253 | David Deutsch on Science, Complexity, and Explanation

0:00:00.4 Sean Carroll: Hello, everyone. Welcome to the Mindscape podcast. I'm your host, Sean Carroll.

0:00:04.5 SC: We've talked about quantum mechanics a lot on the podcast. You may have heard that I'm a fan of the Everettian many-worlds formulation of quantum mechanics. But we have a special treat in that we have a guest who actually met Hugh Everett and was influenced by him and has gone on to be a major proponent of the Everettian version of quantum mechanics. That would, of course, be David Deutsch. And despite that, despite the fact that David is very well-known in his work in quantum mechanics and quantum field theory, he's basically, if you have to give credit to one person for pioneering the idea of quantum computers, it would have to be David Deutsch.

0:00:46.3 SC: There's other people who made very significant contributions there, but David was one of the first to really define what it means to do a quantum computation, to write down an algorithm that was faster than a classical algorithm, to really think about how entanglement can help you encrypt things using quantum mechanics, and so on. It's been super duper influential. He's been awarded various prizes for this, the Breakthrough Prize, the Fellowship of the Royal Society, and so forth. But that's not all. And in fact, in this podcast, we're not even going to talk about quantum mechanics that much. We're going to be talking about various things that David has been thinking about that grow out of, arguably, his combination of an interest in the fundamental laws of physics, but also in epistemology, how we learn things about the world.

0:01:36.9 SC: You've heard me talk about quantum mechanics and Everett. You've also maybe heard me talk about Bayesian reasoning and Bayesian inference and epistemology. And so unlike quantum mechanics, where David and I are very much on the same team, here we are not. And so that's what I wanted to talk about. He's been thinking a lot about, I guess, what you might call Popperian epistemology, after Karl Popper, the idea that we think about possible worlds and we divide them into the ones that are compatible with the data and then not, and then seek the best explanation. It's a little bit fuzzy, I've got to say. What counts is the best explanation, but it's clearly also very similar to what we actually do. I mean, you can recognize this in the actual progress of science.

0:02:24.0 SC: We try to come up with the best explanation for what the world is doing, given the data we currently have, and a way to go beyond that. So David has been trying to formalize that, thinking about it very carefully, and pointing out where traditional mottos that one invokes in the Bayesian context might be hiding some subtleties that make them less applicable than you might think. In particular, there is a theorem due to Karl Popper and Miller, I don't know what Miller's first name was, but the Popper-Miller theorem, that David has been thinking about that he would argue, and I think there's a case to be made, makes it hard to accept traditional Bayesian vocabulary as how we really go about picking our theories. So that's a very interesting conversation to have.

0:03:14.8 SC: And another thing that David has been interested in is constructor theory. I don't know if you listened to the podcast we did a while ago with Chiara Marletto, who is David's collaborator in this. They've been developing literally an entirely new way to think about what it means to do physics, to be a law of physics. Rather than having some dynamical law where you start with initial conditions and just chug forward, they think about physics, and not just physics, but also biology, chemistry, et cetera, in terms of what is possible, what is not possible, and what kind of constructors can actually make things happen in the world.

0:03:54.0 SC: I don't know. I still don't know after talking to Chiara and now to David. I still don't know whether this is going to be super duper useful going forward. It might very well be, though. I'm very open to that. I'm very interested in seeing where that goes. So we talk about that, too. We talk about the space of possibilities and how knowledge and explanation have burst onto the scene in the universe with the advent of human beings and their brains. And he's very careful to say it's not just necessarily human beings. Aliens, computers could also qualify, but it's a dramatic shift in how the universe evolves when you have systems that can think, store information, come up with explanations, use that knowledge to transform the world around them. It's ultimately an optimistic perspective on the world, and that's something we could all use a little bit more of. So I think this is going to be a fun conversation.

0:04:47.5 SC: Occasional reminders that we have a Patreon page here at the Mindscape podcast. You can go to patreon.com/seanmcarroll, kick in a dollar or two per episode, and the benefits will just start flowing your way. The benefits are not huge, but they're still benefits. You get an ad-free version of the podcast. You get to ask AMA questions. You get to participate in those discussions. And also, after every podcast, I do a little reflection video and audio that is for Patreon members only. So join the fun there, patreon.com/seanmcarroll. With that, let's go.

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0:05:39.0 SC: David Deutsch, welcome to the Mindscape podcast.

0:05:42.1 David Deutsch: Hi, thanks for inviting me.

0:05:44.0 SC: I have to start, we're going to get into substantive stuff soon enough, but I've got to start with a question I've had for a long time. I believe that you were in the audience for a seminar given by Hugh Everett at the University of Texas sometime back. Is that true?

0:06:00.3 DD: Indeed, I was.

0:06:00.8 SC: Can you say, was it actually kind of a formative experience? What was it like? What was Hugh Everett like?

0:06:07.2 DD: It was a memorable experience. I had imagined him differently, and I knew that Wheeler invited him. I was quite excited that he'd invited him, because very few people were Everettians at the time. I suppose very few are now still, but...

0:06:29.8 SC: This is the '70s.

0:06:33.3 DD: Yeah. Sorry?

0:06:33.7 SC: This is the '70s?

0:06:36.1 DD: This was, yes, in the '70s, late '70s. So Wheeler had invited him and was treating him like royalty. And one example I remember, I can't remember exact details, but one example I remember is that there was a strict no smoking rule in the seminar room. And, you know, that was quite rare in those days. It hadn't yet become ubiquitous like it is now. But Wheeler asked for this to be waived in the case of Everett because he was a chain smoker. He didn't stop smoking. And, so this, you know, leaning over backwards to make him feel comfortable. And he gave a talk about the Everett interpretation or Everettian quantum theory as we now prefer to call it.

0:07:34.1 DD: And then, we went to have lunch, 'cause the graduate students and the postdocs and the faculty on our floor often used to go and have lunch in one of the places in Austin. And Bryce DeWitt contrived to have me sit next to Everett. So I had lunch, chatting to Everett, and I asked him some elementary questions. I hadn't really started thinking very seriously about it, and I was just very, impressed that he was completely on the ball, up to date with with all the nuances. And so, and we had a nice chat, and that was the last I saw of him.

0:08:28.4 SC: Well, that was my impression, that I only got from finally writing a book about, of writing quantum mechanics, was that, you know, he only wrote the one paper, and we've all known physicists or scientists who have the one paper and they move on, and maybe they were right place at the right time, but you get the impression that he really did very much understand all the nuances that was were going on. It wasn't just that he got lucky.

0:08:51.3 DD: Yeah, very much so. And I got the impression, although I know other people have a different history in mind, but I got the impression that he did not leave research in physics because he was disappointed that the reception his ideas got, or anything like that. He left it because he wanted to do other things and to make a fortune. And you know, he did.

0:09:16.2 SC: That's perfectly valid, and I also got that impression and it sounds like you were Everett sympathetic even before that talk, but did that inspire you to think more carefully about it?

0:09:26.9 DD: Yes. I was Everett sympathetic because of DeWitt. So, I was lucky in that respect. So I met DeWitt and then a couple of years, I can't remember how long later, Everett, so I met DeWitt when DeWitt was on sabbatical in Oxford, when I was a graduate student. I was a first year graduate student. And, there again, not by anyone's contriving, but by sheer chance, I was in Dennis Sharma's department. And we went to have lunch at a pizza place in Little Clarendon Street in Oxford, and I happened to be sitting opposite DeWitt, and I only vaguely remembered that DeWitt had had something to do with the Everett interpretation. So I thought, well, I'll ask him. And I asked him a very silly question. I can't remember exactly what it was.

0:10:26.2 DD: Something like, if there are many copies of me, which am I, or something like that, something as elementary as that. And he was very kind and explained to me that that this was not a good question, and the way to think about this was, and he explained it to me and then I asked him more questions. And by the time we'd finished lunch, I was completely convinced. Previously I'd already thought this was worth looking into because it was a version of quantum theory that was purely physics and didn't have any kind of psychology or assumptions about the brain and that kind of thing. It was just how we'd been taught deal with theories. But what convinced me was that lunch with DeWitt.

0:11:30.6 SC: It actually leads into the broader conversation, because you're giving examples of how the space of possibilities in life is very, very large and tiny unexpected events can steer you in one direction or another.

0:11:44.4 DD: Well, yes, I think that's true, but I'm not sure that these examples were examples of it because, I'm not sure, well, I'd like to think anyway, that I wasn't exactly steered, I was just hastened. I think I would have come round to this eventually, if for no other reason than I would eventually have read DeWitt's work on this, and Everett's, and I would've talked to Wheeler about it and been dissatisfied with his answer. So, I think that would have happened.

0:12:22.1 SC: There's some convergent evolution there. Yeah.

0:12:24.3 DD: Yeah, exactly.

0:12:25.6 SC: So, good. We've already mentioned that there's a lot of things to talk about, but I've chosen as the substantive starting point monotony. You gave a nice little TED talk on the end of monotony and how we're moving into a different era. I thought that the title of the talk was maybe not the most inspiring, and maybe you would get more clicks, if it were not about monotony, but maybe you could explain what the basic idea there is.

0:12:53.0 DD: As always, the titles are not chosen by the author. That title was not chosen by me. So yes. It seems that progress is not uniformly rapid, and progress in various senses, like origin of planets like ours, and the origin of life like ours and the origin of multicellular life, and the origin of explanatory creativity, as in humans, and then the origin of the explosion of the Enlightenment, all those things happened very rapidly after a long period of not happening, and in all cases, you can't really put your finger on why it took so long.

0:14:02.5 DD: I think in a couple of cases, we'd say it's not surprising that it took so long, because it was rather a big step, but why did it take billions of years, in one case, why did it take thousands of years in the case of the Enlightenment, we don't know, but it appears it happens that way. By the way, that's not... In case you were going to ask, this is not punctuated equilibrium, this is not a substantive theory about how or why adaptations or knowledge happens, it's not that there's an equilibrium. I think in none of these cases was there an equilibrium, all of them were unstable to this thing happening. So there wasn't an equilibrium, and the punctuation didn't have anything to do with how it then went on. It could have gone unstable in a different direction. So this punctuated equilibrium, as advocated by Gould, for example, in my view is not a theory of evolution, it's just at best, it's a description of what sometimes happens.

0:15:20.8 SC: Yeah, okay. But is it... All the words you're using about lasting a long time and suddenly something happens, this sounds like phase transitions and meta stability, to me as a physicist.

0:15:33.4 DD: Yes, so in some of these, so the difference between phase transitions and all this other stuff is that we can form a theory of when a phase transition is possible and then when it will happen, and if it's too complex to work out, then we can produce a better theory of it that predicts it better.

0:16:00.3 SC: Sure.

0:16:00.6 DD: And a high level theory and so on. So it's a kind of deterministic thing, and all the other things that I said are indeterministic things, they are things that some people would say they're probabilistic, but I think that's not a good enough take on it either, because they're not something where the probability of it plays an important role in why it happened. If multicellular life had a probability of 10 to -6 or 10 to -7, neither per unit time or something, neither of those explains anything, and if we were told that the probability of multicellular life evolving per unit time was actually 1 in a million years, we'd be wondering why it's a billion, but saying it's a million doesn't help to explain why it was a billion. We'd need something else, something substantive.

0:17:12.1 SC: Are you pointing toward having a theory of why these things can bubble along unchanging for a long time and then suddenly change gears?

0:17:20.1 DD: No, I'm just being blindly critical of expecting everything to be known or expecting every regularity or irregularity in nature to have an obvious explanation. Some of them have an explanation, and when we find an explanation, that's great, that's... And I expect eventually we will find explanations for all these things, but I don't like this jumping into thinking we know almost everything now. We know almost nothing. During the pandemic, I was tweeting all the time: This isn't known. Why are you writing as if this is known, whatever it was. A lot of things were not known and a lot of things still aren't known.

0:18:18.2 SC: That's perfectly fair. Yeah. So you point in the talk to the origin of life as something that really changed things, that in a real sense for billions of years, the things that existed in the universe were the same things that existed a billion years prior, and something very, very new has come on the scene now.

0:18:37.7 DD: Yes. So the new thing is knowledge, and knowledge of particular kinds in all these cases. And some people will say, well, why is that particularly important? Knowledge is important to us humans, because our ecological niche depends on creating and manipulating knowledge, but as as I say in my book, if koalas could speak, then they might say that eucalyptus leaves are important, and the emergence of eucalyptus leaves was... Now, I don't think that is so, because knowledge is different from eucalyptus leaves, both from the point of view of understanding it, and from the point of view of it affecting things.

0:19:29.1 DD: So in terms of it affecting things, an example that I like to cite is that we will soon be in a position where our planet, or the planet Earth will soon be in a position where if asteroids or comets head towards it, they will be repelled, rather than attracted.

[chuckle]

0:19:56.4 DD: For all we know, every other planet in the universe attracts asteroids and comets, and ours will be the only one to repel. Now, that's... I don't need to say anything anthropocentric to note that fact. That's a physical fact, and it's the same as the other kinds of physical facts where we say this phenomenon is different from that phenomenon or we want to explain why. And the explanation in this case is that there is explanatory knowledge on the Earth.

0:20:33.2 SC: And I like the way that you put it, that in most cases in the universe, I'm going to paraphrase here, but big things push little things around.

[chuckle]

0:20:42.7 DD: Yes.

0:20:43.6 SC: And knowledge has flipped that on its head in some sense.

0:20:46.6 DD: Yes. So that is exactly the explanation for this purely physical thing that we have noticed. And then it's also true the other way round, that if you try to understand what's happening on Earth, then you will see... Again, the example I give is that you will see people in the laboratories where they are looking for extraterrestrial intelligence, they will have a champagne bottle in the fridge ready for an event that they are hoping for. And if you were an alien looking down on the Earth with a ultra high power telescope, and you notice that the champagne bottle was there and you wanted to predict something about that champagne bottle, will it always be there? Will it stay there? When will the cork pop out, that sort of thing. In order to, and you'd see that there are, it's not just SETI, I gave the example of SETI, but really any team that is looking for a breakthrough might have such a champagne bottle in their fridge, in their department.

0:22:07.0 DD: And if you want to understand the behavior of those champagne bottles, you must understand not just humans, not just what happens on Earth, not just humans, you must understand whether there's extraterrestrial life, whether quasars do this or that. Dark matter, dark energy, you need to understand basically everything before you can understand how champagne bottles behave on the surface of the Earth. And that again is because of the peculiar properties of explanatory knowledge.

0:22:43.5 SC: I mean, maybe go into that a little bit more. Certainly, it is a feature of life even in primitive organisms that living organisms have some information about their environment and use that. They leverage it, right?

0:23:00.2 DD: Yes.

0:23:00.6 SC: And human beings do so in a very more dramatic way. Are you pointing to the ladder there?

0:23:07.8 DD: Yes. So you might say this is only a quantitative effect, but the difference between, as Richard Dawkins says, every genome has got a blueprint of the environment that caused it. So the environment that caused bats or birds or something tells us something about, if you didn't know the Earth had an atmosphere, you might be able to infer it from the genome of bats or birds. But that's very parochial. The amount of the world that affects that genome is very tiny by cosmic standards, whereas the connection that I just mentioned goes all the way to quasars and to the Big Bang and to the end of the universe and so on. There's nothing in the physical world that can't affect those champagne bottles, and only, only via the intercession of explanatory knowledge.

0:24:21.0 SC: And do you think that it's fair to attribute that to specifically humans here on Earth? I mean, there's going to be debate about what non-human species really understand.

0:24:31.2 DD: Yes. So I prefer when talking about these deep things, I prefer not to refer to humans specifically, because if there are extraterrestrial civilizations, for example, then they will necessarily have this property too. Because they couldn't have become civilizations and make flying saucers and so on without explanatory knowledge. And the same will be true once we have artificial general intelligence. They will also have this properties. I prefer to talk about all those kinds of things, kinds of entities, as people. Humans are people, extraterrestrials are people, AGIs will be people. And I argue in my book that there's nothing beyond that. That there may be AGIs that think many times faster than we do, but there aren't any that are in principle capable of connecting the universe with champagne bottles any more than we can.

0:25:41.7 SC: That's a crucial point. I wanted to get into that. So you think that we have crossed some threshold where things that are understandable, we can understand in some sense.

0:25:54.2 DD: Yes. I think we have, and I think I have a watertight argument for that, but the...

0:26:01.7 SC: So what is that?

0:26:03.3 DD: Well, so it's in two parts. So I think human brains have two kinds of universality that are essential to this. One of them is fairly uncontroversial among sort of scientifically-minded people, and the other one is very controversial, but I think just as compelling. So the one that's uncontroversial is that our brains are Turing complete. That is, we can execute any program that can be executed at all. Now, it might take us more than a lifetime. It might require more memory than we have, but we can augment our memory, we can augment our lifetime, either by living longer or by having a tradition of doing certain things over generations. So those things aren't essential.

0:27:04.2 DD: You know, we are accustomed to saying that the computers that we are having this conversation over are Turing complete, even though they have only finite speed and finite memory capacity. But we know that that those are trivial restrictions because they can, however complex the program that we want to execute with them, we could do it if we had a bit more memory and a bit more speed.

0:27:29.4 SC: Maybe for the audience, define what it means to be Turing complete.

0:27:33.2 DD: Oh, this was defined by Alan Turing in 1936 when he set up the modern theory of computation. And he invented these, what we now call, what we now think of as rather strange computers. They were strange, they were made of paper tape and could move backwards and forwards via a reader. And he proved mathematically that a particular one of these could compute anything that any other one could. And this was a bit of pure mathematics. He also conjectured that the set of all of them was the set of all things that could be computed, that the set, in other words, that his model of computation was complete, that nothing could compute any more than that.

0:28:28.5 DD: He conjectured it, but once we went to quantum computation, I was able to prove that given quantum theory. So if quantum theory is false, it might still be false, but if quantum theory is true, then Turing's conjecture is now proven. So, we know that there's only one kind of universal computation and that there's nothing beyond that.

0:28:51.6 SC: I think that that's, maybe people have heard that before, but I think maybe it just hasn't made as much of an impression as it should. I think this is worth shouting from the rooftops, right? Like, not only can we...

0:29:03.2 DD: Might be.

0:29:04.5 SC: Calculate things and compute things, but we have very good reason to believe that even if we are slow and we make mistakes and whatever, but the kinds of computations that can be done are kinds we can do.

0:29:16.1 DD: Yes. So we're as confident as we can be that when the aliens visit us or when the AGI become our new overlords, that they will not be able to compute non-Turing computable functions. So that's as, or more known to us than other bits of science or bits of physics. So, that's the uncontroversial part, although you say many people aren't, you know, that it's not so familiar to many people. Yes.

0:30:03.9 DD: The other part is, I think... And that's a... By the way, Turing completeness is a property of hardware. It's a property of the brain. It's a property of computers. The other kind of universality, explanatory universality, is a property of software, which I say we have, our software has that property, and no other surviving organism on Earth has explanatory universality. Although we know, basically, for sure that there used to be species related to us on Earth that also had explanatory universality and they died out, which should be a warning to us.

0:30:48.9 SC: What do we have in mind there?

0:30:50.4 DD: Well, like Neanderthals, and I think going back to Homo erectus. Anything that had campfires necessarily has the thing that we have. There is only, again, there aren't gradations of it in the same way there aren't gradations of Turing universality. You either have it or you don't. It's possible that you are rather impeded in using it because you don't have enough memory or whatever, but the basic thing is all or nothing. And I think the same thing is true of explanatory universality, because this, if I can put it in my idiosyncratic way, which I like, the... It's to do with optimism.

0:31:41.7 DD: So the principle of optimism is that everything which is not forbidden by laws of physics is possible with enough knowledge. And the argument for that is that if there was something that was forbidden, sorry, that was permitted by laws of physics, but could not be attained no matter what Turing computable program we ran in our brain to do the thing, then it wouldn't be. That is, it wouldn't be possible. And we could then test the scientific theory that that thing isn't possible after all. And that what we thought of were laws of physics were in fact not sufficient laws of physics. There would be, no matter how we tried, no matter what we tried, we wouldn't be able to do this thing, like exceeding the speed of light or whatever.

0:32:36.7 SC: Yeah.

0:32:36.9 DD: It would be like that. If it was building a certain tower or building a certain society, either it's forbidden by the laws of physics or it's permitted. Because if it weren't permitted, then you could do this experiment. And by the definition of science, you could set up a refutable theory and then so on. So I think there's no getting round that. And therefore, I think that just as there is only one kind of hardware universality, there's also only one kind of software universality, and that's the kind we have.

0:33:14.5 SC: Do we have a definition of explanatory universality that is as rigorous and mathematical as Turing completeness?

0:33:22.5 DD: No.

0:33:22.5 SC: Okay.

0:33:23.9 DD: Because... There's a quite deep reason for that. Explanations. It's because you can't formalize the notion of an explanation. You can always invent new modes of explanation, and they are conjectures, like any theory. So you might conjecture that so-and-so is a good mode of explanation. And the openness of science is connected with the non-formalizability of explanation. And by the way, that's exactly the same as the non-formalizability of mathematics.

0:34:03.1 SC: Ah, okay.

0:34:05.0 DD: So you can't formalize what is a valid proof, because however you formalize it, you can prove that there will be mathematical truths that can't be reached by that formalism.

0:34:18.9 SC: So is it then fair to say that even if we don't have a rigorous mathematical definition of explanatory universality, we have a rigorous mathematical understanding that we never will have a rigorous mathematical definition?

0:34:28.9 DD: I think so, yes.

0:34:30.7 SC: Yes, okay.

0:34:31.7 DD: Actually, interesting point. I never thought of that.

[laughter]

0:34:36.1 DD: But yes, I think we do.

0:34:37.6 SC: Okay, good. Very good to know. But this leads you to... Well, I want to sort of finish up the monotony discussion by reinforcing your optimism that you already mentioned. You make a good case, gently laying it out, that we are just at the beginning of truly transforming the universe based on this knowledge and explanatory power that human beings have developed.

0:35:05.2 DD: Yes. I think that is necessarily true, because the openness and the unboundedness are really the same thing. And again, the same thing is true of mathematics. I mean, we know that there's an infinite amount of mathematics to be discovered, even though there, in the case of mathematics, there's a lot of it that we can't discover, unlike in the optimism case. Although I have a conjecture that we can discover all the interesting things, which are also infinitely...

0:35:45.2 SC: Okay. [laughter] Well, you have mentioned a couple times AGI, artificial general intelligence. I take it that you are relatively optimistic that's on the way.

0:35:57.7 DD: It depends what timescale you're talking about. I think we do not have the slightest clue how to make an AGI. I think what's standing between us and making an AGI is an explanatory theory. It'll be largely a philosophical theory rather than a computer science theory or mathematics or physics or anything like that. It'll be a new way of looking at what creativity is, what explanation is. And I think that qua computation, qua computer program, I would expect it to be very simple. Relatively simple. So it's not going to be reached by more and more billions and trillions of bits of data, that's not the kind of thing it is. We differ from monkeys, who have brains very similar to ours, or apes, the great apes, we differ from the great apes only by a few K of code.

0:37:13.1 DD: In that few K of code is the bootstrap program for bootstrapping this qualitatively different type of program that we run. Infinitely different. You asked how optimistic I am. On the one hand, I think that with hindsight, we'll realize that there wasn't much to it. Like, all we have to do is write this program of a few K and we're done. But on the other hand, I see no sign of the philosophy that would allow us to do that. And it's rather like the question of what is life, what that was like in, say, 1800. People wanted, some people, wanted life to be explicable as an ordinary physical process without any supernatural, without any magic, without any God, just laws of physics.

0:38:21.6 DD: And no one knew how to do that. They had vague ideas, like Lamarck and Darwin's grandfather had ideas that maybe it happened gradually, maybe it happened very slowly. They didn't have the idea of genes and they didn't have the idea of mutations and natural selection. And that solved it. And you could write down that idea in one paragraph.

0:38:48.3 SC: That's very easy.

0:38:51.8 DD: Darwin felt the need to write a whole book, and probably rightly, because from that paragraph nobody but him would have understood it. And it's possible that the idea that will open the door to AGI is that kind of idea. There will come a time when everybody thinks it's obvious and that we in our time were being obtuse for not seeing it. But from this end it might be very, very difficult.

0:39:25.1 SC: But it sounds like it also could be an example of what we started by talking about of we're percolating along in a kind of steady state for a while and then there'll be a sudden change.

0:39:33.7 DD: Yes.

0:39:33.9 SC: Hard to predict.

0:39:34.9 DD: Yes, well that certainly was the case with Darwin, and it also was the case with Turing. Babbage and Lovelace had the idea, they very nearly had the idea, but they were unable to persuade anybody. They thought it was really important. No one else did.

0:39:57.2 SC: Yeah. [laughter]

0:39:57.9 DD: And then Turing, I don't know how long Turing's idea would have percolated if it hadn't been for the Second World War, although I don't think it would have been centuries, but it might have been a couple of decades more before anyone thought of actually making these things. People thought of this as being a bit of mathematics. It's very hard to get into that mindset, because we've got computers all around us. I mean, I'm wearing one on my wrist. That would have been an alien conception a hundred years ago.

0:40:38.0 SC: So there does seem to be some similarity here, but you'll tell me whether it's a real one or not, between this idea of our ability to do Turing complete calculations, get explanatory universality. Now we puny humans can change the universe in a profound way. Does that have anything to do with constructor theory, which is another thing that you have introduced to the world?

0:41:04.3 DD: Yes. I can't yet give chapter and verse, but I think it's very much to do with it. For example, in the theory of computation, you know, the first thing we work out, or that Turing worked out in theory of computation is that there's a distinction between functions from the integers to the integers that can be computed and those that can't be computed. Similarly, in physics, we have physical transformations that can be brought about and ones that can't be brought about. So going faster than light can't be brought about. Going to the Moon can be brought about. So there's this distinction.

0:41:52.5 DD: The basic idea of constructor theory is that all the laws of physics can be expressed in such terms, in terms of a distinction between what can be brought about and what can't be brought about. And we haven't done that yet, I mean, we've basically done it for quantum theory, which was the easiest case, and we were kind of modeling, modeling constructor theory on the existing quantum theory, very conducive to it. And my colleague Chiara Marletto has also done it for thermodynamics.

0:42:24.3 DD: So once we have done that, as it were, or at least conceptually, once we have got, understood what expressing all the laws of physics in constructor theoretic terms would look like, then we can ask, the next question to ask, actually I'm already asking it, but I'm jumping the gun: Is there a universal constructor?

0:42:50.5 SC: Okay.

0:42:51.2 DD: Von Neumann asked that question, but that's only because he gave up on the idea. He wanted to have a theory of constructors, what we would now call constructors, in order to understand what life is. This was before DNA, before DNA was discovered and invented, well, the theory was discovered. But he was unable to, and so he invented the theory of cellular automata instead, and he invented the theory of universal constructors within the theory of cellular automata. But that's not what we want in physics. What we're trying to do is to set up a theory of constructors and of the universal constructor within physics. So now, then, is there, and we don't have a proof, but again, it's very connected with the principle of optimism, is there a principle that says the transformations that can be brought about are precisely the ones that a universal constructor could bring about? And that's as you see, I mean, you're nodding, so I see you're sympathetic to the idea that this is close to the philosophical idea of optimism and so on.

0:44:25.1 DD: And also, that means that human bodies are a kind of hybrid thing, like a brain is both the controller of a universal constructor, which is the human body, because the human body can, or at least in cooperation with others, can build a computer which can build a universal constructor and so on. But it's also the programmer. It's also the entity that creatively invents the programs, which a universal constructor is not allowed to be creative. It has to be perfectly obedient. So obedient is the opposite of creative.

0:45:12.0 DD: It has to, the universal constructor is like a universal computer. If it's not going to obey its program, it's not a universal computer. And same with the universal constructor. But our body, as you said earlier, it's imperfect, obviously, it doesn't always obey what we tell it to do, but those are errors which can be corrected. And in principle, these corrections can be achieved with sufficient knowledge. So it's all down to knowledge. So constructor theory is all down to knowledge ultimately, and same with epistemology, and same with everything.

0:45:48.7 SC: And we are going to get there, but I guess I would just like to clear up, I did have Chiara Marletto on the podcast before. We had a wonderful conversation.

0:45:56.5 DD: Oh, I didn't know that. Yes.

0:45:58.8 SC: But even though I understood much more after talking to her about constructor theory than I did before, I still think there's this lingering sort of naive physicist's question, which is, if I have a planet orbiting a sun and I know its position and velocity, Newton's laws tell me how to calculate Kepler's laws that it will go in an ellipse and things like that. How or why should I think about that kind of problem in terms of what can possibly be done and what cannot possibly be done? Why is that a useful or allowed reformulation?

0:46:38.9 DD: Well, it's not a reformulation. So that type of question, like what will the planet do, will it move in and ellipse and that kind of thing, that set of those questions is a subset of those that we really want to know. So for example, we want to know, are we safe from, to take a thing we mentioned earlier, are we safe from asteroids? Well, for that we want to know what kind of asteroids can be deflected. Now, existing ways of formulating physics can answer questions like what kinds of asteroids can be deflected with chemical rockets and telescopes that see the asteroid from such and such a distance, and so on. But we're not really interested in that. Or that's...

0:47:40.9 SC: A little bit we are.

0:47:43.7 DD: Yes. In the immediate sense we are, but what we really want is to be safe, and we want to be able to say protecting the Earth is possible. Then we can work out what kinds of things would be needed, and then we can use the existing type of laws of physics to work out numerically what will be done here. But this is different from, this is different from, say, can we visit other stars. Well, there, we've got a hard limit of the speed of light. So then the... If you ask a constructive theoretic question about that, you will immediately come to, what do you mean by visit?

0:48:30.6 DD: Some types of visit are possible. Some types of visit are impossible. And that is compulsory, provided that the laws of physics are what we think they are. In other words, provided that their dichotomy, the dichotomy that the existing laws make between the possible and the impossible is what we think it is. It might not be. Constructor theory doesn't, won't claim to be the final truth about everything or even anything.

0:49:03.2 SC: But I guess the thing I'm still not clear on then is constructor theory might say that a planet can move in an ellipse. Is it supposed to also be a way of figuring out that planets move in ellipses, or does it just say, refer to Newton's laws for that?

0:49:21.9 DD: Yeah. So it's not constructor theory itself. So constructor theory is a kind of meta law, like the conservation of energy or something. To derive a actual experimental conclusion from the principle of conservation of energy, you have to know what the energy of a particular type of object is as a function of its parameters. It's half MV squared or something. It's a kinetic energy. Now, if you didn't know it was half MV squared, the principle of conservation of energy would tell you nothing about how it moves.

0:49:52.5 SC: Fair enough. [chuckle]

0:49:54.1 DD: So that principle is a framework within which theories can be formulated. So if we formulate a theory that violates the principle of conservation of energy, we know that we're postulating something very significant, because we consider that principle to be an overarching principle that governs other laws. Now, constructor theory is intended to be such an overarching principle. So things can be expressed in constructive theoretic terms, in other words, in terms that will say, for example, what can be done to a planet to make it do a certain thing? What transformation can be done to it and what can't? And a special case of that is supposing you don't touch it, what can be done to it without doing anything to it. Okay. But that's a tiny minority of the possible interesting questions.

0:50:55.6 SC: And one of the I would imagine hoped advantages of constructor theory is that it kind of crosses levels, right?

0:51:04.5 DD: Yeah.

0:51:04.7 SC: We can talk about biology and chemistry and physics all under the same umbrella.

0:51:08.8 DD: Yes, very much so. And, so probably Chiara already told you that thermodynamics is a prime case of this, because in thermodynamics we really don't want to know what the specific physics of the stuff we are dealing with that do work and they have heat and so on. We want principles that transcend that and talk in terms of those. So we want to say for all theories that govern a thing, you can't convert all its heat into work. And if you had a theory that violated that, you'd be proposing a momentous thing. You'd be proposing that the second law is false and that kind of thing. And we are hoping that the same thing will be true of constructor theory, that there will be momentous principles of constructor theory, which on the one hand will constrain other theories, and on the other hand will give a deeper understanding of why subsidiary theories or other theories have the properties they do.

0:52:20.3 DD: Like we know why kinetic energy in the Newtonian approximation is half MV squared and not half MV cubed. And we know that because we've got a deeper formalism now underlying that which Newton laid down, and Newton didn't know anything about energy. But we know now... Actually, I think he did. I read somewhere that... You can ask Julian Barber about this.

0:52:51.1 SC: Okay.

0:52:51.4 DD: I think Newton did know a lot about what we now call modern theory of dynamics or Lagrangian or Hamiltonian dynamics, but he decided not to include it because it was irrelevant to what he wanted to show. Like, he wanted to have... Three laws of motion is better than five. So, and exactly how you work this out, well, he didn't know the immense power of modern ways of expressing his theory. So I think he wrote down some of these laws, like Galilean invariance, for example, he definitely knew about.

0:53:32.9 SC: Right. That he definitely knew about, yeah. It is interesting. So I perceive dimly through the mists a connection or at least an intellectual affinity between the idea of separating out possible transformations from impossible ones and a kind of Popperian epistemology about possible worlds that are allowed by the data and possible worlds that are not. Is that, am I making that up or is that there in your head too?

0:54:00.3 DD: That's definitely there. So Popper taught us that the content of a theory, of a scientific theory, is in what it rules out. And if you just took that seriously as the basis of your worldview, you'd immediately come to constructor theory, because then you'd say, well, what does it rule out and what doesn't it rule out? And the distinction between those two is the theory. Popper never said that. If he had said that, then he could have discovered constructor theory.

0:54:35.3 SC: There you go. Yeah.

0:54:37.7 DD: But yes, it's very much connected, and it's also connected with, at the same time, it's also connected with optimism. 'Cause Popper's philosophy, he explicitly said it's our duty to be optimistic rather than, I've forgotten the quotation, but it's something like, rather than complain about how things are, it's our duty to make things how they ought to be, and something like that.

0:55:08.2 SC: Okay.

0:55:09.8 DD: So all these things are connected. Yes.

0:55:11.5 SC: And so I, let me confess, maybe you already know this, but I have long been an evangelist for Bayesian reasoning and epistemology, and I'm fascinated by the fact that you more or less thoroughgoingly reject it, or at least in certain cases. So, explain what your objections are to that, 'cause it's subtle, but potentially super important.

0:55:38.5 DD: Yeah. I think it is super important, but it's not... So quite a lot of different things are called Bayesianism. And I don't know which of them you are actually attached to, and which kind of come along for the ride. So I specifically object to Bayesian epistemology, which is the theory of knowledge, that knowledge consists of propositions in a rational mind, each of which is accompanied by a number, not literally, but implicitly.

0:56:18.0 SC: In principle, yeah.

0:56:19.5 DD: And that these numbers obey the probability calculus. And that when we say that we have improved our theory, we mean that we've increased... When we say that we've objectively improved our theory, we mean that we've increased the credence, the probability of true theories and decreased the probability of false theories. So I'd rather not call that thing that those numbers that are supposed to be in the brain, I would rather not call them probabilities at all. So I try to only call them credences.

0:57:00.6 SC: That's fine.

0:57:03.3 DD: Because they are... First of all, I don't think they exist. And secondly, if they do exist, Popper and Miller proved that they don't obey the probability calculus, and couldn't. And the key to understanding what Popper and Miller did, and as you know, I'm writing a paper about this with my other colleague Matjaž Leonardis. We have been writing it for years, so it's quite a thing to get one's head around, but the thing we think is the key nowadays is that increasing your credence... So, okay, let me backtrack a bit. If we were talking about logic, then it would be the case that if you prove a theory logically, you've also proved all its consequences. No matter how arcane the consequence, you prove this, you can't both assert a hypothesis and deny any of its implications.

0:58:17.7 DD: Now, the thing to concentrate on in why Bayesianism, Bayesian epistemology, sorry, is a bad idea, is that this isn't true of probabilistic reasoning. So you can have some evidence that increases your credence for a theory... Oh, and now I have to stress that I'm now talking in terms of credences, which I don't think exist. So rather than...

0:58:47.1 SC: We'll let you do it.

0:58:47.2 DD: Prefix it... Sorry?

0:58:49.5 SC: We'll let you do it. We understand the conditional nature of your statements.

0:58:54.2 DD: Yeah. So rather than say at the beginning, I'll say at the beginning that in arguing about Bayesian epistemology, almost every sentence would have to be prefixed with "assuming that credences exist and obey the probability calculus, then" so-and-so.

0:59:10.9 SC: Okay.

0:59:13.0 DD: The key is that a piece of evidence can increase the credence of a general theory while decreasing the credences of its consequences. And then one has to ask, which consequences? 'Cause we're only interested in some of the consequences of a theory. So, you know, it might be that it only ever decreases the credence of uninteresting consequences. And when Popper and Miller proved their theorem, some people took that tack in criticizing, in saying, well, yes, it decreases the credence of some of its consequences, but those aren't interesting consequences. But Popper and Miller also showed that, they actually provided, proved a criterion for which consequences have their credences increased and which have their credences decreased.

1:00:20.5 DD: And the answer is the ones that have the credences increased the most are the ones that just restate the evidence in other words. The ones whose credences are increased, but not that much, are ones that are very close to the evidence. And then there are most of them, most of the consequences, the ones that are not implied in whole or in part by the evidence. I should say that implying in part is a can of worms, because all theories imply tautologies. Therefore a theory and its negation and everything. So there's no way of ripping apart the one set of consequences from another.

1:01:21.1 SC: This is why it takes a long time to write the paper. I get it. Yeah.

1:01:24.4 DD: Yeah. They just wrote down, they were satisfied with writing down the truth. It didn't, it only took three or four pages. They sent it off to, I think the British Journal for the Philosophy of Science and also to Nature. The papers were accepted. Some people got very angry, and most people didn't notice. And we think that everybody should notice, and nobody should get very angry. So their theorem shows that the only way that interesting consequences of a theory have their credence increased is if they have a lot in common logically with the evidence, if they're just either restating the evidence or almost restating the evidence.

1:02:18.4 SC: Now, is that necessary, or does that happen depending on what your other possible propositions are?

1:02:25.5 DD: It does. So the way we prove it is we take the set of all possible propositions expressed in terms of possible universes. I quite like that framing. So a proposition or a theory, again, it's a bit like constructor theory. A proposition sets up a dichotomy between the universes whose existence is denied by that proposition, in other words, the universes which couldn't exist if the proposition is true, or couldn't be the real one if the proposition is true, and those, that could still be the real one if the proposition is true.

1:03:08.5 DD: You can express it in terms of the set of all propositions or the set of all dichotomies between universes that can and can't exist according to a particular proposition. Another thing it's independent of, so if you are a Bayesian, so there's my prefix again, if you're a Bayesian, you'll want to have a probability distribution function over that set of propositions, and you'll want it to obey the probability calculus. Now, the Popper-Miller theorem is independent of what that distribution is, so long as it obeys the probability calculus.

1:03:49.8 SC: And obeying the probability calculus just means there are numbers between 0 and 1 that add to 1.

1:03:55.4 DD: Yes. But there's also relative probabilities.

1:03:57.9 SC: Yeah. Right.

1:04:00.0 DD: Yeah. So yes, that's all we need to...

1:04:01.3 SC: That set of ideas. Yeah. Okay.

1:04:03.3 DD: Yeah. So the result about the only things whose credence goes up are the ones that are basically restating evidence or something like that, is independent of the priors. It's independent of the prior probability, a credence distribution function.

1:04:28.4 SC: Okay.

1:04:29.4 DD: Their theorem is true regardless of credence distribution function. Not that there aren't other things very wrong with the idea of a credence distribution function, but at the moment, we're assuming Bayesian epistemology. And I should say that other parts of what's sometimes called Bayesianism, for example, the fact that it's a common mistake to use absolute probabilities when one should be using relative probabilities, that's a common mistake that one should avoid making, that's untouched by the Popper-Miller theorem. That's true, and we have no quarrel with that. It's just Bayesian epistemology that is the theory of knowledge that says that we obtain knowledge by increasing our credence for true theories. That's the thing that's false.

1:05:21.8 SC: So what, is it possible to articulate what explicitly goes wrong with an idea that I would happily tell people that, for example, we have two theories of dark matter. There are weakly interacting massive particles or their axions, and we have some credences. The one theory is right, the other theory is right, and we go out and do an experiment and we rule out some of parameter space and now we can use Bayes' theorem to adjust our credences accordingly. Is that okay, or is that problematic in your View?

1:05:57.2 DD: That the way you said it literally is very problematic.

1:06:01.1 SC: Okay.

1:06:01.5 DD: But what you are informally referring to happens all the time and is perfectly legitimate. And so let me try and say what the difference is. So the picture of knowledge and the growth of knowledge that we have in Bayesian epistemology is that all these propositions are kind of in the frame. We're trying to rule out some of them, increase our credence for others. In real life, what we're seeking is good explanations, and they are very rare, and they do not obey. Not only do they not obey the calculus of probabilities, they don't even obey ordinary logic, they don't model ordinary logic.

1:06:49.2 DD: For example, my favorite example, the negation of an explanation is never an explanation. So if you say that gravity is caused by the curvature of spacetime, that's a theory, that's an explanation of, an amazing explanation of why we appear to feel forces and all that. To say gravity is not caused by the curvature of spacetime doesn't explain anything. It doesn't even purport to explain anything. Like it might be part of your psychological journey from Einstein's theory to quantum gravity or something, but it in itself doesn't tell you anything about quantum gravity. It doesn't... I can prove that to you now because we don't have a theory of quantum gravity that works.

1:07:47.1 DD: So, I can prove to you now that merely saying Einstein's theory isn't true doesn't tell you anything about quantum gravity. So, that means that the whole... If even logic doesn't model what we're doing, then certainly the probability calculus doesn't. And then there's this paradox of the intransitivity of support, as the logicians call it. There was logician called Hempel who many decades ago proved some theorems. And so... Can I quickly explain what intransitivity is?

1:08:28.5 SC: Please, yeah.

1:08:30.5 DD: Again, it's just to stress that increasing the credence for a theory does not increase the credence of its consequences typically, only very rarely does it, and those are the uninteresting cases. So let's see, let me borrow the Linda example, you know, Kahneman and so on.

1:08:55.3 SC: Yeah. Okay. Yeah.

1:08:56.5 DD: You have Linda, who we're wondering whether she's a banker and a feminist. So Linda's going to turn out to be a banker and a feminist. And so, by the way, this isn't the Kahneman thing. I'm just stealing the example.

1:09:12.1 SC: Yes.

1:09:12.1 DD: So suppose we find out that... We're interested in whether Linda is a banker or a feminist, that that's going to be our theory that we are wondering about. So then we find that she's a banker. We get evidence of that. We see her going to a bank every day to work, and so on, and it increases our credence to nearly 1 that she's a banker. That will support our theory that she's a banker and a feminist. And once we believe that she's a banker and a feminist, we can go on to deduce logically that she's a feminist. So we've gone by probabilistically from her being a banker to her being a banker and a feminist. And from that we've gone logically to her being a feminist. But her being a banker is no kind of support for her being a feminist. So it, there's a non-transitivity there. In fact, her being a banker is probabilistic evidence against her being a feminist, is assuming that the prejudices embedded in that example are true.

1:10:29.5 SC: For purposes of the story, yeah, we'll go with the prejudices. Yes.

1:10:34.9 DD: So you have banker sort of... Being a banker supports being a banker and a feminist, being a banker and a feminist supports, because it implies being a feminist. So A implies B, sorry, A supports B, B supports C, but A countersupports C. And so what Popper and Miller perhaps should have asked at the beginning of their paper is, which implications of a theory are supported by evidence that supports the theory? And they should have said then, we shall prove actually very few of them.

1:11:18.6 SC: So I guess I don't quite see the force of this example in this case, because I completely agree that the evidence that Linda is a banker increases credence that she's a banker and a feminist. It also increases our credence that she's a banker and not a feminist. [laughter]

1:11:36.8 DD: Yes.

1:11:38.3 SC: So...

1:11:38.6 DD: Absolutely true.

1:11:39.6 SC: So I don't see how I would overall increase my credence that she's a feminist just from that evidence.

1:11:46.6 DD: Well, your credence that she's a feminist has increased from what it was before. Now, it's true that your credence that she isn't a feminist has also increased.

[laughter]

1:12:00.9 SC: That sounds like just a mistake. Is that...

1:12:03.4 DD: So yeah, well, note that what we are really after is explanatory theory. That's why the original Kahneman sort of example doesn't work properly, because they lure us into trying to think of an explanation by telling us all sorts of explanatory content that is relevant to whether she is a feminist or a banker or both. And then they completely discard it and ask the question, is it more likely that she's a banker or that she's a banker and a feminist? None of the story that we're told before that is relevant to that question.

1:12:40.1 SC: Well, they were psychologists, not logicians, right?

1:12:44.3 DD: Yes, yes. Well, no, no, we're scientists. Like we want an explanatory theory. We would like to have, perhaps in an ideal universe, we would like to have a way of deducing the true theory, but there is no such thing.

1:13:03.7 SC: Yeah.

1:13:04.5 DD: The only thing we can do is go for explanatory power and go for good explanations. And in the case that you talked about, the...

1:13:17.3 SC: The dark matter.

1:13:18.2 DD: The dark matter and so on, we don't have infinitely many theories. We have a handful of good explanations, which are good only insofar as the other theories exist. If the other theories didn't exist, any one of those would be our explanation, would be our sole explanation, and we would go around behaving as if we knew it was true. That's the only kind of knowledge available to finite beings.

1:13:52.1 SC: But in this case where we have two plausible, pretty good explanations of the same set of phenomena, and we have to make decisions about where to spend money testing them and who to hire in our physics departments, how can we not say that we have credences on these different proposed explanations?

1:14:12.3 DD: Well, we can have credences, so long as they don't obey the probability calculus. So if you have a credence... Wait, let me first say, maybe this is relevant. You can tell me whether it is. The Bayesian framework for credences does not allow you not to know something. So not knowing, we don't know which of those theories is true. And we don't expect to get to the final truth even once we do know more than we know now. So we're after good explanations. That means that things we do not know, like are we in an alien simulation, we don't know that. It's meaningless to say that we're going to give that a credence of 0.5 or a credence of 0.99.

1:15:18.7 DD: Nor by the way, is it meaningful to ask, do we have a credence for Bayesian epistemology. What's our credence for Bayesian epistemology? Is it 1 or is it 0.5 or is it 0.99? Now, I can remove the prefix and I can say none of those things makes sense. We decide between theories of dark matter or theories of epistemology according to how well they explain what we want to explain. So when we're asking which one we want to fund, which theory we want to test next, we are asking, not our credence for the theories, we're asking for the credence of, we are asking for judgments about what the prospects for increasing knowledge are.

1:16:13.2 DD: So, I think that quantum theory is definitely false. I think that general relativity is definitely false. And I also think they contradict each other. And therefore my credences, like if I talk about my beliefs for those theories, they definitely don't obey the probability calculus, because if they did, my credence for one would be one minus my credence for the other. And yet I have a very high credence for both of them. So probability doesn't provide a proper model for my attitude towards theories. And it's the same with the different theories of dark matter. What we want to do is to do an... Ideally we'd like an experiment that is a crucial test between two of them.

1:17:01.2 SC: Of course.

1:17:01.9 DD: After which one of them would have zero credence. So it's not a matter of credences going up and down, really credence that provided you are confident that the experimental setup is right. Duhem and Quine pointed out that we can't always be sure of that. And in fact, ultimately we can never be sure of that, 'cause there are always the aliens with their virtual reality machine that might be misleading us. So probability doesn't come into any of this. We want to take into account things like how good an explanation was it in the first place? Like if it's a good explanation, can we rule out a bad explanation so that we don't have to consider it anymore? Or can we fail to rule it out, in which case we'll have to consider it more than before.

1:17:56.1 DD: How expensive are these experiments? We cannot work out how much money to spend on testing each experiments by using classical decision theory and seeing which one has the highest expectation value of the benefit that we will get from knowing things or not knowing things, because we don't know what the outcome is going to be. The best thing that can happen in an experiment is that you get an outcome that you didn't foresee. But if you didn't foresee it, you also didn't foresee its probability. What is the probability that doing an experiment on knocking a comet out of the way will tell us something about dark matter?

1:18:40.7 DD: Well, we don't know, we don't know that probability, and that probability is irrelevant. What we can use is our best explanation. We can see that none of our explanations of dark matter say that it will affect comets. And if one of them did, then we would ask, well, can we test this? Or is it the kind of theory, like, well, it could be, could be so, which is always true, but is a bad explanation. We judge on the explanation, not the probability. So if you are alive at the time of Kepler and Galileo and those people, then you are not looking for a high probability theory.

1:19:28.8 DD: The theory that the planets move on epicycles has got a far higher probability than that they move on ellipses, because an ellipse is a kind of epicycle. So by the Linda argument, Galileo should have preferred the epicycle theory because it's far, far more probable than the ellipse theory. But he didn't, he preferred the circle theory, which is even less probable than the ellipse theory, because given what he thought he knew, it was a better explanation, because if it's an ellipse, then you've got to explain more things. There's more things remain unexplained than if it's a circle. In ellipse, what's the eccentricity of the ellipse? With a circle, you don't have that question. So he thought there's going to be a way of making circles work. See, he wasn't looking for a high probability.

1:20:34.9 DD: If anything, he was looking for the lowest possible probability that's still viable as a theory. And that's what we do in science when we're looking for general theories. It's a bit different when we are looking for a particular theory, then, now this comes back to other uses of Bayes' theorem. If you are a doctor and you want to know whether a particular patient has got like dengue fever or something, and you ask them, well, have you been to the Far East lately? Then you're asking for something probabilistic. And if I bend over backwards, I can call that probabilistic. It's really that he's looking at frequencies, first of all, not probabilities. He's looking at there's only a finite number of people that have been to the Far East, a finite number who have got infected with dengue fever.

1:21:35.5 DD: He's approximating those frequencies of probabilities, and he's using the approximation that his putative patient is randomly chosen from the set of all those people, which he wasn't, he wasn't, but he's using that because he doesn't know. But does that mean that he's giving the doesn't know a credence of one half? No, he's using it because he doesn't have an explanation of the patient's contact with dengue fever. Apart from... That doesn't include going to the Far East. Now, if they said, well, I haven't been to the Far East, but I have been to a lecture that was attended by scientists who've recently been to the Far East, then that would change the priors.

1:22:31.5 DD: We call those the priors, but it's just actually just changing the numbers in these frequencies. So it's sometimes a good approximation to approximate frequencies by probabilities, or rather by numbers that obey the probability calculus. And they don't increase our knowledge. You can't increase general knowledge that way. You can't decide between general theories in that way because the set of individuals is infinite there. So it won't work there.

1:23:11.3 SC: It's clear that the idea of a good explanation is kind of crucial here. How clear and formal can we be about what is a good explanation?

1:23:21.9 DD: Well, as we agreed earlier, you can't formalize the concept of a good explanation.

1:23:28.3 SC: Yeah. You know it when you see it.

1:23:32.0 DD: And as a matter of... Sorry, go ahead.

1:23:32.8 SC: You know it when you see it.

1:23:33.3 DD: No. So it's not like a matter of taste. It's a matter of philosophy.

1:23:41.9 SC: Okay.

1:23:42.9 DD: So we can make progress in philosophy by the same method, that is by saying that we're going to exclude solipsism because solipsism could explain anything, could "explain anything," and we're going to exclude the doctor saying, well, the patient could be lying, could have been anywhere. Therefore, I don't know. And I've got no way of assessing whether they've got dengue fever or not. You also exclude that, because that is always true and would always short circuit any kind of trying to approach the truth. But trying to approach the truth about general theories, like solipsism or something, means that you have to adopt the criterion of a good explanation, because, well, this argument that an explanation that can explain anything is a bad explanation, I think has got a transcendent compulsiveness about it, a compellingness about it.

1:24:55.5 SC: Yeah.

1:24:57.4 DD: Which doesn't involve any axioms. Like we're not making an axiom of using the best explanation, 'cause if you make an axiom, you'd want to have a precise definition of the terms in the axiom. But somebody, like I said earlier about the principle of conservation of energy and that kind of thing, if you want to say that bad explanations are actually acceptable, you've got to realize that you are climbing up a philosophical mountain by saying that, you can't just say that just to justify your own theory of, to say that actually mountains don't exist because anyone could say that about anything. And if you say, well, no, although anyone could say it, I'm saying it, and there it's allowed, well, that's just got an obvious flaw in it, that way of arguing.

1:25:55.6 SC: Yeah. One thing... That was very helpful, but one thing you said along the way I can't quite let you get away with, or at least I want to hear more, namely, that you're pretty sure quantum theory is false.

1:26:07.9 DD: Yes.

1:26:08.7 SC: In what sense do you feel that?

1:26:12.4 DD: Pretty sure, and I'm not saying I've proved it. So several things, the main one is what I mentioned about its conflict with general relativity. So in general relativity, we know that the behavior of an object like a planet or whatever is dependent on the behavior of another object like the sun, and that this is mediated by a field, which travels at finite speed. We don't have a theory of what... And quantum theory tells us, with equal confidence, that the sun isn't just in one place, the sun is in a superposition or more generally in a mixed state, where it has many different positions simultaneously. And although some of them are pretty close to where we see the sun, some of them are a long way away.

1:27:18.3 DD: We know that because of the instability of classical mechanics that the sun has been involved in lots of interactions and some of them will have been chaotic, and therefore the end result will have depended sensitively on the initial result, therefore, these positions of the sun that were initially very close to each other will get very far away. And therefore, according to quantum mechanics, some of the suns are far away, and relativity does not, and quantum mechanics, neither of them have a way of telling us that the sun's effect on the planets is different in different universes. I can say that in words, but I can't say it in equations, and therefore we don't have the right equations. So that...

1:28:10.1 SC: Would you not... I mean, I get everything that you said, but then I want to just say there are different branches of the wave function where there's a good semi-classical approximation and general relativity works pretty well.

1:28:22.7 DD: So when I say that the theory is false, I mean that it's not true. I mean, I'm using the words true and false in the sense in which they're used in logic, there is no excluded middle.

1:28:34.2 SC: Sure.

1:28:35.6 DD: Certainly, both relativity and quantum theory are extremely good approximations in the situations where we want to apply them. It's not so clear that we won't very soon be applying them in other situations, like in the early universe, where we want to explain something like the distribution of microwave background radiation over the sky where there are, where billions of light years involved, and this is all due to something that happened on a scale smaller than an an atomic nucleus originally, where definitely quantum effects were dominant, and we don't know what those were and how they affected gravity and dark matter and spacetime and so on.

1:29:36.2 DD: So how close a theory is, how good an approximation is, depends on how you want to use it, how good an approximation of theory is. So, yes, certainly, good approximations for practical purposes, but so is Newton's theory. That's also false.

1:29:56.7 SC: Do you have any hints as to how to modify quantum theory to make it better?

1:30:03.4 DD: Yes, I think so. So there I would have to go to quantum field theory, which has more of an internal problem. Never mind gravity, just the problem of quantum field theory. All existing quantum field theories are based on axioms which include the axiom that fields that are space-like separated commute with each other. That also means that a field at one point commutes with the future light cone of the field at the other point. And the difference between, but on the other hand, field quantities at the same point fail to commute.

1:30:54.9 DD: Therefore field quantities are discontinuous everywhere. So the whole conceptual framework of quantum field theory is not what it's cracked up to be. Mathematicians say, okay, well, it's not a field of, it's not a real valued field. It's not a quaternion valued field, it's, I've forgotten what they call it, but anyway, the only things that are real are the integrals of the field over finite size.

1:31:34.6 SC: Right. Distribution value fields.

1:31:36.6 DD: Distribution... That's what they're called. Yes. Distribution value fields. So, but that hasn't got a conceptual model. I mean, you can't have a distribution over things that don't exist. So you can say that only the distributions exist, but there's got to be, a distribution has to be over something. And so anyway, in short, I have an idea for a variant of quantum field theory where we don't have that axiom, where fields at space-like separated points are allowed to fail to commute and where the thing that they have to do is be continuous. And there's quite a nice theory, again, mathematically it's quite nice, but conceptually it's wild. I rather like it.

1:32:37.2 SC: For that reason.

1:32:38.5 DD: Yes. Yes. So not only do causality and that kind of thing mean a different thing in that theory, but measurement does as well. And the separation of systems into subsystems means something else than it does in ordinary quantum theory. And so I've been trying to get that theory to work for years, and I got some nice equations of motion for it, which I don't know what they mean, but it's rather a nice thing. So because of this pathology in quantum field theory, it's been taken for granted that the way you judge proposed quantum field theories is by how well they let you get round those pathologies, whether you have an infinity that cancels another infinity, and so this discontinuity is not as bad as you might think and so on, and on the other hand, the ones that don't have that property are not really considered.

1:33:44.5 DD: Now, in this unorthodox quantum field theory, as we call it, you have a different criterion, and the criterion is simply that the algebra of the quantum fields does not change with space and time, which we have in the conventional theory as well, except that that hardly makes sense when it's discontinuous everywhere. And then you see that there are only a finite number of possible second order equations of motion. And so that can be the criterion of the ones that are useful to investigate physically.

1:34:28.5 DD: And I and other colleagues, Sam Kuypers, have been investigating an easier version of that, where it's just the qubits that don't have to commute, different qubits, rather than a field, which is an unwieldy thing. So you have qubits which don't have to commute with each other. And that is another rather nice theory, and it's promising in various ways, and we are working on whether this could be testable, like whether if you have, say, a pair of photons or something coming off a decay process, whether those two photons might not commute with each other. And if they didn't, could we detect this? It would produce a kind of entanglement between them that is different from the entanglement that happens in ordinary quantum theory, ordinary quantum field theory. So we haven't got there yet, but that's the kind of fun we've been having.

1:35:39.8 SC: Yeah, that does actually sound like fun. Does it fit into an Everettian kind of formulation of quantum theory?

1:35:48.8 DD: Yes, Everettian and in the Heisenberg picture. I and we think that the Schrödinger picture is very misleading, because the Schrödinger state is global and it leads Everett and DeWitt to thinking about the whole universe as splitting every time the state changes.

1:36:11.9 SC: Yeah, I'm all in favor of that.

1:36:15.7 DD: Well, I think it is too much for many people to swallow and they don't have to...

1:36:19.5 SC: It is.

1:36:20.3 DD: Because in the Heisenberg picture, it's only the observables that split into. And the distant universe is left unchanged by quantum phenomena.

1:36:29.9 SC: And maybe this gets into something I've always wanted to ask you about. I think of worlds in the Everettian quantum theory as arising from decoherence. But I've heard you say things that make me think that you're more willing to talk about multiple worlds even before decoherence has happened.

1:36:52.5 DD: Yeah. So in my view, because I prefer to think in the Heisenberg picture where everything is local. So there are two situations where it is a good approximation to think of quantum physics, of quantum systems as splitting into worlds. One of them is when there's decoherence, but the other one is where there's a quantum computation in progress, but not just any quantum computation. If you have a typical quantum computation, in fact, is that you have a set of worlds that are all identical, then you do something to them that makes them different, like makes them 2 to the N of them, and the register holds a different number in each of the two to the N universes. Then you do stuff to those numbers in those registers, and then you recombine them.

1:37:55.2 DD: So I think that during the process of splitting into multiple copies and in the process of recombining, it's not useful to think of them as being separate universes. They're all affecting each other so much that... A universe conceptually is a quasi-autonomous thing. It's a thing where classical laws almost hold. And that's what happens during this intermediate thing. Where you are doing a different computation in each of a vast number of universes, the computations are classical computations.

1:38:34.0 SC: Yeah, okay.

1:38:36.1 DD: And they're not affecting each other. Each one is autonomous. And so I think you have there, it's useful to speak of the multiverse as having split into universes for a while. And also when there's been decoherence, they're also useful, for like the opposite reason, because there's no hope of recombining them.

1:38:58.0 SC: Well, I guess, yeah, this is very helpful to me because I get it now, but so in that case, in the quantum computation case, you say it's useful to think about them as separate worlds 'cause they're evolving independently, even though they're not really, there's probably some sense in which they're not classical, I think.

1:39:19.4 DD: They're classical computations.

1:39:20.8 SC: But they are classical computations. And furthermore, they do recombine at the end of the day, unlike the decoherence example.

1:39:25.6 DD: Well, if somebody knocks over the computer and they never recombine, and then that happens later, then you know, you can't say, well, retrospectively they weren't universes. I think that wouldn't make sense.

1:39:39.5 SC: Okay. Alright. Well, you've given us a lot to think about. My last question will be, am I right that you recently mentioned that you're working on a third book?

1:39:49.5 DD: Yes, actually, I'm working on several books, and I'm not sure what I can say about the ETA of any of them. So I'm also working with Sam Kuypers and Chiara Marletto on a textbook of quantum mechanics, quantum theory. And I'm also working on a science fiction book.

1:40:11.0 SC: Oh, wow. A novel.

1:40:12.9 DD: Which contains conjectures that I wouldn't dare state seriously, even in an article, but in science fiction you're allowed to.

1:40:24.5 SC: But maybe you have a little bit of sympathy for these conjectures.

1:40:27.9 DD: Yes, I have a bit of sympathy for all but one, which is very horrible.

[laughter]

1:40:36.1 SC: Okay.

1:40:37.4 DD: So, and that's what makes it dramatic. I don't know how to refute it. I mean, it could be true, but as we've just said, a lots of things could be true.

1:40:49.1 SC: Lots of things could be true. And for the quantum theory textbook, is that supposed to be a competitor for standard second year in university?

1:40:55.8 DD: Yeah. Well, it's a competitor in the sense that if somebody wants to change the entire way they teach quantum mechanics...

1:41:02.3 SC: Yeah. Okay.

[laughter]

1:41:04.1 DD: Then this would be a way of doing it. So the Heisenberg picture would be central, not Schrödinger. Everett would be central. Qubits would be central, not hydrogen atom. So it's all about quantum information. It's close to modern kinds of experiment instead of old-fashioned kinds of experiment. And it's conceptually, it doesn't have the baggage that existing things do. Now, I know there are a couple of textbooks already on the market that start with qubits. And I haven't actually read one of them, but I'm sure they don't do those other things that we want to do.

1:42:00.9 SC: Probably not. I will confess, I'm also working on one very slowly, but I don't know whether, how to characterize it. I'm not as ambitious as you are about hoping that people will completely change how they think about, how they teach quantum mechanics. So I'm actually, even though I think that probably I'm sympathetic to the philosophy you put forward in this book, I'm guessing, but I'm going to try to split the difference, right, so that more old-fashioned people are not quite as shocked. So a little bit of everything there.

1:42:33.7 DD: Yes. Well, that'll probably sell much better than our one.

[laughter]

1:42:37.3 SC: You know, I'm not averse to that. We'll have to see. But David Deutsch, thanks so much for being on the Mindscape podcast.

1:42:42.1 DD: Well, thank you for inviting me.

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