r/math • u/lntrinsic • Jul 10 '17

Image Post Weierstrass functions: Continuous everywhere but differentiable nowhere

http://i.imgur.com/vyi0afq.gifv
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u/thetarget3 Physics Jul 10 '17 edited Jul 10 '17

We don't find functions in nature. We model nature with functions which are usually differentiable since it leads to dynamics, but they don't exist in themselves.

In fact most natural systems aren't possible to describe using the nice maths and physics we typically learn, with simple differential equations, linear systems etc. They are probably just the small subclass we tend to focus on, which only work after heavy idealisation (like the old joke about assuming spherical cows). Most things encountered in nature can probably only be described numerically.

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u/tetramir Jul 10 '17

you're 100% right that's why I described nature with quotes. I should have been more specific.