NEW APPROACH PART TWENTY: WHAT DOES THE FUTURE HOLD?

 

Swami Sri Yukteswar Giri

(1855 - 1936)

THE NEW APPROACH, PART TWENTY

© Copyright 2022, Edward R. Close, PhD

‘God doth not need
Either man’s work or his own gifts; who best
Bear his mild yoke, they serve him best. His state
Is Kingly. Thousands at his bidding speed
And post o’er Land and Ocean without rest:
They also serve who only stand and wait.’ - John Milton, “On His Blindness”.

 

Looking Back

The discovery of the existence of a measurable form of consciousness, now known as gimmel, the third form of physical reality after mass and energy, has a well-documented history. Important parts of that history reach all the way back to the works of the French mathematician Pierre de Fermat with his famous Last Theorem in1637, and the German mathematician Georg Cantor with his Infinity of infinities, around 1900. The discovery of the existence of gimmel about a decade ago, led to the formulation of the Neppe-Close Triadic Dimensional Vortical Paradigm (TDVP) a major paradigm-shifting model. A brief summary of that history is an appropriate background for this post. Here it is, presented in reverse order:

I have posted a link to the most recent presentation of the basic ideas behind TDVP and non-physical gimmel on my FB page. It is an April 2022 YouTube video of a zoom recording of Dr Neppe addressing a group of scientists. Here is the link again: https://youtu.be/TTwDgR50DMY. Major parts of the derivation of gimmel have been posted on this blog site. You can search the site from 2019 to the present to find them. Also see  www.brainvoage.com.

The most recent publication of the complete mathematical proof of the existence of gimmel, the non-physical part of reality, is an important part of my chapter in the book IS CONSCIOUSNESS PRIMARI? – Volume 1 in Advances in Postmaterialist Sciences, edited by Gary E. Schwartz and Marjorie H. Woollacott, 2019. It has also been published, with more detail, in Part II of SECRETS OF THE SACRED CUBE, a Cosmic Love Story, Close, E.R. and J.A., Outskirts Press, 2019, available on Amazon.

Dr. Vernon Neppe, MD, PhD, and I have been working together for about fourteen years now, and we have published scores of peer-reviewed papers, and five editions of Reality Begins with Consciousness, explaining TDVP and the mathematics behind it. The fifth edition of the book is currently available at https://brainvoyage.com/shop/catalog . Other relevant links can be accessed through https://www.pni.org/groundbreaking .

I published an infinite descent proof of the existence of a non-physical final receptor in the process of human perception in Appendix C of : A CALCULUS OF DISTINCTIONS PROOF of The Existence of Non-Quantum Receptors, in my third book, TRANSCENDENTAL PHYSICS, Paradigm Press, Jackson Missouri, 1997, and I had previously published the basic development of the calculus of distinctions seven years earlier, in my second book, Infinite Continuity, A Theory Unifying Relativity and Quantum Physics, released in 1990.

Prior to that, in 1965, I used the basic reasoning of infinite descent to prove Pierre de Fermat’s Last Theorem (FLT), which became an important part of the logic leading straight through the calculus of distinctions to proof of the existence of gimmel, the non-physical part of electrons and quarks, the building blocks of the atoms of the periodic table.

The 1965 proof of FLT, with documentation of its first submittal to mainstream mathematicians, was published in an appendix of my first published book, The Book of Atma, Libra Publishers, Inc, New York, 1977, and the history of the various reviews and unsuccessful attempts to disprove FLT65 since then is available in the archive s of this blogsite.

 

Disclaimer

In this series of blogposts, I am discussing science and spirituality from the viewpoint of biopsychophysics, a new scientific discipline initiated by TDVP, with its own system of mathematical logic. Major paradigm shifts of the past have always required new mathematics. Relativity, e.g., required the new mathematics of four-dimensional spacetime, and quantum physics required new geometric and probabilistic interpretations of matrix algebra and probabilistic wave equations. TDVP requires the complexity of quantum equivalence units, a quantum calculus, dimensional extrapolation, and a new interpretation of Diophantine equations. It should not be too surprising that a paradigm shift from the simplicity of materialism to the hyper-dimensional complexity of biopsychophysics, encompassing non-physical phenomena, would require some pretty complex new mathematics.

In this series of posts, I will be making some predictions, but I am not claiming to be a seer, prophet, or spiritual guru, inspired by visions from God, I am simply reporting here on some of the more significant findings resulting from applications of the quantum mathematics of the calculus of dimensional distinctions to human experience. My role at this point, and the purpose of these posts is to explain, to the best of my ability, the mathematical logic of TDVP and the proof of the existence of measurable non-physical gimmel and its relationship to the expansion of consciousness in a way that almost anyone can understand.

 

Looking Forward

In a very important book, The Holy Science, by Paramahansa Yogananda’s Guru, Swami Sri Yukteswar Giri, written in India in 1894, copyrighted, and reprinted in the US by Self-Realization Fellowship in 1949, the periodic astronomical movements of the planet Earth are meticulously traced and correlated astrologically with the historical advancement of science and civilization, reflecting the advancement of mental and spiritual virtue from the time we exited the Kali Yuga (the lowest age of conscious virtue) in 1599, and moved into the Dwapara Yuga, an age of expanding consciousness, until the time the book was written in1894, and beyond, all the way to the next high point of consciousness expansion, 10,477 years in the future.

Please don’t be put off by my use of some remnants of Sanskrit terminology from Jainism, Hinduism, and Buddhism. It is the most expressive way of conveying knowledge from the last apex of human enlightenment in 11,501 B.C, and an important part of what I am trying to do is to facilitate the integration of the core truths of all human efforts to understand the nature of reality, both scientific and spiritual. It is only that kind of integration that will counteract Satan’s devious efforts to divide and conquer the spirit of the human soul.

The group consciousness of sentient beings on this planet will expand into the great understanding of Cosmic Consciousness in the fullness of God’s time, some ten-thousand years in the future. There is nothing the forces of Evil can do to stop it. But, for those on the threshold of true awakening now, that is too long to wait. Even though it may be said by a talented poet who was slowly going blind, that “they also serve who only stand and wait”, God’s Love has provided wonderful ways for beleaguered souls, those of us who do not want to stand and wait for ten thousand years, to forge ahead of the pack. Be forewarned, however, that Satan’s minions will spare no effort to block and throw doubt upon those wonderous ways and those who pursue them!

In future blogposts, I hope to be able to focus on some of those wonderous ways that have been provided for us by God’s Avatars (fully enlightened souls), who have gone before. For now, please receive the waves of Love that I am sending from my heart of hearts, embedded in the substrate of Primary Consciousness, to your heart, embedded in the same pervasive extension of the Great I Am. Shalom, Shanti, Peace. Aum, Amin, Amen.

ERC – 15 April 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

THREE QUESTIONS

©Edward R. Close, January 26. 2018

1.     What is the Nature of Reality?

2.     What is Life?                             
3.     Who am I?                                 
                            

      INTRODUCTION  

      In the January 11 post THE ULTIMATE QUESTION AND ITS ANSWER, Leibniz's question was presented and answered. The answer was proved by application of the Calculus of Distinctions and published some time ago. Having answered Leibniz's most important question: Why is there something rather than nothing? a question current mainstream science has ignored, we are now ready to move on to the next tier of important questions. If you haven't read the ultimate question post, or don't remember how it is answered, please scroll down to the January 11 post and read it before continuing with this up-dated post.

WHAT IS THE NATURE OF REALITY?

This is the root question behind the major efforts of both science and religion. The answers given historically by both institutionalized science and institutionalized religion are basically wrong. Institutionalized (so-called mainstream) science erroneously assumes that reality is limited to matter and energy interacting in space and time (materialism). Less than 5% of reality can be explained based on this assumption; just the tip of the iceberg. The major Institutionalized world religions assume that a priesthood of some sort is needed to explain reality to you. This is almost always the blind leading the blind.

Reality is one. Institutionalized science and religion divide it up to “explain” it. This resonates with the average individual because that is what we do as human beings. Enlightened beings know that this is delusion. To know reality, you must become one with it. Oneness is your natural state. Polymath Erwin Schrödinger had this to say about the nature of reality:” The world is given to me only once, not one existing and one perceived. Subject and object are only one. The barrier between them cannot be said to have broken down as a result of recent experience in the physical sciences, for this barrier does not exist.”

The reality studied by scientists and theological philosophers is triadic. The universe comes into being as a result of dividing the One. Drawing the distinction of self from other creates the illusion of division and separateness. By drawing a distinction in the “other”, consciousness brings the objective physical universe into existence. So, the reality that we can observe, and measure is triadic, consisting of the distinctions of self, other, and everything else; the observer, the observed and the action of observing.

The action of change, or movement from oneness to multiplicity introduces perceptions of space and time. So, we have three triads: 1,) space, time and conscious extent; 2.) mass, energy and conscious content; 3.) the Primary Oneness, the universe and the individual sentient being. In the quantized universe, the calculus of dimensional distinctions (C0DD)^† is the logical system of calculation for dealing with enumeration, difference and equivalence, where all equations describing quantized phenomena are Diophantine equations, and the basic unit of measurement is the triadic rotational unit of equivalence (TRUE), a unit based of the electron, the entity with the minimum mass among the elementary particles (electrons, up-quarks and down-quarks) that make up the protons and neutrons, which make up the atoms of the Periodic Table of Elements.

Application of the process of dimensional extrapolation^†, a triadic method of moving consciousness from any n-dimensional domain to the next larger (n+1)-dimensional domain, using the binary Diophantine equation known as the Pythagorean Theorem, we find that these three triads are represented mathematically by integers, imaginary numbers and complex numbers. By iterative applications of the mathematical process of dimensional extrapolation, we see that, because conceptual zero-, one- and two-dimensional objects are contained within a three-dimensional domain, three dimensional extrapolations move us to the end of the domain of integers and continuing by dimensional extrapolation into the fourth dimension requires using multiples of the square root of negative one, known as imaginary numbers. Continued iterations of dimensional extrapolation take us through three time-like dimensional domains into the third triad of dimensional domains, where we find that we must proceed from multiples of imaginary numbers to multiples of complex numbers. So, we have 3, 6 and 9 dimensional domains of reality represented by the three kinds of numbers of number theory. The take-aways from all this are:

1.) Reality is holistically One. That means that everything, plants, animals, humans, solar systems. Galaxies, and the universe, are intimately connected at the most basic level.

 2.) Separation is illusory. The triadic nature of creation, perceived through the limited physical senses, is caused by the conscious drawing of distinctions.

3.) Consciousness is Primary, the triads perceived as the physical universe, are contingent upon the functioning of consciousness.

^†Discussed in previous posts and in a number of published technical papers.

WHAT IS LIFE?

Niels Bohr, the father of quantum mechanics, said: “It is not the business of the physicist to explain the nature of reality. Physics can only describe what we experience.” And, he was right. To investigate the nature of reality, you must go beyond physics. Erwin Schrödinger, who contributed a lot to the development of quantum theory as it now exists in mainstream science, said about quantum mechanics: “I don’t like it, and I’m sorry I ever had anything to do with it.” Because of his disillusionment with quantum physics, he turned his considerable intellectual talents to philosophy and biology, among other things. In a book containing essays he wrote later in life, published under the title of What is Life, he said: “Quantum physics reveals a basic oneness of the universe.”  And “There is no evidence that consciousness is plural”. 

Today’s mainstream biologists, in much the same way that mainstream physicists confuse form with substance, confuse life with the physical vehicles of life, i.e., bodies, and mistakenly conceptually separate life from consciousness. The discovery of gimmel, the manifestation of non-physical consciousness in every particle of physical reality, means that consciousness is intrinsic and ubiquitous in the universe. Physical bodies are the vehicles of consciousness, and life is the evolving manifestation of consciousness in the physical universe.

WHAT IS THE I AM?

What is the “who” that I am?

I have just finished reading Super Synchronicity by Dr. Gary Schwartz. Surprisingly, I found that I have experienced all of the super synchronicities he describes in this book in my own life, including the synchronicities of the experience of spontaneous appearances of certain numbers, animals, plants, and symbols. Not only that, my experience includes some of the same numbers, animals, plants, symbols, he describes. For example, Ravens and the number 11, significant synchronous experiences in Dr. Schwartz’s life, have also occurred in my life. I wrote about them briefly in my post on synchronicity a few days ago. Dr. Schwartz suggests that the experience of synchronistic appearances of specific things in your life may be taken as guidance and hints, specifically for you, from the One Mind of the universe.

The quantum physicist Niels Bohr and I were born on the same day of the same month, exactly 51 years apart. He died in 1962, the year I received my degree in mathematics and physics and began teaching mathematics. And two of the best students I had during my teaching years also had the same birthday as Niels Bohr. There is no apparent causal relationship between these facts. That makes them synchronicities - by definition. Was the One Mind trying to tell me something?

I was born in 1936, a number that reduces to 1, the beginning number. (1+9+3+6 = 19, 1+9 = 10, and 1+0 =1) And of course, it was the beginning of my life as Ed Close. Factoring, we have: 1936 = 44² = (4x11)². According to Kabbalah numerology*, the number 4 is quadratum, the alignment symbolized by a square oriented North, South, East and West. The number 11 is the “awake’ number, and its repeated appearance in one’s life points to the path to one’s destiny. It indicates that you are following the path to accomplishing what the universe wants you to do. The number 44 is the number of disciplined effort, indicating that focus and perseverance are needed to bring higher knowledge into the world.

What is the “who” that I am? I have discovered synchronicities with the thoughts and experiences of several sparks of consciousness, including Moses, Pythagoras, Diophantus, Pierre de Fermat, a German mathematician named Johann Liebknecht, a friend of Gottfried Liebniz, and a Tibetan monk. Am I the reincarnation of these men? In some sense, perhaps I am, but, ultimately, the “who” that I am is one with the Who that is the One Mind of the universe.

WHO ARE YOU? Can you discover synchronicities with others who lived in the past? I believe that until you find out who you are, you will not know what your reason for being is, and you will be like a ship on a stormy sea without a rudder until you know what your mission, your place in the universe is. If you become motivated to find your reason for being, and look for the guide posts from the One Great Mind, your life will become one filled with meaning and purpose. If you find this an important message, and embark on a journey of discovery, may your life be blessed. If you already know what your mission in life is, why you have been born to live in this place and time, maybe these posts will encourage you by letting you know that others have passed this way, and that the guidance of God and the great Masters of Spiritual Reality are always available to help you, whether you are aware of their presence or not. My hope for you is that you discover who you are as soon as possible. Peace and blessings.

*Kabbalah numerology is one of the most ancient systems of calculating the effects of numbers in our experience of the universe. In Kabbalah, the idea is that numbers can reveal how the mathematical structure of the universe and individual consciousness work together in our lives.

FERMAT'S LAST THEOREM & THE BUILDING BLOCKS OF THE UNIVERSE

Fermat’s Last Theorem

and

the Building Blocks of the Universe

©Edward R. Close, January 18. 2018

There is a deep connection between Fermat’s Last Theorem (FLT) and the geometric structure of the universe. It has been overlooked by mainstream science for nearly 400 years. The connection is simple, but has been obscured by abstract mathematical complexity and the myopic restrictions of academic specialization. It has been 353 years since Fermat died, and I think it is time for the importance of his work to be more fully recognized. This essay is an attempt to do that.

There are many observations about numbers that are easy to state and easy to understand, and yet very difficult to prove, and FLT is a prime example of this kind of statement. Fermat said that he had found a “marvelous” proof, but, because it was never found, and no one else could produce one, mathematicians considered FLT nothing more than a conjecture from 1637, when Fermat made the statement, until 1994, when British mathematician Andrew Wiles produced a 129-page proof that has been accepted by the community of professional mathematicians, allowing FLT to finally take its place as a legitimate mathematical theorem. Because of the complexity of Wiles’ proof, relying on theorems that were unknown in Fermat’s day, many mathematicians doubt that Fermat actually proved it.

Pierre de Fermat was a lawyer and judge at the Parlement of Toulouse, in France, but his real passion was mathematics. In 1637, he wrote the following statement in Latin in the margin of his personal copy of Arithmetica by Diophantus of Alexandria:

"Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.”

Which, translated into English is:

"It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."

The theorem stated in somewhat simpler English is:

Two whole numbers raised to any power greater than 2, and then added together, cannot be equal to a third whole number raised to the same power.

In simple mathematical notation:
Xⁿ + Yⁿ ≠ Zⁿ if X, Y, Z, and n are integers and n ≥3.
For ease of expression in this discussion, I shall call the equation Xⁿ + Yⁿ = Zⁿ Fermat’s equation. Note that the ‘equals’ sign (=) is replaced by ≠ (is not equal to) if Fermat’s Conjecture is true. Fermat’s proofs for the case n = 3 emerged from his writings after his death, but no general proof for all n > 2 was ever found.

FLT is a statement about numbers that is easy to state and easy to understand, but it went without proof for more than 300 years, even though the best and brightest mathematicians tried to prove (or disprove) it. Professional mathematicians correctly labeled Fermat’s Last Theorem a conjecture, which is what a mathematical statement should be called until it is either proved or disproved. It is likely that every mathematician alive in the last three centuries has tried to prove FLT, because the longer it went without resolution, the more famous it became, and resolving such a puzzle would assure the one who was first to solve it great recognition and fame; and mathematicians rank right up there with, or very close to, physicists, as a group of people with well-developed egos.

Karl Friedrich Gauss, arguably one of the greatest mathematicians who ever lived, was no exception. He invented modular algebra as a tool for use to investigate Diophantine equations, which is what Fermat’s equation is. [Diophantus specialized in solving equations with whole-number (integer) solutions. So, mathematicians call equations for which only integer solutions are sought, Diophantine equations.] Gauss proved Fermat’s Conjecture for n = 3, using modular algebra and complex numbers, but failed to be able to generalize the proof to greater values of n. When asked about his interest in Fermat’s Conjecture by Astronomer Wilhelm Olbers, Gauss said:

“I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.”

Could this disdain for FLT be the statement of a big ego, unwilling to admit that he couldn’t prove it, even though he tried? Probably so. Even a great man like Gauss can be blinded by his own brilliance. But I think Gauss can be forgiven his short-sightedness, because many brilliant thinkers believe that there are mathematical statements that can never be proved or disproved, and that FLT is an abstract theorem with little or no practical application outside of abstract number theory. Modern mathematicians, on the other hand, who believe the same things, should not be let off the hook so easily, because they have Gӧdel’s Incompleteness Theorems, which sheds some light on the questions of proof and provability.

In 1931, Kurt Gӧdel proved, with two decisive theorems, that no consistent system of mathematical logic is ever complete. He proved that within any logical system, there will always be statements that, even though they may be easy to understand, cannot be proved true or false within the system in which they are defined. Some mathematicians thought that FLT was actually such a statement, just as Gauss did, even though he died 76 years before Gӧdel published his proofs.

The fact is however, that Gӧdel’s Incompleteness Theorems do not say that there are propositions that can never be proved. They only say that there are propositions that cannot be proved using only the system of logic within which they were stated. Every logical system is based on one or more a priori assumptions. A meaningful statement that cannot be proved true or false within a given logical system, may actually be provable when the a priori assumptions of the system are either added to, or changed in some fundamental way.

I believe that Pierre de Fermat, and Diophantus of Alexandria, - and perhaps a few others – at least had inklings of the importance of Fermat’s Last Theorem as it relates to the building blocks of the universe, but modern mathematicians and physicists, and scientists in general, seem to have missed the point, mainly because of narrow academic specialization, coupled with a bit of human ego and pride.

With the discovery by Max Planck, already more than 100 years ago, that the mass and energy of the physical universe are meted out in multiples of a quantum unit, it should have been obvious that if the right units of equivalence are used, then Diophantine equations will be needed to describe the combinations of elementary particles that make up physical reality. That, however, has not been the case. Current mainstream science has not yet expanded its a priori assumptions to include quantization of the basic parameters of the physical universe. When we do so, as we have done with the definition of Triadic Rotational Units of Equivalence (TRUE), the true quantum units based on the physical features of the electron, Fermat’s Last Theorem emerges as a key mathematical concept in the process of revealing the nature of reality. Please let me explain:

The general Fermat equation, Xⁿ + Yⁿ = Zⁿ with X, Y, Z, and n equal to positive integers, is a special case of the more general quantum combination expression:

When the basic unit of measurement is defined as the smallest quantum equivalence unit, all cases of this expression are Diophantine equations, and when m = 1 and n = 2, we have the equation X₁ + X₂ = Z, which describes the linear actualization of the closure of integers; for example:

1 + 2 = 3, 2 + 2 = 4, 2 + 3 = 5,…etc.

When m = 2 and n = 2, we have (X₁)² + (X₂)² = Z², for which all integral solutions are quantum actualizations of Pythagorean triples; e.g., 3² + 4² = 5², 5² + 12² = 13², 7² + 24² = 25², etc. I have derived a simple ratio formula for producing the Pythagorean triples. See Appendix A of The Book of Atma, Published in 1977.

When m = 3 and n = 2, we have (X₁)³ + (X₂)³ = Z³, for which, Fermat’s Last Theorem tells us there are no integer solutions. This means that there are no quantum actualizations of this equation, because linear values cubed are volumes, and that is why there are no combinations of two quarks forming a larger particle. Two quarks cannot combine volumetrically to form a symmetrically stable third particle. However, when m = 3 and n = 3, we have: (X₁)³ + (X₂)³ + (X₃)³ = Z³, and we find there are quantum actualizations of this equation. For example:

3³ + 4³ + 5³ = 6³, and 1³ + 6³ + 8³ = 9³, etc. 

This is why quarks combine in threes to produce the symmetrically stable particles known as protons and neutrons. This is just the first example of the importance of Fermat’s Last Theorem in understanding the quantum combinations that form the subatomic particles that make up the elements of the Periodic Table.

I proved Fermat’s Last Theorem in 1964, 327 years after Fermat’s statement, and 30 years before Wiles’ proof. I published the original proof as an appendix to in The Book of Atma in 1977.  I documented the proof and began submitting it to professional mathematicians in 1965. For that reason, I refer to it as FLT65 in my subsequent writings. (See posts on Proof of Fermat’s Last Theorem on this blog and Reality Begins with Consciousness). Since 1965, I have submitted the proof to more than fifty mathematicians, both professional and amateur. Out of the fifty plus, four have accepted it as valid, two professional mathematicians and two capable mathematicians with degrees in sciences that require familiarity with advanced mathematics; but, only one has publicly defended it. Why is this?

It must be said in passing, that the validity of the use of FLT in the application of the Triadic Dimensional Vortical Paradigm (TDVP), developed by Dr. Vernon Neppe and myself in 2011, to quantum physics is completely independent of the validity or invalidity of my 1965 proof, because FLT has long been known to be true for values of n between 3 and 9, the range of TDVP. But, if FLT65 is valid, why hasn’t it been accepted by the community of number theory mathematicians, as has Wiles’ proof? I have published what I see as the reasons, and details of this story in other posts on this website (search the blog archives for Fermat’s Last Theorem) but, my intent in this post is to explain it as briefly and clearly as I can.

The FLT65 proof relies on a very simple basic mathematical theorem known as the Division Algorithm. More specifically, it depends on a corollary of the Division Algorithm that says that one integer, call it A, is a factor of another integer, call that integer B, if, and only if, the remainder when B is divided by A is zero. For example, 9/2 = 4, with a remainder of 1, while 9/3 = 3 + 0. So, 3 is a factor of 9 but 2 is not. The requirement for a zero remainder is patently self-evident for integers, and is it proved in FLT65 for algebraic polynomials consisting of real numbers. This part of FLT65 is never questioned by skeptical reviewers.

In FLT65, the Fermat equation for n equal to a prime number greater than 2 is rewritten as Zⁿ - Yⁿ = Xⁿ and factored into two polynomials, one a first-degree binomial (a polynomial of two terms, consisting of the variable Z plus an integer constant) and the other an (n-1)-degree polynomial with n terms:

Zⁿ – Yⁿ = (Z-Y)( Z^n-1 + Z^n-2Y + Z^n-3Y² +•••+ Y^n-1) = Xⁿ

The factored form of the Fermat equation is chosen so that the (n-1)-degree polynomial must be equal to the nth power of an integer factor of X. This means that the (n-1)-degree polynomial factor must be divisible by that integer, a factor of X. None of this is disputable, and was not disputed by any of the reviewers.

The integer divisor, because its value is unknown, and because the integers are closed with respect to addition, can be represented by the variable Z minus an integer constant. When the (n-1)-degree polynomial factor of the Fermat equation is divided by the integer represented by Z minus a, where a is an integer constant, the remainder is a polynomial comprised of positive integers, and thus cannot equal zero for any integer solution of the Fermat equation. The fact that the remainder cannot equal zero for any integer solution of the Fermat equation means that, by the Division Algorithm corollary cited above, the (n-1)-degree polynomial cannot be divisible by an integer factor of X, which proves FLT for all n.

Is FLT65 a valid proof of FLT, or not? It seems that this should be a question that could be answered decisively, very quickly. But, given the 350-year history of FLT, mathematicians consider the claim of a simple proof an extraordinary claim, and, of course, an extraordinary claim requires extraordinary proof.

The question is: If FLT65 is so simple that given the Division Algorithm and its corollaries, the proof can be described in two pages, in contrast with Wile’s proof of 129 pages, given both Ribet’s theorem and a special case of the modality theorem for elliptical functions, why has FLT65 not been accepted by more than a handful of reviewers?

I have answered this question in the History of FLT65 and other discussions previously posted, but the reasons can be summarized as follows:

First, there is a cultural bias in the community of professional mathematicians against considering the possibility that anyone outside the academic mathematics community might be able to produce a valid proof of FLT. This is an endemic attitude epitomized by: “If I can’t prove it, no one can, and it’s not that important anyway.” (Reminiscent, e.g., of Gauss’ denial, and definitely reflected in Descartes’ attempts to discredit Fermat.)

I developed FLT65 while teaching secondary-school mathematics, shortly after earning my degree in mathematics. The first professional mathematician to whom I submitted FLT65, was a math professor at a Midwestern University, who also happened to be the President of the state’s Academy of Sciences at the time. He returned my proof with a brief note that said: “Your proof is invalid because, if true, it would hold for n = 2.” Of course, the case n = 2 of the Fermat equation is the Pythagorean Theorem equation, with integer solutions called the Pythagorean triples, as noted above. I was stunned. His answer was unbelievable! It revealed that he hadn’t read the proof at all. The case n = 2 was eliminated on the first page!

Most of the university mathematics professors to whom I submitted FLT65, simply ignored it. This is actually quite understandable, because they receive hundreds of half-baked proofs and mathematical ramblings from would-be mathematicians every year. Some number theory professors have form letters they send out in response to such unsolicited proofs, while others just refuse to waste their time reading purported proofs submitted by anyone unknown to them.

Second, mathematicians who tried to disprove FLT65 (there were four) were not willing to go beyond trying to disprove it, probably largely because of the endemic attitude of disbelief cited above, or because of the fear of loosing credibility in the professional community. One of these reviewers thought that the notation used in FLT65 was confusing, and suggested that if the standard notations for variables and constants, integers and rational numbers were used, the error in the reasoning would probably become clear. I rewrote FLT65, changing the notation as appropriate, and found that it made no difference, since for integer solutions of the Fermat equation, the only distinction necessary was between variables and constants, which was already done in the original FLT65, and for integer solutions, both variables and constants are integers by definition.

Finally, my submittals of FLT65 to professional mathematicians between 1965 and 2013, a period of nearly fifty years, were sporadic because of my career. Working as a systems analyst, environmental engineer, and consultant, I was involved in projects that required frequent moves from state to state, across the country, and out of the country for prolonged periods. As a result, some reviewers lost interest, and some. unfortunately, have passed away. Over the years, I have kept a file of all meaningful correspondences and attempts to disprove FLT65.

While FLT65 has failed to get support from any mathematician with much influence in the professional mathematics community, no one has been able to actually refute it. All the attempts to do so have involved one or more of the following approaches: 1) The proposition that the Division Algorithm and its corollaries may not apply to integers. 2) The production of a “counter-example”, a set of three integers which, when substituted into the polynomials on FLT65, appear to contradict the Division Algorithm corollary. 3) The argument that even though specific examples failed to disprove FLT65, they could represent a loophole in the proof.

1)    The proposition that the remainder corollary of the Division Algorithm might not apply to integer solutions of the Fermat equation, was suggested by several reviewers. However, none of them offered a general proof of this. In fact, they couldn’t because the opposite is true: The corollary applies over the field of real numbers, which includes the integers, so it applies to integer polynomials. This is stated in FLT65 and demonstrated in the proof of the Division Algorithm and its corollaries, included as the first part of FLT65.

2)    Because of their belief that FLT65 could not be valid, some reviewers tried to produce counter-examples with integer values that appeared to contradict the remainder corollary. This approach proved to be exceptionally subtle and misleading because one can indeed find integers that, when substituted into the n = 3 Fermat equation’s second-degree (n-1) factor, will produce a value that contains the divisor as an integer factor, even though the remainder is non-zero. It was easy to show, however, that the integers the reviewers chose for such examples were not solutions of the Fermat equation. For that reason, the approach was a form of misdirection. It focused the attention on a demonstration that had nothing to do with FLT. Not only that, if anyone could actually produce a counter-example, it would not only disprove FLT65, it would disprove Wiles' proof as well, because it would produce an integer solution for the Fermat equation.

3)    One reviewer, who appeared to be well-qualified to review FLT65, announced that he had disproved FLT65 with a counter-example. When shown that his example was not relevant to the Fermat equation, he admitted that his “counter-example” did not disprove FLT65, but still maintained that it revealed a loophole in the proof, because if integers could be found that produce a value for the polynomial factor of the Fermat equation that contains the divisor as an integer factor, even though the remainder is non-zero, who is to say there isn’t at least one set of such integers that would actually produce an integer solution to the FLT equation?

Position #3 gave me some pause, until I realized it could only be true if proposition #1 were true, i.e., there would have to be integer polynomials for which the Division Algorithm and its corollaries did not hold. But, the Division Algorithm and its corollaries are proved across the field of real numbers in the first part of FLT65, and integers are real numbers. To see the truth of this clearly for the Fermat equation, one only has to do the following:

Assume there is an integer solution for the Fermat equation for some integer value of n ≥ 3, and substitute the three integers of the solution into the factored Fermat equation, (Z-Y)( Z^n-1 + Z^n-2Y + Z^n-3Y² +•••+ Y^n-1) = Xⁿ. Then the integer polynomial f(Z) =  Z^n-1 + Z^n-2Y + Z^n-3Y² +•••+ Y^n-1 must contain a factor of X. (In fact, it must contain the factor raised to the nth power). And since X and Z are positive integers, Z is larger than X, and integers are closed with respect to addition, there is a positive integer a, such that the factor of X is equal to Z – a. Then the integer polynomial f(Z) divided by Z – a yields a remainder equal to:

a^n-1 + a^n-2Y + a^n-3Y² +•••+ Y^n-1, and since a and Y are positive integers, the remainder is non-zero for all values of a and Y. But, the integer polynomial f(Z) can contain Z–a, if, and only if, the remainder is zero.

If there is any lingering concern that when the integer polynomials, f(Z) and Z–a, are reduced to single integers, A and B, respectively, (as they certainly can be, if there are integer solutions for the Fermat equation, because integers are closed with respect to addition and multiplication), A might still contain B as a factor, it is dispelled by the following demonstration:

There is no question that, if there is an integer solution (X,Y,Z) of the Fermat equation, the equation can be expressed as the integer polynomials displayed above. And, as integer polynomials, Z–a divides f(Z), if and only if the remainder is zero. Therefore, if we set the remainder equal to zero and solve for a, and determine the values of X, Y and Z for each value of a, we will obtain exactly n-1 solutions for the Fermat equation. When we solve for a, however, we find that a cannot be an integer, and therefore, if two of the three X,Y,Z values for any solution are integers, then the third is a non-integer. So, solving for a, produces n-1 non-integer solutions to the Fermat equation, and one additional solution is provided by a = Z which implies X = 0, a legitimate solution of the Fermat equation. This means that we have the n solutions of the Fermat equation, and by the Fundamental Theorem of Algebra (FTA), there are no more solutions.

The Fundamental Theorem of Algebra states that every non-zero, single-variable polynomial of degree n with complex coefficients has exactly n complex roots.

For any integral solution of the Fermat equation, f(Z) is a non-zero, single variable polynomial of degree n, and the coefficients of f(Z) are real numbers, and all real numbers are complex numbers with the imaginary term equal to zero. So, there cannot be more than n solutions to the Fermat equation, and none of them are positive integer solutions with X, Y and Z equal to positive integers. 

Conclusion: All of the legitimate questions raised by reviewers of FLT over the years have been eliminated and resolved. Therefore: 

The FLT65 proof is complete and valid as it was written in 1965.

COMMENTARY AND TRIBUTE TO PIERRE DE FERMAT:

The FLT65 proof contains concepts that would indeed have been available to Fermat, even though they are probably in different form and with different notation than he would have used in 1637. I consider FLT65 to be an elegant proof, because it relies on a deep truth about the fundamental mathematical operation of division, which applies to all real numbers. I have also validated the FLT65 proof in previous written presentations using the logic of infinite descent, Fermat’s favorite method of proof. This means that Fermat definitely could have found his “marvelous” proof. 

To Pierre de Fermat I want to say:

Requiesce in pace, Pierre, tuus lumen mathematicum esse iudicavit!