it is genuinely astonishing how often this works. physicists will literally perform taylor series expansions in a parameter that is like ~1 and somehow this doesn't produce total garbage. completely mysterious to me
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the most based calculation i've ever seen in physics is a statmech calculation that works in "4 - epsilon" dimensions where epsilon is "assumed to be small" (for taylor expansions etc) and then set equal to 1, as a way to guess what happens in 3 dimensions. incredible
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i'm actually fine with thinking of d as a parameter that at least some features of the theory should be analytic in in at least some regimes, so i can handwave the 4 - eps with that. and i'm also happy with asymptotic series. but... setting epsilon equal to 1... too chad for me
