Anthropic Principle Question

[ThePinsir]

I'm pretty sure I've got the jist of what the anthropic principle is as it relates to planetary systems and ultimately evolution. I even understand it as it applies to our universe, but only if a multiverse actually exists.

If, say, we found out that there is no multiverse, then how would the anthropic principle still apply to the universe?

[Alex K]

Let me break out Bayes theorem to illustrate:

Let P(U) be the probability that there is at least one universe which in principle allows intelligence.
P(I) the probability that intelligence exists in a universe

For any facts A,B, we define P(A|B) as the probability for A under the condition that B.

The first, maybe a bit trivial statement is:

P(U|I)=1,

i.e. if intelligence exists, the probability for at least one universe to exist which allows intelligence is unity.

Now, why would you now like a multiverse? Because you are not content with that answer - you want to answer the question: is P(I)>>0!

Bayes theorem states that:

P(U)/P(I) = P(U|I)/P(I|U)

so

P(I)= P(U) * P(I|U)/P(U|I) = P(U) * P(I|U)

If we are very optimistic about darwinian evolution and say that universes really tend to be big and stuff, we can put P(I|U) close to one. Therefore, we have P(I) ~ P(U), the probability that intelligence exists, is of the same order as the probability that at least one suitable universe for intelligence exists.

This is where the multiverse comes in: you would like to be able to say something about P(U), which is a probability in the space of universes. There simply is no handle on P(U) if there is not some kind of ensemble of possible universes from which a choice occurs. If you combine a mechanism to generate different laws of physics such as the string landscape with realism of the Schrödinger Wavefunction (i.e. "Many Worlds QM"), it is plausible to argue that P(U)=1.

Maybe you can finde better hypotheses I and U to make the point you want to make...

You can include the explicit background knowledge B that we exist, and put it in the theorem to deduce stuff. Then you have P(I|B)=1, P(U|B)=1. It's a fun game, what you have to do is to try and formalize what the questions and answers are which you would like to ask and get, and set up the respective probabilities.