Complexity Theory: Now a Path to Enlightenment

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I’ve been insanely busy lately, which means I have a gigantic backlog of stuff that I meant to link to, but didn’t.

Scott Aaronson has a knack for taking certain interesting but not obviously revolutionary inspiring concepts in complexity theory and in good Russian-formalist fashion, making them strange. Here are some examples:

  • The Fable of the Chessmaster suggests that a perfect chess master could demonstrate their mastery to a high degree of certainty without revealing their strategies. Scott goes on to suggest that we can think of complexity theory as “mathematical theology” :-)
  • Logicians on safari connects complexity to super-intelligent aliens, the Riemann hypothesis to your car trunk, and that the fact that your computer crashes once a second is no excuse for not finishing your work.
  • More tender nuggets points out, among other things, that if babies can learn languages by example alone, they can also learn to break RSA.

Math Stranger than Fiction

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I just saw the movie Stranger than Fiction, and I noticed a strange pattern in the last names of characters: Pascal, Hilbert, Escher, Cayley, Mittag-Leffler. Also, the main character’s favorite word is “integer”. The main character has a penchant for counting, but other than that the movie is as far removed from mathematics as can be imagined, so it’s all very mysterious.

December Notices

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The December Notices of the AMS are out. The two features articles are:

This month’s What is a… Quasiconformal Mapping introduces a generalization of conformal mappings that makes sense in general metric spaces.

The Illusory Unity

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I will be out of town for a few days for Thanksgiving, so there won’t be any posts from me for the next few days.

Mathematical textbooks take pains to make their subject appear to form a unified whole. Is any such unity an illusion? Discuss.

Kalman Filter

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A friend of mine who’s studying econometrics asked me about the Kalman filter, which is used in estimating the parameters of a time series model. I didn’t know anything about the subject, so I was poking around online, where I discovered that the Kalman filter is rocket science: it was invented to estimate the current position and trajectory of the Apollo spacecraft. And here I thought the only concrete result of the space program was Tang.