Re: poly: The singleton hypothesis

Robin Hanson writes:
> Carl F. writes:
> >My intuition is that given trillions of Jupiter brains working for billions
> >of years, there will be no room left for technological or intellectual
> >improvements: the limits of feasibility will be coincident with the limits
> >of possibility. We will reach the highest possible level of development,
> >and so will any aliens we run into.
>
> What if a war with aliens were like a game of Go, where subtle strategy
> choices could make a big difference? Does analysis of a game like Go also
> reach limits, where more analysis won't give more ability?

Well, naturally, games like Chess and Go in fact have limits -- as
perfect information two player games, a big enough computation (larger
than the universe could likely sustain) could fully expand the game
tree (certainly larger than the known universe could store) and
any more computation than that would, naturally, be wasted.

This is, of course, not the question you were asking, which was, more
likely, "are there multiplayer games for which added (reasonable)
computation will continue to yield advantages?"

Although the question has never been formally considered, and although
it would be difficult to produce a reasonable model right now, I
suspect it would be possible to prove that there exist perfect
information two player games for which there are no limits whatsoever
to the extent to which one may profitably expend computation.

The more interesting question, however, would be whether or not it is
likely that war with aliens is going to be anything like such a
game. I would suspect that any realistic model is certainly not going
to be a perfect information game, or anything similar. Whether
realistic models are possible is, of course, a question for future
history.

Perry
Received on Tue May 5 02:04:39 1998