345 | Adam Elga on Being Rational in a Very Large Universe
episode
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
1h 34m
3 speakers
8 chapters
transcribed
Transcript
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Transcript generated automatically by AI and may contain errors.
What is the main topic discussed in this episode?
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.
How does Bayesian reasoning apply to belief updates?
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 weakly 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, etc., 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. Like maybe in one theory, the universe is a closed universe, a sphere or a torus or something like that, and it doesn't actually extend very far beyond the universe that we can see today. In the other theory, the universe is open, it goes on forever, and there's just an infinite number of things going on. And this person says, so I think that the theory where the universe is bigger is much more likely. You say, well, why is that? Is it because there's some mechanism that gives you that or whatever? And they say, no, it's from updating on the data. And you say, what is that data? And they say, well, the data that I exist. Because in the bigger universe, it is just much more likely that someone like me would exist than in the smaller universe, just because there's random fluctuations because of quantum mechanics.
It's unlikely in any one small universe that I would exist. But as the universe becomes bigger and bigger, the chances of someone just like me get larger and larger. Is that kind of reasoning correct in the cosmological context? The answer is we don't know, or at least we don't have an agreed upon procedure for dealing with these kinds of puzzles. And they show up, these kinds of puzzles, again and again. You can guess that things like the Boltzmann brain scenario, where there's random fluctuations that create observers like us, in the far future or maybe in the far past, but ones that don't arise via thermodynamically sensible evolution from a low entropy Big Bang, like we think we did. There's examples like the multiverse of Everettian quantum mechanics.
When I measure the spin of an electron, and it could be spin up or spin down, I'm saying, okay, now there's a spin up particle, spin down particle. They're two separate worlds, right? And I want to say, what's the probability that I'm in one world or the other? Does it matter how thick the world is or the different things that come into consideration here? So this is obviously a set of puzzles that is very relevant for cosmology and physics, you know, real things we care about, quantum mechanics, the multiverse, things like that, as well as for philosophers who want to know how should we be rational in situations like this?
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Chapters
8 chapters
1
What is the main topic discussed in this episode?
0:01–0:37
2
How does Bayesian reasoning apply to belief updates?
0:37–8:58
3
What challenges arise in cosmological models?
8:58–21:09
4
How do uncertainties in quantum mechanics influence rationality?
21:09–24:38
5
What is the Sleeping Beauty problem and its implications?
24:38–30:41
6
How do Boltzmann brains challenge our understanding of existence?
30:41–40:32
7
What philosophical perspectives are presented on self-locating uncertainty?
40:32–48:18
8
How do these concepts relate to modern physics and cosmology?
48:18–1:34:20
Speakers
3 identifiedMore from Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
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363 | Chandra Sripada on How LLMs and Humans are Cognitive Cousins