I haven’t posted anything in a couple of weeks, not because I haven’t been writing but because I keep writing overambitious longer posts that get to a point where they seem something like 80% done and then die horribly. I’m hopeful that I can reanimate some of the dead posts but in the meantime it would be nice to keep a bit of momentum.
So I was looking at my folder of half-written draft crap (which starts with ‘academia_rant.txt’ and ‘asdfsdffsd.txt’ and doesn’t get any better) and found this thing I wrote for the tumblr blog and had half forgotten about, under the title ‘pretentious theme statement’. Maybe I decided it was too pretentious. But reading it back, I like it, and I think it’s accurate for at least part of what I want to do on this newer blog too:
If this blog has any sort of theme, beyond ‘let’s write the same boring post about mathematical intuition a thousand times’, it’s something like this:
Say you have some idea which can be written down in language in a more or less coherent and logical way. That’s the bit I’m mostly not interested in here. (Though these are really good! I definitely approve of coherent and logical thoughts. Sometimes I even manage to have one.)
Instead I find myself poking again and again at the cluster of stuff that’s packed around it that’s rather more difficult to get a hold on in language – the emotional tone the thought has, the mental images or bits of analogy that support it. Sort of like the ‘dressed’ thought rather than the ‘bare’ thought.
‘The role of intuition in maths’ is how I mostly approach it because it’s close to my own odd obsessions, it has a tiny fascinating literature that I’ve mostly read, and the divide seems particularly obvious there. It’s really common to have the experience of following a mathematical proof with several indisputably-correct steps and get to the end completely convinced of the result, but still have that feeling of urghh BUT WHY is this true?? And it’s really common to then find a reframing that makes it obvious.
But a bunch of my other posts seem to be about this too – there’s the assorted crap under the ‘tastes in the head’ tag, and some throwaway stuff like my new sort-of-interest in geology.
I’m definitely not talking about this because I understand it. Finding ways to talk about all this extra stuff is hard, there’s no one source of literature on it, and it’s possible that it varies so widely from person to person it’s essentially not even worth trying. Certainly people vary widely in their preferred mathematical learning styles. But the topic has some kind of, well, hard-to-describe quality that makes me keep returning to it.
(It’s also well-suited to tumblr because all I really know how to do is produce these sort of confused fragments. I’m definitely not going to be producing a 5000 word chunk of confidently-stated insight porn off the back of any of this any time soon.)