WHAT IS FERMAT’S LAST THEOREM, AND WHY IS IT IMPORTANT?

in 1637, Pierre de Fermat, a judge at the French Parliament of Toulouse, wrote in the margin of a book on Diophantine equations that he had devised a marvelous proof that there are no positive whole number solutions to the equation xⁿ + yⁿ = zⁿ for n greater than two. His proof, for n = 4 is known, but his general proof for all n greater than two was never found.

It is an interesting aside that Fermat was not a professional mathematician. He did not publish his findings, he simply conveyed them in letters to other mathematicians, and thus was considered an amateur. The less than modest French mathematician and philosopher Rene Descartes tried to discredit Fermat by proclaiming that he was “a troublemaker who owed his reputation to a few lucky guesses”. However, in one dispute after another, e.g. their derivations of the sine law for the refraction of light, Fermat proved to be right and Descartes wrong. While Descartes clearly considered himself to be the superior intellect of the day, a comparison of their works reveals the fact that Fermat was the better scientist and mathematician of the two.

Descartes’ arrogance shines out in the following statement: “‎I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.” Implying that he could have explained much more. This is analogous to a classmate of mine who liked to say “I’m not conceited, I’m actually twice as smart as I say I am!”

Peter Bernstein, in his book Against the Gods, states that Fermat "was a mathematician of rare power. He was an independent inventor of analytical geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."

Regarding Fermat's work, Sir Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."

Speaking of Fermat's work in number theory, Mathematician Andre Weil says that: "what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the method of descent which is rightly regarded as Fermat's own. … With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.

Never-the-less, popular history has treated Rene Descartes very well, while ignoring Fermat. The name Descartes is well known to every student of mathematics and science, while Fermat’s name is virtually unknown except for in relation to Fermat’s Last Theorem, -and most modern mathematicians openly doubt that he actually proved it! Why? Because for more than 300 years, professional mathematicians tried to find a proof, and failed.

The power of Fermat’s math lies in his method of infinite descent, and the principle of “efficient purpose in nature”, and in 1964-5, while teaching high school mathematics, using the same simple principles used by Pierre de Fermat, I produced a proof which I first submitted to a professional mathematician in 1966. Because my proof was completed in 1965, I call it FLT65.

To see FLT65 as it was submitted to the first reviewer on January 25 1966, copy the link below and paste it into your web browser.

http://www.erclosetphysics.com/search?q=Fermat%27s+Last+Theorem+Part+1

This link will take you to a lengthy discussion of FLT65. To see the original submitted version, scroll down to Appendix C.

I have submitted FLT65 to more than 50 mathematicians over the years, and only a few of them who responded actually offered any mathematical arguments attempting to disprove FLT65. And while a precious few have admitted it, none of them were able to produce a valid refutation of FLT65. Because I believed it would eventually be recognized as a valid proof, I have carefully documented the submittals and responses.

You might well ask: if no one has refuted FLT65, why hasn’t it been accepted? The answer to this is an interesting story by itself. To learn the details of the history of the odyssey of FLT65, copy the link below and paste it into your web browser.

http://www.erclosetphysics.com/2015/11/fermats-last-theorem-part-seven.html

I believe that the time for Fermat to become a household name has come, because his simple methods of Diophantine analysis are totally appropriate and exactly what is needed for application to quantum physics. It is time to go beyond the calculus of Newton and Leibniz and apply the Calculus of Distinctions to TRUE quantum equivalence units to produce a better description of multi-dimensional reality. See details in the posts of TDVP and www.BrainVoyage.com.

Because of excessive academic specialization, and the fact that modern thinking has lost its metaphysical basis in Infinite Intelligence, science has gone astray and adopted atheistic materialism as its metaphysical basis. The result is a world society that is morally adrift. This lack of meaning and purpose is so dangerous that, if not corrected, it could spell the demise of the human race. It is time to revisit the simple infinite descent and principle of “efficient purpose in nature”, of Pierre de Fermat.

Edward R. Close    August 4, 2017

SPACE, TIME AND CONSCIOUSNESS TRUTHS

SPACE, TIME AND CONSCIOUSNESS

EVERY THING IS EXPLAINABLE!

Let me explain:

By including consciousness in the equations of science (TDVP), Dr. Vernon Neppe and I have reached the point where we have everything we need to explain every thing. For example, I can explain exactly why it takes three quarks to form a proton or neutron, and why it takes three types of elementary particles to form the stable atoms that make up the physical universe. I can explain why fermions have ½ spin, and why the Cabibbo angle and other particle-mixing angles are what they are.

Does this mean that we have the “Theory of Everything” (TOE) dreamed about by physicists since Einstein hypothesized that there should be a unified field theory that would explain all of the known physical forces? No.

Those who think there is a TOE out there waiting to be discovered have not understood Gӧdel’s Incompleteness Theorems. I will explain this, but first, I must explain the difference between explaining every thing and a theory of everything. The word ‘thing’ refers to a finite physical object or concept. The word ‘everything’ means all that exists. To clarify: when physicists talk about a TOE, they are not actually talking about a theory of everything. They are talking about a theory of every thing, i.e. a complete physical theory. But, as I will explain, even that is problematic in light of Gӧdel’s Incompleteness Theorems.

Before I get into discussing Gӧdel’s Incompleteness Theorems, I will state four fundamental truths that can be proved conclusively with what we now know:

1.     Reality, which includes the physical universe, is an infinite logical system.

2.     The physical universe, available through the physical senses, is only a small fraction (less than 5%) of Reality.

3.     Reality is expanding in all nine finite dimensions, not just the three and one-half dimensions of relativistic space-time.

4.     Reality is more than an infinite logical system, it is an Infinite Intelligence that encompasses space, time and consciousness.

As an independent sentient being, you have the right to agree, disagree or reserve judgement concerning these four statements. But they rest on the solid foundations of proved theorems of axiomatic geometry, mathematics, logic, and physical science. These theorems include the Pythagorean Theorem, Fermat’s Last Theorem, the axiomatic principles of Relativity and Quantum Physics, and Gӧdel’s Incompleteness Theorems.  I am as sure of them as I am that I exist. If I can, I will impart that certainty to you in this presentation.

I have touched on the importance and applications of the Pythagorean Theorem, Fermat’s Last Theorem, the axiomatic principles of Relativity and Quantum Physics, and Gӧdel’s Incompleteness Theorems in these posts, and Dr. Neppe and I have published a book (Reality Begins with Consciousness) and a number of papers dealing with their applications in TDVP, but these foundation theorems are so important to TDVP in general, and the four truths stated above, in particular, that I want to elaborate on them a little more here.

Gӧdel’s Incompleteness Theorems

The detailed proof of Gӧdel’s Incompleteness Theorems is beyond the scope of this discussion, but understanding their meaning, importance and impact on human thought, are not. I highly recommend the book “Gӧdel’s Proof” by Ernest Nagel and James R. Newman to anyone who may want to pursue a deeper understanding than I can provide here. This book was written for the non-mathematician. In their words: “The details of Gӧdel’s proofs in his epoch-making paper are too difficult to follow without considerable mathematical training. But the basic structure of his demonstrations and the core of his conclusions can be made intelligible to readers with very limited mathematical and logical preparation.”

In a nutshell, Gӧdel’s Incompleteness Theorems prove that no internally consistent logical system is ever complete. I emphasize the use of the word prove here, because you need to understand that a theorem is not a theory. If it is a theorem, is has been proved. Another way to put Gӧdel’s proof is: In any system of logic, mathematics or geometry, logically legitimate questions can be raised that cannot be answered within the system.

Let this sink in a little. This explains why questions like why it takes three quarks to form a stable proton or neutron, why the Cabibbo mixing angle for quarks is 13.02 degrees, or why the elementary particles making up normal atomic structure have ½ intrinsic spin, are not explainable in the current scientific paradigm.

Gӧdel’s Incompleteness Theorems do not say that there are questions like this that can never be answered; they only say that there are questions that cannot be answered within the paradigm in which they were formed. They may, however, be answerable in a new, more comprehensible paradigm. This, in fact, describes the nature of science and human thought in general. Science, and any system of logical thought, however internally consistent, is never complete. With this in mind, let’s return to the four fundamental truths stated above.

Reality is a logical system, and as such, it is infinite

Reality is the ultimate logical system, which all conceptual models, scientific, mathematical, geometrical, philosophical, theological, spiritual, or whatever, attempt to model. Gӧdel’s Incompleteness Theorems prove that Reality, as the original logical system, is always incomplete from the perspective of finite beings. No matter how many things we explain, the everything of Reality will always be beyond those explanations. Whenever we expand the logical system of our current understanding to explain something heretofore inexplicable, we will find that Reality presents us with new questions that cannot be explained within even our new paradigm. Thus, Reality is an infinite logical system.

The physical universe is a small fraction of Reality

Application of the principles of relativity and quantum physics imply that our physical senses and extensions of them are reduction valves. That is to say that they function not to bring all of Reality into our physical experience, but actually to keep most of Reality out, and bring only a very small part into our physical experience. In fact, our current knowledge of the central nervous system of sentient beings like us suggests that our brains are capable of handling much more than that delivered to them by the senses and neural pathways. Evidence provided by the Hubble space probe and TDVP TRUE analysis strongly support this conclusion.

Reality is expanding in nine finite dimensions

Dr. Neppe and I have developed a comprehensive model that incorporates nine finite dimensions based on the principles of relativity, quantum physics and number theory. Its implications, are vast and far-reaching. It explains why there are no absolute beginnings or ends, only change. In conjunction with the first Truth, it explains many previously inexplicable experimental observations, and implies, among other things, that consciousness, like mass and energy, obeys the laws of conservation, suggesting that survival of consciousness after the death and destruction of the physical body is not only possible, but probable.  

Reality is an Infinite Intelligence encompassing space, time and consciousness

This concept is considered by most people to be objectively unprovable. Some people, including some scientists, accept it, and some reject it. Many claim to have proof by personal experience. It has been considered by organized science and religion to be a matter of personal belief and faith. This is no longer the case. It is logically proved on the basis of the other three truths. Reality is an infinitely logical system that human beings and man-made models reflect imperfectly in mass, energy and consciousness in three dimensions of space and one of time. Proof of this truth changes the world and our understanding of it profoundly.

As far as I am concerned, these four statements are facts that have been proved beyond doubt and are thus unassailable, absolute Truths. The implications of these four truths are profound and far-reaching in their practical implications.

The following is a new addition to the IQNexus feature article by Neppe and Close posted in this blog a few days ago.

Finite-infinite

The continuous infinite “super-reality” is directly inaccessible. However, components of it are mirrored in the finite discrete subreality. These are not separate because the finite is embedded in the infinite. Therefore, the finite in the infinite is not dualistic, like separate minds and bodies, or separate souls and physical beings, but reflects a “one-ness” that is inseparable. Infinity cannot be ignored. We postulate through TDVP, that the essential concepts of life and existence, and of multidimensional order, and of choice, might possibly all reflect different levels of the finite or infinite.

We’re like a finite land contained in an unending ocean in the infinite. The infinite has a different quality. There is no beginning and no end to space, to time and to the infinite repository of information. And this information translates into meaningful consciousness. And yet in the finite, everything manifests as discrete pieces of reality —quanta ²⁰². The infinite is like water from an unending ocean impacting on the large land pieces and manifesting as specific meaningful molecules of H₂O.

For us, we experience this finite subreality as small incomplete pieces of the jigsaw puzzle of our specific 3S-1t. This is limited through our restricted physical reduction valves. Components of this puzzle involve a consensual reality with others (such as seeing broadly the same sports game on television). Other parts are intensely personal and idiosyncratic (even our interpretation of that same sports game).

Yet, the infinite is pervading all Time and all Space, and potentially providing targeted intentioned, impactful, influential, interactive meaning and purpose in everything in the finite. In this way, the infinite is not a “virtual” reality: The infinite is as much a reality as our finite objects, yet we cannot conceive of most of it, and it is always influencing us at any moment. Moreover, we can change our fate and action, if only slightly, in the context of our little personal reality in that vast unending ocean. These are imprinted in that infinite super-reality, but only in the tiny portion that we’re directly involved in, although we may have greater, broader influences, like vortical ripples in a pond.

We, in 3S-1t, could phenomenologically interpret the unification of finite with infinite realities, and their linkage with gimmel, with Carl Gustav Jung’s concept of synchronicity ²⁰³. This is so in that, we, the experients, would be in a particular state of consciousness, when suddenly, something “intrudes” from another "dimension" altogether. This connects the initial state of that particular “something” in space and time, to an object, perhaps a thought, a symbol, or even a dream, that binds that state together with the second thought or symbol. Accompanying this linkage of the consciousness content, is the realization of the “magical” bond like a feeling of the infinite, or of a very important concept in psi research ²⁰⁴, like a blast of the "numinous". The numinous awareness stands out allowing the perception, interpretation, conceptualization and comprehension of two seemingly disparate events, things, thoughts or objects. They become actually joined meaningfully, in this instance, in our 3S-1t reality, which because of the consciousness is likely a 3S-1t-1C or 2C or 3C type experience. The likely unifier is the infinite flow of consciousness information (gimmel) translated and communicated across dimensions through vortical indivension into meaningful numina in 3S-1t [1]. For those in 3S-1t, the synchronicity is “acausal”—it appears without a cause, but that is just relative to 3S-1t, and, indeed, the linkage is more obvious at higher dimensional levels.

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[1]  Numinous is a term deriving from German theologian Rudolf Otto in 1917, and embraced by Jung.  The numinous experience  has a sacred personal quality experienced as a communion with a “wholly Other”. Numina areintense, divine-like and transcendent,  with the tendency to invoke fear and to attract, fascinate and compel. They also might imply an easier psi target because they would stand out in such activities as “remote viewing”.

WHAT TRUE-UNIT ANALYSIS TELLS US AND WHAT IT MEANS

WHAT WE HAVE LEARNED - AND WHAT IT MEANS

Applying the Calculus of Distinctions to Quantum Physics and Relativity led to the discovery of TRUE Units. From the TRUE unit analysis of the elements, we have learned that:

1. There could be no universe without the third form of reality, in addition to matter and energy, existing in every particle of the universe.

2.  The third form is the factor within elementary particles that makes possible the stable atoms and molecules that make up the universe.

3.  The third form is more than 95% of reality and is detected as ‘dark matter’ and ‘dark energy’ in spiral galaxies.

4.  Reality exists in nine real, sequentially-contained finite dimensional domains embedded in a conscious transfinite substrate.

5.  Nine-dimensional space, time and consciousness reality explains things inexplicable in the current scientific paradigm.

6.  The transfinite substrate contains all the logical patterns that manifest as physical reality.

7.  The elements of the Periodic Table, stabilized by the third form, are designed specifically for the purpose of manifesting life and consciousness.

8.  The multi-dimensional third form completes the patterns of Primary Consciousness of mass/energy in the four-dimensions of space-time. This relationship is expressed mathematically by the Conveyance Equations.

9.  The Conveyance Equations include the Pythagorean Theorem and Fermat’s Last Theorem, mathematical invariances that allow us to explore higher dimensional domains through Dimensional Extrapolation.

What it means, in plain English:

We are finite reflections of the Infinite Intelligence from which all reality originates. That Infinite Intelligence is available to all of us. The goal is to be completely and continuously aware of our eternal connection with the Infinite. The difficulty of attaining that state is directly proportional to our resistance to truth.