Differential games lend themselves to a hyperfinite description. You can even have turns. Each player takes an infinitesimal move, then the other goes. A hyperdiscrete approach.
Observing your opponent becomes really important, like in a fight, soccer, or a relationship 😶. I have the intuition that the OODA loop falls out of this.
There’s a classic game here where you run from a lion, and the optimum is running along a harmonic spiral since it’s infinitely long. What would that look like under this?
Differential games lend themselves to a hyperfinite description. You can even have turns. Each player takes an infinitesimal move, then the other goes. A hyperdiscrete approach.
Observing your opponent becomes really important, like in a fight, soccer, or a relationship 😶. I have the intuition that the OODA loop falls out of this.
There’s a classic game here where you run from a lion, and the optimum is running along a harmonic spiral since it’s infinitely long. What would that look like under this?
Relaxing the requirement that surreal number that left side should be less than the right side gets you “games”
Extremely based.
Related: Ends of groups: a nonstandard perspective, Journal of Logic and Analysis, Volume 3:7 (2011), 1-28.
Ends are havens in pursuit games