Tuesday, April 22, 2008

I like words

I've been reading Paul Halmos's autobiography, which he called his automathography, as a break from grading. It does not go into much detail about his personal life, focusing instead on his life as a professional mathematician. In some ways, it is sort of like Quine's autobiography. That didn't focus on his personal life either. Rather it focused more on his travels and his life as a professional philosopher. In fact, both books had decent chunks about various conferences and such. Halmos's book was less interesting on this front since I wasn't familiar with a lot of the people he talked about. I'm not sure that it would be that much more interesting if one knew those people. Halmos's book is boring in roughly the same way that Quine's book was boring, although they are interesting in similar but different ways. (Or maybe Quine's book just seems better than it was when viewed through the rosy lens of memory.)

Halmos is a good writer. He had some tips on writing which seem applicable to philosophy (and moreso to logic). His writing even made mundane things like editing a journal and writing a textbook moderately entertaining. It was kind of interesting to see his evaluation of academia. I'm not sure how much of it was completely unknown. I think the most interesting part of this aspect of the book was about writing recommendation letters. He included a few examples with some commentary. I wonder how philosophy recommendations compare. I've never seen any philosophy recommendation letters.

Another part of the book that was interesting for me was Halmos talking about logic. Halmos was one of the innovators in algebraic logic. He did a lot of work on boolean algebras and polyadic algebras. It was interesting because he expressed a sentiment that I've heard echoed by several friends who studied math. Halmos thought that logic was not particularly interesting and largely consisted of fussy bookkeeping stuff, e.g. keeping a stock of distinct variables. He even thought that logic didn't provide a helpful toolbox of techniques. Yet, when he was able to see that classical propositional logic corresponded to boolean algebra and then came up with polyadic algebras, logic became more interesting. I think his phrasing was that he could make out the algebraic content of various theorems. The sentiment he expressed has kind of puzzled me in the past, but his way of putting it made it seem a little clearer. It still is somewhat puzzling, but this might be partly because of my philosophical upbringing (the only word for it is the German "Bildung") which was at a department in which there were several logicians and the math classes I took tended to be logic friendly. In any case, I'd almost recommend studying some algebraic logic for the excuse of reading some of Halmos's work.

The opening of his book really hooked me, which provided a decent motivation for finishing it. It is: "I've always liked words more than numbers." I can dig that. Words are neat.


Justin said...

Woah, woah, woah. Don't go overboard on praising words. There are other things, after all.

Shawn said...

I like other things too, not just words.