3 ms·
> Let's say the angel could only move in two directions. It would seem intuitively that this would still leave enough room to avoid traps. Nope. Even if you re
by nandemo 11y ago
> Let's say the angel could only move in two directions. It would seem intuitively that this would still leave enough room to avoid traps.
Nope. Even if you restrict the angel to 3 directions (up, left, right), the devil has a winning strategy. This is mentioned in the linked article:
> If the angel never decreases its y coordinate, then the devil has a winning strategy (Conway, 1982).
There's a simple, informal proof in the references:
Conway, H. "The Angel Problem" http://library.msri.org/books/Book29/files/conway.pdf http://library.msri.org/books/Book29/files/conway.pdf
- ewzimm 11y agoThanks for the clarification. I do wonder what other kinds of things this math could apply to. It's pretty abstract, but if you want to direct an unpredictable agent toward a certain behavior, knowing where to place control mechanisms might be interesting.