Memory and Mathematics

I put a weak finish on 2013, reading wise.  I’ve been grinding away at grueling, plotless books for long enough that it’s hard to remember why I started.  I put aside a biography of Borges, in Spanish, that I started a while ago.  I never intended to read it at one go, but it still hangs over me.  Another is the book on Shakespeare’s language: mostly it makes me wish I were reading the plays, though I think it may prove worthwhile.

Finally, there was Philosophies of Mathematics.  It seemed like a good idea at the time.  My college math had a foundational, philosophical bent, and since then I’ve continued to dabble in it.  I don’t really sympathize with fretting over whether math is created or discovered, how we apply it to nature and so forth.  I’m more interested in the constructions and the proofs that crop up in these books.  (Incidentally, it’s observed that Borges, while no mathematician, had his own taste in mathematics.  So maybe it’s not as sorry as it sounds.)

I like to believe I’ve learned a few mathematical habits of thinking.  One idea that comes up often is that of one-to-one correspondence of collections of things, or sets.  When two sets can be matched up one-to-one (like having a right shoe to go with every left shoe in your closet and vice versa) you say you have the same number.  That the correspondence exists is more important, maybe, than exactly what number you have.  This idea leads in short order to fascinating demonstrations about the different sizes of infinity.  It also informs my personal notion (I don’t remember if I might have read it somewhere) of what a number is, which I muse on when others seem to get to bogged down in the ontological status of mathematics, or the being of numbers.  Numbers are just meaningless words that we recite when we wish to compare sets of objects.  We learn numbers as children by counting along with others, the same way we learn other songs.  If you remember the song the right way every time, you can establish a meaningful correspondence between sets.  So how do we learn the song?

A couple of years ago I read Moonwalking with Einstein: The Art and Science of Remembering Everything, by Joshua Foer.  It’s a popular history of mnemonics, with lots of amusing stories about various competitive memorizers, prodigies and a fair amount on their actual techniques.  At least one of them actually worked: By constructing a memory palace based on my old elementary school and an off the cuff list of strange images involving friends and acquaintances, I was able, with a couple hours of practice, to memorize the order of a deck of cards.  Once I got used to it I could do it in a few minutes.

Of course this amazing new skill didn’t turn into much of anything.  I’ve memorized a fair amount of poetry and I’m not bad at geography, either, but I do it by rote, and if there’s much more to it than that, I don’t know what it is.  I certainly helps if what I’m memorizing is beautiful or otherwise interesting.  Maybe when the limitations of my current method become apparent, I’ll turn again to the memory palace.  I’m interested in how other people commit things to memory and otherwise organize their thought.  Has philosophy, or the study of mathematics or some other field, changed the way you think, or do you just bang it out?