Mostly we do formal reasoning on paper, or a blackboard or whiteboard. Some bits are best done in the shower, but most of it critically depends on these external material technologies. Richard Feynman got this:pic.twitter.com/zAFeMumKm0
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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.
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
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
“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
Here’s @greiffenhagen showing the embodied, spacial, temporal, interactive nature of a proving of the Dutch Book Argument (cc @cdutilhnovaes)https://twitter.com/Meaningness/status/1005489362052632578 …
(Going to pick up this unfinished thread tomorrow probably—have other things to do now!)
Yesterday’s logic
got out of control. Shorter
here on formal logic as a social practice that is a somewhat-contingent product of cultural evolution:https://twitter.com/Meaningness/status/1150166188476862464 …
how do we explain ramanujan in this framework
Which part of “goddess” do you not understand?
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