Wednesday, January 16, 2008

A Madman Dreams of Turing Machines

Janna Levin
Where is God in 1+1=2? There is no God.

But we all know you discovered the ultimate limit. Einstein showed that nothing can travel faster than light, Heisenberg realized that we can never transcend quantum uncertainty, and you taught us that numbers, numbers even, are forever beyond human reason.
Some books are worth reading because they are well written, others are worth reading because their topic is interesting. This is one of those others. Janna Levin is not a particularly engaging nor interesting writer. The few points where you encounter her pure voice are mostly characterized by a reliance on the scattered and whimsical-sounding tunes of complex physics. And sometimes the topic is of such interest, bad writing cannot taint it.
Perhaps I'm being too hard on poor Levin, but the distance between subject matter and quality of writing was great. This doesn't mean Levin is an especial bad writer because the topic is an incredibly interesting one.
The stories of Alan Turing and Kurt Godel are out of this world. The intellectual battle Levin demonstrates between Wittgenstein and Turing and Godel is beautiful. It will make you want to read Godel and Turing's work, and perhaps even Wittgenstein's. And the similarities between
Godel and Turing's lives will astound you. The only thing more intriguing is what Godel and Turing are arguing about.
If you have ever encountered a logician who tried to argue determinism or pure chance (randomness) with you, you will no doubt recognize the depressing feeling of being slowly backed into a corner and finally discovering that last beautiful supernatural ground you stood upon was consumed too. Godel dreamed up the escape hole through which one can jump into an infinitely bigger world where logic is no longer the triumphant king, but honest servant.
Godel's incompleteness theorem is beautiful.

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