Saturday, February 28, 2015


With the discovery of TRUE units, TDVP puts consciousness into the equations of the laws of nature and solves hard physics problems that have puzzled physicists for more than 50 years. TDVP also answers questions about real psychic and spiritual phenomena, and gives meaning and purpose to physical existence. Yet, many mainstream thinkers, scientists, philosophers, priests and ministers are hesitant to look at TDVP.
Here are three questions for anyone interested in this issue:
1. What do YOU think should be included in a 'theory of everything'?
2. Why do you think most mainstream scientists are NOT welcoming TDVP with open arms?
3. Why do you think most mainstream philosophers of religion are also NOT welcoming TDVP with open arms?
Please give some serious thought to these questions. Your answers may help us find ways to get more general acceptance for TDVP, the science of the future.

Friday, February 27, 2015


At 7:00 AM, this morning, February 27, 2015, I googled “Theory of Everything”. Sites with information on the new movie about the life of Stephen Hawking came up first, and my post, “THE UNIFICATION OF QUANTUM PHYSICS, RELATIVITY AND THE TDVP THEORY OF EVERYTHING”, with 15,940 views, came up next.

Like the character, Walter O’Brien, says in the intro to the TV series “Scorpion”, I have one of the highest IQs ever documented. But, I quite agree with Stephen Hawking when he says “people who brag about their IQs are losers”. So, why would I say such a thing?

I am saying it because it is true. I am a “Distinguished Member” of the most restrictive high IQ organization on the planet, even though I didn’t seek that membership, and I am saying it to get your attention, because I believe it is vitally important, even crucial for the future of humankind, that the world understands what a real theory of everything has to be.

I admire Stephen Hawking and honor him for all he has accomplished, but note that, in his 1988 book, “A Brief History of Time”, he predicted that a theory of everything would be in hand by 2000. That didn’t happen, and since then, at least a dozen books have been published by or about Stephen Hawking and the theory of everything. But still, no theory of everything.

Hawking thinks that M-Theory is best candidate. He says it is “a theory that unites all five string theories, as well as super gravity, within a single theoretical framework, but which is not yet fully understood”. The M-Theory, however, is not a theory of everything. Why? Because it simply does not include everything! There are no variables in the equations of M-Theory for consciousness. Consciousness connects physical reality with spiritual reality, giving rise to the better qualities in human beings, like honesty, integrity, loyalty, reverence, compassion, and love, yet it is nowhere to be found in any of mainstream science ‘theories of everything’.

Why would scientists call a theory restricted to physical phenomena a ‘theory of everything’? It’s simply because physicists focus on physics. If all you have is a hammer, everything looks like a nail. I know this well, because of my years of training as a physicist and mathematician. 

The portrayal of a ficticious young theoretical physicist, Dr. Sheldon Cooper, on the TV show “The Big Bang Theory” is an exaggeration for comedic effect to be sure, but the character does resemble some intelligent people I know. But, be assured, a real theory of everything is not going to come from highly educated individuals, however high their IQs may be, if they are adolescents spiritually, socially and emotionally handicapped as a result.

Physicists have been seeking a ‘theory of everything’ ever since Albert Einstein spent his final years trying to find a unified field theory. But, by ‘a theory of everything’, physicists simply mean a theory that will accurately explain how mass and energy interact in space and time, from the quantum level to the level of galaxies and the whole universe. Such a theory should answer many questions about the physical workings of the universe and advance modern technology, but cannot answer many of the really important questions like: Why is there something rather than nothing? What is the ultimate nature of reality? What is the meaning and purpose of life? What is consciousness? And how does it relate to physical reality? Who or what are we? Where did we come from, and where are we going?

Dr. Vernon Neppe, MD, PhD, an internationally renowned neuroscientist, and I, with the combined experience of nearly 100 years as scientists, have developed the Triadic Dimensional Vortical Paradigm (TDVP). TDVP provides a new, comprehensive basis not just for physics, but for all of the sciences, including the life sciences, psychology, studies of consciousness and even rare event phenomena. TDVP answers many of the most puzzling questions of modern physics, unifies classical science, modern science and parapsychology, and provides answers to more important questions about the purpose and meaning of consciousness and life in the universe.

Tuesday, February 17, 2015


The reviewer quotes me from my previous comments:
"even the most abstract mathematical theorem finds application in the real world sooner or later"
this is a highly unconventional view, to put it mildly. Sure,  within the discipline of mathematics there are differences in the viewpoints regarding some new math as only becoming real/known after discovery or the more Platonic viewpoint that all possible (logic) math is already 'out there'waiting to be discovered.
However, in mathematical physics, trying to describe our *realities* in line with experiments, whether materialistic, biological, economical, or sociological, or in medical science, it is commonly thought that only a subset of all known math applies; that's why a pure study of mathematics is often considered to be highly theoretical. Which engineer would be interested to prove that the sequence of 'twin primes' (prime numbers with only a  difference

of 2, eg 5,7, or 11, 13) is infinite ? According to Terence Tao this is not proven yet.  Not to mention the infinite number of possible string theories, of which we know that -provided even *one* could apply- they not all can apply to our common physical reality. Hope you see what i mean. For the rest i will revert to Ed by mail, i have some important points where i claim you cannot extend dimensions to known physics theories without having to rewrite all the basics again; well at least for s (which E and V) do not extend beyond 3, but also for t, which is onedimensional in our current mainstream theories. Extend that and you throw five centuries of physics into the garbage tray. And eg. Newton but also many others would turn around in their graves in misery.

My reply:
I don't believe Newton would turn over in his grave, because he was a believer in something more than matter and energy. I think he would accept that new theories like relativity, QM, and now TDVP, extend his work, not throw it into the garbage heap. I think discussions with Standard Model paradigm scientists like you are helpful in the sense that they reveal questions that Vernon and I need to know how to answer, and they provide material for additional books and articles.  But they have also prompted me to think more deeply about why there is such vehement resistance to our ideas. I believe I now know why they will not - and perhaps cannot - open their minds to a paradigm that allows room for paranormal phenomena, conscious spiritual experience and God. It’s not just that they are defending their life’s work, although that is certainly a strong motivator, they are defending what they see as the basis for all certain knowledge and sanity.
Science is about the search for certainty. The scientific ‘laws of nature’ provide some measure of certainty and predictability, which makes us, as small, vulnerable individual life forms, feel more secure and safe in a universe that appears to be violent and chaotic. Even with Heisenberg’s Uncertainty Principle, the uncertainty is contained within a very narrow range that can be managed by a probability distribution function, allowing for reasonable prediction within the limits of our ability to observe and measure quantum phenomena. Standard Model scientists see allowing consciousness into the equations of physical science as opening the door to mysticism, which they see as fantasy and insanity, an anathema to their world of rationality. They will allow this only over their dead bodies!
One has to wonder if such individuals, at least in this lifetime, are capable of understanding that spiritual phenomena are real, and that verifiable paranormal and other phenomena, not explainable in the Standard Model paradigm, can be brought within objective rationality by including consciousness a a variable in the equations describing the laws of nature.

Sunday, February 15, 2015


Dear _____,

First of all, I want to thank you for your continuing interest in what Vernon and I are trying to do. As I think you know, we have asked a substantial number of people, scientists, mathematicians, philosophers, and serious thinkers of various kinds, to review our work. The most important of these reviewers, from my point of view, are those with sufficient training in mathematics and physics to be able to understand the basic concepts underlying Transcendental Physics and TDVP. These thinkers, one would hope, would be very open-minded and objective. However, based on the comments and statements of those who have responded to date, open-mindedness is quite rare. In, my opinion, those who have commented fall into of one the following categories:

1.)  Those who assume we don’t know what we are talking about. Their approach is to look for obvious errors and be done with us.
2.)  Those who have unconventional theories of their own. Their approach is to determine to what extent our ideas might support theirs. When they find at some point that they do not, they quickly lose interest.
3.)  Those with heavily vested interest in the so-called Standard Model. As with group #1, they search for any error at all to discredit our ideas because, if we are right, the paradigm they have invested their lives in must be wrong, and their life’s work is threatened. Our experience shows that they will do anything they can to defend the current paradigm.
4.)  Those who are truly open minded, as all scientists should be, and are willing to follow the logic of new ideas wherever it leads, even when the results conflict with their life’s work and/or their own belief system. So far, our experience is that such minds are very few and far between.

I have found that discussions with people in the first three categories are largely a waste of time. The first two have no interest in anything outside their own ideas, or ideas with which they are familiar, and people in the third group have no interest in anything outside the box of the current materialistic paradigm. I think you can probably identify some individuals in the discussions of the past couple of years who fall in to these categories. Two or three, for example, who sought to find flaws in the math, started by criticizing references to, and use of, some simple, basic mathematical concepts, but failed to understand the significance of these concepts in the new paradigm. Next, they offered counter examples to certain mathematical proofs and conclusions. When I pointed out flaws in their reasoning, they at first grudgingly admitted a mistake or two, and then got upset. One even told me that the discussion was not about criticizing his ideas. He even posted that he had “refuted” certain of my arguments, when it was easy to show that he had not.

I want to address your comments, but first, please permit me to recount a little more history to put the current discussions into proper perspective:

After studying the works of Planck, Einstein, Minkowski, Lorentz, Schrödinger, Bohr, and Heisenberg, while I was an undergrad physics student, I was convinced as early as 1956, that a theory of everything, even if it was defined only as a theory that would unify the known forces of nature, was not possible without including the actions of consciousness in the equations. I wrote about this around 1957 - 1959 or so. I also recognized that new math was needed, and that I needed to know more about number theory. I earned a degree in mathematics in 1962, and started in a graduate program in theoretical physics. I also found the basis for the new math I needed in George Spencer Brown’s ‘Laws of Form’ in 1962; coincidentally about the same time I studied John Bell’s inequality theorem and learned of Alain Aspect’s experimental resolution of the EPR paradox.

I developed the Calculus of Distinctions to deal with the interaction of consciousness and physical reality; and I first published some of the results of including consciousness in the equations in 1989 in “Infinite Continuity”. Prior to publication, I sent a copy of the manuscript to Stephen Hawking for review. He had a problem with the concept of three-dimensional time and rejected, out of hand the idea that consciousness had anything to do with reality at the quantum level.

I expanded some of the ideas, and published them again in ‘Transcendental Physics’ in 1996. My ideas were accepted and heralded as the new paradigm uniting relativity and quantum physics by several, including experimental physicist Dr. Henry Swift and astrophysicist Dr. Philip Anderson. It was discussed for months on the Karl Jaspers Forum and other internet forums and in the journal “Science within Consciousness” in the period 1996 – 1998. One participant suggested that I should be careful about sharing my ideas so freely on the internet, because “the ideas clearly represent a new paradigm, and unscrupulous individuals will steal them and call them their own.” Another participant quipped: “If you have something truly new, no one will steal it. You’ll have to cram it down their throats!” Unfortunately, the second comment proved to be the more accurate. Most people it seems, even scientists, believe that if they don’t understand something immediately, it must be wrong. As Max Planck said, “Science advances one funeral at a time.”

Now, on to your comments:  I am thankful for your comments because they give me an opportunity to more fully explain the concepts underlying the mathematics of TDVP. I will copy from your email and then respond:

You wrote:
“Here´s some new feedback, specifically about theoretical physics (or at least its required methods) within your theories, but not about the *whole* TDVP theory (except physics, possibly extended to broader, non-materialist realms), and especially about QM (again) in relation to your (or Ed's) 9 dim. Spin model:

When I first mentioned to you in some mails years ago theories with hidden
variables in QM (David Bohm), and now when you have a 9D spin model with apparently more detailed variables, I point to the necessity of QM again, or at least consistency with experiments.”

My response:
You refer to ‘hidden variables’. This term, as used in QM, refers to attempts by some physicists, notably David Bohm, Eugene Wigner, and a few others, to explain the non-locality quantum entanglement of Bell’s inequality and the EPR paradox in terms of underlying, inaccessible variables which, if there, would validate Einstein’s opinion that QM as developed by Bohr and Heisenberg was incomplete, and eliminate, theoretically, the probabilistic uncertainty formalized by Heisenberg’s Uncertainty Principle.

The additional variables of TRUE units in TDVP are in no way hidden variables of this sort. They are hidden only in the sense that they are not directly measurable. The magnitudes of TRUE units, including mass, energy and gimmel (the third form) for specific sub-atomic entities are all indirectly determinable, like many things in science. The amount of gimmel in a given particle does not affect the quantum uncertainty between the measurements of location and angular momentum any more than the amount of mass or energy in the particle does. Heisenberg’s relationship of probabilistic uncertainty is not affected by Gimmel, an indirectly measurable variable combining with units of mass and energy to make up the TRUE quantum units of all stable particles, and thus they are not ‘hidden’ variables in the sense proposed by Bohm, et al.

You wrote:
“I do not see how the use of integers only will improve consistency with the known QM framework and the experiments; there needs to be some randomization as well i -strongly-suspect. The reason is, like I posted, because of the (statistical nature of the) measurements.

My response:
Let me explain the importance of using integers in the analysis of the combination of elementary particles to form stable compound particles like protons and neutrons: Planck’s discovery that elementary particles are always integer multiples of a basic unit means that we are dealing with discrete, as opposed to continuous values in the statistical analysis of collider data. A discrete random variable has a very different probability distribution than a continuous random variable, and functions representing compound entities formed by the combination of integral numbers of basic units can only have integer values. This means we are dealing with equations with integer variables, known to mathematicians as Diophantine equations. I’ll elaborate on this more as I respond to your further comments.

You wrote:
In some way with some quantum logic Ed or your other math assistant might
be able to add this to this spin-model, in order to generate the most common
QM experiments, but it won't be easy.

My response:
This has already been done. And, while it wasn’t as difficult as you might imagine, it may be hard to grasp at first. This is actually what Dimensional Extrapolation with unitary extensions and integer solutions to the Conveyance Equations in TRUE units are all about. The 9-D spin model is an outcome of the mathematics, not the other way around.

You wrote:
“For the rest when describing physics at the Planck scale, just a 9D spin model is not enough of course, because it's not only *particle* spin,  there also is QM involved with (mass-less) *photons*, and in fact with a  whole  of other particles (some with rapid decay); called the particle 'zoo'. In fact the existence of most of these particles seems to come out of the quantum field theories inherent in the Standard Model, but that's another -and slightly broader- subject.”

My response:
Actually, the mathematics of TDVP accurately encompasses all known QM processes. The derivation of TRUE units is fully consistent with, and actually dependent upon the statistical nature of the quantum measurements of collider data. TDVP is also consistent with the existence of mass-less photons and the entire ‘particle zoo’. All of the particles detected in the debris from high-energy collisions decay under ‘normal’ conditions into photons, electrons and up- and down-quarks, the four sub-atomic entities that make up the physical structures of our everyday world. The other particles are teased into existence by high-energy collisions here on Earth, or are naturally produced in extreme conditions of heat and pressure like those in stellar processes. This becomes clear in the 9-D integral model. TRUE units describe the total mass/energy/consciousness composition of sub-atomic particles under normal conditions. Only the particle combinations with the TRUE unit values that satisfy integer solutions of the Conveyance Equation for n = m = 3, dictated by Fermat’s Last Theorem achieve symmetric stability.

You wrote:
“Now  I understand you or Ed have to start somewhere within the TDVP framework, i.e. with the 9D particle spin model, but then this would  only be a (minor) start, and certainly not a description or foundation of some 'new physics' or new paradigm in physics at large.”

My response:
As you might gather from my explanations above, I strongly disagree with this statement. While our presentations, as you say, must ‘start somewhere’, as a new paradigm, TDVP does not start with randomly chosen concepts. As a new paradigm must, it starts with proven fundamental mathematical and physical basics and expands them with new mathematics, new definitions and a new, more comprehensive theoretical framework, just as relativity and quantum mechanics the early part of the last century.

Since 1935, there have been no paradigm-shifting new physics discoveries, only experimental and technological evidence of fields, particles and concepts that fit within the current materialistic paradigm. TDVP, on the other hand, with the inclusion of the action of consciousness, and detailed mathematical and dimensionometric applications of the Calculus of Distinctions, Dimensional Extrapolation and the Conveyance Equations, provides a new, expanded paradigm that not only encompasses and integrates known physics, chemistry, the life sciences, and verified paranormal phenomena, it provides answers and explanations for quantum and macro-scale phenomena not explained, or even explainable in the current paradigm.

You wrote:
Also i would like to come back on the subject of peer review (about stuff like
this 9D spin model) in the area of -theoretical-  *physics*.  … I would be more interested with which modern physicists you and-or Ed are talking in detail about the mathematical theories within your TDVP context.

My response:
We certainly agree about the importance of colleague review, and we have been eagerly seeking it for years. I have approached people like Stephen Hawking, Menos Kafatos, Henry Stapp, and Roger Penrose, and a number of mathematicians to get these ideas peer reviewed, and Vernon has approached many others. But finding qualified reviewers who are willing to spend their precious time reviewing something outside the box is easier said than done. See my comments above regarding the four categories of reviewers.

You continue:
This also because imho inventing workable validated theories in mathematical physics usually should not be much determined only by 'creativity' (although this may apply for generating hypotheses) but by having an understanding of experimental physics as w ell. Without the experiments, imho you are most of the  time  -in fact almost always-only  creating (highly) speculative 'theories' (in fact more  hypotheses  than theories); a well known fact in the philosophy of science btw, and mentioning things as new paradigms or being decades ahead of the others do not change such facts. NB it is not intended as (severe) criticism, but more as a suggestion how to continue the research and if also focus on the interconnections between your 'new physics' and the well-established older theories.

My response:
I certainly understand and appreciate this, as I’m sure Vernon does, but you apparently didn’t know that I’ve relied heavily on experimental physics in developing the mathematics.

You continued:
At least in your latest response on Ning you now seem to have acknowledged this, but then you also should admit that there is not much 'linkage' (yet?) between all the new ideas (including these TRUE units) with conventional 'fundamental' physics (apart from the periodic table, but that's not enough. Like i wrote earlier, in theoretical physics the quantum mechanics of the electron bands around the core (and the Pauli Exclusion Principle) are determining the periodic index; and also their reactivity with other elements. But that's another subject.  While it looks like an 'Eureka' experience finding such a new way of setting up the periodic table, together with some possible new findings, imho again more validation and verification is to be done to make it a workable theory instead of just a (wild) hypothesis.”

My response:
Again, you seem to be unaware of much of what we’ve published. As my previous discussion shows, there are multiple linkages between TDVP and fundamental physics, quantum mechanics and relativity. In addition to explaining why quarks combine in triads, the unique value of the Cabibbo angle, explaining the Periodic Table consistent with electron shell theory and Pauli’s exclusion principle, -but in much more detail-, explaining why fermions have an intrinsic spin number of ½, why photons, electrons, protons, and neutrons have the physical characteristics they do, and the quantization of angular momentum, as well as explaining non-locality and quantum entanglement, we are finding more links and explanations almost daily. If this doesn’t make TDVP “a workable theory instead of just a (wild) hypothesis”, I’d like to know what would.

You wrote:
About the methods used in general in your physics theories as part of your
Toe: maybe this '' C.O.D.' theory by Ed indeed is innovative new method which can be used in mathematical physics, to be recognized as such it should  be studied more in detail by others i suppose, and only then later it might be acknowledged as such.”

My response:
Unless you’ve read the published articles associated with “Reality Begins with Consciousness” and/or the posts on my Transcendental Physics blog, located at, you wouldn’t know that over the years, I have discussed the mathematical basis of Transcendental Physics and TDVP with a substantial number of professional mathematicians and mathematical physicists; I have approached at least fifty or sixty. I have documentation of many of these discussions in the form of letters and emails. Of these, only a handful, I believe 5 or 6 actually took the time to look at my work in any detail. The problem, as with getting reviewers for TDVP, is few are willing to invest much time to review anything outside the mainstream paradigm, especially if it involves new math. One professional mathematician, Dr. Vladimir Brandin, has endorsed CoD and used it in his studies of intelligence. We published one paper together:

Brandin V, Close ER: The calculus of dimensional distinctions: Elements of mathematical theory of intellect. Moscow: 2003.

Details of CoD and applications have been published in journal articles. We can supply copies if you want to see them.

I’d like to elaborate a bit more on the mathematical and dimensionometric bases of Transcendental Physics and TDVP for you by pointing out the difference between classical Aristotelian and Platonic reasoning as it pertains to mathematics and scientific research: Aristotelians see mathematics simply as a man-made tool, while Platonists see mathematics as symbolic reflections of an underlying reality. As such, the imperfect tools of human formulation can always be improved to more and more closely mimic and reveal the perfectly logical patterns of reality. I see the value of the Aristotelian point of view in technological and engineering applications, but I also subscribe to the Platonic point of view as valid in constructing a paradigm to illustrate the nature of reality.

To understand TDVP and the use of the CoD, I think it will be helpful for you to know that there are three basic concepts behind the mathematics of TDVP:

1.) There is a direct correlation between the structures of number theory and the structures of the universe. This is why even the most abstract mathematical theorem finds application in the real world sooner or later.
2.) The experimental resolution (Aspect, et al) of the EPR paradox implies consciousness involvement and non-locality. These features are explainable within the framework of a universe with more dimensions than the four of the space-time of Minkowski and Einstein (3S – 1T).
3.) Max Planck discovered that we live in a quantized universe, but mathematical physics has not been properly adjusted to accommodate this fact.

You may agree or disagree with basic concept #1. If you are primarily Aristotelian in your thinking, as many scientists are, you may see the correlation between the types of numbers and the measures of dimensions, as shown by Dimensional Extrapolation, as a remarkable coincidence. If you accept basic concept #1, you will agree that the correlations we’ve discovered are not coincidental.

Basic concept #2 by itself does not imply any specific number of discrete dimensions, but when combined with #1, a maximum number of nine finite orthogonal dimensions are derived.

Concerning basic concept #3, to adjust mathematical physics to a quantized universe, we must first recognize that the calculus of Newton and Leibniz does not apply at the quantum level because, for applications of differential and integral calculus to yield valid results, the domains of the variables involved must be continuous. In a quantized universe, distinctions of content, like mass, energy and consciousness, exist only in finite, discrete integer amounts, and, as we have shown in TDVP, the distinctions of extent, like space and time, are also limited to finite, discrete volumes due to the relativistic light-speed limitation on velocity.
So the dimensional domains of a quantized universe are not continuous. No variable in a quantized universe can approach zero infinitesimally closely, as it must be able to do for Newtonian calculus to yield valid results at the quantum scale. In TDVP, the infinitesimals of Newtonian calculus are replaced by the minimal distinctions of TRUE units, and the Calculus of Distinctions is the mathematical system I’ve developed to extend calculus to the sub-quark level. To be clear, the CoD does not replace Newtonian calculus at the macro scale; it extends calculation to the quark scale, analogous to the way relativity does not replace Newtonian physics at normal scales of measurement, and only comes to play in the vicinity of extremely massive objects, or when relative velocities are near light-speed.

In summary, contrary to the impressions you have portrayed in your email of Feb. 3, 2015, TDVP is, in fact a comprehensive new paradigm with new mathematics, allowing consciousness to be included in the equations of mathematical physics for the first time. This paradigm has explained a number of empirical observations not explained by the current paradigm. The new mathematics, rigorously defined in several published books and articles, reveals an existential nine-dimensional finite domain embedded in an infinite substrate which contains the blueprints of all of the stable forms that support life and consciousness in the universe. I have tried repeatedly since 1989 to obtain competent peer review, and Vernon and I have sought colleague review in every venue available to us over the past six years as we’ve continued to develop the new paradigm. If you have any questions or concerns, or require more detailed explanations, please let me know.


Edward R. Close, PhD, PE, DISPE

Tuesday, February 3, 2015


Clarification of Dimensional Extrapolation, euclidean AND NON-EUCLIDEAN SPACE, and THE DERIVATION OF TRUE units
To understand Dimensional Extrapolation and the nature of TRUE units, it is necessary to unlearn some of the things mainstream physicists think they know. The idea that mass warps space, which is generally accepted as implied by the Theory of Relativity, is one of those things. Einstein himself raised doubt about this when he said in his Note to the Fifteenth Edition of “Relativity, the Special and General Theory” June 9th, 1852: “In this edition I have added, as a fifth appendix, a presentation of my views on the problem of space. … I wished to show that space-time is not necessarily something to which one can ascribe a separate existence. … Physical objects are not in space, but these objects are spatially extended. In this way, the concept of ‘empty space’ loses its meaning.” If space-time does not exist apart from distinct objects, the idea that the 3-D space of our physical observations is warped by mass is, at best, a conceptual analogy that may be useful in helping us to grasp the idea of gravitational gradient in a four-dimensional domain. Is space-time warped by mass? If so, how can we measure the warping if the point from which we observe and measure it is also within the same warped space-time domain?
We exist in a dynamic multi-dimensional reality; but our physical senses only convey the information of one-, two- and three- dimensional conceptual images to our physical brains. We deduce the existence of a fourth dimension based on comparison of current observation with the memory, actually pictures stored in the present brain, of previous observations. Our observations are conceptually limited to one-, two- and three- dimensional slices of a dynamic multi-dimensional reality. “Dimensional Extrapolation” is the term I use for the process of rotation and extension that is necessary to move from an n-dimensional domain into an (n+1)-dimensional domain.
The necessary angle of rotation in the dimensional extrapolation needed to expand our awareness from a one-dimensional Euclidean domain (a line) to a two-dimensional Euclidean domain (a plane) is 90 degrees. This is because this amount of rotation places the extension equidistant in angular degrees from the two directions of freedom of movement in the one-dimensional domain. Similarly, the angle of rotation needed to expand our awareness from a plane, which is a two-dimensional Euclidean domain to a volumetric three-dimensional Euclidean domain is also 90 degrees, and in general, moving from any n-dimensional Euclidean domain into an (n+1)-dimensional Euclidean domain requires rotating a unitary extension to a point that is equiangular in rotation away from all of the dimensions of the n-dimensional domain. This angle of rotation for Euclidean domains is always 90 degrees, and the magnitude of the unitary projection from any n-dimensional domain into the (n+1)-dimensional domain is determined by using the Pythagorean Theorem. With the unitary orthogonal projections in the n-dimensional domain as sides of the Pythagorean triangle, the magnitude of the projection into the (n+1)-dimensional domain is calculated as the hypotenuse.
The Pythagorean equations are sub-sets of the expression described mathematically by Σki=1 (Xk)n = Zn. where n = 1,2,3,…, the natural integers. The Pythagorean equations are obtained when k = n = 2, and two other important equations are obtained when k = 2 and n = 3, and when k = n = 3. Integer solutions to the first of these three equations, the Pythagorean equation, yield the Pythagorean triples. The lack of integer solutions to the second equation, proved by application of Fermat’s Last Theorem, and the integer solutions of the third equation prove to be of primary importance in determining how the stable structures of elementary particles are formed, as we shall see below. It is probable that other values of k and n will produce additional important equations useful in describing combinatorial relationships between particles in the quantized reality of the universe.
A second, related concept that requires unlearning is the idea that there is something called non-Euclidean space. The problem here arises from confusing dimensions of different types. While the dimensions of space and time are both measured in units of distinctions of extent, space domains and space-time domains are quantitatively and qualitatively different. First, let’s see how the dimensions of space and time are quantitatively different: When moving from a 1-dimensional Euclidean domain to a 2-dimensional Euclidean domain and from a 2-dimensional Euclidean domain to a 3-dimensional Euclidean domain, the units of extent are the same, i.e., they can be measured mathematically consistently in real numbers. But when moving from a 3-dimensional Euclidean domain to a 4-dimensional Euclidean domain, rotating 90 degrees away from all of the directions of freedom of the 3-dimensional domain, requires that the extension into the 4-dimensional domain is imaginary, i.e. a multiple of the square root of  minus one, as calculated using the Pythagorean Theorem.
Beyond and even more important than these problems with definitions and the basic logic of mathematical physics, is the failure to include the functioning of consciousness in the equations. Consciousness is intimately involved in our observations. Clarifying the fact that a non-Euclidean domain is only definable relative to the Euclidean domain of conscious observation provides an important step toward understanding how to put consciousness into the equations of mathematical physics.
The problem with the concept of non-Euclidean space as an existing reality is partly because of confusion due to poorly defined terminology, partly because of ignoring the role of consciousness, and partly because of the loss of detail in mathematical generalization. The Perception of a non-Euclidean dimensional domain is necessarily relative to the dimensional domain of the conscious observer. The qualitative differences between the observations of space and space-time domains exist because of the way we perceive reality through the limited physical senses and the way memory is stored in the neurological functions of the brain. Because the observation and measurement of a non-Euclidean domain is defined relative to the dimensional domain of the observer, it should be recognized as a relatively non-Euclidean domain. With these points in mind, we can no longer accept the assumption that space and time exist apart from, and without reference to consciousness.
Mathematicians have generalized the concept of space by considering Euclidean space as only one of many possible ‘spaces’ with different degrees of curvature. In that view, Euclidean space just happens to be the one with zero curvature. Three-dimensional Euclidean space, however, is the most important spatial domain in respect to all physical observations because it is the only space of observation available to our limited physical senses. It is, therefore, the only reference we have from which to define non-Euclidean dimensional domains. Three-dimensional Euclidean space is the natural arena of our physical observations and what we perceive as reality. And because the images of reality created by our physical brains are created within the limits of our physical observations, Euclidean space is the space of consciousness. The terminology can be improved by using the term ‘space’ for the three-dimensional domain only and Euclidean space as the space of reference for all observations.
When n ≠ 3, an n-dimensional domain, Euclidean or otherwise, can only be conceptualized in reference to the 3-dimensional Euclidean domain of our physical observations. For example, if a 2-dimensional plane is curved, i.e. non-Euclidean, its curvature can only be seen from the viewpoint of a 3-dimensional Euclidean domain. Similarly, the curvature of a non-Euclidean 4- or 5- dimensional domain can only be meaningfully measured and described from the viewpoint of our 3-dimensional Euclidean domain of observation. We know from Einstein’s relativity, validated many times by experimental evidence, that the measure of 1-dimensional time is distorted by relative velocity and mass. This means that the 4-dimensional space-time domain is observed as Euclidean or non-Euclidean, depending on the observer’s relative velocity and proximity to massive objects.
Thus ‘Space’ can only be defined unambiguously as the domain of the first three dimensions, within which, because of the limitations of our physical senses, all our physical observations are made. Through the physiological and the neurological processing of the data supplied by our senses, we perceive the 3-dimensional domain of the universe as Euclidean. In fact, if any part of the 3-dimensional domain of our observations is non-Euclidean, it can only be said to be non-Euclidean relative to the 3-dimensional domain of our conscious observations.
The very real differences, both perceptual and mathematical, between space and time domains are generally ignored by human beings, including scientists. They can be ignored without serious consequences in non-mathematical verbal descriptions when comparing one measurement of time with another, but ignoring them in the mathematical equations describing space-time-matter-energy relationships is problematic. This problem, in conjunction with the inappropriate application of Newtonian continuous calculus to discrete quantum phenomena, leads to virtually all of the so-called “weirdness” of quantum physics, as well as most of the apparent conflicts between quantum mechanics and relativity. So, while there may be many non-Euclidean domains relative to our Euclidean domain of observation, the three dimensional domain of space cannot be said to be existentially non-Euclidean.
Many of the problems of mathematical physics, unsolvable in the context of the current scientific paradigm, are relatively easily solved by the concepts presented here and by use of the Calculus of Distinctions, which is applicable where Newtonian calculus is not. Dr. Neppe and I have already published some of these solutions in the book “Reality Begins with Consciousness” ( and in papers explaining the spin number of fermions, why quarks are always found combined in groups of three, and the Cabibbo mixing angle.
These problems with the current paradigm become paramount when dealing with the physics of elementary particles, starting with the quarks that make up the protons and neutrons of atomic structure. In a particle accelerator like the Large Hadron Collider (LHC), particles are accelerated to very high relative velocities and caused to collide, breaking compound particles apart into smaller particles. The mass and energy of the elementary particles flying away from a collision are deduced from three-dimensional snapshots of their apparent paths in a magnetic field. The fact that none of the measured amounts of the mass and energy of these elementary particles obtained in this manner are unitary, or even integer multiples of the unit commonly used, tells us that the unit being used is not the truly minimum sub-quantum unit.
We can determine the relative mass and energy of the minimal elementary particle unit by normalizing the mass and energy of electrons and quarks.  Because of the relativistic light-speed limit to rotational velocity, using the mass of the minimal elementary particle, the electron, and its angular momentum, we are able to determine the minimum possible volume occupied by any elementary particle. Finally, setting the minimal mass-energy and minimal volume to unity (+1), we define the truly minimal unit, the proper unit with which to measure all physical phenomena. Defined in this way, all physical particles will be integer multiples of this sub-quantal unit. Because this sub-quantal basic unit is derived from the existence of a minimal-volume high-velocity rotating particle, and all particles are integer multiple of it, I call it the Triadic Rotational Unit of Equivalence, or TRUE Unit for short.
Given that the stable sub-atomic elementary particles, i.e. electrons and quarks, are high-velocity symmetrically spinning objects, we look at how they must combine to form compound symmetrically spinning objects. The reason symmetry is so important here is because asymmetric objects spinning at angular velocities approaching the speed of light would quickly fly apart because the centrifugal forces of angular momentum, unequal on opposing sides of the spinning object would pull it apart. Thus, the second law of thermodynamics, operating on all particles combining due to the attractions of opposite electrical charges and/or magnetic attraction, would cause any randomly-occurring asymmetric combination to decay almost immediately back to maximum entropy. This means that the complex physical universe as we know it cannot have evolved accidentally from flotsam from a giant explosion however many billions of years ago.
Normalized particle collider data tells us that up-quarks are made up of 4 of the minimum mass-energy-volume units described above, and down-quarks are made up of 9 minimal units. Applying Fermat’s Last Theorem to the equation resulting when k = 2 and n = 3, in the expression Σki=1 (Xk)n = Zn,  tells us that two symmetric objects made up of any integer multiples of the minimum mass-energy-volume unit cannot combine to form a new symmetric object because there are no integer solutions to (X1)3 + (X2)3 = Z3. On the other hand, the equation (X1)3 + (X2)3 + (X3)3 = Z3, obtained when k = n = 3, has integer solutions.
Noting that Einstein’s E=mc2 , validated by empirical data, proved that mass and energy are two forms of the same thing, we deduce that there has to be a third form of  reality, not measurable as mass or energy, producing stable, symmetric triadic particles. This is why under the normal conditions existing in the universe of our observational domain quarks are always seen in triadic combinations: two up-quarks and one down-quark form a proton, and one up-quark and two down quarks form a neutron.
The number of units of the third form needed to form symmetrically stable quarks, protons and neutrons are uniquely determined from the integer solutions of the equation obtained from the general expression Σki=1 (Xk)n  = Zn, when k = n = 3.
Because of the continuing discovery of the relationship of the mathematical structure (rings, fields, etc.) of numbers studied in the discipline called number theory, to the structure of the observable universe, I believe that our discoveries strongly suggest that reality consists of the three forms of distinctions of content interacting in nine finite dimensions of extent: three dimensions of space, three dimensions of time, and three dimensions of consciousness, all contained and pervaded by a conscious transfinite substrate. The logical mathematical patterns of the conscious transfinite substrate are conveyed to the 3-dimensional subdomain of our observations by the expression Σki=1 (Xk)n  = Zn. For this reason, I call this the Conveyance Expression and equations derived from it Conveyance Equations.
Experimental data tell us that the Hydrogen atom is unique, being the only element that consists simply of one electron and one proton; but Fermat’s Last Theorem tells us that this combination is asymmetric, and would therefore be extremely unstable, and would not exist long enough to form the universe we perceive without the addition of a particle composed entirely of units of the third form.
When we determine the number of units of the third form needed to stabilize the Hydrogen atom, and apply this analysis to all of the elements of the Periodic Table, we find that the most stable and most abundant elements in the universe are those that support life and sentient beings. Furthermore, gaps in symmetry that are found existing within the Periodic Table as we have known it, are filled by compounds prominent in amino acids and molecules of DNA and RNA, the building blocks of conscious life forms.
This fits nicely with our hypothesis that the third form of the substance of reality is the original primary form of consciousness itself, guiding the formation of a universe able to sustain life forms that are capable of experiencing consciousness. It also appears that the ratio of the third form to the mass/energy substance, based on abundance of life-sustaining elements in the universe and Hubble Telescope data, conforms with the conjecture that dark matter and dark energy are also composed of the third form.

Perhaps the most important, and consequently also the most controversial aspect of this analysis, is the unavoidable conclusion that consciousness in its primary form has always existed, and will always exist, in the quantized, relativistic universe that we experience, and that life, fully capable of supporting ever-existing consciousness, is the purpose of the physical universe.