Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
345 | Adam Elga on Being Rational in a Very Large Universe
23 Feb 2026
Chapter 1: 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.
Chapter 2: 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.
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Chapter 3: What challenges arise in cosmological models?
And certainly finding out that we disagree shouldn't be evidence that I was the one who was right. And so I should stick with that prior assessment, those prior conditional assessments and, basically often significantly move in the direction of the person who came to the contrary conclusion.
But people don't actually do that, do they?
Sad to say, although there's a kind of escape route here. There are different versions of the view, but the version that I like, and I've been influenced by David Christensen's writing on this, is the version that says you basically should defer to what your prior self would have thought. So here's a case. You come in, you encounter the big disagreement.
And then imagine getting on the time travel phone with your past self. And you ask your past self, hey, suppose this were to happen. Suppose you were to find out that you and this person were to disagree in such and such way. We can't, in the phone, we don't specify the full story about all the evidence and all the arguments because Then we'd just be reproducing the original problem.
But you give enough, you know, they say something that strikes me as totally wacko. They say a certain kind of coarse characterization. And then we ask that past version of yourself, what would you think conditional on that? You know, if that were to happen, how likely do you think it would be that you're the one who's right versus them? And my feeling is you should defer to that person.
And the reason why this doesn't immediately amount to a total, like, wishy-washiness in the face of everyone believing everything and just giving up your entire worldview and just becoming a kind of big averaging machine is that, in fact, in many cases, many of us are wrong. rather non even handed in our answers to those questions.
You'd think, what would you think if so-and-so thought blah, blah, blah. And often the answer is, wow, you know, even though I would say like in polite company, I would say that person's smart and I can't point to any encyclopedias that I've read that they haven't read. But I really am honest and think, what would I say if I found this person discreet?
I would think, you know, I guess I'd think they're probably wrong. And the version of the equal weight view, which is what this side of the view is sometimes called, the version that I like best is the one that defers to your past self in that way. And that's not quite as concessive as a more extreme version of view, which says, really, just always go 50-50.
So I'm a little confused as to why my past self is useful here. If I tell my past self all the relevant new information I've gotten, isn't that just my present self?
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Chapter 4: How do uncertainties in quantum mechanics influence rationality?
Where am I? Which one am I of these two people in duplicate situations?
it seems like a perfectly good question. I will, as a footnote mentioned that I think regular people talk about teleportation and they talk about the transporter machine on Star Trek, but only philosophers talk about teletransportation.
I think that, ah, okay, fair enough.
Okay. But if there are two copies of me, um, I'm, I'm just going to play the dumb podcast host now, 50, 50 that I'm one or the other. What else could it possibly be?
Um, Sounds good to me. Let's add more receiving stations. So let's say there are many Potemkin receiving stations and only one Enterprise receiving station. Now, you can think about your situation. Again, we're using constraints on your enterprise. expectations at an earlier time to guide your intuitions about what you should think at this later time.
So here you are about to step into the transporter and you think, what do I expect? So you certainly expect to wake up in one of the identical seeming receiving rooms. But let us say that on the enterprise, there's a wonderful pleasant experience waiting for you after a few minutes, but on the Potemkin, a less pleasant experience.
So there's just one enterprise though, and there are 100 Potemkins. And then as you step into the transporter, are you scared? Is your attitude more like your attitude when there's a 50-50 bad thing going to happen to you? Or is it more like your attitude when a 99 out of 100 bad thing is going to happen to you?
And it's sort of like this question about like, what do you expect when you open your eyes? Of course, we can't interpret that as what objective thing do we expect to happen in the world? Because when we're talking about those questions, there's only complete certainty. What you expect with 100% certitude to happen is there will be a body created on the Enterprise.
There'll be 99, 100 on the Potemkin. And the good thing will happen to the Enterprise person. The bad thing will happen to the others. But that's not going to tell you the difference between whether you start sweating or not as you press the button.
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Chapter 5: What is the Sleeping Beauty problem and its implications?
So I can't pretend to have the answers. If you have forced me to choose, I'm going to go and go with that view. Um, But they're twists and turns, and I'm not that confident.
I think that's perfectly fair, because Bolson brains do shake one up. But let's table it, because I think it's OK to first talk about the simpler cases, right, and to get them right. But you're right that thinking about complicated cases can shake your confidence in the simple cases. What would be the counter argument to the audience members who don't know?
In my mind, there's people like David Albert and Emily Adlam who have criticized assigning equal credences. But their alternative is just you can't do anything. You're stuck. There's no rational way to behave.
That's rough. Speaking as Mr. Rational, I really like the idea of there being constraints. And I guess I'm not comfortable with just – all actions being on a par. And when we add to the story that there's, for example, a door outside of the receiving room that in the Enterprise leads to a pizza party and in the Potemkin just is an airlock out into outer space.
Hard for me to give up the idea that there's some answer to the question about whether it's reasonable to open that airlock or not. Right. A lot of my... Now, we haven't gotten to the slightly more complicated cases. We're going to get there. We're going to work up to some cases where we add in... Remember, in the case we have so far, it is certain what will happen. Right.
We haven't had any chances. This is what's going to happen. We're going to add in some chances, and that adds something to the mix. But I just want to anticipate that one of the things that makes me uncomfortable about the family of views that's of a piece with the one I just avowed is that it seems to lead to a certain sort of presumptuousness. And I think today we might, I hope we get to
What's presumptuousness? And how do we dodge it?
Okay, good. Yeah, I think we should be able to get there. But I'm just trying to let the audience in on the idea that whether or not it's completely accepted in the community, one can presumably offer up justifications for saying that we should give equal credence to every individual. instance of us that is created in the transporter machine, right? It's not just like, well, it feels right.
We can be slightly more sophisticated in that. There are theorems one can prove under certain assumptions one can specify.
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Chapter 6: How do Boltzmann brains challenge our understanding of existence?
And that principle has some adherence. It's the famous principle of, famous or infamous principle of indifference. And there's a whole battle, a separate battle, I think, to be waged about whether that kind of principle is true. That principle is generally thought to be stronger and a bit more tendentious than the principle that just is like the
analog of that, but only applies as between self-locating hypotheses that are in the same world.
I guess all that is perfectly fair, and I certainly wouldn't want to think that one must assign some symmetry to these two cases of the different cosmologies and therefore give them equal credences. I guess all I'm trying to get at is the idea that we need to have some credences in these situations, just as a matter of practical rationality, right? Some of the pushback I've gotten—
the notion that we need to assign these credences is just, no, I don't. Like, what do I just don't have an attitude, just don't have an opinion about it. And I want to say, well, but to get through life, you kind of implicitly do have opinions about all sorts of uncertainties. And this is just one of them.
Just as a footnote, this idea of, I don't want to have a particular probability about something. I'm really interested in that. And I've tried to argue against that. And along the lines of, hey, if you think there's this special attitude of suspending judgment or my probability is not a probability of 0.3, but it's rather best represented by an interval from 0.2 to 0.7 or something like that.
I'm interested in pressing people who have that attitude on. Well, what is that attitude like? say about what you ought to do, if anything. And I guess I agree with you that it's not so comfortable to just say, well, just be silent about it. But that said, there is a worry lurking here.
And it's the thing that caused me to be cautious before jumping on to your case of, well, you should just be 50-50 between those two scientific hypotheses. And that is, Exactly because, as you said, we have to have some prior degrees of belief in those various hypotheses if we're to end up with some state of mind that could justify our actions.
There has to be some principle that governs those priors. The reason I was cautious is I was thinking, I want to watch out because in some of those cases, the priors that I think are reasonable are are highly non-even. And I'm thinking of cases of theories that are very complicated or ad hoc.
Yeah, no, I'm 100% on board. I guess I didn't explain my example well enough because I didn't want to use that as a case of we should give equal credences. I'm just invested in the idea that we should have credences.
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Chapter 7: What philosophical perspectives are presented on self-locating uncertainty?
In the universe? Yes, yes, yes.
Very roughly speaking, because otherwise it would be so unlikely that you exist. It's worth looking at. It's a wild paper. But Arno Zuboff, as far as I know, gets the credit for inventing this type of problem. And it was also independently came in through in the game theory and decision game theory literature. I learned of it from Robert Stoliker. And the problem is this.
beauty is put to sleep at the beginning of the experiment on Sunday, and then a fair coin toss is going to determine whether beauty will just be woken up on Monday night, or alternatively, briefly woken up on Monday night, and then put back to sleep and woken up on Tuesday night. All the wakings will feel just the same, including there will be
If there are two awakenings after the first one, beauty will be made to forget about the first awakening. So in all cases, beauty will have the sensation of waking up, thinking to themself, this feels like the first waking. I don't have an apparent memory of another one. Is it that the coin landed heads and it's Monday? Or is it that the coin landed tails and it's Monday or tails and Tuesday?
The mnemonic is tails is for the two waking scenario. Okay, good. And I have been persuaded by an argument, or at least tentatively persuaded by an argument that says, we want to set things up so that if the coin toss happens after the Monday waking, we are consistent with a very tempting view that
once beauty finds out that it's Monday, if they are, for example, a few minutes after waking up, told, hey, it's Monday, and they're furthermore told, hey, it's Monday, and we're about to toss this fair coin, and the coin toss is going to determine whether there will be one more waking or not. It seems hard to deny to me that beauty should be 50-50 about how this fair coin will land.
So sorry, so just to be clear, that's an altered version of the experiment where the coin is flipped after she's awakened on Monday. Exactly.
And now let's work backwards from that, what I think of as a kind of very hard to deny claim about this variant case. We can work backwards from that case and think, what Prior, first of all, we can in two steps say things wouldn't have been different. The analysis shouldn't have been different if the coin had been in fact tossed earlier. So, for example, suppose they.
the coin tossed it was just the coin toss outcome was in a box sealed no one's seen it and then they just carry that box and they say we're now going to for the first time open this box yeah it seems uh tempting to think that the verdicts in that case should match the verdicts in the case where the coin toss is really later that's why people don't freak out
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Chapter 8: How do these concepts relate to modern physics and cosmology?
And it's really that I feel that it's forced upon us. And to the extent that someone could give me the common sense way out, the way out such that at the end of it, someone can say, you know what? Turns out all those philosophers, they were wasting their time talking about self-locating belief. It's just plain vanilla, whatever. And we can stop talking about all that and just go on with our lives.
I would be a happy man.
I've certainly heard people say exactly those words, but then when they explain why they think it's true, it's very unconvincing. So I don't know if we're ever going to get there.
It's hard. I mean, we can, we can get away with, you know, you can get away with it. If you say just look, here's my solution. And then just empty silence, meaning the theory that just doesn't say anything about the case. All right. You could do that. But what I want is a case that, um,
gives us the kind of rationality verdicts that we ordinarily thought we were going to have you know the scientists should they run is this particle accelerator worth 600 billion dollars to build or not right that's a question that should have an answer
So the Sleeping Beauty thought experiment, philosophers love talking about it, but it clearly is closely analogous to things that physicists love talking about, both the anthropic multiverse and the many worlds of quantum mechanics. So let's try to draw those out more explicitly.
Would you, as a thirder, as someone who gives more credence in the coin landing tales and leading to two awakenings, does that mean if I'm doing the anthropic principle, I should give more credence to universes that have lots of observers in them? Because I could be any one of those observers.
In consistency, I am forced to answer yes, though I don't like it. That's the real, that's the honest truth. This is an instance of what, I mean, look, we can't not talk about presumptuousness at this point.
Let's do it.
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