This Toothpick Contains Everything Ever Said (Infinity Part 3)

13:28Michael Stevens:And this gets back to like Hilbert's Hotel. if an infinite number of people finish the race and then you do, you got omegas place. But the number of people who raced was still just Aleph Noel, because I can take that, that scenario, an infinite number of people. And then you, and I could just have you actually take first place and I would move first to second, second to third. And now no one got omegas place. So it's the same number of people. In fact, we could even have an infinite number of people finish the race and then another infinite number. And then you, how do I do it? I just have you wait, and then I have all the even numbers go, and then all the odd numbers go, and then you finish.

14:07Michael Stevens:Boom. Still I left no number of people finishing the race, though. That's right. And so all of these omega numbers, they come after each other, but none of them describe more things. But, but, now imagine this. Imagine every possible way a race with Aleph Null people could finish. All the multiples of three followed by all the multiples of four followed by everything else. All the prime numbers followed by everything else. This goes on and on, right? There's so many ways to have a race with Aleph Null people. Let's say that every way Aleph Null people could finish a race, finish the race. And then you do.

14:53Hannah Fry:So it's like a race of combinations, effectively.

14:56Michael Stevens:It's a race of combinations of infinite things. And all of them, every possible combination of aleph-null things finishes, every ordered arrangement finishes, and then you finally cross the finish line. What place did you get? Well, we have a name for it. It's easy to come up with a notation. It's called omega-1, which is omega with a little one subscript. But here's why this is so important. How many people will you need in order for the last person who crosses the line to get omega 1th place? Because it's not Aleph Null. It's not Aleph Null. It can't be. Because if it was, it would have already crossed the finish line.

15:39Michael Stevens:Because remember, we've said that every way you can arrange Aleph Null things already finished the race. And then you did, but you haven't crossed yet. So, Omega 1, getting Omega 1th place requires having a brand new amount of infinite people. And we call that Aleph 1. Yeah.

15:59Hannah Fry:I mean, look at this. We've got all these different types of infinities now. This is, look, this is all ammunition for when a kid tries to play with you, right? Tries to add numbers and add numbers. Be like, okay, sit down. Buckle up, baby. I've got a story for you. But this is it, right? It's like, this is this strange, untamable beast. And okay, maybe there's a little bit here of cheating and just being like, let's call it Aleph, whatever. Let's give it a name. But what we're, what's going on behind the scenes of everything you're describing is that these aren't just people coming up with these ideas and then like throwing them out there like they're spitballing.

16:41Hannah Fry:This is like hard, credible, rigorous mathematical proofs that demonstrate irrefutably beyond any doubt that one of these numbers is larger than the other, that these are not the same size infinities.

16:58Michael Stevens:Yeah. And I love that there's, we've described two ways to do it. One is by arranging things in a well-ordered way, like how a race would work. And the other is by just combining them into all kinds of different groups of different sizes, power setting and ordering. And those give us bigger and bigger Aleph numbers. The power setting gives us bigger and bigger Beth numbers. And we actually aren't quite sure how much bigger they are than each other. So if you're ever in a competition with a child trying to name the largest number, you can choose Alephs or Beth.

17:35Michael Stevens:Just off you go. Now, here's an interesting and important thing to know if you do get into a competition with a child who's trying to name a bigger number than you. You can keep saying Aleph 1, Aleph 2, Aleph 3. but be careful because if the child says beth one the cardinality of the continuum there's no way to prove whether you're naming a larger number than them if you're saying alephs unless you name aleph omega because that's the only aleph number that we can prove is actually larger than the cardinality of the continuum that's the boss that's the boss that's the boss Aleph Omega, which is an aleph number that comes after a countably infinite number of alephs.

18:20Michael Stevens:Aleph Omega is a good one to say. If you want to go any beyond that, you've got to just change the rules up, right? Because what are we doing? We're power setting or we're well ordering things over and over again. But we can, and this is what makes math so incredible. You can just say, all right, but what if you do that forever? Is there something beyond what you could reach with power setting? And we don't have to find it. We can just say that it exists. And that, whatever that first, that least number is that you cannot reach through power setting, that is called an inaccessible cardinal. Now, I think if you get to that, that's sort of, you've gone beyond the boss, right?

19:10Hannah Fry:You've gone beyond the boss. You've hacked into the mainframe at that stage, I think. That's right.

19:17Michael Stevens:You have done a jump. The jump from aleph null, the smallest infinity, to an inaccessible cardinal is like the jump from zero to infinity. In that you cannot take a finite number of things and ever get to aleph null. No matter how many times I add up them or multiply them or whatever, I never get there. In the same way, no matter how many times I arrange and power set an infinite number of things, I will never get to an inaccessible cardinal. So the inaccessible cardinal is inaccessible for that reason. But yet with our minds, we can say it's there. I'm imagining it. Deal.

19:59Hannah Fry:It's like the brick wall at the end of the infinite garden, isn't it? Really? Like you don't know what's there. You don't know what it looks like. You don't know what anything to do with it. But you're like, there's something.

20:09Michael Stevens:Yeah. And you know what? In my head right now, I'm imagining something on the other side. Look how easy that is to do. And it's mathematically rigorous.

20:20Hannah Fry:This, I think, makes me, because I'm sure that there are some people who are listening to this who are just absolutely enjoying the ammunition that we're giving them for the next time that this conversation of naming big numbers comes along. But I think that there must be other people who are listening to this thinking, OK, but what is the point of any of this stuff? I mean, this is just like, this is just imaginary fiction land that you're describing. And I think that what this does is, well, okay, two things. First, I think it calls into the question of whether infinity is real or imagined, full stop, whether there ever actually is something that is genuinely infinite.

20:57Hannah Fry:I mean, we're kind of going back to Aristotle here, who sort of thought that there wasn't. But I also think that what it does is really distinguishes the different types of mathematics. So my background is I was always an applied mathematician, right? And what applied mathematicians do is they take the real world and they take the equations that are used to describe it and then they bend them and they break them and they twist them and they push them to see how far that they can get. Pure mathematicians do exactly the same thing but the world that they're working with is one that is constructed entirely within these kind of rules right.

21:31Hannah Fry:Okay so let's start off with something that we know the list of numbers now let's push it push it further push it further still and further and further and further. And now let's bend it and break it and twist it and see just where the bounds are and what are beyond those bounds still. And it turns out that actually a lot of the time, these wild ideas that these pure mathematicians have about the way that you can bend and twist and shape numbers end up sometimes 150, 200 years later to be absolutely foundational to what we need to understand the world. The pure mathematicians are the ones who are searching for keys without ever caring about what locks they fit into.

22:13Hannah Fry:And it just so happens that very, very often they prove to be extremely useful.

22:18Michael Stevens:Isn't that weird? There's that famous paper, the unreasonable effectiveness of mathematics. You're right. These pure mathematicians are sitting around on podcasts talking about, but what if an infinite number of people finish before you and it's entertaining they've found like the keys to a lock that may or may not exist yeah you're right hundreds of years later someone finds that lock in the real world and they go holy crud math got there before we did yeah and it's happened again and again and again so you know maybe it will be the inaccessible numbers at some point when we are i don't know exploring the

22:55Hannah Fry:outer realms of the universe end up. Maybe there's one of them sneakily hiding out there, and it turns out to be the thing we needed. That's right.

23:05Michael Stevens:That's right. I mean, physics only can go so far, right? Below the Planck length, physics as we know it today doesn't really operate. But for all we know, inaccessible cardinals might describe the actual physical processes that happen down at those scales, right? But even if it doesn't, even if all of this is like completely impractical, it's still so amazing that we can go there anyway. It makes me, when I'm reading this stuff, it makes me go, do we even belong in this universe? We keep leaving it in our minds.

23:38Hannah Fry:My favorite description of pure mathematics, right, which is essentially what this episode has been about so far, is that it is a portal to the playground for the soul. I really like that so much.

23:52Michael Stevens:I think that really captures it well. Exactly.

23:55Hannah Fry:But we're going to come back to a sort of anchoring in reality, kind of, after the break, because we are going to be asking whether anything actually really is infinite or it is just a figment of our imagination.

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26:36Hannah Fry:okay we're back one of the other things that we discussed in the last episode was how Aristotle handled infinity. He was sort of of the opinion that you could have an infinite process. So you could, in theory, have something that went on forever, but you can't actually have something that contains infinity. You can't actually have something that's infinitely small or something that is infinitely large. And then we were talking about how, you know, during the intervening millennia, people started wondering about space. And I think that really, if infinity is for real, if it really, really exists, rather than just as a figment of our imaginations, then space is definitely the place to look.

27:21Hannah Fry:And cosmologists have done exactly that, right? Looked quite hard to see whether there are bounds on the universe. Yeah, they've been looking for a wall. They've been looking for, they've been literally looking for a wall. Okay. So the thing that's worth saying, first of all, is that we are, we're sort of trapped in this kind of spherical bubble of light, because light has this speed limit. So there's, we can only see objects whose light has had enough time to travel to us since the beginning of the universe. And the universe is 13.8 billion years old. So common sense, you would think that you can look at, you're looking back 13.8 billion years effectively.

27:57Hannah Fry:But actually, it's much bigger because that story that we had, the puzzle that we had in the first episode about an ant on a rubber band stretching. That is the best possible way to think about the way at what is happening to the universe.

28:10Michael Stevens:Yeah. Surprise. You are an ant on a rubber rope.

28:13Hannah Fry:You are. You are. Except that you're not, you're not sort of moving along it. You're kind of, if you like, from your perspective, you're kind of staying still. And then the entire universe is expanding around you. And that's a significant difference. That's a significant difference. That is a significant difference because it means you're not going to catch the end for one thing. Exactly. But it also -

28:33Michael Stevens:You will eventually be completely alone. You will eventually be completely alone. Exactly. Eventually, every single star in the universe will have shifted so far away from us that we no longer see it and the skies will be dark. It won't happen in my lifetime.

28:47Hannah Fry:No, no. I mean, we're talking trillions of years here. Trillions of years. Trillions of years. Our sun won't see this happen. No, but there is something quite nice about this. I think nice, maybe. this perfect moment of sort of like cosmic visibility, you know, like, oh, aren't we lucky back in the day, my great, great, great, great, great grandparents, when they could see the universe, whereas now you're just a speck in the middle of nothingness. Yeah.

29:15Michael Stevens:There will be a day where you look out the windshield of your planet and there's just, there's no stars in the sky.

29:20Hannah Fry:Nothing.

29:21Michael Stevens:And, you know, and we weren't born so early that like galaxies hadn't formed yet. We've got beautiful stuff to look at. And so we should be grateful that we're alive now.

29:30Hannah Fry:Lucky us. Lucky us. But that thing about the rubber band, it sort of works in another way, too, partly because it really makes that conclusion quite obvious. But the other thing that's worth saying about it is that it's really easy, I think, to imagine the Big Bang as though it was, I don't know, like a hand grenade going off and sort of spraying stuff outwards, where the kind of edge of the universe is like the dome of the shrapnel as it blows up. But you shouldn't think about it like that because it's space itself that is expanding. It's the rubber band itself that is expanding and the stuff just happens to kind of be going with it.

30:10Hannah Fry:So given that that's sort of where we are, there's essentially three potential options for what's going on at the edge of the universe, right? Either there is a wall, there is like a boundary. Then the question is, well, what happens when you meet it? You know, can you if you if you can stick your hand through it, well, then that's empty space. That's still part of the universe. Doesn't count. Or if if there's true nothingness, like so, you know, you put your arm through it and then there's nothing on the side. There is like a genuine boundary. Well, I don't know. My brain can't handle that. I don't think many scientists brains can handle it.

30:43Hannah Fry:Sort of. It doesn't really feel like it. What does that mean? What does it mean that there's an edge to it?

30:48Michael Stevens:Right. So so wait, this is like that question. If it's expanding, what is it expanding into? Right.

30:53Hannah Fry:and there is there is a way that it can be expanding and uh not have a fixed wall on the edge right there not be kind of like a fixed boundary and this is sort of the pac-man universe essentially because if you imagine with pac-man okay you're you're kind of going along you can travel left to right you can go off the edge of the screen on the left hand side and then you reappear on the right hand side and that is because the pac-man screen is effectively it's playing really on the shape of a donut. If you can imagine the screen, you take it, you kind of pull it away from the computer and you wrap it around itself.

31:31Hannah Fry:So it's kind of running around in a circle. So you now have effectively a tube, but this Pac-Man can also go off the top of the screen and then come back around the bottom. So you can take your tube and bend it round. And it's essentially is operating on a torus, on a donut. You're really playing Pac-Man on the surface of a donut. Pac-Man lives on a donut. Okay. So, so it could be that the universe is actually infinite in the sense that you can carry on going and going and going and going and going forever. The process goes on forever, but it is nonetheless bounded. So there's no edges in Pac-Man.

32:06Michael Stevens:You're not kind of like walking into any walls, but nonetheless, it is contained within a finite

32:11Hannah Fry:surface, right? In a finite amount of area.

32:14Michael Stevens:And we've tried to find out if we live on a donut like pac-man we've looked if if we do then we should be able to look far enough out that we eventually see the backs of our own heads right you should be able to see the backs of your

32:28Hannah Fry:own head or you look off in the telescope in one direction you're like oh hello that's an interesting like star constellation going on i've heard this way there's any galaxies right off in the distance it's very interesting and then you turn around you go the other way it's like hang

32:39Michael Stevens:on a second that's the same one it's the same stuff from the other side yeah it's the same We have not, we have not yet found that to be the case.

32:48Hannah Fry:It wouldn't be the backs of our own heads though, actually. It would be the backs of, I mean, dinosaurs' heads. Actually longer, right?

32:55Michael Stevens:That's true. Yeah. Well, minor, minor point, but yeah. Hang on, that's my house. But before, hang on.

33:04Hannah Fry:Before vegetation existed.

33:06Michael Stevens:It's like, you know, when someone shares their screen during a Zoom call and we're like, whoa, we live on a donut. and everyone else is like, I'm getting sick. It wouldn't be like that. You're right. No, it wouldn't be like that. The light we see is light that left. The delay would be substantial. Billions and billions of years. So it wouldn't quite look the same. But point is, we haven't found any evidence that the universe wraps back on itself.

33:28Hannah Fry:Right, because if it wraps back on itself, then it curves. And if it curves, there should be some hints in the way that things are laid out. You know, we know that on a flat surface, the internal angles of a triangle light up to 180 degrees, right? For example. So you can look out into space and run these kinds of tricks. Like, are there any sort of signs here and there that triangles don't make sense? Does it look like we're sitting on the surface of a sphere? Does it look like we're sitting on the surface of a saddle or on a donut? And nothing. There is nothing. Everywhere you look, no matter how accurate you make your measurements, it's flat, flat, flat, flat, flat.

34:09Hannah Fry:We are on a piece of paper. Effectively.

34:11Michael Stevens:It could be that we just can't look far enough yet to see the curvature.

34:18Hannah Fry:Right. It could be that we are just so small, just so tiny, because actually, if you think about we're on the curved surface of Earth, and yet when you're standing here, it looks pretty flat to all of us. Yeah. Just because we're too small to see it. So it could be, you're right, that the universe is just so big that we just can't see it. But I mean, thus far, no evidence. So now if you put those two things together, that it's not curved and we think there's no wall, well, then the only other conclusion is that it's is that it just goes on forever. It's just flat and goes on forever. And maybe that's it.

34:53Hannah Fry:Maybe there really is infinity. But there's some pretty uncomfortable conclusions if that's the case. because if there is a genuinely infinite universe well then if you throw a loop throw a dome around any amount of stuff right so let's just say you take our solar system there is a fixed finite amount of stuff in our solar system finite amount of quarks of you know of atoms whatever it might be right it's way way less than aleph nol it's finite and there is a finite way that you can combine all of that stuff, I mean, the number is going to be absolutely unimaginably large, right? But it's finite.

35:33Hannah Fry:It's finite. And so if you have a genuinely infinite universe, you have an infinite number of rolls of the dice effectively. And so there's a thing called the pigeonhole principle. If you do something enough times, even if it has a very, very, very small probability of happening, it will eventually come true. And so what that means, the only conclusion you can make is that if the universe is infinite, there must be another solar system out there that precisely down to the quarks mirrors our own.

36:08Michael Stevens:Which means there's another me there and another you there. And we're doing this podcast exactly the way it is, except my shirt's blue. And there's another solar system where my shirt's orange, but we're having the exact same conversation. Let's say the likelihood that all this matter would be arranged like it is at this moment is one in a quadrillion. If you've got a non-million volumes, then you wouldn't be surprised to find that a couple of a match.

36:36Hannah Fry:Exactly right. I mean, we were talking about the number of ways to shuffle a deck of cards a few episodes ago in our finite numbers episodes. It's huge. It's so, so, so gigantic. But if you did carry on going forever, shuffling cards, shuffling cards, eventually you would find the same shufflings more than once. And if you carried on going forever and ever and ever and ever, you would end up basically with an infinite number of every one of those infinitesimally unlikely combinations. It's very uncomfortable. Yeah.

37:11Michael Stevens:You do it long enough, you will have an infinite number of times you shuffled the cards into perfect order and if we consider our you know solar system a perfect order then there's an infinite number of them out there which is very uncomfortable and this bothers me a lot me too because it makes me think well who am i if there are countless other me's out there doing the same thing what makes me special i guess i'm the only michael doing it here yeah yeah i mean this kind

37:43Hannah Fry:of gets onto like, I think there's like a lot of things. So do you, do you believe that?

37:48Michael Stevens:I mean, I don't see how I can't accept it. It is the best picture of the universe as far as I'm concerned. And yet I want to know what you think.

37:59Hannah Fry:I don't know. I think I probably marginally prefer the idea that we're too small and that we are curved and that we are contained within a finite space. I mean, that also has extremely uncomfortable conclusions, by the way. One of the descriptions of the universe that looks like that is this. We're a bubble, effectively. If you imagine that there is a boiling ocean, right, sort of like a pan of water, and the way that you get these bubbles that appear effectively from nowhere as the water is boiling, the physical fluid rips apart it's called cavitation rips apart and sort of becomes filled with gas and the idea behind the bubble multiverse is that big bang is just one of those bubbles appearing it's the way that sort of energy creates you know matter and in this sort of like little explosion within this this wider fluid now the slight problem with that theory is that each of these bubbles could have completely different rules of physics.

39:05Hannah Fry:You know, it could be that one of them, gravity, the speed of light, the mass of an electron, you know, any of those things is just totally different in all of these different bubbles. We just have no idea. And so that, I mean, the conclusions there are, I would say, equally uncomfortable. You can't, you don't have to sit long with this stuff before it starts getting back to Michael with a slightly different color shirt on.

39:27Michael Stevens:Yeah. Well, I mean, and most of these like universes, if they're just randomly being assigned constants like speed of light and mass of the electron, a lot of them would be so unstable, they would just collapse right away. I think it's Lee Smolin who has that theory that, well, if this is happening, then there might be some kind of natural selection process for universes. And the ones that last the longest are sort of ones like ours, where it's possible for black holes to form and for intelligent creatures to come about. And I think his whole theory is that a black hole creates another bubble at its singularity, a whole different universe.

40:03Michael Stevens:And that universe is like the one that the black hole was originally in. It's literally like a child. And so you wind up with many more universes like ours than you do universes where, you know, protons decay in a quarter second.

40:16Hannah Fry:Exactly. I mean, all of this stuff ends up getting really tied in together because, of course, black holes, it's as far as we know, it's just infinite density. But maybe this is actually the secret to what's going on more broadly across the entire universe.

40:30Michael Stevens:And then on the other hand, like how small can we get? Like we can zoom in and look at molecules and then atoms and we know that those atoms are made of things, but how granular does the universe get? Even if it's finite and curved and bounded or whatever, how small does it get? We already talked about the encyclopedia wand or the toothpick that contain everything that can ever be said, how much precision is possible? I mean, famously, we've discussed this many times on the podcast, there is a limit to what our current physics can describe. We've mentioned this on the podcast a few times, but the limit of physics as we have it and know it today is anything that happens within or amongst Planck units.

41:21Michael Stevens:the Planck length is like the smallest sensible length within physics as we know it. If a photon had a wavelength that was the Planck length, which by the way is 10 to the negative 35 meters, if a photon had that small of a wavelength, had that much energy, it would turn into a black hole. So the Schwarzschild radius at that length is a photon's energy. And so we kind of go, oh, well, you can't get any smaller than that because it destroys itself or it's gone or whatever. But that doesn't mean that that's actually the smallest length that anything happens at. It's just we can't describe any further.

42:02Hannah Fry:Because our equations break, essentially.

42:05Michael Stevens:Our equations break, but the equations seem pretty good for everything else. So do we need new equations? Do we need a different interpretation of them? I don't know. I mean, it seems like space is going to need to be continuous. like the real numbers. You just, the closer you get, the more and more detail you see because I don't see how, like Pythagorean, I don't see how the Pythagorean theorem could hold true if things became discrete at a certain level. If eventually you look close enough and you just see a bunch of pixels of space, now it's no longer true that A squared plus B squared equals C squared because C squared is no longer a continuous straight line.

42:48Michael Stevens:It's a stair step.

42:50Hannah Fry:Well, there's also, I mean, a lot of things end up, I mean, circles cease to exist. Perfect spheres cease to exist if down, once you get small enough, the universe is discrete rather than continuous. It's very uncomfortable.

43:05Michael Stevens:Well, and if they cease to exist there, then they never existed. Everything is at every level pixelated.

43:12Hannah Fry:A figment of our imagination, which means essentially, you know, they go hand in hand, either circles and infinity exist for real or neither of them do. Right. You know, you can't say I'm not having infinity without getting rid of circles as well.

43:29Michael Stevens:Wow. Yeah, that's true. So where do you fall? Do you believe that circles and infinity literally exist? I don't know.

43:40Hannah Fry:I sort of think, I don't know, because I think the idea that the universe is discrete, spatially discrete is also really uncomfortable yeah i don't like it i don't like that my brain

43:52Michael Stevens:can go oh really there's a there's a smallest discrete piece of space cut it in half yeah look i just i just just did it went beyond the universe come on i i i think that it's the universe is infinite and space is infinitely divisible you know there are some people some

44:10Hannah Fry:computer scientists who are very comfortable with this idea because they essentially see everything that we're living in as a kind of computer simulation, right? And in computers, the fact that space is discrete, the fact that you can't cut something up small enough because you get down to a pixel and there's nothing smaller than a pixel, there's nothing smaller than a bit. They're, you know, quite happy, quite comfortable with that.

44:36Michael Stevens:Yeah, well, you know, Right. If we if we did find like a unit of space that could not be divided, then we might have found some good evidence that we live in a simulation that like, ah, there it is. That's the bit of the alien computer that we're running on.

44:50Hannah Fry:Cool. I mean, also, you would say if if this was a simulation, that the whole issue of how far out we can see the observable universe and what's beyond it, that's not a problem anymore either, because it's just that the simulation has just doesn't bothered. you know if you're running around in i don't know like grand theft auto and you just go into a new you're always in your own that's how old my reference is or new isn't it coming out the new one yeah um sorry i'm just i'm such a gamer i'm just really eagerly anticipating you're such a pro gamer like i can't even keep up you're talking about pac-man what are you gonna do next pong look i uh you might live in donkey kong country for all we know mathematically

45:37Michael Stevens:your gaming references are superb i i exclusively talk about the ones that have made it cut it

45:43Hannah Fry:across to the mainstream i refuse all of these niche these niche games that people chat about it's just not interesting to me um but the but the reality is when you are in a game i mean you sort of are in your own observable universe like where you're turning your camera around it just

45:58Michael Stevens:hasn't rendered anything outside of it yeah so i mean maybe that is the solution to all of this

46:02Hannah Fry:maybe is that just that actually it's all i mean that would make um that sort of well this is a kind of one for another day i guess but the collapsing of the wave function another deeply weird and troubling physics uh problem with our understanding of the universe that uh we don't actually know where particles are. And they sort of seem to be in many places all at once, exploring all potential possible futures until you actually observe them. We'll definitely do an episode on this at some point.

46:35Michael Stevens:And you observe them and then the simulation goes, oh, you got to render that. Okay, here, it happened to be like this.

46:41Hannah Fry:Exactly. Because actually, if we're living in a computer simulation, that's fine too, right? If a particle is a blob, then it doesn't make any sense that it can be here and there and there and there, all of those places simultaneously at once until you see it and realize exactly you fix its position. But if it's a computer simulation, that's absolutely fine. It can be any manner of things until you look at it.

47:01Michael Stevens:It's absolutely fine. So yeah, saying that we live in a simulation is kind of a good bet, especially because if you really think about it for a long time, you start to go, well, you know, if an alien made a simulation, they could make so many simulations and they could fill it with so many people that like overall, it's more likely that I would find myself in a simulation than in a real universe. So you should probably like, kind of it's like a new version of Pascal's wager. Just wager that you're in a simulation and you're more likely to be right. I'm gonna go on record by saying that I think we just don't know enough about the universe, the real one that we live in to answer the question.

47:44Michael Stevens:but I still think that we are in a real unsimulated universe.

47:48Hannah Fry:I think that we are too, just because I really want to be. But I also, I like it as a theory, because there is some suspicious stuff going on. There is some suspicious stuff.

48:00Michael Stevens:There is, there is. And do you think that we'll have answers within our lifetimes? Or do you think that this is all going to remain very theoretical?

48:09Hannah Fry:I mean, I think for the expanses of space, no. I think that one's going to be way beyond us. but I think that there might be I do think that when it comes to particle physics I think and and thus things like Planck length or Planck length I think that there's a chance you know I think there's a chance that we might get some get a couple of big breakthroughs sort of it sort of feels like there's one the models that they use are so disgustingly messy that it sort of feels like there's something that should be that's pushing at the door waiting to come through

48:39Michael Stevens:Right. Yeah, it does. And then we'll like stand and look from a different angle and go, oh, it was messy, but that's because we were wrong about. And then the Planck length will become a historical unit and we'll get smaller.

48:55Hannah Fry:But here, I guess, is the big conclusion that we have. I mean, either infinity doesn't exist. It's all a figment of our imaginations. Or, and maybe also, there are some really uncomfortable things, really uncomfortable things that are the conclusions that we must draw.

49:16Michael Stevens:I would put it that way. I would say that we founded Infinity like we invented it. But someday we will find that it was always there anyway. Our brains just jumped ahead of our eyes.

49:32Hannah Fry:And particularly Cantor's brain. What an incredible brain that was. Particularly Cantor's brain.

49:38Michael Stevens:Yeah.

49:38Hannah Fry:Yeah.

49:39Michael Stevens:He took the first leap.

49:40Hannah Fry:He did take the first leap. Do you know what, Michael?

49:43Michael Stevens:I think we might have come to the end of infinity. I think we came to our end. I don't know if we've come to its end, but what a blast. That was a blast.

49:53Hannah Fry:Well, I hope that all of you enjoyed it. I know that I did. Let us know in the comments if there are other mind-bending, weird, crazy topics that you would like us to explore. We touched on a few of them there just to give you a little sweetener. as ever you can send us in any thoughts or questions that you have to rest is science

50:14Michael Stevens:at goalhanger.com and you can join our newsletter at the rest is.com slash science i would say

50:19Hannah Fry:actually send us email sure but if you put it on comments on youtube then me and michael can read

50:23Michael Stevens:them as well which we do so that's true yeah we don't have direct access to the email the producers pull out their favorites and they put them into a rolling google doc for us but yeah the comments Ooh, we can see it all. Even the stuff that they don't want us to see.

50:38Hannah Fry:If you want to send us really, you know, like if you think you've solved Riemann's hypothesis or whatever, and you want to like send that, send in 50 pages of proof, send that to the producers. That's fine. That's okay. But if you've got like a nice, quick-witted, interesting thing you want us to know about, chuck in the comments on YouTube. Until next time.

50:57Michael Stevens:See you later.

51:04Thank you.