peteg's blog - noise - books - 2023 10 12 Labatut TheMANIAC

BenjamĂ­n Labatut: The MANIAC. (2023)

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Kindle. It's a good, sometimes fun, well built jaunt through the early days of cybernetics and artificial life that continues with what feels like tacked-on coverage of a recent success. The appeal was that it might reach the heights of Francis Spufford's Red Plenty, which it doesn't. I also hoped for a dash of the crazy inventiveness of Ned Beauman.

For the main meal Labatut ventriloquises various people around John von Neumann as a means of giving some insight into the greatest mathematician of the 20th Century, and, I guess, the madness that hard thinking seems to induce in anyone. He opens promisingly with an account of the unknown-to-me Austrian physicist Paul Ehrenfest committing murder-suicide but soon enough retreats mostly to the well-rehearsed greatest hits: Albert Einstein struggling with a dice-playing God, Oppenheimer, David Hilbert claiming that Cantor had created a paradise and so on. But the opportunity to unpack these things is missed: just why did Einstein struggle with a probabilistic/undetermined universe? Apropos Hilbert, Gianpaolo dug up the following quotes for me:

I stated a general theorem on algebraic forms that is a pure existence statement and by its very nature cannot be transformed into a statement involving constructibility. Purely by use of this existence theorem I avoided the lengthy and unclear argumentation of Weierstrass and the highly complicated calculations of Dedekind, and in addition, I believe, only my proof uncovers the inner reason for the validity of the assertions adumbrated by Gauss and formulated by Weierstrass and Dedekind.

The value of pure existence proofs consists precisely in that the individual construction is eliminated by them and that many different constructions are subsumed under one fundamental idea, so that only what is essential to the proof stands out clearly; brevity and economy of thought are the raison d'ĂȘtre of existence proofs.

In other words, Hilbert relied on some idealised objects (that set theory justifies the existence or at least manipulation of) to obtain general results and felt the increase in quality paid for the ontological complications. (Less generously he declared ontological bankruptcy and thieved some theorems.) Of course many did and do disagree with the formalist position though the vast majority apparently continue to shrug and get on with their knitting. But what did von Neumann think about the foundations of mathematics? What was he aiming for before Kurt Gödel brought absolutist foundations (aka the Hilbert program) to an end? (The sketch at Wikipedia is thin and makes it look like he was completely eclipsed by Gödel and later Gentzen.)

Gianpaolo pointed me to von Neumann's The Mathematician (in Works of the Mind Vol. I no. 1, University of Chicago Press, 1947, pp180-196.) which contains some philosophical musings on these points. He was a fan of the axiomatic method which resolved millennia-long confusions over Euclid's axioms, but knew the lack of rigour did not inhibit the development of calculus/analysis for its first 150 years or so. He reckons it may be mostly just a matter of aesthetics (good taste) informed and freshened by empirical ideas.

The title is the name of von Neumann's computer at the IAS, the model of the JOHNNIACs. I was bothered by some clangers. In the context of artificial life, Labatut has an embittered Nils Aall Barricelli spout off about some of Alan Turing's assertions. He claims "Turing proved mathematically: there is simply no form of knowing what a particular string of code will do unless you run it." — which (under a generous reading) is true of machines but not necessarily of the oracles that are the central concern of this chapter. Also there is nothing so very strange about Turing's oracles: he originally only considered deterministic machines while being aware of the true randomness of quantum mechanical processes, and leaving the possibility that human insight might also add power.

The slight second part makes for a strange counterpoint, being mostly overblown coverage of AlphaGo's match with Lee Sedol in the style of sports journalism. Just the highlights thanks, and not enough to get to grips with anything of substance.

Tom McCarthy at the New York Times. Goodreads. Sam Byers: underpowered, diffuse. Ben Cosman summarises and sets it against Oppenheimer and notes there are three movements not two. Labatut is Chilean and has SBF's hair.