Wednesday, July 11, 2018




© Edward R. Close, July 11, 2018

With  Philosopher Dr. David Chalmers

In 1996, at Tucson II, toward a science of consciousness, and in my third book, Transcendental Physics, first published in 1997, I introduced the concept of the non-quantum receptor. The concept is simple. It is related to Max Planck’s discovery of the quantization of energy and matter, a discovery that revealed the fact that  there is a bottom to physical reality. That fact was totally unknown to science before Planck’s discovery. It means that things can only be divided so far: just to the smallest quantum, not beyond. Similarly, there has to be a bottom to the chain of transfers of information-laden energy from objects of observation into the brain of the observer, where it contributes to an image in the consciousness of the observer. But that image cannot be composed of quanta of matter and energy because it can vary in size and the brain is not large or complex enough to hold the information of trillions of observations and the memories of a lifetime, if they are composed of  quanta of a finite size. Also, the consciousness of the observer appears to be more than the sum total of such images. If consciousness cannot be composed of matter or energy, what is it composed of?


With the development of the Calculus of Dimensional Distinctions in 1989, Dimensional Extrapolation in 2010 and TRUE quantum units in 2011, God’s deepest secret in the physical universe, the existence of non-physical gimmel, something not measurable as mass or energy,
in every bit of stable physical structure, has been revealed. My friend and research partner since 2008, Dr. Vernon Neppe, often chides me for saying the math leading to this discovery is so simple that any bright high school student can understand it. Despite the fact that some people highly educated in the physical sciences have not understood it, the math really is quite simple. Why, then, do most mainstream scientists fail to understand it? The answer is simple: It’s because they have too much to unlearn.

Today, I have copied the March 14, 2016 post and pasted it in below largely as it appeared then, as an introduction to today’s post. It is followed by a condensed form of the main concepts of TDVP, the paradigm shift to a consciousness-based model of reality the details of which can be found in many posts published since then, that reveal God’s deepest secret. It is appropriate to call it God’s deepest secret because it exists at the deepest physical level of the universe. I still believe that anyone can understand it; anyone, that is, who is willing to think about reality in a different way, a way that lies outside the materialistic box of today’s mainstream science.

God’s deepest secret, like most truths, is utter simplicity. I could state it here in a few words, but without traversing the logical terrain in which we dwell in everyday awareness, to arrive at this deepest secret, it would sound like a meaningless tautology. But it is a profound secret, in effect, hidden in plain sight.

There is a pattern of surprisingly complex phenomena, concealed behind the reality we perceive, many orders of magnitude smaller than the smallest thing we can perceive with our physical senses: Only about four to five percent of reality is perceptible through our physical senses, and the average conscious mind functions on only about four to five percent of the brain power locked up inside the human skull. This is not an accident; this pattern of hidden secrets is pervasive throughout the universe. The Hubble space probe has revealed that only about 4.9% of the universe is made of ordinary matter and energy, the nature of the rest, currently called ‘dark matter’ and ‘dark energy’, is unknown to mainstream science. God’s deepest secret is hidden because reality is quantum in nature, ostensibly made up of extremely tiny distinctions of mass, energy, space and time, perceived as separate. But, we find that it is  actually intimately connected when the other ninety-five percent is revealed. Because reality is quantized, God’s deepest secrets are expressed in mathematical terms because reality consists of whole-number multiples of quantum equivalence units. This is why the language of science is mathematics.

What are these secrets, and how and why are they hidden? First of all, quanta are hidden from direct observation and measurement because they are so very small. Everyone knows that elementary particles are very, very, very small, so small that it’s hard to imagine. It would take about one billion (1,000,000,000) Hydrogen atoms laid side-by-side to reach across your little fingernail, and the proton at the center of the Hydrogen atom is about one one-thousandth of the size of the atom. And the electron is even much smaller. But all you really need to know for this discussion is that. while they are almost unimaginably small, they are finite. The purpose of this post is not to impress you with how much I know, so I won’t be talking about all of the particles of the so-called ‘particle zoo’. Most of them only exist for fractions of a nanosecond as debris from reactions engineered in particle colliders, and thus they are almost totally irrelevant to this discussion.

There is another way that the secrets of the quantum world are hidden, unfortunately; it is by the inappropriate application of mathematical tools. Mathematically logical procedures effectively simplify and explain reality, but when misused, i.e. applied inappropriately, they can confuse and conceal; and this is exactly what has happened in quantum physics. Let me explain: ‘The’ calculus, as used today, was devised by Leibniz and Newton more than 300 years ago, based on ideas developed by Fermat and Descartes, and even earlier, by Archimedes. It depends on the concepts of continuity and infinite divisibility; but the quantized nature of reality, which was discovered by Max Planck more than 100 years ago, reveals a world of discreteness and finite indivisibility. The inappropriate application of the differential calculus to quantum phenomena has produced confusion, obfuscations and even some of the so-called weirdness of quantum physics. Before we get into the details of how we can remedy this inadvertent mathematical blunder, I want to write a tribute to Max Planck, the father of quantum physics.

Max Karl Ernst Ludwig Planck was born in Kiel, Germany in 1858. As a young student, he showed promise in music, and played the piano and organ extremely well. But as he prepared for university an exceptional mathematics teacher named Hermann Müller turned his interest toward science. In spite of a physics professor who told him that physics was essentially a complete science, with nothing of any importance left to be discovered, he decided to study the second law of thermodynamics, specifically the dissipation of energy from hot materials by radiation. In 1900 -1901, he developed the theory that energy occurs, not in a continuous manner, but in discrete packets that he called quanta. This was a radical idea, but it fit the experimental evidence perfectly. His new theory explained why the glow of a red-hot iron fireplace poker goes from red to white as more heat is added, without going through any of the other colors in between. Planck was not trying to revolutionize physics, he just wanted to find an explanation for the phenomenon he was studying. But this elegantly simple discovery started a revolution in physics that would be carried forward by Albert Einstein, Niels Bohr, Werner Heisenberg, and Erwin Schrödinger and change the science of physics forever. Planck was awarded the Nobel Prize in Physics in 1919 for this discovery.

Planck, a Christian, openly opposed the national socialist movement (Nazism) that was under way in Germany at the time, and tried to intervene on behalf of Albert Einstein and other Jewish scientists who were being publicly maligned by Adolf Hitler, who was catholic, and had the support of the Catholic Church in Rome. Planck  even resigned his position as president of the Kaiser Wilhelm Gesellschaft in 1937 in protest. His son, Erwin Planck was executed in 1945 for involvement in a failed attempt to assassinate Hitler, and Planck’s home was destroyed by Allied bombing during World War II. When the war ended in August 1945, his discovery was again recognized by the scientific community as ground-breaking. The research center was renamed the Max Planck Institute, and he was named as its director. Max Planck was considered to be one of the most important men of modern science when he died two years later, in 1947.

My favorite Planck quotes are:

As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as the result of my research about atoms this much: there is no matter as such. All matter originates and exists only by virtue of a force. We must assume behind this force the existence of a conscious and intelligent Mind. This Mind is the matrix of all matter.

I regard Consciousness as fundamental. I regard matter as derivative from Consciousness.

“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

The last quote is still relevant today because it explains, at least in part, why mainstream science has not recognized and followed up on the many clear indications from quantum physics experiments that consciousness is a fundamental part of reality.

Max Planck discovered that energy flow only occurs in exact multiples of an extremely tiny unit of energy called a quantum, and Einstein proved that energy and mass, the basic measures of matter, are equivalent and can be converted from one to the other. The famous equation E=mc2  expresses the equivalence of energy and mass when everything is represented in consistent units of measurement. The simple fact that mass and energy are two mathematically equivalent quantized forms of the same substance of physical reality has revolutionized science and technology as nothing else has done in the history of science on this planet. The multitude of electronic devices that have so radically changed the world since 1935, were unimaginable before this discovery. But the full implications of Planck’s discovery have not yet been realized. When they are, the world will be changed more radically than it has been ever before. 

Seventeenth century French mathematician Pierre de Fermat discovered the elegant logic of proof by infinite descent. Proving a hypothesis by infinite descent is probably beyond the average high school algebra student, but the concept is easily understood. Here’s how it works: Suppose we want to determine whether or not something that depends on a variable represented by x is true. If we assume that it is true for some value x = N, and we can show that, if it is true for x = N, then it is also true for x = N -1, we have a way of descending from any assumed true case, however large, to a case where N is equal to 1. Then, if we can show that the simple case, the case when N =1, is false, then the hypothesis is false, because assuming it to be true for an arbitrary case leads to a contradiction. The idea of infinite descent from the largest scale of the expanding universe to the smallest quantum is central to the quantum mathematics of TDVP.

Proof by infinite descent is particularly applicable to what we call Diophantine equations (equations with integer solutions). In particular, equations of the form Xn + Yn = Zn, where X, Y, Z, and n are positive whole numbers. If we look at the equations generated by this expression as n goes from 1 to infinity, we see some equations that any high school algebra student will recognize: When n = 1, we have X + Y = Z, which expresses the simple fact that any two integers (whole numbers) added together will always give us another whole number. For example, 1 + 2 = 3. Mathematicians generalize this fact as an axiom, stated as follows: The integers are closed with respect to addition.
When n = 2, we have X2 + Y2 = Z2. The Greek mathematician Pythagoras discovered that, this equation is always valid when X, Y and Z are the lengths of the three sides of a right triangle. Our high school algebra student will recognize this as the Pythagorean Theorem. This theorem is the basis of the  trigonometric functions and thus is of great use in many scientific and engineering applications. Examples of integer solutions are: 32 + 42 = 52, and 52 + 122 = 132. In general, (2ab)2 + (b2  – a2) = (b2 + a2), where a and b are any two positive integers and b > a. Note that this theorem connects arithmetic with plane geometry, and that it is a Diophantine equation with integer solutions.

When n = 3, we have X3 + Y3 = Z3. It turns out that this equation has no integer solutions; that is to say, if two of the three numbers are whole numbers, the third one cannot be a whole number. In fact, it turns out that for any value of n larger than 2, there are no integer solutions. This is known as Fermat’s Last Theorem. Fermat said he had proved it in 1637, but after his death, his proof was never found, and it remained unproved despite the efforts of some of the greatest mathematicians for more than 300 years. I proved it to my satisfaction 1n 1965, and British mathematician Andrew Wiles produced a proof that is generally accepted in 1994. For our purposes in the quantum mathematics of TDVP, who proved it and when it was proved makes no difference, since for this discussion, we need go no farther than n = 9.

How does this  relate to what I’ve called God’s Deepest secret? That’s very simple: Ever since Max Planck’s discovery, we have known that we exist in a quantized reality, a quantum world, if you will, in which all phenomena are quantum phenomena. This means that, with the proper quantum equivalence unit as the basic unit of measurement, all equations describing the physical universe are reducible to Diophantine equations with integer solutions. Using Large Hadron Collider data, we have naturalized the mass of quarks and protons to the mass of the electron, the smallest mass that makes up the natural elements. Then Fermat’s last theorem tells us that two quarks cannot combine to form a stable structure, but three can, because the equation X3 +Y3 + Z3 = Q3 does have integer solutions, e.g., 33 +43 + 53 = 63. In addition, we find that it is mathematically and physically impossible for up- and down-quarks to form stable protons without a third something that is neither mass nor energy. We called that “something gimmel. The fact is, there would be no stable universe if it consisted only of matter and energy.

This simple fact turns the current materialistic mainstream paradigm on its head. As Planck said, there is no matter as such, elementary particles are not particles, and materialism is refuted. But I’m getting ahead of the story. Especially for readers with an academic background in science, I have to explain how we (Dr. Vernon Neppe and I) developed The Triadic Dimensional Vortical Paradigm (TDVP) from this discovery, and how it refutes materialism as a basis for science.

Before you jump to the conclusion that I’m declaring that everything physicists have been busy doing for the past eighty or ninety years is a waste of time, I want you to know that we’re not saying that. In fact, TDVP would not be nearly as successful as it is without the results of quantum experiments and the data from the Large Hadron Collider. Just as relativity and quantum physics did not invalidate everything in classical physics, TDVP does not invalidate everything in the standard model of current mainstream physics. Relativity and quantum physics have explained things that classical physics could not, and TDVP explains things that the standard model cannot.

The position that mainstream physicists have forced themselves into with the advent of quantum physics is very curious. They have promulgated the idea that quantum physics is so weird that it cannot possibly be understood. Many physicists and their students seem to delight in this disclaimer! This curious attitude is reflected in statements by leading physicists like the following:

Niels Bohr:
“If you aren't confused by quantum mechanics, you haven't really understood it.
(Implying that, if you really understand it, you will definitely be confused.)

Everything we call real is made of things that cannot be regarded as real.”

Steven Weinberg
The more the universe seems comprehensible, the more it seems pointless.”

Richard Feynman
“I think I can safely say that nobody understands Quantum Mechanics.

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school: … It is my task to convince you not to turn away because you don't understand it. You see, my physics students don't understand it. ... That is because I don't understand it. Nobody does.”
(Nobel Lecture, QED, The Strange Theory of Light and Matter)

The more you see how strangely Nature behaves, the harder it is to make a model that explains how even the simplest phenomena actually work. So theoretical physics has given up on that.”

The attitude that quantum reality is too weird to be understood, that reality is basically meaningless and that theoretical physicists must give up trying to explain how even the simplest phenomena actually work is decidedly unscientific.

There is no reason to believe that because there are quantum phenomena that cannot be explained within the current paradigm, they can’t be explained at all. It is far more rational and scientific to suspect that some of the assumptions of the current paradigm are, just as has been the case with classical physics in the past, wrong or incomplete. With a new more comprehensive paradigm, the same phenomena may be completely normal and understandable.

So why are most mainstream physics professors pushing this “don’t even try to understand it” attitude? It is because, even though they can’t explain even the most basic of quantum phenomena, they know it leads to unquestionably important results. Richard Feynman, perhaps the most bluntly honest of the lot, hit the nail on the head when he said: “I don’t understand it.” He should be respected for his honesty; but when he followed this confession with the declaration: “Nobody does”, he displayed the arrogance of mainstream science, an arrogance that says: If mainstream scientists can’t understand it, no one can.

Why this curiously unscientific attitude? Is it because of an unwillingness, or perhaps even an inability to think outside the limiting box of materialism? Qualia, a word used to indicate common conscious experiences like the taste of a tropical fruit, the beauty of a mountain stream, appreciating a poem or song, or the experience of falling in love, are not considered to be real by the physicalist, and consciousness itself is considered secondary to matter and energy.

The fact that the material things physicalists hold to be real actually fade away when pursued to the quantum level, or the cosmic level, beyond the limits of the physical senses, is very puzzling to them because it is counter-intuitive and inexplicable in their materialistic worldview. They simply can’t accept Plank’s view that there is no matter as such.

When consciousness is taken as primary, the universe available to our limited physical senses proves to be a very small part of reality, and a part that is not what it appears to be. Choosing whether to look at reality this way, or as the materialist does, however, is not an arbitrary choice, because if we choose to model reality as matter and energy evolving through space-time, paradoxes appear, but when we model reality as originating in the conscious drawing of distinctions, the paradoxes are resolved. Several instances of this explaining of the “unexplainable” have been identified and published in our books and peer-reviewed papers. I’ll list some of them below. We’ve found that the primacy of consciousness is inescapable when the relativistic and quantum nature of reality is taken seriously, and the logic of a quantum calculus, with a minimum quantum equivalence unit as the basic unit of measurement is developed.

The process of developing natural quantum equivalence units is straight-forward, very much like the development of the natural units called Planck units. The difference lies in what is chosen to use to define the basic units. Planck chose to use known universal constants, specifically, c, the speed of light, the gravitational constant, the Coulomb and Boltzmann constants, and the reduced Planck constant as the basic units of measurement. Planck units are defined by setting these constants equal to unity (one). This process is called naturalization. Planck units are called natural units, as opposed to arbitrary human-based units like feet and pounds or meters and grams. Doing this simplifies computations involving the extremely small measures of physical properties and extremely high velocities. This is appropriate for quantum physics where we are dealing with extremely small objects spinning at enormous speeds, - up to the speed of light.

We are accustomed to units of measurement like inches, feet, pounds, centimeters, meters, grams, etc., but their sizes are arbitrarily chosen in relation to everyday objects at the macro-scale for practical purposes. But, we can choose basic units of any size we please, and for quantum phenomena, the logical choice is to use the measurements of the smallest of the  quantum objects making up the natural elements of the periodic table as the basic quantum units of measurement. This is why I chose the mass of the electron as the basic unit of quantum mass. from which we developed the volumetric unit we call the Triadic Rotational Unit of Equivalence (TRUE), the basic unit of the  Calculus of Dimensional Distinctions. With this approach, we have explained, and continue to explain, many things that are inexplicable within the current paradigm of scientific materialism. Here's a partial list:

Why protons are composed of three quarks
Why the Cabibbo quark mixing angle is exactly what it is
Why most of the particles of the “particle zoo” are ephemeral
Why fermions have a ½ intrinsic spin
Why Hydrogen atoms have no neutrons
Why there are neutrons and deuterium atoms
Why the mass of the proton is exactly what it is
Why the mass of neutron is exactly what it is
Why the neutron is not anywhere near as stable as the proton
Why protons are so stable
Why Hydrogen is stable
The role of Helium and neon
Why the life-supporting elements are abundant
Why the universe is expanding
Why elementary objects are spinning
Why the speed of light is what it is
Why there is no matter as such
Why quanta are not particles
What elementary particles actually are
What quantum entanglement is
What dark matter and dark energy really are
What creates mass
What gluons actually are,
and much, much more.

The discovery of gimmel completes the picture of reality. When the role of gimmel is revealed, it’s like suddenly seeing the missing pieces of a three-dimensional jigsaw puzzle. Without gimmel, we only see random bits of matter whirling around and flying apart in space and time, with the bits of matter interacting dynamically, propelled hither and yon by forces that are related to the mass of the whirling bits by the equation E = mc2. But something is missing, and it turns out that the missing part is by far the most important part of the picture. It is the part that links consciousness with the physical universe.

Gimmel is the missing link with non-physical consciousness that had to have been there from the beginning. Without it, no stable universe could form. Gimmel was God’s deepest secret hidden in the finite universe, and it remained hidden for so long because scientists focused their attention exclusively on visible objects, things that have weight and occupy space and their motions and changes, things with measurable amounts of mass and energy. Gimmel is not measurable as either mass or energy, even though it occupies considerable amounts of volume within atomic and subatomic structure.

The discovery of gimmel has revealed the fact that a pervasive general form of consciousness plays the defining role in the creation, sustenance and dissolution of the eternally changing features of the physical universe. What is the role of individualized consciousness? It’s the drawing of distinctions. The first distinction is the distinction of self from other, which allows the drawing of multiple distinctions in the other. The world you experience as a conscious being is composed of distinctions of various kinds, some of which you can manipulate.

George Spencer Brown was right when he said:
 “… a universe comes into being when a space is severed or taken apart… By tracing the way, we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that seems almost uncanny, the basic forms underlying linguistic, mathematical, physical and biological science. … Although all forms, and thus all universes are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe.” – Laws of Form, George Allen and Unwin Ltd. London, 1969

We divide reality into distinct parts, so, with this insight into the nature of the laws of form that govern the logical structure of reality, why didn’t G. Spencer Brown discover gimmel? It was because he failed to see the connection between pure mathematics and physical reality. Had he done so, he would have discovered the necessity of gimmel. It is very interesting how very close he came. In his notes on Chapter 12 of Laws of Form, he says:

“Let us consider … the world as described by the physicist. It consists of a number of fundamental particles which, if shot through their own space, appear as waves, and are thus, of the same laminated structure as pearls or onions, and other wave forms called electromagnetic ,,, travelling through space with a standard velocity. All these appear bound by certain natural laws which indicate the form of their relationship. …

Now the physicist himself, who describes all this, is, in his own account constructed of …the very particles he describes … obeying such general laws as he himself has managed to find and to record. Thus, we cannot escape the fact that the world we know is constructed in order (and thus in such a way as to be able) to see itself. This is indeed amazing. … But in order to do so, evidently it must first cut itself up into at least one state which sees, and at least one other state that is seen. In this severed and mutilated condition, whatever it sees is only partially itself. … In this condition it [reality] will always partially elude itself.”

It appears that Brown was actually on the verge of discovering gimmel, but fell short because he chose to interpret the calculus of indications as a logical system ontologically separate from physical reality. In Appendix 2 of Laws of Form: The Calculus Interpreted for Logic, concerning the relationship between mathematical logic and existence, he said:

 Existential interpretations [of the calculus], where they are necessary at all, can be confined to entering and leaving the problem, and need not occur in the course of solving it.”

On the other hand, the calculus of dimensional distinctions, developed in the TDVP, is linked to physical reality by using the physical characteristics of the electron as the basis for defining the unit of quantum equivalence, which, when interpreted volumetrically, becomes the Triadic Rotational Unit of Equivalence (TRUE), the basic unit of the calculus. This makes the logical structure of the calculus of dimensional distinctions consistent with the logical structure of physical reality at every step of the process of application, not just when entering and leaving the process of problem solving. Thus, the logical structure of the CoDD reflects the logical structure of reality.

Another example where Brown nudged up against the CoDD, is in the treatment of imaginary numbers. In the preface to the American Edition of Laws of Form he says:

 “Apart from the standard university logic problems, which the calculus published in this text renders so easy that we need not trouble ourselves further with them, perhaps the most significant thing, from the mathematical angle, that it enables us to do, is use complex values in the algebra of logic.”

Complex values are numbers of the form a +bi, where i is the square root of negative one, known as the basic unit of “imaginary” numbers. In contemporary mathematics, imaginary and complex numbers are used extensively, and the advanced mathematical techniques necessary for the development of modern conveniences like the many electronic devices we use so ubiquitously today, would be impossible without them. This is why, in my opinion, it was very unfortunate that they were called imaginary numbers. There is nothing imaginary about them. They represent the link between ordinary 3-D space and other dimensional domains, which are very real. But, Brown narrowly missed this point as well. In Chapters 7 - 11 of Laws of Form, he introduces imaginary numbers, time and a rudimentary form of memory, but fails to connect imaginary and complex numbers with the multi-dimensionality of reality, where time is the fourth dimension.

These examples of where G. Spencer Brown’s work came so close to revealing the connection between consciousness and the physical universe is reminiscent of a famous statement made by philosopher psychologist William James, often called the father of modern psychology:

“Our normal waking consciousness, rational consciousness as we call it, is but one special type of consciousness, whilst all about it, parted from it by the flimsiest of screens, there lie potential forms of consciousness that are entirely different.”

Many of the details of the effects of the discovery of gimmel on mathematics, physics and biology are yet to be fully realized, but, in TDVP, the conclusion is clear: We exist in a multi-dimensional reality, and the logical structure of that reality is reflected in the logical structure of pure mathematics when the basic unit of measurement is the electron. The efficacy of this approach is validated time after time as we explain more and more phenomena that remain a mystery in the paradigm of the standard model of particle physics.

Consciousness is the missing piece of the puzzle in the current mainstream paradigm of scientific materialism. Using the LHC-data-based mathematics of the calculus of dimensional distinctions, and using the Pythagorean Theorem in the dimensional interpolation from one dimensional domain to the next, we have discovered gimmel, the non-physical part of the atomic structure of the universe. This third form of the essence of reality conveys logical structure in exact, mathematically determinable amounts into the atoms of the periodic table of elements, and the amounts of gimmel, measured in TRUE (volumetric quantum equivalence units) are greater in the life-supporting elements than in elements that are non-life supporting and/or hazardous to organic like forms, reflecting the intelligent design mentioned by Planck.

By comparing the structure of reality, gimmel included, with the logical structure of pure number theory, we see that reality consists of nine finite dimensions embedded in the trans-finite and infinite dimensional domains. The first three-dimensional domain is what we think of as 3-D space, the second three-dimensional domain is temporal, i.e., a 3-D time domain, and the third three-dimensional domain is the domain of consciousness. None of these is truly separate, but our physical senses are generally limited to perception of three dimensions of space, one moment in time. And one quantum of consciousness: the observer. So. In this sense, we are always partially experiencing five dimensions, three of space, one of time, and one of consciousness.

The first dimension of the temporal domain includes the past, present and future, which may or may not be linear, but we only have direct awareness of the present; the past and future are both comprehended by logical inference. The second dimension of time can be visualized conceptually by imagining your experience of past, present and future spread out as a personal timeline, or life-track, created by the conscious distinctions you draw and the choices you make. If by dimensional extrapolation, you move into the three- dimensional temporal domain and become aware of your own timeline life-track and the time lines of others, you will see them existing in, and defining, a 2-D plane or 3-D manifold (a curved surface) spread out below you.

The complete experience of your life-track timeline is a partial experience of a seven-dimensional domain. Embedded within the seven-dimensions of your personal space-time-consciousness awareness are three-dimensional images of events on your timeline, at least a portion of the timeline itself, and the instantaneous awareness of your individual consciousness. If you become aware of this 7-D experience while existing in a physical body, it would be like a photographic memory of both the past and the  future. Simultaneous awareness of all timelines, all events, and all conscious entities would be Cosmic Consciousness, the trans-finite portion of the Mind of God.

The discovery of gimmel allows us to put consciousness into the equations of science, thereby expanding the metaphysical base of classical, relativistic and quantum science into a comprehensive scientific paradigm that will provide a basis for the study of the phenomena of physical, psychical and spiritual experience.

In TDVP, A quantum calculus is developed for quantum reality using the naturalized physical dimensions of the electron as the basis for the Triadic Rotational Unit of Equivalence (TRUE), the basic unit of the calculus. The mass of the electron, as determined from LHC experimental data, was used as the starting point because, of the three quanta that form all the atoms of the periodic table of elements, the electron, up-quark and down-quark, the electron has the smallest mass. Other known particles, though smaller, are ephemeral in nature and are not stable enough to form the building blocks of reality.

The mass of the electron, me, naturalized to unity ( me =1) is defined as the quantum unit of mass, and with naturalization of the speed of light, the mathematical equivalence of mass and energy is actualized in the quantum calculus. Then, the volumetric equivalence of mass, energy, space, and time, is established mathematically, and the TRUE becomes the basic unit of quantum equivalence. Planck’s discovery of the quantization of mass, and Einstein’s mass energy equivalence equation make it necessary that all variables and equations describing the combinations of quarks and electrons have to have integer values. This means  that stable combinations of quarks can only occur when the equations describing the combinations have integer solutions. Mathematicians call such expressions Diophantine equations.

Combinations of two quarks are eliminated as possibilities for forming stable subatomic structures by application of Fermat’s Last Theorem, which says there are no integer solutions for binary volumetric combination equations; but triadic volumetric combinations do have integer solutions, explaining why stable protons are only formed by combinations of three quarks, not two or four. By using electrons and up- and down-quarks, the most elementary quanta making up natural atomic structure, and by parsimonious choice of solutions of the triadic combination equation solutions, we discover that no stable structures are possible without the existence of a third form of the essence of reality, in addition to mass and energy. This third form, which we call gimmel, is, by definition, non-physical because it is not measurable as mass or energy.

With the algebraic and geometric linkage of the quantum mathematics, which we call the Calculus of dimensional Distinctions (CoDD) with electrons and quarks, the basic elementary objects of physical reality, the logical structure of reality is clearly reflected in the structure of quantum mathematics.

The logic of the CoDD is also the logic of consciousness, and distinctions are meaningless without the involvement of a conscious participant. As suggested by quantum experiments like the double-slit experiments and the delayed-choice experiments, it is the conscious creation of distinctions and the logical organization of distinctions, that creates the reality we experience, and gimmel is the key to understanding how consciousness creates reality from the infinite reservoir within which the CoDD reveals reality is embedded.

Pure mathematics reflects the logical structure of reality, revealing that  reality consists of a finite nine-dimensional space-time-consciousness mathematical manifold of quantized mass, energy, and consciousness, embedded in a transfinite domain of cosmic consciousness, which, in turn, is embedded in Infinity. Physical objects are composed of materialized distinctions, and there are three kinds of distinctions: Those measured in variables of content, i.e., mass, energy and consciousness, those measured in variables of extent, i.e., dimensional domains, and those of conscious intent leading to impact on objective reality. Primary Consciousness, as the infinite domain in which everything else is embedded, is ineffable.

With the discovery that gimmel, the non-physical particle aspect of reality, must be included as a third variable in the equations describing reality, and is a necessary for the existence of stable subatomic structure, materialism falls into the dust-bin of history as a limited and insufficient basis for scientific enquiry. The inclusion of non-physical gimmel, an agent of consciousness, in the equations of science, opens the doors of science to the study of all aspects of the reality we experience as conscious beings, including non-physical phenomena. This, in my opinion, is the future of science, and without it, extinction may well be the future of our species.

Edward R. Close July 11, 2018

Wednesday, July 4, 2018



Breathe in and out and know somehow,
The infinity of God’s eternal NOW.
Know in the heat of this July,
December’s cold and snowy sky.

Know in the pain that leads to death,
The throbbing gasp of life’s first breath.
Breathe in and out, be here and now
In eternity and infinity --somehow.

When starting down the road of life,
As someone’s husband, someone’s wife.
Then life is good, and future’s bright,
With love and luck, no end in sight,

Know well and sure as night brings day,
That this too, is doomed to pass away.
When the pulse of love and life wears thin,
Remember God’s Kingdom, here, within.

The happiness of life, and pain of death
Both dance the rhythmic tune of breath.
Be still and know that thou art He,
Right here, right now; -- eternally.

Breathe in, breathe out. Now just be
In the infinite NOW --for all eternity.

  --Ed Close July 4, 2018

Saturday, June 30, 2018



“There is no question that there is an unseen world. The problem is, how far is it from midtown and how late is it open?” –Woody Allen

I usually try to make my posts as understandable as I can, by providing the background for a given discourse so that the reader can grasp the message I wish to convey. But in this case, I’m going to forgo any elucidation of contextual predication and accept that those for whom this discussion might be meaningful will understand it, and anyone else will dismiss it as incomprehensible.

So-called “new age” people, and sometimes others, talk about “another dimension” and “planes of existence”. These are inexact and misleading terms that, frankly, indicate to me that those using them probably don’t actually know what they are talking about. For example, I’ve heard someone say: “The aliens exist in another dimension!” Or: My spiritual guides exist on another plane of existence.”

Nobody can exist “in a dimension”. A dimension is a measure of extent like length, width or height.
If those using the term another dimension have any inkling of what they are trying to convey, what they should say is another dimensional domain. Let me explain: A point (mathematical singularity) is a zero-dimensional domain; a line as a one-dimensional domain; a plane is a two-dimensional domain; a volume is a three-dimensional domain, and space-time is a four (or more) dimensional domain. Now, the question is not whether there are higher-dimensional domains. The problem is, how do we get there from here?

The idea of “existing on a plane” comes from the mistaken idea that we literally exist on a plane, the “Earth-plane”. We don’t. We actually exist in a multi-dimensional reality that starts with a three-dimensional domain. The surface of the Earth may be thought of as a plane, but, if you rise above it, but not too far, because if you ascend high enough (about 36,000 feet in an airliner), you will see that it is actually a curved surface, with bumps and divots in it. This should bring the realization that a two-dimensional domain can only be seen as such from the third dimension. This brings to light one of the invariants of dimensionometry: the recognition of the existence of an n-dimensional domain can only be obtained from a vantage point in an (n+1) dimensional domain.

Thinking about this gives you the conceptualization of multi-dimensional reality. In TDVP, with the application of a mathematical procedure I developed in 1989, called Dimensional Extrapolation, we have derived the mathematical nature of the dimensions of domains beyond 3-D. But mathematical derivations are reflections of the nature of reality, not actualizations of it. The ability to be able to describe something verbally and mathematically is the first step to experiencing it. That is the power of science and mathematics, they allow us to conceptualize and visualize reality beyond what is available to us through the physical senses.

Are there methods, processes and exercises that can help us to raise the level of our consciousness to the point of actually experiencing higher dimensions directly? Yes, I believe there are. This is one of the practical applications of TDVP. An understanding of TDVP provides a basis from which to ascend into higher dimensions. Is this the only way? No, but it does unite science and spirituality.

We live in a domain of nine finite dimensions, embedded in a 10-dimensional transfinite domain, embedded in the Infinite. How do I know this? The mathematics of TDVP, the Calculus of Distinctions indicates this, and I have experienced it briefly several times, and experience it partially all the time. How can one become aware of extra-dimensional reality? Remember I indicated above that describing something verbally and mathematically is the first step to experiencing it, 

Verbalization and mathematical description are just two aspects of the same thing, communicating experience with symbols. Most of us remember, as children, saying a word or phrase over and over again until it becomes meaningless, just sounds, conveying nothing. This is what someone speaking a language you are not familiar with sounds like, just noise. Different than the barking of a dog or the cawing of a crow, but just sounds.

Learning mathematics is exactly like learning another language, only it is harder because no one speaks pure mathematics. People do, however, speak German, Spanish, Hebrew, Hindi, etc. So, learning to speak another language is easier than learning advanced mathematics. So, start there. The average person who speaks only English, can learn to speak enough Spanish to get by in about a month if she/he puts his/her mind to it. German is a little harder because the grammar is more complex, but English is basically a Germanic language without the grammar and a few Latin-based words thrown in, so it’s not that hard once you get beyond over the grammar. Dutch and Swedish are “in-between” languages, somewhat intermediate between German and English.

Why should you learn another language? It will help you think in terms beyond your normal habits of speech. Learning to understand and speak another language literally opens a door to  different world. Slavic, Cyrillic, French, Arabic, and Oriental languages really open doors to different ways of thinking, and learning mathematics is like learning Greek or Latin. Learning math as a language, not just a tool to use to balance your checkbook or calculate square feet of floor space, allows you to think in math, and that will open the door to TDVP and extra dimensions.

The step (leap) from writing symbols and making sounds to the actualization of the meaning of those symbols and sounds in direct experience is a big one. The step from intellectual comprehension of the mathematical procedure of dimensional extrapolation (moving from one dimensional domain to another) to directly experiencing it is definitely not an easy one, but one very much worthwhile, because it enables you to perceive matter, energy, space, and time from a new perspective. The next step, however, attaining the awareness of all levels of consciousness of fewer dimensions than the one you occupy is an even bigger jump, but the view is tremendous.

ERC 6/30/2018

Thursday, June 28, 2018


© Edward R. Close, June 28, 2018

Science is not now, and never will be, a complete, unchanging body of knowledge. Our understanding progresses slowly, for the most part, by incremental discovery of the details of reality, but, occasionally science leaps forward, with the sudden discovery of a new and more productive way of thinking about reality. Thomas Kuhn, physicist and historian, in his insightful treatise, The Structure of Scientific Revolutions, called these sudden changes paradigm shifts.

A paradigm shift occurs when there is a complete overthrow of one or more of the basic assumptions of science. For example, the classical assumption that space and time are the same everywhere was overthrown by Einstein’s discovery of the mathematical relationship between the motion and acceleration of the observer and the measurement of space and time. And Planck’s discovery of the quantization of energy and mass overthrew the notion of the apparent infinite divisibility of reality. What basic assumption does TDVP overthrow? The assumption of scientific materialism. With the discovery of the mathematical necessity of the existence of a non-physical aspect of reality, TDVP puts consciousness into the equations of science, and refutes the assumption of scientific materialism, held by most scientists for centuries.

German physicist Max Planck, saw past scientific materialism and started the revolution culminating with TDVP. In the early 20th century. He said:

"I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness." – Max Planck

Einstein added to the developing revolution with his special and general theories of relativity. For the first time in the history of modern science, the state of the observer relative to the dynamics of moving objects was found to affect the observations and measurements of physical reality. Did Einstein, like his personal friend Max Planck, believe that there is something real beyond physical reality? His spirituality is revealed in the following statement:

I want to know God's thoughts - the rest are mere details.” – Albert Einstein

A paradigm shift always brings new science, and new science requires new math. Just as in every other paradigm shift, e.g., Newton’s laws of motion, relativity and quantum physics, TDVP requires new math. That new math is the Calculus of Dimensional Distinctions (CoDD), a mathematical system logically prior to conventional mathematics, adapted for application to quantum reality.

In answering the question “What is TDVP?”, I would be remiss if I did not emphasize and clarify the point that the logic of TDVP shines a bright light on the primacy of consciousness. Why is this important? Because recognizing the primacy of consciousness is the key to understanding how and why applications of the logic of the CoDD answers questions and resolves paradoxes that have persisted unanswered and unresolved for decades in the current mainstream paradigm of scientific materialism. This fact about TDVP may sound amazing, and you might expect its answers and proofs to be complex and difficult to comprehend, but the logic is so basic that I believe that I can explain it in simple terms that anyone can understand.

Because the experience of consciousness is primary, it is best to start with a brief discussion of consciousness. Everyone experiences it, but no one is able to define it completely satisfactorily because it is the essence of what we are, the essence of being itself. Expecting the human mind to analyze consciousness is like expecting an eye to be able to see itself without a mirror. Whatever consciousness is, without it, there simply would be no awareness, no knowledge of this, or any other world. Everything we do, know or think depends upon it.  To define something means to compare it with something already known, but consciousness is unique; there is nothing with which to compare it, and all analogies always fall short. As the primary experience of self, consciousness simply is the essence of self-aware existence. As Max Planck observed: “we cannot get behind consciousness”.

We can, however, identify and describe the actions performed by consciousness: The actions of consciousness arise from within consciousness itself as the desire for experience. That desire is propagated sequentially from self to other-than-self in three stages: 1. The realization of Identity, 2. The formation of a conscious Intent and 3. The actualization of intent as an Impact on other-than-self. Consciousness thus becomes an observer, and a participant in reality by the actions of drawing distinctions and organizing those distinctions into logical patterns.

All possible forms of reality knowable by a conscious observer, arise from the initial act of separation: i.e., the creation of the distinction of self from everything else. Any distinction is triadic, consisting of: 1. That which is distinguished, 2. That from which it is distinguished, and 3. The conscious self that draws the distinction. For the purpose of differential experience, the conscious self must consider itself to be separate from that which it is able to distinguish, and thus the distinction of self from other is the first distinction. All forms of objective reality arise from this initial act of severance, and while it may seem that we may separate reality any way we please, the logic of the CoDD shows us that the basic forms arising from the act of separation are the same. The framework of reality is that of embedded dimensional domains, much like the layers of an onion. The basis of all conceivable symbolic representation, all logic, language, and all knowledge of, and understanding of any reality, is the conscious action of the drawing of distinctions. This is why the CoDD provides a powerful tool for analyzing reality.

The most basic description of reality possible, is a multi-dimensional mosaic, a picture of reality composed of multiples of the most basic distinction possible; and the most basic distinction possible is the smallest possible quantum of the substance of reality. In the TDVP, that smallest quantum of mass that can be distinguished in the three-or-more dimensional reality we experience, and used as the basic unit of distinction, is the electron.

At this point, I must ask you to accept an a priori assumption, an assumption that is the basic foundational hypothesis of TDVP. The proof that this assumption is valid comes in the form of answers to questions and resolutions of paradoxes in the current scientific paradigm that cannot be obtained in any other way. A number of these have been published under the authorship of Close and Neppe or Neppe and Close. The assumption is the proposition that there is a single elementary measure which applies to all aspects of reality; a quantum equivalence unit to which all quantifiable aspects of reality can be mathematically related. In TDVP, we call that quantum equivalence unit the Triadic Rotational Unit of Equivalence (TRUE), for reasons that will become clearer as we proceed.

This is a significant departure from the current methods of mathematical physics, and a deliberate extension of Planck’s discovery of the quantization of energy to include quantization of all observable and measurable aspects of finite reality. Planck started down this path by developing a system of “natural” units that became known as Planck units, with five universal constants set equal to unity, making them natural units of measurement, and Einstein carried the ball a little farther by showing us the mathematical equivalence of mass and energy with E = mc2. In Planck units, c, the speed of light, is one of the five universal constants naturalized to unity. Notice that when c is naturalized to 1, Einstein’s famous equation becomes simply E = m, making energy and mass equivalent in Planck units. In TDVP, we naturalize all of the measures of reality, mass, energy, space, and time to unity, which naturalizes c, but not the other universal constants which were naturalized by Planck for computational convenience.

The TRUE is the basic unit of the calculus of distinctions, a system of mathematical logic designed for application to quantum reality. I use the word “calculus” here in the broadest possible sense, to mean a system of logical processes by which expressions representing a distinction or a combination of distinctions are transformed to other, equivalent distinctions by the fundamental operations of mathematics re-defined for quantum mathematics. Defining the TRUE based on the electron, links the CoDD to reality, so that the the logic of the CoDD correlates directly with the structure of reality. Application of this new quantum math across all scales of measurement, from the quantum to the cosmos reveals the true nature of reality. With TDVP, we not only get to know God’s thoughts, we get a glimpse of how God’s mind works!

I do not claim to have created this major scientific paradigm shift single-handedly. The new science of TDVP is built on foundations laid by many scientists; notably, it stands on the infinities of Georg Cantor and the Diophantine equations of Pierre de Fermat; and more recently, on the work of Planck, Einstein, Pauli, Von Neumann, Gӧdel, and others. I have been blessed to have the support of a number of brilliant people, including Dr. David Stewart, PhD, a geophysicist who was my roommate in college, and for that reason, has listened to my ideas about math and science for more than 60 years, my wife Jacqui, whose unwavering support I’ve enjoyed for more than 40 years, and I’ve been working in equal collaboration for more than 10 years with Dr. Vernon Neppe, MD, PhD, who, without question, is the most brilliant and accomplished polymath alive today.

Recently, TDVP is being considered favorably by an increasing number of scientists, including Dr. Adrian Klein in Israel, Dr. Gary Schwartz, PhD, a respected author and professor at the University of Arizona in Tucson, and several members of the Academy for the Advancement of  Postmaterialist Sciences (AAPS). Further exploration and promotion of TDVP has been energized recently by the enthusiasm of Dr. Surendra Pokharna, PhD physicist visiting from India. The only question I have now is whether this paradigm shift from the dead end of materialism into the expansive realm of consciousness and spirituality will be accepted by mainstream scientists in time to save humanity from the materialistic path to self-destruction. I am optimistically hopeful that it will happen within my lifetime.

With the discovery of gimmel, the indifferent particles assumed to exist in sub-atomic physics and galactic cosmology are gone, replaced by vortices of energy spinning in multiple planes of rotation. I think it is fair to say that TDVP is like a colon cleanse for the body of modern science: The lifeless dirt and grime of materialism are flushed out and swept away by the living energy of dynamic vortices infused with conscious meaning and purpose.

Edward R. Close  6/28/2018