Episode 134: The Deutsch Slot Machine

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Unofficial, reviewed transcript. It may still contain mistakes; check the podcast when wording matters.

Speakers are labeled by first name where identified. Unidentified-speaker labels may refer to different people. Bracketed question marks indicate uncertain wording.

Transcript

[00:00:00]  Unidentified speaker: Hello out there.

[00:00:01]  Peter: This week on The Theory of Anything podcast, Bruce makes his most epic statement about probability ever. He discusses Deutsch's lecture, Physics without Probability, and also pulls from our episode 100 where we interviewed Deutsch. Bruce then methodically goes through why Deutsch's argument may be an example of word essentialism, i.e.

[00:00:25]  Unidentified speaker: an argument about words.

[00:00:27]  Peter: He then makes an impassioned plea for someone out there to help him understand where precisely he is misunderstanding Deutsch's argument. I felt like this was top shelf Bruce Nielson. He goes on a long time, yes, but I personally think it's worth it.

[00:00:52]  Bruce: Welcome to The Theory of Anything podcast.

[00:00:53]  Unidentified speaker: Hey, Peter. Hello, Bruce. How are you doing today? Good.

[00:00:59]  Bruce: Well, we're gonna finally cover Deutsch's, his presentation, Physics Without Probability.

[00:01:08]  Unidentified speaker: Okay.

[00:01:09]  Bruce: And let me just say that I did not answer my questions.

[00:01:15]  Unidentified speaker: So. All right, well, I rewatched it.

[00:01:19]  Peter: I think I've seen it about four times.

[00:01:21]  Unidentified speaker: Given your background and what we've discussed on here, I think I'm almost getting my mind around this controversy. So. A little bit.

[00:01:32]  Peter: I mean, I think the first time I ever watched it, honestly, it sounded like gobbledygook to me.

[00:01:38]  Unidentified speaker: I just I did not.

[00:01:39]  Peter: I just didn't didn't have the background knowledge for it.

[00:01:42]  Unidentified speaker: So I'm getting there.

[00:01:43]  Bruce: What is it you believe he's saying? Like, try to summarize what you think he's saying.

[00:01:47]  Unidentified speaker: Oh, well, I'm not sure I'm quite there yet, but it's fine.

[00:01:52]  Bruce: Like, it can be totally wrong. Like, people watch this video. They're clearly getting something out of it. They point it me to it all the time. And they say, go watch this video.

[00:02:02]  Unidentified speaker: This explains. Right. Well, I mean, it sounds like it's a defense of.

[00:02:08]  Peter: I mean, he's basically proposing the idea of constructor theory as an alternative to probability.

[00:02:18]  Bruce: OK, so you perceive him as as putting forward constructor theory as an alternative to, let's be clear, probability theory.

[00:02:26]  Unidentified speaker: Is that not right? No, no, no.

[00:02:28]  Bruce: I'm asking if that's what you intended to say.

[00:02:31]  Peter: I that that's I think that's what he pretty clearly. Says I think that he says, I was kind of before I was kind of hung up on the multiverse angle. I don't think that he's saying that his argument is completely about the multiverse, though I think that he believes that probability is not, it just doesn't have validity even even from a single universe perspective.

[00:03:06]  Bruce: So, okay, so let's go with that.

[00:03:07]  Peter: And I guess there's just different levels of explanation and probability is just not, it's just not, has limits and very limited in what it explains.

[00:03:23]  Unidentified speaker: I really like, I just want to say one more thing.

[00:03:26]  Peter: I really, the point that resonated with me, I think it was from our last podcast that you said, I think you were describing what Deutsch believes is that if there's an explanation for why probability works, a coherent explanation, then it has validity.

[00:03:51]  Unidentified speaker: But without that explanation, then probability is, I guess, useless.

[00:04:00]  Peter: So it sort of, I think, harkens back to the explanation view of reality.

[00:04:07]  Unidentified speaker: I don't know. That's what I got. I want you to explain it to me, though. Okay.

[00:04:11]  Bruce: Well, I'm not sure I understand it. Like, I think I understand it at times, and I'm going to go through the math.

[00:04:18]  Unidentified speaker: I'm going to give examples.

[00:04:20]  Bruce: So I've gone to great lengths to try to understand it. And I, either he is talking nonsense, or I am just not getting it, because I don't think there's any middle ground here. And I'm not sure what it is, to be perfectly honest.

[00:04:36]  Unidentified speaker: I'm doing my best with it.

[00:04:39]  Bruce: And this is something I want to emphasize.

[00:04:41]  Unidentified speaker: I'm a layman.

[00:04:42]  Bruce: I'm stupid compared to David Deutsch. He probably knows both quantum theory and probability theory better than me. But I'm not an unknowledgeable layman. Like I've got a master's degree in machine learning. I had to have some familiarity with probability theory to get through that. You know, like I'm somebody who knows something about this subject.

[00:05:04]  Unidentified speaker: I know his theories really well.

[00:05:08]  Bruce: And it is not making sense to me what he's saying.

[00:05:12]  Unidentified speaker: Like it seems wrong to me. And I am struggling with trying to get at what he's getting at.

[00:05:20]  Bruce: So let me go ahead and take us through this. So just as a... So recall from past episodes, we've been building this slowly over time where I'm talking through... We had an episode about words and concepts, episode 112 and probability. And is the issue here that I was really kind of asking was, is David Deutsch really just arguing over definitions maybe?

[00:05:49]  Unidentified speaker: And at times it really feels like that.

[00:05:51]  Bruce: It really feels like he's just making the essentialist mistake, that he is arguing over the definition of how to use the word randomness. And he's picking a weird definition. And I keep saying, that's a weird definition.

[00:06:04]  Unidentified speaker: Why are you picking...

[00:06:05]  Bruce: Look, I'll even accept your definition for the sake of argument.

[00:06:08]  Unidentified speaker: I'll actually explain this from the past thing.

[00:06:11]  Bruce: And then I talked about in a different episode, I think it was 129, about this weird conversation I had with David Deutsch on Twitter, where he insisted that he was wrong in fabric of a reality to talk about something being probably incorrect.

[00:06:26]  Unidentified speaker: And I can't even make sense of why he would say that.

[00:06:31]  Bruce: It's wrong to say that. He keeps saying, well, it's because there's no such thing as the characteristic of being probably incorrect, either correct or you're not. It's like, that's not what people mean by that term. That's not what you meant by that term when you wrote it. And so it's a struggle to figure out what he's trying to get at. So let me go ahead and take...

[00:06:51]  Peter: Well, here's what my bestie, ChatGPT, says about his central thesis.

[00:06:58]  Unidentified speaker: Okay.

[00:06:59]  Peter: Deutsch argues that probability is not a fundamental feature of reality. It's a useful approximation or tool, not something physically real in the deepest laws of physics. What really exists are deterministic physical processes, the seeming role of probability in physics, especially in quantum mechanics, arises because of how we describe outcomes and make decisions, not because nature is fundamentally random.

[00:07:33]  Unidentified speaker: I mean, that makes sense to me. I think we would probably both agree with that, right? Okay. So let's take that.

[00:07:38]  Bruce: Let's assume that that is his position.

[00:07:41]  Unidentified speaker: Okay? Why would he say that saying that a simulation of a roulette wheel, because it always lands in the exact same thing, why would saying that probably shows that it's incorrect, that it's an incorrect simulation?

[00:08:06]  Bruce: Why would that, given what you just read, be a wrong thing to say?

[00:08:11]  Unidentified speaker: It doesn't even make sense.

[00:08:12]  Bruce: Even if I accept exactly what ChatGPT says, I cannot make sense of things he's saying.

[00:08:19]  Peter: Well, he is clear that probability can be useful.

[00:08:24]  Unidentified speaker: Yeah.

[00:08:25]  Bruce: Why not say, this is one of those cases where probability is useful, we can talk in terms of probability, it's an approximation. The fact that he declared it an incorrect and he said, oh, I was wrong to say that. I'm glad to say that Brett Hall has this right and I was wrong to say it. How can that even be right since he accepts it as an approximation?

[00:08:47]  Unidentified speaker: Well, to be fair, he is a quantum physicist looking at the deepest theories of reality.

[00:08:55]  Bruce: Okay.

[00:08:58]  Unidentified speaker: I'm confused.

[00:08:59]  Bruce: I'm genuinely confused as to what he's trying to say. Even when you give me a summary of his view, I'm still confused because he does things that don't match that summary.

[00:09:10]  Unidentified speaker: This is what ChatGPT says is the takeaway.

[00:09:12]  Peter: It says, Deutsch's lecture invites a radical rethinking of probability. Rather than treating it as a core ingredient of reality, as many standard scientific interpretations, he proposes treating it as a secondary explanatory layer, useful but not truly real.

[00:09:33]  Bruce: All right, let's go through the actual thing. Just last time on The Theory of Anything podcast, we talked about actual randomness versus pseudo-randomness. What we have here is a picture that was from episode 112 of actual randomness. You can see it's actually random. This is a picture of pseudo-randomness. Notice that there is a pattern. Pseudo-randomness doesn't necessarily have a pattern, but there's no way to guarantee it doesn't have a pattern, whereas with actual randomness, you're guaranteed to not have a pattern.

[00:10:07]  Unidentified speaker: Okay.

[00:10:10]  Bruce: So, my point here is, is that there's a physical real life difference between actual randomness and pseudo-randomness. And any theory of probability or randomness or stochasticity that we're going to come up with must take into account that these two are physically different and that you must be able to talk about both of them.

[00:10:33]  Unidentified speaker: Okay.

[00:10:33]  Bruce: And one of the things I mentioned in 112 is that fans of David Deutsch, who listened to this video of his, this presentation, come away with this idea that there's only one kind of randomness, pseudo-randomness.

[00:10:45]  Unidentified speaker: And that's not true. Okay.

[00:10:47]  Bruce: By the way, these pictures come from boallen.com.

[00:10:50]  Unidentified speaker: Random numbers. You can go look at what he says about this if you want.

[00:10:54]  Bruce: Now, what's the difference between these two? This one is unpredictable in principle. There is no way to predict it, period.

[00:11:02]  Unidentified speaker: Okay.

[00:11:03]  Bruce: This one is unpredictable only in practice. So as we've discussed in our Wolfram episode, deterministic processes are unpredictable, usually, unless they're periodic. Unless you run them once, find out what they do and then go back and run them again, then they're completely predictable the second time.

[00:11:24]  Unidentified speaker: Okay.

[00:11:25]  Bruce: That's the difference between pseudo-randomness on the right side and actual randomness on the left side.

[00:11:32]  Unidentified speaker: Okay.

[00:11:34]  Bruce: So there is no general pattern for test for a lack of pattern. So you're using pseudo-randomness at your own risk that someone can exploit the pattern if it has one.

[00:11:45]  Unidentified speaker: Okay.

[00:11:46]  Bruce: Because of this, Las Vegas goes to great lengths to make sure they're using true actual randomness and not pseudo-randomness in their high-quality slot machines and things like that.

[00:11:58]  Unidentified speaker: Okay.

[00:11:59]  Bruce: What do we mean by true randomness? I keep saying actual randomness, true randomness. So there's this site, random.org. It's an API that allows you to avoid using pseudo-randomness in your software applications so that you can be guaranteed to have no pattern. So if I want to accept Deutsch's view, I could accept it. I could accept it as just essentialism. That we're just arguing over how to use the word randomness, that there's nothing fundamental at stake, that the two kinds of randomness that I understand to exist, the actual versus the true versus the pseudo-randomness, that those still exist even under Deutsch's theory but that he's creating a third kind of randomness. He's saying, okay, what I'm calling true randomness, that is the kind of stochastic event that would exist if we didn't live in a multiverse. And it doesn't exist, okay? Then the second type of randomness would be what I was previously calling true randomness. We're going to call this apparent randomness, okay? The kind of stochastic event from the point of view of an observer in a universe that actually does exist. It's now known to split the multiverse. And then the third kind would be what I was calling pseudo-randomness. I'm going to still call it pseudo-randomness. It's an unpredictable process that is determined at the level of a universe, whereas type 2 is only determined at the level of the multiverse. Deterministic is what I mean, at the level of a universe, as opposed to being deterministic at the level of the multiverse like type 2.

[00:13:34]  Bruce: And that it mimics stochasticity, but it's actually a determined process and it potentially has patterns. You can roll it back and try it again and you can predict it perfectly. It's got negative things compared to type 2 randomness.

[00:13:46]  Unidentified speaker: Okay.

[00:13:47]  Bruce: Now, if this is what Deutsch is saying, and I'm fairly certain at this point, this is what Deutsch is saying, that this is literally just an argument over terms, then this must be true. We can ignore the type that doesn't exist, and we go right back to the original two types of randomness that I knew about prior to hearing Deutsch's theory, which is why I don't think that this is at all useful. When you argue over terms, it's never enlightening.

[00:14:15]  Unidentified speaker: Okay, but it's still kind of interesting, right?

[00:14:17]  Peter: I mean, if we live in a world where probably most people who've never really considered this issue from this perspective do believe that true randomness exists, I mean, it's still an interesting argument.

[00:14:30]  Bruce: So, okay, so you just said they believe true randomness exists.

[00:14:33]  Unidentified speaker: Do they?

[00:14:34]  Bruce: I mean, like, if I had never considered this, what Deutsch is calling true randomness at all, like it wasn't even on my mind, right? And so, he suddenly introduces it, proves it doesn't exist, and then I go back to the two things that I thought existed. Nothing has changed for me, right? And I mean, yes, anything can be interesting. This is interesting in the sense that, let me even go as far as I can, trying to defend Deutsch's view here. I'll steel man it to the max I can. Maybe we could argue that because I was aware there was a multiverse, I was aware that this type, so let me go back one slide, that this type two randomness, I was aware it split the multiverse, but maybe nobody else was aware of that. Maybe we could argue that Deutsch is introducing the type one to make the point that maybe everybody else in the universe thought type two was really type one. Because I knew, I was already familiar with Deutsch's theories, I was already aware there's a multiverse, I just happened to be thinking of type two as type two. It never even occurred to me to think of type one because it doesn't exist. So you might argue that what Deutsch is doing is he's making you aware that the type of randomness that you believe in doesn't exist and that actually it's caused by a deterministic process that splits the multiverse. Maybe that's a good argument and maybe he's right, but I doubt it. I seriously doubt most people have thought that far about what randomness is.

[00:16:14]  Bruce: So this idea that they were all carrying around in their minds that it wasn't a multiverse, I'm not even sure why that matters, because effectively, it doesn't matter if the randomness is due to a stochastic event in physics, a true stochastic event in physics of the type Deutsch says doesn't exist, or if it's because the multiverse splits, from your point of view inside of the universe, those will behave exactly the same way. You could just as well say, you know what, there's only two kinds of randomness, that's what everybody already believes, and what we've done is we've discovered the type one here, now type one is my kind of true randomness. The type one randomness, the actual true randomness, that kind we now know splits the multiverse, and that every single type of possibility happens across the multiverse, and it's deterministic at the level of the multiverse, but it's still random at the level of the universe. We could have said that way, that would have been way less confusing than the way Deutsch is going about this, okay? And in this sense, randomness is very real. In fact, it is absolutely a part of physics.

[00:17:22]  Unidentified speaker: It's a part...

[00:17:23]  Bruce: We now have quantum theory explains why true randomness exists, and that pseudo-randomness is physically different from it. It explains it now, it's because the multiverse is splitting, okay? I don't understand why we didn't take that approach, because that's a way easier to understand explanation. So, that or else, I'm just misunderstanding David Deutsch here, okay? Like, maybe I'm just not getting what his point is, but to me, this seems like an argument of no importance at all, because it's just an argument over how do we use a term.

[00:17:56]  Unidentified speaker: And of course, that's not important, right? I don't... Do you understand what I'm saying here? What I'm saying?

[00:18:03]  Bruce: We could have, instead of creating a third kind of randomness and then saying it doesn't exist, we could have said, the kind that does exist, we now know something more about it than we did before.

[00:18:13]  Unidentified speaker: It's actually deterministic at the level of the multiverse.

[00:18:16]  Bruce: And then we just, we never have to introduce this third type just to say it doesn't exist.

[00:18:21]  Unidentified speaker: Do you understand what I'm arguing here? Okay.

[00:18:23]  Bruce: And why that would have been easier for people to understand?

[00:18:28]  Unidentified speaker: Yeah, I understand. I guess I'm, I'm still... Skeptical?

[00:18:36]  Peter: I'm just, I'm just a little skeptical, I guess, about whether or not you're really disagreeing with him in a substantial way.

[00:18:44]  Bruce: Okay, so if it's just an argument over terms, we are not disagreeing in a substantial way, right? We're only arguing over which term, which way to define randomness is easier to make sense of.

[00:18:56]  Unidentified speaker: Okay. And that's it.

[00:18:57]  Bruce: And part of me really thinks that's all we're arguing over, okay?

[00:19:02]  Peter: You seem to be saying maybe Deutsch is just making it too complicated.

[00:19:05]  Unidentified speaker: Yeah.

[00:19:06]  Peter: And should just state his ideas about probability in a more simple way that doesn't confuse all his followers.

[00:19:15]  Unidentified speaker: Right.

[00:19:15]  Bruce: And it's not like I documented in episode 112, his followers are completely confused as to what he, if this is, if I'm understanding him correctly, which I may not be, if this is what he's actually saying, what you're seeing on the screen right now, then his followers are profoundly confused.

[00:19:34]  Unidentified speaker: Okay.

[00:19:34]  Bruce: He has profoundly confused them because they think there's only one type of randomness, the type two pseudo randomness.

[00:19:41]  Unidentified speaker: They don't understand anymore that there's actually two kinds, true randomness and pseudo randomness. Okay. Of course they're confused.

[00:19:49]  Bruce: He's claiming true randomness doesn't exist and he's not making it clear that he's making a new definition, then declaring that as not existing, and that the other two types still exist. Now, to make matters worse, you might argue to me, no Bruce, Deutsch is literally saying, there's only one kind.

[00:20:10]  Unidentified speaker: You have misunderstood him. That's not true.

[00:20:12]  Bruce: Right here in Fabric of Reality, he outrightly states, quantum systems do not have, okay, here's the whole quote. It is perhaps worth stressing the distinction between unpredictability and intractability. Unpredictability has nothing to do with available computational resources. Classical systems are unpredictable, or would be if they existed, because of their sensitivity to initial conditions. Quantum systems do not have that sensitivity, but are predictable, unpredictable, because they behave differently in different universes, and so appear random in most universes. That is precisely what I'm arguing, okay? Like, exactly, that if you're talking about a classical system, he says they don't exist.

[00:20:54]  Unidentified speaker: They do.

[00:20:55]  Bruce: A computer is a classical system. Now, you might argue, well, it's actually under the hood, a quantum system still, and you'd be right, okay? Let's not get too into the weeds as to what a classical system is versus a quantum system. I would agree that strictly speaking, there's no such thing as a classical system, but there are things that are very much like a classical system. There's a reason why we still teach classical physics to people, okay? Quantum systems become classical at some level of emergence. A computer is classical at the level of emergence of computation. If you're doing a pseudo-random number generator, it is unpredictable because it's intractable. You have to run it to find out what the result is going to be.

[00:21:40]  Unidentified speaker: There's no way to predict it in advance.

[00:21:43]  Bruce: Quantum systems, this is Deutsch saying this, so this isn't me making stuff up. He's saying quantum systems do not have that sensitivity, but are unpredictable because they behave differently in different universes and so appear random in most universes. He's saying appear random. I would have changed that too and therefore are random from the point of view of a single universe. So there's no doubt that the fans of David Deutsch have thoroughly misunderstood his point of view because he is right here in fabric of reality stating that there are two kinds of unpredictability, or in other words, two kinds of randomness. There's true randomness, the kind that's quantum, that's unpredictable in principle, and there's pseudorandomness, which is unpredictable because it's intractable.

[00:22:34]  Unidentified speaker: He's saying that, [not me?].

[00:22:36]  Bruce: We're agreeing on this.

[00:22:39]  Peter: So someone like, well, not so different than me, who is a fan of David Deutsch, loves his stuff, does not have a rigorous background in science and math, but finds these ideas interesting.

[00:23:03]  Unidentified speaker: What would I, can you steel man that position?

[00:23:08]  Peter: Like, what would I say about Deutsch's ideas on probability?

[00:23:13]  Unidentified speaker: Well, if I...

[00:23:14]  Unidentified speaker: Someone like me.

[00:23:15]  Unidentified speaker: If I understood them, I'm okay. So let's go through this like, like, okay.

[00:23:21]  Bruce: I feel, let me be honest. I do have a slide where I'm going to say this, but I'm going to say it in advance. It's it's it's it's humbling to have to on a podcast like this.

[00:23:34]  Unidentified speaker: I disagree with David Deutsch all the time. Right.

[00:23:37]  Bruce: I love his point of view.

[00:23:39]  Unidentified speaker: That's why this podcast exists.

[00:23:41]  Bruce: He's my favorite author of all times.

[00:23:43]  Unidentified speaker: He's amazing.

[00:23:44]  Bruce: He's got to be one of the smartest guys on the earth.

[00:23:47]  Unidentified speaker: Oh, sure. Right.

[00:23:48]  Bruce: Maybe even the smartest guy on the earth.

[00:23:50]  Unidentified speaker: I don't know.

[00:23:51]  Bruce: Like, that would be hard to judge because smart doesn't really exist on an IQ scale of, you know, one to 200 or something.

[00:23:58]  Unidentified speaker: Right. Sure.

[00:24:00]  Bruce: But like, he's way smarter than me.

[00:24:03]  Unidentified speaker: But that's kind of the beauty of his world view in a way is that, you know, he probably would say that even, you know, fairly average people can have brilliant ideas. And, you know, that's real. That's how I mean.

[00:24:22]  Peter: And really smart people can be really stupid, too.

[00:24:25]  Unidentified speaker: I mean, that's pretty, that tracks for me. Yes.

[00:24:29]  Bruce: So, I am basically making one of two claims at this point. I am either really not getting his point of view, and none of his fans are either. Or, he is wrong. I don't see a middle ground, okay? If he's wrong, which could be, right? Then if I were to try to explain to you his view, I would have to explain to you what he is mistaken about to be able to explain his view, okay? And I could do that on the assumption that he's wrong. But like, I don't know that he's wrong. Like, I may just, like, maybe none of us are getting what he's really getting at. Like, there could be some deeper meaning here that I'm just missing.

[00:25:12]  Unidentified speaker: And I'm not that, you know what?

[00:25:13]  Bruce: I'm not that bright a guy, right? If you were, I'd never taken an IQ test, but if I were to take one, I'll bet you, I would be like 120, slightly above average, but like nowhere near genius level, okay?

[00:25:25]  Unidentified speaker: Like not even close.

[00:25:27]  Bruce: And we can talk about whether IQ even means anything or not, because I know a lot of fans of David Deutsch think it's completely meaningless.

[00:25:34]  Unidentified speaker: And I'm like, almost agree with them.

[00:25:36]  Bruce: Like after going through Taleb's disproof of IQ, I basically buy Taleb's View.

[00:25:41]  Unidentified speaker: Okay.

[00:25:42]  Bruce: But even Taleb admitted that it did measure something.

[00:25:45]  Unidentified speaker: Okay.

[00:25:47]  Bruce: So I'm using that roughly as something, and you can decide for yourself if it's meaningful or not.

[00:25:52]  Unidentified speaker: I know I'm just not on David Deutsch's level.

[00:25:56]  Bruce: So for me to say David Deutsch is talking nonsense is a ridiculous thing for me to say, because I just, there's no way I can be sure of that. Like, there just can't be.

[00:26:09]  Unidentified speaker: Okay. Well, you're trying to understand, and that's what we do on this podcast. Right. Okay. And he may be talking nonsense. Like that's not an unthinkable possibility. Okay.

[00:26:20]  Bruce: It may be that the reason I'm so confused by what he's saying is because he's talking nonsense. That absolutely could be. Like, you shouldn't rule that possibility out on the grounds that he's smart.

[00:26:31]  Unidentified speaker: Okay.

[00:26:32]  Bruce: But there's no way that I could tell you in good conscience, you should accept what I'm saying.

[00:26:36]  Unidentified speaker: I understand this better than him.

[00:26:38]  Bruce: Like, there's just no way that's true either. So we're going to do our best, right? I'm going to take you through exactly what he says, and I'm going to explain it as best I can, and then I'm going to explain what I think is wrong with it.

[00:26:52]  Unidentified speaker: Okay? Maybe.

[00:26:54]  Bruce: But like, let's just have epistemic humility here.

[00:26:57]  Unidentified speaker: Okay?

[00:26:58]  Bruce: Like, it is so hard for me to in good conscience say, oh, I know what David Deutsch is saying, and here's how it's wrong. Like, I just can't say that with a straight face, right? So we're just going to do our best, all right?

[00:27:10]  Unidentified speaker: So I'm very confused.

[00:27:12]  Bruce: So my argument is, what you're calling true randomness, David Deutsch, isn't really randomness because... So I'm arguing that David Deutsch is arguing, what you're calling true randomness isn't really randomness because it comes from a determined process, just like pseudo randomness. Now, I asked David Deutsch that on episode 100 when we interviewed him.

[00:27:34]  Unidentified speaker: That is precisely what he told me.

[00:27:36]  Bruce: He said, it's not randomness because it comes from a determined process. But he means determined at the level of the multiverse, not at the level of the universe, okay? So my response is, I didn't say this on the podcast because I didn't even think of it at the time. Yes, but there's a huge physical difference between coming from a determined process in a single universe, which would be pseudo randomness, versus a determined process from the multiverse, which would be true randomness because it's truly unpredictable. Because one splits the multiverse and one doesn't, and that's why they are physically different. So you still need this separation between true randomness and pseudo randomness. Like it doesn't disappear just because you pointed out that true randomness is determined at the level of the multiverse.

[00:28:22]  Unidentified speaker: You still need both those concepts.

[00:28:25]  Bruce: That's why you can't predict true randomness, by the way. Even if you run the same process multiple times, because it will just split the universe in a different way. The universe will split in exactly the same way. You will perceive it differently each time, okay?

[00:28:40]  Unidentified speaker: That's why random processes can guarantee a lack of pattern, and pseudo-random ones, which are determined at the level of the universe, can't guarantee that, okay?

[00:28:50]  Bruce: So I simply don't understand why we're insisting on making up a whole new category of randomness, only then to declare it not real, when there really is a real kind of random process that actually does exist, due to the splitting of the multiverse. So it seems to me that nothing is at stake here, beyond general crit-rat confusion, that is, because we're debating physics.

[00:29:13]  Unidentified speaker: We're not debating physics.

[00:29:14]  Bruce: We're debating how to use the word randomness. This appears to me to be nothing but an argument over definitions or essentialism, okay? And that's why you said, I don't feel like, Bruce, you're substantially disagreeing with Deutsch. You're right, I'm not, okay? If the fans of David Deutsch could accept that there's three kinds of randomness, the first kind doesn't exist, but still accept the other two, David Deutsch's point of view would work just fine because it would still capture the actual physical difference between true randomness, let's call it apparent randomness, and pseudo randomness, okay? As long as you, if you can, for me, I just look at two concepts, true randomness and pseudo randomness. And those are the two that exist, so I can talk about almost anything that way, right? If you want to accept David Deutsch's view, you need three concepts of randomness. You need to declare the first one non-existent, and then you still need the other two. And then you're the same as me, and then there really is nothing at stake, okay? It's just an argument over terms, and I'm happy to accept your version. My experience back in episode 112 was that the crit rats who said they agreed with David Deutsch had no idea they still needed two kinds of randomness. They entirely thought everything was pseudo-random. They were factually confused, okay?

[00:30:36]  Bruce: And that's exactly the problem, is that if we've got this, if there's nothing at stake, if this is really just an argument over definitions, what we could, what I could criticize David Deutsch's point of view on is that he's chosen to say it in a way that is absolutely confusing everybody. And so he should stop doing that, and he should say it in a way that's less confusing. Which would be mine, which is there's two forms of randomness. We've learned something about true randomness. True randomness is actually not stochastic at the level of the multiverse. Say it that way, no one will get confused, because now you've still got them with the two kinds of randomness, and they understand the difference between the two.

[00:31:15]  Unidentified speaker: Okay, so

[00:31:18]  Bruce: At the time, that was all from Episode 112.

[00:31:20]  Unidentified speaker: That was a review of the slides from Episode 112.

[00:31:23]  Bruce: I said, I'm going to take a look at his actual talk, The Deutsch's Quantum Slot Machine. Okay, so let's examine, so one thing I've got to say is, I'm mostly, the slides you're looking at, I'm like literally reading them, so this audio versus video almost doesn't matter. The reason why we're doing it as a video is because there's a bunch of equations, and I can't really read the equations very well. So I'm trying to make it so that if you're listening in audio, just get the gist of what I'm saying and you'll be fine. If you want to check my work, you need to look at the video version. And I hope people will check my work. Like maybe I'm wrong, like maybe I'm, as I put my equations out there, maybe people will say, oh, you've misunderstood this. I'll go, oh, thank you for explaining this to me. Like I would really like to see what it is I'm getting wrong. So let's examine Deutsch's Physics without Probability to address my concerns. I'm trying to understand his argument, but I'm struggling.

[00:32:16]  Unidentified speaker: Like it's a huge struggle.

[00:32:17]  Bruce: I can't make sense of his arguments. Either I'm misreading something or there's a flaw in his reasoning. We should remain open to both possibilities.

[00:32:26]  Unidentified speaker: Okay.

[00:32:27]  Bruce: So Deutsch at the beginning of the talk says, ordinary unitary non-collapse quantum theory, i.e. many worlds, provides a large part, in large part a way out of the whole probability scandal. It's called decision theoretic approach. So he's going to go over the decision theoretic approach in this presentation, which is what I'm going to cover.

[00:32:47]  Unidentified speaker: Okay.

[00:32:48]  Bruce: But just for some background, Deutsch claims there is no need for probability in constructor theory because things either are possible or not. So the first principle of constructor theory, this is from the presentation, his slides. All other laws of physics are expressible entirely in terms of statements about which physical transformation it is possible to bring about reliably and which are impossible and why.

[00:33:11]  Unidentified speaker: Okay.

[00:33:12]  Bruce: So the motivation for why he's trying to do away with probability theory is that it's not consistent with constructor theory.

[00:33:21]  Unidentified speaker: Okay.

[00:33:24]  Bruce: But he says, I'm not actually going to explain this in terms of constructor theory.

[00:33:29]  Unidentified speaker: I'm going to explain it without constructor theory. Okay.

[00:33:32]  Bruce: But he does have this, he's expressing this motivation that constructor theory is either possible or it's not, there's no probabilities in constructor theory. Therefore, he's trying to argue that we don't need probability. Now, I do have to say something about this. I agree constructor theory is about possible or impossible, and I agree that constructor theory has no need for probability theory for that reason. I would say that probability is emergent, and there's nothing wrong with that. Emergent explanations do not have second class status compared to what we would call fundamental explanations, which is a term that is misleading, because it makes them sound like they're first class citizens, and the emergent ones are second class citizens. Now, this is an argument that Deutsch makes in fabric of reality. I know Deutsch agrees with me on this. But if probability theory is emergent, that doesn't make it a second class citizen. It's still physically real.

[00:34:29]  Unidentified speaker: It's in this case due to the splitting of the multiverse.

[00:34:32]  Bruce: Okay, but it's an emergent property that happens at the level of universes because of the splitting of the multiverse.

[00:34:39]  Unidentified speaker: That wouldn't [be true?].

[00:34:40]  Peter: Well, in a way, it's just like any other law of physics, right? I mean, pretty much all most laws of physics are radically different when we consider them from the perspective of the multiverse.

[00:34:53]  Unidentified speaker: Yes. Yes. Right? Yes. Yeah.

[00:34:55]  Bruce: You could argue that all classical physics is emergent, right?

[00:34:59]  Unidentified speaker: Yeah.

[00:34:59]  Bruce: Like all of Newton's classical physics, they're all emergent, okay? Probability is emergent in the same sense that Newton's theories or Einstein's theories are emergent. I don't know about Einstein's theories, but Newton's theories are emergent, okay? So because of that, you have to understand that it's entirely, one option that Deutsch never considers is that probability theory could be real but emergent, okay? That it's not a second class citizen, that it is a fundamental, the wrong term in this case. It's an emergent part of physics, but still very much a real part of physics. And that constructor theory is simply looking at it from a different perspective, and therefore doesn't need it because it's looking at the level of the multiverse, what happens and doesn't happen, okay?

[00:35:46]  Unidentified speaker: But you don't think, do you think he would substantially disagree with that?

[00:35:50]  Peter: Or is he just kind of like...

[00:35:52]  Unidentified speaker: I have no idea. More like a question of emphasis.

[00:35:54]  Bruce: Well, okay, yes, he would disagree with that. And I'm about to actually do on the next slide, I'm going to show where he disagrees with it, okay?

[00:36:02]  Unidentified speaker: Okay.

[00:36:02]  Bruce: So he says, however, Deutsch concedes there might be a place for using probability theory as an approximation of reality. He likens this to treating the earth as flat. So for many purposes, we can treat the earth as flat without any problems. This is where I start to disagree.

[00:36:17]  Unidentified speaker: Okay.

[00:36:20]  Bruce: So it could be that constructor theory has no need for probability, but that other laws of physics do. Like if you're trying to actually figure out what you're going to see happen when you do the double-slit experiment, since you exist inside the universe, you may have a very real need for probability, and probability may be the only really great way to only way to express it.

[00:36:44]  Unidentified speaker: Okay. And it may be exact.

[00:36:47]  Bruce: It may be that it's not like a flat earth, that it's exactly describing proportions of the universe.

[00:36:52]  Unidentified speaker: Okay.

[00:36:53]  Bruce: Or it could be that it's approximate like David Deutsch is saying. And it's like the flat earth.

[00:36:58]  Unidentified speaker: It works in some cases, but you don't need it in all cases.

[00:37:01]  Bruce: What I'm trying to say is the motivation of constructor theory doesn't differentiate between those two cases. It could be it's exact, but emergent, or it could be that it's approximate like the flat earth. Deutsch is arguing it's approximate like the flat earth. He's explicitly using the flat earth. And I don't think it's an accident he uses the flat earth. He points out that like, if you're just like building something on the earth, thinking of the earth as flat is perfectly acceptable because it is for the local problem you're trying to solve.

[00:37:33]  Unidentified speaker: Okay.

[00:37:34]  Bruce: But he says it's going to come back and bite you if you try to like, think of the flat earth and you're instead thinking about, you know, planets orbiting the sun or something like that.

[00:37:42]  Unidentified speaker: Flat earth is going to come back to bite you. Okay.

[00:37:45]  Bruce: If probability is emergent but real, it will never come back to bite you because it's an exactly correct explanation of reality.

[00:37:57]  Unidentified speaker: Okay.

[00:37:58]  Bruce: It's not like the flat earth.

[00:38:00]  Unidentified speaker: He's claiming it's like the flat earth.

[00:38:01]  Bruce: So he's making a stronger claim than it's merely emergent.

[00:38:05]  Unidentified speaker: Do you see what I'm saying here?

[00:38:08]  Bruce: He's saying that it will be wrong in some cases. By the way, if we're talking pseudo-randomness, I would agree. If we're talking specifically pseudo-randomness, pseudo-randomness is, and everybody knows this, kind of like the flat earth.

[00:38:22]  Unidentified speaker: Okay.

[00:38:23]  Bruce: Where it never quite fits, it fits well enough, but it will actually affect.

[00:38:31]  Unidentified speaker: I just read ET.

[00:38:32]  Bruce: Jaynes's book, The Father of Modern Bayesianism.

[00:38:35]  Unidentified speaker: He explicitly makes that argument. Okay.

[00:38:37]  Bruce: So he completely agrees that he doesn't use the flat earth analogy, but he completely agrees that the concept of random is emergent and approximate. And in fact, the reason why he's arguing that is because he's trying to argue that instead, it's degrees of belief or it's credences.

[00:38:54]  Unidentified speaker: Okay. So it's not something that's physically real.

[00:38:56]  Bruce: So Bayesians have a strong reason to want to agree with Deutsch on this.

[00:39:01]  Unidentified speaker: Okay. I'm arguing that they're both wrong.

[00:39:05]  Bruce: That quantum processes, that when you observe them, that they exactly fit probability theory, and that there really is a random process that is exactly random, just like the theoretical concept. And it's only quantum processes, and it's only from the point of view of a single universe.

[00:39:23]  Unidentified speaker: But that's all of us. We all live in the universes.

[00:39:26]  Bruce: So for us, random processes exist, and they're not approximate. But pseudo-random processes are approximate. We use random probability theory to deal with them. But ET Jaynes points out that famous statisticians, not realizing that it's only approximate, will actually draw completely false conclusions, and he gives examples of this. So I would agree that if we're talking about a determined process, then yes, it is kind of like the Flat Earth. But if we're talking about a quantum process, I don't see that it is.

[00:40:01]  Unidentified speaker: Okay.

[00:40:03]  Bruce: So now, Deutsch claims probability theory was only invented by people that wanted to win at games of chance.

[00:40:08]  Unidentified speaker: So he cites Cardano, 1501 to 1576.

[00:40:13]  Bruce: So thus, Deutsch sees games of chance as sort of an idealized example of where probability theory makes sense to use. With other examples, let's say, the probability for using probability for, say, life insurance being a sort of a less pure example compared to games. Deutsch also argues that those of this early era all believed in determinism. So they only intended the probability theory as a purely mathematical model, not as something relevant to physics. Oh, that's true, by the way, would agree with all that. So then he gives a list, further applications of theory of probability. So he has, I won't read the whole list, it's on the screen. The ones that are for our purpose is going to be important is, first of all, actuarial science. I'm going to come back to that one, life insurance, as an example of where you really need probability theory, even though it is just an approximation, okay? But there's not like there's some alternative you could have used.

[00:41:14]  Unidentified speaker: Okay.

[00:41:15]  Bruce: And then he really seems to be going after Bayesian philosophy. So he makes various claims about Bayesian philosophy. He's going about all this, trying to prove randomness doesn't exist because he believes that means he can disprove Bayesian philosophy. Now, famously, Bayesian epistemology and critical rationalism see each other as in a war to the death over who's got the true epistemology. So it makes sense that a critical rationalist would try to take down Bayesianism. And a huge part of the motivation that Deutsch seems to have is that if he can show randomness doesn't physically exist, then he can show that Bayesianism is wrong.

[00:41:58]  Unidentified speaker: Okay. Now, here's the thing.

[00:42:01]  Bruce: I just mentioned this, but let's go over it again.

[00:42:04]  Unidentified speaker: ET.

[00:42:04]  Bruce: Jaynes, who's the father of modern Bayesianism from his book, Probability Theory, The Logic of Science. I read, just finished reading the basic section. I'm not sure I'm going to read the advanced section. Basic section was hard enough for me.

[00:42:19]  Unidentified speaker: Great book, awesome book.

[00:42:21]  Bruce: I understand Bayesian reasoning and Bayesian epistemology way better now than I did before. I might understand it better than most Bayesians at this point, because I've started to notice that a lot of Bayesians make a lot of mistakes that ET. Jaynes calls out and explains why they're wrong. Okay, so I might understand Bayesianism better than most Bayesians at this point, or maybe not, I don't know, depends on the individual.

[00:42:46]  Unidentified speaker: He was a physicist, Jaynes was a physicist.

[00:42:48]  Bruce: Okay, so he's a physicist, but he did statistical mechanics, so he developed the Bayesian philosophy. He didn't himself develop it, he did develop it himself, but he was building off of people who came before him that he thought were right, like Cox.

[00:43:02]  Unidentified speaker: We're going to talk about Cox's theorem.

[00:43:05]  Bruce: And he realized that this was saying something about probability theory, that most statisticians were completely missing. So he developed this Bayesian philosophy that he thought was the correct way to understand probability as a kind of form of logic that allowed for degrees of belief. Okay, so he, he, Jaynes argued that randomness does not physically exist in nature and is therefore only in our knowledge and our ignorance. So for Jaynes, randomness reflects degrees of belief, not a physical process. So he attempts to prove there is no real randomness in nature because if he can show there's no real randomness in nature that forces acceptance of, in his opinion, Bayesian philosophy. Now, it's interesting that Deutsch also argues that randomness isn't physically real. But he mistakenly believes that Bayesians root their philosophy in the existence of quote real randomness.

[00:44:07]  Unidentified speaker: But that would actually be the frequentists that Deutsch would be disproving, not the Bayesians. Okay.

[00:44:13]  Bruce: So it's interesting that Deutsch claims Bayesianism is wrong because randomness does not exist. While Jaynes claims Bayesianism is right, for exactly the same reason. This one seems almost unavoidable to me. Deutsch seems to misunderstand Bayesian philosophy, because he's making an argument that doesn't make sense to a Bayesian. I have to ask Ivan the Bayesian to confirm that for me. But it looks to me like Deutsch is making arguments that he really could probably benefit from reading ET. Jaynes' book and understanding the original Bayesian philosophy better. Now, let me just say, I'm not necessarily arguing that Bayesian philosophy is right. This is a deep, deeply debated, hotly debated topic, even today. And Deborah Mayo, after reading ET. Jaynes' book, if I hadn't read Deborah Mayo's book first, I probably would have said, oh, Jaynes' arguments are so good, they must be correct. But I had already read Mayo's book, so I already knew there were some problems. So it didn't convert me to the Bayesian philosophy entirely. But reading the book did make me realize just how smart the Bayesian philosophy actually is. And they really are, even if imperfectly, they're really starting to grasp something that I think critical rationalists would benefit a lot from, even though we're probably going to have to modify it and error-correct it in some ways. Okay, so I highly recommend CritRats go read ET.

[00:45:49]  Unidentified speaker: Jaynes's book. Like they need to read it.

[00:45:52]  Bruce: They need to take all their misunderstandings of Bayesianism, they need to get rid of those misunderstandings, and they need to start to understand it correctly, and they need to be able to criticize the actual theory, not the straw man version that they've been criticizing. Okay, so a Bayesian would actually welcome Deutsch's argument here, because it would put down the Frequentist philosophy and leave theirs in their mind as the sole survivor, okay? Now personally to me, it seems like both sides are mistaken, because quantum randomness appears to be physically real, for the reasons I just demonstrated earlier. So I actually think Jaynes is wrong about this. Jaynes has a whole section on quantum probability, where he tries to prove that quantum probability doesn't prove him wrong. And I'll have to cover it on a separate podcast, because he's clearly mistaken, because he doesn't know about the multiverse, okay? And so he tries to prove that quantum randomness isn't really randomness either. But because he doesn't know about the multiverse, he makes an argument that's clearly mistaken, okay? And that quantum randomness actually is real randomness, the kind that he thought didn't exist, okay? Now, Deutsch is going to use, explain this decision theoretic approach, using this idea of a slot machine. So you've got the slot machine, it has these eigenstates at the top, you have the result when you pull the thing and you get the payout, okay? So this part of the talk is obviously the part that you said was probably gobbledygook to you.

[00:47:30]  Bruce: And it is kind of gobbledygooky unless you really understand quantum physics, which I have some familiarity with quantum physics. I learned quantum computation instead of quantum physics.

[00:47:42]  Unidentified speaker: And it's kind of different.

[00:47:43]  Bruce: Quantum computation is isomorphic to quantum physics, but their whole language and their whole approach is drastically different because they're trying to teach it to a computer scientist instead of to a physicist. So like when I did our podcast and we talked about with Sam Kuypers C numbers, I had never even heard of them before, even though they're basic to quantum physics, because the way you would do it as a computer scientist doing quantum computation, you would just put it into a matrix.

[00:48:10]  Unidentified speaker: It would give you the same result and you would just use regular numbers. But it's a totally different way of viewing it.

[00:48:17]  Bruce: It's been simplified down for a stupid quantum, sorry, computer scientists, but it gives you the same results in the end. Okay, so I had to like go look up everything Deutsch was saying to try to make sense of it.

[00:48:31]  Unidentified speaker: And maybe I'm getting him wrong.

[00:48:32]  Bruce: Like maybe I'm really misunderstanding him, but I'm going to take his example, I'm going to translate it into a simpler example that I think is equivalent. And I'm going to try to explain it using that simpler example so that it isn't gobbledygook to you, okay? But keep in mind, I'm a layman.

[00:48:50]  Unidentified speaker: I might be misunderstanding him.

[00:48:52]  Bruce: I don't think I am, but I might be misunderstanding him. And if so, then this presentation will be available.

[00:48:58]  Unidentified speaker: People can look it up. They can check my numbers.

[00:49:01]  Bruce: They can show me where I've misunderstood.

[00:49:03]  Unidentified speaker: They can help me understand what Deutsch was actually saying, okay? So come on our podcast and argue with us. It's not that hard. Low barrier for entry here. Yes.

[00:49:16]  Bruce: So let me read what David Deutsch actually says word for word, and then I'm going to give a translation, okay? We imagine an array, this is David Deutsch. We imagine an array of gaming machines. You play by inserting one casino token. The machine prepares a quantum system, measures an observable x, displays the results, always an eigenvalue of x, and then the machine delivers a payoff of the number of casino tokens. Different machines are identical except for the state psi, written on the front as a superposition of eigenstates of x. For machines whose psi is a single eigenvalue, playing is not a game of chance. It's just putting in one token and receiving back x tokens, a classical machine. A rational player will be willing to play when x is greater than one, one being the price to play, and unwilling when x is less than one. Okay, that probably sounded like gobbledygook to you, right? Like when I first heard this, I couldn't even make sense of what he was saying. Okay, so here's an English translation using my example. I'm going to use an example of a quantum die. So you're just rolling a die. It gives you one to six instead of a slot machine because it's easier to comprehend than a slot machine. It's more straightforward, but I'm going to translate it so it's exactly the same thing he's saying, or at least that I think it's exactly the same thing he's saying, but into this quantum die. Instead, so that it's easier to make sense of. So plain English, imagine a rigged quantum six-sided die that always lands on four.

[00:50:45]  Bruce: You're required to bet three tokens, my version is going to be three tokens instead of one, to play.

[00:50:51]  Unidentified speaker: Should you play?

[00:50:52]  Bruce: Yes, you should always play because you will always come out ahead by one. You rolled the four, it always rolls a four, so you pay three tokens, you get four tokens back. Suppose instead the die was rigged to always be two. Now, you would not want to play because you will always lose one token.

[00:51:11]  Unidentified speaker: I'm just hung up.

[00:51:13]  Peter: Can you elaborate a little bit on what a rigged quantum die is?

[00:51:17]  Unidentified speaker: Okay. Just think of it as a regular die. Yeah.

[00:51:21]  Bruce: As we're going to see, in this example, it doesn't need super positions, but in future examples, it will. Just for now, just think of it as a regular die. And it's rigged to always land on four.

[00:51:37]  Unidentified speaker: And you pay three tokens to play. Meaning it's just like a regular rigged die. That's right. Okay.

[00:51:45]  Bruce: So you bet three tokens, it's always going to land on four, should you play?

[00:51:49]  Unidentified speaker: Okay. Okay. So yes.

[00:51:51]  Bruce: Now let's say it's rigged to always land on two, should you play? No, you'll lose a token every single time.

[00:51:58]  Unidentified speaker: Okay. So far, that's all he's saying.

[00:52:02]  Bruce: Very straightforward, nothing to disagree with.

[00:52:04]  Unidentified speaker: Okay.

[00:52:07]  Bruce: So now going back to Deutsch, what about cases when psi is not an eigenstate? Call the dividing line Vpsi, the maximum amount a player would be willing to play. For a classical machine, Vpsi is just the eigenvalue. If the state is a superposition, all of whose eigenvalues are greater than one, it's worth playing. Similarly, with all eigenvalues less than one, it's not worth playing.

[00:52:30]  Unidentified speaker: Okay, plain English.

[00:52:32]  Bruce: Again, just treat it like it's a regular die, okay? Suppose you had a die that only had four fives and sixes on the face, okay?

[00:52:41]  Unidentified speaker: And again, you're gonna bet three tokens.

[00:52:43]  Bruce: Would you be willing, would it be worth playing?

[00:52:45]  Unidentified speaker: So obviously, yes, it's random. It's not determined anymore.

[00:52:48]  Bruce: There is a random element, but it's always gonna be four, five or six, so you're always gonna come out ahead.

[00:52:54]  Unidentified speaker: So obviously you would want to play.

[00:52:55]  Bruce: Now let's say that instead the die had only one, twos and threes on it. So it's gonna be random, but it will always be one, two or three. Would you want to play? Obviously not, because you're always gonna lose money now. Note that even though there are super positions, the decision to play itself is non-random. So there's a random outcome, but the random outcome doesn't tell you anything about whether you should play or not. Collectively it does, but since it's always either less than the amount you paid or more than the amount you paid, in the two examples I'm using, the decision is non-random.

[00:53:29]  Unidentified speaker: All right, now the hard case. So those were easy cases. All right, so he's setting up for the hard case.

[00:53:33]  Bruce: But what if psi is a superposition of two states, one below one and one above one? Collapse quantum theory tells us that probabilities are those coefficients squared, and a rational player should value as if it were guaranteed to produce that expectation value. In general, axioms of stochastic theories are not explanatory. Now, without collapse, take in equal amplitude superposition eigenvalues x1 and x2. We aim to prove that v-psi will be the average of x1 and x2.

[00:54:06]  Unidentified speaker: The devil is in the detail.

[00:54:07]  Bruce: But elementary rationality gives two implications. v-psi does not depend on the exchange value of tokens, and if two machines use superpositions, where each eigenvalue differs by a constant k, the valuations also differ by k. It follows that for the equal amplitude state, v is the expectation value. We can prove the same for a general state, and that's QED.

[00:54:32]  Unidentified speaker: So that was his whole argument.

[00:54:33]  Bruce: And again, that was probably gobbledygook to you, right?

[00:54:37]  Unidentified speaker: Yes.

[00:54:38]  Bruce: Okay, so let's walk through what he just said using my quantum die example, and it's actually not too hard, okay? So plain English, our quantum die now has all six values. Now, you might wonder here, since I keep treating it like it's just a regular die, why do I keep saying it's a quantum die?

[00:54:56]  Unidentified speaker: Well, here's the thing.

[00:55:00]  Bruce: I want it to be a quantum die because I don't want to be talking about pseudo-randomness. I want to be talking about the true kind of randomness, okay?

[00:55:08]  Unidentified speaker: It's the kind that splits the multiverse.

[00:55:11]  Bruce: So we're rolling this die, and it splits the multiverse into six different branches of equal amplitude.

[00:55:19]  Unidentified speaker: Okay?

[00:55:20]  Bruce: Where you get a one, you get a two, a three, a four, a five, a six, etc.

[00:55:23]  Unidentified speaker: Okay?

[00:55:25]  Bruce: But from the point of view, and this is the point I keep trying to make, from the point of view of an observer in a universe, this is exactly equal to rolling a six-sided die. You will get, when you observe it, you will get one of six outcomes and they will be equal chances of each one.

[00:55:40]  Unidentified speaker: Okay?

[00:55:41]  Bruce: So we're assuming equal amplitudes, so this is a fair die. Should you on this die, should you bet three tokens to play? Now, let me actually, this is just simple math.

[00:55:52]  Unidentified speaker: Don't worry about the quantum aspects.

[00:55:53]  Bruce: If you roll a six-sided die, it's a fair die, and you bet three tokens, and you win the number of tokens that is on the face of the die once you roll it.

[00:56:01]  Unidentified speaker: Should you play?

[00:56:03]  Bruce: It's one plus two plus three plus four plus five plus six divided by six, which is 3.5. So the expectation value of a die is 3.5.

[00:56:11]  Unidentified speaker: Oh, okay. Okay. Okay. All right.

[00:56:13]  Bruce: So calculate the expected value. Each side is one in six probabilities of showing. So here's the thing. Probability of one sixth, probability of one sixth. This is what you just said, probability of one sixth for each of the faces. So the probability of one, one sixth, probability of two, one sixth, etc. So the expectation value would be one sixth times one plus two plus three plus four plus five plus six, which is 21 divided by six, which is 3.5.

[00:56:38]  Unidentified speaker: That's the right answer.

[00:56:39]  Bruce: The expected value of a die is 3.5. Now, one thing to pay attention to here is that an expected value is not any of the possibilities. So you can only get a one or two or three or four or five or six. You can't get a 3.5. Despite that fact, the expected value is 3.5. So if you're going to bet three tokens, should you play?

[00:57:02]  Unidentified speaker: Is it rational to play?

[00:57:06]  Bruce: There's an obvious answer here, and yet I would understand if you were hesitant to give it, because there's a good reason why people would be hesitant to give the right answer.

[00:57:13]  Unidentified speaker: Just give me the right answer. All right.

[00:57:16]  Bruce: The expected value is 3.5. So on average, you're going to win 0.5 every single time you play.

[00:57:23]  Unidentified speaker: Okay.

[00:57:23]  Bruce: So it is rational to play. This is how probability theory works.

[00:57:27]  Unidentified speaker: This is what probability theory tells you.

[00:57:29]  Bruce: Now in real life, we all know you might lose. That's why people are sometimes hesitant to give the right answer. They think, well, I know on average I'm going to win, but like I might still lose all my money, right? Is it worth it to me to risk losing all my money when I only have a 0.5, an expected value of 0.5? And it's well known that psychologically humans don't treat winnings and losses the same.

[00:57:57]  Unidentified speaker: We see a loss is more significant than a win.

[00:58:00]  Bruce: You have to win quite a bit more to make up for a loss.

[00:58:04]  Unidentified speaker: Yes, I've noticed that in my life. I mean, you win $1,000, it's like, well, that's great, but you lose it. Yeah, psychologically, it's much worse, isn't it?

[00:58:15]  Bruce: So many people would not play, and they would not do the, quote, rational thing. Now, you have to understand, when we talk about rational decisions, we're not trying to talk about human psychology.

[00:58:26]  Unidentified speaker: We're trying to talk about kind of the mathematics, right?

[00:58:31]  Bruce: We're just, so we would say, rationally, you should play. And we don't really mean rationally, you should play based on your psychology. We really just mean the mathematics show that you will, on average, come out ahead.

[00:58:45]  Unidentified speaker: Okay. Does that make sense? Oh, yeah. Okay.

[00:58:51]  Bruce: So yes, make the bet you're expected to come out ahead.

[00:58:54]  Unidentified speaker: Okay.

[00:58:55]  Bruce: But what we just did uses probability. So what Deutsch is saying is, can we avoid using probability and come to the same answer?

[00:59:02]  Unidentified speaker: Okay. So that we can do away with probability theory.

[00:59:05]  Bruce: So Deutsch argues we don't need to need no stinking probability theory. So he argues that the whole appeal to probability does not explain the expectation value rule. He suggests that we instead, we don't even bother with the Born Rule.

[00:59:19]  Unidentified speaker: Okay. We haven't explained the Born Rule. I'll explain it in just a second.

[00:59:22]  Bruce: But the Born Rule is what converts the deterministic Schrodinger equation into probabilities.

[00:59:29]  Unidentified speaker: Okay.

[00:59:31]  Bruce: He just explained it, but it was gobbledygook.

[00:59:33]  Unidentified speaker: He did actually explain it correctly.

[00:59:36]  Bruce: But I will give you a simpler explanation. So here is the setup for what Deutsch wants to do. So the eigenvalues are the face payoffs. So the eigenvalue, what he's calling eigenvalues, they would be the faces of the quantum die, 1, 2, 3, 4, 5, 6. They are equal amplitude state. So that would mean that the amplitudes for each of the eigenvalues is 1 over the square root of 6, okay? Which is a weird number, but that's the correct number, because then they all have, this would be the normalized version. They've now been normalized, so they will all, when we do the Born Rule, they'll all come out to a sum of 1. So recall the Born Rule is that you square everything, so what you're doing is you're saying it's 1 over the square root of 6, you square it, that's going to turn into 1 sixth.

[01:00:27]  Unidentified speaker: That will be 1 sixth per face of the die, okay?

[01:00:31]  Bruce: So let V psi denote the value of the single play of the machine in state psi, the maximum rational player would pay to play. We want to show that V psi is equal to 1 plus 2 plus 3 plus 4 plus 5 plus 6 divided by 6, which would be 3.5. How would we do this without an appeal to probability theory? So, the Born Rule, this is from Deutsch's slides, he says, if an observable X hat is measured, the state vector psi of a quantum, or actually I don't know how to pronounce that one, of a quantum system collapses to some X, an eigenvalue X, eigenstate with X hat with probability, and then he's got X by that quantum state squared. For our purposes, what we're saying is, is that you take the amplitudes and you square them, okay? Now, that is what he's saying on this complicated slide, and I want to note that we're assuming that the amplitudes are already normalized. If they aren't, the Born Rule would not be merely squaring them. You would square them and then you would take the sum and you would normalize to a sum of one, okay?

[01:01:47]  Bruce: So, Deutsch's slide here is assuming it's normalized. It doesn't say that, but apparently, that is the norm, is that you always normalize them. So his slide is accurate under the assumption that you're following kind of normal quantum physics approaches where you would normalize the amplitudes, okay? Now, this idea that the Born Rule, you square it and then you take the sum and then you normalize to sum to one, that may sound really familiar to someone who's familiar with probability theory and that's not an accident, okay? If this looks like normalizing probabilities, that's not a coincidence, that's exactly what you're doing with the Born Rule. You are translating into probabilities, okay?

[01:02:31]  Unidentified speaker: By coming up with the amplitudes and summing to one.

[01:02:36]  Bruce: So here is the standard Born Rule approach that uses probability calculus first, okay? So we got the equal amplitude quantum die. We've got the quantum state here is 1 over the square root of 6 for each of the different eigenvalues, so 1, 2, 3, 4, 5, 6, just the faces of the die basically. We square each amplitude, so now we got probability of 1 sixth per face of the die, because it's a fair die.

[01:03:06]  Unidentified speaker: And then we take the expected values, 1 sixth times 1, 1 sixth times 2, etc.

[01:03:09]  Bruce: And it comes out to be 3.5, which is the correct expected value. This uses probability theory, though. So Deutsch says, in essence, he's arguing you could skip the Born rule and just do this. So here's the Deutsch calculation without the Born rule. He takes the vector states and he just says, okay, I'm going to just take each of the vector states.

[01:03:32]  Unidentified speaker: There's 6 of them. I'm going to divide by 6.

[01:03:34]  Bruce: And that comes out to be 3.5, which is the expected value.

[01:03:38]  Unidentified speaker: And I'm done. Okay. And that's true.

[01:03:41]  Bruce: You have now skipped the conversion.

[01:03:43]  Unidentified speaker: You didn't use the Born rule.

[01:03:44]  Bruce: You did not have to translate into the probability calculus, and yet you still came up with the correct expected value. So now he does add a few things that I feel like for completeness, I need to mention, although they don't really impact anything that we're discussing. But let me go through them quickly. He says the result is permutation invariant. So, for example, 1, 2, 3, 4, 5, 6 will give the same result as 2, 3, 4, 5, 6, 1.

[01:04:11]  Unidentified speaker: Okay, well, that's obvious.

[01:04:12]  Bruce: It doesn't matter. Like when you're rolling a die, which numbers you have on which faces doesn't matter, as long as it's the same numbers.

[01:04:19]  Unidentified speaker: Okay. It's also shift invariant.

[01:04:21]  Bruce: Let's say that instead you had 2, 3, 4, 5, 6, 7 on the die. Now, obviously, that does change the expected value.

[01:04:29]  Unidentified speaker: Okay.

[01:04:29]  Bruce: But what it does, I won't read through all the numbers here because it's unnecessary, but it's there for completeness if you want to see the video version of this podcast. Basically, if your die says 2, 3, 4, 5, 6, 7, that does change your expected value, but it does so by a value of k.

[01:04:48]  Unidentified speaker: It's a constant.

[01:04:51]  Bruce: So it would still be an expected value of 3.5 plus whatever that k is.

[01:04:56]  Unidentified speaker: Okay, which in this case, I think is 1. So it won't actually change anything.

[01:05:04]  Bruce: It does change the expected value, but whether it's rational to play or not will not change. So he makes a point of pointing this out. So the main point seems to be that we never need the Born Rule to calculate the expected value. Therefore, we need not appeal to probabilities. Therefore, probability is unnecessary because we can make rational decisions without it.

[01:05:27]  Unidentified speaker: QED. He even said QED at the end.

[01:05:30]  Bruce: I think this is his argument. I think he's saying that all that gobbledygook quantum stuff basically says that when you know the quantum states, you never need to actually translate to probability theory, and yet you can still calculate the expected value. Therefore, you don't need probability theory. And probability theory is therefore unnecessary, and therefore he has, so he's claiming, proven that probability theory is unnecessary and doesn't exist and it doesn't really matter.

[01:06:03]  Unidentified speaker: It's just an approximation. You don't need it. Okay.

[01:06:07]  Bruce: Does that argument make at least some sort of sense?

[01:06:10]  Unidentified speaker: And have I properly steelmanded it for you? It's interesting, and it's kind of inspiring me to want to learn more. I'll say that. Okay.

[01:06:24]  Bruce: Let me say that I actually don't disagree with the specifics of what he said. He was able to get to the expected value without using the Born Rule and therefore not having to translate to the probability calculus. If that's what he's saying and that is what he seems to be saying, to me at least, that's all true. Now, I did play with this a little. He's using equal amplitudes, which makes it really easy to calculate the expected value without using the Born Rule to translate to probability calculus. I started playing with this. Could you do it if the amplitudes weren't equal?

[01:07:04]  Unidentified speaker: Well, you could.

[01:07:06]  Bruce: It was kind of nasty, like what you had to do to make it work. But there was always a way to make it work, mathematically speaking, even though it wasn't the nice clear-cut case that he's showing in his presentation. So I'm even going to accept, with a caveat, that it's kind of nasty, that you probably never need the Born Rule and you probably never need to translate to the probability calculus to be able to calculate the expected value. Therefore, strictly speaking, when you say there's no need to appeal to probabilities, if you mean there's no need to translate to the probability calculus, then his argument is correct, okay? That last caveat, though, is where I'm going to now take an issue. The Slot Machine example or my Quantum Die example uses a game of chance, which Deutsch says is probability's original purpose. Since he can show with a game of chance that we don't need probability, Deutsch is in essence I think arguing that for a crazier example like life insurance, clearly his argument must work for that because it's an even crazier example, less appropriate example of use of probability theory than a game of chance, okay? So yes, we can make rational decisions for a game of chance without probability. Yet we can make a rational choice for a game of chance without probability theory. Some of the argument goes probability must be unnecessary for anything on that list because everything else is even more approximate than a game of chance.

[01:08:49]  Unidentified speaker: So do you buy this argument?

[01:08:51]  Bruce: Okay, like I really want people to think about this for a second. There's a weirdness to this argument.

[01:08:56]  Unidentified speaker: Do you buy it? Does it make sense to you?

[01:08:59]  Bruce: Okay, let me kind of go through my thoughts on this. So side note, as a quick side note, I want to emphasize this again. I already said this, but I made this episode of video so I could show my work. I'm an amateur in quantum physics. I have a master's in machine learning with some exposure to probability theory, but I'm an amateur with probability theory. It's possible I misunderstood Deutsch or unintentionally misrepresented his argument. If so, I genuinely want to know where I misunderstood him. That's only possible if I show my reasoning step by step, hence the video format, so that there's just no doubt as to what I thought he said.

[01:09:36]  Unidentified speaker: Okay.

[01:09:37]  Bruce: Even if people disagree with me, I hope they can see that I am making a really serious effort to understand him.

[01:09:43]  Unidentified speaker: Okay.

[01:09:45]  Bruce: Far more effort than I think any of the crit rats I've talked to who have tried to explain it to me have put in.

[01:09:50]  Unidentified speaker: Okay.

[01:09:53]  Bruce: I'm a fairly informed lay person, yet I am really struggling to grasp Deutsch's point. In fact, my background keeps suggesting to me that something is off with his argument. But Deutsch is an actual true QM expert, and his grasp of probability is like, even though he's not an expert in that, it's likely better than mine. So it wouldn't surprise me if I'm misunderstanding him, nor would it surprise me if he made a mistake somewhere.

[01:10:20]  Unidentified speaker: We've talked about all sorts of mistakes David Deutsch has made on this podcast. So he makes mistakes. He's human. He makes mistakes. That's just the way it is. It could be either. Okay.

[01:10:29]  Bruce: Furthermore, at some level, I feel like there's a certain level of emergence at which I agree with what David Deutsch is saying here.

[01:10:35]  Unidentified speaker: So let me try to state what that is. Okay.

[01:10:38]  Bruce: So here's my pro-David Deutsch argument first. Let's read Deutsch as charitably as we can here. His specialized definition of randomness is effectively this. The kind of stochastic event he's defining randomness as, the kind of stochastic event that would exist if we lived in a single universe rather than a multiverse. So quantum physics is exactly the way it is today. But quantum events all collapse and all the other realities disappear. Only one universe remains. That would be what he's calling randomness. Nothing else changes.

[01:11:15]  Unidentified speaker: Quantum theory is still the same.

[01:11:16]  Bruce: This would be the collapse version of quantum theory.

[01:11:18]  Unidentified speaker: This would be the Copenhagen version.

[01:11:20]  Bruce: We're saying if Copenhagen were true and there were no multiverse, that is how he's defining randomness, okay?

[01:11:30]  Peter: So it seems like his stuff works if you interpret him as making an argument about physics rather than an argument about probability?

[01:11:43]  Unidentified speaker: Yes, and that's what [I'm about to say?]. I mean, would you say that's true?

[01:11:45]  Peter: And that's kind of, I mean, it is, to be fair, it is called physics without probability.

[01:11:49]  Unidentified speaker: That's right.

[01:11:50]  Peter: It doesn't say probability without physics or something.

[01:11:54]  Unidentified speaker: I don't know. Yes. Okay.

[01:11:56]  Bruce: So under that narrow definition, I agree with most of what he says. If I can wrap my mind around the fact that he's being an essentialist, that he's actually arguing over a definition, it seems to me that what he's saying is mostly correct. There's a few things I still think are wrong, but it's mostly correct. So physics does not need this kind of randomness.

[01:12:17]  Unidentified speaker: Why?

[01:12:18]  Bruce: Because we actually live in a multiverse, not a Copenhagen universe, okay? And his critique of quantum physicists who reject many worlds when seen in this light is fair, because we do live in a multiverse, not a Copenhagen universe. If this is what he's saying, like there's nothing to disagree with, yes, this is exactly correct. In that specialized definition of randomness, that only allows you to call it randomness if you live in a Copenhagen universe rather than a multiverse, he's right, that kind of randomness we've got no use for. So if all Deutsch means is that we shouldn't expect built-in stochastic events in a single universe physics without a multiverse, then I agree, he's right, okay. The talk is literally, you just pointed this out, the talk is literally called Physics Without Probability. He's shown we do not need probability as he has chosen to define it. Thus, QED, he's right, okay. Nothing for me to disagree with him over if I accept his definition of randomness, okay.

[01:13:26]  Unidentified speaker: Now, what's the problems that I've got with this presentation?

[01:13:31]  Bruce: So, as early as episode 112, I documented the confusion among Deutsch fans about what he's actually saying. They apparently don't see his point as merely a call to discard a narrow definition of randomness in physics, which is, as we just steelmanned, if I read him that way, I agree with him, but then you have to understand him as not making a substantial argument about probability, but simply saying we shouldn't call it randomness. It's just a debate over terminology. That is clearly not what people are coming away from this presentation thinking he said, okay. Instead, they take it as a sweeping claim that all randomness in nature is fundamentally pseudo-randomness. This is a false claim as discussed in Episode 112 and discussed in this episode.

[01:14:22]  Unidentified speaker: We just repeated most of those arguments. It is. It's just a factually false claim. It is wrong. It is wrong. It is wrong. Okay.

[01:14:28]  Bruce: Easily refuted. I just showed you that physically real randomness from quantum events and pseudo-randomness look different, feel different, act different. They are physically different.

[01:14:42]  Unidentified speaker: Okay.

[01:14:43]  Bruce: So the meaning people are taking from this presentation is for sure false. Whether it was Deutsch's intended meaning or not is a different question. By Episode 112, which is Is Probability Real? Fans were making even broader claims based on this presentation. They were denying probability for asteroid impacts, that there was such a thing as the probability that an asteroid would destroy the Earth. Or, there was no such thing as the probability that AGI would wipe out humans. Both of which have perfectly good probabilistic interpretations. Is this just another case of fans jumping to wildly inappropriate conclusions that weren't intended by Deutsch? We know the fans of David Deutsch do this. They take what he says and they just leap to wild conclusions sometimes and then they claim that it came from him. And this is a problem, is that it's often very difficult to differentiate between what David Deutsch actually said and meant and what his fans thought he said and meant. In fact, there are all sorts of problems like that. However, unfortunately, Deutsch himself makes similar overreaching claims. So in episode 129, Deutsch, I covered how Deutsch denied that probabilistic falsification, that was the term, and renounced, it was actually probably incorrect was the term he used. And he renounced a paragraph in his book, Fabric of Reality, for saying probably inaccurate.

[01:16:14]  Unidentified speaker: It was probably inaccurate what he said. He said that was wrong for me to say that.

[01:16:18]  Bruce: Deutsch does allow that probability theory exists as an approximation. So why does he object to use of the phrase probably inaccurate? Deutsch thinks, seems to think that probably inaccurate as a phrase implies a physical property, like a roulette wheel, having a physical attribute of being probably inaccurate. Rather than referencing what we know about a theory about a wheel, okay? Surely that's not what anyone normally means when they say probably inaccurate. The idea that when somebody says, oh, that's probably inaccurate, that they're claiming that that phenomena is probably, that theory is probably incorrect versus being either correct or not correct.

[01:17:05]  Unidentified speaker: Like there's just no way people mean that. Like there's no way people mean that.

[01:17:09]  Bruce: And there's no way Deutsch even meant that when he wrote that in his book back then.

[01:17:13]  Unidentified speaker: Okay.

[01:17:15]  Bruce: So it seems to me that Deutsch also, not just his fans, is making far reaching claims based on what he's discussing here, that just don't seem to work in real life and just don't even ring true to me.

[01:17:28]  Unidentified speaker: Okay. So why am I emphasizing this?

[01:17:31]  Bruce: I'm trying to avoid the motte-and-bailey fallacy here. Some are going to say, Deutsch just means we don't need randomness in the Schrodinger equation.

[01:17:41]  Unidentified speaker: You don't disagree with that, do you? No, I don't.

[01:17:43]  Bruce: The Schrodinger equation famously is entirely deterministic.

[01:17:46]  Unidentified speaker: There is no randomness in it. Okay.

[01:17:49]  Bruce: But his claims and those of his followers go far beyond that, and they always point to this talk as proof. They'll make these claims, there's no such thing as the probability of an asteroid hitting the earth. There's no such thing as the probability of, you know, they make these far-reaching claims. There's no such thing as a theory being probably inaccurate.

[01:18:09]  Unidentified speaker: Okay.

[01:18:10]  Bruce: And you go, I don't get that.

[01:18:13]  Unidentified speaker: That doesn't make sense.

[01:18:14]  Bruce: Like, let's talk about this, and they'll say, oh, just go look at this video from David Deutsch.

[01:18:18]  Unidentified speaker: She explains it.

[01:18:20]  Bruce: And those far-reaching claims are not justified by anything he says in this video. So this does feel to me like he's making a point that is valid, but then we're just jumping off the deep end into other things that just do not follow from what's said in this video.

[01:18:41]  Unidentified speaker: Okay.

[01:18:42]  Bruce: So let me give a deeper example here.

[01:18:46]  Unidentified speaker: Okay. So let's go back to the calculation. There's a deeper problem I want to call out.

[01:18:51]  Bruce: So we have Deutsch's calculation where we had the 1 over square root of 6 per eigenvalue, per face of the die, and then he calculates by taking each of the eigenvalues and dividing by the number of them, and he gets the expected value at the end.

[01:19:07]  Unidentified speaker: Now suppose a sincere...

[01:19:08]  Bruce: So he skips the probability theory, and he just does this calculation. He says, oh, I look at this quantum state, and I can see that all I need to do is take each of them, divide by six, and I can go to 3.5.

[01:19:20]  Unidentified speaker: Oh, you should play this game.

[01:19:24]  Bruce: Suppose a sincere questioner were to look at that and go, look, I don't understand what you just did.

[01:19:30]  Unidentified speaker: What is it that you just did? Why does this work?

[01:19:33]  Bruce: Why should I use this decision theoretic approach instead of probability theory? And so they might ask a rather reasonable question, something like this. So here's our sincere questioner on the left side, on the right side, we've got our person trying to explain Deutsch's theory.

[01:19:50]  Unidentified speaker: Okay. So sincere questioner.

[01:19:53]  Bruce: Okay, but why should I care about this decision theoretic calculation? And the Deutsch defender says, because there aren't enough universes in which you win to make it worth the cost. And the questioner says, well, why does that matter? Because there won't be enough versions of you that come out ahead. I still don't see why that matters. Well, the odds of coming out ahead are too low.

[01:20:23]  Unidentified speaker: Wait, strike that. I'm not supposed to say odds.

[01:20:26]  Bruce: So you mean the probability of winning is too small?

[01:20:30]  Unidentified speaker: Yes.

[01:20:31]  Bruce: I mean, no, I can't use the word probability. What I mean is the proportion of universes where you win is too small. And that proportion is calculated at how? From the amplitudes, you square and normalize them to work out. So you mean the Born Rule converts the amplitudes into proportions equivalent to probabilities?

[01:20:53]  Unidentified speaker: No, we're not allowed to say that either. But that is what you're saying, right?

[01:20:59]  Bruce: That I should bet based on my personal odds as determined by the Born Rule?

[01:21:04]  Unidentified speaker: Sigh.

[01:21:07]  Bruce: So my point here is, is that even though he skipped over the probability calculus step, if you try to explain what's going on to a sincere questioner, you need to explain it to them still in terms of the probability of them winning. There's still an implicit probability going on as part of the explanation. The mere fact that he skipped the math didn't remove that implicit explanation of probability at all, as far as I can tell. If you want to explain, here's why the decision theoretic approach matters to you, you have to be able to say, because you are an observer in a single universe, and from your point of view, your odds are not good enough, and you have to say that, or you will never be able to explain to the sincere questioner why this matters. So I don't see him as having actually removed probability from the explanation, I think he simply didn't mention it, but it's still implicitly there. So yes, Deutsch calculates a rational decision without using the Born Rule or the probability calculus. But a simple analogy shows why this is not remarkable at all. So you don't need quantum physics to make this argument.

[01:22:21]  Unidentified speaker: Classical physics, you could make exactly the same argument.

[01:22:24]  Bruce: Suppose someone told you that you have no need for probability theory to work out the expected value of a fair die, even if you're assuming only classical physics. So here's the argument now. You say, see Bruce, we don't need probability theory at all. We can just use frequencies. So let's calculate the expected values using only frequencies. So a frequency of one out of six for the first value, and then for two, one out of six. So we take one out of six divided by one plus two plus three plus four plus five plus six, that equals 21 divided by six.

[01:22:57]  Unidentified speaker: Oh, we got the expected value of 3.5.

[01:23:00]  Bruce: I never needed to translate to probability calculus, Bruce.

[01:23:04]  Unidentified speaker: I just used frequencies.

[01:23:06]  Bruce: So we don't need probability theory at all. It's the exact same argument, okay? So voila, I just proved that we can make rational decisions without reference to probability theory.

[01:23:19]  Unidentified speaker: Hooray!

[01:23:19]  Bruce: So probability theory is unnecessary, right?

[01:23:24]  Unidentified speaker: Of course this is a silly argument.

[01:23:27]  Bruce: We all know that frequencies are a type of probability.

[01:23:31]  Unidentified speaker: They're the same thing, right?

[01:23:34]  Bruce: So converting to a probability calculus is unnecessary to quote be using probability theory. Probability theory is more encompassing than merely the probability calculus. You can represent it as the probability calculus for convenience, but you don't have to, okay? So granted, funny-looking, imaginary numbers may look different from straight frequencies, but you're doing exactly the same thing here, okay? So here was the Deutsch calculation, where we used the 1 over the square root of 6.

[01:24:05]  Unidentified speaker: Notice that little 1 over the square root of 6, that's a frequency in disguise. It's the same thing.

[01:24:12]  Bruce: The reason why it looks different is because it's a complex number that has an imaginary component. In this case, the imaginary component is 0. But because it exists as a complex number, to be able to work out the actual comparative amplitudes, you have to square them all in normalized to 1, okay? But that really is an amplitude.

[01:24:34]  Unidentified speaker: It's the same as a frequency. It's just in a different format, okay?

[01:24:39]  Bruce: The Born Rule converts amplitudes into a normalized measure, obeying the probability calculus. The probability calculus is just measure theory scaled for convenience, okay? The probability calculus is not mandatory. Now, Cox's Theorem, which we'll do an episode on Cox's Theorem, because I think it's a really important thing for critical rationalists to understand. Cox's Theorem is famous for Bayesian, not for critical rationalists, and it was the basis for Bayesian epistemology, okay?

[01:25:10]  Unidentified speaker: That ET.

[01:25:11]  Bruce: Jaynes started with Cox's Theorem, showed what a deep theory it was, theorem it was, and how deep its implications were. And then from there, he derives what today we would call Bayesian reasoning, Bayesian philosophy, I mean, okay? So Cox's Theorem is super important to Bayesians. So Cox's Theorem, I went through line by line, every single part of Cox's Theorem when I read ET. Jaynes' book, to make sure I understood every single step, and I do not see any problems with it at all. Okay, Cox's Theorem shows that there are infinitely many equivalent isomorphic representations of probability. Okay, it makes no claim you have to calculate, have to convert to probability calculus. What it actually says is, there's an infinity of different ways you could represent this. But for convenience, the probability calculus is the easiest one for humans to understand. Okay, so Cox's Theorem absolutely has no problem with the fact that you can represent probabilities physically using complex numbers. And it has no problem at all with the fact that you don't have to convert to the probability calculus. Okay, so just as you can make rational decisions using frequencies instead of the probability calculus, you can of course make rational decisions using QM amplitudes, which are equivalent to frequencies from the point of view of a member of someone in a single universe, that is. So the Born Rule is the function that maps between representations, just like Cox's Theorem promises will be possible. This does not remove the probabilistic structure, it merely changes how it's represented.

[01:26:56]  Bruce: Claiming that this quote eliminates probability risks misunderstanding the role of the probability calculus. Surprisingly, Deutsch at one point admits that there is a physical way to understand probability in terms of proportions of the multiverse, which is what I've been arguing, though he doesn't dig into it further.

[01:27:14]  Unidentified speaker: But let's look at the actual quote, because I think it's important because it's a place where he says what I'm saying.

[01:27:20]  Bruce: So this is at, in the presentation, 1611, 16 minutes, 11 seconds. Deutsch claims that the probabilistic statement, that a probabilistic statement is not a statement about reality. So this is from his slide, factual statement, a straight flush beats a full house.

[01:27:37]  Unidentified speaker: It's obviously a factual statement. A probabilistic statement, drawing to an inside straight is very risky. That's a probabilistic statement, it's not a factual statement. This is what Deutsch is arguing.

[01:27:50]  Bruce: So, Deutsch goes over the counterclaim. So, when you point out that it's not a factual claim, he claims that people who are defending it will say this.

[01:28:00]  Unidentified speaker: Here's the quote now.

[01:28:01]  Bruce: The statement, it was too risky, is about the physical world. It refers to all the players who drew to an inside straight and lost, and it refers to the fact that there are more of them.

[01:28:12]  Unidentified speaker: They outnumber the winners.

[01:28:14]  Bruce: So this isn't Deutsch's argument, this is Deutsch explaining a Steelman version of the other point of view. Deutsch refers to this argument as a sort of, quote, a sort of desperate denial. Deutsch explains, there have only been finitely many poker games in the world, and they do not match probability theory.

[01:28:33]  Unidentified speaker: Now, that makes sense.

[01:28:35]  Bruce: So probability theory is the way it's typically explained like in class. They would say, if there were an infinite number of poker games, then what you would find is that drawing an inside straight is very risky. But Deutsch is saying, there always isn't an infinite number of poker games. There will never be an infinite number of poker games. So you can't appeal to this infinite number of poker games and therefore turn that probabilistic statement into a factual statement.

[01:29:06]  Unidentified speaker: So far, so good.

[01:29:07]  Bruce: I agree with him on that, okay?

[01:29:10]  Unidentified speaker: But there's a problem.

[01:29:11]  Bruce: He's missing something important here, which he then brings out.

[01:29:14]  Unidentified speaker: And this is where I found so interesting.

[01:29:16]  Bruce: He then says, ignore for the moment the fact that there are parallel universes and in those the particular players both win and loses in different universes. Quantum theory does in fact solve some of these problems.

[01:29:31]  Unidentified speaker: Oh, hell yeah, it does. That's me.

[01:29:35]  Bruce: Let me put this in plain English. There are in fact an infinite number of poker games, but they're across the multiverse, not inside a single universe.

[01:29:46]  Unidentified speaker: And because that's true, the probabilistic statement, drawing to an inside straight is very risky, is a factual statement. I'm going to say it again.

[01:29:57]  Bruce: Drawing to an inside straight is very risky. Across the multiverse is a factual statement because it's about the proportions of the multiverse, okay? So I don't see this as a desperate denial. It's true that when those that have defended this didn't believe in the multiverse, they weren't sure how to explain this. So they would say something similar to Deutsch's Steel Man version of them. They would say, the statement, it was too risky, is about the physical world. It refers to all the players who drew to the inside straight and lost, okay? I agree that that's an imperfect answer. That the right answer is, the statement, it was too risky, is about the physical world. It refers to all, to the player who drew to the inside straight and lost, the number of proportions of the universe where that happened. Once you realize that all you have to do is reference the multiverse here, this does become a physically real statement and it's a factual statement. So what Deutsch has said, that is what I've been arguing all along.

[01:30:57]  Unidentified speaker: Okay.

[01:30:57]  Bruce: One fair way to interpret randomness is as proportions of branches across the multiverse.

[01:31:04]  Unidentified speaker: These proportions.

[01:31:05]  Peter: Yeah, but if I say that in my high school algebra class, I think they're going to, when we're talking about probability, they're probably going to think I'm crazy.

[01:31:17]  Unidentified speaker: I mean, a lot of them already do. I keep thinking of that if I brought up some of this stuff. The world isn't ready for the truth. That's what you're saying. Okay.

[01:31:30]  Bruce: These proportions, which are the Born Rule magnitudes, exactly fit the probability calculus. And then of course they exactly fit the probability calculus. The Born Rule, when normalized, by design, it maps to a value between 0 and 1 for convenience, just like what we do with probability theory.

[01:31:47]  Unidentified speaker: If it's a 1, it happens in all universes.

[01:31:50]  Bruce: If it's a 0, it happens in no universes. If it's between 0 and 1, it happens in that proportion of universes. This doesn't, it's not an accident this looks exactly like probability theory. Okay, drum roll, this is exactly equivalent to probability theory. And of course it is, Cox's Theorem predicts that in a case like this, it should be mappable to probability calculus.

[01:32:17]  Unidentified speaker: And it is.

[01:32:19]  Bruce: Cox's Theorem, we need to cover it as a separate podcast. And it's a tough subject because it took me like 2 months or something to go through Cox's Theorem because he kept losing me.

[01:32:30]  Unidentified speaker: But it's very complicated proof.

[01:32:33]  Bruce: It's probably not a very complicated proof.

[01:32:34]  Unidentified speaker: It's very complicated proof for a layman like me, is what I should probably say.

[01:32:40]  Bruce: Cox's Theorem, it starts with certain axioms. They don't call them that, but it starts with certain axioms. And it tries to show that you can come up with different ways of representing these axioms, but they will always be equivalent to probability theory. So, if mathematically for something to be self-consistent, where multiple things happen across multiple universes, it had to be in some way mappable to the probability calculus. Like Cox's Theorem says, if it's not true, if the quantum multiverse is not mappable to the probability calculus, Cox's Theorem would be wrong, and you would actually have a disproof of Cox's Theorem.

[01:33:29]  Unidentified speaker: But there is no disproof of Cox's Theorem. Presumably, it's because it's correct, right?

[01:33:33]  Bruce: So we're talking the exact fit.

[01:33:35]  Unidentified speaker: This is not a flat earth approximation we're talking about, okay?

[01:33:40]  Bruce: The Born Rule maps precisely to probability calculus because Cox's Theorem says it will, okay? Now as noted in episode 129, there is a physical property corresponding to the probability AGI will wipe out humanity. That is done in terms of, physically, this means the proportion of universes where AGI wipes out humanity.

[01:34:05]  Unidentified speaker: It has to be from a given moment in time, I should note. It's not across the entire multiverse.

[01:34:09]  Bruce: It would be, you would pick a certain world, a certain moment in time, and then you would say, what's the probability from this moment of AGI wiping out humanity? There is some proportion of the multiverse from this moment in time forward for us, where AGI wipes out humanity in the future. That is our probability that AGI will wipe out humanity. Now, that probability changes over time, because at each moment in time, you're now in a different part of the multiverse, and the branches that remain are different now.

[01:34:43]  Unidentified speaker: The proportions change.

[01:34:45]  Bruce: Obviously, if you were to do something, like let's say you enslaved all the AGI's, in the proportions of the multiverse, where AGI rebels and wipes out humanity, it's going to go way up. Okay, so the probability in that case, based on your decisions, changes. Okay, and yet this is what probability of AGI wiping out humanity means. It has a physical meaning across the multiverse. It's physically real. So the claim, there's no such thing as the probability that AGI will wipe out humanity, is a factually false statement. Okay, now, sure, we don't know the value, okay? Bayesians who guess at the value, they are making crap up, okay? And you can ignore them because of that. I don't think Bayesians, the ones who are into this sort of thing, have any clue what would lead to AGI wiping out humanity versus not AGI wiping out humanity. I think their whole philosophy is flawed on this point. So I think when they make up values of, here's the probability AGI will wipe out humanity, I think it is a meaningless number. Even though there is a probability of AGI wiping out humanity, they don't know what it is and you can ignore them. Their theories about it are disconnected from whatever is going to happen in the multiverse.

[01:36:06]  Unidentified speaker: So there's no reason to reference them. It really is. Even I can see that much. That really is a ridiculous line of reasoning.

[01:36:14]  Bruce: But the claim, there is no such thing as the probability that AGI will wipe out humanity, which in episode 129 was made by one of the crit rats, okay, based on what he claims came from David Deutsch, which I think he probably was right about.

[01:36:26]  Unidentified speaker: That's a false claim, okay?

[01:36:29]  Bruce: So key takeaway, probability and randomness have a very real physical instantiation under many worlds. Physics needs probability, but it needs it at an emergent level. The Born Rule is the emergent level because it translates between the deterministic multiverse into the probabilities that an individual observer is going to see, okay? And that is part of physics. So physics needs probability in this sense. Physics without probability is only possible under an incredibly narrow and I would say misleading definition of probability. As a side note, I talked here about AGI. Okay, what about asteroids? Is there a probability that an asteroid will hit the Earth?

[01:37:16]  Unidentified speaker: Now, that is different.

[01:37:18]  Bruce: There is no proportions of the multiverse, where an asteroid is either going to hit the Earth or it's not. That is not from this moment in time forward. What are the odds that an asteroid will hit the Earth this year?

[01:37:31]  Unidentified speaker: Let's start with this.

[01:37:32]  Bruce: What's the probability that an asteroid will, from this moment forward, hit the Earth this year? That is not something that branches across the multiverse. That asteroid exists at such a large macro level that there aren't really quantum events that are impacting its movements. Maybe really tiny quantum events, very slightly, but for the most part, there is no physical meaning to the probability that an asteroid will hit the Earth. Does that mean there's no such thing as the probability that the asteroid will hit the Earth?

[01:38:05]  Unidentified speaker: No.

[01:38:06]  Bruce: You have to understand that the asteroid example, is different, it's a pseudo-random probability. So it is only a flat Earth approximation. But it doesn't, just because it's a flat Earth approximation, doesn't make it wrong or not real, okay? It's still really meaningful. The way you calculate the probability of an asteroid hitting the Earth, if you know nothing else, is that you start with the assumption that the number of asteroids that exist in the path of Earth is constant, and therefore the ones in the past are going to be the same as the number of hits will be spread out in frequency exactly the same as the numbers in the future. Now that may be a false assumption, okay? Like, it's just a theory, right? It could be that we just barely moved into a part of the galaxy where there's, you know, ten times as many asteroids as there was prior to this point, in which case that probability that you're going to calculate using frequencies from the past is going to be false, okay? But you have no reason to believe that. If you have a reason to believe that, then yes, you would use what you see the frequency is going forward. But if you've got nothing else to work off of, your best theory from a critical rational standpoint is that you're in about an equal distribution of asteroids in the past as you are in the future. Therefore, the frequency of hits on the Earth prior to this point is your best theory as to how many hits you're going to have going forward. Now, this is how you use probability theory.

[01:39:43]  Bruce: Yes, as a flat Earth approximation, I will admit, but it still has a meaningful meaning, right? It's not a meaningless thing for you to say, even though it doesn't have proportions, it doesn't have a physical meaning anymore. This is a case where it is much closer to the Bayesian example, where it's really about your knowledge, your state of knowledge and your degrees of belief, your credences, okay?

[01:40:07]  Unidentified speaker: And it does have a...

[01:40:09]  Bruce: If you don't like the term degrees of belief or credences because you have an allergy to them because you're a critical rationalist, there is a critical rationalist version of this.

[01:40:18]  Unidentified speaker: I just tried to explain it.

[01:40:20]  Bruce: And it's really about the assumption that there's an equal number of... Your best theory is that there's an equal number of asteroids in the past as there is in the future, because the proportion of them in the universe hasn't changed.

[01:40:33]  Unidentified speaker: You've got no reason at this point to believe that it's changed. Okay.

[01:40:36]  Bruce: If you did, you would have a different theory. And there is a critical rationalist way of looking at this that's completely valid, that maps mathematically to what Bayesian's called degrees of belief. And yes, that is different than the probability of AGI wiping out humanity, where it has a physical meaning.

[01:40:53]  Unidentified speaker: There's no physical meaning here. Instead, it's an approximation. Anyhow, I'm just trying to make a point here, that there is a difference between these two cases, but that they both map to the probability calculus, but in different ways, with slightly different interpretations.

[01:41:07]  Bruce: This is something we need to probably come back to. When I understand it better, I'll try to explain this better, okay? Let's now look at several arguments Deutsch makes in the presentation that to me, some of them seem kind of questionable, okay? So at 36.15, there are no stochastic processes and no credences in the sense of beliefs with numerical measures that obey the probability calculus. No credences affect the decisions of any rational person making decisions about quantum systems.

[01:41:38]  Unidentified speaker: Now, I do not see how this is correct. Deutsch seems to me to be misunderstanding what a Bayesian credence is.

[01:41:45]  Bruce: Now, I already mentioned that Deutsch seems to misunderstand the Bayesian philosophy, okay? That I gave an example of how he thinks if he can show there's no true randomness that that undermines the Bayesian philosophy when actually it would support it, okay? Now, you can't know a quantum die result, but amplitudes, the proportions of universes or frequencies in a single universe, proportions of universes or think of that as the frequencies in a single universe, they do guide your betting decision, okay? You don't know if you will personally win, but you know the proportion of universes, i.e. the odds of winning.

[01:42:25]  Unidentified speaker: This is with the quantum die example.

[01:42:28]  Bruce: So using the Born Rule shows that proportion is mathematically a credence. Not using the Born Rule doesn't remove the credences, it just represents them differently.

[01:42:37]  Unidentified speaker: So let me say this, okay?

[01:42:41]  Bruce: Multiple times, Deutsch has said that there are no credences in the sense, this is a quote, no credences in the sense of beliefs with numerical measures that obey the probability calculus. The way he's saying that, it's weird. He's almost saying what Popper said, but he's saying it slightly differently. And the way Popper said it makes sense to me, but the way Deutsch is saying it doesn't. And think about the episode, I don't remember the episode number, but we did the episode on induction, where Kieran, the inductivist, was making arguments and I tried to show that he was actually just using an immunizing strategy.

[01:43:26]  Unidentified speaker: In that episode, go back and look at it.

[01:43:29]  Bruce: In that episode, I explain the Popperian sense in which belief in theories do not obey the probability calculus.

[01:43:40]  Unidentified speaker: Okay.

[01:43:42]  Bruce: And what I tried to explain, and I was intentionally doing that first so that I could explain this later when I was talking about Deutsch's version. I was trying to explain that you cannot use the probability calculus in an absolute sense to measure the probability that the theory is true. That's just not how the probability calculus works. That's not how Bayesian reasoning philosophy works. Now, I understand that there's a lot of Bayesians, particularly the effective altruists, who use it in that way, but they are at odds with their own epistemology, or their own philosophy, I should say, because arguably all of Bayesian epistemology is wrong. It's the Bayesian reasoning portion that's correct.

[01:44:26]  Unidentified speaker: Okay.

[01:44:27]  Bruce: Bayesian philosophy kind of sits in between those. It's got some errors and it's got some things correct. And someone who says, I'm a Bayesian epistemologist, they're probably as likely to actually understand Bayesian philosophy as most crit rats are likely to understand Popper's critical rationalism, which is to say, most of them misunderstand it, right?

[01:44:48]  Unidentified speaker: These are tough subjects.

[01:44:50]  Bruce: Misunderstandings are common, okay? So you can't really look at Bayesian philosophy and determine it based on what people on the internet are saying. You have to almost go to an expert like ET. Jaynes, which is what I'm trying to do, and you need to actually look at what a knowledgeable person said about it, and then try to get rid of a lot of the bad examples of it, okay? Now, it's true that Popper said, belief in theories does not follow the probability calculus, okay? That's true, and the reason why is because there's different reasons why you would accept or not accept a theory, and they can't be put into a numerical measure like that.

[01:45:35]  Unidentified speaker: That's why they disobey the probability calculus.

[01:45:38]  Bruce: But if you have a specific model that you're looking at, and under that model you're choosing between theories, it absolutely obeys the probability calculus. I'm going to say that again. If you're looking at a specific model, so you've got certain background knowledge that you're working with, and you're accepting is true for now, you don't know if it's true for sure, but you accept it is true with your best theories. In that case, when you're choosing between theories, it absolutely obeys the probability calculus. It has to, because Cox's theorem says it will. It depends on what your context is. Do you mean it in an absolute sense where you're trying to measure not only the probability between two theories given some background knowledge, but you're also trying to measure the probability that your background knowledge is correct? If that's what you're trying to do, and I'll admit, effective altruists try to do that, then they have misunderstood Bayesian philosophy, because that is impossible and Popper's right, that does not obey the probability calculus.

[01:46:46]  Unidentified speaker: But if you are looking at it from the standpoint of someone who is assuming for the moment tentatively that their background knowledge is correct and that their best theories are correct, in that scenario, it will always obey the probability calculus.

[01:47:03]  Bruce: When Deutsch says this, that there are no credences in the sense of belief with numerical measures that obey the probability calculus, he's making too broad a claim, and the claim is therefore false.

[01:47:14]  Unidentified speaker: Even though it's true in some cases, okay, it's also false in some cases. And he's not differentiating between the two.

[01:47:22]  Bruce: I always felt like Popper did a better job differentiating between the two, kind of, because he's a little more clear. But I always sort of got the sense that Popper didn't quite understand the difference between these two either.

[01:47:35]  Unidentified speaker: And this is one of these cases where I think critical rationalists would really benefit from understanding Bayesian philosophy, even though Bayesian philosophy will ultimately prove false. It's got a lot of truth to it, okay? It's got verisimilitude, if you will.

[01:47:50]  Bruce: And it's got some things that critical rationalists do not properly understand and need to adjust their thinking on, that need to error correct on, okay? And there is cases where, specifically when you're being a critical rationalist, when you're accepting your current best theories as true for now, that is the condition under which choosing between theories, using experiments, let's say, will always follow the probability calculus.

[01:48:20]  Unidentified speaker: And that distinction is necessary here, okay?

[01:48:22]  Bruce: You can't just say credences in the sense of belief, the numerical measures do not obey the probability calculus. That is too broad a term.

[01:48:31]  Unidentified speaker: That's false the way you just said it.

[01:48:33]  Bruce: You have to make the distinction. It depends on whether you're talking about inside the model or outside the model, inside your background knowledge, inside your theories or outside your theories. And with that distinction, I think it then becomes a true statement.

[01:48:46]  Unidentified speaker: But I don't think it is without.

[01:48:47]  Bruce: Sorry, I probably lost everybody there, and I will try to do an episode where I explain this better in the future. This is maybe a setup for when we talk about Bayesian reasoning and my current understanding of it as I struggle to learn it myself.

[01:49:01]  Unidentified speaker: But I want to be clear that Deutsch is showing a misunderstanding of Bayesian credences here, because he doesn't make the necessary distinction between inside of our theories or outside of our theories.

[01:49:14]  Bruce: Okay, at 36.36, Deutsch says, but it's even better than that. Those decisions now on the right hand side are not only derived, but unlike in the collapse case, they are explained because we don't have to introduce all those unexplained probability postulates. Now, let me just say, I'm not arguing that the Constructor Theory of Probability isn't adding to our body of knowledge. I think the Constructor Theory of Probability is correct insofar as it goes. This is similar in my mind to the whole universal explainership thing, where that is a correct theory, but that Deutschian crit rats and Deutsch himself pull implications from it that are false, that aren't actually part of the theory. I think the same thing is happening here. The Constructor Theory of Probability does not seem to me to be wrong. He is correctly explaining certain things using the multiverse that explains what probability is in a way that we couldn't have understood well without it. So there is a genuine additional explanation here that Bayesians would benefit from learning and coming to understand and understanding how their theory fits their philosophy is right and wrong, okay? So this one I kind of agree with Deutsch on, that a reasonable reading is that Deutsch is arguing that many worlds explains what probabilities actually are physically.

[01:50:30]  Unidentified speaker: That's the way I would say it. It's not the way Deutsch says it, but that's what I would say it, okay?

[01:50:35]  Bruce: And it allows you to make a difference to understand the difference between the probability of AGI wiping out humanity, which has a physical interpretation of probability, and something like an asteroid hitting the earth, which is really just a matter of credences or degrees of belief based on a current best theory. Okay, it's a theory that has problems and would have to be improved once your additional knowledge comes in. Okay, and I think it allows us to understand something like why Bayesian philosophy works so well in so many cases, and also where it goes wrong. So from this standpoint, I kind of agree with this statement. Now, however, I've got some concerns over his wording. The postulates of probability theory don't need a physical explanation, and he's kind of acting like they do. He's kind of acting like, well, they have to have a physical explanation. They're supposed to be consequences of mathematics. He's right that originally it was understood to just use mathematics and that it wasn't meant to apply to physics. And Cox's Theorem shows that any decision-making process that matches certain reasonable desiderata, how do you pronounce that?

[01:51:49]  Unidentified speaker: Desiderata.

[01:51:50]  Bruce: So desired-ada is what it's spelled like, but desiderata. So for our purposes, we're going to call them axioms. Any rational decision-making process that matches those axioms will always mathematically be equivalent to probability theory.

[01:52:05]  Unidentified speaker: That's what Cox's Theorem really shows. Okay. But it's a mathematics.

[01:52:10]  Bruce: Like it's literally how our physics matches that, why our physics matches that. That is what Constructor Theory of Probability is explaining. And that's a correct explanation that we should be interested in. But it would hold for any laws of physics.

[01:52:30]  Unidentified speaker: Okay.

[01:52:31]  Bruce: Deutsch sees Probability Theory as non-existent unless you can connect it to physics.

[01:52:39]  Unidentified speaker: But it doesn't have to be that way.

[01:52:40]  Bruce: It could have been that the universe was entirely deterministic and Probability Theory would still have worked as an approximation, admittedly. And in fact, Bayesian philosophy would have been entirely correct had that been the case, because then Probability Theory would only be about degrees of belief or credences.

[01:53:00]  Unidentified speaker: Okay.

[01:53:01]  Bruce: And the fact that that's not true, the fact that there actually is a physical interpretation of probability in some cases, actually undermines Bayesian philosophy.

[01:53:10]  Unidentified speaker: Okay.

[01:53:12]  Bruce: So what Cox's Theorem does is it's pure mathematics. It just simply says no matter which universe you live in, whether it's a quantum multiverse where probabilities are real and there's real frequencies, or if it's collapse or not collapse, if it's purely deterministic and it's just initial conditions, in every single one of those, Cox's Theorem says your rationality will be mappable to probability calculus.

[01:53:36]  Unidentified speaker: And that's true. There's just no way around that, right? It doesn't matter.

[01:53:39]  Bruce: You could make up entirely new physics, and probability calculus would still apply, because it's just a consequence of mathematics. At 40.07, he says, I don't mean that the mathematical formalism of quantum theory isn't sometimes useful. I'm saying that the quantities called probabilities in that formalism do not refer to any stochastic random process in nature, nor to anything in rational minds such as degrees of belief or credences, nothing in physics or in minds thinking about physics.

[01:54:10]  Unidentified speaker: So this honestly, this statement makes no sense to me.

[01:54:13]  Bruce: The Born Rule is useful precisely because it translates amplitudes into the probability calculus. Understanding a quantum state in terms of proportions of universes as 0 to 1 measure has only one consistent way to do it, the Born Rule, because of Cox's Theorem that had to be true. It does refer to a real stochastic process from the point of view of an observer in a universe. The claim about nor anything in a rational mind such as degrees of belief or credences is unclear. QM amplitudes themselves aren't Bayesian credences, that's true. But to explain a quantum outcome to a sincere questioner, you necessarily refer to odds and probabilities, which are Bayesian degrees of belief. Even if you just say, trust me, it will work, and try to avoid that part of the explanation, you're still implicitly using credences in a different representation to calculate the expected value. So this statement, I just can't make sense of what he's trying to say here. At 49.48, he says, now I hope I have shown you can, that probability doesn't make sense as a description or explanation of what really happens. It can be a metaphor, a technique for calculation, or an approximation in a certain sense. But an approximation to make sense has to be an approximation of something. So probabilities are to inform decisions in some approximate way. There has to be an explanation rooted in a description of an actual physical world, in which events and processes happen, not probably happen, and not just some, [just fire?] some ad hoc axioms.

[01:55:59]  Bruce: So I hope I've also persuaded you that it's right and proper to try to expunge every trace of probability of randomness from the laws of physics. Now, I've read this repeatedly and I don't know what it means.

[01:56:11]  Unidentified speaker: Like, I can't make sense of what he's saying.

[01:56:14]  Bruce: Cox's Theorem is a mathematical claim, not a physical one. Probability calculus is a convenient representation, not a physical fact. In the QM Many Worlds version of quantum mechanics, proportions of universes physically exist, which Cox's Theorem guarantees can be represented as the probability calculus, which it can be. This representation is exact, not merely an approximation or a metaphor. Claiming we should remove every trace of probability and randomness is misleading from this point of view, since proportions of universes are literally equivalent to probabilities. So at 50-30-3, repeating this part for emphasis, so I hope I've also persuaded you that it's right and proper to try to expunge every trace of probability and randomness from R, from the laws of physics, from our conception of the world, and from the methodology of science, so that we may fully restore realism as well as rationality. Deutsch has lost me entirely at this point. Probability theory is mathematics. Mapping it to reality is interesting, but it would hold under any laws of physics, according to Cox's theorem. What could he mean in the case of, say, life insurance? Let's use life insurance now as our example. Is he saying that we should not use probabilities at all for life insurance and must always go back to quantum states to compute expected values?

[01:57:38]  Unidentified speaker: Presumably not. That would be silly, so there's no way he would say that.

[01:57:42]  Bruce: Okay, so if he then admits, okay, in this case, use probabilities because they're a good approximation, since you can't know the quantum states. In such case, then what's the point of expunging them for rational decisions such as life insurance? Where apparently you need them, right? Like, he's saying we need to get rid of it to be rational and I don't see that. Like, it seems to be like the exact opposite is true. You need to understand the physics so that you understand how to properly apply probability theories to be rational. You're not expunging, you're not removing it to be rational. You're trying to understand it better, but it's real.

[01:58:23]  Unidentified speaker: It's something you still need to understand.

[01:58:25]  Bruce: It's still a huge part of rational decision making.

[01:58:28]  Unidentified speaker: And it's not going away.

[01:58:29]  Bruce: It's never going away. There's never going to be a time where they're going to do away with probability theory to do life insurance, and instead they're going to use quantum states. That's never happening. You will always use probability theory for that, even though it's an approximate match only.

[01:58:46]  Unidentified speaker: Okay.

[01:58:48]  Bruce: So, and you would need to, to be rational. So like to me, I read this and it just seems wrong to me. Okay, so some probabilities are not approximations. So, for example, the double-slit experiment, when it triggers a detector, is exactly determined by proportions of universe, fully matching the probability calculus.

[01:59:08]  Unidentified speaker: Okay.

[01:59:09]  Bruce: Deutsch might counter this meant that measurements are never exact, so probabilities are approximate. And he did counter that in episode 100 to me.

[01:59:17]  Unidentified speaker: But this is misleading.

[01:59:19]  Bruce: There are two things can be approximate here. Are we saying that probability theory itself is approximate, or are we saying that our measurement values are approximate, but the theory is actually correct?

[01:59:34]  Bruce: Limited measurement imprecision does not justify the claim that probability theory itself is merely an approximation of reality, and it's not. Understand, this is true of all theories. Would you say, oh, quantum physics is only approximately correct because we can never exactly measure the size of the slits in the double-slit experiment? Like, when Deutsch claims probability theory is only approximate because we can't measure the size of the slits, he might as well have said quantum theory is only approximate because we can't measure the size of the slits. He's right that we can't measure the size of the slits. He's right that the values we use are approximate, and therefore the results will be approximate. But the theory itself is not approximate. Okay, one might argue, Bruce, you're a layman amateur and Deutsch is a world famous professional physicist. Why should I take your word for word instead of his? I have to admit the justice of this argument, like I do. And quoting Popper that there are no authorities and we should judge arguments on their own merits is never going to change people's minds. However, let's look at this from the point of view of Ivan the Bayesian, who listened to this podcast fairly religiously. He's going to respond and tell me what he thinks, okay? A Bayesian would be right to expect answers to the questions I'm raising. The burden of explanation is on Deutsch and his decision theoretic approach, okay? I'm raising these issues because I understand critical rationalism and Bayesianism enough that I can immediately see there's a problem.

[02:01:14]  Bruce: And I'm going, look, I don't think a Bayesian would find these arguments compelling even slightly, right? Like to me, if I'm a Bayesian, I'm listening to this, I'm going to go, Deutsch doesn't know what he's talking about.

[02:01:25]  Unidentified speaker: He's totally misunderstood Bayesianism.

[02:01:27]  Bruce: He's totally misunderstood probability and what it means to me as a Bayesian. And it's going to lead to questions, right? And these questions are valid and they need to be answered. Questions must be answered substantively.

[02:01:40]  Unidentified speaker: They can't be glossed over.

[02:01:42]  Bruce: They can't be hand-waved. Cox's Theorem is real. It's mathematically clear. Any serious approach must demonstrate familiarity and show how its framework addresses Bayesian concerns that they're going to raise with this presentation from Deutsch, okay? Saying probability is only approximate under my narrow definition of randomness is merely an argument over definitions. And a Bayesian is going to go, I just don't define randomness that way. To me, it was always about degrees of belief and credences, right? I never thought it was part of physics. The current presentation therefore gives the impression of a lack of familiarity with Bayesian theory, particularly with Cox's Theorem. Now, I'm a layman, yes, but one familiar with critical rationalism and machine learning. I also recently went over Cox's Theorem line by line to make sure I understood it. Even from a layman critical rational standpoint, I can see that there are fair, non-trivial questions that are raised that deserve robust answers. I could not begin to guess how to robustly respond to the questions that I'm imagining Bayesians asking here. In fact, the reason why I believe I can't respond to them is because I don't think Deutsch has this right, okay?

[02:03:02]  Unidentified speaker: Now, I might be wrong.

[02:03:03]  Bruce: He might have this right and I might just be misunderstanding, but if so, he needs to explain it. Like, the burdens on him to explain what's really going on, what he really means. Like when he says there's no such thing as a credence or degrees of belief, there's so many cases where there are. Like there's all sorts of cases where it works perfectly.

[02:03:26]  Unidentified speaker: He has to explain why that is, right? From his viewpoint.

[02:03:31]  Bruce: So I'm not proposing an alternative theory here. I'm asking for clear reasoned responses that show the approach truly addresses the concerns being raised, and that I guarantee, like I'm seeing them. I'm sure Ivan's going to go watch this, watch [Deutsch's?] original presentation and go, yeah, I just don't think he answers any of the questions I would have raised at all, right? So a Bayesian is going to ask these, and the burden is on us as critical rationalists to say, you know what, we got to take these questions seriously. Like we cannot just wave them away. We've got to really say, what is it that's going on?

[02:04:07]  Unidentified speaker: What is a degree of belief?

[02:04:09]  Bruce: What is an approximation of?

[02:04:11]  Unidentified speaker: And I just don't see how Deutsch's presentation even begins to address these issues.

[02:04:15]  Bruce: Okay, so perhaps I have misunderstood Deutsch.

[02:04:18]  Unidentified speaker: This is absolutely possible.

[02:04:20]  Bruce: Okay, I've spoken to several critical rationalists defending his view, and I've noticed that they interpret his theory such that they are making factual mistakes. Okay, where they think all randomness is pseudo-randomness, for example. So either they understand him correctly, in which case he is wrong, or they too are misunderstanding him, which this suggests that his arguments might not be as clear as he intends. For example, I struggle with his claim that randomness is like the Flat Earth Theory. I agree that for pseudo-randomness that's true.

[02:04:56]  Unidentified speaker: What he seems to have in mind is that it's roughly correct in some cases, but it's misleading in others.

[02:05:02]  Bruce: Using the Born Rule to calculate probabilities from the point of view of an observer in a universe seems to me to be precisely correct, not a Flat Earth approximation. Now, Cox's Theorem predicts that proportions of the universe will align with probability calculus when making rational decisions, and that's true. This in turn points to two kinds of randomness, true and pseudo. Deutsch seems to introduce a third, non-existent kind and then shows it doesn't exist, which just returns us to the original two. I also worry that defenders of his theory seem to go too far, making wide claims, strong claims, that probability of AGI risks or asteroid impacts are meaningless, not approximations, meaningless. They're claiming it's meaningless, not approximations. I mean, you have to see this, right? Like if the person, the crit rat who had said, there's no such thing as the probability that an asteroid will hit the earth, if he had said, well, there is a probability that the asteroid will hit the earth, but it's an approximation of something else, right? And it's not an actual stochastic event. That would have been okay. Like that would have been a correct answer.

[02:06:10]  Unidentified speaker: But he was declaring it as just meaningless. There's no reason to bring it up.

[02:06:13]  Bruce: There's no reason to talk about it. It's just not true.

[02:06:15]  Unidentified speaker: Okay.

[02:06:17]  Bruce: So I started with all this with a set of fair questions. And I feel I'm ending with the same set of fair questions. But at least I've tried to lay out my reasoning as clearly as I can. Listen, if I do have this wrong, which I may, I really hope someone will kindly try to build a bridge for me to make sense of Deutsch's arguments, because they're not clicking with me at all. Like not even a little bit are they clicking with me.

[02:06:45]  Unidentified speaker: They seem wrong to me. Okay.

[02:06:49]  Bruce: Now building this bridge shouldn't be that hard if Deutsch is right.

[02:06:54]  Unidentified speaker: He's making factual claims.

[02:06:56]  Bruce: He's saying, he argues probabilities like a flat earth theory.

[02:07:00]  Unidentified speaker: It's an approximation that sometimes predicts correctly and sometimes fails.

[02:07:04]  Bruce: Think about flat earth. It's sometimes corrects, it's as a theory, it sometimes predicts correctly, and it sometimes predicts completely wrongly, okay? That's what he's saying is true of probability theory. So I don't see how that applies to QM, such as the double-slit experiment. Once you apply the Born Rule, you get an exact proportions of universes, at least as exact as you can according to your ability to measure the size of the slits, okay? Not an approximation. So now I did ask some of these questions in Episode 100, although I didn't understand it as well back then. And I'll have to cover in another episode what Deutsch's answers were.

[02:07:41]  Unidentified speaker: I don't want to go into it too much.

[02:07:44]  Bruce: Let me just say that the answers he gives me don't really answer the question, as far as I can tell, okay? So that's why I still feel very confused. I will cover what his answers are, and then I will explain why they don't seem like good answers to me. But like I won't go into it for this episode, because that probably deserves its own episode. Let me also say that when it comes down to it, the question I asked Deutsch in Episode 100 was really the question I'm looking for, okay? I said, is there a theory, like is there a theory we're waiting for that's going to be better than probability theory? And then we can do away with probability theory. And then that theory will make better predictions than probability theory. Because that's what, I mean, he's saying it's like the flat Earth, that's exactly what I should be looking for, right? Because you give me this other theory that does everything probability theory can do, plus it can make better predictions in some cases, okay? Think about Newton versus general relativity, Einstein, okay? That's what I'm looking for. If you're telling me it's a flat earth approximation, I want that to know what that other theory is that makes better predictions. And then we just take the case where the new theory makes a prediction correctly and the old theory makes a prediction wrongly. And when we do that, we now refute the old theory and probability theory goes away, and we have this replacement theory, okay? This isn't an unreasonable thing for me to be asking for.

[02:09:15]  Unidentified speaker: When I asked Deutsch that in episode 100, he said, well, there is such a theory, it's the decision theoretic approach that I've published, but it makes exactly the same predictions, okay?

[02:09:28]  Bruce: This isn't what I'm looking for. If it makes exactly the same predictions, then it's not like the flat earth. It's not an approximation. This is what I keep trying to get at, right? If you got two theories and they make exactly the same predictions, to Popper, we covered this in the concepts episode, to Popper, those are the same theory, because they make exactly the same assertions about the world, okay?

[02:09:50]  Unidentified speaker: So that's not good enough.

[02:09:51]  Bruce: You can't tell me that the decision-theoretic approach is better than the probability theory, but makes the same predictions as it. That simply confirms probability theory as correct. Even if you want to reword it into different concepts and words that feel very different, okay, according to Popper, we covered this in the past episodes, that's still the same theory. No matter how much it feels different, no matter how much it sounds different, no matter how many different words we use, different concepts we use, those are all instrumental. And ultimately, if they make the same assertions about reality, which Deutsch is saying that they do, then they are the same theory. And you can't say it's a flat earth approximation anymore, okay? So it seems like if this is a flat earth approximation, it's so easy just produce the other theory, show it makes better predictions. If there is no such theory, then it's not a flat earth approximation. And that's a misleading thing to claim. Now when we're talking about pseudo-randomness, probability theory, I will admit, is like a flat earth approximation. And I keep wondering if maybe that's what he means, right?

[02:11:00]  Unidentified speaker: Like he's being unclear, and he's maybe even in his mind got a little bit muddled between the quantum version of randomness, which is not an approximation, and the pseudo-randomness, which is an approximation, mathematically speaking, okay.

[02:11:16]  Bruce: The reason why pseudo-randomness is always an approximation, and this is something that ET.

[02:11:20]  Unidentified speaker: Jaynes brings out, okay?

[02:11:23]  Bruce: We talk about like, so ET. Jaynes is thinking that when you roll a die, it's all classical because he's not a quantum physicist, he was a statistical mechanics. And so when you roll that die, there's an initial condition, it's all entirely determined, there are no quantum events, there's no splitting of the multiverse, and you get this result, it's entirely determined, but you just can't measure the starting values well enough to be able to predict the outcome. If that's true, if that were actually the real world, and there was no quantum randomness, like ET.

[02:11:55]  Unidentified speaker: Jaynes thought, there was no quantum randomness, then ET.

[02:11:59]  Bruce: Jaynes points out, so this is the Bayesian we're talking about, the father of Bayesianism we're talking about, he points out that there's really no such thing as randomness in this case, that it's just an emergent idea that we use, and that really, if you just calculated a little bit more, you could figure out what that die was going to land on, and it would be predictable, and there would be no actual randomness in that case. So what you really mean is, is that there's a certain amount of ignorance that I have of the starting conditions, because I roll that die all around and I throw it high enough. He points out that if you roll it really close to the desk or something like that, it's not random, right? It's not, it disobeys the probability calculus. That's the thing that Deutsch always points out, but ET. Jaynes points it out, too. And so you're making certain assumptions. You're saying, well, if I roll it enough, my ignorance grows to the point where any guess is equally good. And in this case, it's going to, at least in the short term, obey the probability calculus. But in the long term, it's not going to. You know, the die is going to get chips. It's going to change its shape as you roll it. And in the long term, it's not really going to obey the probability calculus anymore. And so, Jaynes argues that there's really no such thing as randomness and that we're not even trying to work out randomness in terms of frequencies, that really it's about our degrees of belief or it's our credences, it's our ignorance of that initial starting condition.

[02:13:31]  Bruce: And that's what probability calculus is really a plausibility calculus. It's got nothing to do inherently with frequencies or randomness or stochastic events.

[02:13:40]  Unidentified speaker: This is his whole argument. In that case, I can see that probability theory really works more like a flat Earth approximation.

[02:13:53]  Bruce: And in that particular case, I can see that that's correct. Now, if you knew the exact initial conditions, you could make perfect predictions.

[02:14:00]  Unidentified speaker: But that's not true for QM.

[02:14:03]  Bruce: So I'm seeking a real life QM slash born rule example where probability theory makes a false prediction compared to a better theory. If probability theory is a flat Earth approximation, such an example will exist.

[02:14:15]  Unidentified speaker: If it's not, then such an example will not exist.

[02:14:19]  Bruce: And when I did ask Deutsch this, he said they made the same prediction. So apparently it doesn't exist, which is why I question why we're calling it a flat Earth approximation, right? Now, again, maybe I'm just misunderstanding. Like I keep, I feel this humility over this, that there's just no way, like he's saying so many amazing things in this presentation. And I keep wondering, have I just lost, he just lost me. Am I just totally misunderstanding his point? And I'm doing my best to explain myself.

[02:14:49]  Unidentified speaker: I'm doing my best to show my work.

[02:14:50]  Bruce: And I'm doing my best to say, look, I'm digging into this. It's still not making sense. And that's really where I think we're leaving this, right? I'm not gonna go on record as saying he's wrong.

[02:15:01]  Unidentified speaker: I just don't know that that's the case.

[02:15:04]  Bruce: I do think it's possible he's wrong. I do think it's possible that he is confused and that he's absolutely gone the wrong direction on this. And I even think that's my best current tentative theory. Like my best current tentative theory, absent someone actually explaining to me what I'm misunderstanding, is that he's got a misunderstanding, a probability theory, that he's misunderstood. I think there's good signs that he's misunderstood Bayesian philosophy for sure.

[02:15:27]  Unidentified speaker: That doesn't surprise me much.

[02:15:28]  Bruce: He's not into Bayesian philosophy. He sees it as dismissible because he's a critical rationalist. He's never really looked into how much of it might be true.

[02:15:36]  Unidentified speaker: And this is something that I do feel critical rationalists make a mistake on.

[02:15:41]  Bruce: Critical rationalism contains errors.

[02:15:42]  Unidentified speaker: So does Bayesian philosophy. Both of them have some verisimilitude.

[02:15:47]  Bruce: What you really want is you want to understand both. And I think when you do understand both, if you do find that critical rationalism is the true preeminent epistemology, not Bayesian philosophy, Bayesian epistemology. But I do think it clarifies where critical rationalists have made mistakes and where they have misunderstood things.

[02:16:05]  Unidentified speaker: So I think they should learn both.

[02:16:07]  Bruce: Like I just don't think you should ignore it. And I do think he for sure makes some mistakes in this area, but it's so hard to tell with the rest.

[02:16:16]  Unidentified speaker: The whole decision.

[02:16:17]  Bruce: I know there's a paper out there, and I probably need to go to that paper next, where he actually explains in detail the decision theoretic approach. And I will do that.

[02:16:25]  Unidentified speaker: I will go.

[02:16:26]  Bruce: I haven't read it yet, but I will read that paper next. And then once I've kind of comprehended it, I will do another podcast on it. But at least as far as the presentation people have pointed me to, I do not feel it answers my questions.

[02:16:39]  Unidentified speaker: In fact, I think if anything, it undermines Deutsch's points.

[02:16:44]  Bruce: And at this point, I think that is the state, for me at least, that is the state of the critical discussion, is that Deutsch seems to me to be on a wrong path here, and that there really is such a thing as randomness, quantum randomness, and that there are two kinds of randomness, pseudo and true randomness, and that we do need probability as part of physics. Admittedly, it's an emergent idea, but the Born Rule is an important part of physics. You can't do away with the Born Rule. You can make rational decisions without it, but that's only because Cox's theorem says you can represent a decision like that in multiple different formats.

[02:17:27]  Unidentified speaker: You're still kind of... The fact that you skipped the probability calculus means nothing. Okay?

[02:17:33]  Bruce: And I think this is my state of the... For me, this is the state of the critical discussion.

[02:17:38]  Unidentified speaker: I think he's on the wrong path. I think he's misunderstood numerous things, but I may just be wrong.

[02:17:45]  Bruce: And I don't know where to... It's difficult. You go and you ask people questions.

[02:17:49]  Unidentified speaker: I've tried asking him questions. I've tried sending him questions.

[02:17:52]  Bruce: He'll give me really, really short responses. It's just not enough to get into the very difficult questions I'm trying to ask here that I think are valid, that I think have to be answered if we're going to be serious about this.

[02:18:05]  Unidentified speaker: And so...

[02:18:06]  Bruce: And this is really the end.

[02:18:07]  Unidentified speaker: I'm sorry. I'm sorry. This one went kind of long.

[02:18:09]  Bruce: But I'm putting this out there. I'm very much putting myself out there, opening it up to criticism and discussion. I've shown my work.

[02:18:18]  Unidentified speaker: It should be easy to criticize me at this point.

[02:18:21]  Bruce: I do want you to be kind, right? Like, don't be a jerk about this. There's no reason to be a jerk about this. Like, I'm very sincerely, very sincerely digging deep, trying to make sense of Deutsch's view here.

[02:18:36]  Unidentified speaker: And it just isn't coming for me, right? It keeps looking like he's misunderstanding things. And if that's wrong, I would like to be corrected. And I would like to understand what really he's getting at.

[02:18:51]  Bruce: But to such a large degree, it feels like ultimately it's a collection of misunderstandings and an argument over terms.

[02:18:59]  Unidentified speaker: In which case, I don't think it's that interesting.

[02:19:02]  Bruce: And honestly, I feel like it shows some of the misunderstandings of Bayesian philosophy that critical rationalists hold, that we need to do away with. We need to, if we're going to argue against Bayesianism, which I think we should do, because I do think Bayesian epistemology is false in important ways. But if we're going to make those arguments, we need to find the arguments that are correct and not use kind of hand wavy made up straw man versions. And so based on that, I don't feel like this helps at all. Like nothing in this seems to me to be even slightly useful in dispatching with or even explaining what Bayesians are getting wrong. And if anything, I think a Bayesian would look at this and go, oh, he doesn't know what he's talking about and they'd be done. So, okay, sorry, I feel like I'm repeating myself now. I'm just doing my best to explain. I'm not trying to be hostile.

[02:19:58]  Unidentified speaker: I'm not trying to be hostile here. Like I totally accept I may just be missing this, but I am missing it if that's the case. Okay, well, I think you're coming at this with the right critical rationalist attitude. I guess we're done with shorter episodes now. So, that was great while it lasted.

[02:20:21]  Peter: But this feels like your most epic statement ever on probability.

[02:20:29]  Unidentified speaker: And you've obviously put your heart and soul into this podcast. I hope I'm worthy to listen to you, but I don't know who else is going to edit it. So, I guess you're stuck with me here, Bruce.

[02:20:44]  Peter: And it's been a wild ride as usual.

[02:20:47]  Unidentified speaker: And I appreciate you and love what you say. And I hope one of your critics listens to. All right.

[02:20:58]  Bruce: And if so, if you think you can explain this better, like first contact me, let's talk. I'd love to have you on the show and we can maybe.

[02:21:06]  Unidentified speaker: And I'm not, I'm not into debating. I'm like a terrible debater, right?

[02:21:09]  Bruce: I just want to understand. Like my goal is always just to understand. And I would love to have someone just kind of walk me through this and help me understand.

[02:21:20]  Unidentified speaker: Okay.

[02:21:20]  Bruce: And I've talked to like some pretty knowledgeable people. And they often point out stuff like, well, but this is [an advance?] because blah, blah, blah. And I'm not denying that like that. Like I want to make sure it was clear, even though it wasn't a huge part of this podcast. I don't doubt that the decision theoretic approach and that this whole constructor theory of probability approach has value.

[02:21:46]  Unidentified speaker: Like, like, I think it does.

[02:21:48]  Bruce: I think it's kind of a slightly deeper version where we're connecting the mathematics of probability theory in a good way to physics.

[02:21:58]  Unidentified speaker: And I'm not doubting that it does so in a way that is particularly for quantum physicists helps helps push you back towards the correct many worlds interpretation and away from the wrong Copenhagen interpretation. And in that, in so far as that's what we're talking about, I definitely think that there's value in the way Deutsch is presenting this.

[02:22:24]  Bruce: But a lot of it just breaks down for me. So come on, talk to me.

[02:22:31]  Unidentified speaker: Let's let's do a zoom. Let's do face to face. Walk me through this in detail.

[02:22:35]  Bruce: Help me understand where I'm just not understanding this.

[02:22:41]  Unidentified speaker: Okay, well, I'll look forward to that conversation. Okay. Thank you, Bruce.

[02:22:45]  Peter: And have a wonderful day.

[02:22:47]  Unidentified speaker: All right. You too.

[02:22:55]  Unidentified speaker: Hello again.

[02:22:57]  Peter: If you've made it this far, please consider giving us a nice rating on whatever platform you use, or even making a financial contribution through the link provided in the show notes. As you probably know, we are a podcast loosely tied together by the Popper Deutsch Theory of Knowledge. We believe David Deutsch's Four Strands tie everything together. So we discuss science, knowledge, computation, politics, art, and especially the search for artificial general intelligence. Also, please consider connecting with Bruce on X at BNielson01. Also, please consider joining the Facebook group, The Many Worlds of David Deutsch, where Bruce and I first started connecting.

[02:23:40]  Unidentified speaker: Thank you.