@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
Anti-authoritarian, bleeding-heart Stirnerite,
. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.
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@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
I'd have to see the equations. There are a lot of situations/contexts/words for it. Here the relevant word seems to be 'smoothness', which informally means how *many* times you can take the derivative. https://en.wikipedia.org/wiki/Smoothness
That article is technical but it gives some concrete examples of different degrees of smoothness.
Would help if I could see what you're looking at
The bit I was looking at starts a bit after 22:00https://youtu.be/iHKa8F-RsEM
"loses derivatives" seems to be a reference to https://en.wikipedia.org/wiki/Nash%E2%80%93Moser_theorem … (same wording is used) so...yeah, I got nothin'
I can't make head or tail of what the guy is talking about in that video. But going off the Wiki article, I think what's going on is something like this: Consider y = x^3. This is a super well-behaved function. Smooth as can be. Its inverse is the function y = x^{1/3}.
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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