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Culture War Roundup for the week of October 10, 2022

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What is "topology" in this context?

It's clearly a reference to (geometric but perhaps also algebraic/differential) topology, but he wrote the word in English, which seemingly communicates sarcasm. I believe he didn't mean the genuine application of those mathematical domains to plain word games covered by the rest of the paragraph. It is possible that this is a nod to Lacan style postmodernism. Consider this passage from Alain Sokal & Jean Brickmont's Fashionable Nonsense:

These authors speak with a self-assurance that far outstrips their scientific competence: Lacan boasts of using “the most re­cent development in topology” (pp. 21-22) and Latour asks whether he has taught anything to Einstein (p. 131). They imag­ine, perhaps, that they can exploit the prestige of the natural sci­ences in order to give their own discourse a veneer of rigor. And they seem confident that no one will notice their misuse of scientific concepts. No one is going to cry out that the king is naked. ... Lacan’s mathematical interests centered primarily on topology, the branch of mathematics dealing (among other things) with the properties of geometrical objects— surfaces, solids, and so forth— that remain unchanged when the object is deformed without being tom. (According to the classic joke, a topologist is unable to tell a doughnut from a coffee cup, as both are solid objects with a single hole.) Lacan’s writings contained some references to topology already in the 1950s; but the first extended (and publicly available) discussion goes back to a celebrated conference on The Languages of Criticism and the Sciences of Man, held at Johns Hopkins University in 1966. Here is an ex­cerpt from Lacan’s lecture:

This diagram [the Mobius strip17] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much further than you may think at first, because you can search for the sort of surface able to receive such inscriptions. You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface18, are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresponds to the neurotic subject, and on a cross-cut surface to another sort of mental disease. (Lacan 1970, pp. 192-193)

Jacques Lacan: Analogy to what? “S” designates some­ thing which can be written exactly as this S. And I have said that the “S” which designates the subject is instrument, mat­ ter, to symbolize a loss. A loss that you experience as a sub­ject (and myself also). In other words, this gap between one thing which has marked meanings and this other thing which is my actual discourse that I try to put in the place where you are, you as not another subject but as people that are able to understand me. Where is the analogon? Either this loss exists or it doesn’t exist. If it exists it is only possible to designate the loss by a system of symbols. In any case, the loss does not exist before this symbolization indicates its place. It is not an analogy. It is really in some part of the re­alities, this sort of torus. This torus really exists and it is ex­actly the structure of the neurotic. It is not an analogon; it is not even an abstraction, because an abstraction is some sort of diminution of reality, and I think it is reality itself. (Lacan 1970, pp. 195-196)

etc.

Was that it? Who knows. I can go and ask of course, but don't feel like it.

Somewhat off topic, his dirge to lost playgrounds has reminded me of this blogpost by Hugo de Garis. I thought there was something directly on topology there, but alas.

There is another main motive I have. I call it “Building CATHEDRALS of mathematical logic” The CTFSG is the most beautiful and most powerful piece of mathematics I have ever seen. I call it a cathedral of mathematical construction. It is dense, tight, enormous, extremely rich in structure (e.g. look at the Monster with its 10 to power 54 elements) and has the capacity, for anyone with a good math brain, to become totally engrossed by.

I notice, that when I get heavily involved with it, I begin to feel a happiness that ordinary living, with all its daily frustrations, does not evoke. This total engrossing provides enormous satisfaction as one masters the CTFSG step by step, absorbing and memorizing its huge pile of definitions, and then playing with them, to build massive mathematical structures, i.e. “cathedrals” of logic, mathematical logic.

I don't think advanced mathematics has been solved by computers...