Yeah, the nonlinearity means it’s hard to know what question to ask.
If we just eyeball the graph and say that the Elo is log(log(compute)) + time (I’m totally ignoring constants here), and we assume that compute = et so that conveniently log(compute)=t, thenddtElo=1t+1 . The first term is from compute and the second from software. And so our history is totally not scale-free! There’s some natural timescale set by t=1, before which chess progress was dominated by compute and after which chess progress will be (was?) dominated by software.
Though maybe I shouldn’t spend so much time guessing at the phenomenology of chess, and different problems will have different scaling behavior :P I think this is the case for text models and things like the Winograd schema challenges.
Yeah, the nonlinearity means it’s hard to know what question to ask.
If we just eyeball the graph and say that the Elo is log(log(compute)) + time (I’m totally ignoring constants here), and we assume that compute = et so that conveniently log(compute)=t, thenddtElo=1t+1 . The first term is from compute and the second from software. And so our history is totally not scale-free! There’s some natural timescale set by t=1, before which chess progress was dominated by compute and after which chess progress will be (was?) dominated by software.
Though maybe I shouldn’t spend so much time guessing at the phenomenology of chess, and different problems will have different scaling behavior :P I think this is the case for text models and things like the Winograd schema challenges.