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Book Review: A Madman Dreams of Turing Machines

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This book was a fascinating look at two of the most important mathematicians in the twentieth century, Kurt Godel and Alan Turing, each plagued by his own set of weaknesses, and Turing in particular plagued by a society that just did not appreciate him.

Writing about Turing’s life these days is very much en vogue - his story is almost perfectly tragic, and the shocking injustice of his treatment at the hands of the British government makes for spellbinding drama that has a good liberal message at its heart. More than that, it would not be much of a stretch to say that the modern world is the product of his work: without Turing machines we would not have modern computers, and the cracking of the enigma code helped save democracy in Europe.

Godel though is a more interesting and obscure choice. He made, as far as I know, no significant contribution to political affairs, and his mathematical breakthrough - the discovery that mathematical systems may not be both consistent and complete - is not the sort of innovation that has obvious practical implications. Outside of mathematics itself, Godel’s work has significant implications in philosophy - as Levin demonstrates. Together with Heisenberg’s results in uncertainty, Godel helped overthrow the idea of determinism, or at least the idea that there is any sort of determinism we can ever hope to see.

As a piece of writing this book is quite fascinating; the subject is chosen with such great care. Godel’s and Turing’s lives never quite crossed paths, and they are similar, but different, in complementary ways: Godel the obsessive-compulsive who could not quite see beyond the existential dilemmas that touched so closely on his work, Turing the social outcast who was able to turn his brilliant insights into momentous impact. Close-but-not-quite encounters are interlaced throughout the story, and paramount among them are Godel’s and Turing’s: the two never worked together directly, but were aware of and impacted by one another’s work. Levin’s particular genius is her ability to explain abstract mathematics in readily understandable terms, without losing too much of the meaning in the translation: her exploration of the liar’s paradox and the motif of chess are particularly enthralling in that regard. Her recreation of historical events is similarly breathtaking, and gave me something like the chills: in particular, the scene with Wittgenstein debating Turing in his classroom makes me wish I could have been present for what must have surely been an awe-inspiring conversation. Along similar lines I wonder what it might have been to sit in the faculty lounge of the Institute for Advanced Study, on the day of Godel’s famous remark about European politics.

A relatively minor flaw is that Levin’s choice of imagery is in some places just a bit too neat. In particular I was less than thrilled with the use of apples, and the too-cute-by-half coincidence that both Godel’s and Turing’s methods of suicide both revolved around them, and the role they play in the Disney adaptation of Snow White. Perhaps I’m being picky but I found that coincidence a bit on the cloying side.

A somewhat more annoying flaw is Levin’s insistence on injecting herself as the narrator into the story, and the way that technique touches on the themes of linearity and circularity. Maybe I’m missing something, but I found the technique distracting, and on the whole uninteresting. There is so much wonderful material to work with in this subject area, that the addition of this layer just felt burdensome.

A more important flaw by far is that the book is simply not very pleasant to read: the emotional landscape ranges from sad to depressing. Obviously, the heroes she choose have difficult lives and the time period revolves around a terrible war; and of course, not all literature has to be happy. At the same time, I’ve always found the mathematics at the center of these two lives to be fascinating and a real joy to study; I was hoping to relive some of that experience while reading this book. So I think the emotional bleakness is evidence that Levin has focused overmuch on the personal lives of the mathematicians, without diving deeply enough into the math. (That idea, that we need to examine deeply the personal lives of mathematicians and scientists, is also very much en vogue these days.) Clearly - this is a popular book, not an academic one, so I don’t expect trenchant mathematical tracts or anything like that. But a more thorough, lifelike animation of the mathematics at hand - a real paradox that brings Godel’s theoretical one to life, say - would have been much appreciated.

There’s no question that Janna Levin has a tremendous talent for making mathematics, especially rather complicated mathematics, jump out of the page in gripping detail. Many of the flaws I found could have, I think, been resolved with a somewhat heavier editing hand. I’m glad I read this book and found it very rewarding on the whole.