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Speaker 1: Fans in the UK. Robert Lamb here with a really

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Speaker 1: a little incentive for making the switch, we're including a

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Speaker 1: UK exclusive Monster Fact episode for you, and this episode

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Speaker 1: will be add free, so please don't wait you might forget.

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Speaker 1: Head on over to Apple Podcasts or Spotify and search

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Speaker 1: for Stuff to Blow your Mind UK and subscribe today

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Speaker 1: and be sure to remind any friends who listen in

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Speaker 1: the UK to do the same so you don't miss

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Speaker 1: a single episode. Thanks for listening. Hey, you welcome to

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Speaker 1: Stuff to Blow Your Mind. My name is Robert.

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Speaker 2: Lamb and I'm Joe McCormick and it's Saturday, so we

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Speaker 2: are reaching into the vault to pull out an older

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Speaker 2: episode of the show for you. This one originally published

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Speaker 2: July twenty eighth, twenty twenty two, and Rob this was

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Speaker 2: your interview with Antonio Padilla, author of the book Fantastic

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Speaker 2: Numbers and Where to Find Them.

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Speaker 1: Yeah, this is a fun chat, I think ultimately a

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Speaker 1: very accessible chat, but one that will also probably break

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Speaker 1: your brain a little bit. So have a good time

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Speaker 1: with this one.

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Speaker 3: Welcome to Stuff to Blow Your Mind, production of iHeartRadio.

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Speaker 1: Hey, welcome to Stuff to Blow Your Mind. My name

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Speaker 1: is Robert Lamb. My co host Joe is away from

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Speaker 1: work today, so I am conducting an interview here with

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Speaker 1: Professor Antonio Padella, author of the new book Fantastic Numbers

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Speaker 1: and Where to Find Them, a fascinating read about big numbers,

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Speaker 1: fantastic numbers, black holes, and more. This is a really

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Speaker 1: fun chat. I think you're all going to enjoy it,

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Speaker 1: So go ahead and jump right in with me right now. Hi, Tony,

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Speaker 1: Welcome to the show.

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Speaker 4: Hi, Hi Rop How you doing. Oh?

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Speaker 1: Pretty good? Pretty good. I'm really excited to talk about

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Speaker 1: the new book Fantastic Numbers and Where to Find Them.

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Speaker 1: A wonderful read, and it's a book that gets into

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Speaker 1: some pretty wonderful, mind rending cosmological territory as we'll no

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Speaker 1: doubt I'll discuss here. But first I wanted to start

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Speaker 1: with just a really basic sort of grounding question. I

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Speaker 1: guess we encounter numbers every day, and you discuss some

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Speaker 1: numbers that most of us don't encounter really every day.

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Speaker 1: If we could back up a whole lot, I guess

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Speaker 1: and just ponder the basics here, what exactly is a number?

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Speaker 4: Well, I mean, this is this is an idea I

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Speaker 4: sort of, you know, delve into in my book because

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Speaker 4: of course, when you go really back into history, back

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Speaker 4: to sort of the ancient Sumerians or something like that,

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Speaker 4: you know, obviously they really began to use numbers to

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Speaker 4: talk about, well, I've got five jars of oil, I've

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Speaker 4: got five loaves of bread. But then it sort of

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Speaker 4: begs the question, is that five the same five is

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Speaker 4: the five that describes the jars of oil, the same

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Speaker 4: five that describes the loaves of bread. And then you

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Speaker 4: really sort of when you sort of make that, you

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Speaker 4: disconnect the two and you start to build the idea

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Speaker 4: of like what I call an emancipated number and number

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Speaker 4: that's independent of the thing that it's describing. Then you're

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Speaker 4: really sort of making quite quite an intellectual leap. So

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Speaker 4: that for me is what is what a number is?

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Speaker 4: It's kind of emancipated from the thing that it's describing.

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Speaker 4: Whether such a thing really exists in a philosophical sense

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Speaker 4: is a whole new debate that you can have. But yeah,

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Speaker 4: that for me is the key mathematical lead that I

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Speaker 4: think was made, you know, a long time ago. And yeah,

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Speaker 4: it's really important.

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Speaker 1: Now getting back into that sort of philosophical territory. This

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Speaker 1: is one that I know that you tackle a lot.

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Speaker 1: It's pretty standards for philosophical math question. But is mathematics

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Speaker 1: more of a human discovery or more of a human invention?

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Speaker 4: Yeah, I mean I don't think this is straightforward answer

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Speaker 4: to this. Of course, this sort of you know, boils

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Speaker 4: down to like a sort of alluded to whether numbers exist,

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Speaker 4: whether maths exists, and as kind of I mean, I'm

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Speaker 4: not a philosopher, but I know that philosophers talk about

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Speaker 4: this in sort of this kind of three different angles

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Speaker 4: that you can take on it. So on the one hand,

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Speaker 4: you've got the Platonists who will say that numbers and

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Speaker 4: mathematics is true and it exists, but it exists outside

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Speaker 4: of space time as like an abstract concept. It's not

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Speaker 4: something that can affect the things in space time. It

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Speaker 4: can't affect the material objects that we have around us.

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Speaker 4: You also have the nominalists, who says basically that numbers

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Speaker 4: and maths only exist to of understand stuff. So in

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Speaker 4: some sense, we talked about the five, you know, five

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Speaker 4: jars of oil, the five five loaves of bread. That's

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Speaker 4: the only reason that the number five exists to describe

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Speaker 4: the jars of oil, to describe the loaves of bread.

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Speaker 4: And then of course you've got the third sort of

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Speaker 4: you know school, which is perhaps in some sense the

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Speaker 4: most extreme, which just says the numers don't exist at all.

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Speaker 4: They're just a useful tool that we used to describe

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Speaker 4: the universe surrounds us. And I guess the analogy people

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Speaker 4: use here is it's like saying, well, you could be

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Speaker 4: an atheist, but you could still believe with some of

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Speaker 4: the sort of moral messages that you read in the

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Speaker 4: Bible or the Koran. It doesn't mean that you know,

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Speaker 4: you can't be inspired by them, but you just don't

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Speaker 4: have to believe in every element of it. I guess

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Speaker 4: as a physicist, for me, it's kind of hard to

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Speaker 4: sort of go with that fictionist idea. And yet see

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Speaker 4: universe that is so amazingly described by mathematics. Now, is

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Speaker 4: that something that's embedded in the universe or not? I

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Speaker 4: guess it's really difficult to know. We certainly not seen

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Speaker 4: any evidence that it is.

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Speaker 1: And yet now your book deals with, as the title indicates,

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Speaker 1: fantastic numbers. What defines for you a fantastic number? And

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Speaker 1: are there categories of categorizations of numbers other than that

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Speaker 1: that we need to have in our heads before we

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Speaker 1: can get to the idea of what is truly fantastic.

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Speaker 4: Yes. So for me and my own relationship with numbers,

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Speaker 4: kind of it comes from on the one hand, you

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Speaker 4: have a number, whatever that number might be, and for me,

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Speaker 4: I always want to bring that sort of personality alive.

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Speaker 4: There's sort of real spirit of the number, sort of

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Speaker 4: to the four, and so it's always been physics for

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Speaker 4: me that does that. So when you know you can

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Speaker 4: have these wonderful mathematical concepts ideas like Graham's number three three,

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Speaker 4: these truly bizarre and wonderful numbers, to have a wonderful

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Speaker 4: place in mathematics, but then you really bring them to

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Speaker 4: life when you try to sort of squeeze them into

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Speaker 4: our physical world. So that, for me, is what makes

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Speaker 4: a number fantastic. It's almost like what makes a number

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Speaker 4: fantastic is the fantastic physics that it can lead you

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Speaker 4: towards and lead you to imagine and whatever that might be.

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Speaker 1: You also talk about I believe you specifically, you're talking

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Speaker 1: about Graham's number pretty early on in the book, and

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Speaker 1: you point out that if you if you try and

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Speaker 1: actually picture it in your head, your head collapses into

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Speaker 1: a black hole. And this this made me wonder, like,

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Speaker 1: what are the largest numbers roughly speaking then an average

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Speaker 1: person can fit into their head by one definition or another, Like,

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Speaker 1: at what point does it just become this this other

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Speaker 1: enterprise entirely? Yees.

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Speaker 4: So it's a good question. So, I mean, it kind

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Speaker 4: of depends on how how you sort of defined the question.

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Speaker 4: In some sense, if you're just thinking about neurons, how

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Speaker 4: many neurons have you have? You got in your in

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Speaker 4: your brain as about one hundred billion neurons, and so

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Speaker 4: you might say that you can use them if you

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Speaker 4: manage to clear your mind of every of the thoughts

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Speaker 4: to imagine one hundred billion digit number. Okay, that might

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Speaker 4: not be particularly practical, it might be quite challenging for

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Speaker 4: most of us. But in principle you might say that

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Speaker 4: that that that would be the limit. Of course, if

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Speaker 4: you then go beyond that and start to say, well,

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Speaker 4: what if I could somehow get my head to find

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Speaker 4: a way to actually store information store concepts more efficiently

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Speaker 4: than just the usual idea of neurons firing on it off.

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Speaker 4: Let's suppose that it could do that somehow. Then they

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Speaker 4: numbers get get much bigger, and you start to the

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Speaker 4: things that limit it are literally preventing your head collapsing

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Speaker 4: to form a black hole. Because black holes what they

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Speaker 4: do is that they're they're the best thing at storing information.

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Speaker 4: So if you want to get something the size of

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Speaker 4: a head of a human head, and you want to say,

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Speaker 4: what's the best thing the size for human head that

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Speaker 4: can store information, it's a black hole the size for

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Speaker 4: human head. That's nothing can do it better. And so

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Speaker 4: so that that places a new limit, and you can ask, well, again,

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Speaker 4: what is that limit would be? Well, he's certainly way

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Speaker 4: below grains now, but you're not going to get anywhere

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Speaker 4: near the magnificence of Graham's number, you could probably get

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Speaker 4: a digit that that's about ten to the seventy, but

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Speaker 4: it's about ten to the seventy digits long, so less

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Speaker 4: than a Google digits long. Having said that, you could

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Speaker 4: imagine a number like a Google plex, a google plex

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Speaker 4: has a Google digits. Now I've just said that you

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Speaker 4: can't imagine at Google digits, not possible, but a google

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Speaker 4: plex you could because what you know about a google

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Speaker 4: plex is that it's a one followed by a Google zero.

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Speaker 4: So you know that all the numbers that come later

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Speaker 4: on as zeros, So there's not much information in that,

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Speaker 4: so it doesn't cost as much as many bits. You

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Speaker 4: don't have to put as many bits in your head

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Speaker 4: to imagine that. So what we're really talking about now

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Speaker 4: are really a random assortment of digits, a completely random

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Speaker 4: assortment digits the kind that would appear in Graham's number.

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Speaker 4: And I don't think you can get passed around ten

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Speaker 4: to the seventy, which is a one with with seventy zeros.

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Speaker 4: You couldn't get past that many digits completely randomly sort

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Speaker 4: of allocated. At that point, your head's going to collapse.

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Speaker 4: Into a black hole.

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Speaker 1: Now now backing up to the Google and the google Plex,

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Speaker 1: can't can you? Can you walk us briefly through the

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Speaker 1: difference between a Google, a google Plex, and and and

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Speaker 1: maybe realms beyond that? This is about the only area

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Speaker 1: of fantastic numbers that I'd really heard anything about prior

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Speaker 1: to reading your book.

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Speaker 4: Yeah, so at Google is is it's a number, which

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Speaker 4: is which is a one followed by one hundred zeros.

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Speaker 4: So I think everybody would agree that sounds like quite

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Speaker 4: a big number. It goes back to a physicist called

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Speaker 4: Edward Kasner who was Columbia, and he was writing a

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Speaker 4: popular science book, and he was trying to sort of,

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Speaker 4: you know, convey that he really wanted to show how

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Speaker 4: big infinity he was, and so he wanted to cou

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Speaker 4: up with numbers that we all think are really big,

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Speaker 4: like a one followed by one hundred zeros. And he said, well, okay,

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Speaker 4: that's really small compared to infinity, right, even though something

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Speaker 4: really big is actually really small compared to infinity. So

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Speaker 4: he came up with this one with one hundred zeros.

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Speaker 4: He wanted a name for this number, so at the

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Speaker 4: time he asked his nephew who was nine years old

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Speaker 4: at the time. He was called Milton Soota. He said,

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Speaker 4: can you qu up with a name for this? And

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Speaker 4: Milton said, well, at Google, which is an absolute stroke

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Speaker 4: of genius, right, it's such a great name. And then

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Speaker 4: so they wanted to then develop things further. So then

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Speaker 4: they wanted an even bigger number, again building on this

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Speaker 4: idea that it's nothing compared to infinity. And so he said, well, okay,

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Speaker 4: I'm going to quote with the idea of a google Plex.

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Speaker 4: It's going to be an even bigger number. Well how big?

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Speaker 4: So Kasner then goes to Milton. He says, well, how

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Speaker 4: big should it be? And Milton's like, well, it should

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Speaker 4: be a one, not followed by one hundred zeros, but

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Speaker 4: zeros until you get tired. But Kasner is like, you know,

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Speaker 4: a sort of a you know, esteemed academic at Columbia

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Speaker 4: and all that. That's just not precise enough for him.

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Speaker 4: So he went with a which a much more sort

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Speaker 4: of well defined idea, which is a google plex should

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Speaker 4: be a one followed by a Google zeros. So a

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Speaker 4: Google's already massive, that's a one followed by one hundred zeros.

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Speaker 4: A google plex is a one followed by a Google zero.

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Speaker 4: So it's a whole new level of big compared to

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Speaker 4: what we're normally used to.

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Speaker 1: And then it just it keeps building on that. Right,

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Speaker 1: there's there's even like what a Google plexian is that

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Speaker 1: the next level?

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Speaker 4: So so yeah, I mean this is this is a

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Speaker 4: really nice, nice idea. You can really now start to

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Speaker 4: really build very big numbers, very very quickly using this

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Speaker 4: this mathematical technique called recursion. So for example, you can

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Speaker 4: develop the idea of a Google duplex or what's a

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Speaker 4: Google duplex, Well, it's a one followed by a Google

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Speaker 4: plex zeros, and then you could go to a Google triplex.

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Speaker 4: Well you can probably guess what it's going to be.

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Speaker 4: It's gonna be a one followed by a Google duplex zeros.

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Speaker 4: And then a Google quadruplex is a one followed by

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Speaker 4: a Google triplex zeros. And you can see each time

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Speaker 4: you're growing the number just by so much, by such

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Speaker 4: an unimaginably large and that's what You're not just adding

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Speaker 4: a zero every time, you're kind of really ballooning the

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Speaker 4: number of zeros on the end of this number in

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Speaker 4: Gargangian proportions, and that's what and it's this power of

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Speaker 4: mathematical recursion that allows you to do that.

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Speaker 1: Now, you also talk about fantastic numbers that are I

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Speaker 1: guess you would say smaller. The main example that comes

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Speaker 1: to mind, you refer to this several times in the

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Speaker 1: book is a number associated with Olympic sprinter Hussein Bolt.

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Speaker 1: Would you tell us a little bit about this number?

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Speaker 4: Yeah, yeah, so well, actually this is one of my

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Speaker 4: big numbers. Actually, even though it doesn't seem that thing,

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Speaker 4: it's actually it's one of my big numbers. So I

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Speaker 4: can read out the number. What it is, Okay, one point.

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Speaker 4: I think it's fifteen zeros eight five eight, So it's

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Speaker 4: just a number just slightly north of one. So it's

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Speaker 4: it doesn't seem like a big number, but in my book,

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Speaker 4: I say it is a big number. And the reason

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Speaker 4: is it's it measures the amount by which Usain Bolt

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Speaker 4: managed to slow down time. And when he was he

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Speaker 4: was running in the World Championships and I think Berlin

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Speaker 4: and he set the world record. And this is due

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Speaker 4: to the effects of relativity, so that when when somebody

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Speaker 4: actually moves quickly, they actually slowed. Time actually slows down

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Speaker 4: for them. And this is the amount by which Usain

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Speaker 4: Bolt was actually able to slow down time due to

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Speaker 4: the effects of Einstein's theory. And it's compared to the

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Speaker 4: people in the stadium, for example. This is this was

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Speaker 4: the difference that he experienced. So it's one of the

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Speaker 4: one of the weird consequences of it is that you

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Speaker 4: can actually it's not that you say Bolt, actually even

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Speaker 4: though he slowed down time, it's not that he that

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Speaker 4: he actually ran the race any quicker. He still runs

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Speaker 4: the race at roughly ten meters per second. It's actually

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Speaker 4: an even more strange consequence. He actually the track also

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Speaker 4: shrinks for him a little bit, so so he actually

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Speaker 4: runs it in less time, but in the same speed. Therefore,

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Speaker 4: the track shrinks because relative to him, the track's moving.

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Speaker 4: And this is another effect of relativity, one of the

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Speaker 4: remarkable things. And and yes, you could perhaps argue that

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Speaker 4: he didn't actually finish the race because the tracks rank

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Speaker 4: so he didn't run quite one hundred meters.

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Speaker 1: Wow. I was really blown away with this, because you know,

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Speaker 1: you often hear the standard analogies concerning airplanes and pyramids

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Speaker 1: and so forth when it comes to time dilation and

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Speaker 1: so forth. But I hadn't I hadn't heard this particular

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Speaker 1: example before.

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Speaker 4: This is great. Yeah, I mean it's true if like

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Speaker 4: taxi drivers, if you imagine a taxi driver that's driving

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Speaker 4: around I don't know, any city in New York wherever,

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Speaker 4: you know, sort of for forty to fifty years of

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Speaker 4: their life because of that extra extra speed that they're

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Speaker 4: picking up, that's going to accumulate over time, and actually

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Speaker 4: they can probably leap forward in time by probably I

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Speaker 4: think about a microsecond over the course of their career.

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Speaker 4: It's not a lot, but it's still pretty amazing when

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Speaker 4: you think about it.

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Speaker 1: So they've got the knowledge, and then they have that

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Speaker 1: as well, right.

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Speaker 4: Oh yeah, of course, yeah exactly, not just the knowledge, Yeah,

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Speaker 4: they actually get it. They actually get a little bit younger.

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Speaker 1: So your book makes use of written numbers, and of

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Speaker 1: course you have this wonderful YouTube series number file, and

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Speaker 1: in that you benefit not only from some fantastic descriptions

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Speaker 1: and pop culture tie ins as you do in the book,

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Speaker 1: but you also have a lot of helpful illustrations. So

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Speaker 1: I was curious, since you are a regular communicator of

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Speaker 1: this topic, is it is it more challenging or in

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Speaker 1: some cases almost too challenging to describe some of these

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Speaker 1: numbers without the visual aids or the actual numerals to

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Speaker 1: like visually present somebody with.

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Speaker 4: Yeah, I think so this is where the physics comes

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Speaker 4: in in some respects. Right. So, on the one hand,

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Speaker 4: if you really want to describe the number, like I say,

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Speaker 4: a number like Grames number, you do need those visual

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Speaker 4: aids because it's not a number that you're going to

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Speaker 4: sort of stumble across in any kind of normal environments. Right,

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Speaker 4: It's not a number you're going to see on a

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Speaker 4: price tag, at least you'd hope not. And you know,

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Speaker 4: so these are you need new notation, new sort of

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Speaker 4: symbolism to sort of actually even describe the number. So

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Speaker 4: you've got to introduce that. There's just no getting away

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Speaker 4: from it. But I guess what you can do is

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Speaker 4: describe the physics associated with it, and that you can

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Speaker 4: certainly do, you know, just just just with words. And

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Speaker 4: you know, in the case of a number like Graham's number,

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Speaker 4: you can talk about how you just can't picture it

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Speaker 4: in your head because your head will will collapse to

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Speaker 4: form black hole. And that's already going to make people think, wow,

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Speaker 4: that numbers there's something big of something big and crazy

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Speaker 4: about that number or a google plex, you know, and

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Speaker 4: you can talk about a universe that's that's a google

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Speaker 4: plex meters across, and then you can ask, well, if

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Speaker 4: the universe is that big, if the universe is ritually

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Speaker 4: that large, then it's likely that you would find multiple

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Speaker 4: copies of yourself, like literally exact doppelgangers elsewhere in this

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Speaker 4: ginormous universe.

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Speaker 1: Yeah. I wasn't. I was I wasn't prepared for doppelgangers

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Speaker 1: to enter into the scenario. So another great part about

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Speaker 1: the book for me, and another thing that comes up

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Speaker 1: in the book that I was very intrigued by. I

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Speaker 1: was wondering if you might talk about is the idea

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Speaker 1: of the holographic truth.

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Speaker 4: Yeah, so the holographic truth is. I mean, it's an idea.

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Speaker 4: It's probably the most important idea I would say that's

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Speaker 4: emerged from theoretical physics in the last thirty years, and

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Speaker 4: it's actually mind blowing when you really think about what

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Speaker 4: it pertains to it. It's this following statement that essentially

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Speaker 4: one of the dimensions of space that we experience around us.

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Speaker 4: So we normally talk about say three dimensions of space, well,

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Speaker 4: one of them could well be an illusion. It might

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Speaker 4: not exist and it's really remarkable. So what we're saying

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Speaker 4: is that there are two ways in which you can

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Speaker 4: describe the physics that we see around us. On the

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Speaker 4: one hand, we can imagine three dimensional world with a

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Speaker 4: gravitational force and the force of gravity doing its thing

364
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Speaker 4: with planets around the Sun and so on and so forth.

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Speaker 4: On the other hand, there's a completely equivalent description of

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Speaker 4: the same phenomena which just uses two dimensions and no gravity.

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Speaker 4: So think of it a bit like, you know, on

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Speaker 4: the one hand, somebody's you know, in English, we say

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Speaker 4: if we see a plate of meatballs, we call them meatballs,

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Speaker 4: but a Spaniard might call them album the gas. They're

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Speaker 4: both describing the same things, they're just using a different language.

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Speaker 4: And that's kind of what the holographic truth says. It

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Speaker 4: says that you can have a theory like a three

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Speaker 4: dimensional world with gravity, and you can use that to

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Speaker 4: describe all the physical phenomena you see, or use this

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Speaker 4: different language which has no gravity and only requires two

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Speaker 4: dimensions of space. So is it true of our world?

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Speaker 4: We don't know. It's a conjecture. It's a conjecture that

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Speaker 4: has sort of evidence coming from the physics of black holes.

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Speaker 4: There are actually concrete examples that we know of of

381
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Speaker 4: sort of toy universes, so not our universe, but but

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Speaker 4: space times that maybe the higher dimensional they may be

383
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Speaker 4: warped in weird and wonderful ways. And you can think

384
00:20:08,080 --> 00:20:12,199
Speaker 4: about gravity in these in these simple toy universes, and

385
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Speaker 4: you can show that there's an equivalent description in one

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Speaker 4: dimension less like a holographic description, and it's called a

387
00:20:18,960 --> 00:20:21,800
Speaker 4: hologram because that's essentially what holograms do. Right, If you

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Speaker 4: think of a HOLOGRAMD, what have you got? You've got

389
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Speaker 4: an image on a that's stored on a holographic plate.

390
00:20:27,840 --> 00:20:29,800
Speaker 4: You know, it's just some light and dark bands on

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Speaker 4: a holographic plate, a two dimensional plate. It stores a

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Speaker 4: bunch of information that way, but that's just one way

393
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Speaker 4: of looking at the information. You can decode it in

394
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Speaker 4: a different way by shining monochromatic light through it and

395
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Speaker 4: creating a three D image. You're not creating any new information.

396
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Speaker 4: It's the same information, just stored either in two dimensions

397
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Speaker 4: or three. And it seems to be that that seems

398
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Speaker 4: to be a fundamental property of gravitation, of gravitational worlds

399
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Speaker 4: that you can think of them as as like, as

400
00:20:59,400 --> 00:21:01,720
Speaker 4: I said, three, the world with gravity, or you just

401
00:21:01,920 --> 00:21:05,600
Speaker 4: forget about gravity and consider a world with one dimension

402
00:21:05,680 --> 00:21:08,640
Speaker 4: less and you can describe exactly the same physical phenomena.

403
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Speaker 1: Wow. Now here's another question that came up reading the

404
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Speaker 1: book that I don't know if of all of our

405
00:21:16,920 --> 00:21:19,200
Speaker 1: listeners necessarily would have thought of this question. I don't

406
00:21:19,200 --> 00:21:23,719
Speaker 1: think some of them would have. And that comes to infinity. Infinity,

407
00:21:24,480 --> 00:21:26,840
Speaker 1: Like sometimes it's easy to think of like, Okay, infinity

408
00:21:26,920 --> 00:21:29,200
Speaker 1: is the If we think of it as a number,

409
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Speaker 1: we think it's the aid on its side representing infinity.

410
00:21:31,960 --> 00:21:34,439
Speaker 1: Is infinity a number? And if it's not a number,

411
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Speaker 1: like what do we think of it as? How do

412
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Speaker 1: we classify infinity?

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Speaker 4: So I love this question because the answer is that

414
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Speaker 4: it's both not a number and lots of numbers. This

415
00:21:43,400 --> 00:21:46,479
Speaker 4: is a wonderful thing about infinity. So it depends how

416
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Speaker 4: you want to think about infinity. And I think most

417
00:21:49,720 --> 00:21:52,160
Speaker 4: of us when we intuitively think about infinity, we kind

418
00:21:52,160 --> 00:21:54,879
Speaker 4: of think of like I don't know, the infinite distance,

419
00:21:54,960 --> 00:21:57,480
Speaker 4: you know, or infinite time, And what we're really thinking

420
00:21:57,480 --> 00:21:59,119
Speaker 4: there is we're thinking of it is like a limit

421
00:21:59,280 --> 00:22:02,160
Speaker 4: is something that's just just beyond our finite realm. That

422
00:22:02,160 --> 00:22:05,240
Speaker 4: that that's you know, if you keep on counting forever,

423
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Speaker 4: you know, it's kind of the at the end of that,

424
00:22:07,960 --> 00:22:11,040
Speaker 4: or sort of almost beyond the end of that. Now,

425
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Speaker 4: that's in some sense thinking of infinity as not a number,

426
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Speaker 4: as a limit of say, you know, the whole numbers.

427
00:22:19,800 --> 00:22:22,600
Speaker 4: But what cant or George cantor the you know, the

428
00:22:22,600 --> 00:22:26,800
Speaker 4: great German mathematician from the late Victorian times, what he

429
00:22:26,840 --> 00:22:30,719
Speaker 4: did was actually taught us how to count beyond infinity.

430
00:22:31,240 --> 00:22:35,360
Speaker 4: So literally, using really smart ideas associated with something called

431
00:22:35,400 --> 00:22:38,840
Speaker 4: set theory, he was able to show that actually you

432
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Speaker 4: can have all the sort of finite numbers, and beyond

433
00:22:42,280 --> 00:22:45,040
Speaker 4: that you can have infinity. But that's just one layer

434
00:22:45,040 --> 00:22:47,520
Speaker 4: of infinity. You can have the infinity, which is all

435
00:22:47,600 --> 00:22:49,840
Speaker 4: the whole numbers, but you can also have a different

436
00:22:49,920 --> 00:22:53,480
Speaker 4: layer of infinity, which is all the numbers between zero

437
00:22:53,520 --> 00:22:55,639
Speaker 4: and one. So think of the continuum of the numbers

438
00:22:55,640 --> 00:22:58,880
Speaker 4: between zero and one. That's you think there's an infinite

439
00:22:58,960 --> 00:23:01,440
Speaker 4: number of numbers between zero and one, but that's actually

440
00:23:01,480 --> 00:23:04,920
Speaker 4: a different infinity to all the whole numbers. So you've

441
00:23:04,920 --> 00:23:09,879
Speaker 4: got you know, these discrete infinities continuum infinities, and they

442
00:23:10,720 --> 00:23:13,399
Speaker 4: have different sizes, and they you have many layers of

443
00:23:13,840 --> 00:23:16,760
Speaker 4: what can be an infinite number. And this is what

444
00:23:17,680 --> 00:23:21,679
Speaker 4: Cantor really really began to explore and develop, and he

445
00:23:21,720 --> 00:23:23,240
Speaker 4: met a lot of resistance when he was doing it.

446
00:23:23,280 --> 00:23:25,679
Speaker 4: He actually people thought he was crazy. He sort of

447
00:23:25,720 --> 00:23:29,639
Speaker 4: fell into a lot of depression. You know, he was

448
00:23:29,640 --> 00:23:32,280
Speaker 4: in battles with with someone called Chronicer, who was kind of,

449
00:23:32,359 --> 00:23:34,280
Speaker 4: you know, the big guy in Berlin at the time,

450
00:23:34,600 --> 00:23:37,960
Speaker 4: the elite university in Germany. He thought that Cantor was

451
00:23:38,040 --> 00:23:41,120
Speaker 4: just delving into sort of witchcraft and he was a shot.

452
00:23:41,119 --> 00:23:43,919
Speaker 4: He called him a charlatan, a corruptor of youth. And

453
00:23:43,960 --> 00:23:46,600
Speaker 4: this really bothered Cantor and actually is quite a sad story.

454
00:23:46,720 --> 00:23:49,160
Speaker 4: I mean, Cantor actually sort of really fell into into

455
00:23:49,240 --> 00:23:52,040
Speaker 4: quite bad depression. Whether it's because of this or whether

456
00:23:52,080 --> 00:23:56,119
Speaker 4: he was he was predisposed anyway, it's not clear. But

457
00:23:56,160 --> 00:23:58,320
Speaker 4: he actually ended his days sort of very sort of

458
00:23:58,320 --> 00:24:02,320
Speaker 4: emaciated in it in a sanity Toorium, essentially starving because

459
00:24:02,320 --> 00:24:04,359
Speaker 4: of the effects of the First World War at the

460
00:24:04,400 --> 00:24:06,920
Speaker 4: time and not having enough foods. So it's quite a

461
00:24:06,960 --> 00:24:09,520
Speaker 4: tragic tale in the end, but he was certainly a

462
00:24:10,240 --> 00:24:13,639
Speaker 4: tremendous mathematician, and now all his ideas are really you know,

463
00:24:13,920 --> 00:24:16,679
Speaker 4: I think people acknowledge him for the genius that he was.

464
00:24:17,119 --> 00:24:20,199
Speaker 1: Yeah, it of course brings to mind those like the

465
00:24:20,240 --> 00:24:24,560
Speaker 1: infinity hotel discret scenarios that are used to describe infinity.

466
00:24:24,600 --> 00:24:28,159
Speaker 1: I've always found those to be super interesting and and

467
00:24:29,000 --> 00:24:29,600
Speaker 1: mind blowing.

468
00:24:29,880 --> 00:24:31,919
Speaker 4: Yeah, I mean, that's so, that's what I mean. So, so,

469
00:24:32,640 --> 00:24:35,080
Speaker 4: as I said, cancer sort of had these different layers.

470
00:24:35,080 --> 00:24:37,880
Speaker 4: So you can sort of imagine the first infinity, which

471
00:24:37,880 --> 00:24:40,800
Speaker 4: he called alif zero, which is he defined as the

472
00:24:40,840 --> 00:24:43,040
Speaker 4: set of all of all the whole numbers, essentially all

473
00:24:43,080 --> 00:24:45,760
Speaker 4: the natural numbers you know, one, two, three, four, all

474
00:24:45,760 --> 00:24:48,560
Speaker 4: the way up to well infinity, all of them basically,

475
00:24:48,720 --> 00:24:51,919
Speaker 4: so that that's what he called the sort of first infinity.

476
00:24:51,920 --> 00:24:53,800
Speaker 4: But then you can have these high infinities, which are

477
00:24:53,800 --> 00:24:58,560
Speaker 4: the you know, things like the set of the continuum,

478
00:24:58,640 --> 00:25:01,320
Speaker 4: essentially the continuum between zero and one. So not just

479
00:25:01,440 --> 00:25:05,600
Speaker 4: all the fractions and rational numbers, but also the irrational numbers,

480
00:25:05,680 --> 00:25:07,959
Speaker 4: numbers like one over the square root of two, that

481
00:25:08,040 --> 00:25:12,399
Speaker 4: kind of thing. And this is a new letter. He

482
00:25:12,440 --> 00:25:16,240
Speaker 4: actually proved that they're actually that's a bigger infinity, and

483
00:25:16,440 --> 00:25:18,520
Speaker 4: it's not easily obvious, but he did show it, and

484
00:25:18,560 --> 00:25:22,920
Speaker 4: it's remarkable. And there's so many sort of things about infinity.

485
00:25:22,960 --> 00:25:26,520
Speaker 4: There's so many paradoxes associated with them. For example, one

486
00:25:26,560 --> 00:25:28,160
Speaker 4: thing you can say is you think about the number

487
00:25:28,240 --> 00:25:32,560
Speaker 4: of are there more square numbers or whole numbers? And

488
00:25:32,600 --> 00:25:35,720
Speaker 4: you think, well, you think naively, obviously there are more

489
00:25:36,240 --> 00:25:39,720
Speaker 4: whole numbers than square numbers, because one is a square,

490
00:25:39,760 --> 00:25:42,480
Speaker 4: but two isn't a square, and three isn't a square. Okay,

491
00:25:42,520 --> 00:25:44,560
Speaker 4: four is So it seems that there's obviously more whole

492
00:25:44,640 --> 00:25:47,520
Speaker 4: numbers than square numbers. But actually it's not true. And

493
00:25:47,560 --> 00:25:49,679
Speaker 4: the reason you know that's not true because you just

494
00:25:49,720 --> 00:25:52,240
Speaker 4: take a square number and you can map it to

495
00:25:52,280 --> 00:25:55,560
Speaker 4: its square roots and you get the whole numbers. So

496
00:25:55,960 --> 00:25:58,320
Speaker 4: the number of whole numbers is actually exactly the same

497
00:25:58,320 --> 00:26:00,920
Speaker 4: as the number of square numbers. It's completely crazy. I mean,

498
00:26:01,200 --> 00:26:03,800
Speaker 4: these these parrot it's the same. There are same number

499
00:26:03,800 --> 00:26:05,719
Speaker 4: of even numbers as there are even in odd numbers,

500
00:26:05,920 --> 00:26:07,919
Speaker 4: and there's all these one there's the same number of

501
00:26:07,960 --> 00:26:10,200
Speaker 4: numbers between zero and one as there are between zero

502
00:26:10,240 --> 00:26:13,879
Speaker 4: and two. There's all these paradoxes that emerge the minute

503
00:26:13,920 --> 00:26:15,760
Speaker 4: you start to think about infinity. And that's why most

504
00:26:15,760 --> 00:26:18,199
Speaker 4: mathematicians for a long time just stayed away from it.

505
00:26:18,680 --> 00:26:21,000
Speaker 4: But Canto was brave enough to climb into this infinite

506
00:26:21,080 --> 00:26:28,520
Speaker 4: heaven and explore it.

507
00:26:29,400 --> 00:26:32,960
Speaker 1: Now one of the numbers that comes up a lot

508
00:26:33,000 --> 00:26:34,919
Speaker 1: in your in your book, and I know you've done

509
00:26:35,160 --> 00:26:38,440
Speaker 1: videos on this as well. I'm also afraid to ask

510
00:26:38,480 --> 00:26:41,400
Speaker 1: about it because it just seems kind of I get

511
00:26:41,440 --> 00:26:44,359
Speaker 1: confused anytime I read anything about it. And that's this

512
00:26:44,560 --> 00:26:47,240
Speaker 1: idea of I'm not even sure if I'm saying it correctly?

513
00:26:47,280 --> 00:26:47,479
Speaker 4: Is it?

514
00:26:47,520 --> 00:26:48,560
Speaker 1: Do we say tree? Three?

515
00:26:48,920 --> 00:26:50,880
Speaker 4: Yeah, that's right? Yeah, yeah, yeah, three three?

516
00:26:51,080 --> 00:26:52,000
Speaker 1: So yeah, what is this?

517
00:26:52,359 --> 00:26:55,800
Speaker 4: What is three? Three? So? So there's a particular game

518
00:26:56,600 --> 00:27:00,439
Speaker 4: that was that was developed involving some trees. So details

519
00:27:00,440 --> 00:27:03,480
Speaker 4: aren't too important, it's just but basically, you draw these

520
00:27:03,480 --> 00:27:05,720
Speaker 4: little stick trees and you have some seeds, you have

521
00:27:05,800 --> 00:27:07,920
Speaker 4: some lines which are kind of like the branches, and

522
00:27:08,000 --> 00:27:12,320
Speaker 4: you build these trees. Right, So one of the rules

523
00:27:12,320 --> 00:27:14,120
Speaker 4: of the game is is that you know, for example,

524
00:27:14,160 --> 00:27:15,600
Speaker 4: you can't have a tree that's got a bit of

525
00:27:15,600 --> 00:27:19,199
Speaker 4: a tree that has appeared before. So if I draw like,

526
00:27:19,280 --> 00:27:21,840
Speaker 4: you know, one particular tree, then later on you can't

527
00:27:21,880 --> 00:27:24,199
Speaker 4: draw a bigger tree that's got my tree stuck in

528
00:27:24,240 --> 00:27:26,840
Speaker 4: it somehow, it's just not allowed. That would end the game.

529
00:27:27,680 --> 00:27:29,760
Speaker 4: So there's a bunch of rules in how you draw

530
00:27:29,800 --> 00:27:32,480
Speaker 4: these trees and build up this particular game, which I

531
00:27:32,520 --> 00:27:36,120
Speaker 4: call the game of trees. Now, how long the game

532
00:27:36,240 --> 00:27:39,560
Speaker 4: lasts depends on how many different types of seeds you have.

533
00:27:39,680 --> 00:27:43,880
Speaker 4: So you could have, for example, just black seeds, okay,

534
00:27:44,240 --> 00:27:45,920
Speaker 4: or maybe you could have black seeds and you're also

535
00:27:46,080 --> 00:27:49,520
Speaker 4: got white seeds, or maybe you've got black seeds, white seeds,

536
00:27:49,520 --> 00:27:52,639
Speaker 4: and yellow seeds. You know, there's a whole bunch of possibilities.

537
00:27:53,080 --> 00:27:55,439
Speaker 4: How many seeds you play with sort of sort of

538
00:27:55,520 --> 00:28:00,320
Speaker 4: changes how long the game can last. For now, if

539
00:28:00,359 --> 00:28:03,639
Speaker 4: you've just got one seed, the game can only last

540
00:28:04,040 --> 00:28:06,800
Speaker 4: one move. You can just write down one seed and

541
00:28:06,840 --> 00:28:08,920
Speaker 4: that's it. You can't write down anything else because anything

542
00:28:08,920 --> 00:28:10,439
Speaker 4: else that follows is going to contain the tree that

543
00:28:10,480 --> 00:28:14,000
Speaker 4: went before. Okay, you've got two seeds, like a black

544
00:28:14,000 --> 00:28:16,919
Speaker 4: and a white seed, the game can last up to

545
00:28:17,240 --> 00:28:19,200
Speaker 4: you can draw up to three trees, and the game

546
00:28:19,200 --> 00:28:22,520
Speaker 4: will automatically end after just three moves. It can't go

547
00:28:22,600 --> 00:28:25,080
Speaker 4: beyond three moves. So you've got this this sort of sequence.

548
00:28:25,119 --> 00:28:28,160
Speaker 4: So you've got one seed, you can play only one move.

549
00:28:28,240 --> 00:28:30,480
Speaker 4: If you've got two seeds, you can play three moves.

550
00:28:31,280 --> 00:28:34,560
Speaker 4: And so then you go to three seeds. And you

551
00:28:34,640 --> 00:28:36,960
Speaker 4: might think, well, I started off with one and it

552
00:28:37,000 --> 00:28:38,840
Speaker 4: went to three, and now I've got three seeds, maybe

553
00:28:39,120 --> 00:28:41,760
Speaker 4: maybe I can play ten moves or something called fifteen moves.

554
00:28:41,600 --> 00:28:44,320
Speaker 4: It's not gonna be some it shouldn't be anything crazy.

555
00:28:44,400 --> 00:28:47,520
Speaker 4: Well it is. So this sequence just goes bang. It

556
00:28:47,560 --> 00:28:49,440
Speaker 4: just goes from one. So just for one seed you

557
00:28:49,440 --> 00:28:52,400
Speaker 4: get one move, two seeds you get three moves, and

558
00:28:52,440 --> 00:28:56,640
Speaker 4: then three seeds you get three. Three moves is where

559
00:28:56,640 --> 00:28:58,520
Speaker 4: the game will last too. And this is a number

560
00:28:58,640 --> 00:29:02,120
Speaker 4: which just blows everything else. So we talked about Google

561
00:29:02,160 --> 00:29:04,240
Speaker 4: and a Google plays, well, that's just nothing compared to

562
00:29:04,280 --> 00:29:06,880
Speaker 4: three three. Talk about Graham's number, which will collapse your

563
00:29:06,880 --> 00:29:09,720
Speaker 4: head's form black hole. That's nothing compared to three three

564
00:29:09,880 --> 00:29:14,680
Speaker 4: three three is just it. It's impossible. I mean, I

565
00:29:14,680 --> 00:29:18,240
Speaker 4: actually think it is impossible to imagine how ridiculously big

566
00:29:18,280 --> 00:29:21,040
Speaker 4: this number is. And it's just so mundane. Where it

567
00:29:21,040 --> 00:29:23,760
Speaker 4: comes from? Is this game so if he starts off you.

568
00:29:23,800 --> 00:29:25,640
Speaker 4: So so you're playing this game with two seeds. This

569
00:29:25,720 --> 00:29:28,360
Speaker 4: game keeps ending after three moves, and if somebody comes

570
00:29:28,400 --> 00:29:31,560
Speaker 4: along and adds a different colored seed, and you're like, okay,

571
00:29:31,600 --> 00:29:33,440
Speaker 4: how is how long can the game last? Now? And

572
00:29:33,520 --> 00:29:35,840
Speaker 4: somebody says tree three and this is three three. It's

573
00:29:35,840 --> 00:29:38,200
Speaker 4: just a number that's actually too big for the universe.

574
00:29:39,120 --> 00:29:42,280
Speaker 4: It just whow where did that leap come from? Leaps

575
00:29:42,280 --> 00:29:45,000
Speaker 4: should not be that big. But that's so that's in

576
00:29:45,000 --> 00:29:47,640
Speaker 4: a essence what tree three is, and it is too

577
00:29:47,680 --> 00:29:49,400
Speaker 4: big for the universe. So one of the things I

578
00:29:49,880 --> 00:29:53,760
Speaker 4: worked out was suppose you're playing this game involving these trees.

579
00:29:53,800 --> 00:29:56,920
Speaker 4: So you're writing drawing these trees, right, so you play one,

580
00:29:56,960 --> 00:29:59,440
Speaker 4: go draw a tree. Play next, go draw a tree,

581
00:29:59,440 --> 00:30:01,960
Speaker 4: and so on. You've got three seed, three different colors

582
00:30:01,960 --> 00:30:04,600
Speaker 4: of seeds. So we know the limit of the game

583
00:30:04,720 --> 00:30:07,880
Speaker 4: is three three moves treating three three different trees in

584
00:30:07,920 --> 00:30:11,719
Speaker 4: the forest. How long are you going? Could you finish

585
00:30:11,720 --> 00:30:13,440
Speaker 4: the game? And one other thing I imagine is you

586
00:30:13,440 --> 00:30:15,600
Speaker 4: know you're playing this game at high speed, so you're

587
00:30:15,600 --> 00:30:18,040
Speaker 4: playing it as fast as space time will allow. So

588
00:30:18,080 --> 00:30:21,000
Speaker 4: you literally if you play any faster space time will

589
00:30:21,040 --> 00:30:24,080
Speaker 4: break due to quantum effects. So you play it super

590
00:30:24,080 --> 00:30:27,400
Speaker 4: super fast, and so you play again, you play again,

591
00:30:27,440 --> 00:30:29,520
Speaker 4: You'll play it through a lifetime. You'll get nowhere near

592
00:30:29,560 --> 00:30:32,720
Speaker 4: tree three. After you die, and maybe you replace yourself

593
00:30:32,760 --> 00:30:35,880
Speaker 4: with some artificial intelligence. You've got two art Ai machines

594
00:30:35,920 --> 00:30:38,240
Speaker 4: playing against each other, you know, powered by the light

595
00:30:38,280 --> 00:30:40,320
Speaker 4: of the sun. They'll keep playing the game at this

596
00:30:40,480 --> 00:30:42,840
Speaker 4: crazy pace, and they keep going, and they keep going.

597
00:30:42,840 --> 00:30:44,640
Speaker 4: The sun gets bigger, you know, it goes to a

598
00:30:44,720 --> 00:30:47,480
Speaker 4: red giants. All these things happen. Eventually it falls back

599
00:30:47,520 --> 00:30:50,600
Speaker 4: forms a white dwarf. Over many billions of years, and

600
00:30:50,680 --> 00:30:53,560
Speaker 4: still this these two ais are still playing the game

601
00:30:53,640 --> 00:30:56,280
Speaker 4: because they have got nowhere near tree three, and they're

602
00:30:56,320 --> 00:30:59,760
Speaker 4: playing at breakneck speed as well, and so eventually they

603
00:30:59,760 --> 00:31:03,160
Speaker 4: lose power. They can't get any power because the sun dies, right,

604
00:31:03,240 --> 00:31:06,480
Speaker 4: so they need to somehow develop some new technology which

605
00:31:06,640 --> 00:31:09,640
Speaker 4: gets energy from I don't know, the cosmic microwave background radiation.

606
00:31:09,840 --> 00:31:11,360
Speaker 4: And the game goes on, and the game goes on,

607
00:31:11,400 --> 00:31:13,000
Speaker 4: and the game goes on. In fact, the game will

608
00:31:13,040 --> 00:31:16,120
Speaker 4: go on way beyond the sort of heat death of

609
00:31:16,160 --> 00:31:19,040
Speaker 4: the universe, and still you will not get to the

610
00:31:19,120 --> 00:31:23,040
Speaker 4: end of tree three. And actually there's a phenomena called

611
00:31:23,200 --> 00:31:27,240
Speaker 4: Puancore recurrence, which says that in any system, in any

612
00:31:27,280 --> 00:31:30,560
Speaker 4: finite system, you'll eventually get back to where you started.

613
00:31:31,080 --> 00:31:33,520
Speaker 4: And that applies to our universe too. So you can

614
00:31:33,560 --> 00:31:35,120
Speaker 4: imagine a pack of cards. You know, if you shuffle

615
00:31:35,120 --> 00:31:38,760
Speaker 4: a pack of cards enough times, you'll a lot of times,

616
00:31:38,760 --> 00:31:40,920
Speaker 4: but enough times you'll eventually get back to the point

617
00:31:40,920 --> 00:31:43,160
Speaker 4: where all the cards are in order. It'll take a

618
00:31:43,200 --> 00:31:46,840
Speaker 4: long time, but it will happen eventually. It's the same

619
00:31:46,880 --> 00:31:49,240
Speaker 4: with our universe. You shuffle the universe enough times, you

620
00:31:49,320 --> 00:31:51,880
Speaker 4: allow it to evolve for long enough, eventually you'll get

621
00:31:51,960 --> 00:31:55,239
Speaker 4: back to where it started. It will reset. And that

622
00:31:55,320 --> 00:31:58,680
Speaker 4: reset time for our universe is actually shorter than the

623
00:31:58,720 --> 00:32:01,520
Speaker 4: time it would take to play this game of trees

624
00:32:01,560 --> 00:32:03,440
Speaker 4: all the way up to three three moves, playing as

625
00:32:03,480 --> 00:32:07,520
Speaker 4: fast as you possibly can. And so even even if

626
00:32:07,520 --> 00:32:09,200
Speaker 4: you could do it, even if you could live past

627
00:32:09,280 --> 00:32:12,720
Speaker 4: all these you know, Gargangian timescales, the universe is just

628
00:32:12,760 --> 00:32:16,480
Speaker 4: going to go, nah mat, game over. We're resetting. You

629
00:32:16,520 --> 00:32:18,080
Speaker 4: ain't going to get to the game which you ain't

630
00:32:18,080 --> 00:32:20,160
Speaker 4: going to end this game. So three three is actually

631
00:32:20,160 --> 00:32:22,680
Speaker 4: a number that's that's actually too big for the universe.

632
00:32:22,720 --> 00:32:23,560
Speaker 4: That's how big it is.

633
00:32:23,960 --> 00:32:26,320
Speaker 1: It's just so astounding that as you describe it, it's

634
00:32:26,320 --> 00:32:28,760
Speaker 1: just it's such a short step to reach that point,

635
00:32:28,800 --> 00:32:30,239
Speaker 1: because because a lot of these notmes, like when you're

636
00:32:30,240 --> 00:32:33,320
Speaker 1: talking about the Googles and the Google Plexus, it's easy

637
00:32:33,360 --> 00:32:35,480
Speaker 1: to think, well, those those big numbers live out there

638
00:32:35,560 --> 00:32:37,880
Speaker 1: like they're like in the deep water. But then this

639
00:32:38,000 --> 00:32:41,040
Speaker 1: seems to illustrate that now the deep water is is

640
00:32:41,080 --> 00:32:42,640
Speaker 1: far closer than you think.

641
00:32:42,600 --> 00:32:44,960
Speaker 4: And it's not I wouldn't even call it deep water.

642
00:32:45,000 --> 00:32:47,440
Speaker 4: It's it's water. That's you know, you're sort of like, yeah,

643
00:32:47,440 --> 00:32:50,000
Speaker 4: you're just sort of tiptoeing across the you know, through

644
00:32:50,040 --> 00:32:53,280
Speaker 4: the shallows and there, and then bang it just gives

645
00:32:53,320 --> 00:32:57,120
Speaker 4: away underneath you. And there's just it's it's bottomless as

646
00:32:57,120 --> 00:32:59,520
Speaker 4: far as you're concerned. You know, I wouldn't even got

647
00:32:59,520 --> 00:33:02,600
Speaker 4: a d watter is beyond deep. It's too it's too

648
00:33:02,680 --> 00:33:03,600
Speaker 4: deep for the universe.

649
00:33:04,280 --> 00:33:10,280
Speaker 1: Wow. So ultimately, what do fantastic numbers reveal about the cosmos?

650
00:33:10,320 --> 00:33:12,080
Speaker 1: Like what is the I guess what is the lesson

651
00:33:12,240 --> 00:33:14,800
Speaker 1: of big numbers? Fantastic numbers et cetera.

652
00:33:15,160 --> 00:33:18,000
Speaker 4: So for me, I think all the ideas that I

653
00:33:18,120 --> 00:33:20,600
Speaker 4: talk about in the context of the big numbers in

654
00:33:20,640 --> 00:33:22,600
Speaker 4: the book, they all come back to the same thing

655
00:33:22,640 --> 00:33:25,200
Speaker 4: which we've talked about, which is the holographic truth, the

656
00:33:25,320 --> 00:33:29,200
Speaker 4: idea that a lot of the ideas associated with black

657
00:33:29,240 --> 00:33:32,280
Speaker 4: holes and and how much information you can fit inside

658
00:33:32,280 --> 00:33:35,080
Speaker 4: a black hole. Where that information stored, for example, is

659
00:33:35,120 --> 00:33:37,520
Speaker 4: it stored inside the black hole or is it stored

660
00:33:37,560 --> 00:33:39,600
Speaker 4: on the edge of the black hole? And these are

661
00:33:39,640 --> 00:33:43,880
Speaker 4: ideas which which which leads you to to to the

662
00:33:43,960 --> 00:33:47,040
Speaker 4: to the holographic truth, to the idea that actually, maybe

663
00:33:47,160 --> 00:33:51,120
Speaker 4: the information in our world isn't stored inside the world.

664
00:33:51,160 --> 00:33:53,880
Speaker 4: Maybe it's stored on the boundary of the world, at

665
00:33:53,880 --> 00:33:56,760
Speaker 4: the edge, on the walls that surround it. And in

666
00:33:56,760 --> 00:33:59,920
Speaker 4: that sense, that's why it's it's holographic. All the ideas,

667
00:34:00,080 --> 00:34:02,080
Speaker 4: all the limits that we're talking about, you know, counting

668
00:34:02,400 --> 00:34:04,880
Speaker 4: how much information you can store in a head, you know,

669
00:34:05,560 --> 00:34:07,360
Speaker 4: and when it's going to turn into a black hole,

670
00:34:07,720 --> 00:34:10,320
Speaker 4: you know, counting how long it takes for our universe

671
00:34:10,360 --> 00:34:12,880
Speaker 4: to reset it up. All these ideas come back to

672
00:34:12,920 --> 00:34:16,680
Speaker 4: the question of how our universe stores its information. Does

673
00:34:16,680 --> 00:34:18,560
Speaker 4: it store it inside, and if so, how does it

674
00:34:18,600 --> 00:34:21,479
Speaker 4: store it? Well, actually, no, it turns out it's seem

675
00:34:21,600 --> 00:34:24,040
Speaker 4: like it stores it on the edge of space, and

676
00:34:24,080 --> 00:34:26,319
Speaker 4: that allows you to count how much information there is

677
00:34:26,400 --> 00:34:28,359
Speaker 4: in that space and how many different ways you can

678
00:34:28,360 --> 00:34:31,160
Speaker 4: combine things. But it all comes back to that holographic truth.

679
00:34:32,239 --> 00:34:35,520
Speaker 1: I have to ask about this because I, again most

680
00:34:35,920 --> 00:34:40,200
Speaker 1: I'm not as versed in mathematics. There's a lot of

681
00:34:40,200 --> 00:34:41,880
Speaker 1: people out there, and one of the things that I

682
00:34:42,000 --> 00:34:46,399
Speaker 1: kept thinking about reading the book was just a one

683
00:34:46,520 --> 00:34:49,520
Speaker 1: quick joke from the season one episode of the British

684
00:34:49,560 --> 00:34:53,400
Speaker 1: comedy look Around You, in which the narrator the episode

685
00:34:53,440 --> 00:34:56,200
Speaker 1: is about math, and the narrator tells us that the

686
00:34:56,239 --> 00:34:59,279
Speaker 1: largest known number is around forty five million, but the

687
00:34:59,480 --> 00:35:02,960
Speaker 1: larger numb umbers might exist, and they like speculate forty

688
00:35:02,960 --> 00:35:06,600
Speaker 1: five million in one could be an number, and you know,

689
00:35:06,640 --> 00:35:09,799
Speaker 1: of course that's absurd, and that's absurd ast humor. But

690
00:35:11,120 --> 00:35:13,480
Speaker 1: there's something about that that seems to sort of ring

691
00:35:13,600 --> 00:35:18,160
Speaker 1: true with a lot of these these concepts, and I

692
00:35:18,200 --> 00:35:20,799
Speaker 1: was wondering what you thought about the role of absurdity

693
00:35:21,280 --> 00:35:22,960
Speaker 1: in contemplating big numbers.

694
00:35:23,320 --> 00:35:26,080
Speaker 4: Yeah, absolutely, no, I really do think so. When you

695
00:35:26,120 --> 00:35:30,160
Speaker 4: think of something like three three, at least within our universe,

696
00:35:30,800 --> 00:35:33,239
Speaker 4: you can't fit it in. It cannot fit in. There's

697
00:35:33,320 --> 00:35:36,120
Speaker 4: nothing that could, you know, you could describe, because it's

698
00:35:36,320 --> 00:35:38,480
Speaker 4: just too big for anything that we can talk about

699
00:35:38,480 --> 00:35:42,040
Speaker 4: in our universe. Now, you might imagine other universes which

700
00:35:42,080 --> 00:35:44,879
Speaker 4: could accommodate it, and in a you know, a sort

701
00:35:44,880 --> 00:35:47,560
Speaker 4: of multiverse scenario, like maybe you get from something like

702
00:35:47,600 --> 00:35:51,880
Speaker 4: string theory, could you get universes that can contain tree three.

703
00:35:52,640 --> 00:35:55,680
Speaker 4: Well maybe we don't know, right, we don't know enough

704
00:35:55,680 --> 00:35:58,440
Speaker 4: about about the multiverse of string theory, but it's not

705
00:35:58,520 --> 00:36:02,520
Speaker 4: inconceivable potentially so, but certainly in our world you can't.

706
00:36:02,760 --> 00:36:04,760
Speaker 4: It's interesting. One of the things I did a video

707
00:36:04,960 --> 00:36:08,360
Speaker 4: quite quite recently actually about the biggest number that nobody

708
00:36:08,400 --> 00:36:10,920
Speaker 4: will ever think of. And I did these sort of

709
00:36:11,000 --> 00:36:14,960
Speaker 4: quite a bunch of estimates based on a bunch of

710
00:36:15,080 --> 00:36:19,080
Speaker 4: dubious sort of you know, sort of assumptions, which I

711
00:36:19,160 --> 00:36:21,560
Speaker 4: acknowledge with quite jubious, But I think I came up

712
00:36:21,560 --> 00:36:23,560
Speaker 4: with an estimate that if you think of a random

713
00:36:23,800 --> 00:36:29,560
Speaker 4: seventy three digit number, also something of that order, then

714
00:36:29,640 --> 00:36:33,279
Speaker 4: probably nobody's going to ever ever think of it. Other

715
00:36:33,360 --> 00:36:35,719
Speaker 4: than you. I mean, you know, so, I'm not saying

716
00:36:35,760 --> 00:36:38,319
Speaker 4: I just think of a one followed by seventy two zero.

717
00:36:38,360 --> 00:36:40,640
Speaker 4: It's clearly not something like that, but just completely random,

718
00:36:41,080 --> 00:36:45,319
Speaker 4: random seventy two to seventy three digit numbers something like that.

719
00:36:45,719 --> 00:36:49,120
Speaker 4: Chances are nobody in the history of humanity, either before

720
00:36:49,640 --> 00:36:52,839
Speaker 4: or to come, we'll ever think of that number. And

721
00:36:52,880 --> 00:36:54,600
Speaker 4: it's kind of that's kind of mind blowing. I think

722
00:36:54,600 --> 00:36:56,080
Speaker 4: it's kind of yours. Just think of it, and that's

723
00:36:56,080 --> 00:36:59,040
Speaker 4: yours forever. So just everybody should just write down a

724
00:36:59,080 --> 00:37:01,640
Speaker 4: seventy three digit numb and name after themselves.

725
00:37:03,520 --> 00:37:07,239
Speaker 1: Well that's wonderful. Well, Tony, thanks for taking time out

726
00:37:07,239 --> 00:37:09,000
Speaker 1: of your day to chat with us. I want to

727
00:37:09,000 --> 00:37:13,360
Speaker 1: make sure we're hitting all the plugs here. The book

728
00:37:13,560 --> 00:37:16,280
Speaker 1: Which Which is? Which? Is out? I believe it's out now? Correct?

729
00:37:16,600 --> 00:37:19,400
Speaker 4: Yeah? Yeah, it's actually released today in the US. I

730
00:37:19,400 --> 00:37:21,839
Speaker 4: probably should say today, should I?

731
00:37:21,840 --> 00:37:24,080
Speaker 1: I guess it'll be. It will have been released two

732
00:37:24,160 --> 00:37:26,759
Speaker 1: days ago when we published this, So yeah, it's it's out.

733
00:37:26,880 --> 00:37:30,160
Speaker 1: It's fantastic numbers and where to find them? And then

734
00:37:30,360 --> 00:37:33,080
Speaker 1: the YouTube series is number file, correct?

735
00:37:33,400 --> 00:37:35,439
Speaker 4: Yeah? So I appear on number File. There's another channel.

736
00:37:35,480 --> 00:37:38,200
Speaker 4: I appear on which is more physics based called sixty Symbols.

737
00:37:39,120 --> 00:37:42,160
Speaker 4: So they're both made by by Brady Harran. And yeah,

738
00:37:42,239 --> 00:37:44,799
Speaker 4: so I appear regularly on both of those. So it's

739
00:37:45,000 --> 00:37:47,960
Speaker 4: a lot of fun. But yeah, it's I hope people

740
00:37:48,080 --> 00:37:51,520
Speaker 4: enjoy enjoy the book. It's and I just don't think

741
00:37:52,360 --> 00:37:55,040
Speaker 4: too recklessly about Grahams number because you going to have.

742
00:37:55,760 --> 00:37:59,800
Speaker 1: Yeah, we don't want anybody's heads to collapse into black holes.

743
00:38:00,040 --> 00:38:00,600
Speaker 4: Absolutely.

744
00:38:01,400 --> 00:38:04,080
Speaker 1: All right, Well, thanks for coming on the show. I

745
00:38:04,120 --> 00:38:08,520
Speaker 1: hope you have a great day, Thanks Chub. All right, well,

746
00:38:08,560 --> 00:38:10,600
Speaker 1: thanks once again to Tony for taking time out of

747
00:38:10,640 --> 00:38:12,399
Speaker 1: his day to chat with me here. The book again

748
00:38:12,480 --> 00:38:16,120
Speaker 1: is Fantastic Numbers and Where to Find Them. Highly recommend

749
00:38:16,120 --> 00:38:18,520
Speaker 1: it for anyone who is at all intrigued by what

750
00:38:18,560 --> 00:38:21,960
Speaker 1: we were talking about here today. As always, if you

751
00:38:22,000 --> 00:38:25,440
Speaker 1: want to reach out to us and ask any questions,

752
00:38:25,440 --> 00:38:30,080
Speaker 1: share your relationship with Fantastic Numbers, well, you can find

753
00:38:30,160 --> 00:38:32,640
Speaker 1: us in a number of ways. Let's see if you

754
00:38:32,719 --> 00:38:34,600
Speaker 1: email us and I'll give you that email in a second.

755
00:38:34,719 --> 00:38:38,040
Speaker 1: You can have access to the discord where you can

756
00:38:38,080 --> 00:38:42,719
Speaker 1: discuss show matters with other stuff to blow your mind listeners.

757
00:38:43,080 --> 00:38:46,600
Speaker 1: There's also the Stuff to Blow Your Mind discussion module

758
00:38:46,680 --> 00:38:49,480
Speaker 1: that is on Facebook. You can find that and seek

759
00:38:49,560 --> 00:38:51,920
Speaker 1: access to that as well. And of course, thanks as

760
00:38:51,960 --> 00:38:55,800
Speaker 1: always to Seth Nichols Johnson for producing the show here

761
00:38:55,960 --> 00:38:57,680
Speaker 1: and yeah, if you want to get in touch with us,

762
00:38:57,760 --> 00:39:01,000
Speaker 1: you can simply email us at content Act. It's Stuff

763
00:39:01,040 --> 00:39:10,080
Speaker 1: to Blow your Mind dot com.

764
00:39:10,080 --> 00:39:13,040
Speaker 3: Stuff to Blow Your Mind is production of iHeartRadio. For

765
00:39:13,120 --> 00:39:16,960
Speaker 3: more podcasts from iHeartRadio, visit the iHeartRadio app, Apple Podcasts,

766
00:39:17,040 --> 00:39:33,040
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