TITLE: This and That from Douglas Hofstadter's Visit AUTHOR: Eugene Wallingford DATE: March 09, 2012 3:33 PM DESC: ----- BODY:

Update: In the original, I conflated two quotes in
"Food and Hygiene". I have un-conflated them.

In addition to his lecture on Gödel's incompleteness theorem, Douglas Hofstadter spent a second day on campus, leading a seminar and giving another public talk. I'll blog on those soon. In the meantime, here are a few random stories I heard and impressions I formed over the two days. The Value of Good Names.   Hofstadter told a story about his "favorite chapter on Galois theory" (don't we all have one?), from a classic book that all the mathematicians in the room recognized. The only thing Hofstadter didn't like about this chapter was that it referred to theorems by number, and he could never remember which theorem was which. That made an otherwise good text harder to follow than it needed to be. In contrast, he said, was a book by Galyan that gave each theorem a name, a short phrase evocative of what the theorem meant. So much better for reader! So he gave his students one semester an exercise to make his favorite chapter better: they were to give each of the numbered theorems in the chapter an evocative name. This story made me think of my favorite AI textbook, Patrick Henry Winston's Artificial Intelligence. Winston's book stands out from the other AI books as quirky. He uses his own vocabulary and teaches topics very much in the MIT AI fashion. But he also gives evocative names to many of the big ideas he wants us to learn, among them the representation principle, the principle of least commitment, the diversity principle, and the eponymous "Winston's principle of parallel evolution". My favorite of all is the convergent intelligence principle:
The world manifests constraints and regularities. If a computer is to exhibit intelligence, it must exploit those constraints and regularities, no matter of what the computer happens to be made.
To me, that is AI. Food and Hygiene.   The propensity of mathematicians to make their work harder for other people to understand, even other mathematicians, reminded Doug Shaw of two passages, from famed mathematicians Gian-Carlo Rota and André Weil. Rota said that we must guard ... against confusing the presentation of mathematics with the content of mathematics. More colorfully, Weil cautioned [If] logic is the hygiene of the mathematician, it is not his source of food. Theorems, proofs, and Greek symbols are mathematical hygiene. Pictures, problems, and understanding are food. A Good Gig, If You Can Get It.   Hofstadter holds a university-level appointment at Indiana, and his research on human thought and the fluidity of concepts is wide enough to include everything under the sun. Last semester, he taught a course on The Catcher in the Rye. He and his students read the book aloud and discussed what makes it great. Very cool. If You Need a Research Project...   At some time in the past, Hofstadter read, in a book or article about translating natural language into formal logic, that 'but' is simply a trivial alternative to 'and' and so can be represented as such. "Nonsense", he said! 'but' embodies all the complexity of human thought. "If we could write a program that could use 'but' correctly, we would have accomplished something impressive." Dissatisfied.   Hofstadter uses that word a lot in conversation, or words like it, such as 'unsatisfying'. He does not express the sentiment in a whiny way. He says it in a curious way. His tone always indicates a desire to understand something better, to go deeper to the core of the question. That's a sign of a good researcher and a deep thinker. ~~~~ Let's just say that this was a great treat. Thanks to Dr. Hofstadter for sharing so much time with us here. -----