Differential equations where one variable also determines which derivative of a function is used
f^{(k)}(x) = log_{x}(k)
Using fractional calculus of course
Might sometimes result in differential equations on smooth functions where one can take the infinitieth derivative of a function
Thoughts had while thinking about the dynamics of Omohundro sludge, where there's meta-dynamics of trying to outwit on higher orders all the time, while keeping in mind all the lower orders of the game
Also related to fix-point solutions for regress problems
@niplav "Omohundro sludge" is that your nym? Supposed to evoke a sense of the unmanageable dynamics between meta-levels of a competitive game between agents with theory-of-theory-of-mind? I like it.
If you know a superintelligent hostile agent is guaranteed to accurately model all your intentional cognitive moves, where do you inject a RNG in order to level the playing-field? Are there games you can force them into such that the outcome is closer to p=0.5?
@niplav In a sword-fight at least, if your opponent can precisely predict where you intend to strike, your best bet is to close your eyes and sync your moves with a random element in the environment. or something.
interesting quadrant btw!
someone should make a large collection of all interesting conceptual quadrants like that.
*sigh*
TODO
@rime I think most Nash equilibria are mixed equilibria? So it makes sense to randomize (relation to augury is obvious I reckon)
Interestingly, nearly all games have an odd number of Nash equilibria! I find that very curious
@niplav relation to augary acknowledged, but it took me ~30s to see, so idk if it qualifies as "obvious", but it certainly goes without saying.
@rime
Oh yeah the perils of "trivial"… 😁
@rime my thinking was about the coordination hard/attack favored quadrant
Not sure about stochastic solutions, but I think I was assuming these are already incorporated?