Purity and Aberration

The story I want to tell here isn’t all that difficult. It speaks of an initial insight, or an initital moment of purity governed by what I want to call the equivalence hypothesis. The equivalence hypothesis is the says, basically, that there is no development “beyond” the initial, tautological understanding: that an intital tautology / rejection is equal to the “familiar” understanding, the profound, deep, undertanding or the state of being “within”. It is basically the hypothesis or the principle that there is nothing “deep” or experiential about our understanding of something, that there is no difference between an “external” tautological understanding and an “internal” familiar one.

I don’t want to be overly conceptual, but we can see, even thinking generally, how the equivlance hypothesis is equivalent to the distinction between purity and aberration we want to make here. The purity, the state of purity, is the “initial” tautological understanding, while “aberration” is what we remember of it, it may be associated with the return of factors of “experience”, etc, the renewed distinction between inner and outer.

Let me give an example, our experience with math — the entirety of the experience I mean, from intitial exposure, to fascination with rigor, to disillusionment, to the social aspects, to myths of great mathematicians, to metaphysical questions, to models of the brain, and so on. I find it remarkable, now, how long and how pervasive my misconception of math has been. What’s remarkable is that one can be “good at” math while holding serious misconceptions. But this may be because being good at math becomes much like being good at any technical or semi-technical activity. Our initial understanding (“initial” here, simply meaning, our first, and not in the “initial-purity” sense I spoke of above) of math is an aberration, it understands math much like any other thing. One finds it hard to distinguish between, for example, math, athletics, religion, etc., except superficially. We may even be aware of this, which is why we fall into “humanism”, as if the human underlies all these activities. “The human” seems to be the persistent error for the young, who are always discovering that superficial differences melt away into a common human — and not being aware that this is because their understanding is fundamentally an aberant, that it is a misunderstanding. The young are not pure.

But what is purity, in math, what is the original, or perhaps, both the original and the final understanding — the specificity? It is, I want to say, a combination what I want to call (1) absolute negation and (2) a kind of living on. This is not fundamentally different from what I proposed a few weeks ago in “Bartleby’s Tautology”, or, it is simply saying that we reject and affirm at the same time, and that the affirmation is in fact “tautological” — so that it is not really a choice (where what we affirm is a positive alternative to what we reject.) But the word “pure” has an interesting .. valence, or brings to mind an interesting picture, thought not reallyall that definite. It seems to underly everything we think about, including “Bartleby’s Tautology”. I don’t want to get too personal here, but it strikes me, as I skim that essay, that the understanding of the situation there was too general, it doesn’t say enough. It wants to equate purity with negation and tautology, but it doesn’t, and instead, leaves open the possibilty of creativity, allowing the old notion of the human to sneak back, eventually. Logically speaking, that essay is really about the creative, it is the self-creation at the moment of negation. But that is only logically, it is almost as though a genuine understanding of that essay necessarily requires the idea of the pure, and of a more intense form of rejection.

The pure is an understanding of universal sentience — all intelligence, including animals, aliens, etc., must have some understanding of the pure. But precisely because of this, the pure can never be confused with the rigorous — the pure is not a consequence of rigor, but it is anterior to rigor — so much so that our later (“intitial”, in the sense of, “novice”) understanding of rigor is aberrational.

But what is math, if not technics? It involves a kind of absolute negation in our dealing with numbers…



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