2024-12-22 at 00:03

for things like tennis n rock climbing, perhaps the partial derivatives are approximately only dependent on that variable

like, at any point, you can improve any part of your technique and expect a reasonable gain in performance, and it doesn't rly matter what order you do this in, because the improvement from URGH im gonna stop explaining it in english i already understand it . whatever.

a little more formally, let's say you have a cost function C which depends on factors x, y, ...
let's say you try to ascend the hill via following dC/dy
the partial dC/dx will approximately stay the same and you can follow the dC/dx whenever you want, whether it's before or after following the dC/dy

but for things like life happiness, thats like a rly weird PDE with time dependence that changes things and just lots of random variables and ur partial derivatives r different at different t values -- and not just that time-varying stuff but also if u change one thing it's like . it changes the other partial derivatives too bc theyre dependent and not independent

but for tennis n rock climbing, the variables r very independent and if u change one thing then the other partial derivatives dont rly change

i think things like Reasoning or Chess or Etc r sorta in the middle .. because for these things u can do gradient descent and then it's like DFS and then you can take a very long time before you realize it's a dead end (as in it is suboptimal)