(Finite) Numbers So Large They'd Destroy You

It starts as a friendly challenge: who can name the biggest number? The only rule? Infinity doesn’t count. What follows is a journey through the biggest finite numbers ever imagined. From Archimedes’ grains of sand to Graham’s Number, a sequence so vast it stretches the limits of human comprehension, Professor Hannah Fry and Michael Stevens tumble through this strange landscape of scale, tracing how mathematicians have pushed counting to its absolute edge. But beyond vast calculations, perhaps this is less about numbers and more about us. Why do humans push at the limits of finitude at all? How do we represent the biggest numbers in existence? Why can’t our brains feel the difference between a million, a billion, and a trillion? And when do big numbers affect our ability to empathise with others? ------------------- For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit ⁠⁠https://cancerresearchuk.org/restisscience⁠⁠ Cancer Research UK is a registered charity in England and Wales (1089464), Scotland (SC041666), the Isle of Man (1103) and Jersey (247). A company limited by guarantee. Registered company in England and Wales (4325234) and the Isle of Man (5713F). Registered address: 2 Redman Place, London, E20 1JQ. ------------------- Find The Rest Is Science all over the internet by ⁠⁠clicking here.⁠⁠ ------------------- Video Producer: Adam Thornton + Oli Oakley Video & Social: Bex Tyrrell Assistant Producer: Imee Marriott Senior Producer: Lauren Armstrong-Carter Head Of Digital: Samuel Oakley Exec Producer: Neil Fearn Learn more about your ad choices. Visit podcastchoices.com/adchoices

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Hannah Fry?

  Hello, welcome to The Rest of Science. I'm Hannah Fry.

• 0:03Michael Stevens?

  And I am Michael Stevens. Today, we're gonna play a game, Hannah and I. Who can name the biggest number?

• 0:09Hannah Fry?

  Infinity.

• 0:10Michael Stevens?

  Infinity not allowed.

• 0:12Hannah Fry?

  Okay, finite numbers only.

• 0:14Michael Stevens?

  Finite numbers only. Only a number that if you had enough time, you could count to and be done, and then move on to something else.

• 0:21Hannah Fry?

  All right, well, I mean, that seems like quite simple rules. No infinity.

• 0:27Michael Stevens?

  No, infinity is too easy. There are different sizes of infinity, and we will cover them soon. But what is almost more terrifying to me, to be honest, are just large, finite numbers. Numbers that you could count to if you lived forever, you'd reach the end, but yet their magnitude is beyond incomprehensible. Hey, but first, let's address the jellyfish in the room.

• 0:51Hannah Fry?

  Okay, go on. What's the... Is it a jellyfish on your plaster? Is that your daughter's plaster?

• 0:56Michael Stevens?

  Yeah, it's the only Band-Aids I have. Like, I'm a grown man. I... Actually, I shouldn't say that. I don't know anything about grown men. I know about myself, and I don't use Band-Aids very often. But yesterday, I walked into a tree branch. And that sounds fake, but the truth is that I was just like walking across a parking lot. I thought, oh, I'll stay on the crosswalk. And I turned and went right into this low tree branch. And luckily, there's no welt or bump, but it scraped the skin.

• 1:28Michael Stevens?

  So I actually just went home. I'm like, I can't walk into the store with a bloody head wound. Like, that would be...

• 1:38Hannah Fry?

  If it was a pharmacy, you're probably all right. But, um, but yeah.

• 1:41Michael Stevens?

  Better work not a pharmacy, it was a hardware store. It would look like, sir, I think before you buy anything else here, you need to maybe get a hard hat or something.

• 1:50Hannah Fry?

  We need a little chat with you about health and safety.

• 1:52Michael Stevens?

  So I wore a hat yesterday because I was embarrassed, but I just, especially on the show, I want to be a good role model for the baldies out there.

• 2:01Hannah Fry?

  Yeah.

• 2:01Michael Stevens?

  You know, I'm not ashamed, you know? Flaunt what your momma gave you. That's what I do. And my mom gave me this. Baldness comes from the maternal inheritance.

• 2:12Hannah Fry?

  How old were you when it went?

• 2:14Michael Stevens?

  I'd say about 17.

• 2:16Hannah Fry?

  Oh, that is young.

• 2:17Michael Stevens?

  That's when, that's when people were like, wow, your hairline is really high. And I'm like, yeah. And then by college, it was here. And now it doesn't exist. It just, it never, it's just empty. But I've got the side. I've got the sides.

• 2:33Hannah Fry?

  Yeah.

• 2:34Michael Stevens?

  They keep me a little bit warm.

• 2:36Hannah Fry?

  Just where, where you need it. Okay, you ready for our game?

• 2:39Michael Stevens?

  Yeah, enough about my head. Okay, let's talk about numbers. Can I start?

• 2:43Hannah Fry?

  Go on then.

• 2:49Hannah Fry?

  This episode is brought to you by Cancer Research UK.

• 2:52Michael Stevens?

  So when most people think of naked mole rats, their unusual relationship to cancer probably isn't the first thing that comes to mind.

• 2:59Hannah Fry?

  But maybe it should be because it is incredibly rare for them to develop cancer, which could be partly down to their unique immune system, or it might be the way that their cells respond to damage.

• 3:12Michael Stevens?

  So scientists are studying their biology for its cancer fighting secrets. It's a reminder that discoveries can sometimes come from places you don't expect.

• 3:20Hannah Fry?

  Cancer Research UK is the world's largest charitable funder of cancer research. Thousands of scientists and doctors and nurses work across more than 20 countries to help turn discoveries in the lab into new tests, new treatments and new innovations.

• 3:36Michael Stevens?

  And the impact is clear. Over the past 50 years, the charity's pioneering work has helped double cancer survival in the UK, meaning more people living longer, better lives, free from the fear of cancer.

• 3:49Hannah Fry?

  For more information about Cancer Research UK, their research, their breakthroughs, and how you can support them, visit cancerresearchuk.org/restiscience.

• 3:58Speaker 02

  Observe the North American dad. 50s, great polo collection. He enters his vehicle information on Carvana. An offer appears in minutes. Remarkable. He squints, reads it again, smiles and says, dang, that's a good offer. The highest form of approval. No haggling, no hassle. No one called him boss. He's still on the couch. Astonishing. Sell your car today on carvana.com. Pickup fees may apply.

• 4:30Speaker 03

  This episode is brought to you by Google Chrome. You think you know a browser, but Gemini and Chrome? That's new. It can help you with practically anything on the web, like restoring a vintage motorcycle from a 50-page restoration blog, or finally break down that long article you've had open for weeks. Gemini and Chrome is here for it. Ready to make anything online make sense? There's no place like Chrome. Check responses set up required. Compatibility and availability varies 18 plus.

• 5:00Michael Stevens?

  Remember that the game is to name the largest finite number. I would say that finite is a number that you can count to, given enough time.

• 5:13Hannah Fry?

  Yeah, one that eventually stops.

• 5:16Michael Stevens?

  It eventually stops. And that that excludes any kind of infinity, because infinity isn't some number that you reach. It is the act of never stopping.

• 5:28Hannah Fry?

  I mean, there's a bit of a debate about whether infinity is a number at all, rather just a concept or a collection of concepts. But this is not an episode on infinity. We're going to do that later in glorious, weird detail. Right, let's start with the biggest number. The biggest number you can think of.

• 5:44Michael Stevens?

  The biggest number? I think we should start with eight. It's pretty big in some ways.

• 5:54Hannah Fry?

  Sure.

• 5:55Michael Stevens?

  And let me justify why I'm starting at eight. It's famously been found that the most chunks of information a person can store in their short-term memory is seven.

• 6:06Hannah Fry?

  Really?

• 6:07Michael Stevens?

  Yeah, it's literally from like the most cited psychology paper ever. And it was a study of like, how many words or things or like meaningful chunks can a person keep in their head right away, short term? You'd give someone a list of like, a grocery list. Banana, eggs, butter, blah, blah, blah. Seven, they can do. But eight, it's like just across cultures, across, not quite across ages. We're mainly talking here about like...

• 6:35Michael Stevens?

  Younger adults. Seven was the max.

• 6:38Hannah Fry?

  But wait, was seven the max or seven was the average? Cause

• 6:42Michael Stevens?

  I'm sorry.

• 6:43Hannah Fry?

  I don't like to big myself up here, but I think I could, I think I could beat seven. But mostly because I'd be using like memory techniques.

• 6:49Michael Stevens?

  Thank you. I take that back. Seven was the average.

• 6:51Hannah Fry?

  Okay, okay. All right. So we're going eight.

• 6:54Michael Stevens?

  But it's an average that doesn't have a whole lot of skew. Like it's not like there's long tails in either direction. It's kind of like everyone's pretty close. There, there aren't like a lot of people who can do twenty five.

• 7:09Hannah Fry?

  Yeah.

• 7:10Michael Stevens?

  And there aren't a lot of people who could only do two.

• 7:13Hannah Fry?

  Eight's more than you can hold in your head supposedly. I sort of want to test you.

• 7:17Michael Stevens?

  You want to test me?

• 7:18Hannah Fry?

  Yeah, I do. I do want to test you because I think that you, um, I've seen you memorize scripts before. And I think, I think, um, I think you might be better at memorizing eight. All right. Oranges. Coffee.

• 7:34Hannah Fry?

  Um, squirrels, uh, mushrooms. Um.

• 7:43Hannah Fry?

  Cards, uh, teaspoons, pins.

• 7:50Hannah Fry?

  Strawberries. How many was that?

• 7:53Michael Stevens?

  I don't know. I'll just say them back. We've got coffee, oranges and teaspoons, squirrels and mushrooms and pins and cards.

• 8:02Hannah Fry?

  There wasn't pens.

• 8:04Michael Stevens?

  Was it pins?

• 8:05Hannah Fry?

  Pins, you're right. Sorry. You're right. You're right. Like just does the, an accent thing.

• 8:09Michael Stevens?

  I did a bit of, a bit of a like painting a picture. You know, I put the teaspoon in the coffee cup.

• 8:14Hannah Fry?

  Yeah.

• 8:15Michael Stevens?

  I had the squirrel live in a mushroom house.

• 8:18Hannah Fry?

  Nice.

• 8:20Michael Stevens?

  So I was cheating, using some ancient techniques. Okay, here we go.

• 8:24Hannah Fry?

  Come.

• 8:26Michael Stevens?

  Ketchup, justice, green, tomorrow, tetrahedron, bicycle. Haircut, irony, third.

• 8:41Hannah Fry?

  Okay. All right. Um, justice, ketchup, green, irony, tomorrow, third, tetrahedron.

• 8:55Hannah Fry?

  I'm missing one.

• 8:56Michael Stevens?

  You're missing two.

• 8:57Hannah Fry?

  Oh, damn.

• 9:00Hannah Fry?

  How many did I get?

• 9:01Michael Stevens?

  You got seven. You got exactly seven. There's the list. You missed bicycle and haircut, which we've also demonstrated two other really famous psychological phenomena, which are that people tend to remember the first and last parts of lists, but not the middle.

• 9:18Hannah Fry?

  Wow, there you go.

• 9:20Michael Stevens?

  There you go.

• 9:21Hannah Fry?

  Okay, talking of lists of words, here's a number for you. Hundred eighty thousand. That's that's apparently the number of words in the English language.

• 9:29Michael Stevens?

  A hundred and eighty thousand words in our language. That's a lot more than eight.

• 9:33Hannah Fry?

  I it is. Look, we're getting there. We're getting bigger and bigger as we go.

• 9:37Michael Stevens?

  How many words do you think you know?

• 9:42Hannah Fry?

  Not a hundred eighty thousand, that's for sure.

• 9:45Michael Stevens?

  Yeah, no, same here. And what if there's a test that can be done? I'm sure it wouldn't be like a hundred eighty words are shown and you say you define it or not. I think it'd be like, we'll test you on like a thousand. And from there, we can extrapolate how much of the language you know. I would love to know that.

• 10:03Hannah Fry?

  I want to know how many the average adult knows.

• 10:05Michael Stevens?

  I'm going to guess about like eighty thousand.

• 10:08Hannah Fry?

  Wow, okay. The average native English speaker actually knows between twenty and thirty five thousand words.

• 10:15Michael Stevens?

  Twenty and thirty five thousand.

• 10:16Hannah Fry?

  Yeah.

• 10:17Michael Stevens?

  And you only need about ten thousand to have conversations. So we're all doubly prepared.

• 10:23Hannah Fry?

  I mean, that doesn't seem like very many.

• 10:25Michael Stevens?

  It doesn't seem like very many, but why doesn't it? Because it is a lot, like it's that's a lot. Twenty to thirty five thousand. Um, I guess it feels like compared to like the amounts of money we read about in the news, it doesn't sound like a big number.

• 10:40Hannah Fry?

  It doesn't feel like a very big number.

• 10:42Michael Stevens?

  I would love, we should do this someday, maybe not like on a podcast, but we should just sit down and list every word we can think of. Could you could you list thirty five thousand words in one sitting? Just like, oh, let's see, have I done, have I done, uh, yesterday? Uh, yeah, I did. Shoot.

• 10:59Hannah Fry?

  Uh, I mean, the cheats way would just be to start off with the word one and then go two and then go three.

• 11:04Michael Stevens?

  Oh, no, of course. Does that count, though?

• 11:08Hannah Fry?

  No, of course. Compound words is cheating.

• 11:11Michael Stevens?

  By constructing number names, you can go way past thirty five thousand. How about thirty five thousand and one?

• 11:16Hannah Fry?

  Hmm, exactly. Okay, bigger numbers, bigger numbers still.

• 11:20Michael Stevens?

  I got one, I got one. Um, that's gonna way, way beat your hundred eighty thousand. And this is going off script, so you better be ready.

• 11:27Hannah Fry?

  Go on.

• 11:27Michael Stevens?

  I was, I was just looking this up, uh, last night. One billion.

• 11:32Hannah Fry?

  That's, that is, that, that's a, that's a big number.

• 11:36Michael Stevens?

  That's a big number. And here's what's special about one billion.

• 11:40Hannah Fry?

  Yeah.

• 11:40Michael Stevens?

  That, that, that kind of put, puts us up against another limit. One billion is about how many heartbeats anything gets in its life.

• 11:51Hannah Fry?

  Oh, that's a beautifully poetic idea. Because of course, if you're a teeny tiny mouse, your heart beats faster, but your life is shorter.

• 11:59Michael Stevens?

  That's right. And if you're a human, you know, heart rate does correlate with longevity. Really, fast heart rate is not great. Um, I mean, a really slow one isn't great either. But, uh, in general, um, we find that, yeah, faster heart rates are found in animals that don't live as long. Animals that live a long time, turtles, slow heart rate. And so when you do the math, it equals out and we all get around a billion. Plus or minus a billion, like chickens get about two billion. But today's chickens are quite engineered for our pleasure.

• 12:35Hannah Fry?

  A factor of two. I'm not, I don't care about a factor of two. If it's one billion plus one billion, I'm fine with that. That's still about a billion.

• 12:41Michael Stevens?

  It's, it's within an order of magnitude and it's kind of, it's kind of, yeah, almost too poetic. Like, we each get a billion, whether you're tall or short, a mouse or a whale, here's your billion, do what you want with it.

• 12:56Hannah Fry?

  Hmm. Have the best life possible. I like the idea that there's some sort of quota. I sort of think that about words sometimes, that there is actually a set number of words that I will speak in my entire lifetime. Um, and, uh, all I've got to do is work out the order of them.

• 13:12Michael Stevens?

  That's right. You've got them all in a bag. Now, you can build whatever you want with them.

• 13:16Hannah Fry?

  Yeah, yeah. Um, the one number that comes up a lot, actually, when you're talking about big numbers is, I don't know, like the number of stars in the galaxy.

• 13:24Michael Stevens?

  Right.

• 13:25Hannah Fry?

  Which is actually. Sort of not that big. It's about a hundred billion, somewhere between a hundred billion and four hundred billion.

• 13:32Michael Stevens?

  Okay, we're getting, we're, I love that we keep getting bigger and bigger. This is like very fun. Okay, so a hundred billion stars, that's a hundred times more than I'm gonna get to have heartbeats.

• 13:41Hannah Fry?

  But not as high as the number of trees on earth, which is three trillion. That's, I mean, that's a whole order of magnitude bigger.

• 13:48Michael Stevens?

  Isn't that cool? I've talked about that before in videos because it's just, it's so surprising.

• 13:56Michael Stevens?

  And it's also poetic because it's like, you know what, outer spaceman, like, grow up. We've got more trees here than our entire galaxy has. And like, that makes me really proud to be an Earthling.

• 14:07Hannah Fry?

  Yeah.

• 14:08Michael Stevens?

  Three to four trillion trees, Hannah.

• 14:11Hannah Fry?

  The other one that comes up quite a lot is the number of grains of sand. That's something that people, uh, people like to use as a big number.

• 14:18Michael Stevens?

  Oh, yeah. You know what? And I actually calculated some things about grains of sand. Like grains of sand comes up all the time when you're reading about big numbers or the history of mathematics. Because of Archimedes' little paper. Did they call them papers back then? A treatise? What do you, what do you call a thing that's written 2,000 years ago that's eight pages long?

• 14:42Hannah Fry?

  A treatise. I think a treatise.

• 14:43Michael Stevens?

  A treatise?

• 14:44Hannah Fry?

  Yeah.

• 14:44Michael Stevens?

  Yeah. Okay, we're speaking, of course, about the sand reckoner. And I'm sure we're both pretty familiar with it, but for the audience out there, it's a cool story. Basically, it feels like back in Archimedes' time, which was like the third century B.C. Okay, the 300 to 200 B.C. area, there was this, probably like an idiom that like, you, you could not even name the number of grains of sand on earth. Because in their numbering system, a myriad was the biggest, which is 10,000.

• 15:17Michael Stevens?

  There weren't names for numbers above 10,000. So the number of grains of sand on the entire planet, come on. A mathematician could never even come up with a name or a symbol for that number that that made sense and followed a system. And what Archimedes did in the Sand reckoner was he said, I bet I can. In fact, I did. I can name you numbers and give you ways to reach them that surpass the number of grains of sand on Earth. And in fact, surpass the number of grains of sand that would fit in the universe.

• 15:52Hannah Fry?

  Because this is the thing, it's like there's the sort of separation of the number of things, number of actual objects, right? Because that that obviously exists. It was more that like the the way of naming them, the ability of maths stopped. There was like not a finite number in the sense of of objects, but there was a finite limit to what maths could do.

• 16:16Michael Stevens?

  Yes, that is such an important pivot point in mathematical history. The like, we can count things. But using math and language, we can go beyond what can be counted or what we can even imagine there being. Because the universe is not full of grains of sand. And yet, if it were, Archimedes calculated that it would contain about 10 to the 63 grains of sand. That's a one followed by 63 zeros.

• 16:45Hannah Fry?

  He did something quite clever, actually, to get there. Because you had myriad, 10,000, as you say. And they would have myriads of myriads. So like 10,000, 10,000s, as it were.

• 16:57Michael Stevens?

  Sure.

• 16:58Hannah Fry?

  But but the way that he got there was he was sort of saying, okay, well, imagine you've got a myriad of myriads. And then you sort of put that in a box. And now you get a myriad of myriads of those boxes. So he was sort of kind of raising numbers to to powers before that stuff had been existed. Remember, zero wasn't even a thing at this point, right? I mean, the Romans who came after were still using their silly numerals, right? The the way that they counted stuff, they did not have this easy decimal, you know, positional system that we have at the moment.

• 17:34Michael Stevens?

  I know. And so I recommend that you go and read it. It's only, like I said, eight pages long. And it's fun because it does feel like an early viral YouTube educational video, you know? Because he's like, okay, guys, like, I'm gonna try to do this. And, you know, you could read some other little things that have been written about it. But like, I'm gonna guess that the, the, the distant stars are as far away from the sun as the, I don't remember all the ratios, but he had to make a lot of assumptions about how big a grain of sand was and how, how many Greek stadiums could fit inside the universe. And he always tried to overestimate, so he could be like, this is an upper bound. Like, the real number will be smaller, but that's fine, because I'm trying to show you

• 18:18Michael Stevens?

  that I can think of some big numbers.

• 18:20Hannah Fry?

  Yeah. He also, I mean, the, the actual universe itself, there was, this is before they even decided that the, that the sun was the center of the solar system, let alone the universe, right?

• 18:33Michael Stevens?

  I know. And that's what's also, I think, so important about being familiar with the sand reckoner. It's that Archimedes went ahead and assumed that the sun was the center of the solar system. So when you have this whole, like, oh, we all thought that the earth was the middle until recently, it's like, no, in 300 B.C., in the 200 B.C., like, some guy was like, well, obviously, the sun's in the middle, we go around it. Anyway, 10 to the 63 is a really big number. That's how many grains of sand Archimedes calculated could fill the universe as he knew it. We know the same universe, we see the same distant stars. I mean, we can see actually further because of telescopes, but the number of grains of sand I calculated, this will help us go even higher, that could actually fill

• 19:15Michael Stevens?

  the observable universe is more like three or four times 10 to the 85.

• 19:21Hannah Fry?

  Oh, okay. Because the number of particles in the observable, observable universe is 10 to the 80, which on the surface sounds like quite similar numbers. 10 to the 80, 10 to the 85, sound quite similar. But when you get to the number of particles, you're, you've still got, what is it, 100, 10 to the 5 to go, 100,000 to go. You need to do that 100,000 times over.

• 19:47Michael Stevens?

  Yeah, yeah. And I, so I guess the number of particles is smaller, because particles do not pack the universe. But, but the sand in our example does.

• 19:56Hannah Fry?

  And then, of course, because this is a very early version of a YouTube educational video, at the end of the sand reckoner, Archimedes says, if you enjoyed that content, please hit that like button and subscribe, right? Yeah.

• 20:08Michael Stevens?

  Well, actually, he, he, he does, but then he finishes with box for box. Because this was old YouTube, you know, this was a long time ago. And he was like, oh, and click here on this annotation to watch Leave Britney Alone.

• 20:25Michael Stevens?

  No, but it's really fun. And it was not the largest number we found in ancient texts. There are Indian and Chinese texts that come up with names for even larger numbers.

• 20:37Hannah Fry?

  There's, there's a few different stories, but I think one of my favorites is the future Buddha. This is Prince Siddhartha, and he wanted to marry this really beautiful princess Gopala. But her father was like, I'm not sure about this guy. I'm not sure about this kid. This is sort of this pampered prince. He's never done a day's work in his life. Is he actually capable of doing anything? And so to win her hand, the challenge was set that he had to compete against other suitors in like all of the manly stuff. So archery, wrestling and arithmetic. That was, that was the main role. And it came down to this showdown between him and this mathematician who was called Arjuna.

• 21:18Hannah Fry?

  And Arjuna tries to sum the prince and he's like, okay, do you know any numbers beyond the koti? Which, and a koti was, was 10 million, right? Siddhartha doesn't just say yes. He, he basically on the spot, supposedly how this is how the story goes, starts to construct this numerical system that is so incredibly complex that it makes everybody's head spin. He comes up, he starts counting essentially in multiples of 10. So he has the koti, which is 10 million. Then he has the ayuta, which is a billion, then the nayuta, which is 100 billion. And it keeps going, keeps going, keeps going until he comes up with the talakshana, which is 10 to the 53. And he doesn't stop there. He then like enters this second numbering system,

• 22:03Hannah Fry?

  goes through more tiers and more tiers. He's sort of, it's not that you're multiplying by numbers. You're adding additional zeros on the top, right? So you're, you're kind of using an exponent is what the mathematicians would say. And then eventually he gets to a number that is one followed by 421 zeros. This is known as Buddha's number. And it's so big that if you turned every single particle in the universe into another universe and counted all of the particles in those universes, you would still be nowhere near this number. And I mean, in conclusion. He won the math battle. He got the girl.

• 22:42Michael Stevens?

  Deservedly.

• 22:43Hannah Fry?

  Deservedly. That would be me, I've got to be honest.

• 22:46Michael Stevens?

  A one followed by more than 400 zeros, we've gone past a googol.

• 22:51Hannah Fry?

  We have.

• 22:52Michael Stevens?

  We had gone, we as a species went past a googol long before the Greeks.

• 22:56Hannah Fry?

  Yeah, yeah.

• 22:58Michael Stevens?

  Long before google.com, the search engine.

• 23:00Hannah Fry?

  Google, by the way, is a one followed by 100 zeros, sort of like a nice, neat, cute little number. Quite small, actually, in comparison to what we're describing here.

• 23:10Michael Stevens?

  Speaking of nice round numbers, 10 to the 100, which is a one followed by 100 zeros is a googol. A one followed by 200 zeros is called a gar googol.

• 23:21Hannah Fry?

  Is it?

• 23:22Michael Stevens?

  Yeah, there's a whole field of naming big numbers called googolology. And it's pretty fun. If you're ever like trying to go to sleep and or you can't sleep, just look up names of big numbers. And everyone's like, we need to agree on these so that they become official.

• 23:36Hannah Fry?

  Hmm. Gaskillian, yeah, has not, has not, uh.

• 23:40Michael Stevens?

  It's that.

• 23:42Hannah Fry?

  It's one that, you know, you sort of say in joke, it's never, it's, it hasn't yet been adopted as an official number, but I'm, I'm, I'm holding out hope for it. Thing is, up until this point, though, all of these stories are essentially people trying to come up with names for big numbers. And it's like, let's just make a name for it. But these numbers don't actually really relate to very much, apart from maybe these theoretical ideas of the number of grains of sand in the universe. There are very real objects and very real situations in which you do reach these unfathomably large numbers, right? Anytime that you're dealing with a combination of something. I'm teeing you up here, Michael.

• 24:22Michael Stevens?

  You're teeing me up, yeah. What a perfect tee up for me to share one of my favorite little factoids. I talked about this in a video many years ago, and it's the scale of 52 factorial. Written as 52 with an exclamation point after it, and that simply means mathematically. Every number from one to fifty-two, every integer, from one to fifty-two multiplied together. So one times two times three times four times five, all the way up to fifty-two, which is the number of cards in a deck of cards. And in probability theory, fifty-two factorial is also the number of ways you can arrange fifty-two cards uniquely, where the arrangement means something like the top card is the ace of spades, the next one is the two of spades, and so on, right? You could do that.

• 25:06Michael Stevens?

  You could also put the king of hearts at the top and change nothing else, and that's a whole new order. How many of these unique orders are there? There are fifty-two factorial. And fifty-two factorial, I think, is a great place for us to start talking about how inconceivable the sizes of these numbers are. Because you mentioned that the number of particles in the universe is a one followed by about eighty zeros. Well, fifty-two factorial is an eight followed by sixty-seven zeros. These visualizations of fifty-two factorial came from Scott Cheepeal, and they scare me to think about. All right, so set a timer for fifty-two factorial seconds.

• 25:51Michael Stevens?

  And do this at the equator, standing on the equator of Earth. Just stand there, start the timer, and do nothing. Let it go and wait a billion years.

• 26:03Michael Stevens?

  After a billion years have passed, take one step forward.

• 26:08Michael Stevens?

  Let's say you're traveling east. Fine. And also, you can walk on water. Anyway, wait another billion years. The clock is running this entire time. You wait another billion years, and you take another step.

• 26:20Hannah Fry?

  Hold on, we're going here for one second represents one unique order that a deck of cards can be in.

• 26:29Michael Stevens?

  That's right. That's right.

• 26:30Hannah Fry?

  Okay, we've already got to a billion years.

• 26:33Michael Stevens?

  Yeah, we've already passed. A billion years have to pass before you even do anything. You take one step around the equator every billion years. By the time you have walked all the way around the Earth, take one drop of water out of the Pacific Ocean and set it aside.

• 26:54Michael Stevens?

  And again, you wait a billion years to take one more step. Once you've gone all the way around the world again, you take one more drop, a single drop out of the Pacific Ocean, and you keep this up until the Pacific Ocean is empty. And at that point, you place a sheet of paper on the ground, and you refill the Pacific Ocean, and you keep waiting a billion years for each step. After you've gone all the way around again, um, you know, you take one drop out. This whole process continues until the Pacific Ocean is empty again, and you put a second piece of paper on the ground. By the time the stack of paper reaches the sun,

• 27:38Michael Stevens?

  there will still be eight times 10 to the 67 seconds left.

• 27:42Hannah Fry?

  What?

• 27:44Michael Stevens?

  If you put all the paper away, you start the whole process again, and you do this whole process of walking around the Earth, one step every billion years, taking one drop out after each trip around the Earth, refilling the ocean, putting a sheet of paper on the ground, repeat, repeat, repeat, do that a thousand times, you will be one-third of the way done. Two-thirds of the time on your timer will still be there.

• 28:09Hannah Fry?

  So hold on, hold on, hold on. You have to do a complete loop of the Earth before you take one drop.

• 28:15Michael Stevens?

  That's right.

• 28:15Hannah Fry?

  At every drop, it also has a complete loop of the Earth. And then, once you've filled, emptied all the oceans, then you get one sheet of paper.

• 28:24Michael Stevens?

  That's right, and you start all over.

• 28:25Hannah Fry?

  Wow.

• 28:27Michael Stevens?

  Two sheets of paper, three sheets, four sheets. Once it reaches the sun, you are still a thousand, you have to do that a thousand more times before you're even a third of the way through 52 factorial seconds.

• 28:41Hannah Fry?

  So, I mean, the conclusion of that then is that if you shuffle a deck of cards, you can pretty much guarantee that no other human who has ever existed or ever will exist. Has effectively landed on that same one second as you, right? Has got that exact same configuration as you have because there are so many.

• 29:00Michael Stevens?

  Isn't that weird? Like a deck of cards that's been properly shuffled has never been in the same order as any other shuffled deck of cards. If you want to feel unique, go shuffle a deck of cards. You've just created something that has never existed, an order that has never been seen and will never be seen again.

• 29:17Hannah Fry?

  I like that so much. I like that so much. Those analogies, those ways to understand how big these numbers are. I mean, you sort of have to turn it into time, really, don't you, to be able to get a grasp of it? But I think Buddha himself, or Siddhartha, who was coming up with all of these big numbers I was talking about a moment ago, he had an example of this about how you have a bird with a silk scarf. And once every number of years, every hundred years, you would, the bird would fly past a mountain with a silk scarf. And then eventually, eventually, eventually, the whole mountain will be worn away by the...

• 29:58Michael Stevens?

  Worn away by just the scarf touching it, once every hundred years.

• 30:02Hannah Fry?

  I don't think it was an exact precise calculation of how big these numbers were, but it was a sort of, as you say, a visualization, a way to start imagining the like vastness of these numbers. Thing is, I mean, all of these numbers that we've described so far, that fifty-two factorial is like, is phenomenal. It's not as big as some of the other numbers we've mentioned, though. I mean, not by long stretch.

• 30:24Michael Stevens?

  No, fifty-two factorial is just, what, eight times ten to the sixty-seventh? But thousands of years ago, Indian mathematicians were talking about ten to the four hundred.

• 30:36Hannah Fry?

  It's also not, we don't stop there. There are numbers that are even bigger than that, so big that you, I mean, they're... They're quite literally inconceivable. Quite literally, you are not capable of even talking them about them in terms of the number of zeros, because they are just way too big. I think the most famous example of that is Graham's number. Now, okay, Graham's number is a little bit difficult to explain where it comes from, but I'm going to give it a go, okay? It's a number that arises from a mathematical theory called Ramsey theory. And essentially, if you imagine that you've got, it's all about cubes. It's all about joining together the corners of cubes. That's where it all comes from.

• 31:19Michael Stevens?

  Like connecting them with lines.

• 31:20Hannah Fry?

  Connecting them with lines, exactly. So, okay, let's imagine that you've got a square, just a flat square. I mean, a cube in two dimensions. You've got the lines around the outside, but you can also have diagonal lines, which are connecting up the diagonal corners. Okay, you could colour all those in, right? You could make some of them red, you could make some of them blue. You can, you know, colour them whatever way you like. That's all very nice and simple. Now, if you include an additional dimension, if you go up to three dimensions, so you have a normal cube, you can imagine now that square with the diagonal cross on it appears on every face of your three dimensional cube. But you also have additional crossings on the inside,

• 32:04Hannah Fry?

  where you're connecting up the opposite and diagonal corners from within the cube. Okay, you could colour in all of those, blue and red, however you wanted. Now, if you're a mathematician, why stop there? Why stop at three dimensions? You can describe what four dimensional cubes look like. It's just, you know, the coordinate system, you just add an extra zero on the end. You could do five dimensions, you could do six dimensions, you could do as many dimensions as you like. You can start talking hypothetically about, I mean, enormous numbers of dimensions, but ultimately, the idea is the same. It's a cube and you're talking about joining up all of the corners. Now, there was this question in Ramsey theory, which was going back to that square,

• 32:45Hannah Fry?

  that original square where you have the cross in the middle of the square and all the corners are connected. This question in Ramsey theory, I'm really simplifying here slightly, a lot, actually.

• 32:58Michael Stevens?

  I'm really glad you are, by the way, because I've read the Wikipedia page for Graham's number and it does not simplify. It just jumps right into, hey, here's a bunch of words and a cube and a square. And like, you get it.

• 33:10Hannah Fry?

  You get it. And on you go. I mean, we're getting to the point now, this is the field of combinatorics, by the way, and there are going to be mathematicians listening to this who know way more combinatorics than me and who are, I'm sure, going to write in angrily about the way that I'm absolutely butchering this description of Graham's number. But I'm doing my best. Okay. So just go with me. Okay. So here is the question. If you colour in all of those links, blue and red and do whatever, is there a point at which you cannot find one of those original squares, two dimensional squares, where all of those links are the same colour? In 3D, there's a way to colour it in that you can avoid it. The question is, what dimension do you have to go to until it becomes absolutely

• 33:54Hannah Fry?

  inevitable that you will find these slices through your cubes, your hypercubes, where all of the nodes are connected and they're all the same colour? That's essentially the question. It sounds completely theoretical, and it absolutely is. There is, uh, pure mathematicians really enjoy coming up with these challenges for themselves and then spending their entire lifetimes trying to solve them, right?

• 34:18Michael Stevens?

  Yeah, I was going to say, no one was actually like, please help, I have a higher dimensional cube I need to decorate with blue and red. What are those things? Garlands?

• 34:27Hannah Fry?

  Garlands, exactly. Yeah, no one was, no one was saying that. I think this is the thing, actually. I think there is a misconception that what mathematicians do all day is just count really big numbers. And I mean, that is what we're doing in this episode. But actually, what mathematicians do all day is come up with crazy questions for themselves, puzzles about many dimensional cubes and the colouring of edges on it. Anyway, okay. So here was the, here was the, the challenge, right? Is like, what's the number of dimensions at which point you cannot avoid this? You cannot avoid finding a slice where all of the links are the same colour. And Graham came up with an upper bound. He said, okay, well, I know it's more than six. And I know that it's less than this number, which I'm going to call Graham's number.

• 35:12Hannah Fry?

  Now, Graham's number is called Ronald Graham, is so gigantic that it is, you cannot explain it in terms of zeros anymore. It is, you have a whole new notation, a new way to describe how numbers relate to one another in order to even be able to describe what it is. Here's, here's the way that this, this extra notation works. So if you have three plus three plus three, that's the same as three times three, right? If you had three times three times three, that's the same as three to the power of three, which you could also write as three up three, because it's sort of like you write the three up.

• 35:54Michael Stevens?

  Oh, okay, okay.

• 35:55Hannah Fry?

  But when you have this up arrow, you, you can go a bit further because you could say three up up three, which is three to the power of three to the power of three.

• 36:08Michael Stevens?

  Oh, yes.

• 36:09Hannah Fry?

  Or three to the power of twenty seven.

• 36:10Michael Stevens?

  Up arrow notation, it's like another operation after exponiation.

• 36:15Hannah Fry?

  Exactly. Now, the thing is, is that these get very big, very, very quickly. So three up three is twenty seven, three to the power of three. But three up up three is seven point six trillion.

• 36:29Michael Stevens?

  Whoa.

• 36:30Hannah Fry?

  Get big.

• 36:30Michael Stevens?

  Just one arrow brings us into the trillion.

• 36:33Hannah Fry?

  An additional arrow, exactly. I mean, it's crazy. So when you get to three up up up three, you have got three to the power of seven point six trillion, which is already a ridiculous, massive, crazy number. Okay.

• 36:51Michael Stevens?

  That's three times itself, seven trillion times.

• 36:54Hannah Fry?

  Yeah, yeah, exactly. Seven point six trillion times, exactly. That is already a giant number, right? Three to the power of seven point six trillion is, I mean, it destroys fifty two factorial. It makes, it makes your crazy number look like, looks like a, a speck in, in the ocean, right? I mean, not even that, that's, dwarfs it way more than that. It's a sort of like, there's no, there's no comparison.

• 37:18Michael Stevens?

  Yeah, if you compare them, fifty two factorial is pretty close to zero compared to where we already are with just what, three up up up?

• 37:26Hannah Fry?

  Three up, up, up. Yeah, exactly. Now, the way that you make Graham's number is you say, okay, we're just gonna call the new number, we're just gonna call it G1, just this new number. And that is three up, up, up, up, three. So three and, and four ups and then three. Okay. So it's already absolutely massive. Then G2 is three up, up, up, up, up, up, up, up. G1 ups, three. Okay. It's just, it's, it's so ridicu- that was, that was G2.

• 37:58Michael Stevens?

  G1 ups.

• 37:59Hannah Fry?

  G1 ups, right?

• 38:01Michael Stevens?

  That sounds like an amazing nickname, by the way.

• 38:03Hannah Fry?

  G1 ups.

• 38:04Michael Stevens?

  Oh, that's G1 ups. How you doing, man?

• 38:08Hannah Fry?

  He's a big dude.

• 38:08Michael Stevens?

  But we're still not at Graham's number.

• 38:10Hannah Fry?

  We're, oh no, we're nowhere near. We haven't even started. So, so G2 is three to the G1 ups, three. Um, G3 is three, G2 ups, three. And you carry on going over and over again until you get to G64.

• 38:30Michael Stevens?

  G64, which is three sixty-three up, G63 ups.

• 38:36Hannah Fry?

  Yeah.

• 38:38Hannah Fry?

  Which itself was G62 ups, which itself was G61 ups, which itself was da, da, da, da, da, da, da, da, da, da, da, da. And remember, three ups absolutely dwarfs your 52 factorial number.

• 38:52Michael Stevens?

  I heard something like, the number, Graham's number is so large, if you actually could imagine it, just imagine it, your brain would become a black hole.

• 39:03Hannah Fry?

  That's not, I mean, that's not theoretical. That's, that's, I mean, people have literally done the calculations to this in the sense that there's a limit to the amount of information which you can measure that your brain can hold. And if you do that, the density of information is so big that you exceed the, the Schwarzschild radius of your own head. So, yeah, if you could, if you could imagine this number, your head turns into a black hole. However, two things I will say, we know, we know the solution to this problem is between six and Graham's number. In the year 2000 or so, uh, someone actually worked out that it's between 11 and Graham's number now. So we're getting closer. We're narrowing it down. Right?

• 39:40Michael Stevens?

  Sorry, six, seven, eight, nine and 10. You're out of the running.

• 39:44Hannah Fry?

  Yeah.

• 39:44Michael Stevens?

  But I love that this isn't just a fun game or a story. Graham's number had a purpose, which is that it was an upper bound on a mathematical problem.

• 39:54Hannah Fry?

  Mm hmm.

• 39:55Michael Stevens?

  It's not just, wow, here's this big number. I hope I win the girl. It was, hey, I'm doing math and I've found an unhelpfully large boundary.

• 40:05Hannah Fry?

  Yeah.

• 40:05Michael Stevens?

  For the answer.

• 40:06Hannah Fry?

  But here is the answer. I tell you what we do know about Graham's number, though. It ends in a seven.

• 40:12Michael Stevens?

  That I read that and I find that really impressive that we can find sequences within it. So we know the last few digits of it. It's not like we know how it starts, but not how it ends. We, we can tell you it ends in a seven.

• 40:25Hannah Fry?

  Yeah, it's, I mean, this is the thing. It's a proper, like it's a proper number that exists. It's just completely beyond our comprehension.

• 40:36Michael Stevens?

  And yet it is still finite. If you had enough time, you could count to it. And then you would be done and you'd have to find something else to do.

• 40:47Michael Stevens?

  But what we're going to do after the break is we're going to move on. Because for a while, Graham's number was thought to be the largest number ever imagined. The largest finite number you could count to, you know, could count to. But after the break, we're going to look at two mathematicians locked in a battle to find even bigger numbers.

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• 42:47Hannah Fry?

  Welcome back. Hopefully you are suitably refreshed by that ad break after the mind melting number weirdness of the first half. Thing is, there is this idea of like naming larger and larger numbers. I mean, there's something quite delightful in it, isn't there, Michael?

• 43:05Michael Stevens?

  Yeah, there is. I mean, it's, it's a battle, you know? It's a battle of the wits, but it's really trippy to think that we're reaching numbers that have no physical significance. Like, we still haven't left our solar system as a species, and yet mentally, we've left the universe. We're talking about numbers that are larger than the number of combinations of particles that could fit in the observable universe. There is no reason ostensibly to worry about these numbers, and yet we can because our brains are like the most bizarre vessel ever.

• 43:42Hannah Fry?

  But don't you think that that's what's so delightful, so delightful about human curiosity is that even though there is no point, even though it just melts your brain completely to even try and conceive of them, let alone actually successfully do so, all the same, we still kind of want to.

• 44:01Michael Stevens?

  Maybe there's no point, but it's like asking, well, what's the point in an eagle living?

• 44:08Michael Stevens?

  You know, we can get into philosophical discussions of purpose and it's like it's just the the nature of the beast. It's the nature of the universe and for us, that role is stuff like this. What if I loved you? What if I counted beyond the universe? That's just what we do.

• 44:28Hannah Fry?

  Yeah. What if this benchmark that you set or has been set by people before by by Buddha and Archimedes can be beaten? That was the the great idea between two mathematicians who had their own showdown. This is at MIT. They wanted to go so far beyond what Graham's number had had had had, I mean, the bar essentially set by Graham's number, which until that point was the largest number that had appeared in a mathematical paper. So this is the idea. This is at MIT in 2007. There are these two mathematicians called Adam Elga and Augustine Reo. And they're like, OK, let's take each other on. Let's have the ultimate duel.

• 45:11Hannah Fry?

  But rather than being weapons involved, let's just come up with the biggest numbers we can possibly write down. Graham's number is a good threshold, but let's see if we can go further. So Adam Elga, he's sort of the challenger in all of this. He comes up with an idea that is actually kind of similar in some ways to the the sort of the basis behind Graham's number. He has this idea of creating, the mathematicians call them trees, but essentially it's dots and lines that are connected with each other. And he comes up with a way of it's setting up a number that is the number of combinations of a different way that you can join dots and lines and different colors together. OK, it's really impressive. Everyone finds him extremely excellent and intelligent as a result of this.

• 45:57Michael Stevens?

  What I find impressive isn't just that, you know, a big number was described, but that it could be shown that this number was larger than Graham's number.

• 46:08Michael Stevens?

  Like, how cool. Like, we're not just going there, we're kind of like making a map.

• 46:13Hannah Fry?

  Yeah.

• 46:13Michael Stevens?

  And yet. Reo comes in and wins the competition.

• 46:18Hannah Fry?

  Reo comes in and wins the competition and he does it with this absolute genius move. He's like, I'm not gonna, I'm not gonna play around with dots and lines. I'm not gonna mess around with combinatorics. No, no, no, no, no. What I'm gonna do is I'm gonna say, all right, Graham's number, your number, Adamelga, all of that can't, they are real numbers and they can be described using symbols. And some of them need more symbols than others. Graham's number, for instance, needs actually quite a lot of symbols to, to properly describe it. Think of all of them ups. Reo is like, okay, if I say that there's like a category of all of the numbers that can be described by up to a googol of symbols, right?

• 47:00Hannah Fry?

  So like the number 453 needs three symbols, four, five, three. 52 factorial also needs three symbols, five, two and an exclamation mark.

• 47:10Michael Stevens?

  Yep.

• 47:11Hannah Fry?

  Graham's number needs a lot more because you've got all of them ups.

• 47:15Michael Stevens?

  You've got a lot, yeah, sure.

• 47:16Hannah Fry?

  There's a lot of G1, G2, G whatever. So Reo says, okay, well, look, if you count the number of symbols that you need to describe this number, right? And let's say you've got like a category, like a, all of the numbers that need less than a googol of symbols to describe them, that's all there. I'm gonna say my number is the smallest number that cannot be described by a googol of symbols. So all of those numbers in there, I'm gonna do that, plus one, basically. That's essentially what he did.

• 47:51Michael Stevens?

  Which is brilliant because you just, it's, it's just so impervious to any, any, any, but what if? Because look, fine, I can compress the number of symbols required to represent a number. I could say, you know what? Graham's number, let's just represent it with a really bold G. Now it only takes one symbol. And he's like, yeah, I know, but my number, Reo's number is defined as the one that's, that's, that can't in your system. No matter how much you compress it, I'm always beyond you.

• 48:21Hannah Fry?

  I mean, the thing is, we could come up with our own number. We could come up with a Frye Stevens number, which is the smallest number that's larger than any number that can be named in an expression of the language with a googolplex symbol or less. I mean, you can't, you can't, you can't out Raio Raio.

• 48:37Michael Stevens?

  Yeah, couldn't say the smallest number that cannot be described in a system using Raio's number of symbols? You might run into a paradox.

• 48:49Hannah Fry?

  I think there might be some circular logic going on in a minute, yeah. But anyway, I mean, this is all fun and games, right? This is all fun and games.

• 48:57Michael Stevens?

  It is, it is really fun and games, but yet there's something so important in this because we're, we're trying to describe and, and kind of give some scale to these large numbers. But there are much, much smaller numbers that we as a society and as a species need help understanding. Even the difference between a million and a billion is something that we, the more we talk about big numbers in, in our real lives that really do count things like dollars, like people, we just become numb to them. And it's, it's a struggle, but yet it's so important that we help people picture how large these quantities are.

• 49:39Hannah Fry?

  The difference between a million and a billion is one that I, that I, that I always think of because I mean, they sort of sound so similar. They're just different by one letter in a way. And again, if you turn it into time, I think suddenly it becomes a bit more natural. The difference between a million seconds, a million seconds is 11 days, a billion seconds is 31 years. I mean, it's like they're gigantically different. There was this study back in 2013 where people were investigating exactly this idea. Can people really conceive of the difference of these numbers? This is by David Landy and they, they had a number line. This number line had a thousand on it and it had a billion and they asked people to place one million on it.

• 50:22Hannah Fry?

  And about 40% of people placed one million halfway, about halfway between a thousand and a million. And in reality, a million was barely a pixel above one thousand.

• 50:35Michael Stevens?

  I know, I know, you need a thousand millions to get a billion.

• 50:38Hannah Fry?

  Yeah.

• 50:39Michael Stevens?

  And of course, people put it in the middle. I would have thought that they would because it's in the middle. You go thousand, million, billion. That's it. That's how the naming works. And yet they're so far apart. Yeah. A million seconds is 11 days. A billion seconds is 31 years. A trillion seconds is 31,000 years.

• 51:00Hannah Fry?

  Is it?

• 51:02Michael Stevens?

  Which it's just, it's just times a thousand. Because a trillion isn't like the next number after a billion. It's the next name for a number after a thousand billion.

• 51:13Hannah Fry?

  Hmm.

• 51:14Michael Stevens?

  And so I think that politically and journalistically, we should start pushing to get people to use only one kind of number, like just let's only talk in billions. So don't, don't say the national debt is a trillion and we're cutting 2 million in funding. Because those both sound like they are close to each other. They've got alien in the names. Trillions and millions are the difference between a thousand billion and point 002 billion.

• 51:45Hannah Fry?

  Hmm.

• 51:45Michael Stevens?

  If you saw those together, you'd go, that doesn't make a difference.

• 51:49Hannah Fry?

  I saw a really amazing visualization about how rich Elon Musk is.

• 51:53Michael Stevens?

  Yeah.

• 51:53Hannah Fry?

  Um, and I think it's, it, I mean, it goes back to that number line, right? Like to get that answer correct, what you needed to do was to cut up that line into a thousand pieces and just choose one of them. That would be where a million is. This idea that, you know, Musk is worth, I mean, some, by some estimates, close to a trillion, if not over. It's so gigantic. It's not just like a bit bigger. It's absolutely inconceivable. I mean, quite literally inconceivable, the difference between these numbers. But it also, I think this ends up really mattering when it comes to charities and not for profits, trying to get support for people.

• 52:35Michael Stevens?

  Um, yeah.

• 52:36Hannah Fry?

  This is like something that's been really noted. I think that we inevitably hone in on stories about individuals way more than we do about large numbers. Um, you know, the statistic doesn't really. Draw empathy from us in quite the same way. There was one really interesting study by, this is by Paul Slovic, who wanted to try and understand, like, in what ways do we stop caring? And he presented participants with these various humanitarian cases. And he would have a picture of a person and ask about the amount of donations people wanted to do. And he found that if you show that exact same picture,

• 53:19Hannah Fry?

  but underneath it, say, there are a million people like this who are also suffering, donations went down, not up, which is really extraordinary. Like, this is counterintuitive to us, which on the one hand is what makes the fact that these mathematicians are doing this for fun all the more impressive, I think, or all the more, I don't know, it makes me love the strangeness and curiousness of humanity more. But at the same time, I think it really demonstrates how we are not wired for this stuff. Like, this is not innate to us.

• 53:55Michael Stevens?

  That's right. Yes, we can be proud that we're capable of describing numbers this large, but yet we aren't really wired to feel it. I once worked with a charity and they said something somewhat similar. They said, "The thing that helps donations the most isn't statistics or numbers, and it's also not any kind of extreme case. It's not as effective to show the story of a guy who overcame some hardship and just climbed Kilimanjaro. It's more effective to say, 'This guy overcame the hardship because of your donations, and because of that, he was able to take his daughter to the park.'"

• 54:41Michael Stevens?

  That that means so much more to people than, oh, he climbed a mountain. I haven't climbed a mountain. So why do I care that this other guy did? But to not be able to make dinner for your son? Like, that matters so much more than any number we can come up with.

• 54:58Hannah Fry?

  There's Hans Rosling, who is just this absolutely extraordinary statistician and global health advocate. His daughter, Anna Rosling, who wrote the book Factfulness, she also is, I think, really very aware of this tension. That on the one hand, you need the statistics in order to make the bigger argument, to make the sort of the data-driven logical case. But that ultimately, without the emotional side of it, you know, when people don't connect with big numbers, we just don't. So what she has is something that she calls the bird's eye view and the worm's eye view.

• 55:40Hannah Fry?

  So there's one of her websites, this amazing thing where you you see all of the maps, you see the larger statistics. But at any moment, you can zoom in and find individual stories of the people who are actually affected. And I think that that's the most impactful way that I've ever seen these two things tied together, knowing that that our brains really don't work in the same way as those mathematicians' brains do, not when it comes to having empathy towards other people.

• 56:09Michael Stevens?

  So today, we've reached the largest described finite number. But then we kind of like found something even bigger. And that's what I love about this show.

• 56:19Hannah Fry?

  Yeah, that's what I love about this show, too. Also, the fact that we didn't just decide to describe the largest finite numbers to you by just reading off all these zeros. Because it could have been-

• 56:28Michael Stevens?

  Imagine if we had, if we had just been like, okay, eight. How about 100? How about a billion? How about a trillion? We just kept doing that with no explanation.

• 56:37Hannah Fry?

  Hey, look, we haven't launched our members-only podcast yet. Maybe that could be the first episode.

• 56:41Michael Stevens?

  That could be a members-only episode. Michael and Hannah try to beat each other with larger and larger finite numbers until one of them falls asleep.

• 56:49Hannah Fry?

  You can read out your Square Root of Four book for us.

• 56:53Michael Stevens?

  Ooh, yes. The square root of four to a million decimal points.

• 56:58Hannah Fry?

  All right. Well, thank you so much for watching and listening to us on The Rest of Science. Make sure you're following wherever you get your podcasts. Be sure to like and subscribe on YouTube. Smash that like button, Archimedes.

• 57:10Michael Stevens?

  Smash it, hit the bell and sign up for our newsletter at therestis.com/science.

• 57:17Hannah Fry?

  If you would like to answer any of your questions, especially on our Thursday episodes, our field notes episodes where we, I mean, we're even more rambling and meandering than we are on this one, you can send us in anything you like to [email protected]. See you next time.

• 57:34Michael Stevens?

  Next time.

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