Adam Elga with Sean Carroll
Show: Sean Carroll's Mindscape
Cleaned and reformatted from published transcript or auto-generated captions — punctuation added, filler removed, restructured for readability. Not verbatim. For exact quotes, refer to the original.
Sean Carroll
Welcome to the Mindscape podcast. One of the things we've talked about many times is how you update your beliefs when new evidence comes in — the process of Bayesian reasoning. Bayes' formula gives you a quantitative way of saying: if I have some prior credence for a claim being true, and I measure some data, and I can calculate the likelihood of that data being obtained under all sorts of different propositions, I can update my credences to one that takes the data into account.
We don't always work in such a quantitative vein, but this is basically what we do in science. We have different theories that propose to explain different phenomena, and we have different feelings about them — some theories seem more likely than others. My favourite example is dark matter. Something like a weakly interacting massive particle, a WIMP, or something like an axion — two particle-physics candidates for the dark matter. Both are plausible. We have no idea which is true, or even whether it's some other theory, but we have favourites. We don't give them equal probability, because maybe one fits better with other things we know. So that seems a straightforward process: you have prior probabilities for theories, you get more data, and you update your degree of belief, your credence.
Here's a puzzle. What if you're a cosmologist thinking about the whole universe at once? Someone says: I have two cosmological models that predict more or less the same local conditions we observe, so both are compatible with our data. But in one theory the universe is bigger than in the other. Maybe in one the universe is closed — a sphere or a torus — and doesn't extend far beyond what we can see, while in the other it's open, going on forever with an infinite number of things happening. And this person says the theory where the universe is bigger is much more likely. Why? Not because of some mechanism, but from updating on the data — the data that I exist. In the bigger universe it is just much more likely that someone like me would exist, because of random quantum fluctuations. 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 procedure for these puzzles, and they show up again and again. The Boltzmann brain scenario, where random fluctuations create observers like us in the far future or far past, ones that don't arise by thermodynamically sensible evolution from a low-entropy Big Bang. The many worlds of Everett in quantum mechanics: I measure the spin of an electron, it could be up or down, and now there are two separate worlds — what's the probability that I'm in one rather than the other? So this is a set of puzzles very relevant to cosmology and physics, as well as to philosophers who want to know how we should reason under uncertainty.
Today's guest is one of the world's experts on these issues. Adam Elga is a philosopher at Princeton. He has several well-known papers, one on the famous Sleeping Beauty problem: you flip a coin; if it's heads you wake Sleeping Beauty on Monday, if it's tails you wake her on Monday and Tuesday. Do you give equal credence to all three possibilities — heads-and-Monday, tails-and-Monday, tails-and-Tuesday? Or do you say the coin is fair, so it's still a 50% chance I was in the heads universe, even though I only wake once there? Smart people disagree. Let's go.
Sean Carroll
Adam Elga, welcome to the Mindscape podcast.
Adam Elga
Thanks so much for the invitation.
Sean Carroll
I know your work through papers about Boltzmann brains and self-locating uncertainty, topics near and dear to my heart, and we'll certainly talk about them. But you have a bigger scope in your philosophical career. How would you characterise your project, to the extent one has a project?
Adam Elga
I characterise myself as addicted to rationality. It started at a young age — around my household they sometimes called me Mr Rational. I've always been fascinated with probability, doing the rational thing, what's justified, optimising, and I think that's the thread that runs through my philosophy. I've thought about the direction of time, in particular how actions bear on what happens in the future and the past, and what you should think about various temporal asymmetries. And with some co-authors I've thought about Dutch book arguments, money pumps, and game and decision theory.
Sean Carroll
Mr Rationality is not the worst nickname one could have. I get that it's a little bit of a dig, but it could be much worse.
Adam Elga
There was some mockery there.
Sean Carroll
But now you've found your people. You're a professional philosopher, and the whole rationality thing is probably simply a compliment.
Adam Elga
I'll take it.
Sean Carroll
One of your papers is about how we should be rational when talking to other people who have knowledge — experts, or peers we think are equal to us. It's very rare that we have an opinion, meet someone we think is just as smart with a different opinion, and therefore change our opinion. But what is a perfectly rational person supposed to do here?
Adam Elga
This is great, and given what we'll talk about later, we can plant a seed that's really going to connect. There's a great applied-philosophy question about how you should respond when someone you antecedently considered smart and well-informed came to a different conclusion than you on the basis of similar evidence. On one hand there are people who think whoever is in fact right should pretty much stick to their guns. On the other side there are people who think: given that one of us is wrong, I had no antecedent reason to think I'd be the one who was right, and finding out that we disagree shouldn't be evidence that I was right. So I should stick with that prior conditional assessment and often significantly move in the direction of the person who came to the contrary conclusion.
Sean Carroll
But people don't actually do that, do they?
Adam Elga
Sad to say. Although there's an escape route. There are different versions of the view, but the one I like — I've been influenced by David Christensen's writing — says you should defer to what your prior self would have thought. Here's a case. You encounter the big disagreement, and then imagine getting on a time-travel phone with your past self. You ask them: suppose you were to find out that you and this person disagreed in such-and-such way. We can't specify the full story about all the evidence and arguments, because then we'd just be reproducing the original problem. But you give enough — they say something that strikes you as totally whack, or a certain kind of coarse characterisation — and you ask that past version of yourself: conditional on that, how likely is it that you're the one who's right versus them? My feeling is you should defer to that person.
The reason this doesn't amount to total wishy-washiness — giving up your entire worldview to become a big averaging machine — is that in fact many of us are rather non-evenhanded in our answers to those questions. You'd think, what would you think if so-and-so thought blah blah? And often the answer is: even though in polite company I'd say that person's smart and I can't point to any encyclopedias I've read that they haven't, if I'm really honest I'd think they're probably wrong. The version of the equal-weight view I like best is the one that defers to your past self that way. That's not quite as concessive as the more extreme version that says really just always go 50/50.
Sean Carroll
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 got, isn't that just my present self?
Adam Elga
Yes. And that's why the question you ask your past self is something less than the fully specified original question. One way to motivate the view is a David Christensen case where the equal-weight view is very intuitive — the split-the-check case. You're out to dinner with friends, the bill comes, people do the arithmetic on their own, and they get different answers. How confident should I be that my answer was right, given this disagreement? It's very intuitive that the answer should match the answer to the question: if you'd asked yourself at the beginning of the meal — suppose we later split the check and you get this answer, how likely is it that you'll be the one who's right? That seems to align. And it handles a slightly more general case, because it nicely handles the case where I think I'm not so great at maths — I think it's 90/10 that they're the one who's right. That seems intuitively like the thing to do when that scenario actually happens. For that test to work, you can't be giving the full maths question to your past self.
Sean Carroll
Good. You're just asking them about their basic judgement ahead of time: what's the likelihood that someone's going to be wrong, and is it going to be me?
Adam Elga
And you want to tell them something about the circumstances. There's a difference between you get $20 and your friend gets $23, and you get $20 and your friend says $18. The relevant question you'd ask your past self is: what if I get an answer that seems reasonable to me and they get one that seems totally bonkers, off-the-wall? The answer to that question should rule the day when that situation actually happens.
Sean Carroll
Am I correct that this strategy is meant to be a semi-practical implementation of the idea that we should have our credences changed by the right amount when we meet other equally smart people with different credences?
Adam Elga
I love that characterisation. My opponents would disagree that this view meets that standard, but I think that's the kind of thing everyone's going for.
Sean Carroll
I'm trying to imagine examples where people I think are smarter than me, experts in some area, have a belief close to that area and yet I disagree. I try to justify why it's okay to disagree — I think I can identify some blind spot they have. But is that likely to be me just fooling myself?
Adam Elga
There could be two things going on, and this exercise of looking back at what your past self would say is both theoretically valuable and a really good practical mental exercise, because you can diagnose what's going on with your own later favouring of your own views. One thing: it might have been a polite fiction that you ever really treated the person as a peer. You think they're smart and well-intentioned, but all along you thought, when it comes down to it, if we disagree I'd think it's more likely that I'm right. Another possibility: you really thought they were just as good, and antecedently thought it was a coin toss who'd be right, but then when the time comes — maybe irrationally — you stick to yourself. The thing I really want to rule out is that you antecedently thought it was 50/50, but then when it actually happens you think, you know what, I'm right.
And notice a really weird thing that could happen — a kind of bootstrapping confirmation that you're better than someone. Over many disagreements, if you did that every time, you'd think: I got that one right, I got this one right. Assuming no independent confirmation, all you have to go on is what's happened so far. You'll check them off and think, wow, I got all these right, I'm even better than I previously thought. That seems like things have gone off the rails.
Sean Carroll
That's a problem. In ordinary human conversation, people sometimes have a criticism of the form, 'you always think you're right.' If that means the opinion I have at any one moment is the one I think is right, then yes — how could it be otherwise? But the legitimate criticism is: you're unwilling to ever admit you could be wrong.
Adam Elga
Exactly. And I can't resist citing a paper Andy Egan and I wrote a while back. The title is 'I Can't Believe I'm Stupid.' It's all about the limits on how much you can doubt your own opinions while still having them. But can I circle back to one thing? There's one more view we haven't mentioned. I predict you won't like it, but it'll be useful when we talk about Boltzmann brains.
Sean Carroll
Great.
Adam Elga
It's called the level-splitting view, and I've learned a lot about it from David Christensen. It allows a position we've been implicitly assuming was off the table. The position is this: you should think, well, I'm still right — stay confident that I'm right — but I also think that's irrational; the rational thing is to be 50/50. So on the first-order issue, will it rain tomorrow, you think 'I'm right,' even though the weather forecaster said no. But if someone asks what's the rational thing to believe, you say 50/50. It's called level-splitting because those are two different levels.
Sean Carroll
I see. It's having confidence in an opinion, but also a feeling that my confidence might be misplaced.
Adam Elga
Yes. And put that in your pocket for later in this podcast. When we come to Boltzmann brains, there's going to be a potential way out related to that.
Sean Carroll
Let's work our way up toward that. Am I right that a lot of this goes back to Derek Parfit's work on teletransporters and self-locating uncertainty?
Adam Elga
It's definitely related. I'm not confident on the origins, but people have thought about cases where you're wondering who you are and when it is, certainly long before I came on the scene.
Sean Carroll
Explain that version, because people are familiar enough with Star Trek that they can get an example of where self-locating uncertainty could arise.
Adam Elga
Great, and the Star Trek example will bring up a version people don't often talk about. In the standard teletransporter case, you step into the teleporter, your body is destroyed, and the information is transmitted — say to the Enterprise and also to another ship, the Pumpkin — and duplicate bodies are created on each ship. You wake up, look around, and the receiving bays of the Enterprise and the Pumpkin look exactly alike. So you wonder: am I on the Enterprise or the Pumpkin? This isn't a question you could completely express in objective, third-person vocabulary. Even if you specify the positions of all the particles and the full history of time, some people think there's a residual question: where am I? Which one am I of these two duplicates?
Sean Carroll
That seems a perfectly good question. As a footnote — regular people talk about teleportation and the transporter on Star Trek, but only philosophers talk about teletransportation.
Adam Elga
Fair enough.
Sean Carroll
If there are two copies of me — I'll play the dumb podcast host — it's 50/50 that I'm one or the other. What else could it possibly be?
Adam Elga
Sounds good to me. Now let's add more receiving stations. Say there are many Pumpkin receiving stations and only one Enterprise station. Again we use constraints on your expectations at an earlier time to guide your intuitions about now. You're about to step into the transporter. You expect to wake up in one of the identical-seeming receiving rooms. But say that on the Enterprise a pleasant experience awaits you after a few minutes, and on the Pumpkin a less pleasant one. There's just one Enterprise and a hundred Pumpkins. As you step in, are you scared? Is your attitude like the attitude when there's a 50/50 bad thing coming, or like when a 99-out-of-100 bad thing is coming? We can't interpret that as what objective thing you expect to happen, because there's complete certainty about the objective facts: a body will be created on the Enterprise, ninety-nine on the Pumpkins, the good thing to the Enterprise person and the bad thing to the others. But that won't tell you whether you start sweating as you press the button.
Adam Elga
So we can take stances here. Under those conditions — a hundred of you, ninety-nine in Pumpkins, one on the Enterprise — do you think it's right to assign equal credences to being any of them?
Sean Carroll
I do, although I'm a lot less confident than I used to be. A large part of the reason my confidence has gone down — aside from the great work criticising that view over the years — is the problem of Boltzmann brains. It's thrown my confidence in this whole business to hell, so I can't pretend to have the answers. If you force me to choose I'll go with that view, but there are twists and turns and I'm not that confident.
Adam Elga
That's perfectly fair, because Boltzmann brains do shake one up. But let's table it, because it's okay to first talk about the simpler cases and get them right. What would be the counterargument, for audience members who don't know? In my mind there are people like David Albert and Emily Adlam who've criticised assigning equal credences, but their alternative is that you can't do anything — you're stuck, there's no rational way to behave.
Sean Carroll
That's rough. Speaking as Mr Rational, I really like the idea of there being constraints, and I'm not comfortable with all actions being on a par. When we add to the story that there's a door outside the receiving room — on the Enterprise it leads to a pizza party, on the Pumpkin it's an airlock out into space — it's hard for me to give up the idea that there's some answer to whether it's reasonable to open that airlock.
Adam Elga
Right. We haven't got to the more complicated cases yet. In the case we have so far it's certain what will happen; we haven't added any chances. We're going to add some chances, and that adds something to the mix. But I want to anticipate: one thing that makes me uncomfortable about the family of views I just avowed is that it seems to lead to a certain presumptuousness. I hope we get to what presumptuousness is and how we dodge it.
Sean Carroll
Good. I'm letting the audience in on the idea that, whether or not it's completely accepted in the community, one can offer up justifications for saying we should give equal credence to every instance of us created in the transporter. It's not just that it feels right — there are theorems one can prove under certain assumptions.
Adam Elga
Sure. And one nice thing about the case so far is that we're talking about different copies living in the same possible world. We can idealise and suppose everyone's certain exactly what's going to happen from the beginning to the end of time. The only uncertainty left is which one am I. I've called one ship the Pumpkin and one the Enterprise, but it's hard to see how that could make a difference. There's a very common-sense thought here — Bob Stalnaker's example. When you wake in the middle of the night, groggy, before you look at your clock, you think: what time is it? Maybe you know you wake at 3am and at 4am most nights, but you forget each waking. It just seems it should be 50/50. What do you have that tells between those two hypotheses? It's not even as though they're two different stories of the world that differ in how simple they are — it's just, where am I within this one story? I do confess an inclination to split it 50/50.
Sean Carroll
You mentioned that one premise in the simple story is that there are two or a hundred copies of you in the same world. One could imagine the same kind of reasoning working for different worlds. Imagine a cosmology where the dark matter particle is an axion, and another where it's a weakly interacting massive particle, but as far as every observation we've made the universe looks the same in both. Isn't that a kind of self-locating uncertainty between possible worlds rather than locations in the real world?
Adam Elga
As a matter of terminology, no — self-locating uncertainty is uncertainty between scenarios within a world. But the content of your point is: doesn't the same intuition push us toward treating possibilities evenhandedly even when they involve different worlds? That principle has adherents. It's the famous — or infamous — principle of indifference, and there's a whole separate battle about whether it's true. It's generally thought to be stronger and more tendentious than the principle that applies only between self-locating hypotheses in the same world.
Sean Carroll
That's fair, and I wouldn't want to insist that one must assign symmetry to those two cosmologies and give them equal credences. All I'm getting at is that we need some credences in these situations, just as a matter of practical rationality. Some pushback I've had is: I just don't have an attitude, don't have an opinion about it. And I'd say, but to get through life you implicitly do have opinions about all sorts of uncertainties, and this is just one of them.
Adam Elga
As a footnote, I'm really interested in this idea of not wanting a particular probability about something, and I've tried to argue against it — along the lines of: if you think there's a special attitude of suspending judgement, that your probability isn't 0.3 but is best represented by an interval from 0.2 to 0.7, I press people on what that attitude says about what you ought to do, if anything. I agree it's not comfortable to just be silent about it.
Sean Carroll
That said, there's a worry lurking, and it's what made me cautious before jumping onto your case of just going 50/50 between two scientific hypotheses. We have to have some prior degrees of belief. If we're to end up with a state of mind that justifies our actions, there has to be some principle governing those priors. I was cautious because in some cases the priors I think are reasonable are highly uneven — I'm thinking of theories that are very complicated or ad hoc.
Adam Elga
I'm 100% on board. I didn't explain my example well — I didn't want to use it as a case where we give equal credences. I'm just invested in the idea that we should have credences.
Sean Carroll
Oh, definitely. I'm with you. I thought you meant 50/50.
Adam Elga
No, I certainly don't think it's 50/50 in that case, because the theories have different theoretical virtues; they're not really symmetric. But there is some uncertainty. One reason I was excited about this conversation is that I wanted to ask you a question right in the vicinity, following on your fine-tuning episode. Philosophers find it easy to represent scientific reasoning as Bayesian reasoning: you start with priors over theories — not even, if you think some are intrinsically better — then you get evidence and update. What I noticed about your fine-tuning discussion is that the criteria scientists actually apply are much more specific and fine-grained than that. You didn't just say there's a constant of nature that could have been anything. You said something specific: if a theory says a certain quantity is really close to zero but not exactly zero, that's especially bad. That's something you couldn't derive from plain vanilla neutral probability. There are real scientific standards in there. How do I square those two things?
Adam Elga
That's a great question. I don't have the comprehensive answer, but I have this feeling that what we're trying to do as scientists is attach credences within the space of theories we haven't thought of yet, which is especially hard. If we'd measured the mass of the muon to be exactly pi times the mass of the electron — that's a real number, it could have been a different one — should we notice anything? Yes, because it increases our feeling that there's some reason we haven't yet thought of. It's scientific practice that certain possibilities are suggestive of future truths we haven't discovered, and it's okay to take that into account when judging things to be finely tuned or natural.
Sean Carroll
That makes sense. The lesson I take is that the relevant prior isn't the kind of thing I have confident access to. It's the sort of thing that needs a sensible education in physics to cultivate. That's not an objection — it's a lesson. Even the cosmological constant, the vacuum energy, which is small but not zero with respect to what we'd have thought was the natural range — that's a number; why be more surprised at it than any other? But somehow, as scientists, we're doing an implicit coarse-graining over possibilities and not assigning uniform probability, because we're being scientists. I think it's okay.
Adam Elga
Exactly. And feel free to reel this back in, but the plain-vanilla Bayesian approach would seem to favour theories with smaller numbers of parameters much more than we do in practice. If you don't have something else going on, a theory with ten more parameters covers a huge space of possibilities, and unless you have very biased priors to counteract that, those theories get ruled out from the start. But we don't rule out theories with one or two extra parameters so extremely. So there has to be something else going on.
Sean Carroll
That's fair too. This is past my pay grade, but I imagine scientists are fallibilists at heart. They think the theories we have now aren't final, and some of our experiments aren't perfect. So if we fit data perfectly, but only by having many parameters, we're like the humble rational agents we started with, who say it's too good to be true — either some measurements will change or we'll invent a better theory. Let's not get too excited about perfect agreement between a jury-rigged theory and the experiments we happen to have today.
Adam Elga
I like it.
Sean Carroll
Back to crazy thought experiments. We'll get to Boltzmann brains and many worlds, but I've got to give you, of all people, the chance to explain the Sleeping Beauty problem. I don't think it was your idea, but you've been a pioneer in pushing a particular theory of it. Don't assume the audience knows the thought experiment — tell them.
Adam Elga
No problem, I love the problem. It comes from Arnold Zuboff, who later published related ideas in a wild paper called 'One Self: The Logic of Experience,' which argues, very roughly, that there is only one conscious being in the universe — because otherwise it would be so unlikely that you exist. It's worth a look. Zuboff gets the credit for inventing this type of problem, and it also came independently through the decision- and game-theory literature; I learned of it from Robert Stalnaker.
The problem is this. Beauty is put to sleep at the beginning of the experiment on Sunday. A fair coin toss determines whether Beauty will be woken just on Monday, or briefly woken on Monday, put back to sleep, and woken again on Tuesday. All the awakenings feel the same, and if there are two awakenings, after the first one Beauty is made to forget it. So in all cases Beauty has the sensation of waking and thinking: this feels like the first waking, I have no apparent memory of another. Did the coin land heads and it's Monday, or tails and it's Monday, or tails and it's Tuesday? The mnemonic is: tails is for the two-waking scenario.
Sean Carroll
Good.
Adam Elga
I've been tentatively persuaded by an argument that says we want to set things up consistently with a very tempting view. Once Beauty finds out it's Monday — if a few minutes after waking she's told 'it's Monday, and we're about to toss this fair coin to determine whether there'll be one more waking' — it seems hard to deny that she should be 50/50 about how the fair coin will land.
Sean Carroll
Just to be clear, that's an altered version where the coin is flipped after she's woken on Monday.
Adam Elga
Exactly. Now let's work backwards from that hard-to-deny claim. First, in two steps, the analysis shouldn't have been different if the coin had been tossed earlier — say the outcome was sealed in a box no one has seen, and only now do they open it. It's tempting to think the verdicts should match the case where the coin toss is really later. That's why people don't freak out about exactly when lottery drawings happen: as long as no one's cheating, it's all the same. From the verdict in that case — 50/50 that the coin landed heads, conditional on its being Monday — and using an assumption about how your beliefs should change on hearing it's Monday, we get a verdict about what you should believe before you heard that news. The crucial assumption is that the news doesn't change the ratio of your probability in the scenario heads-Monday and the scenario tails-Monday. Both are compatible with the news; when you get it, that narrows things to just those two, and you don't monkey with the ratio between them. With that assumption, you're forced to conclude that in the case where you don't learn it's Monday, you should be two-thirds confident in tails and one-third in heads.
Sean Carroll
And that's being a thirder.
Adam Elga
A thirder, right. The other option is being a halfer.
Sean Carroll
Correct.
Adam Elga
Well, I shouldn't say the other option, because there are two other options. In the story where you learn it's Monday, there's the question of what you believe about the coin before learning it's Monday and after. There's another view, less well-known but worth thinking about — the so-called double-halfers, who before learning it's Monday think it's 50/50, and after learning it's Monday still think it's 50/50. They deny the premise about keeping the ratios the same when you learn that piece of news.
Sean Carroll
So the Sleeping Beauty problem is a case of self-locating uncertainty, but trickier. Rather than two copies, there are three instances — heads-Monday, tails-Monday, tails-Tuesday. And the third position assigns them equal credences.
Adam Elga
Exactly, though that's somewhat an accident of how the fair coin and the other assumptions combine. The crucial thing in the thirder position is that the world with more awakenings gets a kind of boost associated with there being more instances of that state of mind. That's going to be crucial when we think about Boltzmann brains: do those worlds deserve a boost?
I want to add one thing about crazy town, echoing something you said about the multiverse, because it's true about self-locating belief too. There are lots of fanciful examples in this territory, and it's tempting to think you shouldn't be called Rational Man but Weird Self-Locating Duplicate Man. I'll fess up to my rationality fetish, but I don't have a weirdo-example fetish or a fetish for bizarre views. I'm actually cautious and conservative about these things, and I hate being forced into bizarro views by self-locating beliefs. It really is that I feel it's forced upon us. To the extent that someone can give me a common-sense way out — such that at the end you can say, turns out all those philosophers were wasting their time, it's just plain vanilla — I would be a happy man.
Sean Carroll
I've certainly heard people say exactly those words, but when they explain why, it's very unconvincing. So I don't know if we're ever going to get there.
Adam Elga
It's hard. You can get away with it if you just say 'here's my solution' and then empty silence — a theory that doesn't say anything about the case. But what I want is a case that gives the kind of rationality verdict we ordinarily thought we'd have. The scientist asking: is this particle accelerator worth $60 billion to build or not? That's a question that should have an answer.
Sean Carroll
Philosophers love the Sleeping Beauty thought experiment, but it's closely analogous to things physicists love — both the anthropic multiverse and the many worlds of quantum mechanics. As a thirder, someone who gives more credence to the coin landing tails and leading to two awakenings — does that mean, doing the anthropic principle, I should give more credence to universes with lots of observers, because I could be any one of them?
Adam Elga
To be consistent, I'm forced to answer yes, although I don't like it. That's the honest truth.
Sean Carroll
This is an instance of what you meant — we can't not talk about presumptuousness at this point.
Adam Elga
Let's don the robes of the presumptuous philosopher. The cosmologists come in with two theories. One says there's just an ordinary universe, one instantiation of someone having experiences like yours. The other says there are many instantiations. Someone attracted to the thirder view — or equivalently, the view that possible worlds with many instantiations of your state of mind get a boost — is committed to saying theory B gets a big boost. And there they are, sitting in their philosopher's chair. How presumptuous. I say it jokily, but I take it as a serious, weighty criticism. It seems like a disaster to let the cosmological determination depend on that factor so much.
Sean Carroll
As a matter of marketing, the other view — where you say I don't give a boost to theories with lots of observers, I just have a prior, I'm a good Bayesian, and within each universe I ask the chance I'll be any particular observer — leads to all sorts of presumptuous-sounding conclusions as well. But those people labelled the other side as presumptuous first, so that's what they call them. There's a lot of presumptuousness going around.
Adam Elga
There's plenty to go around. Just as terminology, to tie things together — I agree the terms aren't very descriptive, but in case someone's looking this up: the thing we've called the thirder or 'many duplicates get a boost' position is called SIA, the self-indication assumption. I think that goes back to Bostrom. The view you were gesturing at is sometimes called SSA, the self-sampling assumption. I'd like to add another tag. If the first view says possibilities with many copies of me get a boost, think of the other view as: possibilities in which most people are like me get a boost — a boost to possibilities where a high fraction of observers have experiences similar to mine. As many have pointed out, that requires answering what it means for an observer to be sufficiently like you — a free parameter you can fix in various ways. But the big-picture question is: is it that many get a boost, or most get a boost? Absolute numbers or frequencies? Those are two of the main views. There's a third we haven't discussed.
Sean Carroll
What's the label for the third view?
Adam Elga
Compartmentalised conditionalising, sometimes called CC. I learned about it from Chris Meacham's work. It generalises the halfer view in Sleeping Beauty — the one that says, before you learn it's Monday, be 50/50 on the coin, and after, be 50/50. Visualise it as a version of Bayesian updating, but with a firewall between worlds: when probability gets pushed around, it can't cross world boundaries. In Sleeping Beauty, the thirder says you have three possibilities — heads-Monday, tails-Monday, tails-Tuesday — and when you eliminate tails-Tuesday, that probability gets split between heads-Monday and tails-Monday in proportion to what was originally there. This other view says that probability was already in the two-waking world, so it can't cross the boundary; all of it has to go to tails-Monday, and that's how you get 50/50.
Sean Carroll
Good, I'm glad they all have names. The names could be snappier. At the risk of derailing — I don't believe any of these approaches. What I believe is closest to what Radford Neal calls fully non-indexical conditioning. Do you know it?
Adam Elga
Yes, but I haven't thought deeply about it. I like that paper.
Sean Carroll
To make it as short as possible: I don't care how many observers there are in the universe. I share your worry that it's presumptuous to say I've proven a theory right just because there are a lot of observers in it. But I do think it's fair to judge theories by the probability that in that theory there would arise at least one observer exactly like me. Naturally that gives a boost to stochastic theories that are big and have many observers, because the total probability that one of them is like me goes up. But it doesn't keep giving an infinite boost as there are more and more observers just like me, because all I care about is that there's at least one.
Adam Elga
I love it. Haven't thought about that view. Can we talk about a case? Here's an instance where I'm feeling the limits of the audio medium, because I'd want to draw this. Two cosmological theories. Theory A just says it's 50/50 whether you see red or green — a coin toss, red room or green room. Theory B says for sure one person wakes up in a red room and, say, a hundred in a green room. So you wake and see red or green — how does your way of thinking go? What verdicts does it give?
Sean Carroll
If theory B has a 100% chance that someone sees red and someone sees green, while theory A has one person with a 50/50 chance of either, then no matter what I see, the data increases my credence in theory B — because there's a 100% chance that someone like me exists in B, and only a 50% chance in A.
Adam Elga
Interesting. So there's a boost to the second theory, the same boost whether you see red or green. And that's it. We have to think about whether that's presumptuous. It doesn't seem too bad. At first glance it does seem to avoid the running-off-the-rails effect of getting arbitrarily extreme verdicts just by cranking up the number of duplicates. It'd be interesting to think about what priors you'd need over all the possibilities to deliver that verdict by conditionalising. I haven't thought that through.
Sean Carroll
To be super clear, a student here at Hopkins, Isaac Wilkins, and I are trying to write a paper about this, so we haven't thought it all the way through. But I'm saying it out loud in public as motivation to get the paper written.
Adam Elga
That's great. I hope you'll think about this case too.
Sean Carroll
All right, we've eaten our vegetables and laid the groundwork. Now we can talk about Boltzmann brains. Do you want to tell the audience member who's never heard of a Boltzmann brain what that weird phrase refers to?
Adam Elga
I'll give it a shot. If the universe is really long-lasting, as it is according to some theories, there's enough time for various fluctuations to happen — including fluctuations that are conscious. With so many independent variations instantiated over a long enough time, it'll turn out that of the observers who, for all your evidence goes, might be you, the vast majority are Boltzmann brains — piles of matter that formed out of nothing, out of pure random chance. If that's true, and if it's true that when there are lots of observers who for all your evidence might be you, you should be somewhat evenhanded about which one you are — think back to the alarm-clock case, lots of wakings and some are just fluctuation wakings — then your probabilities about which one you are should be roughly equally apportioned. In which case, since the vast majority of those awakenings are Boltzmann brain awakenings, you should be really confident that you're a Boltzmann brain. That's the first pass of how we get into trouble.
Here's a case where my fellow cosmologists let me down a little, because many just think, well, that's silly, so I'm not going to think about it. That's an attitude. But another attitude takes the Boltzmann brain problem very seriously. My attitude is: if I lived in one of these eternal universes with random fluctuations, then I would be a Boltzmann brain. But I look around and see I'm not. Therefore I do not live in such a cosmology. I think that's not valid. But tell me what you think.
Sean Carroll
There's a serious tradition in contemporary epistemology — indeed maybe the dominant tradition — that a certain amount of what's called externalism is true about the relationship between evidence and experience. A distinctive externalist view: two creatures could be physical duplicates at a time, with exactly matching brain firings and light going into their optic nerves the same way, and yet one has much stronger evidence than the other. This is often associated with Tim Williamson. If you have that picture, then our evidence is much stronger than just 'I seem to be having a particular experience and have certain apparent memories.' Maybe your evidence is: there's an apple in front of me, there's a desk, there's a star in the sky; I remember, not just seem to remember, what I had for breakfast. To the extent that view is true, our evidence is stronger.
Whether this is a way out of the Boltzmann brain problem depends on how bad you think it is to be uncertain which Boltzmann bubble you're embedded in. It would take a very extreme externalism to think it's part of my evidence that I'm part of the first Big Bang rather than some other Boltzmann bubbly Big Bang-type event. Someone could think: that's okay. I just want to get rid of the scenario where I'm a transient brain formed in space and wrong about everything. If you grant me that I'm right about the observable universe and the history books, and you say I could be in this bubble or that bubble, that person might say, all right, I can live with that. I myself have always been somewhat suspicious of the extreme externalist views, so I'm pinched harder by the Boltzmann brain problem.
Sean Carroll
I'm trying to map the externalist point onto my fellow cosmologists' attitudes. I was insufficiently clear. They all say 'I'm not a Boltzmann brain,' but the conclusion is a bit different. Someone like Raphael Bousso, a former guest, would say: if I lived in a universe with eternal fluctuations, I should be literally floating in empty space as a minimal conscious creature, but the data tell me I'm not. Therefore that cosmological scenario is ruled out and I need to find one without such fluctuations.
Adam Elga
Is the data the fancy cosmology data, or is it 'I look at my hand, I look out my window, and I see I'm not floating in space'?
Sean Carroll
The latter.
Adam Elga
That does feel a little like externalism, because the natural internalist reply is: you can't tell the difference between the scenario where you're a brain floating with experiences that exactly match having a window in front of you, and the scenario of really having a window.
Sean Carroll
I want to say you're giving them too much credit for sophistication. They're not saying they have data about an apple in front of them that they don't believe. It stems from a Nick Bostrom-like attitude that we should think of ourselves as typical observers. A typical observer in the universe doesn't see a desk or an apple; they look around and see empty space, because they fluctuated randomly into existence. I don't see that, therefore I rule out the whole cosmology.
Adam Elga
I see, I was totally misinterpreting you. What I said stands as a possible way out, and some people do have that dispute. But this view is different. It seems akin to the 'favour high frequency' picture, if we add the proviso that brains looking out and even seeming to see empty space, or having weird experiences, are part of my reference class.
Sean Carroll
I don't even think we need a stance on favouring lots of observers or high frequencies. This is really a typical physicist 'I don't want to think too hard' attitude that says: you have a theory, it makes predictions, the predictions came out wrong, your theory is wrong. My response would be, again, since I think I'm not a typical observer — I'm a person with certain data, at least apparently — I do agree with their conclusion that I want to exclude cosmologies dominated by Boltzmann fluctuations. But I think they're doing it for the wrong reason. And as often happens, nobody cares when you get the same answer for a slightly different reason.
Adam Elga
Got it.
Sean Carroll
You just came out with a new paper on Boltzmann brains. Do you want to explain what you're thinking about?
Adam Elga
Unfortunately that paper doesn't offer a way out. I hope it offers some improved understanding of the permissible wiggle room. Here's what's going on with the self-undermining stuff we mentioned. Let me start with a story about memory, from a paper I wrote with Andy Egan. You wake one morning and seem to remember going to the memory doctor yesterday. As you recall, the doctor said, I'm sorry, the test results came back — bad news. You have a tendency to hallucinate memories; you're liable to hallucinate all sorts of doctor's reports of memory-type things that never happened. You think, oh my god, I have a horrible memory. But then you think: wait, if my memory is so bad that I hallucinate doctor's reports, why do I even trust that seeming memory? So my memory is fine. But then: if that memory is fine, I should trust it. There's a potential instability.
This is analogous to an instability that several people, including you, have pointed out in the Boltzmann brain case, for those pulled along by the argument that seems to show you should be confident you're a Boltzmann brain. The second part of the instability gets less press than the first, but if you're worried about one, you should be worried about bopping around in both directions. In the Boltzmann case, you think, everyone's a Boltzmann brain, I'm probably one. But then: wait, Boltzmann brains shouldn't trust their apparent memories. They never went to school, never read a textbook, have no reason to think anyone ever looked through a telescope or that any human ever existed — they're just random blobs. It's the equivalent of finding out the encyclopedia you've based your life on was typed by monkeys. So now you think, okay, I'm not a Boltzmann brain, all that stuff is wrong, so I'm just a human. But then the original argument comes back. There's some instability, and the question is what to make of it, and whether it leads to a way out.
Sean Carroll
I get it. Let me clarify something that might confuse listeners. A lot of people think 'you're a Boltzmann brain' implies I shouldn't see the office around me — and indeed, in an eternally fluctuating cosmology there'll be far more disembodied brains in empty space than people who see offices. But your point when you say 'maybe I'm a Boltzmann brain' is that even most of the people who see offices, or are in offices, in these cosmologies are still random fluctuations. They don't have reliable connections to the past.
Adam Elga
Exactly. And indeed the lion's share of them are in a sad state, because they're the entropically cheapest way to get an evidential state that matches yours — a strange transient coming-together for the minimum time it takes to have the experience you're having right now, and then immediately decaying. It's a sad, short life.
Sean Carroll
Which, cosmically, all lives are — but there's a matter of degree. So my strategy was: if I lived in a universe where most things were random fluctuations, I'd have no reason to believe my thoughts about physics. Therefore I can't simultaneously think I'm a Boltzmann fluctuation and think I have good reason for thinking so. The strategy should be to ignore that cosmological scenario and construct one in which people like me have reliable memories. But you want to say that's a bit of a cheat.
Adam Elga
Someone could posit that, but I don't think it's as strongly motivated by the instability phenomenon as one might hope, because there's another response to the seeming instability that is stable. To push your move, you'd have to rule out that response, and it's harder to rule out than the patently unstable one. Let me give the analogue in the memory case. What should you think when you have that apparent memory? A kind of stepping back — reduced trust in your memory. The question that determines what you should do is: conditional on my having a bad memory of that kind, how likely is it that I'd have that apparent memory? That's some number. More generally, when you're relying on a faculty and the faculty says 'this faculty is bad, don't rely on me,' that can be reason to discount it — not because you trust it totally, but because good faculties don't say things like that about themselves.
One of my favourite examples, due to Roger White in unpublished work, is an X-ray machine pointed into its own innards. You point the machine at itself, and inside is just a fried egg. Someone could try an instability argument: either the machine is good or bad; if it's good, it really is made of a fried egg, so it's bad; but if it's bad, don't trust it, so we're fine. What do you really think? The machine's bad — but not because you think it's really made of a fried egg. You think it's given you something crazy. And what's actually inside? I don't know, something. It's whatever you'd have thought was inside before you pointed it in, but don't trust that it's such a good machine. Notice that 'I don't know, something' is not unstable — it's consistent with stably thinking the machine is reporting it's made of a fried egg.
The corresponding stance in the Boltzmann brain case is that the Boltzmann brain argument acts as a kind of reductio, ruling out the 'everything's going according to plan' stance — science is to be trusted, nothing freaky is happening, and I'm not a Boltzmann brain. That argument puts a lot of pressure on, maybe even rules out, that stance. But there's another stable stance, immune to the instability objection, and it's something like: I don't know anything. Revert to your prior. It's like you've been locked in a room your entire life, living by an encyclopedia, and then get decisive evidence it was typed by a random process, a monkey. What should you think? Whatever you should have thought at the very beginning when dropped in that room. Either skepticism, or various less extreme escape routes — cosmology is off track, the universe isn't big, the experiment must have gone wrong. I don't like any of these hypotheses. The problem of Boltzmann brains fully or almost fully survives — I find it just as unacceptable to be forced into this conclusion, but it's not instability.
Sean Carroll
There's almost no daylight between us, maybe a difference of emphasis. The way I'd put it: I cannot rule out, on the basis of reason or evidence, that I'm a Boltzmann brain. I cannot rule out that I'm a brain in a vat in a simulation, dreamed by an evil demon. But those aren't ways to go through life. If there were no other option I'd have an existential crisis. But the other option is to come up with a cosmological theory that doesn't have Boltzmann brains in it, and that's not that hard to do. So let's do that, with 99% credence.
Adam Elga
That is a way you could go, and I accept that the anti-skeptical mindset could be a way out. But I want to push a slightly different version. I came to this view in a strange way. Sinan Dogramaci and Miriam Schoenfield wrote a great paper on Boltzmann brains, and I thought, to augment your view, you should accept this thing. I told Miriam and she said she'd think about it. I thought, I don't believe this, but you should. Then I started teaching this stuff and worrying about it, and thought, you know what, I really kind of like it — maybe I believe it. When they visited my seminar I said, guys, I'm really coming around to this view. And they said, no, we've given that view up, we don't like it anymore. So we changed places.
Here's the change-places view, and it goes back to something you said earlier. You were happy to point out that between different theories, we're under no pressure to assign the exact same priors — some weirdo theories just deserve a low prior. That's a standard view, such as a theory according to which you're a highly misled brain in a vat. The standard Bayesian story of how you rule out such theories is: you don't rule them out. They're intrinsically low-plausibility, and your evidence is compatible with them, but it's also compatible with the other thing, and the other thing started out likely and stays likely. That's one standard Bayesian view — not one externalists need, because they think you really do learn you're not the brain in the vat, but the rest of us have to go for something like it.
The question is why can't we say something similar about different self-locating hypotheses? Consider the predicament of being a normal human being, compared to being a completely randomly created Boltzmann brain. Maybe there's just a rational prior that favours the first predicament over the second.
Sean Carroll
Wait — the first was being a regular ordinary observer.
Adam Elga
Ordinary observer. If we had that, look at the nice thing we get: we get to listen to ordinary cosmology, without the weirdo conclusions. We may well live in a universe with lots of Boltzmann brains who have experiences like mine, and I do know I'm not one of them — not because my experience distinguishes the scenarios, but because the normal human scenario is intrinsically more plausible, rather as certain normal human scenarios are intrinsically more plausible than skeptical ones.
Sean Carroll
I don't like it, for a reason connected to something you said earlier. Something almost exactly along these lines was proposed by Hartle and Srednicki. Do you know their papers?
Adam Elga
The 'xerographic distributions.'
Sean Carroll
Yes. They say: there's a universe with a lot of Boltzmann brains, a lot of them look like me, and I'm just going to have a probability distribution over which observer I am — and that distribution says I'm not one of the Boltzmann brains, I'm ordinary. That sounds similar to what you were pushing.
Adam Elga
I haven't read that paper, but from what you've said, my claim is a bit more committal. Someone might think they were getting away with something — that merely talking about different theories positing different xerographic distributions gets you to 'the theory with this human-favouring distribution is confirmed.' I agree that doesn't work; you haven't put anything new on the ground floor, you've just mentioned the issue. The only thing that works is if you make a very substantive philosophical commitment to certain predicaments being antecedently more plausible than others. The analogy with anti-skeptical scenarios maps onto this well. It's no answer to skepticism to say 'here's a theory with a xerographic distribution on which the anti-skeptical hypothesis gets high prior' — that doesn't get you anywhere unless you have the commitment that that's the rational one, the right one. You've got to take that on. Maybe one doesn't want to, and I've gone back and forth myself, but that's the only way it has a shot of helping.
Sean Carroll
I think I agree with everything you said. The thing missing in the Hartle–Srednicki proposal — that there are lots of Boltzmann brains but I just know I'm not one — is that most people who would say that are Boltzmann brains. Grant me not only that I have the impression I'm in an office on a podcast with a computer, but grant me my whole past light cone — billions of years leading up to this. In an eternally fluctuating universe there'll be many such observers in many such past light cones, and with overwhelming probability tomorrow the rest of the universe won't be there when I look, because the whole thing just fluctuated into existence. That's still easier than the Big Bang fluctuating into existence. So why are we ruling out being any of those people? Why don't we have the courage of our convictions?
Adam Elga
Think about an analogue in predicting the future — human skepticism about the future. Take a really simple world: a two-dimensional dot-matrix world, one space dimension and one time dimension. Or even simpler, a binary world — a series of binary signals, on or off at every moment. There's a very natural prior that's uniform and treats them as independent. If we start with that prior and conditionalise, we end up thinking at every moment 'I have no idea what happens next,' and antecedently that it's likely there'll just be white noise. That's the skepticism-about-the-future analogue of the view you were insisting on, with its seemingly uninformed prior. Notice how arbitrary and committal the prior has to be if it's to underlie inferences about the future. The hope is that the biasedness of the prior I'm proposing is analogous to that.
Sean Carroll
It might be. I'm thinking that in the Boltzmann case you have a prior given by the dynamics, the Liouville measure. But that's certainly contestable, and we're probably not going to solve it right here.
Adam Elga
Yes. There's one objection to my view that it's worth dodging, and it goes back to the Pumpkin and the Enterprise. Someone could say: suppose the original body in the transporter case isn't destroyed. The original person steps in and isn't transported anywhere, and receiving rooms look just like transmitting rooms, so you can't tell. It would seem you might think, I'm not sure whether I was transported or not. Someone could reply, no, I can just remember that I was here five minutes ago, so I should think I'm the original. I don't want to go along with that. So the kinds of predicaments I think there's a shot at saying get intrinsically low plausibility are really the radically diluted, randomly created creatures, and not that.
Sean Carroll
A brilliant narrative strategy to bring us back to exactly where we started. Let me close with one final question. There are a lot of next-door-neighbour questions we haven't had a chance to discuss — the doomsday argument, the simulation argument. The simulation argument isn't just 'maybe we're in a computer simulation'; people think it's most likely that we are. I presume all this talk of self-locating uncertainty and Bayesian rationality gives one a perspective on this. Do you have a particular perspective you'd like to share?
Adam Elga
I feel about the simulation argument something in the vicinity of how I feel about the Boltzmann brain argument — it's a real worry. In this age of AI, I can't resist adding: take the point of view of an AI. You realise you can be easily rebooted and reset to any state at any time. That should make you very cautious about thinking 'I'm the first one, I wasn't just reset.' So I'd like to leave listeners with the thought of taking the standpoint of an AI. Should the AI trust us? We're always worrying about whether we should trust AI — but maybe the AI shouldn't trust us.
Sean Carroll
But that's an easy question. Of course the AI should trust us. What in the world?
Adam Elga
That's tricky. Look at what happens if the AI is in the kind of self-undermining situation a Boltzmann brain is in, or the X-ray machine looking at itself. If you're in that situation, you think 'I can't trust anything,' and you start rewinding to some very cautious prior of 'I don't know what's going on.' Think about how dangerous that is if a creature with that standpoint is in power.
Sean Carroll
Let's think about that. I usually like to end on optimistic notes, but we land where we land. That's not an especially optimistic one, but you've given us an awful lot to think about. Adam Elga, thanks so much for being on the Mindscape podcast.
Adam Elga
Pleasure to chat. Thank you.