@johncarlosbaez "The arguments are quite solid if the universe is infinite and homogeneous." Agreed.
"And it's simpler to assume the universe is infinite than to assume it goes on for a huge finite distance..." eh...
I like the infinite in a few different ways it gets used. Infinite as "all the basis vectors", sure (cf. Fourier basis). (Even if our universe appears to only be able to represent frequencies between 1/(the Planck time) and the Hubble constant.)
Infinite as a limit to extract asymptotic behavior, great.
Infinite as a completion, such as the point at infinity in complex analysis, love it.
Infinite processes, such as moving through a continuous path between two points, I start getting twitchy. (cf. your own series on struggles with the continuum.)
Infinite as an infinite amount of stuff? That seems a big assumption. I see approaches to make toy models of an unbounded but finite universe, with a finite amount of stuff as the result of a process through time. But models that simply assume an infinite amount of stuff? I don't even see how to approach writing something precise down about that, other than starting with it as an axiom. That's where I feel like we're heading beyond physical theories and into pure speculation.
"I think some people find the possibility of distant near-copies of themselves upsetting, or at least interesting - to which I'm tempted say, "get over yourself!""
Actual lol. Getting over myself has also been a process through time 😉
"In general the right response to questions about an [...infinite vs finite] universe seems to be letting other people think about them while I do more productive things."
Fair enough. Besides, I have a quaternion paper to read 🙂