[ben_w]

This feels similar to something I came up with a while back; for various reasons[0], I hope it isn't true.

https://kitsunesoftware.wordpress.com/2018/08/26/mathematica...

[0] Boltzmann brains are cognitively unstable, because the logic leading to them says you should expect to be one, but also that they have exponentially increasingly false "memories" the further back they "remember", including the beliefs leading to the conclusion that you probably are one. If all maths is real, this is worse to at least the degree that Aleph one is bigger than Aleph null, possibly more.

[14]

The Boltzmann brain theory is not something I have heard before but have to say I love the idea. The thing is if the universe is infinite and you believe that, then by default many other things also have to be true. I do hope the universe is infinite which means I exist many times over in many different states of being, hopefully one such state where the Canadian housing market isn’t so crappy and I get to afford a house one day ;)

[ShamelessC]

Infinite universe doesn’t necessarily imply what you’re suggesting. Removing all even numbers from a set gives you another infinite set - but it is still an infinite set that will never contain a multiple of 2 in it.

Similarly, our universe may be infinite but isn’t at all guaranteed to produce multiple Earths with identical evolutionary history such that another or even many “versions” of you exist somewhere/when.

[14]

I’m not sure I agree on your take. There are of course different definitions of infinity which would have different rules based on said definition. But if our universe is infinite and physics as we know it remains true then we would have to run into all the variations of every molecule combination possible again and again.

Saying we won’t see any even numbers in an infinite set of odd numbers is obvious as the rules of that infinite set have been defined. There are no such rules in the universe.

[ben_w]

The universe appears to be expanding close to e^t. If it continues to do so, each fundamental matter particle may end up isolated in a Hubble volume where the only photons from the rest of the universe have been red shifted to wavelengths larger than that Hubble volume.