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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taylor expansions are the turtles in the turtles all the way down joke except it isn’t a joke
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i feel like one of the most important steps in scientific maturity is realizing this
i used to confuse the map for the territory; the final nail in the coffin for doing this was in learning some pertubative methods in QM
"wait we only have exact solutions for hydrogen?"
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So I'm like I'm a pretty self-taught data analyst at my work, but am I right to assume a 1st order Taylor series expansion is just a needlessly convoluted way to say "line of best fit"?
like a least bust out a second order term before you disenfranchise all the layman's 😂
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No, it's closer to "line tangent to a curve at some point", and only when you take only the 0th and 1st order terms.
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I'm reminded of these lectures by Carl Bender where answers are beaten out of divergent series.
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