SIO411: Zeno, Pascal, and Sleeping Beauty All Walk Into a Bar...

Transcript

This transcript was generated automatically and may contain errors — the audio is the record.

0:00:16 Thomas: Hello and welcome to Serious Inquiries Only. This is episode 411. I'm your host, Thomas Smith. I'm here, I'm you're simulator for the day. I'll be conducting this experiment on you. No, this is kind of a second part of the "Do We Live in a Simulation" series. More to come. This one has some very interesting philosophy that I teased last time. We talk about something called the Sleeping Beauty problem.

We talk about Pascal's wager, and also talk about some other kind of probability stuff, summing infinite series, lots of fascinating stuff here, this one. Okay, so I'm going to say this one, I think, could possibly be tough to follow, maybe, or lose some people.

So I want to tell you, at the end of the episode, I'm going to come back around and do a little bit of a postscript, again, with so if you have a little trouble following all the nuances of this philosophy and this math in this one, hang bad. Hang around to the end, I'll try to, you know, kind of reiterate things, make it a little bit easier for the take -home. It's some really cool stuff, but, you know, philosophy, math, physics, always easy.

We, again, you can avoid the auto -add you're about to hear by going to patreon.com/seriouspod, pledging as little as a dollar. Avoid all that garbage. You don't want to hear those ads. They suck. The way, if you do have to hear them, skip them. I have no problem with anyone skipping the ads. If you'd like to save your thumb from having to push the skip button, patreon.com/seriouspod. right, that said, let's get on over to the interview, and then I'll see you after, some extra thoughts and extra help with the takeaways from this episode. All right, here we go.

0:01:52 Bryan: Take this seriously and work through how much sense this makes. And are two ways to attack it. One is how plausible is it to make a simulation either of the entire universe or just of ancestors? And the other is the argument itself. And so it's the argument itself I want to talk about now, and the rest we can do in a follow-up episode. The argument itself, it turns out that what Bostrom described and the logic happens to align with a previously discussed thought experiment called the sleeping beauty problem, which actually was talked about around 20 years before, but it turns Turns out the setup is identical. And so we can go off all of the discussion around that to inform the simulation argument.

0:02:45 Thomas: Sure. Is this going to be like, if you could be in a dream and there's way more people having dreams and blah, blah, is it going to do that?

0:02:51 Bryan: It's actually a bit simpler that. We don't have dreams within a dream. We just have sleeping beauty and getting woken up. So this doing a thought experiment here. We have a woman sleeping beauty. We put her to sleep with some medication which wipes her memory, or at least some extent. And we put her asleep, and then every Sunday, we take out a coin, flip it, and if it's heads, we'll wake her up the next Monday. It's tails, we're going to wake her. We'll wake up on both Monday and Tuesday.

Or you could extend it, say, Monday, Tuesday, Thursday, Wednesday, Thursday -Friday, the whole week for sake of this problem. And whenever we wake up and put her back to sleep, we'll give her medicine which wipes her memory of any time she was awake. So from her experience, she just wakes up, gets interviewed for a bit, goes back to sleep, and has basically no memory of anything other than that. She doesn't know if she's been woken up before or not.

Does know the way the experiment is set up. She knows what the rules are. She just doesn't knows if this is her first time being woken -up, second, or something after that.

0:02:51 Thomas: Oh, okay. Hmm.

0:04:02 Bryan: So. The question is, when Sleeping Beauty is woken up, they ask, okay, what is the probability that you'd estimate that the coin we flipped landed on heads? So, remember, from arc's outside of this, we flip the coin once. It's either a 50 chance of heads or 50 chance of tails. If it's heads, she's wokenup once. If it's tails, she's woken up twice. Now, we can extend this, but for now, we'll just say twice. So, for us looking at the coin, we pretty straightforwardly say 50-50, but would that be the right thing for sleeping beauty to say? Yeah, at least a question worth asking.

0:04:03 Thomas: That's right. Yeah, sure.

0:04:41 Thomas: Right. Probably not. You would think. Yeah.

0:04:46 Bryan: We end up saying it is. So, like, say she says, well, it's a coin, it's probably 50-50. So let's say, based on that, she says, well, either guess is as good as the other, I'll say heads. So when we look at it, she say heads every time. Her brain is reset. It works the same way every time, so she says heads, and in the weeks where it was heads, she'll be right, right. So that's 50 percent of the time. But in the case where it's tails, she'll be wrong twice. So imagine this takes place over two weeks. First week, coin is head. Second week, it's tail. So we'll see her be right once and wrong twice. Now, if she were to instead say tails, he would be wrong once and right twice. So from her perspective, saying tails would be right. Well, it would be write more often than heads, although she doesn't really have the perspective where we see this. From our perspective, it would be better for her to say tails.

0:05:44 Thomas: Yeah, right.

0:05:45 Bryan: So that's kind of where your intuition was probably getting at, that her, it seems to make more sense to say tails, because she'll be right more often, yeah,

0:05:54 Thomas: And for any given time, she's waking up and being like, what the hell is happening for in reality? That's happening because a result of tails, two to one odds to heads. Right. From that perspective, you'd like, well, it makes more sense to guess tails because you'll be right more often.

0:06:06 Bryan: And so this is what the simulation argument is saying. So let's say instead of being woken up twice, you're woken a million times, and what they're saying is in the case where simulations exist, there will be many simulations. And we are the conscious observers being woken up inside a simulation. For us where we don't know if we're in reality or simulations, we can look at this, that we see, okay, there are two cases where we're in reality. One is no simulations, and the other is there are simulations, but we're on the top layer, and millions of cases where there are simulations and we're in one of them. So the argument goes, from this perspective, we should say that we are probably in a simulation.

0:07:02 Thomas: Right? Right.

0:07:03 Bryan: Do you agree with that logic so far?

0:07:05 Thomas: I mean, I have a bigger problem with the Bostrom thing that I don't know if I can wrap my head around, but I don't know if now is the time to talk about it.

0:07:12 Bryan: Yeah. Sure. It could well be related to this. Why don't you go ahead?

0:07:16 Thomas: Well, Yeah, I just think that the whole thing with the Bostrom paper that has bothered me is it's using whatever reality you are in to then reason about the rest of reality. So it's like if take that paper on board and we might be in a simulation, but then we're also judging, we're formulating these kind of probabilities based on already we're in a simulation, then we wouldn't actually be obtaining real useful data about that top layer reality. So that was always my issue with it.

I don't know if I've worded it well, but it's like the whole paper in and of itself, in order for it to tell us anything interesting, I believe we have to already assume we are the top layer. And then we're like, well, OK, reasoning from here, you think things like, OK. How many simulators? What does it take to have a simulation? How many simulations could there be? Oh, okay. Therefore we've reasoned there from that, that it's more likely if you just wake up that you're in a simulation or whatever, but we aren't just waking up. Like we, we started here and we're reasoning about the simulations based on where we are. You know, does that make sense? I don't know. Maybe

0:07:49 Bryan: Yeah. Yeah.

0:08:21 Thomas: That I could never fully wrap my mind around that.

0:08:22 Bryan: And I think you've actually intuited one of the subtle problems with this. And, I'll get to kind of sketching out exactly why it's a problem later. And the first thing I want to note is kind of what I'm laying out for you, you one way you've got, just there's one outcome. And the other way, you can say there are a million simulations. But if you think about how people present this, they'll often say, well, if you can do simulations, you'll do millions, tons of them.

0:08:51 Thomas: Yeah.

0:08:52 Bryan: And so they expand this. And one of the things that struck me is this reminds me a lot of Pascal's wager, where they try to convince you of their side of the argument, not by convincing you of the odds of either side of it, but by the payout of one of them. So they're not spending any time convincing us that this coin is anything other than perfectly fair in the Slaving Beauty problem. They're just saying that the payout from one of these options is much larger than the other. And because of that payout, you should bet on that more often, which, yeah, if you're betting, if you're betting on tails and the payout on tails is bigger than heads, even if it is 50 -50, then there is an incentive to bet there. But that doesn't mean the odds are any different.

0:09:08 Thomas: Yeah, yeah.

0:09:42 Thomas: Interesting. Okay.

0:09:43 Bryan: Yeah. I think probably the better way to illustrate this is let's go back to the Sleeping Beauty problem. And let's say that Sleeping Beauty has a bank account. She can't see what's in it. But every time she's woken and she's asked this question, she's told if she gets it right, they'll add a dollar to her bank account. If she gets it wrong, they'll take a dollar out. They'll leave her in this state, do this test over and over again for many weeks. And she's just asked, guess heads or tails? You can say from her perspective there, it makes sense to guess tails because if she does, she'll be woken up more times, like twice as often. Over time, more money will be added to her bank account. You follow me there?

0:10:27 Thomas: Sure. Yeah.

0:10:28 Bryan: Yeah. That's not what we're doing when we're asking, are we in a simulation? Because let's imagine somebody is doing a simulation and they decide that they're going to simulate you. They've got a simulated Thomas and a million other simulated Thomases. And at some point asked, Yeah, don't worry, you won't have any contact with them.

0:10:33 Thomas: Okay.

0:10:47 Thomas: Sounds like a nightmare. Yeah? I'm

0:10:53 Bryan: The simulations are completely independent.

0:10:53 Thomas: Not worried about me. I'm worried about everybody else. No, I'm just kidding.

0:10:54 Bryan: Okay. Okay. Yeah, some point you get a voice of god, uh, saying, "Okay, I've got this cosmic coin. I flipped, Thomas. If you guess heads or tails right, I'll give you a dollar. If you get it wrong, I'll take away a dollar." And it's the same thing that's happening to you and every other simulated Thomas, and you each have your own bank account. And when you each have your bank account, things differ because from your perspective, well, a cosmic coin is either heads or tails, and it's 50% either way. And on one end, if, if it's tails, every, you guessed tails, every simulator Thomas is also going to guess tails, and so they'll all get a dollar into their bank, bank account, but any individual Thomas only gets one. So the payout is also split among all of these Thomases. Is that the proper plural of your name?

0:11:49 Thomas: Yes.

0:11:51 Bryan: Okay, good. Okay, every Thomas gets one dollar. From your perspective, it actually doesn't matter which you pick as your expected expected value is the same either way. Is kind of what you were intuiting that the perspective from inside looks different than the perspective from outside. Let's just say the case is we are trying to answer for ourselves, are we in a simulation? And there's some indescribable value to getting that question right. If we say we are or aren't, and it's hard to say exactly what that value is, each person would weigh it differently, but we're making that call just for us. It doesn't add to some cosmic bank account outside the simulations. And absent that outside cosmic bank account, there isn't this expanded payoff in the branch of reality where there are multiple simulations. We've only got what we have in here. And for us in here, it's the either way.

0:12:57 Thomas: That's interesting. Yeah, I don't know. I mean, I still feel like there's got to be some mathematical way in which you would account for probabilities in ways. But yeah, I don't know. That's interesting.

0:13:10 Bryan: Well, the tricky part this is why it's called a paradox. So, you know, I was looking up on this and

0:13:14 Thomas: Oh, is it called a paradox?

0:13:16 Bryan: Yeah, well, Beauty problem or Sleeping Beauty paradox, because there are good arguments both ways. Come down on the side that it's a paradox because the answer is definitively different depending on subtleties of the question, like whether you're taking the view from outside or the view from inside. And I actually think it's good to look at it in the context of having a bank account you're betting on as Historically, the reason mathematicians invented probability was to understand gambling. That's really what...

0:13:19 Thomas: Oh, gotcha.

0:13:49 Thomas: Sell more math.

0:13:50 Bryan: Yeah.

0:13:50 Thomas: Oh, no, yeah.

0:13:51 Bryan: Yeah. Can make money at casinos. And This shows that if you structure it so that there's an outside bank account that all instances of Sleeping Beauty add to or subtract to, then they would always want to bet on heads because they get the better payoff that way. But if you just have a bank account that only lasts for as long as you're awake, then you'll see no difference either way. For your perspective, it's either heads or tails. You'll that 50-50 bet.

So way to look at it, I, um, let's say that instead of being woken up or not, you've just got this box and if it coin lands on heads you put one green ball in the box, if it lands on tails you put two red balls in the box, and so the question now is, um, show the box to somebody. Do this many times, over and over, until the box is full of balls of both colors.

And then you draw a ball from the box, and then you look at it, but you don't show it to the person doing the experiment. Experiment, um, then you ask them, okay, what color is the ball or what odds would you place on the ball, so that person knows, okay, this has been done a lot, if it heads you put one green, if it tails you put two red, well, they're probably going to be twice as many red balls in the box as green.

0:13:54 Thomas: Yeah.

0:15:13 Bryan: So Yeah So I'm going to say it's a two-thirds chance of being a red ball and, yeah yeah, that is how it works. But there's also a different question you could ask, which is in in the Sleeping Beauty paradox, what we're really asking is what happened on the last time the coin was flipped? So when the coin was last flipped, did we put one green ball in the box or two red balls in the box?

And if we focus in on just the last time that way, you can see that, okay, the chance of the last time it was flips being heads versus the last time it flips being tails, well, that's obviously 50 -50. And so kind of what this is illustrating is that the two ways of looking at this problem are asking slightly different questions. One question is from the external point of view, what is the state of affairs, and the other is from the internal point of view.

So it's the difference between asking, what was the last thing we put in the box versus what we take out of the box if we draw from it at random? And those answers don't have to be the same.

0:15:13 Thomas: That's what you'd think.

0:16:25 Thomas: I mean you can you can make the payout be anything crazy, you know, know, a million a trillion or whatever, and yeah, it is a different question. I, I'm still, that's interesting to try to compare that to the simulation theory, um, I, I think my, uh, issue is actually a little different than that, think, I, the thing I'm grappling with on Bostrom's paper is it's like if somehow Sleeping Beauty was asking questions about that, but like from a time in her life before this experiment or something, it's like, you can't use the reality you're in to intuit how that experiment's even going.

For all we know, that that's what I want to ask you about simulation theory. Theory, I, it interesting to try to intuit things about the outside world, assuming we're in a simulation, using what we know. There's absolutely no reason. You said a moment ago, or actually you said earlier in the episode, and I made sure I didn't want to interrupt you. And I tried to make sure to remember though, you said something about like, To oh, see if we're in a simulation, you know, you could maybe look for signs of things that are counterintuitive in that way. And I want to interrupt and

0:16:41 Bryan: Yeah. Yeah.

0:17:32 Thomas: Be like, well, why? Like, why would that tell you anything about whether or not you're in assimilation? Our intuitions are based on, you far as we know in the real world, if we are in the reality, are based upon our evolved sense of things. And there is absolutely no reason why, A, our intuitions should tell us anything about the physics of this reality, but especially, B, they should tell us absolutely nothing about the physics of the parent reality that that we'd be trying to intuit information about under the premise that we are in a simulation. This would be like Mario trying to figure out, OK, well, what is real life like out there using, you Mario one physics and stuff? It's like maybe there's a sense in which Mario could grasp some things about our universe, but also he'd have no guarantee at all that anything that he thought of as pointed to as a sign of like, well this must be how the parent reality works, have no guarantee that that was actually something that corresponds to the parent reality. Does that make

0:17:32 Bryan: It does.

0:18:31 Thomas: Sense at

0:18:32 Bryan: I think you've got a good point there. If we think we might be in a a simulation, it is very hard to leap from that to any conclusion, almost at all about the parent reality

0:18:42 Thomas: All? Yeah. That's, that's what I think. Yeah. I think that about the nature, you know, could we go so far, maybe this is too crazy, but could we go so hard as to say even the nature of like math and stuff, you therefore math and logic.

0:18:44 Bryan: Yeah math math is harder to break, um, physics, well, actually I want to say one thing, we could probably make some guesses about it because, like, let's look at all the video games ever made, and for one, it is like very common for the video games we make, particularly in modern days, to have some sort of physics simulation which resembles what we have, and yeah but yeah well

0:19:03 Thomas: Sure.

0:19:15 Thomas: Well, maybe it just depends on what video game, though, snake say your snake and you wake up in that one, oh

0:19:22 Bryan: Just because it's not everyone doesn't mean it isn't very common, and it's common because it is easy for people to get into because you can use your intuitions about it for how physics works, and there are video games that don't, like, I even found this, this one guy who's deliberately making games that break physics in interesting ways. One is called

0:19:41 Thomas: That's fodder for your channel, huh, for for your YouTube channel from

0:19:47 Bryan: Where, instead of taking place in what we call flat Euclidean space or even spherical space on top of a planet, it's in what's called hyperbolic space, where space really expands the further you get. Like flat space, work is like the radius of a circle is two pi times its radius. In spherical space, it's something less than that. And in hyperbolic space, it something more than that. So that means as you go out from where you are, there's more space than there would be that we're used to.

0:20:19 Thomas: What the center of the universe or something from anywhere what

0:20:21 Bryan: And Anywhere, really, like you draw a circle around anything, and the circle is too big, and this guy, or

0:20:26 Thomas: If you go what if you walk 10 feet one way and then come back 10 feet the other, have you expanded more? Hmm.

0:20:31 Bryan: Yeah, that's actually one thing you can do is just like, uh, walk in a square. Like, well, actually, imagine this, you're on the surface of the earth, you start at the North Pole, you walk like one quarter of the way around the earth, take a turn 90 degrees to the right, walk a quarter of a way around the earth again, turn to the right 90 degrees again, and walk a corner of the way back and you'll be right back where you started on the North Pole, after taking three right turns. Now, in flat space, that doesn't work. You would need to make four. In hyperbolic space, you might need to make five or even more.

0:20:36 Thomas: Okay sure right it

0:21:06 Bryan: Is a spherical geometry. More is hyperbolaic geometry.

0:21:05 Thomas: Wouldn't be less, okay more, okay yeah yeah, cool, oh, okay, interesting

0:21:12 Bryan: Yeah. So there definitely are games which break assumptions. So if we're is mostly flat, lap, though we live on a spherical planet, you we can't say for sure that that's true of the surrounding universe if we are in a simulation. It's really hard to jump to make conclusions about it.

0:21:13 Thomas: Interesting. Right.

0:21:31 Thomas: Returning to the original point, I think you're saying, you probability wise, perhaps there would be some commonalities to these simulated universes like that, to which I would say, well, OK, I mean, I could throw a million hypothetical wrenches and all this stuff. Like, what If we are within a simulation that an AI is making to make sense of the world? And the future, we have AI that uses bunch of little simulations to make sense of the world and answer questions, but it's not doing so in a way that would be intuitive to us. It's doing so, it could be reasoning along completely different dimensions and stuff like that we can't even describe, in order to make sense of the world. And that AI may spawn more AI and more, you know, and then you can do that thing where it's like, well, now the odds of that are way higher because AI

0:21:39 Bryan: Yeah. Yeah, definitely.

0:22:13 Bryan: Yeah?

0:22:13 Thomas: Are going to do that for every thought it has. That's just off the top of my head. Like, I feel like it's, it's virtually impossible to, to make any deductions for sure, I think, based on our reality, if we are stipulating that our reality isn't the parent reality.

0:22:17 Bryan: Yeah.

0:22:29 Bryan: That's true. Now, if you want to go back a bit, I thought of another good argument about kind of the sleeping beauty problem and whether whether or not we live in a simulation. So one thing about probabilities is that if you take the probability for every possible outcome and add them up, the probabilities always add up to one.

0:22:35 Thomas: Oh, okay. Sure.

0:22:46 Bryan: That's just how probabilities work. So let's say we're doing the Sleeping Beauty problem, but with simulations. And let's look just at the top layer. So instead of flipping a coin, we're asking, okay, how many simulations exist in this universe? And we're like ancestor simulations of the type we care about. And there's going to be a big probability that the answer is zero. And then, okay. Maybe the universe contains one simulation. We'll say that as a probability of X. Okay. What about a universe that contains two?

Now would that be greater or less than one that contains one. We don't know, but we could keep doing it and say, okay, what about one that can needs three? What about one that contains four? One that contains five? And so on until the point we're at, okay. What's the probability that this contains 1 billion simulations?

At that point, you you kind of get to the point where, okay so universe is finite in In size and time, there there's only going to be a certain amount of space to possibly fit simulations into it. So at a certain point, the probability of having more simulations is going to being less. Like, let's say you have a universe that can only fit at maximum two simulations. Simulations.

Well, probability-wise, two is the maximum, and most of the time, maybe you won't even get up to two, you might not even get to one. So the probability of more simulations becomes less and less.

0:24:19 Bryan: So what we're doing mathematically is we're basically taking this whole set of, okay, what's the probability?

0:24:19 Thomas: Okay, we summing an infinite series.

0:24:27 Bryan: Yeah, an infinite series, series, and the sum of all of these probabilities has to add to one.

0:24:28 Thomas: Okay, it's got to be one. Yeah.

0:24:33 Bryan: And as we go off, as there are more and more simulations, the probability of any given number has to fall off. Mathematically speaking, I believe that the probability, in order for this to converge, the possibility of of N simulations has to fall off by a factor of N cubed, at least, if not stronger than that. It's just math. I'm not going to go into some...

0:24:43 Thomas: Hmm. Sure. Yeah? Otherwise, we wouldn't get one, we would get an infinite, I guess.

0:25:07 Bryan: So, yeah. No, it is N squared for this. So yeah. Yeah. N squared here. I was thinking a step forward. So the probability of having a universe with N simulations is 1 over N squared, maybe times a constant. And so each of these times, if you look at it, the number of simulations you have times the probability, well, you multiply N times 1 over N squared, you get 1 over N. And so what we see is that this long tail of all of the cases where the universe has multiple simulations gets smaller and smaller. So the probability of your mind winding up in one of those doesn't strictly multiply by the number of simulations. You also have to multiply by the probability that the universehas that many.

0:25:10 Thomas: Okay?

0:25:53 Thomas: That we were there. Okay!

0:25:55 Bryan: And that probability drops off faster than the number of simulations increases by definition of the probabilities having to sum to one.

0:25:55 Thomas: Interesting. Well, that's That's interesting.

0:26:05 Bryan: So if you look at the probability carefully that way, now, then it could be that the base rate of this is high enough that there is still a good probability you're in a simulation, but it isn't as clear-cut as the initial argument makes it seem. It's of kind the same problem that Pascal's wager has, is they're increasing the payoff, but this ridiculously high payoff has to be tied to a ridiculously small probability because you're just making up some possibility and assigning a probability to it. And when you're making things up, there are so many any possibilities of what you can make up. They all have to fit into a probability of one. And when you try to squeeze them in, they get to ridiculously small probabilities.

0:26:23 Thomas: Yeah.

0:26:53 Thomas: And I think there would do a better job than me at this, but there is a sense in which it has that feel of like one of those ontological arguments that really feels like it's bootstrapping itself, you know? And I think that's a reason why there's a lot of appeal to this paper. It's like, wow, that seems crazy. But it has this feel that like, well, okay, can I do the same thing but with other things? Can I say, well – hypothetically, there be some realities in which instead of us just being humans limited to human powers, there's other realities in which we are – all of us is like a god.

And each of us would probably make our own reality that we, you know, and then can you do that where you're like, well, then I guess the odds are then that we're probably in a reality that's created by one of us who's a God. And it's like, there's no real way in which you could say, well that's wrong in that again, that's off the top of my head, but it does have that feel where it's it's like, I think that doesn't work. And

0:27:47 Thomas: I'm trying to figure out why. And that's why in the end, and this was years ago, again, that I covered this, but in the end, in my mind, I still couldn't get past that component of it where it's I still think you're bootstrapping yourself by reasoning about simulations, not knowing whether or not you're in one. But maybe that's not precisely the problem with it, but yeah, what do you think?

0:27:29 Bryan: Yeah. Yeah, yeah, yeah. I think it's kind of like that. And as I say, I think this kind of feels the same reason Pascal's wager does is that when you're making things up, You can make up an infinite number of things, but since the probabilities have to sum to one, all of these possible things you can make up are infinitely improbable. Like, the classic Pascal's wager is you've got a god that says, believe in me or go to hell for infinite torment. And then, yeah.

0:28:28 Thomas: Yeah, and so it's like, wow, and we should have explained that earlier, sorry, I just assumed, but, yeah, it's, like, oh, you know, the punishment is so severe that even if there's only a low probability that you'd want to, you might as well just believe for the sake of not burning in hell. There's a bajillion problems with that argument, as I'm sure many of the listeners are familiar with.

0:28:49 Bryan: Yeah. Yeah, of the simplest ways to show it is just make up something else. Like I say, okay, well, well, you've got your God, I've got God too. And God too says, don't believe in me or else you'll get infinite torment. And so you can't believe any gods or you'llget infinite.

0:28:56 Thomas: Yeah. Yeah, God 2. Yeah totally. God 2 is really, really hates insincerity. And so God 2, is like if you ever, ever believe believe in a God for reasons other than true, perfect belief, then

0:29:13 Bryan: Yeah. Yeah. See, look, I created this universe. I made sure there was no evidence I existed. If you do believe in a God, you're doing something wrong and I will punish you.

0:29:19 Thomas: Yeah, exactly. Yeah, no, totally. And though I would describe that as kind of an absurd problem, it's a very legitimate problem with the argument, but even less absurd is like, well, what if we're in a universe with a God, but he doesn't punish you in that way? Like, Like, I feel like that's also a perfectly, perfectly reasonable universe. And so using that infinite, as you say, using that Infinite cost or outcome, you you know, want to say reward or cost to then multiply by the probability and say, well, you better make sure you do this just because, you don't want to risk it. You're right. You got to, you got to account for like, well okay, how unlikely is this? And then actually you do need to discount for that, even though humans are pretty bad at that.

Know, humans are like, you see that somebody, you know, died by getting struck by lightning by walking in a certain place. And then I, well then, okay, I'm not doing that because that's, it's just not worth it. And we do that with a lot of things where we're like, well, the cost of this particular behavior or superstition, the cost feels pretty low. So just in case, I don't want to get struck by lightning. I'm going to walk under a ladder, do some other thing like that. Even though that one sounds like it's It's just a legitimate safety tip.

0:29:39 Bryan: Yeah. Yeah.

0:30:31 Bryan: Yeah. Yeah. I think that's why it's just a bad idea to walk under a ladder.

0:30:34 Thomas: Yeah, like don't. Your odds of something dropping on you slightly increase walking under a ladder just definitionally. So that one's a bad example. But the point is, like, we have a lot of those things in life where we're like, shit, averse than we are reward oriented or whatever the term for the other thing is. Is, where we're like, I, cost would, even though it's a low probability, that I was the guy who got struck by after walking under a ladder, I'm going to feel like a real asshole, you know? So I'm just, so I'm not going to do it kind of thing. And I feel like that applies to that Pascal's wager argument a little bit. And think that most people don't realize that you can sum an infinite series and get something less than infinity, do you get that sense, I feel like that's a math innovation that math people haven't fully yeah, good, really

0:30:50 Bryan: Yeah, yeah, yeah. Yeah, that's a good point. And yeah, and in fact, that was relatively recent math wise over the whole history of doing

0:31:25 Thomas: Oh

0:31:25 Bryan: Math is you really need. I'm not sure if it's specifically calculus or related to it. But yeah, it was around like the last few hundred years that they really started talking Yeah, you actually can handle infinities in sensible ways, and it's just kind of how the concept of integration works, is it's summing up an infinite number of infinitely small things and coming to something finite. Night that no you

0:31:30 Thomas: Okay yeah yeah right well, I would have thought something like freaking Pythagoras figured that out or something, because I think there's the way of representing it where. Where it's like, take a square and then subdivide that square, you a, with a, well, yeah, yeah.

0:32:01 Bryan: Be thinking of uh, Xeno's paradox, which is basically yeah, you shoot an arrow and before it gets to the target, it has to travel halfway, and then between that Point against the target has to trouble half of the remaining distance and then half of that and half of that. And this was considered a paradox because they didn't really have the math to understand how Now you could, yeah, it's provable.

0:32:10 Thomas: Oh, so, so it's, like, they knew the answer. They just don't know how to, like universe. Yeah, well.

0:32:26 Bryan: Like, yeah.

0:32:27 Thomas: Right, right. Well, what I was going to say is, if you take the square and you divide it in half and you add that, and then you divide in fourth and add that and divide it and, you know. Now, now an eighth of it. Now that you can see visually, well the answer is one because I can see the fucking square. Like I know, I know the answer is one. And I know that I'm adding one half plus one, you know, one fourth plus one eighth, all that kind of thing. And you could draw it out visually and say, well, it has to be one, but maybe it's like those, those things in math where it's like, well we're, we're virtually certain this is true, but we haven't proven it yet. And that can stand for like 2000 years until finally somebody proves it. Is it that kind of thing maybe?

0:32:35 Bryan: Yeah. Yeah. Yeah. Yeah. Yeah. It basically took that, that there wasn't a rigorous mathematical formula for that type of thing until I think around the time of Isaac Newton, when he was figuring out his laws of physics and Leibniz around the same time, I think. Yeah. Yeah. They formalized it. And that's one of the things you have to take into account with things like Pascal's wager or the simulation hypothesis, which I think is doing the same thing as Pascal's Wager, that they're the deck on one side saying, well, if this is true, the chance of being right so much more, so you should believe in this side. They're just increasing the payoff, but they're really doing the same thing of just picking a large value. They give it a bit more veneer of plausibility as nobody's ever going to say infinite simulations, but They're going to say there's a large number of

0:33:08 Thomas: Hmm. And calculus and yeah, crazy.

0:33:35 Thomas: Mm -hmm. Mm

0:33:49 Bryan: Simulations. And because of that large number, which, you you know, could do the same Same thing with Pascal's wager. Just say, like well, imagine a guy comes up to you on the street and says, OK, there's a 50 percent chance I've got a gun in my pocket. And if you give me a hundred dollars, I won't shoot you. Therefore, yeah, kind of mugging you with chance the that they have.

0:33:49 Thomas: Hmm, hmm, they're math mugging you, they're mugging you with math. Oh, no, it's a new TikTok trend. Taking, is your child mugging people with math?

0:34:16 Bryan: Yeah. Except they, yeah. Yeah. There actually is a saying called a Pascal's mugging. And it basically, it's basically this. Somebody comes up to you on the street and says, give me $100. Okay, why? Well, I'm God. And if you don't give me a hundred dollars, then when you die, I am sending you to hell for infinite torment. And so that's basically it's Pascal's.

0:34:43 Thomas: Yeah, well, shoot, I can't afford not to.

0:34:46 Bryan: Yeah, It's Paschal's wager, except we're adding a definite cost on to it. Whereas the it traditionally says, well, any finite cost is worth it to avoid infinite torment. Torment, and this is one of the ways Pascal's wager is kind of debunked, is the Pascal smugging, is that like, okay, you do that, but then as soon as that guy's leaves, another guy comes and says, okay, now, now give me a hundred dollars because I'm God. And if you don't give it to me, I will torment you when you die. And you said, wait, wait, but that guy. And then this keeps happening. Guy after guy after gal after enby comes along and says they're God, and you have to give them all $100 because, well, any finite probability times infinite pain.

0:34:46 Thomas: Yeah, yeah.

0:35:23 Thomas: Plus, There's that Ghostbusters quote, if someone tells you to give them a hundred dollars because they're a god, you say Yes. No, it's not exactly that. No. That is a good way. It breaks down. Eventually you're like, well, I'm out of money, which, I think it's a good way of pointing out. There isn't really a zero cost to believing something like that. You know, like you have to do something and you just shows how motivated reasoning that is, you Know, because like, well, why did you pick the Christian God? That's weird. You know, why do we start there? There's so many deities throughout all of time. If you're going going to try to properly evaluate the odds of this thing, you'd have to calculate which ones are, you know, which ones are going to reward you forever, which ones are gonna punish you forever. And, you know, you have to do some math based on that to even get close to a legitimate calculation here. But they definitely didn't do that. They're just like, I want you to believe my Christian thing. How can I make you do that?

0:35:40 Bryan: And yeah.

0:35:52 Bryan: No.

0:36:10 Bryan: Yeah. Yeah. And and this is kind of what happens with the simulation hypothesis, too, is that if you believe in it, But it's hard to state exactly what the cost is. But particularly if you believe in it incorrectly, we're not in a simulation, but you believe we are, there's some cost there. And I'll go back. A while back, I referenced the game AI, the Nirvana Initiative. And there are actually two groups of people who believe they're in a stimulation. One group believes it and wants to break out. The other believes it and wants to go all Grand Theft Auto because they believe, oh, this has no meaning. So nobody else here is a real person. I can do whatever I want and have fun with it. If you believe it's simulation and that causes you to devalue everything that's going on, that's a definite cost.

0:36:39 Thomas: Mm -hmm.

0:37:03 Thomas: Yeah, for sure. Here, I'm curious if there's anything else computation-wise that we want to talk about, because I've always wondered about that. And applying the reason I bring it back up is applying my same principle of you can't reason about the base reality using our simulated reality, does that break down?

Because I hear a very common counter -argument to the simulation hypothesis is it takes too much resources, you resource intensive, to which I'm always like, well, I don't know, what would Mario think about that, would Mario be like, well, I've, I've come up like Dr. Mario or somebody, one of the Mario games, where maybe you can start making something like a computer, and Mario's sitting there like, man, I can make a computer, what if I could make a Mario of my own inside a computer?

And then you'd be like, well, the resources would be intense, but you're thinking of it in terms of like mushrooms and crap, you're like, I would never have enough mushrooms to make a, a Mario, of my own. But it's like, yeah, but if you went to the real reality, you're not running computers on mushrooms, who knows what you're running them on, and who knows what the resource intensity would be, et cetera, et cetera. So what do you think about all that?

0:38:07 Bryan: Yeah, a good point is that we don't know, like, if it's practical in the outer reality, but I will say that for talking about the simulation theory and trying to get people, they say, well, they're going to do ancestor simulations, that they always say that

0:38:22 Thomas: What is it? Oh, they're always simulating like themselves in the past. Is that what? Yeah. Yeah. And

0:38:23 Bryan: Yeah themselves or previous generations of humans. And so if you accept that premise, then that, that it basically says, okay, this is the same universe, just further into the future. Now, there is a good question there, yeah, about how complicated, how difficult it is to simulate that universe. But unfortunately, looking at the time here, I think we might have to put that off to another episode.

0:38:36 Thomas: It feels, yeah, another premise.

0:38:49 Bryan: Because before This, I actually did go through the calculations and try to come up with a good estimate of how hard it would be to simulate the universe. And I'll just say it's pretty hard.

0:38:49 Thomas: Oh, okay. Sure.

0:39:00 Thomas: Pretty hard. Yeah. No, well, for sure. But it's hard based on the universe we're in. Yeah. No, if you do, I get the ancestor thing, but I also, I don't know. Is there a sense in which you, still could think, well Well, perhaps what if the real us, what if the real reality is like multidimensional in a way that we aren't, but they're, they're using fewer dimensions, still getting meaningful simulation results, but using fewer dimensions for math reasons or for computational. I don't know. Like we don't, we don't know that. Is that, is that a crazy thought? What do you think?

0:39:01 Bryan: Yeah. Yeah, yeah, yeah. Yeah. Yeah. That's a good point, and as you said, like, we simulate video games that are simpler than our universe. Like, we we have 2D Mario games that have fewer dimensions, and so, you know, we can't rule out that another, the higher level of reality is simulating us, and they've got, you know, four spatial dimensions, but they've just simplified it to three, for simplicity. The, we simplify Mario to two, so.

0:39:56 Bryan: Yeah, possible, but as to what to do with that, that's more a thing philosophical.

0:39:56 Thomas: Yeah, Yeah. Yeah. There's definitely, I've, I'm, I've enjoyed dipping back into philosophy here. It's been a minute. That was a lot of fun, Brian, for taking us through all of that and getting me back into Futurama again. Was the rest of the season any good? This one was okay. It was, you know.

0:40:01 Bryan: Yeah. Yeah. Um, As, I said it was hit or miss. I, you want to get all the callbacks, go through it all, or or go to IMDb, look at the individual episodes, because there were some that were not very popular, like episode nine, almost no one seemed to like. One of their, like, where they do just three random stories that are disconnected, and that particular one, just none of them clicked with anyone. But other ones, like the one I recommend, I forget which number it was, it's called I Know What You Did Last Xmas. It's their Christmas-themed one, which I really enjoyed.

0:40:46 Thomas: Hmm. All right. Well, as usual, check out your YouTube channel. Anything else you want to throw out there or throw out more details?

0:40:51 Bryan: Oh, yeah. So I haven't done much on my YouTube channel. So a different plug. Know, you probably heard in the news about the war in Ukraine. They're worried that they won't get any US funding or support. And people might not know, but if you have money to spare, you can directly support the Ukrainian government. They've set up a website for this called United24. So you can either search for United24 online or I'll send the link to Thomas to put in the show notes. It's just u24.gov.ua. And this is their hub for whatever you want to donate for. You can decide exactly what your money goes to. You can choose defense, humanitarian demining efforts, medical aid, rebuilding Ukraine or education and science and send the money directly to them to help out while the U.S. Congress is in gridlock.

0:41:03 Thomas: Yeah. Oh, wow.

0:41:44 Thomas: Because the Congress needs to decide, are we going to just fuck over some immigrants in order to also help the Ukrainians or not? Like, that's a... it's kind of... it's one of those Cash 22s we have to, for some reason, do those things Yeah, it's not... that's not that inaccurate of a description. Okay, that's really cool, I actually didn't know about that, I'm going to check that out, and thanks as always, Dr. Brian Gillis, for joining us on the show

0:41:54 Bryan: Yeah, that's their Pascal's mugging, basically. Yeah. Yep. Problem. Thank you for having me on, Thomas. I'll talk with you later.

0:42:15 Thomas: Okay, so here I am at the end, the restaurant at the end of universe, talking about what you just heard. So I've gone on quite a long journey on this one. We recorded this a little bit ago, and this is almost like back to the quantum computing episode, and I just got obsessed with it, and I could not stop thinking about it, and it delayed what I was doing. This happened a little bit here too, quite a, well, I've actually quite a lot because.

So we talked about the sleeping duty problem. Brian took us through that. He took us it, through it very well, but I there think I might not, see, I'm reflecting upon this a lot and I haven't talked to Brian about this. And so I'm excited to have further conversation on this, either on or off the air. I don't know one way or the other. But I don't think I quite agree with Brian on the implications for the simulation hypothesis regarding the sleeping beauty problem.

I understand, and maybe I don't understand correctly, but if I understand Brian correctly from this episode, the analogy is to the Beauty, the, even if you were keeping track of a bank account and betting, you would want it to be a third and would be smart to treat the odds that way. If you were Sleeping Beauty and you were betting on the outcomes, you would wanna bet a third or use that as your credence to place your bets.

I took Brian to be saying, the other way to look at it is it can still be a half and therefore the comparison to the simulation argument, I he was trying to make is that even though if simulations exist and are prevalent and therefore there's a gazillion simulations, that you can look at it both ways.

And so if I'm drawing that analogy, you would say, well, that take the fact that there would be a gazillion of us if there were simulations, because simulations would outnumber under this thinking, outnumber vastly the real world. Take Brian to be saying, maybe don't use that reasoning. Maybe that shows the reasoning can be faulty to take that to mean the odds are we're in a simulation. What I took him to be doing. I listened to this a lot of times and I've read a lot.

Now, if I'm wrong about that, apologies, Brian, but that's what I took him to mean. But I think the analogy doesn't quite work. Now, you, I have my other reasons that I don't believe in the simulation hypothesis as Bostrom formulates it. I actually, I have a lot of problems with it. We're going to get to that later. But for now, when problem, I think the analogy would be the beauty waking up multiple times doesn't change the odds of the actual coin.

Coin is still a coin, coin is still 50-50. By analogy, us being simulated a gazillion times doesn't change the odds that there are such a thing as simulations. So let's say if our prior credence for some reason is that it's like a 50-50 question whether or not we humans or equivalent humans can develop simulations. The analogy would be, yeah, well, the fact that if we do, in like within that 50% win percentage, there's a bajillion more of us.

That doesn't actually change the fact that it's still a 50-50 question whether or not simulations can exist in this way. I agree, but I actually don't really think that says all that much. I think took Brian to maybe be implying that therefore we shouldn't trust Bostrom's argument because of this. Like we shouldn't put way more stock in the idea that we're in a simulation because of that kind of analogy I just made. I hope that makes sense.

Don't think that actually changes the calculus as Bostrom lays it out. I think as Bostrom lays it out, you would still say that the number of simulated us's in the universe would still vastly outnumber the regular us's. And so I think that's a good thing. I don't think that that's in the universe. And therefore the odds would still be that we are in a simulation. Now, maybe I missed something.

Maybe that's not how Brian meant it, but I wanted to clear up my thinking on that. That's how I took that. And that's what I think of that. That Brian said that I don't quite think was right was he was talking about, well, if you reset the bank account every time, she doesn't notice a difference was the quote I jotted down.

Wrote and I'm not really sure what he was driving at with that, because if you reset it every time she asked the question, then they're like, is there any sense in which there's any way that you would, like the only way you can track whether or not she's going about her betting correctly is by tracking the results over time.

Like, by that logic if you asked her, well, was it heads or tails, and she answered fish, but every time it reset her bank account, she still wouldn't notice the difference. You know what I mean? I don't really understand. Maybe I misunderstood the point, but that was one thing that jumped out at me that I wanted to mention.

Like, if you were confused by that, I just want to flag that I also was and maybe we'll get a little follow-up with Brian and he can clarify. We'll see. Now I just want to speak about my observations on the Sleeping Beauty Problem because I read the main, not it's the origination of the problem, but the popularization of the problem was by a paper by Adam Elga. Read that about 1,500 times. And then I read the kind of most popular reply.

Adam Elga is a thirder. And again, that's the position where you think that the credence should be one third. So if you ask Sleeping Beauty, you wake her up, you ask her, what is your credence that the coin landed heads, for example? Should answer a third. Now, David Lewis, very well-respected philosopher, wrote a reply, and I read that 1,500,000 times, that it should be one half. Separate this from the Simulation Hypothesis.

This is now just, I read a bunch of philosophy for hours because I was trying to get to the bottom of what the hell was happening here. And I just want to tell you about it. I have read this so many times. I even like learned the stupid probability notation that I, that I learned in college at some point and then forgot. Relearned all that. Adam Elga's paper is pretty graspable in certain ways. David Lewis's is way denser in terms of that notation.

It makes it a little harder to. But I'm going to say something, thing, but I want to encourage, if you're going to reply to me about this, make sure you have read these actual papers. It comes to this, I actually don't think the Wikipedia entry or even a lot of the analysis I see captures what's really going on in these papers because there's something weird going on here. I actually think the disagreement just comes down to a bit of a bait and switch by Adam Elga.

Could be totally wrong, but if I'm wrong and you want to tell me about it, make sure it's because you actually read the real papers and not because you read the Wikipedia, because that's this level of detail isn't actually in the Wikipedia. So if you heard that Sleeping Beauty problem and you were wondering, well, how on earth could anyone say it's one half? Which is what I was wondering.

Like the way it was presented initially to me, I thought, well, yeah, it has to be a third. Why would you ever argue that it's not a third? I mean, the in same way that if I say, hey, here's the deal. I'm going to flip a coin. And if I win, I win a Super Bowl tickets, for I lose, I lose. I win these tickets, I'm gonna call you and tell you. If I lose, I am not going to call you. I'll be too depressed.

And then you get a phone call from me. Going to be like, well, you won. You know, like that's going to be that's the most basic, obvious, easy thing. It doesn't mean that I believe a coin is 100% chance of landing heads or some crap like that. It means, well, I've been given the information that you called and that tells me all I need to know. And in some ways, I was wondering why are we even bothering with this whole Sleeping Beauty thing?

Like you might ask, like, why is all the hubbub if the situation is really as simple as, yes, it's a coin flip. But the fact that you're getting woken up kind of gives you a little bit of information such that it changes your odds. Like who would argue with that?

And so in who would argue with that, how could David Lewis, somebody I know to be a pretty prominent philosopher, like I remembered the name and I refreshed, like David Lewis is very key in a lot of areas of philosophy, specifically like possible worlds and that kind of thing. How could that guy think that it would be a half? I think because of some ambiguous wording by Elga. And here's the key setup and I'll add a wrinkle that makes it interesting.

So it's, it's as Brian described, but slight modification here, and this is an optional modification, but it highlights something interesting. Okay. The the setup, you tell Sleeping Beauty, here's what's going to happen. We'll wake you up on Monday if it's heads or tails. We'll wake you up Monday and Tuesday if it is tails. Here's the interesting wrinkle. You could also flip the coin after Monday. So you could wake her up Monday and ask her, what do you think the coin going to be?

We could have not flipped it yet. And we'll have functionally the same result. Interesting to think about. So give Sleeping Beauty the sleeping medicine, you know, and we wake her up. It's Monday. Well, naturally, if she knows it's Monday, she's going to say, well, it's a 50-50 question. That I think we can all agree on. If somebody were to tell her, hey, it's Monday, she'd be like, well, it's 50-50 because I know Monday happens either way.

If you were to tell her it's Tuesday, well, you know it's tails. That's easy. But here's the little bait and switch that I think happens in Adam Elga's paper. The way he presents it ultimately is by, you know, a series of logical steps and probability notation crap that I don't really need to go into because I actually don't think it adds much more than we already can just intuit in normal everyday words.

Does this math of like, well, the probability that it's heads or tails is 50-50, sure. The probability that it's on Monday heads or tails is 50-50. Those are equal. The probability that its tails Monday and tails Tuesday is equal. Those probabilities are equal. And then he does some steps. And so therefore by the transitive property, all three probabilities are equal and that's how you get a third, et cetera, et cetera. It's a fancier way of saying what we already kind of basically knew.

The the trick is, here's the trick and the source of the disagreement. He says it's because of the way you can formulate the problem where you're not giving her the amnesia stuff until after you wake her up Monday. So think about the timing. This actually stupidly matters. You tell her about the experiment Sunday, you put her to sleep, you you were to wake her up on that first Monday before you've done anything. So you haven't given her amnesia because you didn't need to yet.

You haven't even tossed the coin yet. If you were to ask her, hey, what's your credence on heads or tails? She should say a third. And that's the part that David Lewis is really hung up on because he's like, well, nothing's changed. There's no difference. Like you you went to bed Sunday night. You're like, OK, yeah, we're going to do this. You go to bed, you wake up. And then Sunday night, you're like, hey, we're going to do this.

And Sunday night someone asks you, what's the odds that's the heads or tails? You're like, well, it'll be 50-50. That's my credence. That's what it'll be. And then they wake you up Monday morning. Nothing's happened. You haven't gotten the amnesia juice and you haven't even tossed the coin. And yet when you wake up Monday morning, you ask, hey, what's the chances the heads are tails?

You should say a third, and David Lewis is saying how, like, and again, it's through tons of fancy notation and crap. I believe I've distilled what the problem is here. I believe he's saying, how could that have changed? There's no way anything could have changed from Sunday to Monday. I think the key part that is genuinely possibly some kind of accidental bait and switch by Elga.

Key problem there is, yes, even though from a bird's eye view, you and I will, like if we're the experimenters, we will know that we put her to sleep and then we woke her up Monday morning and nothing had changed and she answers a third, but she won't know that. That's the bait and switch. The changed, the information, if you want to call it that, that she now has is that she has begun this experiment during which she could have already been woken up before.

On Monday morning, when she is woken up, she actually does not know, even if it's the first time and you haven't given her any amnesia juice because she knows she's in this experiment. Now she's entering into this experiment now when she wakes up that first Monday morning. Again, you haven't done anything yet. She doesn't know that though, because it's all agreed the minute you tell her, hey, it's Monday.

She's like, oh, okay, 50-50 because, you know, you wake up Monday either way, but that's the bait and switch that I think actually, I'm pretty sure by my reading is the source of a lot of disagreement here. Now there may be other things going on, but like that to me is not really that interesting. Like I think what's going on there is, yeah, from, from a bird's eye view, you can see that nothing's actually changed from Sunday to Monday on that first go round.

You can seethat, but she doesn't know that. She's going to answer a third if she's a rational person, because she doesn't know if this is the first time she's being woken up or the millionth time she's been woken up. And so, honestly, if by my reading again, if you read these original papers, feel free they're not that long but I read them 20 times each I'm not even joking because I was trying to figure out like what is the actual disagreement here and I honestly think that's it I think that's all it is I think I think Elga is kind of using the fact that from a bird's eye view, we know nothing's changed to say, hey, you could go to sleep one night and say, my credence is one half and wake up the next morning with nothing changing and say my credence is one third, but something has changed.

What's changed is you've entered into this fucking experiment. So you don't know that it's that first Monday. I have no idea if this will be interesting to anyone, but I spent so many fucking hours trying to figure out that thing. I just told you, and I, I'm pretty sure that's it. I'm sure that the game that's going on now, there's tons of other solutions and papers about the, is a sleeping beauty problem. Nick Bostrom has his own solution. That is fucking insane. His solution.

I'm not even joking is two fifths and it has to do. Yeah, I, that's a whole nother story. I had to stop myself from trying. I read the paper a couple of times. I'm like, what the dude, what are you on about? So Bostrom, very interesting, that guy. But anyway, one of those things where I could not let go of it until I figured out what the fuck was going on. And I had to relay that to you because that's all that's happening.

But one comparison I did want to make, something that occurred to me is, even though it seems like nothing's happening, it's kind of like the Monty Hall problem. If you aren't familiar with that, you probably are. Most people listening, I imagine, are. It's a really interesting thing where it has to do with that old fucking game show from the 1960s, I don't even know, where it's like, there's three doors, there is a prize behind one door, you pick a door, so like, ah, door one.

One, and then whoever the Monty Hall or somebody, whoever the guy is, if that's the show or the guy, I don't care. It's 100,000 years old. Whoever the guy, Alex Trebek, comes over and is like, all right, I'm going to eliminate door number three, for example. And now the choice is, do you stick with your door number one or do you change to door number two?

And it's a very interesting mathematics probability thingy because what you absolutely should do mathematically is switch your guess, and it might seem weird at first, you're like, well, why would I switch my guess, I already, like, I've already chosen one of them, and if he eliminates one and it's a 50-50 choice, why wouldn't just my choice always be the statistically correct move? And it's because mathematically your first choice was one out of three. It was a random one out three guess.

Now, once Alex Trebek eliminated one of the doors that doesn't have a prize, and that's important, the door doesn't. Obviously, he's eliminating one that doesn't have a price. I don't know if that was obvious or not. But once he's eliminating one that doesn't have a prize, if you switch your guess, that second choice, that switch you do is made with a 50-50 chance. Kind of a cool thing that seems a little weird at first.

And then what I always do is I try to turn the knobs and dials on these things. And I think, okay, what if it was 9 million doors and you choose one? And then Alex Trebek is like, all right, I'm going to eliminate 8,999,998 doors. And now it's just, you choose between these two doors. You'd be an idiot if you're like, yeah, I feel good about my first one. You know, I feel good about my first one out of 9 million guests.

I'm gonna stick with that. No, like the fact that he eliminated all the rest of the infinite doors, except one other one, tells you, well, the prize is probably in that one other way. So that's a way that in my mind, I'm like, oh yeah, that makes sense. It's harder to see when it's lower numbers, but, but like, that's the mathematical principle going on. And a little bit analogous in my mind to this Sleeping Beauty problem.

Like, yes, it seems like nothing has changed, but it actually has changed because you've sort of entered into this game. That's the bit of information that you now have. And so that's, analogy, that's kind of what changes your odds, your credence, your whatever you want to call it, from a half to a third. So was just something I thought of. I don't even know if that's a good philosophy thingy, but that's, it's a comparison that made sense to me.

Only other thing I wanted to say is I kept it in there because I thought it was interesting and it led to the discussion on infinite serieses. And I just thought that was interesting in general, but I actually think it was off the cuff. And again, I haven't talked to Brian about this, but, uh, I think his argument about the probability, you can't just do the probability of a lot of simulations.

You got to do like, well, what's the probability of a billion, a billion plus one, a million plus two. I actually don't think that's a great argument. I could be wrong, but it strikes me by analogy. If you're, go back to the coin, if you're saying like, well, we're going to flip a coin, it's 50 -50. And then you're like, well, no, no. The tails part, I'm going to break that down.

I'm gonna subdivide that to not only heads or tails, but the tails part I'm gonna say, is it tails, but it's pointing, you know, 12 o'clock, one o'clock, two o'clock, three o'clock, like the actual orientation of the coin, and you have to like add that into it, like add that complication into it, and because you have to do each one of those possibilities and you could subdivide it as much as you want by, you know, 360 degrees, 720 degrees, whatever, like get super fine detail, and then you say, ah, see, it's not just 50-50 because once you add up all those, you know, gets infinite when you, you know, have to say, well, what are the odds it's going to be tails, but also exactly three o'clock on the, on the orientation.

Well, I think it's pretty obvious that all you're doing is subdividing something that's still 50-50. So it's still going to be 50 that it is tails. And in that way, I don't know that the argument Brian was making about simulations changed all that much. I think if you're, all it did was restate what your original credence on the simulations or no simulations thing was.

If you were 50-50 on that, it doesn't do much good to subdivide the 50% with how many different possible numbers of simulations there would be in that 50%, if that makes sense. So that's one where I think Brian was going off the cuff. And in my view, I don't think that argument says much. I think it just basically cancels out to what you thought the credence was anyway. Way. But again, I could be wrong. And also I still thought it, it was interesting discussion.

So I left it in there. All right. Well, I hope you find this a 10th as interesting as I do. And I am just such a sucker for philosophy. I had a great time here in the next part. I haven't decided exactly how I'm going to divide it out. Um, an hour of Brian, an hour of me, do I do a half hour of each of us per episode or do I do an hour or so of Brian and then an hour so of me?

I'm a note if you want on your preference, or I'll probably end up just already working on it and doing what I think, but that's what you're getting for the next two parts. The part, that's the Brian part, is the actual math, the the physics, the computing portion of the simulation argument. This is fascinating. This is stuff where Brian did some initial calculations. Next time on Serious Inquiries Only. How hard would it be to actually simulate the universe?

And then what I have left is all the applications on Bostrom's argument and the things I haven't gotten to, some of the other reasons why Bostrom's argument may or may not work. That's the remaining me stuff that we have. So I may end up doing just all Brian, then all me. That actually probably makes the most sense. Either way, there's a lot of interesting stuff here.

By the time you're done, you're going to be able to have as many conversations with Elon Musk about living in a simulation as you want, which for me would be zero because why would you ever have a conversation with a brick wall? But maybe you'll have a productive conversation with someone who's not an egomaniac billionaire who doesn't care about anyone but himself. Uh, and and if that's that's the result of all this, then well, I will have done my job.

All right, so next time on SIO: so you want to build a simulation of the entire universe? Well, how many Pentium CPUs, 486s, is that gonna take? See you then.