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Basically he is talking about the trench war one has in scientific writing. Call one side side A, and the others side B, and imagine there is a student who tried to read a thesis and did not get it. Side A will say: "Well, he is too stupid to unterstand my thesis", while Side B will say: "well, he might not know enough basics to understand your thesis, but I rather think that you just wrote incomprehensible gibberish".

I second his part about the informal parts very, very much, even though I would call this 'informal part' examples and motivations. Tell us in simple examples what your definition means, what your algorithm does, how your consideration works in this simple example, even if the example might be borderline with wrongness and oversimplification. It helps a lot, even though it is hard to find good examples :)



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