@St_Rev I have a math question, if you have time. In what sorts of situations do the solutions to equations lose derivatives? I think I understand why it happens wrt a sphere, but not well enough to generalize itpic.twitter.com/QH53LV8dyp
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y = x^{1/3} is less well-behaved. It goes vertical at the origin, ie it's not differentiable at x = 0. So even if a function is super 'nice', its inverse (a function that un-does it) may not be. This is bad if you want to be able to get back to where you started!
Like a road that's smooth in one direction but bumpy in the other. (Took me a while to write previous tweet, sorry to leave you hanging.)
No worries, didn't. Going to take me a while to think about it anyway
I understand what you're saying, but I don't think I'll be able to understand the theorem until I better understand what smoothness means. Gonna dwell on it for a while
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