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?

@rime yeah, I think the term's mine :-)

The associations seem right

@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?

@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