peteg's blog

Martin Davis: Engines of Logic (softcover, previously The Universal Computer)

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Professor Martin Davis got sick of engineers getting all the credit for the omnipresent computational machines and wrote this book, released in 2000, to reclaim some ground for the grand tradition of logic. It is lively, well-written, but too short, selective and incomplete, as it is driven by the author's interest in particular topics, which he doesn't always contextualise sufficiently for the non-expert to nod along with.

The Professor is most famous in computer science circles for his propositional calculus, which is still the basis of modern SAT technology as far as I know. This doesn't really come out here, or why SAT is so important. Similarly Wittgenstein gets mentioned in passing, but nothing is said of his contributions to the story of logic, or his overlap with Russell and Turing. This book seemed a prime opportunity to canvas his opinions of Gödel's work and also Turing's. The micro-biographies of the logicians are quite well done, I think, albeit with a slightly jarring special focus on their political stances and (anti)semitism. (Many Jewish intellectuals oppressed by the Nazi regime moved to U.S. academia, with Princeton a major beneficiary.) Even so I came away with no better conception of David Hilbert than that with which I started. I guess mathematicians don't stick.

Personally speaking, I'm not interested in reading pop sci accounts of Turing or his machines; his biographer Hodges has more details, and it is difficult to get excited about the 1001st popularisation of the universal machine. I skipped those bits, and for that reason this wasn't the book for me. Conversely I was interested to know how set-theoretic esoterica like the Continuum Hypothesis (that Davis goes on about) fit with notions of computability. What do the constructivists think? What does Davis think about the rise of neo-Brouwerism, the contemporary flowering of type theory as a (the?) logical foundation of programming? We want to know! Instead we get some engagement with the philosophy of AI types like Penrose and Searle, which seems so quaint in these days of Google-level natural-language processing, and what IBM recently did with Watson. Intelligence is so 20th century.

The obvious comparison to draw is with Logicomix. I'm not going to attempt that.

Some money quotes: On Kurt Gödel:

When Gödel: sought to become a U.S. citizen, he prepared, in typical Gödel: fashion, for the perfunctory examination on U.S. institutions before a judge — he submitted the Constitution to the kind of meticulous analysis only he would have performed. Moreover, he became quite agitated when he concluded that the Constitution was actually inconsistent. While driving to Trenton, the [New Jersey] state capital, for the procedure, Einstein and Morgernstern his supporting witnesses, tried to distract Gödel from his discovery, fearing it might cause trouble if broached. Einstein told one joke after another. But when the judge asked Gödel whether he thought a dictatorship like that in Germany was possible in the United States, the candidate began to explain his discovery. Fortunately the judge quickly understood with whom he was dealing and interrupted, so that all ended happily.

Davis also recycles Turing's good point that Gödel's incompleteness theorem only applies to sound systems, i.e. in a limiting sense intelligence requires us to be prepared to speculate. Turing made similar observations.

On Hegel:

[...] Despite Kant's emphasis on the importance of science, post-Kant philosophy in nineteenth-century Germany evolved in a different direciton, moving to an absolute idealism that conceived of ideas and concepts as primary and sought to understand the world almost as though these were what it was made of. One of the leaders of this movement was Georg Wilhelm Friedrich Hegel, whose lectures were attended by hundreds of eager disciples. Hegel had many followers (among whom, famously, were Karl Marx and Friedrich Engels), and scholars still find much worthwhile in his writings. However he was capable of contorted reasoning that simply invites ridicule, especially in his massive two-volume Science of Logic in which readers were asked to ponder the deep thoughts:

Nothing is simple equality with itself.

Being is Nothing.

Nothing is Being.

Both of these categories in the transition from each to the other dissolve into the further category: Becoming.

That probably tells you if this is the book for you. In any case, do read this good interview with Davis.

Saving Private Ryan

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With one half of Hollywood off fighting in Guadalcanal, crowd pleaser Spielberg took the remaining men to the beaches of Omaha on D-Day, 1944, delegating operational command to Captain Tom Hanks and his band of teary-eyed cannon fodder. The opening action is incredibly well-shot, perhaps the best unreal war footage I've seen, which makes the dialogue in the less breathless scenes so much more painful. (I remember being completely overwhelmed by that opening scene when I saw this at a cinema back in 1998.) The incredible scale of these scenes and the rhythm of life in the army (at least as I imagine it, tedium interlaced with adrenaline rushes) are somewhat ruined by the impression that these boys barely know each other, let alone themselves.

Matt Damon is actually pretty decent here, maybe because he has a bit part. Tom Hanks always strikes me as hokey, in a way that American audiences seem to love. Wave that flag, shut up and love your country already (or leave). #43 in IMDB's top-250.