Examples: Putting terms in a commutative expression in the right order helps a lot even though “logically” it makes no difference. Align key symbols in formulae vertically on the page to group analogous clauses to make it clear what the next step is.
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Einstein notation replaces enormously complicated algebraic work with visually simple sub/superscript fiddling that analogizes kinesthetically to physically moving things around by hand. Also uses visually different symbols to track vector dimensions. https://en.wikipedia.org/wiki/Einstein_notation …pic.twitter.com/oBfWkyENZR
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Two quotes here from
@cdutilhnovaes about this. Also two of her key sources, which I haven’t yet looked into myself (but intend to).pic.twitter.com/CqSK3SAcna
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“The materiality of mathematics: Presenting mathematics at the blackboard” by
@greiffenhagen makes this much more concrete, through close study of a video of a lecturer presenting a proof of the completeness theorem for propositional logic.pic.twitter.com/Ru0J6xGfmz
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Replying to @Meaningness
I did a lot of my dissertation research in bed with a pillow over my eyes, though
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Replying to @St_Rev @Meaningness
Yes, I’m unconvinced that blackboard lecturing is anything more than a small (and mostly unimportant) fraction of “learning about” and “thinking about” mathematics.
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How people behave when they read a textbook/paper and hit something they want to understand seems to me far more important. And this seems to be very idiosyncratic. I do it eyes closed, talking to myself. But others are v different. (Some via diagrams, some via algebra, ...)
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Replying to @handleym99 @Meaningness
I think blackboard/paper work is important, possibly central, but also _legible_ in a way other kinds of work aren't, so likely to dominate any ethnomethodological study.
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I bet varying levels of a/phantasia matter, too - different capabilities, different ways of making ideas legible to oneself (ethnomethodological inquiry aside)
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Absolutely. My own rhythm was a sort of dialectic between kinesthetic work in my head and symbolic work on paper. But I've known mathematicians who didn't seem to do anything but grind chains of symbols.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.