Thursday, January 11, 2018



©Edward R. Close January 11. 2018

The year was 1685. Traveling across Germany in a Pferdekutsche (stagecoach), Gottfried Wilhelm Leibniz and a traveling companion stopped at an inn for a short rest and a drink. Leibniz was already famous. About as famous in Germany as Einstein was in the US in the 1950s. He was a polymath: a medical doctor, mathematician, linguist, philosopher, scientist; he had invented something called “the calculus”, and he had produced the world’s first mechanical calculator that could perform multiplications and divisions. When he identified himself, the people in the inn laughed. They could not believe that this mud-spattered, ordinary-looking man could be the most famous man in Europe!

“So, then, Mr. Philosopher, what is the most important question a human being can ask?” One of the scoffers queried.

Leibniz frowned, cleared his throat, and said: “The first question a man of science should ask, is ‘Why is there something rather than nothing?’”.

Everyone laughed, and returned to their bier steins, shaking their heads, not realizing that what they had just dismissed as nonsense was, in fact, the ultimate question.

Why is there something rather than nothing? Modern science’s answer is “the Big Bang”. But that is actually no answer at all. The idea of something exploding into existence from nothing, is nonsense, and you don’t have to be a scientist to know that it is nonsense.

To find the answer, we must go back another 1,435 years, to the time of Diophantus of Alexandria. Diophantus was a Greek mathematician who lived in the third century, and died at the age of 84, sometime between 285 and 299 AD. How do we know how old he was when he died? He left a mathematical puzzle on his grave stone, which, when solved, reveals his age.

Inscribed on his tombstone was the following poem (translated from the Greek):
Here lies Diophantus. Now this wonder behold,
Through art algebraic, the stone tells how old:

God gave him his boyhood for one-sixth of his life,
One twelfth more as a youth, his whiskers grew rife;

After another one-seventh, had marriage begun;
And five years later, came a bouncing new son.

Cruel Fate took the child of this master and sage
When he was only one-half his father's final age.

Consoling four years with the science of numbers,
The sage ended his life, and in this grave slumbers.

A high school algebra student today can solve this puzzle by writing and solving two equations in two unknowns. Hint: Let X = Diophantus’ age at the time of his death, Y = the son’s age at the time of his death, and use the clues given in the poem to construct simultaneous equations.

Diophantus specialized in finding whole number (integer) solutions for algebraic equations. As a result, equations for which there are integer solutions are now called Diophantine equations.

What does this have to do with Leibniz’s “ultimate” question? To answer this question within the question, we have to refer to the mathematical work of a man who was nearly 40 years old when Leibniz was born, and died when Leibniz was only 19.

In 1637, an obscure French jurist, an amateur mathematician named Pierre de Fermat, had already answered Leibniz’s ultimate question, but he probably didn’t know it! In the margin of a page in a book on Diophantine equations he wrote: “I have found a marvelous proof, but the margin of this book is to small to contain it.”

Fermat’s proof of what became known as “Fermat’s Last Theorem”, was never found, and the renowned French thinker of the day, Rene Descartes, called Fermat “an uneducated trouble-maker” and tried to discredit him as an amateur. As it turned out, Fermat was at least as good a mathematician as Descartes. You may recall Descartes’ statement: “I think; therefore, I am!” But, of course, this is no more an answer to the question of existence than the Big Bang answer, because it leads to the deeper questions of what is ‘thinking’ and what is ‘being’.

Fermat’s proof ultimately depends upon the logical method of infinite descent. If something is assumed to exist on a large scale, and can be reduced by logical steps to a version of the same thing, but on a smaller scale, then it can be reduced again and again, until you arrive at a version of the same thing at the smallest possible scale. Then it can be easily proved to be either true or false, existing, or not existing.

Notice that the Big Bang theory is a form of infinite descent. The idea that the universe is began as the result of an explosion from a dimensionless point 13.8 billion years ago is obtained by an infinite descent in space and time, starting with something, i.e., what we have now, descending to nothing. But, that makes no sense. So, maybe it was a very dense mass that existed before the big bang? But, if so, where did that come from? What existed before it exploded? Something or nothing? If it was something, then the big bang was not the beginning of everything, only the beginning of the expanding universe we have today. If it was nothing, then we have a paradox with the production of something from nothing. If your answer is “God created it”. Then God existed before the big bang, and you can’t say there was nothing before the big bang.

Is there an answer? Yes, there is an answer, and Pierre de Fermat discovered the key to it while studying Diophantus’ equations. But, as I said, Fermat himself, probably did not realize that he had the answer to the ultimate question. That realization had to wait for more than 300 years.

In 1900, Max Planck discovered that the matter and energy of the physical universe exist only in multiples of a very, very small unit. This means that in the physical universe, infinite descent to zero is impossible. Descent stops at the smallest quantum. This is, after all, what Fermat’s infinite descent is about. It stops with an integral form, not zero. The infinite part of the name infinite descent is used because it can start with any assumed object, however large, and then descends to its smallest possible integral form.

In 1986, I developed the calculus of distinctions, derived from George Spencer Brown’s calculus of indications, adapted it for use in a quantum reality, and applied it to the big-bang expanding universe theory. I published the results in a book titled Infinite Continuity in 1990.

Here are two excerpts from Infinite Continuity:

From the first paragraph of the Preface:
“The digital clock beside my bed read ‘1:11’. It was one-eleven am, January 16th, 1986, and I had just awakened from a very vivid dream. A stone had dropped into a clear, dark pool, filling it with golden ripples of spreading light, and at the center of my awareness the pieces of an intricate puzzle had suddenly fallen together. Grabbing a pencil and paper, I began writing as rapidly as I could. So vivid were the details, so clear the understanding, that the heart of the vision flowed out onto the paper that night.”

From the last paragraph of Part V, Summary and Conclusions:
“We stand again on the threshold of a new scientific frontier. As science recognizes the connectedness of all things, the need to integrate the knowledge we have gained becomes more urgent. The formalization of a new science is required. This new science will encompass the existing paradigm, and yet transcend it by including the relationship of [Primary] Consciousness to matter and energy, and the relationship of individual consciousness to existential reality.”

The calculus of distinctions applied to quantum reality became known as the calculus of dimensional distinctions and one application developed in collaboration with Vladimir Brandin, was published in Elements of Mathematical Theory of Intellect, Moscow Interphysics Laboratory, Moscow, Russia, 2003.

Finally, in 2011, in collaboration with Vernon M. Neppe, MD, PhD, internationally renowned neuroscientist, I completed the proof of the existence of a third form of reality, which Vernon named gimmel, not measurable as mass or energy, and therefore non-physical. With that, the proof was complete, and the answer to Leibniz’s question was finally clear: There is something rather than nothing because there is no such thing as nothing.

This also validates Einstein’s statement in the final appendix of his book on relativity, written only a few years before his death, where he suggested that there is no such thing as empty space.

This answer bears emphasizing:

Fermat’s method of infinite descent applied to quantum cosmology proves that there never was nothing, there is no absolute beginning or end, only changes in form. Nothingness is a fiction, a meaningless concept conjured up by confusing changes of form with beginnings and ends.

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