Eigil Rischel - abstr/acc 💎 @ayegill@schelling.pt

The main ingredient in proving this is the observation that the coordinate-change maps must be linear on infinitesimals, so the infinitesimal neighborhood of a point is a vector space in a canonical way, which is isomorphic to the tangent space at that point.

I.e it's just a *discrete* dynamical system with the constraint that each step is infinitesimal.

In synthetic differential geometry, giving a smooth dynamical system on a manifold is equivalent to giving, for each point x0, the "infinitesimally next state" s(x0), i.e a point so that if x(t) = x0, then x(t + h) = s(x_0) (where h^2 = 0).

... is the ring of global sections of a scheme X just the limit in CRing of the dual of the colimit diagram in Scheme that presents X as glued together from affine patches?

The idea in this one, that you can classify the behavior around equilibria using linear algebra (because the dynamics are "locally approximately linear") is very cool.
https://www.youtube.com/watch?v=7Ewe_tVa5Fs&list=PLUeHTafWecAUqSh3Gy0NNr7H3OsXoC-aK&index=21

Watching these videos now, they're really good 😀
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RT @sarah_zrf
im gonna do it. im gonna learn dynamics. im gonna watch the videos https://twitter.com/RossDynamicsLab/status/1432690088723587076
https://twitter.com/sarah_zrf/status/1433074184578600961

If the sausages in the first picture had been dyed red that one alone would've pretty much nailed it down tbh.

Using only food, where did you grow up?
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RT @mechanical_monk
god bless the motherland https://twitter.com/made_in_cosmos/status/1435181546198155266 https://t.co/2yhJhHlv37
https://twitter.com/mechanical_monk/status/1435238587369500678

I also think nobody (probably not even economists who used ergodicity as a technical assumption) ever believed that "this strategy has a high expected payoff" meant you were guaranteed a high payoff eventually - that would be a weird way to talk about probability!

The use of "almost certainly" when people talk about ergodicity economics drives me nuts - you can't actually bet an infinite number of times so the question about whether a (tiny) chance of a huge win is worth it is still relevant!

I had good luck finding writing on thermodynamics here a while ago. Now for hard mode: does anyone have a good explanation of renormalization for a mathematician?

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The amount of hate people are willing to heap on anyone with a low-status food opinion is really something to behold.

Hope you guys manage to bring it home

Can I get an F in the chat boys?

Teleology: the study of things that are far away.

There should be bad fansubs of EGA.

"*Translator's note: étale means spread"

Not sure if I feel tired and unmotivated because of vaccine side effects, or because I'm a lazy piece of shit.