# What does the path of least resistance really mean?

by parsec
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 HW Helper P: 2,155 Wow, well... I think the "path of least resistance" is just something that was invented to justify to laypeople (i.e. curious non-physicists) why objects behave the way they do. Like many analogies, it works if you don't think about it too closely, but once you start asking detailed questions (as you have) the "path of least resistance" principle falls flat on its face - it's just not able to provide any sort of rigorous justification for anything. I suppose it could have been inspired by the minimization of potential energy, i.e. to explain why, when you do a sit-up, your upper body rises instead of your legs (or maybe the other way around, for many people): it increases your potential energy less to raise the lighter half of your body. It does remind me of Hamilton's principle of action minimization. If you're not familiar with it, basically the action is defined as $$S = \int L \mathrm{d}t$$ where L is the Lagrangian (kinetic minus potential energy in classical mechanics) and the integral is taken along some path; the path that minimizes the value of S is the one that actually occurs in reality. This is actually the basis of all of modern physics; you can describe anything just by coming up with the right expression for L. Now, I suppose you could very roughly associate S with "resistance" in some metaphysical sense, but it's quite a stretch. I really couldn't see the "path of least resistance" idea that the public is familiar with coming from that equation. But who knows :?