[vidarh]

> And even taking that for granted, what is so astonishing that the actual one is the one that is compatible with our existence?

You've just verbalized the weak anthropic principle. The entire point of it is that this is not astonishing (at least not without additional knowledge), but a necessity for the universe to be one compatible with our existence, irrespective of how rare the conditions are, given we're here to observe it. The prior probability of "us" arising might have been incredibly small (or not, we can't tell), but the posterior probability is 1 - we're here.

> I mean, if any possible universe could have happened, then the one we live in had actually an equal chance to exist with any other.

Yes, but that does not mean that the odds of any given configuration need to have an equal chance.

What GP is saying is if there is an infinite number of universes and if life is extremely unlikely, then the odds of any given universe with life only having one life form might be very high, even if there being even one life form might be extremely unlikely.

We know that the posterior probability of there being one suitable for us is 1, since we're here. But we don't know whether or not life is a rare event or not.

The antrophic principle explains why we "won the lottery" so to speak in being in one of the universes with at least one life form, but life being incredibly scarce might be one explanation for why we might be in a universe with only one life form.

Though of course we can not infer that life is rare across any given set of universes if we determine we're alone in this one, because we don't know how other universes would be configured.

[0-_-0]

> Though of course we can not infer that life is rare across any given set of universes if we determine we're alone in this one, because we don't know how other universes would be configured.

Not necessarily, you could assume a universal prior distribution over possible universes and count how many of those that have life have more than one.

https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

This might be a sort of a "last tool of science", a way to discover the laws of our universe without observing them.

[vidarh]

That presupposes knowledge of more than one universe to even start to enumerate the possible parameters deciding the set, and without a sufficiently complete sequence we would be unable to determine all of the possible parameters, or how they can change.

E.g. even given that we know, say, gravity exists, we do not know if or how its strength varies in a set of infinite universes. Based on a sample of one universe, it could be constant or vary in an infinite number of ways.

[0-_-0]

> That presupposes knowledge of more than one universe to even start to enumerate the possible parameters deciding the set

I think you entirely missed my point (because you didn't read the link!). You could use the universal prior, that is, you could enumerate all possible computer programs (e.g. Turing machine programs) starting from the shortest and find the shortest one that generates our universe. Now, 2^L where L is the length of such program is the prior probability of our universe.

So to determine e.g. the average value of the gravitational constant across all universes, you would measure the gravitational constant in all universes and calculate a weighted sum where you weight the value of the constant by the prior probability of the corresponding universe. The same for the occurrence of life, etc.