of expanded consciousness in NDEs and OBEs for me to realize exactly what dimensions are. The path was complex, but in the end, the truth was and is simple. Dimensions are the measurable connections between geometric simplicity and complexity, eventually leading back to simplicity again. They are also the connections between mundane existence and exotic experiences of reality, enabling one to return to the simplicity of oneness. Dimensions delineate the pathway from the discrete separation of quantized reality to the infinitely continuous reality of conscious enlightenment.

The discussion of dimensions should actually be about dimensional domains, not about dimensions, because a single dimension by itself is meaningless beyond being part of a logical framework for observation and measurement. And dimensional domains are of interest primarily not because of what they are, but what they may contain. Starting with the mathematicalogical invariants discovered in the relationships between the first four dimensional domains of space and time, the triadic invariances of dimensionality can be traced upward from the dimensional domain of the smallest quantum of reality to the logical patterns of consciousness, or downward from the logical patterns of consciousness, back to the dimensions of time and space. This can be accomplished using Fermat’s method of infinite descent translated into the mathematical notation of the CoDD. See Transcendental Physics, Close (1997)

Defining the mathematical operations of the primary quantum calculus of dimensional distinctions is a complex task, but the underlying metaphysical basis of the calculus and the resulting structure of reality that its application reveals, can be described in plain English:

The Metaphysical Basis:

Reality as we experience it, consists of quantized manifestations of the essence of reality in three forms: mass, energy, and consciousness-as-content. Mass is condensed energy, in the form of quantized vortexes spinning in at least three dimensions, measured by the strength of their inertia (resistance to motion). Energy is a condensed form of consciousness, measured by its quantized force, equivalent by a multiplicative factor, to the quantized inertia of mass. Quantized consciousness (gimmel) is the first manifestation of the conscious essence of reality in the physical universe, and it is capable of expansion and the conveyance of patterns of the logical structure of Primary Consciousness, the substrate of manifest reality, into physical reality.

Space, time, and conscious extent are the three forms of dimensional domains created by the existence of quantized mass, energy, and conscious content. Please notice, in what was just said above, that consciousness plays a key role in the expansion of both content and extent. It is in this way that living organisms are developed by Primary Consciousness for the purpose of functioning as vehicles within which quantized consciousness can expand by self-effort from the bare awareness of self and other, to Cosmic Consciousness, the complete awareness of everything, including Primary Consciousness itself.

Dimensionality and the Structure of Reality:

Dimensions are very simple geometrical concepts. They are straight lines, constructed for the purpose of representing the location and extent of observable phenomena from the location of an ostensibly arbitrary reference point chosen by a conscious observer. But the reference point is not actually arbitrary; it represents the observer’s personal location, based on the sense of separation from observable phenomena, projected out of the observer’s consciousness onto a sheet of paper as the zero point of an analog model of the observer’s personal frame of reference in the dimensional domain of his existence in the physical reality of his experience. You may need to read that again to understand every word, but it is a very detailed description of the very simple concept of location.

An n-dimensional domain is a region of interest and focus of a conscious observer, defined by the extent of the dimensions and the content of the region so defined. In a domain of two or more dimensions, the dimensional lines are constructed at 90-degree angles from each other. The choice of 90-degree angle separation of dimensions is not arbitrary or random. It is chosen because it results in the smallest number of straight-line cardinal dimensions equally dividing a circle and a sphere. Any other angle of separation makes quantification and visualization of the reality represented much more difficult. Lines intersecting at 90 degrees are called orthogonal lines.

To paraphrase Albert Einstein: dimensions can claim no existence of their own, they are simply structural features of the distribution of the density of the substantial field of reality.

Despite their lack of substantial existence, dimensional domains convey a lot of meaningful information about physical, mental, and spiritual reality. For that reason, they are worthy of detailed study and analysis. Here are some of the things the TRUE CoDD analysis of TDVP reveals about dimensional domains:

A zero-dimensional domain is a dimensionless point, also called a singularity.

A one-dimensional domain is a straight line segment extending from a zero-reference point in opposite directions.

A two-dimensional domain is an area defined by the extent of two orthogonal one-dimensional line segments.

A three-dimensional domain is a volume defined by three mutually orthogonal one-dimensional line segments.

A four-dimensional domain is a region defined by four mutually orthogonal 1-dimensional line segments.

An n-dimensional domain is a region defined by n mutually orthogonal one-dimensional line segments.

In domains with 1 through 3 dimensions, distances are measured, and phenomena are described, in terms of integer multiples of TRUE (quantum equivalence units) of the CoDD. But they must be measured and  described in terms of integer multiples of imaginary numbers in domains with 4 through 6 dimensions, and in terms of integer multiples of specific complex numbers, known as the nth roots of unity, in domains with 7 or more dimensions. This unitary change from integers to imaginary numbers, to complex numbers is mathematically necessary for a consistent quantized description of the rotation and projection from geo-centric dimensional domains into hyper-dimensional domains. Proof of this is relatively straight-forward using the CoDD and application of the Pythagorean Theorem. The Proof, translated into conventional simple mathematical notation, has been published in several books and papers, some of which are listed in two blogposts: REFERENCES Sept. 17, 2016, and THE ANSWER  Nov. 7, 2021. I call the process of rotation and expansive projection from one dimensional domain into the next one, Dimensional Extrapolation because it demonstrates the way both consciousness and physical reality expand.

In 2011, the first CoDD analysis I did, using TRUE quantum arithmetic, was to describe in detail the combination of quarks to form protons, the sub-atomic entities that, along with electrons, form all of the stable building blocks of the natural elements of the periodic table. What I discovered, was surprising, even though something like it should have been expected from the moment I included consciousness in the definition of the basic distinction of the primary calculus in 1986 for application at the quantum scale of physical reality. That discovery was the existence of multiple occurrences of TRUE units of non-physical gimmel at the heart of  physical reality, an undeniable indicator of consciousness – literally the fingerprints of God showing up on the most abundant stable object of the physical universe, the proton. See footnotes in Reality Begins with Consciousness, Neppe and Close (2011) and my chapter in the AAPS Volume I, first edition entitled Is Consciousness Primary? Edited by Drs G.E. Schwartz and M.H. Woollacott (2019).

Triadic Rotational Units of Equivalence (TRUE) are defined by the mass and volume of the free electron, tying the quantum mathematics of the CoDD to physical reality, and Dimensional Extrapolation is a mathematical process analogous to the conscious movement, by rotation and projection, from an n-dimensional domain into an n+1 dimensional domain. The appearance of gimmel in the CoDD TRUE analysis of the combination of two up-quarks and one down-quark to form a proton, also ties the analysis to consciousness, providing a basis for the integration of consciousness, spirituality, and physical reality.

Dimensional domains are geometrical patterns that originate in the logical structure of consciousness and have no existence of their own. A domain is defined by the number of dimensions needed to describe it, but the number of dimensions and the extent of those dimensions are completely determined by the domain’s content of mass, energy, and gimmel. In efforts to describe relativistic effects, physicists and science writers often describe space or spacetime being warped, curved, or distorted by mass. But there is no such thing as bent or distorted space, time, spacetime, or any hyper-dimensional region. Curvilinear paths of moving objects are caused by the distribution of the density of substance within a domain. This is actually what is  known in modern physics as a field.

Dimensional domains with zero, one, or two dimensions, are archetypes of the logical structure of Primary Consciousness. They can be conceptualized mentally, and represented on a piece of paper, but do not exist in physical reality because they have no capacity to contain quanta of the substance of reality. Because of this, CoDD analysis, as it applies to physical reality, begins with n = 3, the first dimensional domain that can contain volumetric structures of mass and energy. This gives it a distinct advantage over conventional mathematics in hyper-dimensional analyses but requires a radical re-defining of the fundamental operations of arithmetic and algebra appropriate for our quantized reality.

An n-dimensional domain is capable of containing all smaller domains (i.e., domains with fewer dimensions than n) if  such domains exist within the n-dimensional domain of interest.

A conscious entity can only be fully aware of the existence of an n-dimensional domain of reality when that entity’s awareness is expanded enough to include at least one quantum of an n+1 dimensional domain.

In an infinite or effectively infinite reality, logically, physically, and mathematically, every n-dimensional domain, from n=0 to n=9, is embedded within an n+1 dimensional domain.

This brief introduction to the way CoDD dimensionometry models the structure of reality is a first step in relating the logic of the TDVP to direct human experience of reality. The second step is the geometric process of Dimensional Extrapolation. The third step is virtual rotation and projection of human consciousness into higher dimensional domains. The prime example of this third step in my life was my experience in 2010 in the Great Pyramid of Egypt. [Described briefly in Secrets of the Sacred Cube, a Cosmic Love Story, Close, E.R. and Close, J.A. (2019)].

“Not ignorance, but ignorance of ignorance is the death of knowledge. … The aim of science is to seek the simplest explanations of complex facts.”    – Alfred North Whitehead 

In the next installment of A New Approach, I will continue to discuss how the logic of the Triadic Dimensional Vortical Paradigm (TDVP)  relates to the direct human experience of reality.

ERC 1/29/2022

RECENT DISCUSSION OF THE 1965 PROOF OF FERMAT'S LAST THEOREM

I think that this recent exchange with a friend who has been looking at FLT65 for some time may be of interest to  those who are following the subject of Fermat's Last theorem, which as they may know, is importent to the explanation of quantum phenomena in TDVP. This conversation may be helpful for anyone interested in understanding the logic of the 1965 proof. For this reason, I am posting my latest response here without identification of my friend or his math professor friend.

MY RESPONSE OF AUGUST 12, 2017

I spent some time thinking about Prop. P between meetings and events in LA last week. There really should be no confusion about when P is true and when it is false. I will attempt to clarify this while answering your latest comments, because they do reflect what I see as confusion about what FLT65 says and does. I shall also attempt to show you how distinguishing when Prop. P is true and when it is false, and when the identity sign is appropriate, leads to a better understanding of FLT65. 

From your email earlier today:

      Q: Do you believe that Prop P is ever false?

Let’s consider this. Here is Prop P as you stated it:

     P: Equating a polynomial to a constant, for the purpose of finding a  

        specific solution, automatically turns the polynomial itself into a  

        constant.

This should not be a matter of “belief”, because it is easy to show that P can be either true or false, depending upon the nature of the polynomial, and the circumstances. And, it is an added benefit that the circumstances also allow us to clarify the proper use of the identity symbol ≡.

P is true, if and only if, all variables are specified as constants. For example, we know that, if Y in the FLT equation is an integer, then for any Y there is some integer factor A such that z – a = A. If we should also know that Z and Y are the specific integers Z₁ and Y₁, then a is determined, and we have: Z₁ – a₁ ≡ A, an identity.

But in FLT65, z is an unknown. Clearly, integers can be assumed for X and Y, and if so, then whether or not z can be an integer is as yet, in the proof, unknown. To assume that it is an integer at the beginning, is premature and leads to circular reasoning. For the polynomial z – a in FLT65, z is a real number, but its specific value is unknown, so when we set the polynomial z –a = A, a known integer factor of Y, P is false, because z and a can take on an infinite number of values. The only requirement imposed by setting z – a = A is that their difference is always A. The value of z can vary, and thus this equation is not an identity.

 I once sent you the judgement of a mathematician who had spent his entire working life as a mathematics professor in a university. You dismissed his judgement that FLT65 was invalid as “something you had seen before.” 

To be clear, I had seen this line of reasoning several times before, and have given it all the serious thought it deserves, so I saw it as the same knee-jerk reaction I’ve seen numerous times, and refuted every time. I felt that you should have recognized the circularity of the argument. But I apologize for my abrupt manner. I should not have been so abrupt, and I certainly should not have been condescending. I’ll copy the math professor’s comment here and try to respond more appropriately.  He said:

“Here is a possible way of putting it that might convince Mr. Close.  In his argument he sets  a = Z - A   and considers the divisor polynomial  g(Z) = Z - a, which he says is a polynomial of degree  1  in Z.  But  g(Z) = Z - a = Z - (Z - A) = A,  which is not of degree  1  but of degree 0.  When the divisor A  is a (nonzero) constant, the polynomial division algorithm over the reals just says there exists a (unique) polynomial  q(Z)  such that  f(Z) = Aq(Z) + 0, where, of course, q(Z) = f(Z)/A.  so there is no  f(a).”

This argument completely misses the point of FLT65 by assuming the definition a = Z – A which is not the case in FLT65. His statement that I set a = Z – A is false. You will not find this anywhere in FLT65. Z is the unknown, the dependent variable. Z – a is defined as a polynomial of the 1^st degree, meaning that the value of Z depends on the value of A, an integer factor of Y and the value of a, which is an integer if there is an integer solution of the FLT equation, which is as yet, in the FLT65 chain of logic, unknown. By assuming that Z is an integer by definition, the conclusion that Z –a is a constant, and therefore of 0 degree, is of course, circular reasoning, as mentioned above, and stated in my more abrupt response. By the way, I meant no disrespect to your professor friend by dismissing his comments. A university professor known as a number theory expert made the same mistake, but he quickly acknowledged that it was circular reasoning when I pointed it out to him.

Thank you for your statement of what you see as a disproof of FLT65. It enables me to better understand why you kept coming up with propositions that had nothing to do with FLT65. I think other critics may have had this same misconception about how FLT65 goes about proving FLT.

Your statement has the logic of FLT65 completely backward:

 “The equation of constants, f(Z₁) = A^p = (Z₁ - a)^p, does not imply that the variable (Z - a) is a variable factor of the variable f(Z). 

I agree! However, what FLT65 says is the converse: the fact that f(z) cannot contain z – a as polynomial factor for real number values of the variables, implies that, if there were an integer solution for the Fermat equation, then there would be an integer version of f(z)/(z – a) = q(z) + f(a) where f(a) would equal zero, and that would violate the ‘if and only if’ condition of the division algorithm for polynomials.

It appears to me that the confusion comes from considering Z to be a specific integer before it is known whether z can be an integer or not. Maybe this will be clearer if we go step-by-step:

Dividing f(z), a polynomial of degree p-1 by z - a, a 1^st degree polynomial, we have unique polynomials q(z) and f(a) of degree less than p such that:

(z^p-1 + z^p-2x + z^p-3x² +•••+ x^p-1)/(z-a) = q(z) + f(a)/(z-a). Multiplying through by z-a, we have:

f(z) = (z^p-1 + z^p-2x + z^p-3x² +•••+ x^p-1) = q(z)(z-a) + f(a).

From this we see that the polynomial f(z) is factorable into two polynomial factors, q(z) and z-a, if and only if f(a) = 0. But f(a) = a^p-1 + a^p-2x + a^p-3x² +•••+ x^p-1, which cannot equal zero because a and x are positive for any integer solution of the FLT equation.

Therefore, the FLT equation factor polynomial f(z) cannot be factored into two polynomials of degree less than p, one of which is z - a.

If there is an integer solution, then with the term-by-term substitution of the integer variables into the variable polynomial f(z), we obtain the variable polynomial f(Z) for any integer solution of the Fermat equation. But, for any integer solution, f(Z) = (Z-a)^p, where Z-a = A, a single integer factor of Y^p. So now we have:

The hypothetical integer polynomial f(Z) = (Z^p-1 + Z^p-2X + Z^p-3X² +•••+ Z^p-1) = q(Z)(Z-a) + f(a) = (Z-a)^p.

By inspection of this integer polynomial equation we see that f(a) contains Z - a as a factor, and although we don’t know what the specific values of a and X are for an integer solution, we know that they are positive constants. So f(a) = M(Z-a) where M is an integer constant, and we have f(Z) ) = (Z-a)^p, = (Z^p-1 + Z^p-2X + Z^p-3X² +•••+ Z^p-1) = q(Z)(Z-a) + M(Z-a), from which we have: f(Z) = [q(Z) + M](Z-a).

And q(Z) + M is a variable polynomial in Z of degree less than p, call it q₁(Z). Thus for hypothetical integer solutions of the FLT equation, we have the variable polynomial f(Z) = q₁(Z)(Z-a). But this is a violation of corollary III of the division algorithm, which tells us that the variable polynomial f(Z) cannot be divided into the factors Z - a and another polynomial of degree less than p. The only way we can avoid this contradiction is for z to be an irrational real, not an integer. 

I have demonstrated in at least three different ways, including Fermat’s favorite method of proof, infinite descent, that if we ignore this contradiction, and assume that two of the three variables x, y and z are integers, and solve the FLT equation for the third variable, then that third variable cannot be an integer.

I don’t consider adding such demonstrations to FLT65 to be necessary because the contradiction f(a) ≠ 0 versus f(a) = R = 0 is sufficient to prove FLT by itself. This contradiction is valid because it is obtained by applying the division algorithm and corollaries to variable polynomials, not constants, and a single contradiction is sufficient to prove there can be no integer solutions for z^p – x^p = y^p.

I believe the whole confusion for most critics arises from assuming that the division algorithm and corollaries are inappropriately applied to constants. They think this because they jump to the conclusion that all three variables must be treated as integer constants from the beginning of the proof. Thanks to you, this confusion has been made clear with the analysis of Prop P! 

Once you see that P can be true or false, depending upon the nature of the polynomial, and that in FLT65, f(Z) and Z – a are still polynomials of the variable Z, even though for a hypothetical integer solution, they are equal to the constant integer factors of Y^p, the logic of FLT65 becomes clear, and the search for counter examples and counter propositions becomes unnecessary and irrelevant.

Edward R. Close  August 12, 2017