Wednesday, June 21, 2017


The link below is to an image of the paths of the total Solar eclipses of 2017 and 2024. The X happens to mark a spot a few miles from the epicenter of the largest known earthquake ever in the US, the New Madrid quake of 1812. We're told that a large quake, 8 to 9 0n the Richter scale, has happened about every 200 years in this area according to geological evidence.  Will the combined gravitational pull of the earth and sun lined up in a total solar eclipse on August 21, 2017 be enough to trigger the next one? Incidentally, we live about the same distance from the center of the X as the epicenter of the New Madrid Missouri quake of 1812, well within the paths of both solar eclipses! We have a front row seat to view the 2 minute and 40 second maximum eclipse on August 21, and we're only a few miles from the New Madrid fault. Would you be excited, or scared?


Monday, June 19, 2017






COME EXPERIENCE A PRESENTATION OF THE DISCOVERIES OF Vernon M. Neppe and Edward R. Close, creators of the new science of Dimensional Biopsychophysics



Dates and locations of presentations to be announced.

Friday, June 16, 2017


 A recent email to an ISPE friend:

A good friend does not give up trying to convince someone he considers to be his friend of the truth. I believe that you are my friend, because if that were not the case, you would have given up trying to convince me that my FLT65 proof is flawed long ago. So, in return, I must not tire of trying to convince you that FLT65 is valid, as long as I see it that way.

After responding to your recent email containing the short circular argument put forth by your retired math professor friend, I had an inspiration. I believe I see a more direct way to explain FLT65. Here it is:

If one number is divisible by another, then dividing the smaller one into the larger one produces a zero remainder, while if they are not divisible, the remainder is non-zero. These simple facts are expressed by the division algorithm and its corollaries and they are true for all polynomials over the field of real numbers, whether reducible to integers or to any other real number.

Recalling FLT65, we see that when p ≥ 3, p a prime number, the FLT equation can be factored and expressed in the form (z-x)( zp-1 + zp-2x + zp-3x2 + ••• + xp-1) = yp. If there are integer solutions for zp – xp = yp, then, with specific integer values of x, y and z, g(z) = z–x and f(z)= zp-1+ zp-2x + zp-3x2 +•••+ xp-1 must be equal to relatively prime integers raised to the pth power. That is to say that, if there is an integer solution, then yp will be equal to BpAp, where Bp = z –x, and Ap = zp-1+ zp-2x + zp-3x2 +•••+ xp-1, A and B relatively prime integers. Furthermore, for an integer solution, the fact that integers are closed with respect to addition guarantees that there is always an integer a, such that z –a = A.

Of course Ap is divisible by A, so Ap = zp-1 + zp-2x + zp-3x2 +•••+ x p-1 must be divisible by A = z – a, and the division algorithm Cor. III says that f(z) is divisible by z – a, IF AND ONLY IF, the remainder, f(a), is equal to zero. Therefore, to find the value of x for any given values of z and a, we must set f(a) = ap-1 + ap-2x + ap-3x2 +•••+ x p-1 = 0 and solve for x. There are exactly p-1 solutions to this equation and for all of them, x is non-integer. This proves that for z and y equal to integers, x cannot be an integer, and FLT is proved.

I believe that the argument above is a more direct way to see FLT65, and it is completely equivalent to FLT65. I also believe that it becomes even clearer when illustrated with a numerical example, and I will use one provided by the critics.

While there are a few competent mathematicians who agree with me that FLT65 is a valid proof of FLT, more of them agree with you. For example, while reviewing my work, a Nobel Prize physicist and a very competent Israeli number-theory professor of mathematics, responded with what, in their opinions are counter examples that call FLT65 into question and, they believed, might even refute it. 

They both correctly noted that my argument in FLT65 is that when the factor of the Fermat equation f(z) = zp +xzp-1 +… + xp-1 is divided by z – a, the remainder, f(a) cannot be zero, while, for any integer solution, f(z) is definitely divisible by z – a. In fact, f(z) = Ap divided by z - a = A is Ap-1, where, if there is an integer solution to the Fermat equation, A is an integer, and this produces an inescapable contradiction. They argued that this is, or may be, incorrect because they could produce examples  for the equation when p = 3 with the remainder f(a) non-zero even though f(z) is clearly divisible by z - a when certain integers are chosen for z, x and a.

Here is one such example offered by the math professor:
Let z=7 and x=4. Thus 3 divides z2 +xz+x2, because f(z) = 49 + 28 + 16 = 93 = 3x31. So for a=4, the integer z - a = 3 divides the integer z2+xz+x2. However, in the polynomial ring R[Z], the polynomial z - a does not divide the polynomial z2+xz+x2 =z2+4z+16.  Indeed, the remainder is a2+xa+x2 > 0. Thus, he reasoned, the non-zero remainder when dividing polynomials does not prove that f(z) is not divisible by z – a = A if x, y, z, and a are integers.

There is however, a serious error in this argument. The error lies in the fact that, after choosing z = 7 and a = 4, the value for x is arbitrarily, and incorrectly chosen to make f(z) divisible by 3, allowing the production of a spurious “counter example”. The error is compounded by assuming that this supposed disparity in divisibility between the polynomial f(z) and its integer value may exist for the Fermat equation.

In fact, if z = 7 and a = 4 in the Fermat equation, then x cannot be equal to 4. This is easily and clearly demonstrated as follows:

The division algorithm expresses the essence of the fundamental operation of division for all real numbers, including integers. Corollary III of the division algorithm says that f(z) is divisible by z – a IF AND ONLY IF f(a) = 0. Therefore, in this example fabricated by the math professor, in order to see what x must be to satisfy the equation when z = 7 and a = 4, we must set f(a) = 42+4x+x2 = 0. When this equation is solved for x, we see that x cannot be equal to 4. In fact, solving this equation for x, we see that the two values of x satisfying the equation with z = 7 and a = 4 are – 2 + 2Ö3i and – 2 - 2Ö3i, which are complex numbers, and definitely not integers.

This is easily generalized for all integer values of z and a, and for all p>2 because all values of p are odd allowing the factorization into z – x and zp-1 + zp-2x + zp-3x2 + ••• + xp-1, a polynomial of p terms; and that is exactly what FLT65 does. The polynomial f(a) can never equal zero if x, z and a are integers, which they must be for an all-integer solution of the Fermat equation zp – xp = (z-x)(zp-1 + zp-2x + zp-3x2 + ••• +  xp-1) = yp. This proves FLT.

Now one must ask: Why has this simple proof, which I believe is, in essence, Fermat’s “marvelous proof”, been overlooked for more than 300 years, even by the world’s most brilliant mathematicians??? 

It appears to go back to Leonhard Euler and Carl Friedrich Gauss, arguably two of the most brilliant mathematicians of all time. Euler used complex numbers to prove FLT for p = 3, and Gauss developed modular algebra in an effort to prove or disprove the solvability of Diophantine equations including FLT. Unfortunately, like many mathematical procedures, modular algebra obscures as much about integer and non-integer polynomials as it reveals. When Gauss was unable to produce a proof using this method, he famously announced that he could produce any number of such theoretical propositions that could be neither proved nor disproved, and thus would waste no more time on it. This set the tone for many professional mathematicians in the years to follow.

Kurt Gӧdel’s incompleteness theorem proved that there are always logical propositions that cannot be proved or disproved within the mathematical system giving rise to them. This strengthened Gauss’s speculation that FLT might not be provable using basic mathematics. Add to this the increasingly extreme specialization encouraged by academia in the last 200 years, and you have a general attitude that Fermat must have been mistaken about having a proof.

Especially after Andrew Wiles and Richard Taylor produced a torturously complex proof of hundreds of pages in 1995, it was thought probable that Fermat had fooled himself into believing that he had a proof, when in fact he had not, because the complex theorems used in Taylor and Wiles’ proofs were not available to Fermat in 1637. This line of reasoning, while convincing, of course does not prove there can be no simple proof.

After many years of trying to get professional mathematicians to take my 1965 proof of FLT seriously, I had given up. When I discovered in about 1989 or 1990 that FLT had an important application in quantum physics, I revisited FLT65. In 2010, even though the quantum physics application only required FLT to be true for p £ 9, I mentioned my 1965 proof to Dr. Neppe, who was intrigued, and after studying it and proving it correct for himself, urged me to resume efforts to get it recognized and accepted.

To date, only a few competent mathematicians have agreed with me that FLT65 is a valid proof, but, importantly, no one has shown me any real proof that FLT65 is not valid. The proclivity of professional mathematicians to dismiss it because of the belief that no simple proof is possible has led even otherwise competent mathematicians to think erroneously that examples like the one presented above disprove FLT65. 

Even those who have acknowledged that such examples are not counter examples because they have no relevance to actual solutions of the Fermat equation, apparently are loathe to think that FLT65 could be valid.

I believe that the simplified FLT65 approach presented above should convince some skeptics, perhaps including you, my friend, of the truth of FLT65, if it is carefully and thoroughly considered.

With Regards,

Ed Close June 16, 2017

Tuesday, June 6, 2017


HELLO from Chapel Hill!

Click on the link below to read our new article on IQNexus Joirnal.

On thhe IQNexus Website click on Magazine and then scroll down to lhe latest volume.

Saturday, June 3, 2017


I thought those of you who have followed my posts on Fermat's Last Theorem might be interested to know that another university math professor has tried to disprove my 1965 proof of Fermat's Last Theorem. I'm posting it and my reply below; but I am witholding the names because I don't want to embarass anyone.

I received this email message from a friend in ISPE who doesn't believe my 1965 proof is valid:

Dear Ed,                                                                                  June 2, 2017

I tried to send this note to you on May 31. I probably used the wrong e-mail address. I’m trying again with this address.

Because of a common interest in music for big jazz bands, I recently made friends with a retired professor who taught mathematics in a university for years. Even more recently, I showed him a copy of FLT65. He agrees with my claim that FLT65 is flawed, but this note is not just to tell you that. I want to give you his explanation.

He has shown me what purports to be a more rigorous way to describe what he and I see as the flaw. My “arm-waving” description of it never convinced you, but perhaps his approach will be more persuasive. In any case, I think that you should see it, so I’ve pasted it onto this note below.

                        Sincerely, _______

I think I may have a useful thought for you on FLT65.  Your criticism of the proof is, I believe, exactly correct.  Here is a possible way of putting it that might convince Mr. Close.  In his argument he sets  a = Z - A   and considers the divisor polynomial  g(Z) = Z - a, which he says is a polynomial of degree  1  in Z.  But  g(Z) = Z - a = Z - (Z - A) = A,  which is not of degree  1  but of degree 0.  When the divisor A  is a (nonzero) constant, the polynomial division algorithm over the reals just says there exists a (unique) polynomial  q(Z)  such that  f(Z) = Aq(Z) + 0, where, of course, q(Z) = f(Z)/A.  so there is no  f(a).

My Reply, sent  7 AM, June 3, 2017:

Dear _____,

It's nice to hear from you; I hope you are doing well. We're leaving tomorrow for a conference in Chapel Hill NC, and we're busy packing today, so I'll have to be brief. I've seen this argument a couple of times before. One time was from a university prof considered by many to be one of the best in number theory. It only took a few lines to reveal his error. FYI, he acknowledged his error, and could never produce a disproof of FLT65, but he still felt that it must be flawed! I’m sure you will agree that mathematics should not be about feelings or beliefs.

Think about it for a minute. If you argue that z - a is not a 1st degree polynomial, you destroy the division algorithm for all polynomials. Yes, for specific values of Z and a, Z - a is a constant. But that is true for any and every polynomial. And the variables of any polynomial factor of any equation will take on specific values determined by the solutions of that equation.   

Your friend also says "the polynomial division algorithm over the reals just says there exists a (unique) polynomial  q(Z)  such that  f(Z) = Aq(Z) + 0, where, of course, q(Z) = f(Z)/A.  so there is no  f(a)".

This is a fine example of circular reasoning! When you set Z - a equal to a constant, which you can do for any polynomial, this statement is true, but, if it disproves FLT65, then it means that every polynomial is divisible by Z - a because every polynomial has solutions for which z - a will be constant. The point of the division algorithm is that f(Z), defined for all real numbers, is only divisible by Z - a when the remainder disappears, i.e. f(a) = 0. And the point of FLT65 is that because of the unique form of the Fermat equation’s factor, f(a) can never equal zero, and integers are reals, as stated in FLT65, a fact that no one disputes. 

All the Best,


Ed Close

NOTE (Not a part of the exchange copied in above.): The argument put forth by most who don't want to believe that FLT65 is actually a valid proof, is that the division algorithm works for polynomials of a continuous variable, but may not work for integers. This is handled in the 1965 proof by noting that the division algorithm holds over the field of real numbers, and integers are a set included in the field of real numbers. In the case of X to the nth power plus Y to the n power equals Z to the n power, when n = any prime number greater than 2, (the equation of Fermat's Last Theorem), no one has proved otherwise. 

Monday, May 22, 2017



Read about it in a book written for the general public

Help us get this book out! Send a donation of $25 or more to Ed and Jacqui Close, P.O. Box 368, Jackson, MO 63755. Include a mailing address, and we will send you an autographed copy as soon as the book is published.


Notice how, in the process of solving the cube, just as in the course of our lives, there is no simple formula with a set number of rules and deterministic steps to the solution. There are many choices at every turn, and many, if not most of them may lead into time-consuming loops that take us nowhere, and often only make matters worse. In life, as in the course of solving the cube, the path from pain, chaos and confusion to a coherent and stable existence is not obvious. We are constantly struggling to understand where we are in the process of learning the lessons of life, looking for hints, in the form of patterns that occur as results of our actions. Sometimes we make wrong decisions that lead to time-consuming sidetracks, just as in solving the cube. But there is always something to be learned...

...In most cases, we have no conscious memory of what happened before we opened our eyes as an infant, but this is an illusion. We do have a deep somatic memory hidden in the structure of our slowly forming bodies. We are not born as empty containers, little blobs of unstructured protoplasm with no knowledge of the past. Not at all. In fact, each blob of protoplasm blossoming into this world has within it a vast storehouse of memories, physically manifest in complex single and double spiral structures called RNA and DNA, containing records of the distant past and blueprints for the distant future...

...Also hidden from us as long as our consciousness is focused on and attached to the physical body, is the complete record of the process of the manifestation of Primary Consciousness in the finite worlds of nine dimensions. This memory, existing beyond time and space, in Primary Consciousness, is called the Akashic Record. Our sub-conscious and super-conscious connection with Primary Consciousness is the reason we have an intuitive sense of direction, of meaning and purpose. Without this intuition, we are nothing, full of sound and fury for a while, signifying nothing. Without intuition, we have no way of knowing who we are, where we came from, or where we are going. We only know that we are conscious, and truly, for us, reality begins with consciousness...

…The finite, measurable manifestation of Primary Consciousness in the physical universe, shapes reality from the quantum level to the cosmic level, and how experimental data and the known laws of dimensional mathematics and physics reveal the existence of gimmel, and our connection with infinite Primary Consciousness. In the process of learning who and what we really are, we become aware of all our memories and our connection with Primary Consciousness. Achieving this level of individual awareness is called cosmic consciousness. Cosmic consciousness is the purpose of finite reality, the physical universe, life, and the consciousness manifested in it...

… Life, in its many forms, is finite manifestation of consciousness, which is infinite. The most important discovery of TDVP is that there is a third finite form of reality, in addition to mass and energy. We call it gimmel. Gimmel is mathematically and physically required for sub-atomic, atomic, and molecular stability. 

[Gimmel is the first manifestation of consciousness that makes atoms, molecules and life possible. Gimmel is the simplest form of consciousness that organizes physical reality to allow the kind of stable structure that supports organic life, the physical vehicle of consciousness.]
...The discovery and proof of the existence of gimmel eliminates materialism as a viable basis for science and human understanding. Spiritual evolution is the driving force behind the universe, not some random meaningless explosion, the conclusion of reductionist materialistic science. Reality does not, and cannot exist without consciousness.

© Edward R. Close May 21, 2017

Sunday, May 21, 2017


How can this popular puzzle/toy have anything to do with serious questions about reality?

© Edward R. Close May 21, 2017

For me, the first glimpse of the potential utility of the Rubik’s cube for explaining the geometrical aspects of reality came when I found that the “intrinsic ½ spin” of fermions, the building blocks of the universe, could be physically simulated using the cube. Not only that, I discovered that the simulation provides a visual physical understanding of how intrinsic spin is simply the natural result of an object spinning in three, six or nine dimensions. This was an exciting discovery, but when I found that electrons, quarks, protons, and neutrons could also be modeled using the cube, I knew I was on to something. Imagine my excitement when I discovered that the cube could be used to simulate not only quantum physics, but also relativistic cosmology, and even spiritual evolution!

To understand how a simple Rubik’s cube can be used to simulate things as different and complex as particle physics, galaxy formation and spiritual advancement, it is necessary to realize that all possible finite patterns and forms are reflections of the structure of infinite reality, and that the structure of reality is pure invariant mathematical geometry.

The Greek philosophers Pythagoras and Euclid developed much of the logical and geometrical basis for the mathematics of modern science. The axiomatic concepts upon which their work was based were drawn from observations of the natural world. They were, in fact, symbolic representations of the structure of reality. But the various forms of mathematical methods based on their work developed over the past few hundred years, have been used primarily for practical engineering and technical purposes. Because of this, most scientists, and virtually all engineers and technicians, consider mathematics to be nothing more than tools for solving physical problems, and the connection between mathematics and reality has been blurred, if not completely lost. Because of this, we find modern scientists and mathematicians expressing surprise when theorems developed in pure mathematics turn out to have direct correspondence with observable physical phenomena.

This loss of awareness of the connection between mathematics and reality is the hidden cause of a major problem in modern scientific efforts to produce a successful mathematical representation of reality. Without re-establishing this most basic connection between mathematics and reality, finding anything approaching a “theory of everything” is impossible. This problem, endemic in modern science, once identified, is surprisingly easy to resolve. Let’s have a brief look at how the problem arises, and the solution.

Some statements we hear from modern scientists are symptomatic of the problem: Physicists today declare that there are two different sets of mathematical rules for physics, one for the macroscale and another strange, counter-intuitive set of rules for the quantum realm. And they can’t seem to resolve the conflicts between the two sets of rules. Intuitively, they must know that reality is internally consistent, and that the conflicts really just indicate that one or both sets of rules are either partially wrong, or incomplete.

At the root of the problem is the misapplication of a mathematical method that has been known as “the calculus” for more than 300 years: the calculus of Newton and Leibniz. The fact that it is called the calculus, and not just “a calculus”, is also symptomatic of the problem. It is in fact, just one of several calculi that can be defined at the interfaces of dimensional domains. It happens to be defined at the interface of space and time, which makes it very useful for analyzing and solving everyday problems involving motion.

Like all puzzles, once the nature of the problem is understood, and a solution is found, we often wonder how we could have missed it for so long. This is no different: The fact that “the calculus” doesn’t apply at the quantum level should have been obvious. The only excuse we have is that the calculus was so successful solving everyday problems that we simply didn’t think to look at the basic assumptions behind it. If we had, it would have been obvious that there was a serious problem.