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IlyaShpitser comments on LessWrong 2.0 - Less Wrong
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Yes I think even in math a lot of what is called "mathematical sophistication" is implicit knowledge that's hard to communicate without being steeped in the social context in which math is developed and read.
As an example, do you mean something like correctly understanding how to "abuse" mathematical notation in a way that remains rigorous?
It's hard to explain, it's the way you think and talk about math, it's not about visible signs like notation.
I like the Scott Bakker analogy for magic, there is the visible part of math (formulas, etc.), and the corresponding mental habits. The visible part without the correct way of thinking behind the scenes doesn't work.
I guess one example is an ontology of "the type of math that's being done" in one's head, that lets people quickly figure out what the paper is trying to do after reading relatively little of it.