From the Vault: Fantastic Numbers, with Antonio Padilla - podcast episode cover

From the Vault: Fantastic Numbers, with Antonio Padilla

Jul 29, 202340 min
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Episode description

In this classic episode of Stuff to Blow Your Mind, Robert chats with theoretical physicist and cosmologist Professor Antonio Padilla, author of the new book "Fantastic Numbers and Where to Find Them." Strap in for big numbers, fantastic numbers, black holes and more. (originally published 07/28/2022)

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Transcript

Speaker 1

Fans in the UK. Robert Lamb here with a really important message. If you're a listener in the UK, you will stop receiving new episodes in this feed after July thirty first, twenty twenty three, but don't worry. You can still listen to the show. All you have to do is switch over to the brand new Stuff to Blow your Mind UK podcast feed and subscribe. There so no cause for alarm. It's just to click away. The feed is called Stuff to Blow your Mind UK and it's

already live so you can subscribe right away. And as a little incentive for making the switch, we're including a UK exclusive Monster Fact episode for you, and this episode will be add free, so please don't wait you might forget. Head on over to Apple Podcasts or Spotify and search for Stuff to Blow your Mind UK and subscribe today and be sure to remind any friends who listen in the UK to do the same so you don't miss a single episode. Thanks for listening. Hey, you welcome to

Stuff to Blow Your Mind. My name is Robert.

Speaker 2

Lamb and I'm Joe McCormick and it's Saturday, so we are reaching into the vault to pull out an older episode of the show for you. This one originally published July twenty eighth, twenty twenty two, and Rob this was your interview with Antonio Padilla, author of the book Fantastic Numbers and Where to Find Them.

Speaker 1

Yeah, this is a fun chat, I think ultimately a very accessible chat, but one that will also probably break your brain a little bit. So have a good time with this one.

Speaker 3

Welcome to Stuff to Blow Your Mind, production of iHeartRadio.

Speaker 1

Hey, welcome to Stuff to Blow Your Mind. My name is Robert Lamb. My co host Joe is away from work today, so I am conducting an interview here with Professor Antonio Padella, author of the new book Fantastic Numbers and Where to Find Them, a fascinating read about big numbers, fantastic numbers, black holes, and more. This is a really fun chat. I think you're all going to enjoy it, So go ahead and jump right in with me right now. Hi, Tony, Welcome to the show.

Speaker 4

Hi, Hi Rop How you doing. Oh?

Speaker 1

Pretty good? Pretty good. I'm really excited to talk about the new book Fantastic Numbers and Where to Find Them. A wonderful read, and it's a book that gets into some pretty wonderful, mind rending cosmological territory as we'll no doubt I'll discuss here. But first I wanted to start with just a really basic sort of grounding question. I guess we encounter numbers every day, and you discuss some numbers that most of us don't encounter really every day.

If we could back up a whole lot, I guess and just ponder the basics here, what exactly is a number?

Speaker 4

Well, I mean, this is this is an idea I sort of, you know, delve into in my book because of course, when you go really back into history, back to sort of the ancient Sumerians or something like that, you know, obviously they really began to use numbers to talk about, well, I've got five jars of oil, I've got five loaves of bread. But then it sort of begs the question, is that five the same five is the five that describes the jars of oil, the same

five that describes the loaves of bread. And then you really sort of when you sort of make that, you disconnect the two and you start to build the idea of like what I call an emancipated number and number that's independent of the thing that it's describing. Then you're really sort of making quite quite an intellectual leap. So that for me is what is what a number is? It's kind of emancipated from the thing that it's describing. Whether such a thing really exists in a philosophical sense

is a whole new debate that you can have. But yeah, that for me is the key mathematical lead that I think was made, you know, a long time ago. And yeah, it's really important.

Speaker 1

Now getting back into that sort of philosophical territory. This is one that I know that you tackle a lot. It's pretty standards for philosophical math question. But is mathematics more of a human discovery or more of a human invention?

Speaker 4

Yeah, I mean I don't think this is straightforward answer to this. Of course, this sort of you know, boils down to like a sort of alluded to whether numbers exist, whether maths exists, and as kind of I mean, I'm not a philosopher, but I know that philosophers talk about this in sort of this kind of three different angles that you can take on it. So on the one hand, you've got the Platonists who will say that numbers and mathematics is true and it exists, but it exists outside

of space time as like an abstract concept. It's not something that can affect the things in space time. It can't affect the material objects that we have around us. You also have the nominalists, who says basically that numbers and maths only exist to of understand stuff. So in some sense, we talked about the five, you know, five jars of oil, the five five loaves of bread. That's the only reason that the number five exists to describe the jars of oil, to describe the loaves of bread.

And then of course you've got the third sort of you know school, which is perhaps in some sense the most extreme, which just says the numers don't exist at all. They're just a useful tool that we used to describe the universe surrounds us. And I guess the analogy people use here is it's like saying, well, you could be an atheist, but you could still believe with some of the sort of moral messages that you read in the

Bible or the Koran. It doesn't mean that you know, you can't be inspired by them, but you just don't have to believe in every element of it. I guess as a physicist, for me, it's kind of hard to sort of go with that fictionist idea. And yet see universe that is so amazingly described by mathematics. Now, is that something that's embedded in the universe or not? I guess it's really difficult to know. We certainly not seen any evidence that it is.

Speaker 1

And yet now your book deals with, as the title indicates, fantastic numbers. What defines for you a fantastic number? And are there categories of categorizations of numbers other than that that we need to have in our heads before we can get to the idea of what is truly fantastic.

Speaker 4

Yes. So for me and my own relationship with numbers, kind of it comes from on the one hand, you have a number, whatever that number might be, and for me, I always want to bring that sort of personality alive. There's sort of real spirit of the number, sort of to the four, and so it's always been physics for

me that does that. So when you know you can have these wonderful mathematical concepts ideas like Graham's number three three, these truly bizarre and wonderful numbers, to have a wonderful place in mathematics, but then you really bring them to life when you try to sort of squeeze them into our physical world. So that, for me, is what makes

a number fantastic. It's almost like what makes a number fantastic is the fantastic physics that it can lead you towards and lead you to imagine and whatever that might be.

Speaker 1

You also talk about I believe you specifically, you're talking about Graham's number pretty early on in the book, and you point out that if you if you try and actually picture it in your head, your head collapses into a black hole. And this this made me wonder, like, what are the largest numbers roughly speaking then an average person can fit into their head by one definition or another, Like, at what point does it just become this this other enterprise entirely? Yees.

Speaker 4

So it's a good question. So, I mean, it kind of depends on how how you sort of defined the question. In some sense, if you're just thinking about neurons, how many neurons have you have? You got in your in your brain as about one hundred billion neurons, and so you might say that you can use them if you manage to clear your mind of every of the thoughts to imagine one hundred billion digit number. Okay, that might not be particularly practical, it might be quite challenging for

most of us. But in principle you might say that that that that would be the limit. Of course, if you then go beyond that and start to say, well, what if I could somehow get my head to find a way to actually store information store concepts more efficiently than just the usual idea of neurons firing on it off. Let's suppose that it could do that somehow. Then they numbers get get much bigger, and you start to the things that limit it are literally preventing your head collapsing

to form a black hole. Because black holes what they do is that they're they're the best thing at storing information. So if you want to get something the size of a head of a human head, and you want to say, what's the best thing the size for human head that can store information, it's a black hole the size for human head. That's nothing can do it better. And so so that that places a new limit, and you can ask, well, again,

what is that limit would be? Well, he's certainly way below grains now, but you're not going to get anywhere near the magnificence of Graham's number, you could probably get a digit that that's about ten to the seventy, but it's about ten to the seventy digits long, so less than a Google digits long. Having said that, you could imagine a number like a Google plex, a google plex

has a Google digits. Now I've just said that you can't imagine at Google digits, not possible, but a google plex you could because what you know about a google plex is that it's a one followed by a Google zero. So you know that all the numbers that come later on as zeros, So there's not much information in that, so it doesn't cost as much as many bits. You don't have to put as many bits in your head

to imagine that. So what we're really talking about now are really a random assortment of digits, a completely random assortment digits the kind that would appear in Graham's number. And I don't think you can get passed around ten to the seventy, which is a one with with seventy zeros. You couldn't get past that many digits completely randomly sort of allocated. At that point, your head's going to collapse. Into a black hole.

Speaker 1

Now now backing up to the Google and the google Plex, can't can you? Can you walk us briefly through the difference between a Google, a google Plex, and and and maybe realms beyond that? This is about the only area of fantastic numbers that I'd really heard anything about prior to reading your book.

Speaker 4

Yeah, so at Google is is it's a number, which is which is a one followed by one hundred zeros. So I think everybody would agree that sounds like quite a big number. It goes back to a physicist called Edward Kasner who was Columbia, and he was writing a popular science book, and he was trying to sort of, you know, convey that he really wanted to show how big infinity he was, and so he wanted to cou up with numbers that we all think are really big,

like a one followed by one hundred zeros. And he said, well, okay, that's really small compared to infinity, right, even though something really big is actually really small compared to infinity. So he came up with this one with one hundred zeros. He wanted a name for this number, so at the time he asked his nephew who was nine years old at the time. He was called Milton Soota. He said, can you qu up with a name for this? And Milton said, well, at Google, which is an absolute stroke

of genius, right, it's such a great name. And then so they wanted to then develop things further. So then they wanted an even bigger number, again building on this idea that it's nothing compared to infinity. And so he said, well, okay, I'm going to quote with the idea of a google Plex. It's going to be an even bigger number. Well how big? So Kasner then goes to Milton. He says, well, how big should it be? And Milton's like, well, it should be a one, not followed by one hundred zeros, but

zeros until you get tired. But Kasner is like, you know, a sort of a you know, esteemed academic at Columbia and all that. That's just not precise enough for him. So he went with a which a much more sort of well defined idea, which is a google plex should be a one followed by a Google zeros. So a Google's already massive, that's a one followed by one hundred zeros. A google plex is a one followed by a Google zero. So it's a whole new level of big compared to what we're normally used to.

Speaker 1

And then it just it keeps building on that. Right, there's there's even like what a Google plexian is that the next level?

Speaker 4

So so yeah, I mean this is this is a really nice, nice idea. You can really now start to really build very big numbers, very very quickly using this this mathematical technique called recursion. So for example, you can develop the idea of a Google duplex or what's a Google duplex, Well, it's a one followed by a Google plex zeros, and then you could go to a Google triplex. Well you can probably guess what it's going to be. It's gonna be a one followed by a Google duplex zeros.

And then a Google quadruplex is a one followed by a Google triplex zeros. And you can see each time you're growing the number just by so much, by such an unimaginably large and that's what You're not just adding a zero every time, you're kind of really ballooning the number of zeros on the end of this number in Gargangian proportions, and that's what and it's this power of mathematical recursion that allows you to do that.

Speaker 1

Now, you also talk about fantastic numbers that are I guess you would say smaller. The main example that comes to mind, you refer to this several times in the book is a number associated with Olympic sprinter Hussein Bolt. Would you tell us a little bit about this number?

Speaker 4

Yeah, yeah, so well, actually this is one of my big numbers. Actually, even though it doesn't seem that thing, it's actually it's one of my big numbers. So I can read out the number. What it is, Okay, one point. I think it's fifteen zeros eight five eight, So it's just a number just slightly north of one. So it's it doesn't seem like a big number, but in my book, I say it is a big number. And the reason is it's it measures the amount by which Usain Bolt

managed to slow down time. And when he was he was running in the World Championships and I think Berlin and he set the world record. And this is due to the effects of relativity, so that when when somebody actually moves quickly, they actually slowed. Time actually slows down for them. And this is the amount by which Usain Bolt was actually able to slow down time due to the effects of Einstein's theory. And it's compared to the people in the stadium, for example. This is this was

the difference that he experienced. So it's one of the one of the weird consequences of it is that you can actually it's not that you say Bolt, actually even though he slowed down time, it's not that he that he actually ran the race any quicker. He still runs the race at roughly ten meters per second. It's actually an even more strange consequence. He actually the track also shrinks for him a little bit, so so he actually

runs it in less time, but in the same speed. Therefore, the track shrinks because relative to him, the track's moving. And this is another effect of relativity, one of the remarkable things. And and yes, you could perhaps argue that he didn't actually finish the race because the tracks rank so he didn't run quite one hundred meters.

Speaker 1

Wow. I was really blown away with this, because you know, you often hear the standard analogies concerning airplanes and pyramids and so forth when it comes to time dilation and so forth. But I hadn't I hadn't heard this particular example before.

Speaker 4

This is great. Yeah, I mean it's true if like taxi drivers, if you imagine a taxi driver that's driving around I don't know, any city in New York wherever, you know, sort of for forty to fifty years of their life because of that extra extra speed that they're picking up, that's going to accumulate over time, and actually they can probably leap forward in time by probably I think about a microsecond over the course of their career.

It's not a lot, but it's still pretty amazing when you think about it.

Speaker 1

So they've got the knowledge, and then they have that as well, right.

Speaker 4

Oh yeah, of course, yeah exactly, not just the knowledge, Yeah, they actually get it. They actually get a little bit younger.

Speaker 1

So your book makes use of written numbers, and of course you have this wonderful YouTube series number file, and in that you benefit not only from some fantastic descriptions and pop culture tie ins as you do in the book,

but you also have a lot of helpful illustrations. So I was curious, since you are a regular communicator of this topic, is it is it more challenging or in some cases almost too challenging to describe some of these numbers without the visual aids or the actual numerals to like visually present somebody with.

Speaker 4

Yeah, I think so this is where the physics comes in in some respects. Right. So, on the one hand, if you really want to describe the number, like I say, a number like Grames number, you do need those visual aids because it's not a number that you're going to sort of stumble across in any kind of normal environments. Right, It's not a number you're going to see on a price tag, at least you'd hope not. And you know, so these are you need new notation, new sort of

symbolism to sort of actually even describe the number. So you've got to introduce that. There's just no getting away from it. But I guess what you can do is describe the physics associated with it, and that you can certainly do, you know, just just just with words. And you know, in the case of a number like Graham's number, you can talk about how you just can't picture it in your head because your head will will collapse to

form black hole. And that's already going to make people think, wow, that numbers there's something big of something big and crazy about that number or a google plex, you know, and you can talk about a universe that's that's a google plex meters across, and then you can ask, well, if the universe is that big, if the universe is ritually that large, then it's likely that you would find multiple copies of yourself, like literally exact doppelgangers elsewhere in this ginormous universe.

Speaker 1

Yeah. I wasn't. I was I wasn't prepared for doppelgangers to enter into the scenario. So another great part about the book for me, and another thing that comes up in the book that I was very intrigued by. I was wondering if you might talk about is the idea of the holographic truth.

Speaker 4

Yeah, so the holographic truth is. I mean, it's an idea. It's probably the most important idea I would say that's emerged from theoretical physics in the last thirty years, and it's actually mind blowing when you really think about what it pertains to it. It's this following statement that essentially one of the dimensions of space that we experience around us. So we normally talk about say three dimensions of space, well, one of them could well be an illusion. It might

not exist and it's really remarkable. So what we're saying is that there are two ways in which you can describe the physics that we see around us. On the one hand, we can imagine three dimensional world with a gravitational force and the force of gravity doing its thing with planets around the Sun and so on and so forth. On the other hand, there's a completely equivalent description of the same phenomena which just uses two dimensions and no gravity.

So think of it a bit like, you know, on the one hand, somebody's you know, in English, we say if we see a plate of meatballs, we call them meatballs, but a Spaniard might call them album the gas. They're both describing the same things, they're just using a different language.

And that's kind of what the holographic truth says. It says that you can have a theory like a three dimensional world with gravity, and you can use that to describe all the physical phenomena you see, or use this different language which has no gravity and only requires two dimensions of space. So is it true of our world? We don't know. It's a conjecture. It's a conjecture that has sort of evidence coming from the physics of black holes.

There are actually concrete examples that we know of of sort of toy universes, so not our universe, but but space times that maybe the higher dimensional they may be warped in weird and wonderful ways. And you can think about gravity in these in these simple toy universes, and you can show that there's an equivalent description in one dimension less like a holographic description, and it's called a hologram because that's essentially what holograms do. Right, If you

think of a HOLOGRAMD, what have you got? You've got an image on a that's stored on a holographic plate. You know, it's just some light and dark bands on a holographic plate, a two dimensional plate. It stores a bunch of information that way, but that's just one way of looking at the information. You can decode it in a different way by shining monochromatic light through it and creating a three D image. You're not creating any new information.

It's the same information, just stored either in two dimensions or three. And it seems to be that that seems to be a fundamental property of gravitation, of gravitational worlds that you can think of them as as like, as I said, three, the world with gravity, or you just forget about gravity and consider a world with one dimension less and you can describe exactly the same physical phenomena.

Speaker 1

Wow. Now here's another question that came up reading the book that I don't know if of all of our listeners necessarily would have thought of this question. I don't think some of them would have. And that comes to infinity. Infinity, Like sometimes it's easy to think of like, Okay, infinity is the If we think of it as a number, we think it's the aid on its side representing infinity. Is infinity a number? And if it's not a number, like what do we think of it as? How do we classify infinity?

Speaker 4

So I love this question because the answer is that it's both not a number and lots of numbers. This is a wonderful thing about infinity. So it depends how you want to think about infinity. And I think most of us when we intuitively think about infinity, we kind of think of like I don't know, the infinite distance, you know, or infinite time, And what we're really thinking there is we're thinking of it is like a limit

is something that's just just beyond our finite realm. That that that's you know, if you keep on counting forever, you know, it's kind of the at the end of that, or sort of almost beyond the end of that. Now, that's in some sense thinking of infinity as not a number, as a limit of say, you know, the whole numbers. But what cant or George cantor the you know, the great German mathematician from the late Victorian times, what he did was actually taught us how to count beyond infinity.

So literally, using really smart ideas associated with something called set theory, he was able to show that actually you can have all the sort of finite numbers, and beyond that you can have infinity. But that's just one layer of infinity. You can have the infinity, which is all the whole numbers, but you can also have a different layer of infinity, which is all the numbers between zero and one. So think of the continuum of the numbers

between zero and one. That's you think there's an infinite number of numbers between zero and one, but that's actually a different infinity to all the whole numbers. So you've got you know, these discrete infinities continuum infinities, and they have different sizes, and they you have many layers of what can be an infinite number. And this is what Cantor really really began to explore and develop, and he met a lot of resistance when he was doing it.

He actually people thought he was crazy. He sort of fell into a lot of depression. You know, he was in battles with with someone called Chronicer, who was kind of, you know, the big guy in Berlin at the time, the elite university in Germany. He thought that Cantor was just delving into sort of witchcraft and he was a shot. He called him a charlatan, a corruptor of youth. And this really bothered Cantor and actually is quite a sad story. I mean, Cantor actually sort of really fell into into

quite bad depression. Whether it's because of this or whether he was he was predisposed anyway, it's not clear. But he actually ended his days sort of very sort of emaciated in it in a sanity Toorium, essentially starving because of the effects of the First World War at the time and not having enough foods. So it's quite a tragic tale in the end, but he was certainly a tremendous mathematician, and now all his ideas are really you know, I think people acknowledge him for the genius that he was.

Speaker 1

Yeah, it of course brings to mind those like the infinity hotel discret scenarios that are used to describe infinity. I've always found those to be super interesting and and mind blowing.

Speaker 4

Yeah, I mean, that's so, that's what I mean. So, so, as I said, cancer sort of had these different layers. So you can sort of imagine the first infinity, which he called alif zero, which is he defined as the set of all of all the whole numbers, essentially all the natural numbers you know, one, two, three, four, all the way up to well infinity, all of them basically, so that that's what he called the sort of first infinity.

But then you can have these high infinities, which are the you know, things like the set of the continuum, essentially the continuum between zero and one. So not just all the fractions and rational numbers, but also the irrational numbers, numbers like one over the square root of two, that kind of thing. And this is a new letter. He actually proved that they're actually that's a bigger infinity, and it's not easily obvious, but he did show it, and

it's remarkable. And there's so many sort of things about infinity. There's so many paradoxes associated with them. For example, one thing you can say is you think about the number of are there more square numbers or whole numbers? And you think, well, you think naively, obviously there are more whole numbers than square numbers, because one is a square, but two isn't a square, and three isn't a square. Okay, four is So it seems that there's obviously more whole

numbers than square numbers. But actually it's not true. And the reason you know that's not true because you just take a square number and you can map it to its square roots and you get the whole numbers. So the number of whole numbers is actually exactly the same as the number of square numbers. It's completely crazy. I mean,

these these parrot it's the same. There are same number of even numbers as there are even in odd numbers, and there's all these one there's the same number of numbers between zero and one as there are between zero and two. There's all these paradoxes that emerge the minute you start to think about infinity. And that's why most mathematicians for a long time just stayed away from it. But Canto was brave enough to climb into this infinite heaven and explore it.

Speaker 1

Now one of the numbers that comes up a lot in your in your book, and I know you've done videos on this as well. I'm also afraid to ask about it because it just seems kind of I get confused anytime I read anything about it. And that's this idea of I'm not even sure if I'm saying it correctly?

Speaker 4

Is it?

Speaker 1

Do we say tree? Three?

Speaker 4

Yeah, that's right? Yeah, yeah, yeah, three three?

Speaker 1

So yeah, what is this?

Speaker 4

What is three? Three? So? So there's a particular game that was that was developed involving some trees. So details aren't too important, it's just but basically, you draw these little stick trees and you have some seeds, you have some lines which are kind of like the branches, and you build these trees. Right, So one of the rules of the game is is that you know, for example, you can't have a tree that's got a bit of

a tree that has appeared before. So if I draw like, you know, one particular tree, then later on you can't draw a bigger tree that's got my tree stuck in it somehow, it's just not allowed. That would end the game. So there's a bunch of rules in how you draw these trees and build up this particular game, which I call the game of trees. Now, how long the game lasts depends on how many different types of seeds you have.

So you could have, for example, just black seeds, okay, or maybe you could have black seeds and you're also got white seeds, or maybe you've got black seeds, white seeds, and yellow seeds. You know, there's a whole bunch of possibilities. How many seeds you play with sort of sort of changes how long the game can last. For now, if you've just got one seed, the game can only last one move. You can just write down one seed and

that's it. You can't write down anything else because anything else that follows is going to contain the tree that went before. Okay, you've got two seeds, like a black and a white seed, the game can last up to you can draw up to three trees, and the game will automatically end after just three moves. It can't go beyond three moves. So you've got this this sort of sequence. So you've got one seed, you can play only one move. If you've got two seeds, you can play three moves.

And so then you go to three seeds. And you might think, well, I started off with one and it went to three, and now I've got three seeds, maybe maybe I can play ten moves or something called fifteen moves. It's not gonna be some it shouldn't be anything crazy. Well it is. So this sequence just goes bang. It just goes from one. So just for one seed you get one move, two seeds you get three moves, and then three seeds you get three. Three moves is where the game will last too. And this is a number

which just blows everything else. So we talked about Google and a Google plays, well, that's just nothing compared to three three. Talk about Graham's number, which will collapse your head's form black hole. That's nothing compared to three three three three is just it. It's impossible. I mean, I actually think it is impossible to imagine how ridiculously big this number is. And it's just so mundane. Where it comes from? Is this game so if he starts off you.

So so you're playing this game with two seeds. This game keeps ending after three moves, and if somebody comes along and adds a different colored seed, and you're like, okay, how is how long can the game last? Now? And somebody says tree three and this is three three. It's just a number that's actually too big for the universe. It just whow where did that leap come from? Leaps should not be that big. But that's so that's in a essence what tree three is, and it is too

big for the universe. So one of the things I worked out was suppose you're playing this game involving these trees. So you're writing drawing these trees, right, so you play one, go draw a tree. Play next, go draw a tree, and so on. You've got three seed, three different colors of seeds. So we know the limit of the game is three three moves treating three three different trees in the forest. How long are you going? Could you finish

the game? And one other thing I imagine is you know you're playing this game at high speed, so you're playing it as fast as space time will allow. So you literally if you play any faster space time will break due to quantum effects. So you play it super super fast, and so you play again, you play again, You'll play it through a lifetime. You'll get nowhere near tree three. After you die, and maybe you replace yourself

with some artificial intelligence. You've got two art Ai machines playing against each other, you know, powered by the light of the sun. They'll keep playing the game at this crazy pace, and they keep going, and they keep going. The sun gets bigger, you know, it goes to a red giants. All these things happen. Eventually it falls back

forms a white dwarf. Over many billions of years, and still this these two ais are still playing the game because they have got nowhere near tree three, and they're playing at breakneck speed as well, and so eventually they lose power. They can't get any power because the sun dies, right, so they need to somehow develop some new technology which gets energy from I don't know, the cosmic microwave background radiation. And the game goes on, and the game goes on,

and the game goes on. In fact, the game will go on way beyond the sort of heat death of the universe, and still you will not get to the end of tree three. And actually there's a phenomena called Puancore recurrence, which says that in any system, in any finite system, you'll eventually get back to where you started. And that applies to our universe too. So you can

imagine a pack of cards. You know, if you shuffle a pack of cards enough times, you'll a lot of times, but enough times you'll eventually get back to the point where all the cards are in order. It'll take a long time, but it will happen eventually. It's the same with our universe. You shuffle the universe enough times, you allow it to evolve for long enough, eventually you'll get

back to where it started. It will reset. And that reset time for our universe is actually shorter than the time it would take to play this game of trees all the way up to three three moves, playing as fast as you possibly can. And so even even if you could do it, even if you could live past all these you know, Gargangian timescales, the universe is just going to go, nah mat, game over. We're resetting. You ain't going to get to the game which you ain't

going to end this game. So three three is actually a number that's that's actually too big for the universe. That's how big it is.

Speaker 1

It's just so astounding that as you describe it, it's just it's such a short step to reach that point, because because a lot of these notmes, like when you're talking about the Googles and the Google Plexus, it's easy to think, well, those those big numbers live out there like they're like in the deep water. But then this seems to illustrate that now the deep water is is far closer than you think.

Speaker 4

And it's not I wouldn't even call it deep water. It's it's water. That's you know, you're sort of like, yeah, you're just sort of tiptoeing across the you know, through the shallows and there, and then bang it just gives away underneath you. And there's just it's it's bottomless as far as you're concerned. You know, I wouldn't even got a d watter is beyond deep. It's too it's too deep for the universe.

Speaker 1

Wow. So ultimately, what do fantastic numbers reveal about the cosmos? Like what is the I guess what is the lesson of big numbers? Fantastic numbers et cetera.

Speaker 4

So for me, I think all the ideas that I talk about in the context of the big numbers in the book, they all come back to the same thing which we've talked about, which is the holographic truth, the idea that a lot of the ideas associated with black holes and and how much information you can fit inside a black hole. Where that information stored, for example, is it stored inside the black hole or is it stored

on the edge of the black hole? And these are ideas which which which leads you to to to the to the holographic truth, to the idea that actually, maybe the information in our world isn't stored inside the world. Maybe it's stored on the boundary of the world, at the edge, on the walls that surround it. And in

that sense, that's why it's it's holographic. All the ideas, all the limits that we're talking about, you know, counting how much information you can store in a head, you know, and when it's going to turn into a black hole, you know, counting how long it takes for our universe to reset it up. All these ideas come back to the question of how our universe stores its information. Does it store it inside, and if so, how does it

store it? Well, actually, no, it turns out it's seem like it stores it on the edge of space, and that allows you to count how much information there is in that space and how many different ways you can combine things. But it all comes back to that holographic truth.

Speaker 1

I have to ask about this because I, again most

I'm not as versed in mathematics. There's a lot of people out there, and one of the things that I kept thinking about reading the book was just a one quick joke from the season one episode of the British comedy look Around You, in which the narrator the episode is about math, and the narrator tells us that the largest known number is around forty five million, but the larger numb umbers might exist, and they like speculate forty five million in one could be an number, and you know,

of course that's absurd, and that's absurd ast humor. But there's something about that that seems to sort of ring true with a lot of these these concepts, and I was wondering what you thought about the role of absurdity in contemplating big numbers.

Speaker 4

Yeah, absolutely, no, I really do think so. When you think of something like three three, at least within our universe, you can't fit it in. It cannot fit in. There's nothing that could, you know, you could describe, because it's just too big for anything that we can talk about

in our universe. Now, you might imagine other universes which could accommodate it, and in a you know, a sort of multiverse scenario, like maybe you get from something like string theory, could you get universes that can contain tree three. Well maybe we don't know, right, we don't know enough about about the multiverse of string theory, but it's not inconceivable potentially so, but certainly in our world you can't.

It's interesting. One of the things I did a video quite quite recently actually about the biggest number that nobody will ever think of. And I did these sort of quite a bunch of estimates based on a bunch of dubious sort of you know, sort of assumptions, which I acknowledge with quite jubious, But I think I came up with an estimate that if you think of a random seventy three digit number, also something of that order, then probably nobody's going to ever ever think of it. Other

than you. I mean, you know, so, I'm not saying I just think of a one followed by seventy two zero. It's clearly not something like that, but just completely random, random seventy two to seventy three digit numbers something like that. Chances are nobody in the history of humanity, either before or to come, we'll ever think of that number. And it's kind of that's kind of mind blowing. I think it's kind of yours. Just think of it, and that's

yours forever. So just everybody should just write down a seventy three digit numb and name after themselves.

Speaker 1

Well that's wonderful. Well, Tony, thanks for taking time out of your day to chat with us. I want to make sure we're hitting all the plugs here. The book Which Which is? Which? Is out? I believe it's out now? Correct?

Speaker 4

Yeah? Yeah, it's actually released today in the US. I probably should say today, should I?

Speaker 1

I guess it'll be. It will have been released two days ago when we published this, So yeah, it's it's out. It's fantastic numbers and where to find them? And then the YouTube series is number file, correct?

Speaker 4

Yeah? So I appear on number File. There's another channel. I appear on which is more physics based called sixty Symbols. So they're both made by by Brady Harran. And yeah, so I appear regularly on both of those. So it's a lot of fun. But yeah, it's I hope people enjoy enjoy the book. It's and I just don't think too recklessly about Grahams number because you going to have.

Speaker 1

Yeah, we don't want anybody's heads to collapse into black holes.

Speaker 4

Absolutely.

Speaker 1

All right, Well, thanks for coming on the show. I hope you have a great day, Thanks Chub. All right, well, thanks once again to Tony for taking time out of his day to chat with me here. The book again is Fantastic Numbers and Where to Find Them. Highly recommend it for anyone who is at all intrigued by what we were talking about here today. As always, if you want to reach out to us and ask any questions, share your relationship with Fantastic Numbers, well, you can find

us in a number of ways. Let's see if you email us and I'll give you that email in a second. You can have access to the discord where you can discuss show matters with other stuff to blow your mind listeners. There's also the Stuff to Blow Your Mind discussion module that is on Facebook. You can find that and seek access to that as well. And of course, thanks as always to Seth Nichols Johnson for producing the show here and yeah, if you want to get in touch with us,

you can simply email us at content Act. It's Stuff to Blow your Mind dot com.

Speaker 3

Stuff to Blow Your Mind is production of iHeartRadio. For more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts, or wherever you listen to your favorite shows

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