AMA | July 2026

0:00:00.2 Sean Carroll: Hello everyone. Welcome to the July 2026 Ask Me Anything edition of the Mindscape Podcast. I'm your host Sean Carroll. I'd kind of planned out an intro here because I just wrote a thread on Bluesky where I talk about Boltzmann brains. I went on a little Boltzmann brain rant and I thought that would be a perfect lead-in to the AMA. But then I realized there we have an AMA question about exactly this topic, so it just makes more sense to do it in the body of the podcast, which leaves me nothing to say for the intro. And you know what? That's okay. We don't need anything special for the intro. You're here for the AMA, not for the intro. I will do the usual thing of thanking Patreon supporters of Mindscape, who are the people who make these AMAs possible. Patreon supporters of Mindscape, well known worldwide to be the most attractive, intelligent and charming people than anyone has ever met in their lives. And it's kind of amazing that there's such a coincidence or correlation between being a Mindscape supporter and those other good qualities. No real idea why that's true, but it turns out to be true empirically. And amazingly, you could be a Patreon supporter of Mindscape. It's not that hard. No initiation, hazing rituals or anything like that. Just go to patreon.com/seanmcarroll and sign up. Nominal fee gets you membership in this elite community as well as ad-free versions of the podcast and the right to ask AMA questions. So your name could appear on a future Mindscape episode. It's just all part of the bargain. And with that, let's go.

0:01:54.9 SC: Eric Olav Chen asks, "Could you give an overview of the current state of debate on Boltzmann brains? I'm specifically curious about, number one, how strong the current evidence is from the Swampland program that long-lived de Sitter space is not possible at all in quantum gravity. And number two, how widely accepted is the argument you put forward with Boddy and Pollack that eternal de Sitter space does not support the kinds of fluctuations that give rise to Boltzmann brains at all?" Right. So as I mentioned in the intro, Boltzmann brains have been on my mind for a while. So I've been thinking about them and I did a little thread on Bluesky. It really belongs like a blog post, but right now my blog is kind of down. It's not 100% down. The website was down for a day or two. The blog is just messed up. The theme is messed up. I need to get around to do that, but as I will complain about later in the podcast, I've been too busy to do things like that. So the reason why I was thinking about Boltzmann brains is because there's a question, how big is this problem? Well, actually, let me start with my own perspective on the problem, and then I'll back up and explain what the problem is. But my perspective on it is the prospect of Boltzmann brains dominating the universe is an absolute killer for models that predict that. And among the models that plausibly predict that is Lambda CDM, the best, most popular default cosmological model among modern cosmological thinkers. And so this is a potential disaster. We're saying that everyone's favorite cosmological model is potentially incoherent, potentially inconsistent internally. It can't possibly be the right theory of the world. Now, of course, you can say, "Well, okay, we'll tweak it to make it more compatible." Great, tell me exactly how you're going to do that. So you would think that given this situation where you have a very popular theory and it's potentially self-undermining and completely incoherent, that a huge amount of work would be done in the theoretical cosmology and physics community trying to come to terms with this problem. And the fact is that there isn't. And I'll explain a little bit about what exactly that means, that there isn't any work being done. But I really do think that there is a certain thing that I would like to label Boltzmann brain blindness. I wonder if the cuteness of the name, which is kind of fun, Boltzmann brains, and the wackiness of the scenario, that random fluctuations make a conscious observer, and like all of that kind of comes together to make working scientists feel a little uncomfortable worrying about this problem. It seems a little bit less than totally serious. The name is silly. The prospect is very speculative. But still, if you have a problem that gets in the way of your best possible model, then you should address that problem, I think. And so I think that we're sort of in denial about this and we need to do better.

0:04:51.5 SC: Okay, so let me back up and explain where we are here. The name Boltzmann brain comes about not because Boltzmann predicted the idea, but because it's based on things that he said back in the 1890s when he was trying to explain why entropy increases over time. He wrote a couple of papers about where the initial conditions come from in some sense. These days, what we would just say, 'cause remember, in the 1890s, we didn't have the Big Bang. We didn't know about expanding spacetime. All we knew about was our galaxy. We didn't know about other galaxies. So there's a lot of cosmology that Boltzmann didn't know about. Today we would just say the past hypothesis. There was an early condition near or just after the Big Bang where the entropy of the universe was extremely low in the right way to sort of make the subsequent evolution perfectly respectable and reasonable, thermodynamically speaking. And that does all the work. Once you have that, you have entropy increasing, the second law of thermodynamics, the arrow of time, et cetera. We don't know why our early universe had that low entropy, but that's a good question and that's a separate question, okay? So you can at least understand what the question is.

0:06:02.7 SC: Boltzmann didn't know about all of this. And so one of the ideas he put forward, which sometimes he attributed to his assistant, Dr. Schuetz, whose info is otherwise lost to history. Boltzmann said, "Look, maybe the universe is eternally old. Maybe it is mostly in thermal equilibrium, and maybe it fluctuates around thermal equilibrium so that there are random fluctuations. I'm Boltzmann. I know that the second law is not absolute. There can be fluctuations. If you wait long enough, there will be a fluctuation so monstrously big that it will basically go from thermal equilibrium to our galaxy." Galaxy is the word he used because he didn't know about the rest of the universe or the Big Bang or anything like that. So maybe we just live in the aftermath of one of these fluctuations. That's the idea he put forward. He didn't dive into it in any detail, and he left it at that and never returned to it as far as I know. So it was later that people pointed out that this can't be right. Okay, so this is the Boltzmann brain problem. This is Boltzmann's eternal fluctuation scenario that he put forward as a viable alternative. It was only later that people pointed out the problem. And the people who pointed out the problem include Arthur Eddington in the 1930s talking about the arrow of time, Richard Feynman in the 1960s. I swear to God, if you look up in the Feynman Lectures on Physics or the Feynman Lectures on Gravitation, and I think but I'm not 100% sure about this, in The Character of Physical Law, he talks about this problem, that if you just have random fluctuations, you would expect entropy to increase both toward the past and the future. That's the problem.

0:07:46.3 SC: And so the problem is, if you imagine that everything that you currently think is true about the universe right now at a macroscopic level is true. And so let's be careful. Let's just for definiteness restrict it to your immediately observable universe, which might just be the room you're in, or it might just be the outside if you're walking around outside or something like that. But let's imagine that your sense data and your interpretation of them are accurate. Okay? Then we know that in conventional thermodynamics, you predict that entropy increases toward the future in a very sensible way. And in conventional thermodynamics you say that entropy was lower in the past, but you can't actually predict that entropy was lower in the past just on the basis of your current information, because all of the arguments that you use to say that entropy will be higher in the future also work going to the past just with T goes to minus T, 'cause the underlying laws of physics are reversible. So we fix that by making an assumption that entropy started very very low near the Big Bang, and it all fits together. But so Eddington and Feynman are pointing out that if you don't make that assumption, entropy was higher in the past. And what that means is that all of your... They didn't go into all the details here because they didn't quite have the detailed technology that we have now to understand what it means to say that entropy is increasing and what that means for memories and records and things like that. But if you think that our entropy of our local region was higher in the past, what that means is that our current situation looks like just like what we think our future looks like but run backward in time. So it is a thermodynamically unrespectable... Unrespectable? Disreputable version of history where you start from thermal equilibrium and randomly fluctuate into wherever you are today.

0:09:45.9 SC: That is the overwhelmingly likely way to get to where you are today, whatever you construe where you are today to mean. So I know a very very popular attempt out of this argument, a way to wriggle out, is to say, "Well, I want to add this or that condition to what it means to be where I am today." Fine, it doesn't matter. Add whatever conditions you want. In this scenario, where the universe spends most of its time in thermal equilibrium, it will always be true that entropy was higher in the past no matter what you do, no matter how big you want the region to be, how long you want it to last. None of those things will matter at all. So Feynman and Eddington both pointed this out, and they sort of gestured toward why it would be bad. Eddington, in particular, came up with what we would now call the Boltzmann brain version of the problem. He said, "Look, what if I wanted to just wait around for a mathematical physicist to appear in the universe?" Okay. I don't need to wait for the whole universe or the whole galaxy to randomly fluctuate into existence. I just need to wait for that one particular physicist to fluctuate into existence. And there is math here that tells you the relative likelihood of these different things happening. And what the math tells you is whatever you want to wait around for it to happen, it will be the minimal deviation from equilibrium that gets you there, which will happen the most often. So what Eddington says is that this single mathematical physicist will be surrounded by nothing, just popping into existence in the universe.

0:11:22.0 SC: Now, the modern version of this was labeled by Andy Albrecht and Lorenzo Sorbo in around 2004, 2006, I forget exactly when. They're the one who finally labeled it the Boltzmann brain problem, 'cause they said, "Well, who needs the rest of the physicist? We can just wait for a brain, a single, the minimal possible thing that you would imagine counts as an observer." Those would be most of the observers in this eternal, randomly fluctuating universe. Okay. So they might be disembodied brains just floating out there, aka Boltzmann brains. Now, one thing that I need to emphasize is that as much fun as that thought experiment is, it's not the problem. The problem is not most observers would be Boltzmann brains, and I'm not a Boltzmann brain, therefore the theory is ruled out. Okay. That is not the problem.

0:12:13.1 SC: You know you're not a Boltzmann brain. There was never any chance you were. You never lived in any sense of thought about the universe or epistemic state which said, "I don't know, maybe I'm a Boltzmann brain. Who knows?" Okay, you know something about who you are right now. The problem is, even given exactly who you are right now and what you know about what you are right now, it is still true that you came from a higher entropy state with overwhelmingly large probability in this scenario. So the problem is not a Boltzmann brain. The problem is a Boltzmann you. The problem is fluctuations into your current state, including all the state of what is going on in your brain. And if it just randomly fluctuated, then that includes all of the knowledge that you think you have about what happened in the past, even your knowledge of arithmetic and the laws of physics and all that stuff. It just randomly fluctuated into your brain, and therefore you have no right to trust it. And therefore you can't actually accept that as a theory of nature. It is cognitively unstable. There's no situation in which you can both believe it to be true and have good reasons to believe it to be true. It's not that it's ruled out by data. It's that it's ruled out a priori by logic, okay? It's not an acceptable way to think about the universe.

0:13:23.1 SC: Anyway, who cares. Like so Boltzmann was wrong. He put out other scenarios too. He wasn't wedded to this particular one. So the Boltzmann scenario just says the universe is eternal and has random fluctuations. That seems to not be compatible with the data. But everything changed in 1998 when we discovered the acceleration of the universe. And that was when suddenly we realized that the future, this is the beginning of the Lambda-CDM model, Lambda standing for the cosmological constant, which is the simplest way of accounting for the acceleration of the universe, and CDM standing for cold dark matter. If the dark energy, if the thing making the universe accelerate really is the cosmological constant, so there's different things it could be, different dynamical dark energy candidates, as you know from two weeks ago's solo episode. But if it is the cosmological constant, which is the simplest possibility, then we know what our future holds. Our future will just be an empty universe with nothing in it but cosmological constant.

0:14:33.1 SC: In the 1970s, Gibbons and Hawking showed that empty universes, this is called de Sitter space. An empty universe with nothing but a positive cosmological constant is called de Sitter space. Such a universe has a horizon and an entropy and a temperature. Okay? So by having a temperature, that means if you have a detector in de Sitter space, which you don't, because de Sitter space is empty, but if you did, it would detect occasional photons and things like that. It would detect random fluctuations. So in an influential paper, I think in 2002, by Dyson, Kleban, and Susskind, they point out, former Mindscape guest Lenny Susskind, they point out that what this means is that if you wait forever in a positive cosmological constant de Sitter space universe, you will get random fluctuations into everything. Okay? And it was Albrecht and Sorbo who then followed up exactly on that paper and talked about what this meant for thermodynamics of individual observers.

0:15:33.7 SC: So the point is that in 1895, Boltzmann had a random, wild speculation like, "Maybe the universe is eternal and maybe it fluctuates forever." In the 20th century, people like Feynman and Eddington and so forth said, "Nope, this doesn't work. There's good reasons why that can't possibly be the right answer." But no one cared because no one thought it was the right answer. Starting in 1998, it basically becomes the favorite answer. You can have a universe that lasts forever in the future with eternal fluctuations. The fluctuations might be very, very small, very rare, but you have forever to wait. And so eventually you will get fluctuations into individual brains, people like you and me, our whole galaxy, the whole bit. So you're back in this situation that can't possibly work. Okay, that's the Boltzmann brain problem. We call it the Boltzmann brain problem, even though, like I said, it's really about Boltzmann yous that are the real problem but that's okay. Everyone calls it the Boltzmann brain problem, that's where we are. And you would think, like I said, that the theorists would be absolutely up in arms about this. Our prospective best theory doesn't work. Isn't that bad? So there's a lot of different possible ways out of this. One way out, as Eric points out, is something like the Swampland program, but that's sort of a particular subset of the particular way out, which is just to say the cosmological constant doesn't last forever. Okay, that's an obvious way out. The cosmological constant could not last forever for basically two ways, maybe three ways but two covers the main possibilities. One is that the dark energy is dynamical, as we were talking about a couple weeks ago. It's slowly changing with time. It's quintessence or something like that, and it will eventually fade away. 100% allowed. That possibility is on the table. The other possibility is that it changes sort of dramatically, like at a first-order phase transition, where you make a bubble of true vacuum and that sweeps outward at the speed of light and takes over the universe. That second possibility is really, really difficult to pull off because it's almost too late. The rate of creating new vacuum states needs to be high enough that this transition can complete all throughout the universe. Otherwise you still get an eternally expanding de Sitter space in most of the universe. And the time scale for these transitions needs to be comparable to the current age of the universe. So basically, once you're in that phase where you're dominated by dark energy, it's almost too late to get rid of the dark energy entirely by a first-order phase transition. There's still the second-order possibility, which is the dynamical dark energy, the slowly rolling thing. So that's absolutely on the table. That is a possibility.

0:18:22.4 SC: So the rolling scalar field thing, which would be compatible with the Swampland, the Swampland we talked about with Cumrun Vafa here on the podcast. It's an idea that there are plenty of low-energy effective field theories of gravity and particle physics that are perfectly good by their own lights as effective field theories but have no way to be matched onto complete ultraviolet theories at high energies like string theory. String theory famously has a landscape of possible low-energy theories you could end up with. The Swampland are those low-energy theories that you can't end up with in string theory. And we don't know this for sure by any means, but there's an absolute feeling out there that perhaps theories with a positive cosmological constant are all in the Swampland, that is to say, not reachable from string theory as the high-energy completion. So you can still get an accelerating universe, it just needs to fade away, so dynamical dark energy or whatever, so that's 100% plausible. But there's no evidence for it, or there's very little evidence for it. I mean, we talked about there's a little bit of evidence from the Dark Energy Spectroscopic Instrument and other places that maybe the dark energy is changing. But I would call that still quite tentative and I would just counsel patience about where the observations come in about that. The other way out of the dominance of random fluctuations is this paper that I wrote with Kim Boddy and Jason Pollack, which raises a conceptual point. We said that the idea of a thermal state in quantum mechanics is fundamentally different than the idea of a thermal state in classical mechanics. In classical mechanics, when you talk about a box of gas with a temperature, you're talking about it at a higher emergent level. You know that really deep down there's a bunch of particles moving around with different velocities but you don't know what they are. So you're talking about these reduced information descriptions that just have things like temperature and pressure in them.

0:20:33.8 SC: So the higher-level description of the thermal equilibrium state by the laws of thermodynamics, if you're in thermal equilibrium and you're isolated from the rest of the world, you stay there literally forever. It's just a static state, nothing ever happens. But we know that in the real world where there are fluctuations, because the world is really made of particles bouncing around, that thermodynamic description is incomplete and there can really be fluctuations. Quantum mechanics is different. Quantum mechanically, a thermal state can be the fundamental description of a system. In fact, that's what you would expect it to be in precisely the situation we're talking about here, where you have an expanding universe with an accelerating universe with dark energy given by the cosmological constant and we call it de Sitter space, and there's a horizon, et cetera, et cetera. So phenomenologically it's very similar. If you have a quantum thermal state, what you mean operationally is that if you put a thermometer in there, you'll detect a temperature. Okay? But when you don't put a thermometer in there, maybe unsurprisingly, quantum mechanics and classical mechanics are different. In classical mechanics, those fluctuations are intrinsic and real. In quantum mechanics, if you just have a stationary thermal state, then nothing ever happens, really. There's no real fluctuations. The fact that if you put a detector in there you would see fluctuations is not incompatible with the idea that there are no fluctuations when you're not looking at it, because that's how quantum mechanics works at a fundamental level.

0:22:11.5 SC: So there is a footnote here. This only works if Hilbert space is infinite-dimensional. The thing I talked about, I guess, in the last AMA, the new paper I have with Nadia Denchenko and Sakshi Dhulani, where we talk about a finite-dimensional Hilbert space. You can be close to thermal equilibrium for a very long time, but you will eventually move away from it because of the recurrence theorem. In an infinite-dimensional Hilbert space, you can truly relax to a stationary state and stay there forever. There is absolutely no reason to recur. The recurrence time that Poincaré calculated a long time ago goes inversely with the size of the system. So if the system becomes infinitely big, infinitely big Hilbert space, I'm sorry, the recurrence time goes as the size of the system or even as e to the size of the system. So if the system becomes infinitely big, which in this case is the dimensionality of Hilbert space, the recurrence time goes to infinity, which means you don't recur.

0:23:07.0 SC: So that's a simple conceptual way out. Maybe you do have a positive cosmological constant. Maybe Hilbert space is infinite-dimensional. Maybe you don't have Boltzmann fluctuations just because you settle in to a perfectly quiescent quantum thermal state and there are no real fluctuations. Now, when we wrote that paper, we knew that people would have different opinions about it because our version of what happens relies on conceptual questions in the foundations of quantum mechanics, "What happens in the quantum state when you're not observing it?" Okay, this is not a question to which physics has a consensus answer. And so we knew people would have different opinions about it and they would presumably put forward their opinions and argue about whether or not Boltzmann brains really do fluctuate into existence in empty space but no. And this is what got me thinking about it. I'm not sure if it was Eric's question, but a whole bunch of things had me thinking about Boltzmann brains recently. I've been looking around and there's just not a lot of research being done on whether or not Boltzmann brains fluctuate into existence in a thermal vacuum state. I am not sure why that's true. So I don't know. So the answer to Eric's question is, I don't think it's widely accepted. I don't think it's widely disagreed with either. There is a scenario or a syndrome in psychology, and I'm gonna forget what it's called, but it's something like false consensus, where everyone thinks that there's a consensus but no one talks to each other, so they don't realize that there's really not a consensus at all. I suspect that's what it is. I suspect this Boltzmann brain problem strikes working physicists as a little bit icky and untoward because it involves speculations about the far, far future and foundations of quantum mechanics and weird scenarios about brains and things like that, the kind of thing that theoretical physicists don't like talking about in general. So I think it's a kind of a sticking point that I think that people need to face up to a little bit here. Boltzmann brain blindness. Why aren't we more worried about the Boltzmann brain problem than we seem like we are? And I would love it if everyone just read my paper with Kim Boddy and Jason Pollack and said, "Oh, yes, you're right." That would be great but that's not the point. The point is I want them to think about the problem and put forward what they think the answer is, 'cause I think it's kind of a crucially important problem to modern cosmology.

0:25:42.3 SC: Okay. Sorry for the extended disquisition there but it's been on my mind. So Michael Astor says, "I'm writing a science fiction novel, and while I don't believe good science fiction requires good science, I do like to stay within the bounds of plausibility. That said, a lot of concepts are over my head, so where it concerns technical details, I'm trying to keep it simple and vague. A central technology that enables my story to happen is a machine or process that directly converts raw matter into energy or energy into matter, not necessarily one-to-one efficiency 'cause I don't want it to be too miraculous. Do you think such a machine or process would be practical both for operations on a planet as well as to propel a spaceship to relativistic speeds?" Well, I'm not gonna give an exact answer to the question but I will make an important point that is relevant to the question, which is that there's no such thing as converting matter into energy because matter and energy are not two different equivalent versions of something. Energy is a quality or a property that matter has. It's not a thing that matter could be instead of being matter. A ball rolling down a hill has a potential energy and a kinetic energy. Photons moving through space have energy depending on their frequencies, all of that stuff. Energy is a measurable quantity that a physical system can have. I hesitate a little bit to say matter can have it because maybe you want to get into intricate arguments about quantum mechanics and what counts as matter versus radiation or whatever. Who cares? That's not the point. The point is that physical systems are described as particles or fields or quantum wave functions or whatever, and energy is not a separate thing than them, it is a property that they have. So you can never convert raw matter into energy. That is literally a meaningless statement.

0:27:37.8 SC: You can convert different kinds of matter doing certain things into other kinds of matter doing certain things. When you burn a piece of wood, you are releasing some of the energy that was in the wood already into heat and light and things like that. So you're just changing the energy from one form or another. You're not turning matter into energy. So with that footnote there, otherwise, there's a lot of energy piled up in a bunch of matter. We know that because if we take matter and knock it into antimatter, you get a big explosion. Now, the explosion is not into energy, it's into other particles that have energy. But I think that's what you want to propel a spaceship. So in principle, the important question here is, can you imagine processes that do something to materials, matter or whatever, that help you propel a spaceship? Yes. I mean, that is always what happens when you propel spaceships.

0:28:43.3 SC: Ben Lloyd says, "Now that it's been around a year, are you satisfied or do you regret that you debated Eric Weinstein? Looking at the comments on his latest Joe Rogan episode, I think it's safe to say the public perception of him has changed in a very negative way, and I think that debate had a lot to do with it. But I also know you said the debate was unproductive." Well, the debate was unproductive in terms of learning anything about physics or the way that physics is done or anything like that. That's entirely unsurprising. I would say that the debate on the Piers Morgan show went more or less as I would have expected. It was even more tawdry and full of personal attacks on Eric's side. I wasn't quite expecting that, but who cares? I'm a big boy. I can take that. I wasn't expecting Eric to like ask questions and try to learn things and try to get better. That was never something that I anticipated. I just wanted to get across to people the impression that this particular person did not represent an actual, legitimate, respectable challenge to physics as it's traditionally done, whether it's string theory or anything else. And I knew that in the process of doing that, I would get a lot of abuse and it would not be very productive or interesting or worthwhile otherwise, but maybe that particular lesson was conveyed to some people and not to others. That's the best I can hope for. So I think I did it knowing what I was getting into, and I think it was the right thing to do. I'm not gonna make it my career. I'm not gonna keep talking about it. I've had plenty of requests to keep talking about it more or whatever, but there's much more fun things to do for me personally.

0:30:20.9 SC: One more thing worth remarking on, I guess, in terms of me personally and why I did that was that Eric is not alone. We are in the middle of a really historically terrible time for science in the United States and maybe worldwide because the government is terrible in all sorts of reasons and all sorts of ways, and it's cutting scientific support and it's rediverting resources to its own quirky priorities, and it's just a disaster for the United States and for the world. And in part, that's because of the individual weirdness of the Trump administration, but it's in some part enabled by a feeling out there in the world that scientists kind of deserve it or aren't that deserving of the system of grants and support that we currently have. They're spending their time working on these ridiculous, unfalsifiable ideas or they're completely woke or whatever it is. And that is a real problem. Like some guy going on podcasts and saying that he has a better idea than string theory, who cares? I'm very happy to ignore that. But science being dismantled as part of a broader attack on expertise and institutions and academia and all that stuff is really, really, really harmful. And that is not all due to Eric, but he is part of that program indisputably, and I wanted to push back against that a little bit.

0:31:59.1 SC: A little while ago, Tim Maudlin, who is a physisist on BlueSky, pointed to a lecture that you can find on YouTube by Peter Thiel. It was the Scruton Lectures. Roger Scruton is a famous conservative thinker. So Peter Thiel you know, one of the co-founders, I guess, of Palantir, of PayPal before that, someone with a whole bunch of kooky ideas about the Antichrist coming and how Western civilization should be reorganized and things like that. So he has an agenda, let's put it that way. And he was also formerly, maybe formerly, maybe currently, who knows? This is all very mysterious, Eric Weinstein's employer. Eric worked or does work at Thiel Capital. And so Peter Thiel gave this talk, and he's very explicit about it. These people are not subtle or secretive. They'll just come out and tell you what they think. And he says the following thing, which is kind of astonishing.

0:32:55.6 SC: He says, "We have our values that we would like to have the world adopt. One of the obstacles to having the world adopt our values are universities and academia because they're full of woke liberals poisoning the minds of the youngsters," and so on and so on. But then he very explicitly says, "So how do you strategize this? How do you undermine the credibility of academics and universities? Well, you could try to attack them at their most vulnerable points, but alternatively you could try to attack them," says Peter Thiel, "at their strongest points, at their most respectable kind of aspects because if you can undermine that, then you undermine the whole shebang. You undermine the whole idea of universities and professors and institutions." And he says, "So what is the most respectable field within academia? It's physics. And what is the highest status subfield within physics?" And again, this is Peter Thiel saying these things. I'm not making them up or insinuating them or interpolating them. He says, "It's string theory." And so if you can undermine the idea in the eyes of the general public that people doing string theory, supposedly the smartest people we have and the best physicists, are somehow illegitimate, are somehow captured by institutional blah, blah, blah, then you've gone a long way towards undermining universities as a whole, and that project will help us get our values supported around the world rather than theirs.

0:34:36.9 SC: Now, I'm not saying that there is some shadowy conspiracy funded by Peter Thiel. You don't need that. You don't need a shadowy conspiracy. You just have people who talk to each other. Like Peter Thiel and Eric Weinstein and a whole bunch of other people, like-minded people get together and they complain about universities and academia, and they figure out that if they could undermine the sense of trust and general positive feelings towards people doing physics, then that's a big step towards undermining universities more generally, and that's a big step in our program. So it doesn't need to be shadowy. It's right out there in the open, just a bunch of people with these ideas and a large amount of money to support them. And they're doing it not because they're paid to do it, because that's what they believe. And I do think that pushing against that is important. I think that I absolutely get my fellow physicists who would rather just ignore all of this stuff going on in the background and work on their physics. That's extremely tempting. And frankly, some of them I don't want out there fighting the fight in public 'cause they're not very good at it. But some fraction of us, just like some fraction of people have to do public outreach and education, some fraction have to fight against the forces who are trying to undermine the entire university academic project and just like Eric is a small part of the anti-intellectual project here, I want to be my own little small part of the pro-intellectual project.

0:36:09.7 SC: Keith says, "With the recent systematic erosion and stigmatization of diversity, equity, and inclusion initiatives in academia, I suddenly felt like the notion of the big picture illustrated the shortsightedness of condemning programs that encourage diverse backgrounds. I think DEI is compatible with merit-based achievements. It's all such a mess how we got here. And though, like many things, I would like to hear your thoughts on the topic, how it got here, how to make it better. I don't really know what or how to ask. It's sad, frustrating, and has affected many people negatively." Yeah, so I don't really know how to answer 'cause the question is not that precise, but I can give some thoughts, which is maybe what you're looking for here. Diversity, equity and inclusion are three words that I'm very much in favor of, either individually or combined. And equity and inclusion we can put to the side. I think those are good things. It's really diversity that rubs people the wrong way. And I think that there's two things going on here that are worth keeping in mind. One is purely at a value-free, how do you solve problems kind of level. Is it useful to have more diversity in either your team or your set of possible strategies for solving problems or is it better to have more or less focus on the most effective kinds of people and kinds of strategies? And I think that there's literally been all sorts of studies done that actually address this question, and they always come up, as far as I can tell, with more or less the same answer, which is that diversity is good. If you have anything that is more complicated than a sort of well-known, perfectly understood problem in front of you, if you have a situation where things are fluid or things are not very well defined or you're coming up with a new problem that you've never faced before, diversity is helpful in solving those problems. And you might say, "Well, yes, but that's just intellectual diversity, that's not like personal diversity." No, no, no. Actually, personal diversity also really helpful. Turns out that people coming from different backgrounds, having different experiences and things like that, super helpful to coming up with different possible solutions to problems. It's something I've said many times in a different way here on Mindscape, that different individual physicists who are human beings, when they're faced with unknown questions like, "What is the dark energy?" or "What is the right solution to the foundations of quantum mechanics and the measurement problem?", by definition we don't know the answer to this. There's different possible answers on the table. And remarkably, despite the fact that we don't know the answer, different people will be very very devoted to one answer or another. And a lot of that comes from their predispositions, their inclinations, their intuitions about how nature works, how science works, what counts as simple, what counts as complicated. Some people will say that many-worlds quantum mechanics is the simplest possible version of quantum mechanics. Some people will say it's the most extravagant version. That's a feature, not a bug. If we knew what the answer was and were just trying to calculate something within that framework, then you don't need diversity, you just need to be good at calculating things. But when you're approaching a deep problem where you don't even know the right way to ask the question, then it is literally true that people who have undergone different experiences in their lives will sometimes have different suggested answers or strategies to this problem and that is good. That is helpful. And I think that's just the sort of narrow physics version of it, but there's a broader picture here that academia or intellectual life, which is all about probing deep questions, asking difficult questions and thinking carefully about them, is just unambiguously helped by diversity in all of its forms. Okay. The other point to make is a much more down-to-earth, practical, moral question. Like in a society where there has been discrimination against certain groups, what is the right way to combat that discrimination? And I absolutely get the attitude that would say, "Look, the right way to combat discrimination is to look at every possible candidate for every possible job opening or acceptance into university or whatever, learn about their individual experiences." After all, not all Black people experienced the same situation growing up. Some of them might have actually come from otherwise very privileged backgrounds. Some of them might have really struggled. Some non-black people might have really struggled for example and so we should just treat every individual as an individual.

0:41:05.7 SC: Well, that's adorable, that kind of attitude, but it's also completely unfeasible. John Skrentny, who we had on the podcast a while back, a sociologist at UC San Diego, we talked about the scientific enterprise in the modern world, but some of his early work was on affirmative action. The idea here in the United States that we would just increase the number of underrepresented minorities in universities and in other kinds of jobs to help combat the pre-existing legacy of discrimination. And he made the point in that work. It's a lot of the motivation for affirmative action was not just "let's make the world a more just and fair place," but it's easy, it's simple. It's bureaucratically undemanding. Just say, "Look, I don't know, I don't have the time to figure out who the people who are really discriminated against are. So let's just take the groups that were subject to systemic discrimination over the years and give them a boost in terms of letting them in to whatever the positions are." And the amazing thing is that even though from that perspective, it was kind of like a cheap strategy for dealing with this problem, it worked. It worked in that... There's a great book by Derek Bok and oops, I forget the other guy's name. Derek Bok used to be the president of Harvard. And he and the president of Princeton, so two elite institutions, they did this serious study of like, has it worked? Has affirmative action actually succeeded both in keeping up standards at the university but also in infusing the population with a set of people now who have elite college educations who might not have had those before, and has that affected the population in a positive way? And the answers are yes, yes, and yes. It kind of works remarkably well, despite the fact that it's kind of a silly, cheap mechanism for getting things done. It's by no means perfect, but it might be the low-resource way of making things better. So I think that in the real world, the fight against DEI is just sort of a culture war kind of thing. It's not based on science or knowledge or research. It's just based on feelings and sometimes those feelings are bad, whether it's explicit racism, which it is in some cases, or other times just these feelings of "The world is not treating me with the respect that I deserve because all of these undeserving people are getting what really belongs to me." And I think that's also a bad attitude to have. And so there's a lot of bad-faith actors fighting against DEI, and I think that those of us who believe in it should just stand up for it very explicitly.

0:44:02.3 SC: Okay, I'm gonna group two questions together. One is by Thomas Anderson, who says, "Where is Complexity and Emergence by Sean M. Carroll? Will my kids be able to get it for me for Christmas?" And Scott Farris says, "I love the first two books in the Biggest Ideas in the Universe series, when is Part 3, Complexity and Emergence, going to be published? I saw somewhere online that the publishing date was earlier this month, but cannot find the book. Will the audiobook be published at the same time as the physical book?" So this is entirely my fault, not the publisher's fault or anything like that. I've just been overly busy, so I was late with the manuscript. The manuscript is now turned in. It is in the hands of the publisher. Will it be out for Christmas? I honestly don't know. That's a choice for the publisher to make. The Biggest Ideas in the Universe books as you know, if you've looked at the first two, they're aiming at a very kind of specialized audience, a non-physicist audience, one that is not a textbook or anything like that, but the subset of the non-physics enthusiast audience that is happy with equations. That's the subset I'm aiming at. And it's not the biggest subset in the world. So there's a lot of you out there, but there's a whole bunch of people who are not in that group. And therefore, there's all sorts of calculations that go into the mind of a publisher, okay? So many, many books are purchased for Christmas presents. Like I don't know, a third, half of the books that are bought every year are purchased for Christmas. So if you think your book is gonna do really, really well, then you publish it in September or October because that sets it up for being purchased for Christmas presents.

0:45:43.3 SC: And my last couple books were, or my last couple before the Biggest Ideas books anyway, I forget when the Biggest Ideas books were published in terms of what time of the year. But The Big Picture and Something Deeply Hidden were definitely published for the Christmas rush. Now, it's probably... I'm gonna guess that it's already July and there's not enough time to get this one out for the Christmas rush. But the other thing is you could publish things in like January or February where the Christmas rush is over and you have less competition from other big-selling authors. So they might just be going for that. That's the best I can say. I will say that I like the book I handed in. It's a little bit too big 'cause there were too many good things to say. I'm sure I'm gonna get a lot of groans and moans from people who are experts in complexity and emergence because I had to squeeze a lot of material into a very short period, a very short amount of words, even though I went too long, and I needed to make choices, and I need to like propose organizational schemes for all these difficult ideas that not everyone will agree with. So that's okay. I think for the target audience, hopefully the book will be very enjoyable.

0:46:53.8 SC: Qubit says, "In the context of Many-Worlds, when talking about the quantum state of the whole universe, you sometimes have the footnote that it might as well be a mixed state. Could you give us more details on that? Naively, I would think that the concept of a mixed state breaks down when it comes to the whole universe. To me, a mixed state is just a probabilistic description that people in individual branches can use, but one that isn't meaningful on a global scale where you keep track of all the microscopic information." So this is a little bit technical, but I think it's worth getting into a little bit. You often hear me talk about the quantum state of a system or the universe as a vector in Hilbert space. Hilbert space is the space of all possible quantum states. It's a vector space, so the state is a vector. And then there's a footnote as Qubit points out, that says, "Well, okay, there's another way of talking about quantum states, which are as mixed states." And these are defined not as vectors in Hilbert space but as density operators. That's the technical term. You don't need to know what that means. What you need to know is the following, that there's an analogy but the analogy is not perfect, between the classical mechanics idea of a pure microscopic state of the system, that would be I tell you the position and momentum of every part of it, versus some sort of distribution function for the probabilities of being in different states of the system, which we call a mixed state. So if you know that the box of gas is in thermal equilibrium with a certain temperature and density and things like that, then there's a probability distribution for the individual microstates, the Maxwell-Boltzmann distribution or something like that. And as we were just discussing a little bit ago, that's just an expression of your ignorance. You think that there is a true microstate, but you don't know it, so you describe the system using this probability distribution.

0:48:44.3 SC: Now, in quantum mechanics, that kind of clean distinction breaks down a little bit. And it has nothing to do with measurements or anything like that. It just has to do with the formal structure of quantum mechanics. You might think, it would be very natural to think that you do exactly the same thing in quantum mechanics you do in classical mechanics. That is to say, rather than just telling me the pure, crisp, exact microstate of the theory, you give me a probability distribution over all the microstates. That turns out to not actually be what you need. In fact, it's not less than what you need, it's more than what you need, so people came up with a more clever way of encoding only what you need. And what do I mean by what you need? What I mean is, and let's forget about the foundations of quantum mechanics and Many-Worlds or hidden variables or whatever. Let's just think in ordinary textbook Copenhagen quantum mechanics terms, okay? I have a system. I describe it using some kind of formal mathematical structure. I use that to make predictions for the outcomes of observations. And what matters to me is that, the predictions for the outcomes of every possible observation that I might want to do on the system. And the thing about quantum mechanics is, because all you can do are predict probabilities, when you take two different vectors in Hilbert space and say, "Well, I'm gonna have a probability distribution that maybe the state is in vector A, maybe it's in vector B," they sort of smush together when you make the predictions for experimental outcomes. I can have two different orientations of a spin that have some non-zero probability that I will measure the spin to be up. And then if I'm in a combination of both of them, I still get some non-zero probability to measure the spin to be up. It's an average of the two there. So to actually have an explicit probability distribution over the microstates is more than you need to predict experimental outcomes. This idea of a mixed state or a density matrix or a density operator is precisely the information you need in a statistical mixture to do all of the predictions for all of the experiments you might want to do. So in that sense, it is the correct generalization of the classical distribution function or probability distribution.

0:51:09.4 SC: But then now something deep about quantum mechanics does come in, entanglement. So if I have two systems, A and B, which are entangled with each other, then the whole combined system, the AB system, maybe it has a vector, a quantum state vector that is its quantum state. And then you might want to say, "Well, okay, what is the quantum state vector for A all by itself or B all by itself?" And the formal mathematical answer is there's no such thing. There is a density operator. Because of the entanglement, there is no way to say... There are ways to say what are the measurement outcomes you're gonna predict, that's exactly what the density operator tells you, but there's no answer to the question, "What is the state just of... What is the pure vector in Hilbert space that tells me the state of just subsystem A?" The thing that tells me the state of subsystem A is a density operator. Okay? So that's different. Nothing like that appears in classical mechanics. And so that's sort of hinting, although not telling you, that maybe there's something a wee bit more fundamental about mixed states or density operators in quantum mechanics than there would be in classical mechanics and there's a whole nother perspective on quantum mechanics that is not the one I usually talk about. The one I usually talk about, again, forgetting about Many-Worlds, none of this is special to interpretational or foundational issues. We talk about vectors obeying the Schrödinger equation. That is the Schrödinger picture of quantum mechanics, and it's probably the most intuitive one. But there's also the Heisenberg picture, which leads in more sophisticated guises into the algebraic view of quantum mechanics. And there, what you actually track are the operators that would tell you what measurement outcomes you might possibly get rather than the underlying quantum state. You can still define a quantum state, but that's not sort of the central object of your attention. And in that perspective, there's sort of no... You don't start by starting with pure states as vectors in Hilbert space and then generalize them to mixed states. It's the other way around.

0:53:25.3 SC: In the algebraic perspective on quantum mechanics, states just naturally are mixed. That's just a fact. And then you have to specialize to pure states if you want to, you can. So that is another piece of evidence that says maybe there's just a fundamental ontological oomph to the idea of mixed states in quantum mechanics that there isn't in classical mechanics. And the final bit of information is I do think that there's this problem of time that people talk about where in quantum gravity you don't have any time evolution in the Wheeler-DeWitt equation, which is the most famous version of ordinary classical, well, quantizing general relativity approach to quantum gravity. And that's a problem of time. There's no time evolution. What do you do about it? I think that existing solutions to that problem are not as good as people think they are. And maybe one way out is to think about mixed states and density operators rather than pure states. This is an idea from Carlo Rovelli, former Mindscape guest, the second ever Mindscape guest, in fact, among other people, the thermal time hypothesis. So anyway, it's not a definite once and for all answer to your question, but I'm giving you a bunch of little hints that density operators or mixed states are not simply statistical generalizations of pure states. They might be the fundamentally right way to think about the universe as a whole. I don't know, but I'm open to that possibility.

0:55:01.7 SC: Okay, I'm gonna combine two questions here. The first is by Peter M. Caruso, and he asks a priority question. Remember that Patreon supporters of Mindscape get to ask one priority question during their lifetimes, that'll come up again in a later question. You only get to ask one, so you better make it a good one. And the idea is that there's usually too many questions for me to answer, but the priority question, I'm gonna do my best to try to answer it. So Peter asks, "It's my understanding that the light that forms the cosmic microwave background left our young universe about 300,000 years ago as we measure time, and that its frequency is shifted by two factors, the expansion of our universe and the gravity it is subject to from the object it is escaping from. However, from the point of view of the individual photon, zero time passes between its emission from the atom it originated from and the atom it excites in the detector in our own telescope. Since our universe was much smaller and more dense when it was only 300,000 years old, the light our telescope sees today simultaneously sees a very dense gravitational background field behind it and a very much less dense gravitational foreground field in front of it thus lowering the light's frequency. Has that dense background gravity effect been properly accounted for in discussions of the discrepancy between the measured and calculated theoretical strength of the cosmological constant?"

0:56:19.1 SC: And then Larry Latson Jr. asks, "When talking about the Big Bang in the very first moment of the universe, we often hear things describing the state of the universe in the first microseconds, et cetera, et cetera when talking about the cosmic background radiation, describing the state of the universe after a few hundred thousand years et cetera, et cetera. But I always wonder, can you talk about time using our usual definitions when talking about such extreme environments and states? We know our usual conceptions of time are distorted at the event horizon of a simple black hole, so surely time must be distorted in the very first few seconds when the entire universe was compressed into a tiny ball." So there's a subtlety here that is a little, the math behind it is perfectly 100% clear but the words that we usually bandy about can be confusing. So it's absolutely true, you've all heard that in general relativity, spacetime has curvature, and that curvature... It's really spacetime that has curvature, right? The whole four-dimensional thing, not just either space or time by themselves. And one effect of that curvature is that the amount of time that is elapsed along a path, that is to say, the amount of time that is measured by a clock moving in a certain way through the universe, will depend on the curvature of spacetime through which it passes in exactly the same way as the length of a curve in space will depend on the geometry of the surface on which it is moving like a hilly terrain might give you a different length than a flat terrain, okay? All that is true. And then so people want to know, well, in the early universe where everything was really, really dense, there's a lot of matter and energy and therefore a lot of gravity, what effect does that have on time and how time passes? And the answer is absolutely no effect at all. Now, I can justify that in two different ways. One way is the pure math way, which anyone who has gone carefully through the first book in the Biggest Ideas in the Universe series, Space, Time, and Motion, will have no problem understanding. But we quantify the curvature of spacetime in terms of the metric tensor, the thing that tells us the length along different curves in spacetime. And if you think about the metric tensor for an expanding universe, for a cosmological spacetime, there are coefficients of the displacement in any pair of directions. So the idea of the metric tensor is it's basically a generalization of Pythagoras's theorem. If you give me two sides of a right triangle, Pythagoras's theorem tells you the length of the hypotenuse. The metric tensor is a generalization of that. So it says you give me two infinitesimal displacements in time or space, and I will tell you the total displacement along connecting both of them. And so there's a coefficient for dt squared, where dt is an infinitesimal time variation. There's a coefficient of dx squared, of dy squared, of dz squared, but also there are coefficients of dxdt, dxdy, all of those things, okay? Every possible pair of directions you can move in space has a metric tensor component attached to it.

0:59:40.5 SC: In cosmology, two things are true. There are the coefficients of dtdx. So I'm moving a little bit in time and a little bit in space. Those are all zero. There's no crosstalk between time and space. And secondly, the coefficient of dt squared, which is literally telling you how fast time is passing, is one. It is not changing. It is not changing with time or with space or anything like that. So the evolution of time, as long as you are doing the sensible thing and using the same time coordinate in the universe as for your clocks, the amount of time you measure on your clock is exactly the same for all observers who are moving at much less than the speed of light compared to the background cosmic radiation and matter and all those things, that is to say, moving basically in the timelike direction. And that seems weird. So I'm basically saying there is no time dilation whatsoever because of the gravitational field of the universe, even though the gravitational field is very dense, the matter is very dense. What's going on? Well, like we just said, and here's the more intuitive explanation, just like in space, the length of a curve can change depending on whether you're on hilly terrain or whether you're on a flat plane. But the length of a curve doesn't change if you're on a flat plane at sea level versus being on a flat plane on a plateau at high altitude. It's the flatness that matters. It's the deviation from point to point that matters, not the overall altitude. What that density of matter is doing in the early universe is it is true that it's very dense and it creates a large gravitational field, but that large gravitational field is entirely encoded in the expansion of the universe.

1:01:28.3 SC: There's no difference in the curvature of spacetime from point to point in space in cosmology in the approximation where things are really, really perfectly smooth. So there is no gravitational field that is pulling you in any direction if you're there in the early universe because there's an equal amount of matter on all sides. That's what it means for the matter to be uniform. And as a result, time is doing the same thing. All of the clocks are ticking at one second per second, no matter where you scatter them through the expanding universe. So time just works normally in cosmology. So hopefully that answers Larry's question. To Peter's question, there's a little bit of a wrinkle here. What happens to the redshift of a photon, which, after all, does not stay stationary with respect to the background? It's moving with respect to the rest frame of the universe. But at any one moment, it feels the same gravitational field just behind it as just before it. And therefore all of its redshift comes from the expansion of space itself. There's no extra redshift from the fact that the density of the universe that it passed through a minute ago is different than the density of the universe that it will pass through a minute from now, because it doesn't know about the past and future, it only knows about the moment. And in the moment, the gravitational field in front of it or behind it are exactly the same. Now, that can change if you look at deviations from perfect smoothness. If you have a lumpy universe, then indeed a photon can be redshifted as it climbs out of a gravitational potential or blueshifted as it falls into one. That is 100% taken into account. Even I've written papers about that when we calculate what happens to the microwave background. But in the approximation where everything is perfectly smooth, there's no effect at all.

1:03:20.3 SC: Jeffrey Siegel says, "Listening to the last latest solo episode, I was curious how you would rank the significance of the cosmological constant discrepancy with for example, the ultraviolet catastrophe problem that helped lead to the formulation of quantum mechanics." Well, that's a good question. They're not completely analogous but there's a sort of spiritual resemblance there, no doubt. I mean, in both cases, you're taking a theory that you think works pretty well and you're extrapolating it into a regime where it doesn't work pretty well and you're finding a disaster, kind of like the Boltzmann brain problem in that aspect. But it's a little bit different because in the case of the ultraviolet catastrophe, this goes back to the blackbody radiation problem that faced Max Planck and other people who were trying to understand thermal radiation circa 1900. One way of thinking about what the problem was was that in a certain way of calculating the amount of blackbody radiation, it became infinitely strong at low wavelengths, small wavelengths, high energies, the ultraviolet, as we call it. So it was labeled the ultraviolet catastrophe, although I think, as a matter of historical fact, you'd have to check me on this, but I think that the label ultraviolet catastrophe, which is just an awesome title and a good band name, wasn't actually attached to it until much later. But later on, when we had quantum field theory, then we had a new kind of set of ultraviolet catastrophes. We had all the infinities that happened in scattering theory with Feynman diagrams and stuff like that, which were eventually figured out by a renormalization. So there's three problems here that are kind of ultraviolet problems, the blackbody radiation problem, the infinities in quantum field theory problem and the cosmological constant problem. And they're all very similar but different, okay? So the real problem with the blackbody radiation thing was that we thought we had a reliable theory and it just gave wrong answers physically. There was no ambiguity about how to do the calculation. That was pretty clear how to do the calculation. It just gave a wrong answer. So you really needed to physically change what your theory said and that's why Max Planck invented Planck's constant and the quantization of radiation.

1:05:45.1 SC: In the mid-century work on quantum field theory, it was more like we had the theory but we weren't sure that we were making predictions correctly from the theory. And that's what was resolved by understanding renormalization. We had a better way to make predictions given the theory we already had. We didn't really need to change the theory. Now, when Ken Wilson comes along in the '60s and '70s and introduces effective field theories and ultraviolet cutoffs and things like that, then you can say we have a different perspective on what it meant to renormalize away those infinities. Rather than saying we have a delicate procedure for taking infinity minus infinity and getting a finite answer, we instead have this admission of guilt that we just don't know what happens in the ultraviolet, and we don't need to know what happens because we just put a cutoff on and deal with it. So it's a shift of focus, but in either way the problem is solved. For the cosmological constant, in some ways, here's what is really extra different about it. We don't think we have a good theory. No one is saying, "I can predict the exact numerical value of the cosmological constant on the basis of known theory, and here's the answer and it disagrees with experiment." What we have is the same sort of effective field theory philosophy that suggests what natural values of certain quantities should be, including the cosmological constant. And there's a huge discrepancy between our expectation and the reality. But a couple things is, number one, like I said, we don't have the right theory but number two, you might try to take the way out that is offered by effective field theories and say, "Well, okay, there's new physics at high energies that I don't understand, and maybe that will solve the problem." This is exactly what makes the cosmological constant problem a little different than the other problems because if you just naively do that, if you say, "Okay, what is the energy scale at which I have to think I don't understand physics to put an ultraviolet cutoff on and get the right value for the cosmological constant?" It's much less than a single electron volt and the mass of the proton is a billion electron volts. So in other words, you can't solve the problem of the cosmological constant just by choosing a really, really low ultraviolet cutoff and hiding everything in ultraviolet physics. The cosmological constant is by itself an infrared phenomenon. It shows up at large distances, and you can't get rid of it just by messing with short-distance physics. This is the thing that makes it weird. Again, it's weird by the lights of working quantum field theorists. Quantum field theorists are very, very used to a situation where something mysterious is going on at high energies. Like they know how to accept that and move on with their lives. That's not gonna be enough to solve the problem of the cosmological constant. Maybe it could be enough to solve the hierarchy problem of the Higgs boson. That was the hope when we turned on the LHC, that we would exactly see the new physics that would help solve that problem. It's not there yet, anyway. So that's worrisome and maybe is an example of, again, ultraviolet physics is not able to come to our rescue here.

1:07:30.6 SC: Martin Squibbs says, "In your Royal Institution talk in 2016 entitled 'The Big Picture: From the Big Bang to the Meaning of Life,' you state, 'We remember what happened yesterday. We don't remember the future.' May I question this statement? Isn't it true that for all the artificial products we actually invent and make, we must first invent the idea of them, create their design, et cetera, all of which must be done within our minds before we can actually make this idea of a product invention within our minds into an actual artificial product external to our minds, that is, into a reality which we can actually observe within our unchanging experiences or past. Before we make the first instance of a new artificial invention, we have no factual evidence of its existence at all and in truth, it may be impossible to make when we try. In short, for all the ideas of product inventions, their future must always precede their past." Well, I kind of want to say, come on. Sure. We think about the future, we imagine the future, we even predict the future. No one denies any of that. All I would say is there's clearly a difference between all of those things and remembering the past. By remembering, I'm not literally confining our attention to what is happening in our brains. Okay? Memories can take the form of records, of photographs, of fossils, of history books, of all sorts of things about the past. The thing is that we have artifacts, we have configurations of matter here in the present moment, which, given our understanding of entropy and the arrow of time, blah, blah, blah, we associate with a record of a specific thing having have happened in the past. I have a photograph that came from the pre-AI era, so it came from the '70s. There's a picture of me as a youngster. This means that that really happened. I can imagine all sorts of things happening in the future. There's just no record that they will happen. There can't be because maybe tomorrow an asteroid hits the earth and none of it comes true. There's no connection between those imaginative views of the future and what actually the future holds. There might be better predictions or worse predictions, but they are of a different character than an artifact that has a direct, tangible relationship to a different moment of time like we have for the past.

1:11:34.2 SC: Tucker Hyatt says, "Have we adequately solved Hume's problem of induction?" I have to say, I almost never do this, but there was a comment following up in the Patreon discussion from Jamie, who says, "How do we know that our solution will still be valid tomorrow?" which, if you understand what's going on here is hilariously funny. That is the funniest comment I've ever read in a Mindscape discussion thread, and maybe you will understand it in a second. So Hume's problem of induction. David Hume, of course, was famously good at differentiating between what we really know and what we kind of glom onto what we know because it helps us make sense of things. So that's the origin of being a Humean about the laws of physics, is that you just say that what exists, what is real, are the various things that happen in the universe. The laws of physics, et cetera, are not themselves real. They're just the best things... I mean, they're real as descriptions, but they have no role in bringing the universe about. The laws of physics are just descriptions of what already happens in the world in what is called the Humean mosaic, the set of things that actually occur in reality. That's the idea of being a Humean about the laws of physics. And the problem of induction is very, very similar to that. Hume says, you know, there's... And this confused me, so let me make it clear to anyone else who's listening here. In mathematics, there's a technique called induction, sometimes called logical induction or mathematical induction, as opposed to deduction. Deduction says, "If P, then Q, P, therefore Q." It's a sort of generalization of a syllogistic kind of reasoning where you get ironclad conclusions from whatever premises you put in. Induction, in the mathematical sense, says, "I assume that property P is true at n equals 1 and I assume that if property P is true at n equals x, then property P will be true at n equals x plus 1. So basically I have a baseline assumption and then I have an induction rule that says I can go from one to the next one, and then I start from zero and I work my way up, or I start from one and work my way up, and so I prove this property for every single possible example. Now that's valid. That's a logical way of proving things. That is not what Hume is talking about. He has no problems with that kind of induction. There's another kind of induction that just says every single day I look outside in the morning and the sun rises in the east, therefore the sun will rise in the east every day. It's an attempt to reason from repeated patterns in the past to rock-solid, definite, predictable patterns in the future. That's the kind of induction that Hume is aiming at. And he just makes the completely correct statement that you don't know. You don't know what's gonna happen tomorrow. Like we said, we might be hit by an asteroid, there might be no Earth to revolve or to rotate and therefore to let the sun appear to be arising in the east. And that's completely correct. He's just right. And we can be surprised. But it's part of just maturing as a species philosophically that we realize that there's more ways to live than perfect Cartesian formal certainty, foundational certainty.

1:15:11.9 SC: René Descartes, when he did his thought experiments about being fooled by a malicious demon or whatever, what he wanted was a rock-solid foundation for all of human knowledge. And he eventually found it in cogito ergo sum, I think therefore I am. And he also needed to invoke the existence of God, and God wouldn't be fooling us, et cetera, et cetera. But there's a million ways in which people don't believe Descartes's argumentation all the way. And a big part of what Hume was doing was pushing back against the big program of foundationalism. And I think that was correct. And I think that the... I don't know what it means to be adequately solved. I don't think there's any consensus among philosophers what the solution is. I think there's a more than good enough solution, which is just to say, sure, we don't know for sure. What we do instead is talk about credences, talk about likelihoods and probabilities. And I'm someone who thinks that our credences in things like "will the sun rise tomorrow?" are not objective. There's a fundamental degree of subjectivity in them. But the good news is that all actually existing human beings have a lot of overlap in how they assign credences to different possible models of the world that lets us get along both in our personal individual lives and in the world more broadly. So not all potential extrapolations of the past toward the future are created equal in terms of credences. I think that's roughly the solution. Simple theories are better, fruitful theories are better, theories that fit in together with other things we've learned about the universe are better. There's sort of a laundry list of theoretical virtues for a good scientific theory that help you decide where to put your credences. There's nothing ever that stops someone saying, "But I don't want to do that." And I think that if you want to have logically airtight refutations of people who want to extrapolate in bizarre ways from the past to the future, you cannot stop them from doing that. So in that sense, there's no solution to Hume's problem but in the sense that we can nevertheless get on with our lives, I think the solutions are perfectly well understood.

1:17:37.6 SC: Steve Bellamy asks a question about the physics of democracy. He says, "Where I live in rural England, we used to have European, Westminster, county and local elections. So people participated in direct democracy most years. Only the Westminster election got good turnout with research showing that too many elections in the same period causes voter fatigue." By the way, for those of you who are not in England, Westminster elections mean parliamentary elections. Your Member of Parliament is being chosen. So anyway, "Having left Europe and with county and local councils being merged into new regional structures, we will only have elections every two to four years going forwards, which doesn't seem very often. Is there any indication that fewer elections will mean greater engagement? Is there a sweet spot in the participation curve? What are your thoughts on voting frequency?" I think this is a great question. It's not something that I've thought a lot about, and so I don't know what the state of the research is. I'm not gonna try to guess what it is. It's worth looking up. I do think that... I don't know what it's like in the UK, I do think that in the United States, there's not enough feeling that voting is natural and you should do it. The moral persuasion for people to participate in democracy is not what it could be. Some people do it, people have opinions and they want to let their voice be heard and so we get even in presidential elections, in the biggest stakes elections that we have, 50-ish percent of people actually vote. In these local elections, it's much less. I do think that part of it is there's been a complete collapse of the infrastructure for local news and information. It used to be you have your local paper, your local radio station or whatever, and now everything has been internetized and the local newspapers have collapsed and so people just don't even know what's going on in their own community. They don't have opinions about who would be the better person to vote for, et cetera. But that's more about the question of local versus national elections as opposed to the question of the voting frequency.

1:19:48.2 SC: So I don't know. I'm saying this question out loud because I think it's an interesting one that I haven't thought about, not because I know what the answer is. I can see it either way. You can see it, well, if you make it more frequent to have elections, people get in the mood. They get in the groove. They're just like, "Oh yeah, okay, it's November whatever, I'm gonna go participate in the election. I do that every year." Versus also, if there's too many elections, then you get fatigue like, "Oh man, I gotta go vote again." I do think that it's crystal clear that we should make voting easier and we should make how we count the votes and report the votes easier. I think that there should be a national holiday, which there's not here in the US, to go vote. I think it just should be very, very straightforward to get this done to increase the amount of participation we can possibly have. I don't see that actually happening because one side of our political debate has turned any questions of voter participation into an entirely fake discourse about voter fraud. Voter fraud is really, really tiny, almost completely negligible, and not a real problem here in the United States but certain people want to suppress the number of people who vote overall, and they do that by ginning up fake controversies about voter fraud, which will make it very hard going forward to make progress on making it easier for people to vote.

1:21:20.6 SC: Linda Tulberg says, "I was just listening to Neil deGrasse Tyson's interview with neuroscientist Donald Hoffman. He says his team of scientists are working on a new mathematics called TRACE, based on Markov chains, and they hope to derive both special and general relativity from this en route to a theory of consciousness. Do you have any thoughts on this?" I'll give you my very brief thought, which is that as soon as someone says they're gonna derive both special and general relativity en route to a theory of consciousness, I stop listening. I don't think that special and general relativity have anything to do with a theory of consciousness other than they're both really cool. And I don't think that just 'cause two things are cool, they should be part of the same scientific explanation. And it's also part of, I guess the one other thing I can add to that is one of the aspects of somewhat crankish scientific theorizing is grandiosity. You can't just explain this particular neural pattern. You have to explain consciousness. You can't just explain this particular decay pattern of a particle, you have to have a theory of everything that unites everything. And it's a fundamental misunderstanding about how science works. Like maybe at some point you get a theory of everything, a unified thing that combines various things, but you get there by many, many, many small steps. And if you can't show me that you've done the small steps and gotten something interesting, I'm not gonna put a lot of credence in your success on the bigger picture questions.

1:22:48.9 SC: Jennifer Lecompte says, "What does teaching natural philosophy look like in terms of scope? Asking as an astronomy teacher who wants more philosophical content in my class." Well, so I take it from the second sentence here that you're asking about introducing little bits of philosophy into a class that is mostly about science. So that's different than teaching philosophy of science as a course all by itself, which is also a perfectly respectable thing to do. So again, I don't know. I don't have a well-developed theory for how to do that. I do think that in the course of teaching an ordinary course on science, there will always be parts of the course where you're gonna bump right up into questions that have philosophical components to them.

1:23:40.4 SC: If you're teaching astronomy, look, if you mention the Big Bang, is the Big Bang the beginning? Is it more natural to have a universe that lasts forever or a universe that has a beginning in time? Is that even a meaningful statement? Why is there something rather than nothing? Are there other universes, other people who have different experiences? Is there fine-tuning about the parameters we see in the universe? Like there's a million different places where right away you get into philosophical questions. Even in a slightly more down-to-earth vein, there are plenty of other planets, we know that now. What does it mean to ask whether there's life on those planets? Does life always look like it looks like here on Earth? Is it robust? Is it hard to make? Is it easy to make? There's philosophical aspects there also. How will we know life when we find it, if we do?

1:24:24.9 SC: So I think that there's two things I can do. Number one is to cheer you on, to say that that's a wonderful thing to take seriously. Like I taught quantum mechanics last year, the regular old undergraduate physics major quantum mechanics course. I didn't do a lot of philosophy or foundations of quantum mechanics in that course, but I didn't pretend it didn't exist either. Like I noted where these questions existed and I mentioned what the possible ways of solving them were and encouraged people to look it up if they wanted to know more. I do think that besides cheering you on to do it, the one other thing, which I'm not sure if this is gonna be helpful advice or not, but it's really, really easy for people to look at philosophical problems, which by their nature are often very grand and general and of immediate resonance with our intuitions, and say, "By thinking about this hard for a few minutes, I could more or less figure it out." That's not a good way to go forward. Like if you wanted to talk about the philosophical implications, I think you kind of need to do some work, some work in figuring out what real honest-to-goodness living philosophers think and say about these things. I mean, the good news is we live in an era with the internet in general, but also with LLMs and so forth, where that's fairly easy to do. I mean, you can go to an LLM and, again, you don't trust what the LLM says, but you use it as a way of getting into the knowledge base that is out there around you. So if you say, "Okay, why is there something rather than nothing?", don't just ask Claude or ChatGPT that question. You can ask them, "Who has thought about this question? What are the main voices that have opined about this?" And they'll tell you Derek Parfit or Gottfried Wilhelm von Leibniz or something like that, and then you can go look them up and read about them. Likewise for fine-tuning or what happened at the Big Bang or whatever. So I think it's a non-trivial task but a very worthwhile task to do to dig into the philosophical aspects of whatever it is you're teaching and include them as an enrichment material in the class.

1:26:42.8 SC: Nikhil says, "The sun will slowly fry the Earth in the next one to two billion years due to its increasing luminosity and red giant phase at five billion years. I do not have a nihilistic view of the survival of humans 'cause I believe that humans have an underrated self-preservation quality. If preservation of Earth is the highest priority rather than galaxy colonization, solutions such as artificially expanding the Earth's orbit using gravitational assist to keep it in a habitable zone or tampering with the sun's mass to lower its rate of fusion are proposed. Assuming solving quantum gravity doesn't drastically change the available solutions, how would you approach the task of protecting Earth by keeping it in a habitable zone?"

1:27:20.9 SC: I wouldn't, to be perfectly honest. So I think with very high credence that quantum gravity is not going to drastically change the available solutions, so I wouldn't put your hopes on that. I would ask about good old moving stuff around using the laws of physics as we know them kinds of solutions. And in that way, like if you're gonna literally keep the Earth in a habitable zone, there's kind of two choices. One is to move the Earth and the other is to shield it from the sun. I think that the second way is much more technologically feasible: shielding the Earth somehow, cutting down the amount of radiation that it gets. It's still incredibly difficult, don't get me wrong. It's just easy in our minds to extrapolate from building a house to pushing around the Earth or many, many thousands of kilometers worth of materials in a structure you're building, but in the real world, that's gonna be hard.

1:28:21.3 SC: Moving the Earth is nearly impossible, not just because it's big but because it's rotating and people live on it. If you wanna literally move the Earth, you gotta push it somehow or pull it. Those are the only two choices that I see. I don't see how you could push it without stopping it from rotating and then putting a rocket on it or something. None of that is at all feasible or advisable as far as I can tell. If... I mean, pulling it, you could pull it gravitationally, I suppose, but that means pushing around something equally massive as the Earth or close to it. I mean, maybe you could put a rocket on the moon and gently tweak the Earth's orbit by moving the moon around and having it drag it. Tremendously inefficient, and I don't know whether it'd even work, but you could at least contemplate that. But anyway, talking about what's gonna happen in the next few billion years to humanity is hard to constrain by rational requirements, so I'm not gonna pretend to know what's going on. But I don't think that the Earth is something to be sentimental about. If we're talking about what's going on three or four billion years from now and there's still something called humanity, which there probably won't be. I mean, there might be something, some descendant of humanity, but the chances that our species as it currently is conceived of lasts for another billion years are incredibly tiny. Just move. Just go somewhere else. Don't fall in love with the Earth just 'cause that's where we were born. Things change. The universe changes. Not every structure that is built here on Earth has to last forever. Likewise, not every planet that life arises on has to last forever either.

1:30:04.3 SC: Alan says, "You've described physicists reacting to certain ideas like space being emergent rather than fundamental, with reluctance or discomfort, and have also discussed how career incentives and peer perception shape research choices. Personal bias, practical considerations and social pressure can affect which ideas are taken seriously and cannot just be eliminated. What's your take on how problematic this is in reality, and how should responsibility for preserving the intellectual integrity and rigor of physics be divided between individuals and institutions?" I don't necessarily think that the idea that people have reluctance or discomfort about certain theories of physics is bad. I mean, that's good. Certain theories in physics are not very good theories to waste your time thinking about, so having some feeling that it's not worth your time is just a feature, not a bug. I have no way of installing complete rationality among people or institutions that would make them think more clearly about what their reactions are. I don't think, by the way, that people are especially reluctant or discomforted about emergent spacetime, most people. I do think that it depends a lot on the specific subset of people you're thinking about. There are absolutely people who think that space is just where we live and that's fundamental and you can't get around that, but I think a lot of people doing quantum gravity and things like that think otherwise. So I think that there's lots of things to do but this particular axis of personal bias versus pure rationality is probably not the right way to phrase the issue. There's lots of ways to make academia and research better. We should encourage people to try different things. Most of the effort should go toward the most promising research directions, that makes perfect sense. But some of it should go to a diverse set of alternative possibilities, as long as they're respectable.

1:31:58.8 SC: I think more important, I would rather put trust in the individual researchers to do good things, especially if those researchers have a track record of doing good things. Well, there's a lot of very practical things. It shouldn't be as much work to apply for grants as it is. We have this thing that applying for a grant is practically doing the research project even ahead of time, and it's just an enormous amount of work. And when people have a track record of always doing good work, I would rather have them spending their effort doing the work rather than writing a grant proposal. I also think it should be made easier for people to switch research fields or start different research projects. We reward people right now in the current system by doing the same thing over and over again or just by very gradually, slowly changing their research direction, but nothing dramatic. And I think that holds us back in coming up with inventive new ideas.

1:32:55.6 SC: After all, a lot of people choose their research direction, broadly speaking, when they're in graduate school, when they're in their 20s. And roughly speaking, that sets the agenda for the rest of your life. That's why I tell my students that picking your PhD advisor is the second most important person you will intentionally choose in your life after your spouse, because it affects the rest of your career in a very dramatic way. But what do you know when you're in your 20s? Like you might be smart and you might know a lot about your individual field, but you haven't had exposure to many different fields so that you can choose what is the most directly, let's say, productive way for you to spend your time. It should be easier for people to change their research direction later on. We should also spend more resources on supporting young people who want to do things that are very promising research directions but don't necessarily fit into one box in terms of is it physics or is it biology or whatever. It's hard for those people to get jobs and sustain their careers and be productive scientists in those crucial years in between graduate school and being a tenured professor. So I think there's lots of things we can do to increase the diversity of things going on and therefore increase the probability of hitting on the right answers, but I don't think removing personal bias is one of the high priority areas for that.

1:34:22.8 SC: Paulina Vino says, "In an AMA this year, you mentioned that you subscribe to the liberalism system of values. In another question later, you give the example of a specific problem with liberalism, which is in the case of university departments making decisions, that what's better for the community will not come about as a result of each department doing what's best for itself. Any further thoughts on reconciling liberalist values with striving for the common good?" Well, I don't remember exactly what I said. I don't think that I would make a statement like I subscribe to the liberalism system of values. I don't think of liberalism as a system of values. I think of it as an approach to politics, to government, to political philosophy. In that particular subfield, I would definitely classify myself as a liberal. We're talking now about sort of the political theory version of what liberal means, not liberal versus conservative in the sense of modern US politics or anything like that, where I'm also a liberal, but it means something different. So that's a distinction worth keeping in mind.

1:35:21.9 SC: To me, liberalism as a political philosophy puts a lot of emphasis on individuals and the rights of individuals. And there's sort of two sides to that coin. If you are the individual in question, then liberalism says that you have rights. Your particular interests should not be subsumed, all else being equal, to the interests of the community. It's not a utilitarian kind of philosophy where what's overall best matters even if we have to sacrifice some people to get there. There's sort of a minimum amount of care and importance given to the interests of individuals within liberalism. So something closer to a Rawlsian version of a political arrangement would be compatible with liberalism. The other side is that when other people, not you, are the individuals in question, then you have to give them rights. So liberalism is a philosophy of equal rights for all different kinds of people, even if some people don't like it that way. So that's the area where your choices get cut off by liberalism, because you're not allowed to trample on the rights of others. And in many cases, I mean, Adam Smith talks about this in economics, but in democracy, the philosophy is that letting individuals pursue their self-interests will often give rise to a good outcome for society as a whole. But we all know that's not always true and that's why we go out of our way to protect the rights of individuals, of minorities, and things like that. So you can't ever be too extremist about any particular simple idea in political philosophy. You have to actually think things through.

1:37:14.1 SC: And then when you apply these kinds of ideas to areas that are not political theory or the foundations of government like running a university, then the considerations are very, very different. Like forget about universities, think about a basketball team. I'm the coach of a basketball team and I'm giving different assignments to different people to do things. I don't care about individual rights in that situation. Some basketball players are going to have to sacrifice their shots and their opportunities for the betterment of the team. That's a case where liberal values would not be an appropriate structure if what you want to do is win basketball games. And something like a university is something in between. We do think... I think it's a pragmatic view that says that individual departments are often the best at making choices about what they should pursue and I think that's usually what happens, roughly speaking, in most universities. There's a bit of a give and take because a department will say, like Johns Hopkins did a few years ago, they said, "Look, we're a pretty good physics department. We're excellent in some areas. We have nobody at all doing atomic and molecular physics, AMO physics, and that's a really important area of modern physics. We should grow in that area." And so the university... They make a pitch to the university. They say, "We want more resources to do this." And the university decides whether or not they deserve the resources to do it. In this case, they said yes and so we're growing in that area. But it's a give and take. The department decides what they want. The university decides whether or not to let them have the resources to make it happen.

1:38:51.3 SC: Now, where that fails is when there's something that would be good for the university overall but no individual department wants to get behind it and push it. And then you have to make some sacrifices. Then you have to think of a different way of doing things. The danger in doing that is you don't want to give the administration too much power to just come up with new initiatives that might not even be aligned with the academic mission of the university at all. Administrations, for all sorts of reasons, positive and negative, do not necessarily have interests that are purely aligned with the academic mission. There are other things going on, whether it's fundraising or politics or alumni relations or the football team or whatever. So that's okay. I think in all of these situations you have to accept the inevitability of compromise and hybrid structures that allow for different interests to get their voices heard and ultimately have a say in where the institution goes.

1:39:47.9 SC: Pete Faulkner says, "I think I understand your view that what fundamentally exists is the quantum state, a vector in Hilbert space, and that space emerges from the structure of the Hamiltonian, with locality and dimensionality read off from the pattern of entanglement and interactions. That program recovers emergent space. But it seems to me it recovers space by relying on the Hamiltonian, and the Hamiltonian is a generator of time evolution. So the construction appears to presuppose a time parameter in order to derive space, which makes the fundamental ontology sound less like a vector in Hilbert space and more like a vector in Hilbert space plus some notion of time for it to evolve along. Space tends to be emergent, but time tends to stay in as a fundamental element hiding inside the word evolving. The answer might be Wheeler-DeWitt and the Page-Wootters style internal clock recovering apparent time from a fundamental timeless universal state. My question is whether you think that genuinely closes the gap or just moves it."

1:40:39.8 SC: So you're 100% correct in that for the most part, in the research I've been doing for the last 10 years or so on trying to extract the manifest image, the world we see around us, from the very simple idea of a vector evolving in Hilbert space, time is absolutely taken as fundamental. There's a Schrödinger equation. That's what makes everything go. And you're also absolutely right that there's another perspective that says that time is not fundamental but time is emergent as well as space and other things. And that leads us to the Wheeler-DeWitt equation and some notion of emergent time. So what I think, and I've said this before, but I can say it again, I think that there are approaches to getting time to emerge from a timeless formalism such as the Wheeler-DeWitt equation, but mostly they're cheating. Mostly they're not actually rigorously, carefully examined moves that fall out of the theory themselves. It's that we know ahead of time what answer we want to get, and so we force the theory to give it to us. And I don't think that's quite valid. I think that Andy Albrecht has been a very strong voice here in talking about what he calls the clock ambiguity, the fact that if you want time to emerge, and Page and Wootters, Don Page and Bill Wootters, wrote a famous paper in the '80s about how time might emerge, and Albrecht points out, but there's lots of ways in their formalism for time to emerge, and they're completely incompatible. You need some kind of rules or standards to say what is the right way, the correct way that time emerges in this theory. And I don't think that the Wheeler-DeWitt equation gives it to you straight away. So you need something more than that, and I think that's an active area of investigation right now.

1:42:31.4 SC: Robert Ruxandrescu says, "I noticed over the years you've referenced Bayesian reasoning quite a bit. Given this, how come you don't adhere to Bayesian reasoning in quantum mechanics as well by being a QBist? After all, wavefunctions, Bloch spheres, matrices and so on are just predictive models in our minds, not real things out there in nature so a QBist position would be more reasonable. Just like we don't say the spin of an electron is a Bloch sphere, we shouldn't say that reality is a vector in Hilbert space, and we shouldn't believe in the wavefunction as a real entity out there other than a tool to make predictions with."

1:43:02.7 SC: So Robert is referring to an approach to quantum mechanics known as QBism, or previously it was known as quantum Bayesianism, so QBism, not from the art movement, but from quantum Bayesianism. And the idea there is it is an instrumentalist version of... It's an instrumentalist concerning the wavefunction or concerning the quantum state. Now, one problem with QBism is that they are... All the QBists are extremely cagey and hard to pin down on what they think really exists. And I think when you talk to them, different people give you different answers to that. Some will say nothing exists other than the outcomes of measurements. Others will say something exists and it's real, I don't know what it is. What they agree on is that what exists is not the quantum wavefunction. And now, I just think that there's zero evidence for that. I mean, I think that there's plenty of evidence that what exists is represented very, very, very well by the quantum wavefunction. Now, there is a subtlety here and it's a slightly tiresome subtlety in my mind. When I say reality is a vector in Hilbert space, I'm not making a claim about mathematical platonism or anything like that about mathematics being real, I'm making a statement about physics, because that's what I do for a living is physics. And the statement is reality is reality. It's what it is. It's the real physical stuff of the world. The statement is that that real physical reality is represented mathematically as a vector in Hilbert space. And ordinary people understand this perfectly well. Some certain subset of professional physicists and philosophers choose not to understand it perfectly well, but it's a statement about the best theory that fits the data. That's what it's a statement about. And when I say reality is a vector in Hilbert space, what I really mean is there's no extra variables, and it's not less than that either. The wavefunction represents something physically real. Nothing in that point of view prevents you from being a Bayesian. I'm perfectly Bayesian in the sense that I have credences over things and I update them when new information comes in. Quantum Bayesianism is not saying, I believe in quantum mechanics and I'm a Bayesian like everyone agrees in those two things, it's saying that that's all you need. I mean, really, quantum Bayesianism makes its money by saying wavefunctions are not real, all that really exists are credences in people's heads, and we update them when we make quantum measurements. I just see plenty of reason to doubt that as a way to move forward.

1:45:44.2 SC: Bandon asks a priority question. "In the recent Iran conflict, when an aircraft was shot down over Iran, Donald Trump claimed that some top-secret device that uses quantum magnetometry was used to locate the heartbeat of the pilot from long range. As you're the only expert I can ask this question to, can you please explain what quantum magnetometry is, and how can it be used in the device mentioned to locate a heartbeat? Is this something that is even possible?" So I'm sorry to let you down for your priority question, but I have no idea what quantum magnetometry is. I could try to invent some answer based on the words "quantum" and "magnet" and "ometry," but I'm not gonna do that because I can't do it any better than you could, and I might very well be wrong.

1:46:26.7 SC: I will simply say that the fact that Donald Trump says something is not a reason to think that that something is true, especially when it has to do with secret technologies using quantum in the name that are used to do impossible sounding things. Obviously the difficulty with believing a claim like this is that there are a lot of things going on besides the heartbeat of a pilot. Like why are you hearing the heartbeat rather than the blood running through the veins or whatever, much less all the noise that is going on in the airplane? The heartbeat seems like a very, very quiet thing compared to other things that you could somehow pin on. I mean, it's possible that there is some intricate, top-secret technology that actually does gather data on many, many, many different kinds of sound and then somehow, just like modern AI can pinpoint, isolate the drum track in a song or the vocal track or whatever, maybe you can isolate the heartbeat from a whole bunch of data. Maybe, I don't know, I'm just making it up. I have no idea what that would have to do with quantum mechanics whatsoever. Sorry.

1:47:36.7 SC: Mike VR says, "Setting quantum measurement aside at the macro level, thermodynamic, biological, institutional, not quantum, what kind of thing is an observer? I can point to a detector, a record, a system that acts on the record, but the observer doesn't seem to sit cleanly in any of them. And I can't tell whether that's because it's a higher-level thing or because observer is just a convenient way of talking with no real referent." Well, I wouldn't sweat this too much. In quantum mechanics, quantum mechanics is distinguished by the fact that you are driven to talk about observers because there are things that are involved in the way you describe a physical system that cannot be observed. And when an observation does happen, the wavefunction collapses or you get a probability or something like this. And therefore you need to start talking about observers. And the point is, when you're not in quantum mechanics, you mostly don't need to talk about observers unless you happen to be specifically asking a question about observers. So in those contexts, the word observer just means a person who can do observations. If you want to expand that to include robots or video cameras or whatever, go ahead. No one stops you. There's no special ontological role for being an observer in theories other than quantum mechanics. You can use it as is most convenient to the task at hand.

1:48:58.3 SC: Armen Delennian says, "You mentioned that once you set the speed of light, c, to equal one, you stop worrying about where the cs go. As a casual science follower, I've always wondered, how do you know which power of c to put back and where and when you're switching back to normal units, whether it's c, c squared, or c to the fourth?" Yeah, I think the answer is pretty straightforwardly dimensional analysis. So a speed in ordinary physics parlance has units of distance divided by time. And what happens when you set c equal to one, which also happens when you set h-bar equal to one, which often happens in particle physics, et cetera, some general relativists set Newton's constant G equal to one, but I think that's kind of a... That hides some things in ways that we don't like.

1:49:46.8 SC: So the idea is that you have a bunch of quantities and you know what their units should be. And if by setting c equal to one, you can express them in different units. For example, you can convert time and space back to each other, back and forth. If you have a unit, if you have some length, some distance, just divide it by the speed of light and then suddenly you get a time. And then if you have a time, you can divide that by the speed of light and you get a distance. So you can measure time in units of distance or vice versa when you set the speed of light equal to one because really, secretly, there are factors of c in there. So, for example, we might talk about the Hubble time. So the Hubble constant is usually expressed in these weird units of kilometers per second per megaparsec. So that's distance divided by time and that whole thing divided by distance. Now, the reason why that's a very strange thing to do is because you're taking distance divided by distance and they cancel out and the whole thing just has units of one over time, so why don't you just say one over time? Well, the answer is the Hubble parameter or the Hubble constant appears in Hubble's equation, Hubble's law: velocity equals H naught times distance. Distance is usually measured in megaparsecs or something like that. Velocity is usually measured in kilometers per second when you're talking about a galaxy. So measuring the Hubble constant in kilometers per second per megaparsec lets you very easily translate a distance in megaparsecs into a velocity measured in kilometers per second. But if you did just set c equal to 1 and use units where you're measuring everything coherently in the same units, then the Hubble constant is a unit of one over time. It's kilometers per second per megaparsec. So the kilometers are distance, the megaparsecs are distance. They cancel out. It's in units of one over time, one over seconds. So there's something called the Hubble time, which is one over the Hubble constant. It's just the simple inverse, that's all it is. That is a unit of time that, roughly speaking, tells you the time scale over which the universe is expanding at any one moment. There's also something called the Hubble distance. Sometimes it is confused with the horizon distance. Those are not exactly the same thing, but they're kind of morally the same, roughly speaking, the distance to very distant galaxies, almost the most distant galaxies you can get to. That's the Hubble distance. And if you set c equal to 1, you say the Hubble distance is 1 over the Hubble constant. That's all it is. But then you say, wait a minute, but one over the Hubble constant is the Hubble time, so how do I convert a time into a distance? Well, you multiply by the speed of light because the speed of light has units of distance divided by time. So if you know that the thing you have looks like it's in units of time but it should have units of distance, you know where to put the speed of light. You just multiply by one factor of the speed of light. That converts it into the right thing. And the same thing works for any other unit you want. If something is measured in units of energy, so the Hubble constant has units of energy when c equals 1, you just multiply by the right things and you convert back and forth pretty straightforwardly.

1:53:11.0 SC: Jeff B... I should have said when h-bar equals c equals 1, not just when c equals one. You gotta be careful here. I always set them all equal to one, so I actually don't remember where things go. Anyway, Jeff B. Says, "I'm reading Douglas Hofstadter's book I Am a Strange Loop, where he describes an interesting thought experiment. He asks us to imagine a world where essentially everyone is born as a conjoined twin. In this world, we are told, the pair is considered an individual, and it would be strange to think of them separately. One pair gets married to another pair, and so on. Hofstadter argues that this twin pair would develop a unified sense of identity and self, which he then likens to the two hemispheres of our own brains. Do you agree with this assessment, and do you think the conclusion extends to consciousness? Is there a difference between having a sense of self and having a consciousness?"

1:53:53.0 SC: So I don't agree, but I don't have very strong feelings. I could be wrong about this. I do think that, among other things that are necessary to have a single unified consciousness or a single unified sense of self, you need not only to be in the same body, but you need what's happening in your brain to happen relatively quickly. It has to happen sufficiently quickly that the signals sent from one part of your brain to the other are happening faster than the overall decision-making process. This is a whole thing in physics where we talk about separation of scales between microscopic and macroscopic. One big. One big thing which will be emphasized in the new book, Complexity and Emergence, once it comes out, is that when you have emergence, it's very often a matter of separation of scales. The reason why you can ignore the atoms and when you talk about the fluid mechanical description of air in the room is 'cause the atoms are very close by and very quickly moving. They're bumping into each other on a very short time scale. And if you perturb them, they relax back on a very short time scale. That's what allows you to have a successful description of the slowly moving features of temperature and density and so forth. If you had two different brains in two bodies that were conjoined, I think that the interactions within each brain are happening very rapidly. The interactions between the brains are happening relatively slowly, so there is no good regime in which you could unify them into a single thing. That would be my guess. Of course I'm happy to get it wrong. We have conjoined twins in the real world. I don't think there's any temptation to treat them as a single entity. So that's my guess, but it's a very different world than we live in, so I don't have much more than a guess to offer you.

1:55:42.5 SC: Peter 42 says, "Can you think of any measurement or observation that doesn't involve the electromagnetic field? After all, we detect neutrinos by looking for specific photons, and we measure gravity with a spring where electrons push or pull on each other." Well, it depends exactly on what you mean by "doesn't involve the electromagnetic field." Electromagnetic fields are everywhere, so it's very difficult to get around to something involving them in some very broad sense. The electrons that have different structures in atoms and molecules that are in different orbitals and different energy levels, that's all because of electromagnetism. It's the electromagnetic force that holds electrons to the nuclei of atoms, and therefore all of chemistry, which is most of life, is a matter of electromagnetic forces. So electromagnetism is ubiquitous in that sense. But there are other things going on. In particular, when you touch something, the atoms in your fingers do not go through the table when you touch the table. They are repelled by it. That's actually not electromagnetism doing that repulsion. You can make an argument that you feel it because there are electromagnetic signals sent up through your nervous system, but what is actually going on at the level of your finger touching the atoms in the table is the Pauli exclusion principle. It's the fact that electrons are fermions and they take up space, and you can't just move one electron into the same space as another one. And this is, by the way, not at all obvious that that's the correct way of thinking about it. I don't think it was really settled until the 1970s. Elliott Lieb and others finally did show that it really is fermionic repulsion, the Pauli exclusion principle, that is responsible for the fact that you can touch things rather than electromagnetism. But it's all really fields at the end of the day, so I'm not gonna be too much worried about ascribing different versions of what's going on to different forces of nature.

1:57:52.6 SC: Nigel Benjamin says, "If you are Laplace's demon, could you predict when a uranium atom will undergo nuclear fission?" Well, Laplace's demon, let's just be very clear. The whole point of Laplace's demon was to illustrate a remarkable feature of classical mechanics. So there's no such thing as what Laplace's demon does once quantum mechanics comes along. So you can invent versions of Laplace's demon that would apply to quantum mechanics but it's up to you to invent them. So it's nothing that Laplace would have been able to answer for. Now, there is famously a set of different ways to address what goes on in quantum measurement, which is involved when a uranium atom undergoes nuclear fission. If you believe in many worlds versus hidden variables versus objective collapse models, you have a different story to tell about the question, "When does the uranium atom undergo nuclear fission?"

1:58:46.0 SC: There are versions of the story that are completely deterministic, namely the hidden variable versions of the story, the pilot wave theories. You can easily imagine what is essentially Laplace's demon in a world that is governed by hidden variables. There's an extra step that isn't there in the classical world, which is that in conventional versions of hidden variables, there literally is no way to know where all the hidden variables are and what they're doing. But that's okay, we can nevertheless give Laplace's demon that mystical ability. That doesn't break any rules, and then it's perfectly deterministic. And then, yes, Laplace's demon could predict when the uranium atom would undergo nuclear fission. In many worlds, you have a weird hybrid story where there are underlying rules that are 100% deterministic, namely the wave function obeys the Schrödinger equation. And so what Laplace's demon could do in that case is to tell you when the universe would branch, but there would be a branch on which the atom had decayed and a branch on which it had not decayed. And Laplace's demon has nothing to say about which branch you will find yourself on because that's just not a well-posed question. There's a version of you that thinks you're on the branch where the uranium atom did decay and one where it thinks it didn't, and both of those will exist, so there's really nothing about that indexical uncertainty for Laplace's demon to have an opinion about. Finally, there are objective collapse models where there is something truly stochastic about quantum mechanics and then you would say, no, if Laplace's demon simply knew the current state of the universe, they would not be able to predict when the uranium atom would undergo nuclear fission, because that's not a deterministic theory and all Laplace's demon ever does is vividly illustrate what determinism is supposed to be all about.

2:00:33.1 SC: Theo Lind says, "I've noticed that the podcast theme song varies a bit. Do you welcome guest renditions?" I'm not sure why people think that the theme song varies a bit. That was certainly not intentional. I think it's the same clip that I'm playing every time. But more than one person has said this, so maybe there's something about how it gets output from the audio file or something. I really don't know. I've never solicited or contemplated guest renditions of the podcast theme song, which was composed and performed by my friend Ted Pyne, who was a friend of mine in grad school, who I wrote papers with, we're co-authors on a couple of papers. But then he went in a different direction after grad school, including experimenting with being a rock star, which didn't quite work out. But he has some good songs. Euphonic is the name of the band, you can look them up. I thought, yeah, I should do this. I should just like... I think that the Euphonic MP3 files are still out there on the internet somewhere. I will try to find a link to them and put them on the Patreon page. But I mean, part of me wants to say I would welcome guest renditions and if a good one appears, then I'm happy to play it on the podcast or even use it as a special change of pace for the usual theme song. On the other hand, I'll be honest, I do not have time to listen to a bunch of guest renditions or make decisions, and I would feel bad if people did guest renditions that weren't chosen. So I'm not gonna propose any official contest to give me guest renditions, but I won't discourage you from doing that if you just happen to do it with no expectations whatsoever.

2:02:15.2 SC: Niklas Viberg says, "What are your thoughts on scientific plausibility in science fiction? Does it add value? Do you have any favorite movies or stories where plausible science provides an interesting plot aspect?" I'm pretty loose about this. I don't demand that science fiction has plausible science. What I do think is super important is logical consistency. I think there should be some rules. If by scientific plausibility you mean the rules of the fictional universe are exactly the same as the rules of our universe, I don't think that's important at all. One of my favorite movies to illustrate science is the original Iron Man movie. Not because you can do any of the things that Tony Stark really does, that's completely implausible, but you see the process. You see hypothesis testing involved in a very realistic way. What's unrealistic is a lone genius doing all the work, which would not be practical. But okay, you can't get everything right. So what I like to see in movies or novels are systems of ways the universe can work which are internally consistent and also at least known enough to the audience that they can get a feeling for the jeopardy, for the stakes of any one particular situation. What I don't like is where things are just magic and you never know what the capacities of a certain superhero or scientific wunderkind really are, and then anything goes. And it's like, okay, they'll come up with something, like I don't know what it will be. If you know what the constraints are, then to me it's much more interesting. That's actually what it's all about. I mean, my motto here is, without science, there is no drama. Because science is the set of rules by which the universe runs and if there are no rules, if anything can happen, then there's nothing to worry about. Like yeah, eventually it will be fixed. But if there are true obstacles to things happening that science can summarize in some way, then you actually have stakes and a more interesting story.

2:04:25.4 SC: I'm gonna group two questions together. It can't be an accident these two questions both got asked, because they'd never been asked before. One is by Vykintas Morkvenas, who says, "Imagine classical immortal vampires exist. Would you want to become one and why yes or why no?" And then Heather Heise says, "How would you strategize your life if given the opportunity to be immortal? Based on comments made in previous episodes, I assume you would relish the endless pursuit of knowledge, but immortals face dilemmas. Others around you notice you do not grow old, your beloved may not be immortal. If a vampire, you need to figure out your blood situation, et cetera. My question stems from the current enjoyment of the Vampire Lestat on AMC+, and I like contemplating the puzzle of practicalities an immortal might face."

2:05:12.9 SC: So I'm guessing that it is this TV show that is causing these two questions to be asked, not just Heather's. I think that these are underdetermined questions a little bit. You can't just say "immortal" and stop there. There's a lot of details that need to be filled in. Like vampires. Okay, vampires are supposed to be immortal but vampires also have to eat. They consume the blood of the living. What happens to a vampire if there is no blood supply out there? Does it just decay? Does he grow older, or she? Do they eventually actually die and not become immortal? Is it just like potential immortality? Does immortality mean you're immune to accidents, being crushed by an anvil falling or anything like that? I truly don't know. But my short answer to all these questions is the ideas like immortality are just asked in situations where people don't want to quite face up to what infinity or eternity really means. There's this temptation to say, well, once a number gets big enough, it's practically infinite. And that's not a good temptation to give into. You should be a little bit more rigorous than that. I mean, really, if you're truly immortal, then the sun will die out, the Earth will fall into a black hole, the black hole will evaporate. Does your immortality mean that you maintain your bodily integrity even after you've fallen into a black hole and then get spit out in Hawking radiation? I truly don't even know what that means. You approach eventually a thermal equilibrium and there's nothing around. Do you somehow maintain a departure from thermal equilibrium that allows you to think and feel and breathe and things like that? None of these questions really make sense.

2:07:02.6 SC: So I just don't think it's an interesting thought experiment to worry about true, honest-to-goodness, physical immortality. But there's a big difference, as I was just saying, between big numbers and infinite numbers. Forget about immortality. Just ask what it would be like to live for a million years or a billion years, keeping in mind that a billion years is a thousand times longer than a million years, so that's a very, very different question. And I do think that you would absolutely get bored at some point. I do think that the human mind is finite, the human capacity to do different things is finite. I think that I personally would not get bored for a very, very long time. If, again, you need to define more what is going on in the problem, if I could imagine health and enough resources, whether it's money or whatever, to live a comfortable life, then I could be very happy for a very long time. But I can't guarantee those things, so the real world is trickier. Happily or sadly, none of us is going to get to actually be faced with this puzzle anytime soon.

2:08:06.1 SC: Alex says, "In a previous AMA, you said that neutrinos could not be considered matter during the early age of the universe. Could you elaborate? I'm not sure I understand how a particle that has mass can be considered non-matter." Yeah, this is an example where scientists use the same word in different senses and you shouldn't feel bad that you're not completely tracking what they mean. In the early universe, the people who talk about the early universe tend to be cosmologists and cosmologists distinguish between two different ideas, matter and radiation. And the only difference between matter and radiation in the eyes of a cosmologist is they're both made of particles but are the particles moving at or close to the speed of light, or are they moving substantially slower than the speed of light? If they're moving slower than the speed of light by a good amount, they are matter. And neutrinos in the present universe are moving slower than the speed of light and they are matter. But in the early universe, just like photons lose energy by redshifting as the universe expands, neutrinos lose momentum by redshifting as the universe expands, which means they were higher energy in the past. And not too long ago, the typical energy of a neutrino was comparable to its mass, which means it's moving at the speed of light or very close to it. I shouldn't say at the speed of light. It's moving close to the speed of light. So in the regime where the neutrinos are moving close to the speed of light, they are considered by cosmologists to be radiation rather than matter. And the reason why the cosmologists care about this is the energy density changes as a function of the size of the universe differently for matter and radiation. This is all covered in chapter three of my upcoming book, Complexity and Emergence, which I hope you will all look for when it appears in bookstores.

2:09:58.3 SC: Bill McDonald says, "Who would be more deserving of an additional priority question, a survival of clinical death, cardiac arrest, or a born-again Christian?" So I like this question. You get the joke, right? The priority question rules are that you can do it once per your lifetime but what if you have more than one lifetime? And the options are physical reincarnation, I guess, after clinical death, or being a born-again Christian. I think I'm gonna give the surprising answer here. I think the born-again Christian is more deserving. Neither one are deserving at all, I have to say that but by the spirit of the game, what is meant by being born again? Neither one of these are really getting a new life. There is some sort of figurative, imaginative language being used when we talk about a different life. So when you die in the sense of clinical death on an operating table, for example, and are revived, in a very real sense, you are certainly the same person as you were before the operation started. You're never exactly the same person just as you're never exactly the same person now as you were an hour ago. Things have changed you a little bit, so you're different a little bit. But there's a continuity of overall both physical matter and intellectual state and memories and things like that. The fact that maybe some doctor standing next to you declared you not to be alive anymore doesn't really reset your priority question counter. It is an interesting question about starting and stopping computer programs. If you think that an AI could be a conscious agent, what happens if you stop it from running and then start it again later on? Is that something that still counts as the same lifespan? But we're not gonna get into that right now. AIs do not get priority questions, sorry. The born-again Christian, of course, is an even more figurative notion of being born again. But if you take it seriously, then what you're saying is that that person, through their new relationship to Jesus, is now a new person. And that's actually closer to what I would count as deserving of a new priority question because in the sense of Laurie Paul and transformative experience, if you change who you are, how you think, what is important to you, what your goals are, what your values are, that's closer to me to being a new kind of person than simply having your heart stop for a little while, whatever the criteria for that are. So again, neither one of them gets another priority question, but changing who you are inside is actually closer to qualifying.

2:12:42.1 SC: Steve Odendahl says, "Your recent solo on interpretations of quantum mechanics led me to take a look at the Big Mysteries Survey dashboard." This is referring to the survey that was done by Niayesh Afshordi and Phil Halper, asking physicists what their big questions were, or what their answers were to big questions, I should say. So, the Big Mysteries Survey dashboard. And Steve says, "I was surprised to see under gravitational anomalies that dark matter as the explanation for the observed rotational rate of galaxies did not get a majority of the votes. What is your view on this question, and why do you think there is significant support for other explanations: MOND, quantum gravity effects, primordial black holes?"

2:13:27.7 SC: I don't really claim to know the answer to this. You would have to do a better follow-up survey for that. Why anyone would think that quantum gravity has anything whatsoever to do with rotation curves of galaxies, I have no idea. And primordial black holes, of course, are dark matter. If they exist and they have mass and there's enough density of them, then they're just dark matter. So that's not even a separate category. So really the only plausible explanations are MOND or dark matter. And as I've said before, MOND is ruled out by data, by the cosmic microwave background. But I believe that probably most working physicists don't know this 'cause they don't think about it that much. Physics is a highly hyper-specialized field. If you asked me about what are the leading candidates to explain high-temperature superconductivity and gave me a list of options and forced me to choose, it would be basically picking a random number. I have no expertise in that field and I don't pretend to. I do think that the people who are experts could do a better job in spreading the word about what is allowed by the data and what is ruled out but we do the best we can, and it's up to others to listen.

2:14:36.9 SC: Fabian Rosdalen says, "I'm getting into research and reading papers and struggling with organizing and remembering what papers I've already read and things I wanted to note from them. How do you organize papers that you read?" So the honest answer to this question is like many related questions about like what is my writing style and what tools do I use, which is that I'm a mess. I don't have any systematic way of doing this. I never have. I have a pile of papers, and I print them out, and I print out other copies 'cause I forgot that I printed it out before, and I forget that I've read a paper before, and it's just very, very haphazard and that's the kind of personality type that I have.

2:15:17.9 SC: It's true there are too many papers out there right now to keep track of. The other part of the answer is that there are apps or software packages you can buy to help you with this. I've recently discovered Zotero, I'm getting no money from this. This is not a paid advertisement, but Zotero does quite a good job for me of organizing papers. And it's also shareable. That's why I stumbled upon it, because my research group at Hopkins is sharing a bunch of papers together. So you can have, it'll save papers, both the links to them and also the PDFs so you can actually read the papers, and it will output references like BibTeX files and things like that, and you can share them among groups of people who are doing research together, so I think it's a good way to organize things. Again, I'm still not very good at it. It's more likely that if I have a half-baked memory of having read a paper that I will go back to either INSPIRE or Google Scholar and look for the paper again. That's just how I roll.

2:16:19.1 SC: Donald Wilcox says, "Since the energy density of spacetime remains constant as it expands, where does the added energy come from? Please speculate if this is not known." So only for the cosmological constant, only for the vacuum energy does the energy density remain constant. But the answer to where the energy comes from is nowhere at all. Energy is not conserved. You can Google this. Sadly, because my blog is down, I can't point you to the blog post, but I have a blog post called "Energy is Not Conserved" where I explain that in general relativity, the energy is just not conserved. Now, this is a contentious statement because it depends on what you mean by the word energy. There were other questions, actually questions in the AMA that I didn't get a chance to answer this time around about why don't we just define energy to be something that is conserved rather than trying to define it separately and then proving it's conserved?

2:17:09.8 SC: Well, the answer is energy has a meaning when you have laws of physics that are independent of time. Noether's theorem, which we talk about in my Biggest Ideas books, says that if there is a symmetry of nature, a continuous smooth symmetry, then there will be a conserved quantity. And energy is defined to be the conserved quantity under time translation invariance. So the fact that the laws of physics stay the same from moment to moment in time imply the existence of a conserved quantity, and that's what we call energy. It's not just we come up with a bunch of equations and add them together to get something that is conserved.

2:17:46.9 SC: Now, in general relativity, you have a choice. Do you try to come up with a definition of energy following Noether's theorem that includes both the gravitational field, the curvature of spacetime and all of the matter fields within it? If you do, you can do that, you can try to do that, but you run into conceptual difficulties. The expression that you end up with is not local in space, and that might bother you. More importantly, if you live in a closed universe, the total energy you get is zero, just as a number. No matter what is happening inside that closed universe, the total energy is zero. It's a topological invariant. And you can sort of hand-wave your way into saying that there's energy in matter that is exactly compensated by negative energy in gravity, but that's more just a set of words to make you feel better than a really helpful way of saying what's going on. The other thing you can say is, okay, let's put aside the energy in spacetime and just think about the energy of stuff in the universe. But then in an expanding universe, the relevant laws of physics are not time translation invariant because the universe is expanding, things are changing. The arena in which things are playing out is not invariant under time translations. It's different from moment to moment. So there's no reason for energy to be conserved, and indeed it's not. And furthermore, that lack of conservation has nothing to do especially with the cosmological constant, it's just as true for photons. Photons, a gas of photons, loses energy as the universe expands.

2:19:23.0 SC: Now, it's not that all hell has broken loose. You took what used to be a very simple rule saying total energy is constant, and you replace it with a different rule called the covariant conservation of energy, which says, given that space and time are changing in the following way, here's how the energy changes. And so if you want to, if it makes you feel better, you can say that it's the expansion of the universe that causes the energy to get added. That's not especially satisfying because both the expansion of the universe and the added energy have no limit, they can go on forever. So it's not like you're using up some finite resource. It's better just to say the universe is changing, spacetime is expanding, the ordinary notion of energy conservation doesn't hold anymore.

2:20:07.9 SC: Anonymous says, "I'm about to move in together with a partner for the first time. Got any reflections from your experience making the same transition that you would like to share?" I like trying to answer these questions 'cause I like venturing outside the usual topics that we cover. But I gotta be honest like I usually am with these questions, when they're personal advice kinds of questions like these, you shouldn't believe anything I say because every person is different and every pair of people are different. You have to have your eyes open to the particular challenges that are facing you rather than listening to someone else's general advice. In general, especially depending on your age and your prior experience, you may or may not have lived by yourself for a very long time, I don't know. And you may very well have fallen in love with certain habits, certain styles of living. And someone else who you're moving in with might have their own styles and habits, and you need to somehow find a happy medium there. There's obvious cliché things to say, like communicate with each other. Like if someone wants to load the dishwasher in a certain way and someone wants to load it in a different way, don't just rearrange it while they're not looking. Talk to each other about it. I think that's definitely a way to go forward. But I think more importantly than that, you need to decide what are the parts of your cherished habits that you really care about and which ones are the ones you don't care about that much, and you have to be willing to give up on some of them. Whether it's who takes out the trash or who cleans the cat box or how you load the dishwasher or whatever. When you go to bed, when you wake up, all of those things, how clean you are and what the morning routine looks like. These are all things you have to negotiate. Some things that you will have thought were really, really important to your lifestyle, if you really think about them, you realize, you know what? Those are not that important. I could give up on those. I can happily compromise on those.

2:22:12.0 SC: And the little bit of personal experience I can say is that the chances that it will work out the best are when both members of the partnership, both people in the relationship, are really very devoted to the happiness of the other one. If your goal in the relationship is that you think that person makes you happy, that's good. But it's even better if you get happiness from them being happy. If the two of you both actually value each other's happiness for its own sake, not just because if they're happy, they're nicer to you, but you actually get something out of them being happy, then you will both find yourself working together to make things work in a relatively painless way. Otherwise, yeah, the communication thing is important. If someone does something to annoy you and it's the kind of thing that you're gonna have to tell them about, tell them about it sooner rather than holding it for six months and letting it all burst out. That's a bad strategy. I can say that in an almost universal way.

2:23:11.2 SC: Erkan Sertelli says, "How do you measure formally the usefulness of an emergent description? Let's say I set a model where every possible microstate maps onto the macrostate zero and the theory says zero always evolves to zero. This model is perfectly predictive under the coarse graining, but obviously useless. Perhaps the grains are too coarse in this example, but is there an algorithmic way of comparing its usefulness to something like fluid mechanics?" Well, I think that the whole thing with emergent descriptions is there can be more than one of them. There can be multiple layers of emergent description, and at each of them you're keeping some information and throwing away other information. And the point is, it's not arbitrary. What you're doing is trying to ask yourself the question, how much information can I throw away and still maintain some predictability? So if I flip a coin, for example, there's a level of description at which I say, I'm a human being, I have some meager amount of control over my hand and my finger and the air currents and things like that, and the best I can tell you, if I flip a coin high in the air, is it's gonna be 50/50. That's an emergent description because the microscopic theory is the position and momentum of every atom in my hand and in the coin and in the air and everything. And in that description, I could tell you exactly what's happening. I could tell you whether it's gonna... I could predict heads or tails, with very high fidelity. So both of those descriptions are valid. One is saying with an enormous amount of information, you can predict the coin flip with high fidelity. The other is saying with much, much less information, the best you can predict is 50/50. But still, that can be useful. Like if it's a six-sided die rather than a coin and you say, well, I predict that the chances of rolling a four are one in six, that's very, very relevant information, even though it's essentially random. So you look for those sweet spots where you have included enough information to make useful predictions without just having a huge amount of information. And there's no one right answer to that, and there's no algorithm for finding it. People have tried, and I have friends who've thought about, I mean, Ed Seth and others have thought about this question of where are the emergent sweet spots where you get the most out of the least input. But I don't think there's one agreed-upon algorithm for that. They invoke this notion of Granger causality to quantify that, and other people have had different ideas. But in practice, it's more like what we can think of is what works.

2:25:51.1 SC: Mirza Hadzic says, "Multiverse theories imply countlessly many copies of myself across reality. Physicists usually treat these as separate consciousnesses even while they remain computationally identical. But if consciousness is an emergent phenomenon, shouldn't we view it as an abstract mathematical entity like the number five? Until these branches actually diverge, wouldn't it make more sense to say there is only one identical conscious experience existing simultaneously across multiple physical substrates rather than many separate copies? Why should an emergent computation care about which physical reality or realities it emerges from?"

2:26:26.9 SC: Well, part of the answer to a question like this is it is a matter of taste. It is up to you. Like I kind of don't care to some level whether you want to call two literally identical copies the same entity or whether you want to call them two different entities. However, my preference is to call them two different entities. That's where my taste leads me. Your taste may lead you somewhere else. And part of the reason is what matters is not just what is going on but the entire set of things that might go on in the future, counterfactually. Even if they won't separate effectively in the future, they could. We can imagine different things happening to them in the future, and they would react differently 'cause different things are happening to them. So in that sense, if I want to not just say what is happening right now, but also have an understanding of what is the space of possibilities going forward, treating two physically distinct, non-interacting copies as two different things is just a sensible thing to do. It has nothing really to do with consciousness or anything like that. You could say the same thing about two perfect spheres or two copies of the sun or whatever.

2:27:35.2 SC: Malte Übel says, "The universe seems surprisingly young. Earth and life on Earth has been around for a substantial portion of it. Should we be surprised, and what does it tell us about being an average observer?" I don't know if we should be surprised, but I do think that we should make a bigger deal out of it. Of course, the statement that the universe is surprisingly young is relative to some notion of oldness or youngness. One way of saying it is that the last star will sort of peter out, according to our best current projections, in about 10 to the 15 years from now. And the universe right now is about 10 to the 10 years old. So a factor of 100,000 current universe lifetimes before the last star burns out. So that's very, very young compared to that way of dividing things. But here's another way of dividing things. Look at star formation in the universe. So not how long the stars will shine, but when they are created. Most of the stars that will ever be created in the history of our universe have already been created. We are on the far side of the star formation peak. So in that sense, the universe is not surprisingly young. We're sort of at the era where interesting things are happening or even maybe after the peak era of interesting things happening by some ways of measuring it. Again, other ways of measuring it give you different answers. Don't get too excited about that. But I do think that compared to the equilibration time of the universe, the time for it to all empty out and go dark, the universe is pretty young right now. And I think that that is an important fact to notice, but it is not what I would call surprising because there's a burst of activity in these early billions of years in the history of the universe, and we are just part of that burst of activity. So in retrospect, I don't think it's that surprising that that's where we find ourselves in history.

2:29:33.7 SC: Richard Kynenborg says, "Priority question: Do functionally complete logic sets like AND and NOT have a direct use, analog, or expression in physics, or are they just of use in computation?" I'm not gonna give a great, satisfying answer to this because I'm not quite sure what it means for logic gates to have a direct use in physics. Can I get through life without mentioning them? Probably. In terms of physics, I could probably formulate physics without using those operations. Can I use those operations in formulating laws of physics if I choose to? Probably. I think that's very plausible. I think that in either case, what we're talking about are descriptions of the world. So do you think that plus and equals have direct uses, analogs, or expressions in physics? Like there's no place out there in the physical world I can point to and say, "Oh, yes, that's plus," but nevertheless, the idea of plus, the idea of addition, is super useful in formulating laws of physics. So if that counts, if the way that we use plus and equals and other arithmetic operations count as in your mind, having direct uses in physics, then I would say AND and NOT have direct uses just as much. Yes.

2:30:56.7 SC: Nanu says, "My question is, what does your gut feeling tell you about spacetime? Is it infinite or finite? If it's infinite, how do you personally feel about such potential reality, and what does that tell us about all the vectors in Hilbert space?" Look, I think that you shouldn't have gut feelings about this kind of thing. Like there's something called gut feelings. They come from somewhere, from a combination of evolution and your personal history and your diet, I guess, if it's your gut feelings literally, and certainly your education and experience, and none of those have any bearing whatsoever on whether spacetime is finite or infinite. I think that the right question to ask is can we build mathematically consistent models that fit the data? And it's very possible that the best fit to the data is a model that invokes infinity in some crucial way. It is also possible that the best fit to the data doesn't invoke infinity in any crucial way. I'm entirely 100% open-minded about either one of those possibilities.

2:32:04.5 SC: C. Gerlando says, "I'm curious about your thoughts on the philosopher Stanley Cavell, who I believe was at Harvard during your graduate years there." So, aside from me, he was, I think he was there when I was at Harvard, but I never met him or took a course with him or anything like that. I never read any of his stuff, to be honest, so my response to the question is gonna be based on what's in the question, not on my deep background knowledge of Stanley Cavell thought.

2:32:31.2 SC: So anyway, the question continues. "A recurring theme in his work is that many philosophical problems arise not from a lack of information but from a desire for a kind of certainty that human life structurally cannot provide, so that the task is not to resolve skepticism once and for all, but to acknowledge and live with the conditions that make it recurrent. This underwrites a kind of political humility since it signals a resistance to any program that promises to finally get human life right once the right theory or technology is in place. In relation to your own work, I think his suggestion would be that even a final physical theory wouldn't touch the kind of existential uncertainty he has in mind because that uncertainty doesn't arise from gaps in our knowledge, but from the conditions of being a finite creature who has to act and commit without guarantee. Do you think scientific inquiry genuinely resolves the sorts of questions that Cavell regarded as permanently constitutive of the human condition? Or is there a domain where you'd concede that acknowledgment rather than resolution is the right response? And if so, where does that domain begin and end for you?"

2:33:30.7 SC: So, like I said, I'm not super familiar. I know who Stanley Cavell is, but I'm not familiar with his work. From the description in the question here, I'm extremely sympathetic to that point of view on the universe. And I think I would state the distinction raised in those latter sentences a little bit differently. The idea of a Theory of Everything, a complete and comprehensive physical theory of the world, is sort of a compact statement that summarizes a whole bunch of things that actually happen. When two billiard balls bump into each other with these velocities and these angles, this thing is gonna happen. So the Theory of Everything summarizes all of that stuff. It certainly doesn't summarize what actually happens.

2:34:18.2 SC: Now, you might even be able to come up with a compact summary of that in a sort of many-worlds kind of scenario. I think in a single-world kind of scenario, if you think of the world around us as all that exists, then you're stuck with the minimal, compressed, informationally dense description of our universe nevertheless being very, very, very long. 'Cause there's a lot of stuff in the universe. You might hope in a many-worlds context that the overall wave function of the universe is actually simple, and what we see as the complexity around us is just reflection of the fact that we're only seeing one little branch of the wave function of the universe, not the entire thing.

2:34:58.0 SC: Okay, put that aside. I think the relevant part of the question is that even if you had the Theory of Everything from a physics point of view, as a human being, you are finite. You are finite in knowledge about what is actually happening. You're finite in the ability to calculate and think about what that means, what is going on around you, what it actually implies for what's happening next and what's going on elsewhere in the universe, things like that. And furthermore, we're not perfectly rational. We're not perfectly good observers of the universe. We're not perfectly good thinkers about what we do observe implies, or any of that. We're just finite. We're finite and we are imperfect in all sorts of ways. And I think that that's not going away. I do think that that is constitutive of human nature, at least what we mean by human nature as we think of it right now. I can't say, like as I already admitted, I don't know what is gonna be the successors to human beings a billion years from now, so let's ignore that and think about real human beings. And furthermore, so I do think that human beings are finite, limited, bounded. And I do think that that boundedness has important practical implications, and political humility is one of them.

2:36:10.8 SC: I think there's a very common mistake, or at least let's say a failure mode that exists in a lot of philosophizing where you say, okay, here's the messy world around me. I'm gonna try to make sense of it by inventing a system that I think describes it well, and maybe it's not just description of what happens, but maybe even a normative theory about what I think should or should not happen. And then I'm gonna just assume my theory is right, or maybe not assume, but I'm gonna believe my theory is right 'cause I think I have good reasons to do so, and I'm gonna extend it to realms where it hasn't been well tested or does not comport with my intuitions or instincts or whatever. I think that's an easy way to go wrong in philosophy. It's kind of the worry I have about people like Peter Singer, former Mindscape guest. Peter Singer has a theory, his version of utilitarianism, that he takes very seriously, and it leads him to conclusions that I don't agree with. And his response would be, but it's the utilitarian right thing to do. And I would say, well, maybe that's not a statement about the world, but a statement about a failure of your version of utilitarianism.

2:37:18.4 SC: So I do think we should be humble. I do think we should be open-minded about the possible limitations of our not only theories of the universe, but our theories of right and wrong. And again, that has practical implications. I always mention Elizabeth Anderson here when she appeared on the podcast, making the point that it's more practically useful to think about how to take the world as it is right now and make it a little bit better than it is to think about what the perfect world would be like and then hope to get there in some way because we don't know what the perfect world would be like. We're too limited to figure that out. So I do think that taking us seriously as tiny, fallible beings in a vast universe is a very smart and wise thing to do.

2:38:02.4 SC: Niles Tahar says, "Is there any merit to the idea that position isn't fundamental? That on some deeper level, what we perceive as distance emerges from a more fundamental description of reality? Does quantum entanglement provide any evidence in that direction, or is that a misconception?" I'm gonna be very brief 'cause I've already mentioned, I already talked about today things like this. Yeah, I think that there's merit to that idea. In fact, I would go further than that. I think that the strong implication of quantum mechanics is that position isn't fundamental, because it's not in quantum mechanics. Position is an observable in quantum mechanics, just like many other things are observables. It's on exactly the same metaphysical grounds as something like momentum. And no one thinks that we live in momentum space. They think we live in position space. So I think that quantum mechanics by itself, not to mention more modern attempts at quantum gravity and things like that, make position look like it is not fundamental at all. Not to mention things like the holographic principle, which makes things look wildly non-local. So we don't know. We could be wrong. There's absolutely smart people out there who think that position is fundamental. But I would say there's plenty of reasons to doubt that and to think hard about what that might mean.

2:39:18.1 SC: Evan Doran says, "In your last AMA, you discussed what you do and don't consider acceptable uses of LLMs in the process of writing and editing a paper. That got me thinking, what if authors were encouraged or even required to include their LLM prompt history as a digital appendix to paper submissions? I've always supported the use of digital appendices to attach raw data or other info that can be used to improve transparency and allow others to double-check and validate the work. A similar strategy could be used to see how authors used AI in their workflow. Do you think there's merit to this idea?" Well, roughly speaking, no. I don't think there's much merit to that for two reasons. One is very practical. How do you get people to give you their AI workflow? Maybe they just don't want to. Maybe they say that, oh, I didn't use it, but they really did. It's just completely unenforceable in practice, and therefore you run the danger of giving a leg up to the people who will violate that rule that you just invented. But the other thing is, I do think it is appropriate for scholars to separate out the process by which they came to their conclusions from the conclusions themselves. I certainly wouldn't want a rule that said all of my scratch paper and notes that I was taking along the way have to be submitted every time I submit a paper. Like I make mistakes. Maybe I'm embarrassed by the mistakes, maybe I was doodling. There's a whole bunch of things I just don't want the world to hear about, and I think that's fine. That's the way it should be.

2:40:46.5 SC: So I think that I'm sympathetic with the goal that you're getting at, but I don't think that's quite the way to do it. There might be some circumstances when including AI prompts into the text of a published intellectual scholarly paper is appropriate and interesting and good, but I definitely don't think it should be mandatory or even expected.

2:41:12.2 SC: Randall Davis says, "Is there anything interesting to say about a hypothetical pair of entangled particles where one is sent into a black hole with an observer? When it's measured beyond the event horizon, would the entangled particle outside the event horizon still know?" Well, no, it would not, but it never does. That's the whole point of spooky action at a distance is that the entangled particle outside the event horizon can't be described any differently once its partner... Well, if you have... Let's go back. Sorry, I'm bungling it here a little bit. I have two particles. I entangle them. I move them apart. Alice has one, Bob has the other. Alice may or may not make a measurement of her particle. Bob knows that the particles were initially entangled and he uses that to make a prediction for what his measurement outcomes will be. The fact is that Bob's best prediction of what his measurement outcomes will be are the same before and after Alice makes her observation, as long as Alice doesn't tell Bob what the measurement outcome is. If Alice measures spin up and the two particles we know were entangled so that their spins were opposite, then she could tell Bob, "Oh, I measured spin up," and then his prediction changes. But before he knows what Alice's measurement outcome was, his predictions are the same. There's no observable difference in Bob's spin just because Alice did a measurement. Now, if you're separated by an event horizon, that's just, as far as I can tell, a fancy way of saying Alice is never going to tell Bob what the measurement outcome is. So it's exactly the same as no event horizon, just a promise that Alice and Bob are not going to communicate the results of their classical measurement outcomes.

2:42:56.3 SC: Simon Carter says, "From one over 50s guy to another, have you had a glow up? Just saw your recent New Scientist interview on YouTube and you look great. Have you found a way to reverse entropy?" So I like questions like this that imply that I'm looking good, but the sad answer is no, I've not had a glow up. I don't look any better than I ever do, and entropy is not being reversed. It is working on me. My age is showing more than it did in the past. That's just how life works. I've not had any work done or any new cosmetic routine or anything like that. The real reason I wanted to answer the question is to just let people know when you appear on these videos... Like so I recently did a YouTube video for New Scientist where we talk about quantum mechanics and also a little bit about the new paper on the cyclic universe model. You don't control as the person being asked questions, the space you're in, the lighting, the video camera, a million things that actually make a big difference to how you look. I mean, you can comb your hair and you can get dressed in the certain way you want to get dressed, but other than that, there's a lot that is outside your control. And the fact is that observations in the physical world are not value-free. Taking a photograph or a video of someone matters a lot what your equipment is, what the lighting is, what the environment is doing, and so forth. So sometimes you're gonna look good, sometimes you're not gonna look good. You just have to roll with those punches.

2:44:24.5 SC: Okay, I'm gonna group two questions together. One is from Blagoja Alampieski, who says, "I've heard you say a few times that quantum mechanics isn't deterministic when talking about free will but if you are an Everettian, I would have thought that it would be. When a decoherence event occurs, both worlds actually exist and you're on both. Is there something I'm missing?" And Mark Kumari says, "Returning to everyone's favorite topic of free will, I think I'm mostly in your compatibilist camp, but here's where I get stuck. If I choose to go left rather than right, the underlying arrangement of fundamental particles in my brain is different in those two scenarios. I assume I can't control the arrangement of particles, rather their state determines my choice. So if the particle configuration already fixes that I'll go left, in what meaningful sense could I have gone right? I understand that I'm not Laplace's demon. We use everyday language to say I could have gone right and contemplate what could have been. But if we replayed the universe from exactly the same physical state, wasn't it always going to be left? Ignoring the quantum, as we know that doesn't help the cause, is that an accurate understanding of compatibilism, or am I missing something?"

2:45:23.8 SC: So these are not the same question, but they're sort of in the same bucket that I'll put them in. For Blagoja's question, it's very clear, and I have said this before, I'll say it again. Everett says that the wave function of the universe evolves deterministically but you and every other person in the universe does not experience the wave function of the universe. So the right thing to say, which I typically say when I'm talking about this, is the universe that observers experience is not deterministic. And that's true. That's just a way of saying that you cannot predict, even if you knew exactly the quantum state of the universe, what the measurement of some spin going through a Stern-Gerlach experiment was actually going to come out to be. That's all that it is. It's the difference between the global view that God has but no people have versus the actual view that individuals have.

2:46:18.8 SC: Now, to Mark's question. This is a classic question. I think this is an important one that philosophers don't really get as right as they could, although some of them get it very right. One way of thinking about free will is to say, "I want to know whether my actions, whether my choices, whether my decisions could have been different." And if they could not have been different, then I don't think I can have free will. That sounds like a good argument. It sounds pretty convincing at face value. But there's a huge, huge problem with that argument, which is, what do you mean by "could have been different"? When you ask the question, "Could things have been different?", you mean keeping what fixed? You have to say what exact parts of the universe I keep precisely the same when I ask, "Could things have been different?" For example, if I keep fixed precisely what happened and I say, "Could things have been different given what happened?", no. It's just a matter of logic. It has nothing to do with physics whatsoever. If I know what happened, then that's what happened. There's no way it could have happened differently. That's therefore not what people mean usually when they talk about free will. Usually what they mean is, given some past condition, could what have turned out in the present have been different? Well, what are you fixing about the past condition? If the laws of physics were deterministic, if classical mechanics had been right and you fixed the microscopic state of the universe, then nothing different could have happened. But guess what? You're not Laplace's demon.

2:48:06.1 SC: So even if you can imagine that the same exact thing would have happened if the microscopic state of the universe had been the same, who cares? No one has access to that. It is completely irrelevant for any important question about human behavior, responsibility, agency, anything like that. The appropriate question is, given the macroscopic state of the universe, even as we might imagine the best possible observer could have measured it, could something different have happened? And the answer is yes. Different things can happen because the world is complicated. Finally, quantum mechanics is not irrelevant to this particular question of could things have happened differently. Some macroscopic observables don't depend on quantum uncertainty. You have quantum uncertainties but they all sort of average out and you get clean, crisp classical behavior. Other classical observables do depend on quantum uncertainty. When will the Geiger counter click? That is not a matter of averaging out many, many different random things. It's one random thing, and the randomness truly matters. So even if you were Laplace's demon and you knew the exact quantum state of the universe, given what we just said in response to Blagoja's question, you can't predict what is going to happen and therefore, in a very real physical sense, something different could have happened.

2:49:35.3 SC: James Pertusi says, "My question is about Hawking radiation. I understand that pairs of virtual particles pop into existence and then quickly annihilate each other, and this is happening everywhere all the time. I understand that when this happens near the event horizon of a black hole, sometimes one particle of the pair can cross the horizon and ultimately fall into the singularity, leaving the remaining particle to fly off into space, and that makes it appear that the black hole is emitting radiation. I'm told that the constant rain of abandoned particles will slowly erode the mass of the black hole. This is where I'm confused. It seems to me that 50% of the time, the particle that crosses the event horizon would be the negative particle, and 50% of the time it would be the positive particle, with the net effect to the mass of the black hole being zero."

2:50:18.1 SC: So, nope, that seeming to you there at the end is not correct. 100% of the time, if by positive and negative you mean positive energy or negative energy, negative energy particles cannot escape from the black hole. There's just a feature of physics, according to the laws of physics as we know it, that if you have a particle in front of you and you measure its energy, you will always get a number greater than or equal to zero. In fact, it will never be zero if there's actually a particle there. The energies can only be positive for particles that are in front of your nose. The only reason that a particle inside a black hole can have a negative energy is that it's not in front of your nose. It is far away. It is on the other side of an event horizon. And the fact that spacetime is curved in between you and the particle changes the formula that we use to calculate the energy. And so when we say the particle has negative energy, we mean from the perspective of an observer outside the black hole. And so there's this feature of general relativity and the Schwarzschild solution or other black hole solutions that even though every particle has positive energy from the point of view of a person right in front of it, black hole geometries have the feature that there can be particles inside the event horizon that appear to have negative energy from the perspective of an observer outside the event horizon. But that's a strict way of saying it. If the particle is outside the event horizon itself, it can only and ever have positive energy. So it's not a random number flip between those two choices.

2:51:52.8 SC: Lois Bolous says, "I heard you talking about how some guests would not understand compatibilism in the way that you mean it and actually take it to be out of this world free will. Have you thought about the tension between fighting for a word versus giving up a word?" I have found that instead of insisting, when I say X, you understand Y, but I mean Z, bringing up a new word to say, "Okay, I'll give you that X means Z, so to mean Z, I'll use OX, not X," can help conversations. But then you give up some territory because if your definition can win, it does a lot of the spread for your point of view. For compatibilism, it would be asking opponents, "How should we call a position where we admit that the mind does not have special powers on the laws of physics, but where we find it relevant to keep using the language of responsibilities?" My assumption is that these conversations would go differently.

2:52:39.6 SC: So I get the point you're trying to make. Sometimes you're trying to understand the meaning of a word or define it. Other times you're trying to really understand substance, and the latter is much more interesting than the former if what you're trying to do is understand how the world works. I don't think that compatibilism is the problem, though. I mean, what do people think compatibilism means? It's not one of these things like illusionism in the philosophy of consciousness where you talk about, "Oh, I'm an illusionist about the philosophy of consciousness," and people say, "Oh, you think that consciousness is an illusion?" and they have to say, "Oh, no, no, I don't believe that." Compatibilism is what it says. It says that the underlying laws of physics and free will are compatible with each other. That's what the word says. I can't think of a better word to use. I do think that free will might be a term that is not very helpful, and I've tried to stop using it. When I was on Sam Harris's podcast, I, before the podcast, said, "Would it be okay if we just agreed not to use the term free will and just talked about what happens and what doesn't happen?" No, he was not okay with that. So we're stuck with that. I'd be happy to change free will, but I think compatibilism is as good as it's gonna get.

2:53:51.9 SC: Stephen Goodwin says, "I find your explanation for the arrow of time fascinating, and it makes sense to me that time moves in a certain direction because entropy was low in the past. Could you please explain how the direction of time could be dependent on the past state of entropy without the speed of the passage of time being dependent on the rate of change of entropy? How can time adopt a binary state of either forward at one second per second or backward at one second per second?" Neither one of those. There's no such thing as the rate of change of time. That just doesn't apply. One second per second is how much time elapse per unit time. That's always gonna be true in whatever direction you want. Time is just like space. Time can exist without an arrow. Time is a coordinate on spacetime. We can easily imagine situations in which there's no entropy or there's no change in entropy and there's no arrow of time but there is still time, just like there is still space even though there's not an arrow of space. So time is a way of locating things in the universe. The arrow of time is an anisotropy. It is a directionality to some things happening with respect to time. It's not a rate of time itself. It has nothing to do with time itself. It's just a feature of the evolution of stuff in the universe that is oriented in a particular way with respect to the time coordinate. That's all.

2:55:19.2 SC: Anthony Rubbo says, "How were the workshops?" Oh, so I was in Switzerland for a workshop and then in Ireland for a workshop, both on the philosophy of physics. They were a lot of fun. They were really good. These are sort of my people talking about the foundations of physics and one was on the metaphysics of spacetime and how it can emerge, and the other one was on the arrow of time. Plenty of people who were former Mindscape guests were at the various workshops, Laurie Paul, David Albert, Tim Maudlin, David Wallace, Barry Loewer. So a lot of good old friends that I could talk to and so forth. Sakshi Dhulani, who was my collaborator on the recent cyclic universe paper, was at one of them. I wouldn't say there were any great breakthroughs or anything like that, but that's not the right way to judge a workshop. What you want to do at a workshop like that is talk to people, share ideas, get a feeling for both what they're thinking about these days and how they react and respond to your ideas.

2:56:21.5 SC: I think that we don't understand very well where ideas come from. And sometimes people say like conferences or in-person meetings are overrated in science, but I think completely the opposite. I think that just the process of interacting, sharing ideas, even if five years later you've forgotten that interaction, all of those processes can have a huge effect on the ideas that you come up with down the road. So, in general, I would say, yeah, the workshops were great. It's definitely a fun thing to do.

2:56:55.5 SC: Calvin Firth says, "Do you ever feel FOMO, which is fear of missing out for the old people in the audience, specifically in your research? I'm a young physicist and there are so many different research topics that I want to pursue, but there's no way I could pursue them all. This makes me feel anxious at times like I'm gonna miss out on something really cool and that I better choose the right topic. Do you ever have similar feelings?"

2:57:16.7 SC: Well, look, you're gonna miss out on some things 'cause there's far more interesting things going on than you can possibly be responsible for. I think that, but I'm extremely sympathetic in the following sense. It's not so much FOMO for me, but I do feel like there's just too many good things to think about, and therefore I want to spend a little bit of time thinking about all of them. And that gets in the way of concentrating on thinking about one thing at a time and making progress there. Certainly most physicists who are very successful are more likely to concentrate on one thing at a time, basically, and make progress that way. I do think that there's a way to make progress, philosophy as well as physics for that matter, by stretching yourself a little bit and trying different things and therefore being able to draw connections that you wouldn't otherwise draw. But it can also just be an excuse to have fun and learn a lot of things and think about a lot of things, and maybe that's what I'm doing. I'm not going to deny that. Especially when you're young, I do think that for better or for worse, as a young academic, as a young scientist, as a young physicist, whatever it is, you need to come up with an identity. I mean, it's a killer if you go to a conference or you're talking to an older, respectable physicist and they say, "So, like, what do you do? What are you working on?" And you stumble for an answer, or you say like, "Oh, I work on lots of things." You've already lost their interest when you say that. You need an answer to the question, "What is it you work on? What is it you do?" Even if you do more than that like even if in your mind you are rich and multifaceted, it's good for purposes of communicating with other people to have a short, punchy answer to the question, "What do you do?" or "What are you working on?"

2:59:00.3 SC: And likewise, it's important, it's useful certainly, to have a short, punchy and true answer to that question because you really want to get to know something very specifically and become the world's expert at it as much as you can and really show that you can make a contribution to this kind of thing. I've known a lot of young physicists who, graduate student level, not assistant professor or postdoc level, but grad students who are just starting out, and some of them say like, "I really want to meet this physicist and talk to them," or "I want to give a seminar" or whatever, because that's how to get known. "I want to be known out there." And I feel like saying, "But you haven't done anything." There's nothing for them to be impressed by. You have to first do something and then people will be impressed by what you've done. And you kind of start by picking something. And this is something that is absolutely an issue when you're young and you could do anything 'cause you could do anything. In terms of doing the right thing, you've gotta find the intersection of what you're good at, what you love doing and what the rest of the world cares about. And how to figure out what that intersection is, that's a longer conversation that you should be talking about with your advisor or whatever, depending on how old you are. I don't know, you might be young in the sense of being an assistant professor, I don't know. But I would say think of it as fun. Yes, there's some danger that you'll be missing out, make the wrong choices. But also, it's kind of exciting like bungee jumping is exciting. You have to commit to it, and then you have to see where gravity pulls you toward.

3:00:38.0 SC: David Carr says, "I was watching your Biggest Ideas in the Universe YouTube series and you were talking about Humean versus anti-Humean views of physics and remarked that you mostly hold Humean views. Is this still true? For example, my understanding is that believing in the wave function of the universe as real would be anti-Humean. Am I misunderstanding what Humeans or anti-Humeans believe?" Well, I think it depends on your construal of the word Humean. I mean, remember, Hume was working in the 18th century. He didn't know about quantum mechanics or general relativity or whatever. So he would have said that the world is a set of things happening at events in space and time. If you knew what was going on at every point in space at every moment in time, that's the entirety of what happens. And a lot of modern-day Humeans do in fact talk that way. They sort of have borrowed exactly that. They've not updated their way of talking because of quantum mechanics or anything. But I don't think there's anything stopping you from updating it in terms of quantum mechanics. Instead of saying what happens at every point in space and time, you just say what the quantum state of the universe is at every moment of time or whatever. In other words, the complete mathematical description of the universe is the Humean mosaic in the modern physics way of doing it. You have to be willing to update what ingredients are in your ontology without changing the basic attitude toward that ontology, which is that what exists is the stuff, not some set of dynamical rules bringing that stuff into existence.

3:02:08.5 SC: Dan R. Says, "I'm a professor teaching social science courses at the undergraduate and graduate levels. What I've seen over the last few years is that AI plagiarism is quickly eroding the credibility of a liberal arts degree. I believe there are several contributing factors at play. First, many of my colleagues do not actively enforce AI plagiarism violations. Often they lack the energy to construct the time-consuming digital forensics, keystroke analysis and such, that is especially daunting when trying to identify sophisticated plagiarists. Second, there's also a high administrative burden associated with building a case of documentation for academic dishonesty incidents. Lastly, many want to avoid confrontations with students, especially if they feel they're unable to prove 100% improper AI use. As a fellow educator, I'd like to hear your thoughts on the best way to deal with this erosion of academic norms and higher education credibility."

3:02:58.2 SC: Well, I do think that using AI to do your academic work for you among students is absolutely a huge growing problem. And I don't have any clever solutions to this. I think the most basic solution is the one that I use, which is mostly grade on the basis of evaluations for things done in class where you don't have a computer in front of you and you can't use AI. In-class exams or talks or projects or whatever. You can sort of supplement that with papers or problem sets done outside of class as long as those are not most of the grade. And ideally, if you're in a small enough class to do it, or you have enough teaching assistants to do it, when you have a paper assigned, make sure the students don't simply hand in the paper and get graded. Rather, they have to talk to you about the paper. You have to discuss it with them and they have to rewrite it to improve it in a certain way. That doesn't make it impossible to use AI to help or to cheat, but it does make it much harder for them to hand in a paper they don't understand at all. Like the idea at the end of the day is to make the students understand more things. And whatever tools you can use to make that happen, then I think that's great.

3:04:10.7 SC: In terms of like keystroke analysis and whatever, I just don't, once again, think that's at all realistic for the real world. People are just gonna find ways around that too easily. And I agree that if you're teaching a class with 100 students and you think that 50% of them or 90% of them are using AI on some assignments, you're not going to individually spend hours on every student building a case that they are cheating. It's just a fact of the modern world that you have to assign grades based on work that can't be cheated with using AI. And that's too bad, but it's what we have to adapt to.

3:04:48.7 SC: Sean Sullivan says, "After reading your paper Toward a Phenomenologically Acceptable Quantum Cyclic Universe, I had a question. If an advanced civilization manages to survive into the universe's final heat death, their continuous quantum entanglement would prevent the wave function branches from cleanly recohering into an empty state. Does the rigid unitary mathematics of your model guarantee that their survival is fundamentally impossible or would their persistent observation prevent the bounce from happening at all?"

3:05:15.3 SC: Yeah, the rigid unitary mathematics guarantees that their survival is fundamentally impossible. There's not something called the universe obeying the laws of physics and something separate called an advanced civilization being clever and trying to survive it. Every little part of that advanced civilization is just obeying the laws of physics. And so if the laws of physics say that you're gonna decay into thermal equilibrium, there's no clever choices you can make to prevent that from happening.

3:05:44.0 SC: Casey Mahone says, "I'm very interested in the probably fake Einstein quote, 'Coincidence is God's way of remaining anonymous.' It seems possible that the world appears to simply follow emergence from fundamental rules while actually having a teleological direction when viewed as a whole. What do you make of this idea that teleology can be hiding in the laws of physics? And what is your credence on it being true?" Well, as you know, if the question begins with "is it possible that", the answer is always yes. So sure, it's possible that secretly there are hidden fundamental teleological rules driving the universe toward some future state. I would say that the evidence for that being true is very, very close to zero. Both because we don't see explicit evidence of teleology in nature, but even more importantly, we do see evidence of the success of dysteleological rules, things that do not have a future goal in mind. Everything that we know about general relativity and quantum mechanics and the Standard Model and whatever, there's no teleology built into them. There's no obstacle to building up everything we see from them, so there's no reason to believe in teleology. I think that if you're interested in that kind of angle, you have to do much more than just say, "Well, I think it's possible." You have to present a convincing affirmative case for why people should take that possibility seriously and give it a non-trivial credence.

3:07:11.8 SC: Alexander Kondratsky says, "I was fascinated by the cyclic cosmology with a U-shaped entropy curve from the previous AMA. Is there a phase transition with scale invariance where there are islands of different arrows of time? Or does that not make sense unless you talk about the arrow of time of the universe as a whole? It starts to feel like the movie Tenet." So no, there are no islands or anything like that. In our model, and of course there are other models, we're not saying that our model is the only right one, but in our model, the wave function of the universe starts in a very, very specific low-entropy early state. "Starts" is arbitrary. You can pick the starting point whenever you want. But let's start it mentally in a low-entropy early state and let it evolve. And what happens is, when I say low entropy, I mean sort of two things at once. There are very few branches of the wave function of the universe, and on each branch, thermodynamically, the entropy looks low. So both of those things are true. And what happens is over time, more and more branches appear. Measurement happens, decoherence happens, et cetera. And on each branch, the thermodynamic entropy increases. And this happens, roughly speaking, until on all of the branches the universe equilibrates and reaches a de Sitter phase, and then everything recoheres and smooths together and so it's sort of marching in lockstep. I mean, entropy is increasing in each branch of the universe. Is there a probability that the entropy could decrease? Sure. But anytime you have more than like 100 particles in the universe, the probability of entropy spontaneously going down is incredibly low. And there are way more than 100 particles in the universe, so it's extremely low. We don't need to worry about that. Roughly speaking, on every branch, the entropy goes up consistently until it sort of hits a maximum, hangs out there for an extended period of time, and then kind of mysteriously and spontaneously starts decreasing, and the whole thing just plays out backward in time. So on every branch, it's completely consistent, and within every branch, it's also completely consistent. There's never any worry about the arrow of time pointing in two different directions in two parts of the universe that are communicating with each other.

3:09:20.8 SC: Dylan says, "What is your favorite season of The Wire?" I think here my opinions are more or less the same as everybody else's, so I can't decide. The candidates are Season 1, Season 2, and Season 4 out of the five seasons of The Wire. They're all good. Season 5, by consensus, is a little bit less good than the others. Season 3 has individual highlights. There's definitely dramatic events that are very, very exciting and important, and I'm not gonna spoil them for those of you who haven't seen it. But the sort of theme... Every season more or less has a theme. The Wire is really about, I know this sounds very boring, but it's really about the American city, the urban environment in which people live and how the different structures within that city interact with each other and how individuals within that city try to survive and flourish in this environment. And some do and some don't. That's how things are gonna be. But so it picks on different aspects of the city. Like Season 1 is about the police and the drug trade, that's the highlight. And those aspects are there for all the seasons, the police and the drug trade, but that's the focus in Season 1. In Season 2, it moves to the docks and the unions on the docks and their smuggling operations. And this sounds like it's almost a completely different TV show, but it's just as good. It's different. Season 2 is probably the most impressive season 'cause given how good Season 1 was and given the fact that there was such a shift of emphasis in Season 2, even though the same characters from Season 1 mostly carried through, but there were a whole bunch of new characters that were introduced, the fact that they pulled off telling just as good a story in Season 2 is probably the most impressive thing.

3:11:10.1 SC: Season 3 was great, like I said, but it's more sort of almost back to Season 1. Like there was some focus on politics, but it was kind of more... It was less special, I thought, the political angle there than the other seasons. And then in Season 4, they come in with this focus on kids and education and going to school, and it just breaks your heart and blows your mind. And that was once again, like how did they do that? That just was... It's hard to watch sometimes, it's uplifting other times, it's just a work of genius. And then Season 5, they focus on the media and the newspapers, and it was once again just like the politics season, Season 3 it was a little bit less inspired, I thought, a little bit less special and heartwarming or heart-touching than the other seasons. But everyone's allowed to enjoy their own seasons. That's okay. This is our fifth year in Baltimore. We're just beginning our fifth year. So one year from now, we will have been in Baltimore for as many years as The Wire covered. Then we'll start a new adventure, not by moving from Baltimore, but we'll be in territory where it would be longer than the extent of The Wire TV show.

3:12:24.1 SC: Okay, I'm gonna group two questions together. One is from Jamie, who says, "From the point of view of a driver, the driver can't move forward because a car in front of them is stopped. But it is "traffic" that provides a better explanation for the jam. The emergent property of heat isn't just a coarse-grained average of jiggling particles, it's also a state where any individual particles becomes more likely to bump into other particles and so points to a limiting factor in their future actions. Higher levels might not change the physics of lower ones, but they describe sets of constraints that we can't see when we focus on a lower level. Coarse-graining throws away a lot of details, but it also seems sometimes to genuinely add something that was invisible. If higher-level patterns are where we can see limits of what lower-level systems can do, then don't they contain more rather than less information?" Okay, keep that one in mind. And then Ed Saidstuff says, "In the last AMA, you said that emergence involves coarse-graining and throwing away information but if explanation is supposed to come from having more information, why does losing information sometimes give us better explanation? Is this a paradox built into emergence? And if so, is there anything to learn from it?" So the questions kind of point in slightly different directions. I guess let's go Jamie's question first. He wants to know, isn't there more explanatory power at the higher emergent level because you can make statements like, "Oh, the car moves slow because of traffic," that are a little bit more explanatory than "The car moves slow because the car in front of it was moving slow?"

3:13:57.5 SC: I would say that both explanations are perfectly good. There's no sense in which saying that my car moves slow because the car in front of it moves slow is wrong or misleading or even incomplete. That's a 100% fully good explanation for why my car moved slow. Now, you might also want an explanation for why that car moved slow, and you might appeal to the car in front of that, and you might end up reinventing the concept of traffic. Now, there's an equally good explanation at the higher level where you say that there was a traffic jam or something like that. I think what you're... Maybe what you're getting at is what you say is coarse-graining throws away a lot of details but also seems to add something that was invisible. I think that's not true. I think what it does is reveal something that was always there but was hard to see because the fine-grained information was just too voluminous. There's nothing in principle that is in the traffic-level explanation that was not implicit in the car-level explanation. It might just have been hard to see it, but that's your fault, not the physics's fault or the science's fault. I think the correct thing to say is not that there's more information or anything genuinely new at the higher level. It's that it can be a more efficient explanation and therefore it can seem more explanatory. So to make it at the extreme level of absurdity, anything that happens in the universe, whether you're late for work, you lose your keys or whatever, you forget your spouse's birthday, you can say, "Well, that's because of the wave function of the universe and the fundamental laws of physics." That's not wrong, but it's also not helpful. It's not pointed at the correct level of explanation.

3:15:43.4 SC: The reason why the traffic-level explanation seems better is because you need less input to get just as much output. If the output you want is "Why were you late for work?", then giving details about what every car on the road is doing is just a lot more effort than giving the detail that traffic was slower. So it doesn't have any more explanatory power, but the explanatory power is more efficient, bottled up and contained in a simpler explanation, therefore it seems more useful to us, but it's not more explanatory, it's just more useful. And then to Ed's question, he wants to say if explanation is supposed to come from having more information, I think that what we just said points out that that's not true. Having more information does not necessarily lead to better explanation. Like if I have an explanation for why I was late for work and also I read to you the contents of the dictionary, I've given you a lot more information, but I have not in any way improved the explanatory power of my explanation. So there is explanation in the sense of, did you really provide the sufficient amount of information I needed to understand why the phenomenon happened? And then there's this idea of the efficiency of the explanation, which actually improves by throwing away the information you don't need. That's exactly what emergence lets you do.

3:17:08.3 SC: Paul Hess says, "I notice in the particle chart," I guess there's a particle chart out there, there's probably more than one, "that the gluon has no mass. Does no mass mean it travels at the speed of light like a photon does? Does a term like travel even apply to a gluon? Or is the gluon restricted within a tiny range of particles it glues together, making the word travel meaningless? Are we certain that it has no mass based on theoretical reasons, or might it be that the gluon has mass that we will later discover? I think it's closest to the gluon is restricted within the tiny range of the particles it glues together, making the word travel meaningless. I mean, the word travel is meaningless because the gluon is never an isolated particle. Gluons and quarks are confined at zero temperature inside zero, inside, yeah, zero color particles like baryons and mesons, like protons and neutrons and pions and so forth. And what that means is when you talk about the fact that a massless particle moves at the speed of light, there is an assumption there, namely that the particle can move all by itself through the universe, but the gluon just can't do that. And what's happening is really a breakdown in the idea of a particle. And I talk about this at some length in Quanta and Fields. If you really want to talk about what's happening inside a proton or a neutron, you have to face up to the fact that the particle language is not up to the task. It is insufficient. Ordinarily we say, okay, we know the world is really made of quantum fields, but as long as all we care about is a single little vibration in a quantum field and we're gonna measure it in some detector, it is 100% legitimate and okay to talk about this as if it's called a particle. But if you're stuck inside a confined, strongly interacting system like a proton or a neutron, that is just not the regime where it's okay to talk about it using particle language. It really should be using field language 'cause that's what's going on. So when you say the gluon is a massless particle, which is a completely okay thing to say, but that has a meaning, and the meaning is not the obvious one. The meaning is in the equations of motion for the gluon field, there is a mass term you could imagine writing down, but it's zero. And it's zero for reasons that are demanded by theoretical reasons in this particular case, gauge invariance. The symmetry of the theory doesn't let you have a mass for the gluon. So it is both demanded by theoretical reasons and 100% compatible with experimental data. It's even very difficult to ask the question, might it have a mass that we will later discover? There's basically no way to give it a mass without doing some really theoretical heavy lifting. You could, okay, what you need to do is break the SU(3) symmetry spontaneously. This is why the W and Z bosons have a mass, because in their own rights, they would be massless, but the Higgs boson broke the symmetry that they were associated with and gave them a mass. As far as we know, there's nothing that breaks the SU(3) symmetry of quantum chromodynamics. If there were, you could give the gluon a little mass and you could ask, how would we know? How would it show up? I'm not even sure how it'd directly show up. Probably something to do with the properties of protons and neutrons. That's a level of physics knowledge that is a little bit beyond my pay grade.

3:19:25.7 SC: So James Brown says, "How is your bass playing going? Do you get much of a chance to see live music, and do you find it inspiring and motivating?" I love live music, going to see it, and I love playing the bass and noodling around on it. And no, I have not done any of that recently. I think I've alluded to this before, but right now, it's okay, it's no problem, but I'm at a time in my life when I have other things I gotta do. Like during the pandemic, I was having fun beginning to learn how to play the bass guitar. Since moving to Baltimore, I've just not had that time. I have to teach my classes, I have to do the podcast, I have to finish writing these books. This is what I have to do, not to mention doing scientific research and writing papers. Those are the things that are filling up my time. I'm looking forward, once 2026 is over, to basically be done writing books for a little while, and then I'll have a little bit more breathing room and get to have a little bit more fun and the bass guitar will 100% be one of the things I spend my fun time doing.

3:21:36.9 SC: Eugene Brevdo says, "Having grown up in the '80s and '90s, watching the Terminator movies was one of those formative experiences for me. The idea of agents in the future going back in time and causing their own creation seems to be the modern version of the Greek self-fulfilling prophecy. At the same time, these feel like the macro version of closed timelike loops. Is this how you think philosophically about impossibly macro-scale closed timelike loops? Are they basically akin to self-fulfilling prophecies, agents from the future come back to create their own predecessors? And more importantly, which is your favorite, Terminator 1 or Terminator 2?" I like both Terminator 1 and Terminator 2. I think that Terminator 1 gets points for, there's always something to be said for the founding entry in a series, like that's where the ideas came from, and you get the origin story and things like that. Probably on pure attempts at being an objective measure of cinematic greatness, Terminator 2 is a better movie. I think it's more well-done, more professional, more nuanced in various ways. So I like that one too.

3:22:42.7 SC: Yeah, obviously the time travel in the Terminator movies is loosely related to closed timelike loops or closed timelike curves. It's not exactly the same because like many science fiction versions of time travel, you just mysteriously disappear in the future and reappear in the past, which is not a closed timelike loop, it's just magic. But that's okay. There are absolutely questions that are raised by the logical questions having to do with time travel and free will and things like that. Now, as far as I know, at least in those two movies, the franchise sort of veered off at later points in its development, but in those two movies, it's an interesting tension because people in what was nominally the present day are fighting to make things happen in order to create or prevent things from happening in the future.

3:23:40.1 SC: Now, I think that in some sense they, I'm not actually sure. It's been a while since I've seen the movies. I think that if you're gonna have good, logically responsible time travel, it has to be consistent. So whatever happened in the past happens in the future. The future thinks that the past was the past. There's not a different future and past that are somehow incompatible with each other. In the movies, Skynet happened. We know that because Skynet sent the Terminator back in time. So in some sense they had to fail. But like in the movies, there's jeopardy and they succeed. So I'm not quite sure what the consistent story there is. I like the movies. The short version is I like the movies, but they really weren't logically consistent. Now, it's possible that they were logically consistent, but they had to act like they weren't in order to raise the dramatic stakes, that's perfectly allowed. Maybe if the people don't know the logical consistency requirements of time travel, then they would act just as if they did. But in fact, I think that they were just playing a little fast and loose with the requirements of internal consistency.

3:24:54.0 SC: Jacob says, "How do the many major interpretations of quantum mechanics, hidden variables, many worlds, spontaneous collapse, relate to quantum gravity theories like string theory?" Well, in practice, they don't. In practice, everyone who does quantum gravity is either a many-worldser, an Everettian, or someone who has some hazy commitment to something like the Copenhagen interpretation without thinking about it very carefully. Essentially nobody in the modern world of quantum gravity and black hole information and all those things who even know what hidden variable theories are or spontaneous collapse models are, much less try to relate them. If you read papers on quantum gravity done by people doing quantum gravity, they're not talking about hidden variables or objective collapses in any way. Should they? Eh, I don't know. I mean, I talk about hidden variable theories and spontaneous collapse models because it's good to have diversity, like we talked about. It's good to have a diversity of approaches. But I personally don't think that they're at all very likely to be true as descriptions of nature, so I'm not gonna spend any time thinking about them, so I'm not surprised that other people don't either.

3:26:10.6 SC: Christoph Radomsky says, "I can't shake the feeling that there's an analogy between the Hilbert space from which our universe emerges, as you described in your previous solo episode, and a computer simulation emerging from the ones and zeros stored in a computer's memory. I know you reject the simulation argument, but if I wanted to explain to someone what the Hilbert space underlying the universe is, I'd be tempted to use that analogy. How correct is it?"

3:26:34.4 SC: I think it's pretty much not correct. Let's put it this way. What if quantum mechanics were not true? Then I would not say the universe is a vector in Hilbert space. I would say the universe is a point in phase space. That's what classical mechanics would say. It's got nothing to do with the simulation hypothesis. It's just a way of saying our best mathematical representation of reality takes this particular mathematical form: a point in a symplectic manifold called phase space. In quantum mechanics, we change that to saying that our best representation of the physical world is a point in this vector space called Hilbert space. But there's nothing otherwise new about it. It's just what is the mathematical representation of reality according to the current state of the art?

3:27:22.4 SC: Travis A. Says, "What are some of your favorite artistic visualizations of physical models that we have or representations thereof? I'm interested in getting a tattoo playing homage to all of the great progress physics and the natural sciences have made and wanted to pick things that are visually compelling without looking like a blackboard equation. Some ideas I have include fluid turbulence for the Navier-Stokes equations in fluid dynamics, or a black hole with an accretion disk for general relativity, a bubble chamber particle tracks for particle physics in E&M, graphing the standard model particles in some fun ways, et cetera. Things that are visually striking but carry some deep understanding of the physical world."

3:28:02.5 SC: I'm gonna kind of let you down here because I think that you have done a better job of coming up with good examples than I could have done. I mean, one big question here for the down-to-earth issues of getting a tattoo, which I don't have any tattoos, so I'm not an expert, but there are some tattoos that are more or less simple line drawings, sort of cartoon diagram kind of things, and there are some tattoos that are pretty realistic, that are very detailed, portraits of people and whatever. And science has both of those. Science has artistic representations, usually imagined artistic representations of things like a black hole accretion disk, or maybe a photograph of turbulence in some fluid or something like that. Those would be great. I mean, they're both very artistic and beautiful, and they stand for something real out there in the world.

3:28:53.1 SC: Likewise for the particle tracks in a bubble chamber. I wouldn't do bubble chamber. I mean, you might as well go all the way to either a simulated or real data version of a collision at the LHC, which is much more vibrant and a lot going on and also a lot more modern than a bubble chamber. Graphing the standard model particles, I'm always a little skeptical. I mean, the reality is the standard model's a mess. There've been various attempts to make it look pretty by putting the particles together in certain arrangements, but those are all a little bit fake, so to me, that's a little bit less compelling. If you're happy just with a line drawing, then in general relativity, I would contemplate a conformal diagram, otherwise known as a Penrose diagram, which can capture all of a spacetime in a little tiny package. So you could get a conformal diagram of a black hole or of cosmology or something like that. But honestly, the black hole accretion disk or Navier-Stokes or bubble chamber particle tracks, those are all great, great choices. I don't want to dissuade you from those.

3:29:53.2 SC: Tim Falzone says, "I've been thinking a lot about the Rebecca Goldstein conversation on mattering. How do you think about the nature of goal seeking in an LLM versus how people pursue goals? Can you imagine a kind of LLM for which anything matters? Can mattering emerge even when nothing is at stake for the system?" So at zeroth order, that is to say, my first gut reaction is an AI someday I could imagine having a notion of things mattering, but an LLM I cannot. By construction, LLMs are fed every sentence ever written or whatever, all they can get their hands on, and they try to do next token prediction, or they try to in some slightly more sophisticated way string together sentences that they think are things that a certain person would say in response to the input that they're given. But as we've discussed, when no one's asking the LLM any questions, nothing is happening inside the LLM. The LLM is not hooked up to a body that has metabolic processes. There's no mitochondria sending power to the cell. There's no generation of ATP or anything like that. There's no heartbeat and no breathing. It's not an open system whose non-equilibrium configuration is sustained by the use of free energy in the same way that a biological organism is.

3:31:17.4 SC: And I'm one who thinks that that connection between the biology and the brain matters for things like consciousness, thinking, agency, all of those things. Again, not that it's impossible in an AI, but the whole idea of an LLM is to not do any of those things. Like if you just let it sit there, it doesn't get bored. It doesn't say, "Hey, why aren't you talking to me?" Like you could write a little subprogram that would make it do that but not for the same reasons why people do that, not because there's really internal change going on even when the program isn't running. So I don't think it's the same sense. The whole point of an LLM is to fake acting human. We have to be careful, this is a problem we've never had as human beings, to tell the difference between acting human and being human.

3:32:05.9 SC: Ken Wolf says, "Are you a fan, at all a fan, of multi-volume epic SF or fantasy series? If so, are there any that are your favorite? Or alternatively, is there any that you decided just to stop reading?" I'm pretty good at deciding to stop reading. So yes, I was a big science fiction reader as a youngster, and in more recent years, I've taken up to occasionally reading SF and fantasy again. And so I read a bunch of things and have read more recently some things. My favorites would be the Culture series by Iain Banks is definitely my favorite. Big fan of the Chronicles of Amber by Roger Zelazny, the Dragonriders of Pern by Anne McCaffrey. What other ones? I mean, all of Heinlein's future history novels, if they count, I'm not sure. All of the Song of Ice and Fire novels by George R.R. Martin, definitely big fans of those. The TV show was better, when the TV show was good, it was better than the novels because Martin would easily overwrite and just write too much in the novels, but still the novels were really, really good, I gotta say that. Never really got into the Discworld novels or the Wheel of Time. So yeah, for novels just as much as for music, I'm a creature of my era, and I was much more likely in the 1970s to read a five or ten-volume series than I am today, let's put it that way.

3:33:40.7 SC: Nick C. Says, "In your recent interview with Christian List, he talked about an argument for free will based on the inability to describe most of the uncountable set of macrostates in terms of microstates using a countable language. This reminded me of a result showing that whether a many-body Hamiltonian gives rise to a spectral gap is an undecidable problem. I never know how seriously to take these things. They sound important on the surface, but on the other hand, almost every real number can neither be computed nor defined. Neither... Sorry, it's getting late in the podcast, I'm stumbling over reading and sometimes it does matter, so let me start there again. On the other hand, almost every real number can neither be computed nor defined, and yet we do math with real numbers all the time without a lot of trouble. So I sometimes wonder if these results are true, but maybe not as practically important as they sound. How do you think about the salience or lack thereof of such results? I think it's a great question. I think even Christian would probably agree that there's some concern that this kind of hyper-careful, mathematically formal argument is not the relevant one for thinking about these questions. That's why he called it the nerdy argument. It's like if you buy into all the assumptions that we need to underpin this maximum level of nerdiness, we get this cool result out of it, does reasoning... As we said before, human beings, as Stanley Cavell would have taught us, are limited creatures. We don't have the real continuum at our disposal or uncountable or even countable sets of numbers at our disposal. We can reason about them without actually having all of them. So are we fooling ourselves a little bit?

3:35:21.6 SC: So I'm 100% on board with a point of view that says a lot of this is sort of formality for its own sake. And it's not really relevant to the important questions that we want to address as finite human beings. There is a little bit of a footnote there, which is you do want your theoretical understanding, your theories you're proposing to understand the world, to be internally consistent. So if we go to the very beginning of this AMA and think about the Boltzmann brains, the one big reason why the typical cosmologist on the street doesn't worry about Boltzmann brains is because it's a hilarious extrapolation into the future to say that there's going to be more Boltzmann brains than ordinary observers and maybe they feel like they don't have the right to trust their theoretical predictions extrapolated that far into the future. I think that's 100% valid. You're completely correct to not trust your theories past a certain point. But I also think you need to take them seriously past that point. In other words, if you think your theory has a certain domain of validity, then you have to figure out what its predictions are in that domain and whether or not they are internally coherent and fit the data. And if you think your theory has a limited domain of validity or applicability, I should say, then you gotta tell me why. What is that domain of applicability? You can't just say, "Well, it's far away." That's not good enough. You have to say, "Oh, here's where my theory breaks down for this principled reason."

3:36:53.8 SC: So in cosmology in particular, there are questions that depend sensitively on the interplay of, is time finite or infinite, and is the number of things that can happen in the universe finite or infinite? So even though we are limited, we are both finite in space and time, asking what the universe is matters in some way. And by the way, this is a reason why there is some interest in certain tiny circles of math and philosophy in finitism and ultrafinitism as an approach to the philosophy of math. The point there is that all of this talk of infinity is just talk. It doesn't map onto anything real. No one has ever seen infinity. All you've ever seen are finite sets of symbols which you claim capture some aspects of infinity. And the ultrafinitist will say, "But they don't capture reality. They're just tools that you're choosing to use and you could just as easily not use them." And one of the initial motivations for the recent cyclic universe paper was a previous paper I wrote saying that you could discretize Hilbert space into a set of discrete possibilities so that quantum mechanics would not need to use the continuum. It could be purely based on discrete sets of numbers. So I do think that there's some question to be asked about do you really need infinity in this case or that case? But I also agree with your intuition that if a certain argument for a real-world result seems to hinge on the difference between different sizes of infinity, then you might be like pushing your ideas past their point of true relevance. Let's put it that way.

3:38:38.5 SC: Brandon Lewis says, "Chatting over beers with a friend of mine in academia, he mentioned in passing his belief that peer reviewers should not be anonymous. This is based on the rather inane reviewer feedback he and his colleagues have received over the years, and he points out that it's rather unfair that perfectly valid work can be relegated to obscurity with no repercussions for the reviewer. They may have a conflict of interest or else insufficient subject matter expertise. After playing devil's advocate for a couple rounds, I conceded that he might have a point and promised to submit this in the next Mindscape Ask Me Anything call for questions. What is your take on this? Is there a rationale for keeping reviewers anonymous, or should we encourage journals to make the names of reviewers known?"

3:39:19.8 SC: So I get the problem. I have definitely come across my share of inane reviewer comments. And I think I mentioned this before, but it's really telling and a little bit sad that I can absolutely write a paper and get it published with 100% confidence that the referees will accept it if the paper is boring. If I just do a calculation that is sort of a mild relevance, but I do it respectably and get all the right answers and it's well within the realm of things that people consider acceptable and the kinds of things that physicists do, the referees will accept it, no questions asked. If the paper is interesting, if it is creative and is proposing something new and different, those are the papers that the referees like to object to because like, "This isn't what I'm used to seeing." So I 100% appreciate that the ability of referees to just anonymously take potshots from the sidelines can be very annoying. On the other hand, the incredible damage that can be done by referees not being anonymous would be much worse. I mean, you instantly imagine that no young physicist who is still in the job market is going to write a harsh referee report for a senior physicist who might someday be offering them a job or vice-versa, a senior physicist doesn't want to be getting a reputation for submarining the careers of young physicists, et cetera. You don't want it to be clear that people are the referees who are just your enemies or your friends or whatever. There's a whole bunch of reasons why anonymous refereeing is much better.

3:41:05.4 SC: Indeed, outside of physics, like in philosophy, for example, it's double-blind refereeing, where not only does the author not know the name of the referee, but the referee doesn't know the name of the author. When you get the paper to referee, the name has been removed. And it's not just in philosophy, that's in many other fields as well. The idea being you can be more objective. Now, how do you get around the problem of inane referee comments? The way that it's supposed to happen is there's somebody called the editor of the journal. And you're supposed to make an appeal to them. It is very, very common that a referee report says, "No, don't publish this," and then the author doesn't agree. And the author says, "No, here's my response. I think you should publish it for the following reason." And at some point, either the journal editor makes a decision or they pass it to a different referee or the same referee again or whatever. And that's what's supposed to happen. Now, sometimes, like I'm just too old for this. Sometimes, like we submitted a paper to Physical Review Letters. Physical Review Letters asks for two referee reports for every paper 'cause they want higher standards. And both referee reports came back saying, "No, this paper should not be published," but for two completely inconsistent reasons. Like one says, "Well, this point is obviously false. How could you be so stupid as to say this?" The other says, "Well, this point is obviously trivial and everybody knows this. Why would you bother writing a paper about it?" But they agree that it shouldn't be published. And so what I wanted to do, and I could very well have done, is say to the editor, I could say, "Look, it's okay to reject the paper, but there should be a reason to reject the paper. And in these two referee reports, there does not emerge a single good reason to reject the paper 'cause the referees don't agree with each other." But instead we just said, "Screw it. Let's go to a different journal where we don't need to deal with those referees anymore." And that's what we ended up doing, and we got it published.

3:43:10.7 SC: So there are ways to deal with that. And so I think that no system is perfect. Journal editors are overworked and underpaid, and it's a tough job. I wouldn't want it myself. So you can't completely fault them. But I definitely don't think that letting authors know the names of their referees is the correct strategy here.

3:43:31.7 SC: Anonymous says, "How was Ireland? Immediately after graduating from college in 1994, I spent two or three weeks traveling around the southern and western counties, tagging along with musicians and playing impromptu gigs as an opening act most nights. It was a dream and recently I've daydreamed going back for an extended tour. I'm curious to hear your experience." Well, my experience was not that. That sounds like a great trip that you had, traveling around the counties, tagging along with musicians, playing impromptu gigs. So, look, as I just said, I'm right now, and again, no complaints whatsoever, but I'm in a time of my life where I gotta get work done. And that's true even if I'm at an Airbnb in Dublin. So most of the time during the day, I'm sitting in the Airbnb finishing my book. That's what I'm doing. I'm not touring around. Jennifer came to visit and we spent one day sightseeing, that was it. But with that caveat aside, Ireland was great. Ireland is wonderful. Those are my ancestral people in some sense. They're very, very friendly. Dublin in particular is full of immigrants, which I love. So it's part of the European Union. It's the only part in the British Isles which is part of the European Union. So anyone from Europe can just come in. So you hear not just Irish accents, but all sorts of accents.

3:44:51.3 SC: There's a whole bunch of bad pub food and good pub beer, but there's also really good food if you make an effort to find it. So we went to Chapter One, which is a Michelin-starred restaurant, which is super duper good. As good as a... It's a world-class restaurant, let's just put it that way. We also found this South American tapas bar which was just fantastic. And I will get a lot of mileage going forward telling people that the best margarita I've ever had was in Dublin. We visited a sheep farm. We toured some ruins and things like that on our one sightseeing day. I will say that there was a bus involved in going on some of the sightseeing, and never again. I have passed the age of my life where I'm gonna go on a bus to do sightseeing. The being packed in there at close quarters, it's just not what I do anymore. I'm gonna have to move in comfort from now on. But Ireland was great. We were at the beginning of the heat wave hitting Europe, and of course there was no air conditioning in our Airbnb. It was not so hot that it got uncomfortable for us because like France and the UK had much more severe heat waves than Ireland did, so it wasn't so bad, but it was noticeable. I think they're gonna have to get air conditioning spread around that island pretty soon.

3:46:13.9 SC: Nate Wilcox says, "For a busy layperson with some 20 years of rusty engineering bachelor's math, who wants to improve the rigor of my intuition of an Everettian perspective, what mathematical abstraction should I focus on learning to understand the process of branching? Is there a simplified pedagogical form or setup of the Schrödinger equation which starts pre-branched and captures the branching process I can target for hobby study? Well, look, you could, as I'm gonna always say, you could pick up Quanta and Fields where I do talk about this at a relatively accessible way but my real feeling about this question is 20 years of rusty engineering math notwithstanding, it's probably a mistake to think I want to understand branching of the wave function at a strict mathematical level, but not understand quantum mechanics more broadly. Really what you have to do is understand quantum mechanics because these are all processes that happen within quantum mechanics. So you need the linear algebra and the differential equations and the Fourier analysis that everyone needs in quantum mechanics. And then you need a little bit of operator theory to understand density operators that we were talking about before and things like that. And you can define entropy and so forth. It's all just quantum mechanics. There's no special thing called Everettian quantum mechanics. That's the whole point of Everettian quantum mechanics. Now, you could pick up something like David Wallace's book, The Emergent Multiverse. It's probably bigger and longer than you want 'cause he's being philosophically very careful but his particular interest is Everett, so he will do the amount of work you need to do to understand Everettian quantum mechanics. But mostly I think understanding quantum mechanics should be the goal, not specifically understanding the process of branching.

3:48:01.2 SC: Elijah Massey says, "Is it possible to contribute to philosophy without getting a master's or PhD? I also want to become a programmer, and it seems easier to make a living as a software developer than becoming a philosophy professor if I have to choose. But I still want to do both. If I get a double major in computer science and philosophy, is it feasible to continue philosophy as a hobby and make meaningful contributions to it and write papers while having another career?" So guess what? Questions that begin "Is it possible?" will always be answered with a yes, as long as they're logically not inconsistent. So yeah, it's possible to contribute to philosophy without getting a master's or PhD. Now let's be a little bit realistic and talk about probabilities, not just possibilities. It's hard to contribute in a constructive way to philosophy even with a PhD. The academic job market is hard and many people who even get employed as professors don't do a great job in contributing to human knowledge. They maybe have a little burst of productivity and then taper off later in life. It's just hard. Basically, you're trying to contribute amidst a whole bunch of other people who are trying to contribute and those other people have it as a full-time job. They've devoted their lives to it. They do nothing else. They get a PhD, they study, they think about it all day. And you're saying, can you come up with something that they haven't? Sure, maybe. It's possible, but it's hard. And what's gonna happen is almost always, but not always, you're gonna lose the motivation that is required. I mean, are you really keeping up with advances in the field? Are you reading all of the papers that are being published? Are you going to seminars and conferences and hearing what people say and talk about, which, like I just said, is an important part of that process of coming up with new ideas? So in the modern world, it's 100% possible to do it, but it's not usually gonna work, let's put it that way. So I always, I want to encourage people, but I don't want to encourage them based on false pretenses. So I want to be super realistic. Like you can do it, but please appreciate how difficult it will be. So are you gonna really put enough work into it to do a good job? Are you gonna be especially honest enough with yourself about whether you're doing a good job? A big part of being a successful academic is going from, "Oh, I think this idea is cool" to, "But is it really cool? Am I really doing something new here? Is it really better than what other people are doing? Have I really looked through all the ins and outs?" That's part of the process that separates real academics from the crackpots. And it's just hard to do that. So it's doable. If you're gonna do it, I'll encourage you to do it. I think it'd be great if you did it. But I can't promise you that it's straightforward or that it will work. That's entirely in your hands.

3:51:03.6 SC: David says, "Maria Ubiali has discussed an interesting phenomenological attitude to effective field theories. The usual route is to propose a new particle like a dark matter candidate, and then calculate and look for its influences but instead, assume the existence of some very general effective theory beyond the standard model with unknown parameters, then look to narrow the available parameter space using observational data. Does this approach seem practical?"

3:51:29.3 SC: Yeah, in the right circumstances, that's super practical. I don't even think it's especially new. I think plenty of people do that. There's certainly something called the Standard Model Effective Field Theory, which is just the Standard Model plus all of the non-renormalizable extra terms you might think to add that could be generated by new things going on at high energies. And then imagine testing that and measuring against experiment what the predictions are and sort of deciding whether or not there are signals hidden in the values of the measured parameters that might indicate some departure from the bare-bones Standard Model. You can do the same thing with beyond Standard Model physics. Like in some sense, I'm not invested enough in that particular field to say how efficient it is, whether it's the best way to think about finding new physics, to develop an effective theory at the level that is already beyond the Standard Model. Is that something worth doing versus just sticking with the Standard Model Effective Theory and seeing if it matches with the bare-bones predictions or not? But possibly it could. Yeah. No, I think that the whole brilliance of effective field theories is you can say a lot about what the possibilities are without knowing the specifics of what is going on at all scales.

3:52:41.6 SC: And with that, we are at the last question of this month's AMA. Scott says, "In a recent episode, I recall you saying that all Hilbert spaces of a given size, finite or infinite dimension, are the same with no other properties to distinguish them. Among infinite-dimensional Hilbert spaces, is there no difference between those with countable and uncountable dimensions? For a particle in an infinite square well, it has uncountable position eigenstates, but countable energy eigenstates. What is going on here?"

3:53:10.2 SC: So usually I like to end the AMA with some broader reflective question. This is maybe not that. This is a little technical, but I think I want to give a technical answer to it, so I put it at the end of the AMA in case you want to tune out if you're not interested in this kind of thing. So look, finite and infinite dimensions. Yeah, in finite dimensions, all Hilbert spaces with the same dimensionality are the same. That's also true in infinite numbers of dimensions. But countable and uncountable are not the same number. Countable and uncountable infinities are different numbers. So those are different numbers of dimensions even though they're both infinite dimensions. Just like two and three are different numbers even though they're both finite numbers. Aleph-naught, aleph-one, all these different versions of infinity, some of them are countable, some of them are uncountable. The continuum hypothesis comes into whether they're all uncountable past the first one, but okay, we're not gonna get into that.

3:54:06.7 SC: In physics, almost always, we work with countable-dimension Hilbert spaces, which are often called separable Hilbert spaces. Part of that is that there are various theorems like the spectral theorem, that only work if the dimension is countable and those theorems are super-duper useful in analyzing quantum mechanical systems. So we assume that that's true and we get on with our lives. Other reasons are that we can always find a countable basis for the Hilbert spaces that we know and love in physical theories. Now, like you say, the infinite square well has an uncountable set of position eigenstates and countable energy eigenstates. What is going on here? That's a very good question. The answer is those position eigenstates, which are uncountable, the states of definite X, the location in space, are not in Hilbert space. Now, you know they're not in Hilbert space because they're not normalizable. In the language of wave functions, psi of x, you have psi of x is a complex number for every value of x. For an infinite square well, let's say between 0 and 1 is the square well's extent, then the wave functions are going to be 0 for x less than 0 or x greater than 1 and do some interesting thing between 0 and 1. You want to normalize the wave function so you can predict probabilities, and normalizing it means the integral of psi star psi dx equals 1. For a position eigenstate, the wave function is a delta function. Delta of x minus x-naught is the position eigenstate at x-naught. You can't take the integral of a delta function squared. That is not allowed. Delta functions themselves aren't functions, they're really part of defining what are called distributions. So there's clearly something weird going on. And like many things in quantum mechanics, it's all fine, but there's a whole bunch of math that goes into showing that it's fine, which we don't tell you about. Here's one way of thinking about that math. You can define a Hilbert space by defining what is called L2, which is the space of square-integrable functions. Square-integrable means the integral of psi star psi is less than infinity, is a finite number. That's what square-integrable means. So take the set of square-integrable functions over some domain, for example, between x equals 0 and x equals 1. That would be L2 of that interval. So that's a Hilbert space in the sense that that space of square-integrable functions satisfies all of the axioms of a Hilbert space, and you can say, "Okay, that is my Hilbert space for the particle in that infinite square well, L2 of the interval." Now, that doesn't include delta functions 'cause they're not square-integrable, so that's not in that Hilbert space. So what you do is you say, "Well, in fact, there's a bunch of operators that you might be interested in like the momentum operator." Okay, the momentum operator is minus i d by dx, the derivative with respect to x. You might want to apply the momentum operator to a wave function. That's a natural thing that you might want to do. But you notice that there are elements of L2, the space of square-integrable functions, on which the momentum operator is not defined because you're taking a derivative, and you can easily have a function that is square-integrable, that is to say normalizable, but is not differentiable. Maybe at a single point it's not differentiable, maybe it's nowhere differentiable. Who knows? There's all sorts of weird, crazy functions out there. So you're already a little annoyed because you thought this was Hilbert space, but your Hilbert space includes functions that you can't differentiate and therefore can't operate the momentum operator on. What should you do? The answer is you can define a smaller space, which is a subset of L2, which is the space of test functions. The space of test functions means not only are they square-integrable 'cause it's a subspace, but they're also differentiable, so you can take the derivative of them with nothing going wrong. Or they could even be smooth. If you're not in the square well but you're on the real line, they would also be of compact support or something like that. So multiplying by a plane wave still gives you a square-integrable function 'cause they have compact support.

3:58:50.5 SC: So anyway, the test functions are a dense subspace of L2 of R. They are not a Hilbert space by themselves 'cause it's not complete, I think. I think that's the right answer there. But anyway, they're not a Hilbert space by themselves. They're a smaller space than Hilbert space, but you can act all of your operators on them, no problem. Okay, good. So that's the space of test functions. And now we're going to do the following thing that you always do in linear algebra. We're going to think about the space of maps from our vector space to the real numbers. That is to say, we're going to take the dual space of our vector space. So for L2, its dual space is itself. That's straightforward enough. But for the space of test functions, there are more operators that we can act on it because they're nice. The test functions are nice, they're smooth, they're differentiable. So the dual space, the space of operators, which is itself a linear space, a vector space, is a bigger vector space than the space of test functions itself. And how can it be bigger, even though they're both infinite? That's exactly because these infinities are not all the same size. So what you can prove is that the space of test functions has a dual space that is not only bigger than the space of test functions, it's also bigger than the original Hilbert space you started with. So you have this kind of nest. You have the test functions are a subset of the real Hilbert space you care about, L2, which is a subset of the space of operators on the test functions that give you linear maps, the dual space to the space of the test functions. And you can sort of dualize the dual space to make another big space if you want to. There's various subtleties here that I'm skipping over, but the point is you take your original Hilbert space, you think of it as a subset of a bigger space and having its own subspace of test functions. This whole setup is what's known as rigged Hilbert space or a Gelfand triple. And the answer to your original question, there's a reason I'm saying all this stuff. Scott's question says, "What about these position eigenstates?" The position eigenstates live in the bigger space, the one that should be thought of as the space of linear operators on the space of test functions. And then you prove a theorem that says the real Hilbert space you care about is a subspace of this big space, but it's a subspace with the property that you can use a certain set of elements of the bigger space as a basis for Hilbert space. So the position eigenstates are not in Hilbert space but they are in a space that Hilbert space is a subset of, and you can define sets of vectors in Hilbert space as linear combinations of them. So for all intents and purposes, you can use them as a basis even though they are not in Hilbert space. And the relevance to your question is, aren't position eigenstates uncountable in number? Yes, but they don't tell you the dimensionality of Hilbert space 'cause they're not in Hilbert space. The dimensionality of the Hilbert space for the infinite square well is countable. It is infinite but countable, and you could say the same thing for the simple harmonic oscillator, et cetera. But you can use an uncountably denumerable basis to do your analysis in. No one ever tells you that when you take your first semester quantum mechanics course, but it's true. You can look it up. Google rigged Hilbert space and you will find explanations of it. So I hope that's helpful. Little foray into slightly more technical things that I know some of the listeners really love. Some have no use for it. That's okay. We celebrate diversity here at the Mindscape podcast, and we hope you celebrate it along with us. Thanks as always for supporting Mindscape to the Patreon supporters out there, and thanks for everyone for listening. I'll talk to you next time.