Modulo

I.

An axiom, we know well, is a police officer. The vagrancy law that no officer can abet is the identify of indiscernibles. This legal instrument regulates that which can be reasoned about; it demands that the objects of thinking are perceivable in their plurality — more simply, that two indiscernible things must be thought-of as one.

But humans, peckish and thieving, have a way around this. The law establishes identity from indiscernibility, but (in the generic case at least) leaves discernibility as non fingo. We can therefore use the up-to structure to commandeer and puppeteer identity. We can say “noon” up-to the day and never specify a date. We can reason about noons in general; we can, for example, invent longitude by measuring how fast noons are coming as we sail. This is how “applied” anything works.

In mathematics the up-to structure is available for integers in modular arithmetic. It is also available generically through equivalence classes and quotients (sets, groups, what have you). The theory of parity (odd/even structure) is ordinary arithmetic modulo 2; hours are arithmetic modulo 12 or 24: in the mod-12 style, 3 hours and 15 hours past midnight are both “three”. Each of these is an example of equivalence classes. Equivalence is a true upgrade from indiscernibility, one of those rare cases in which metaphysical conceit gets pwned by simple formal maths. Indeed, maybe there is no such thing as indiscernibility — maybe everything is indefinitely distinct, pantha rhei, and identity is a fully bogus idea.

This is immaterial — equivalence, a true gentleman, frees us from identity without undue punishment of its vanquished rival. We get a call-the-manager bell, a rape whistle, a get-out-of-jail-free card called modulo. Whenever in trouble, it’s always possible to scream it, modulo! The indefinite wealth of lived experience — each gust of wind, each passing wink — is safe and tucked away from mean cops.

II.

A good friend of asemic horizon counsels me on occasion to leave politics alone if I expect to make anything out of theory. He’s right — the political take space is way overcrowded and an interest in politics is an unwelcome signal of being chiefly interested in posturing about unactionable scenarios. Of course, asemic horizon emerges from politics originally; it emerges from the theoretical desire (the libido sciendi) of discussing the Brazilian situation modulo surface-level news events that obscure always-ongoing structural affairs. Improbably, this got us somewhere: everything worth discussing was worth something; structural affairs were always quotient affairs with axiologies.

[“Quotient” is very closely related to “modulo”; roughly, the quotient set of integers towards parity, or Z/2, is the set of integers modulo 2, or up-to-parity, or the set of equivalence classes of integers resp. parity; ultimately, the “set of parities”, an adjective having been wonderfully transmuted to a substantive. Political “affairs” are, of course, not sets; but every time “modulo” can be clearly used, so can “quotient”, wonderfully blinking between adjectival (theoretical) and substantive (actual-structural) form.]

This is not actually how theory was first discussed. Objects of discourse were declared not as actual classes, but as models of their quability conditions. Quability was akin to satisfiability in constraint-satisfaction theory. Everything was in the implicit solution to a (possibly unsolvable) system of equations, an inevitable consensus, a mad drift towards infinity. Talk of “quables” (which would be more or less amenable to the quotient form treatment) was sparse at first and died down entirely. There was, ultimately, a sense that this cosmic ambition — speaking only of the large-scale, inevitable conditioning factors, and the conditions on that, if needed – was the only way to build something that might, at some point, produce the vocabulary needed to say the unspeakable.

It can only follow that theory in the asemic horizon sense must be unintelligible. As forceful and overflowing with technicalia, the stuff of theory is in its minor inconsistencies. Theory is a mood. The mood sets the conditions for thinking; conversely, thinking must satisfy the mood.

III.

If I was to drop all pretense of quability theory to give a report on the ongoing situation, I’d have also to drop all of the sequence of quotients afforded by theory: I’d have to report on my city, on my neighborhood, on my street, on the birds and tree maintenance and emerging styles of leisurewear. I would need to become descriptive and colorful and convey an entirely new mood of exotica (not Colombian Magical Realism; maybe Structural Tropicalia) that set the conditions for understanding… something.

But it’s increasingly unclear that Structural Tropicalia holds any interest. All world politics has been suspended in favor of American politics, which sets the tone and the terms of (symbolic and monetary both) exchange. To the extent that politics away from the real world (i.e. America) still takes place, it does so in contravention of structural affairs. It’s reasonable to assume that even the Revolutionary Guard will lose its efficacy, that its gradual coup will lead to rule over empty cities.

The cosmic ambition that agitates quability theory can only grow in answer to this. Theory is waiting: therefore, it thrives in the despondency of the Real. The only real answer to stagnation and diminishing returns is to eat the sun itself. Given that theory is the theory of generic structure, and nothing at all can be meaningfully thought-about except if modulo generic structure, theory is the only means we have to prevent an ongoing symbolic (cultural, cognitive, hydraulic….) collapse.