Is the Third Derivative of Position Really Important?

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The second derivative of a position tends to be really important but the third derivative not so much. The laws of physics, as Isaac Newton handed them to us, say that the state of a system is given by the position and the velocity. But there's no absolute position or absolute velocity, right? So why do we treat position and momentum so differently? That's a highly non-trivial question that nobody knows the answer to.

Welcome to the October 2022 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!

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