Origins

In the beginning was the Element. It was an undifferentiated mass of infinite entropy. It would take an Omnipotent being to sort it into order. What happens when an Omnipotent Being meets an Impossible Task? We get a logically flawed universe, with two contradictory elements in it. And yet, a merely possible task is not fit for a truly Omnipotent Being. The universe thus begins with a paradox at its heart.

Out of the Element the Being creates Order, otherwise known as the World. The World is different from the Universe. The Universe is a totality of possibilities and realities, with nothing to distinguish the two. The World is unmistakably real. It is made up of dry dust, wet water, and the fiery firmament. It is where we wake up in the morning, where our feet touch the cold, hard ground as we yawn and stretch.

The Being has left the traces of his identity all over the World. He has wrestled with the elements. He has tamed them and sculpted them into the World. Much as the fingerprints of a potter on a vase conatin his idenity, the marks of the Omnipotent Being on the Order unerringly point to him.

No origin story worth its salt can have a prequel. We cannot ask for the origin of the Element, or about the formation of the Being. All matter originated in the Element, and that’s where the final bedrock of material existence is to be found. The order in the World may be traced all the way back to the Being, but no further. Our childish insistence on asking an infinite sequence of where-did-it-come-from questions is a sin, or worse, a fallacy.

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Some legends have it that the World has existed forever. Every moment is the end of an eternity. The present bears the terirble burden of an infinite past.

No amount of reasoning can rule out this absurd notion. But it is a welcome idea to those who believe that a universe of finite age cannot host a truly cosmic drama. It is also of comfort to believe that things have always been, and therefore will always be. Time, of neccessity, is timeless.

This raises consternation among those who believe in the Origin. Time, they insist, began at the Origin. If so, asks the skeptic, what were the Element and the Being doing before the origin? The believer replies that doing could not exist before the Origin. To do is to change things, and for things to change, time must pass. Where there is no time, eternity is identical to an instant. Those who believe in an infinite past really believe in no more than an instant. It is the instant of Origin, when change and time began.

The moment of the Origin or the eternity preceding it is called the Chaos or the Void. The terms are identical. Complete randomness has no more subsatnce than utter non-existence.

Excerpt from The Growth of Mathematical Thought

Once upon a time there were no numbers. We don't know exactly how long ago that was, because to measure that you would need numbers, and they weren't around yet. But it must have been fairly long ago. According to current scientific theories, numbers must have taken considerable time to evolve into their present state of complexity.

Homo Innumerensis - our ancestors - were a race not yet endowed with the ability to measure anything. They survived in an ancient world they didn't know how old, lived under a sun they didn't know how bright, and thrived amid a terrible paleolithic weather for which they had no predictions, especially wrong ones. It couldn't have hurt their chances.

And then, at some point, the numbers started appearing.

Admittedly, no one knows exactly how that happened. Where did all those numbers come from? The School of Exponentially High Divinity maintains that all species of numbers were designed by an Intelligent Designer in the space of a working week (the weekend being set aside for rest). How else would one explain the mind-boggling complexity of numbers, especially that of the complex numbers, not to mention the octonions and the operator fields? Surely, if you stumbled upon a complex object like a smartphone while walking in a garden, you would promptly put it in your pocket and proceed to infer that there must be a smart phonemaker somewhere? Likewise, if you stumbled upon an irrational number in your mathematical ramblings, would you not infer an intelligent, if not actually irrational, number-maker behind it?

There were a few minor glitches in this view, of course. Sometimes, for example, the the Design would not seem as intelligent. What kind of Intelligent Designer, the critics would ask, would consciously design such useless and grotesque absurdities like automorphic modular forms or the theory of superstrings? At this point the professors of Divinity are known to collapse into silence, occasionally after mumbling something about the Creator working in mysterious ways.

So far the most successful explanations have come from The School of Evolutionary Numerology (not to be confused with Revolutionary Numerology, which maintains that the world revolves around certain mystical properties of whole numbers expressed in base ten.) They explain that the simplest numers, the "natural" ones, spontaneously emerged from the primordial soup. After that it was the process of Mathematical Selection by gifted thinkers that produced a succession from natural numbers to rationals to reals to complex numbers and beyond. When asked for the place of the Creator in such a scheme of things, a famous mathematician is known to have remarked - "We did not have need for such an axiom."

Of course, criticisms of such an evolutionary theory have been widespread. Could highly complex mathematical structures really have evolved piecemeal, given that its coherence depends on the simultaneous existence of its many interlocking parts? What would a "field" do, for example, without its identity element? The answer is that it would be a "ring", which, while maybe not as well adapted as a field, is still a consistent mathematical structure capable of independent existence. In fact, the evolutionists explain that all complex structures can develop by a step by step evolutionary process - by a succession of mutations that lead to the addition of one axiom at a time to already existing theories.

In addition to the standard repertoire of Mathematical Selectionist theories, a different school of evolutionary thought maintains that a lot of structures (though not all) evolve simply out of random mutations in certain mathematical minds - mutations that are adaptively neutral. These mathematical theories are often considered "useless" by natural scientists, causing the aforementioned mathematical minds to feel a not inconsiderable degree of pride. But even though such structures resulting from "playful mathematics" may not have immediate practical value, they might later be co-opted for adaptive purposes, especially by physicists who are notorious  for such things (cf. "The theory of Spandrels" by Gould and Lewontin).

Though all the finer details of evolutionary change are still debated, the natural history of numbers continues to be best explained in the light of macro-evolutionary theories. It is expected that numbers will continue to evolve following the same broad patterns, although some have expressed the apprehension that an impending intellectual catastrophe, such as an excessive obsession with smartphones, may render humanity too dumb to carry on with Mathematical Selection. Others have expressed the view that if the invention of the automobile or the motion picture did not do the trick, perhaps nothing will.

“No man becomes this or that by wishing to be it, however earnestly.”
― Arthur Schopenhauer  

I wished to be a mathematician or a physicist. This was when I was 16 years old. I have since become a physicist. Of sorts. Not famous or important, but an average Joe scientist who conducts research in physics for a living. I suspect that, nonetheless, Schopenhauer was right. I feel that I am a physicist in letter, but not in spirit. I am assured that this is the "impostor syndrome" commonly found in young academics who believe that, unlike their gifted colleagues, they are bluffing their way through the system. I do not believe it to be the case with me. While others are only fake impostors, I am the real deal. Of course, this feeling could be part of the syndrome itself, or perhaps it is a syndrome in its own right. In any case, I will paraphrase Schopenhauer to reflect the reality of how I feel: “A man becomes but a pale imitation of this or that by wishing to be it.”

I also wanted to become a writer. This was when I was twelve, but also when I was sixteen, and when I was twenty and then twenty-five. Now that I am  thirty-five, I no longer wish to be a writer. But I wish to write. Perhaps it increases my chances of becoming, or being, a writer. In any case, it averts the possibility of an impostor syndrome, for I do not claim to be a writer in the first place.

I do not have a coherent story to tell. But at times I am gripped by the feeling that I have some things to say that are worth saying. When I say them to myself, they sound perfect. It is no fun. When I say them to others, they sound incomprehensible or pretentious or both. So I am writing them down, in the hope that a sympathetic reader will find them, and that the written word will survive longer than the echoes in an empty room.

There are only two more things I have to say by way of introduction. First of all, I claim no originality or accuracy for what I say. I doubt that anything new is really ever said at all. Only the way one says it is new. As for accuracy, it is a concept that I can barely fathom as a physicist, let alone as a (pseudo-) writer. Secondly, my outlook is fundamentally that of a pessimist. I do not  do things because I expect rewards to be the common or natural outcomes of efforts, but because I know that one gets lucky occasionally, and because the passage of time is its own reward.