Is anyone from LW going to the Worldcon (World Science Fiction Convention) in Seattle next year?
ETA: I will be, I forgot to say. I also notice that Burning Man 2025 begins about a week after the Worldcon ends. I have never been to BM, I don’t personally know anyone who has been, and it seems totally impractical for me, but the idea has been in the back of my mind ever since I discovered its existence, which was a very long time ago.
Growing slower than logarithmic does not help. Only being bounded in the limit gives you, well, a bound in the limit.
“Bounded utility solves none of the problems of unbounded utility.” Thus the title of something I’m working on, on and off.
It’s not ready yet. For a foretaste, some of the points it will make can be found in an earlier unpublished paper “Unbounded Utility and Axiomatic Foundations”, section 3.
The reason that bounded utility does not help is that any problem that arises at infinity will already practically arise at a sufficiently large finite stage. Repeated plays of the finite games discussed in that paper will eventually give you a payoff that has a high probability of being close (in relative terms) to the expected value. But the time it takes for this to happen grows exponentially with the lengths of the individual games. You are unlikely to ever see your theoretically expected value, however long you play. The infinite game is non-ergodic; the game truncated to finitely many steps and finite payoffs is ergodic only on impractical timescales.
Infinitude in problems like these is better understood as an approximation to the finite, rather than the other way round. (There’s a blog post by Terry Tao on this theme, but I’ve lost the reference to it.) The problems at infinity point to problems with the finite.