explanation & the compatibility of minds.

i'm becoming predictable. two days back in ann arbor, and my research conjectures remain the same. i've made no more progress since i left on holiday, a week ago.

i remember a quote, which is something like this:

insanity is doing the same thing each time,
yet expecting a different outcome.

i suppose i haven't yet reached insanity, but perhaps a quasi-insanity: i try one idea and it fails, but then i try a similar idea, only to reach a slightly different failure. who knows: maybe the map

{hypotheses} → {conclusions}

is continuous. q:

maybe no progress is not quite right, either.

it may not be the guts of research, but i think i've become better at explaining what i study to other mathematicians.

i've narrowed my soliloquy down to ~5 minutes, if i pare down the motivations. so accounting for questions and retorts, i suppose it would take about 15 minutes to explain it to a michigander.

just to clarify, that's NOT meant to be a slight to my friends and peers.

five or so minutes is the bare-bones explanation to a random mathematician; it doesn't account for whether that mathematician actually cares about what i'm saying or not.

in contrast, it may be more likely that my fellow analysts @ um might have some genuine interest in my work, if only because they know me personally and are motivated socially, or because we have a common intersection of research interests and they are motivated by curiosity.

you'd think that an explanation would take less time between two persons of similar background and sometimes it does .. but not all the time, necessarily.

first, the level of understanding which a curious listener expects may be substantially higher than a non-curious listener.

then there is the issue of "compatibility," in that two mathematicians may know the same things, but their methods of understanding may be completely different. so in explanations to a curious listener, one also has to account and adjust for a different set of expectations.

i liken it to de-fragmenting the hard drive on a windows machine: the more data you have in memory, the longer it takes to rearrange the data into that pleasant looking contiguous block in the end.

at any rate, my research woes continue.
i wonder if i will graduate on time.