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100 Years of Markov Chains: Back in January I took a little trip to Boston and hung out with Kirk. Among other things, we attended an event at Harvard celebrating the 100th anniversary of the paper that kicked off the Markov chain craze. I only wish Adam had been there. I've held off on talking about the event because I've been waiting for Harvard to put the video of the talks online. But that's a sucker's game, and now I have something better!

See, the first talk, by Brian Hayes, covered the amazing history leading up to the publication of Markov's seminal paper. He's now turned his talk into an article in American Scientist. The first few pages of that article are a basic introduction to Markov chains; the history starts on page four. Basically, Markov was a cranky old man who liked picking fights.

Markov’s pugnacity extended beyond mathematics to politics and public life. When the Russian church excommunicated Leo Tolstoy, Markov asked that he be expelled also. (The request was granted.) In 1902, the leftist writer Maxim Gorky was elected to the Academy, but the election was vetoed by Tsar Nicholas II. In protest, Markov announced that he would refuse all future honors from the tsar... In 1913, when the tsar called for celebrations of 300 years of Romanov rule, Markov responded by organizing a symposium commemorating a different anniversary: the publication of Ars Conjectandi 200 years before.

As acts of political protest go, the well-timed symposium is pretty great. At that symposium Markov revealed the Markov chain, which he'd invented as a way to smack down the dumb theological arguments of rival mathematician Pavel Nekrasov. His paper wasn't called "Markov Chains: Future Basis for Art and Scientific Discovery, Named After Me, A. A. Markov." It was called called "An Example of Statistical Investigation of the Text 'Eugene Onegin' Concerning the Connection of Samples in Chains".

Markov had manually gone through the first 20,000 characters of Pushkin's "Eugene Onegin", looking at every pair of letters, writing down whether the letters were both vowels, both consonants, vowel-consonant, or consonant-vowel. Then he'd modelled the transitions between those four states with a Markov chain. The result disproved an assumption about the law of large numbers, an assumption crucial to Nekrasov's mathematical argument for free will. There's something about this mindset that always gets me--inventing the sledgehammer so you can use it to kill a fly.

The other two talks were a lot more technical. I was mostly able to follow them, but I don't think I got much out of them. Here's a summary of all three talks from someone else who was there. But I strongly recommend Hayes's article to anyone who reads this weblog.


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