Hello, everyone, and welcome to the Mindscape Podcast. I'm your host, Sean Carroll. One of the things we've talked about many times on the podcast is how you update your beliefs when new evidence comes in. That is to say, the process of Bayesian reasoning. Bayes' formula, of course, gives you a quantitative way of saying if I have some prior credence

for some claim being true and I very quantitatively measure some data and I can calculate

the likelihood of that data being obtained under all sorts of different propositions being true,

I can update my credences to get one that takes that data into account.

We don't necessarily every time work in such a quantitative vein, but this process is basically what we do in science, right?

In science, we have different kinds of theories that propose to provide explanations

for different kinds of phenomena, and we have different feelings. Some theories are more likely

than others. My favorite example is always is the dark matter, something like a weekly

interacting massive particle, a wimp, or something like an axion. So these are two different

particle physics candidates for the dark matter. They're both plausible. We don't have any idea,

which one is true, or even if it's some other theory, but we have favorites, right? We don't

give them equal probability because maybe it fits in better to other things we know, et cetera.

So that seems like a pretty straightforward

kind of process. You have prior probabilities for theories being true or whatever, and then

you get more data and you update your belief, your degree of belief, your credence. Here's a puzzle.

What if you're a cosmologist? What if you're thinking

about the whole universe all at once? And someone says, okay, I have two cosmological models,

two theories that describe all of the universe at once, and they predict statistically,

more or less the same local conditions that we observe.

So they are compatible with the data that we already have.

But here's the difference.

In one theory, the universe is bigger than in the other one.

...