Is 100 Better Than 101?

Is 100 really such a special number? Or have we spent thousands of years getting excited about something completely arbitrary? To celebrate the 100th episode of The Rest Is Science, Professor Hannah Fry and Michael Stevens (Vsauce) go head-to-head in a mathematical showdown: which is the better number, 100 or 101? It sounds like a simple question, but the answer takes them from the strange history of counting, to the psychology of numbers, the mathematics of primes and the possibility of communicating with alien species. Why do we find round numbers so satisfying? Would 100 mean anything if we'd evolved with 9 fingers? And is there a single number that’s fundamentally special, regardless of the counting system we use? Can Hannah and Michael settle the debate once and for all? Or is the most ‘important’ number of all one they haven't even considered yet? ------------------- 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 + Jack Meek Animator: Sam Benson Video & Social: Bex Tyrrell Assistant Producer: Lucy Lipscombe Producer: Simona Rata Senior Producer: Lauren Armstrong-Carter Chief Digital Officer: 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.

• 0:01Michael Stevens?

  Hello and welcome to The Rest Is Science. I'm Michael Stevens.

• 0:03Hannah Fry?

  And I'm Hannah Fry.

• 0:05Michael Stevens?

  And this is our 100th episode.

• 0:08Hannah Fry?

  What a big deal. What a great big deal.

• 0:11Michael Stevens?

  Congratulations, Hannah. This has been, it's been a real pleasure, but today I want to question that. Is it a big deal?

• 0:19Hannah Fry?

  Of course it's a big deal. What are you talking about? We're in triple digits. Come on.

• 0:23Michael Stevens?

  Triple digits, yes, that feels like a milestone, but it also feels very decimal base system dependent. Today, we're going to debate what's a better number, 100 or, in my opinion, 101.

• 0:40Hannah Fry?

  So we're going for correct opinion, mine, 100, and incorrect opinion, Michael's, 101. Let's go. Do you want to go first?

• 0:47Michael Stevens?

  Well, yes, since you framed it so kindly to me. Also, here's the thing. Okay, right off the bat, we got to start here. 101 is better because, um, excuse me, it's bigger.

• 0:59Hannah Fry?

  Right, but hang on.

• 1:00Michael Stevens?

  Just going purely off of greater than, less than, 101 is more. By the way, I looked into the etymology of the word 100. 100 used to be bigger. They don't make 100 like they used to.

• 1:11Hannah Fry?

  By the way, to be absolutely clear, me and Michael do not share our research until we're, you are seeing us having a genuine conversation with each other in real time, because I've also found something about how 100 used to be bigger. You go first.

• 1:23Michael Stevens?

  Okay, well, it might be the same thing. We'll find out.

• 1:26Hannah Fry?

  Go on.

• 1:26Michael Stevens?

  But the, I don't know how to pronounce it, but across Northern Europe, 100 began as hunroth, perhaps.

• 1:32Hannah Fry?

  Right.

• 1:32Michael Stevens?

  I don't know how to pronounce it. You'll have to time travel to tell me. But the point is that 100 meant six score. And a score is 20. So 100 meant 120, what we call 120 today. And the 100 being 10 squared was the short 100, which I just love. I'm going to be using that in casual conversation all the time. Whenever 100 comes up, I'll like ask for clarification. Do you mean a long 100 or a short 100?

• 1:59Hannah Fry?

  Or the great 100. Sometimes they would call it the great 100. That's the other.

• 2:03Michael Stevens?

  Ooh, the great 100.

• 2:04Hannah Fry?

  That's the other phrase for it. Yeah.

• 2:07Michael Stevens?

  The long 100 is like the baker's dozen. It's 120. So today, 100 means just five score, five groups of 20, which is 100. But, but the great 100, the long 100 as 120.

• 2:19Hannah Fry?

  12D, 12D is the other word for it.

• 2:26Hannah Fry?

  This episode is brought to you by Cancer Research UK.

• 2:29Michael Stevens?

  All right, here's something really cool. The earliest written description of cancer that we've ever found is from an ancient Egyptian papyrus that was around before even Cleopatra was on the throne.

• 2:40Hannah Fry?

  It described tumors being removed by a tool that they called the fire drill, which we think was used to burn off diseased tissue.

• 2:49Michael Stevens?

  Beating a disease that's so ancient and complex with over 200 different types, it's not going to happen overnight.

• 2:55Hannah Fry?

  But thanks to research, cancer treatment has advanced a lot. And Cancer Research UK is driving further innovations like cancer sniffing robots and drugs made from gut bugs that could change the future of medicine.

• 3:08Michael Stevens?

  Over the past 50 years, Cancer Research UK's work has helped double cancer survival in the UK. And today, it's continuing to save and improve lives around the world.

• 3:19Hannah Fry?

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

• 3:28Speaker 02

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• 5:02Michael Stevens?

  12D.

• 5:04Hannah Fry?

  Yeah, isn't that cute?

• 5:05Michael Stevens?

  Yes.

• 5:05Hannah Fry?

  Because in Old Norse, right, so 200 would be 240, 300 would be 360, and so on, so on. There's also, actually, you know, Tolkien, who was a professor of Old English? And Bilbo throws a party for his 111st birthday.

• 5:21Michael Stevens?

  I love that. I know.

• 5:22Hannah Fry?

  Because the other thing I discovered about the long 100 is that there is this idea that the survivor of the long 100, the great 100, the 12D, is the British hundredweight is 112 pounds, not 100.

• 5:35Michael Stevens?

  112?

• 5:37Hannah Fry?

  Yes, I know, but 112 isn't 120, so it's all a bit murky. But why is the hundredweight 112 pounds instead of being 100? It doesn't make any sense.

• 5:44Michael Stevens?

  Do you know?

• 5:45Hannah Fry?

  No, no, that's the theory is that it comes from the Old Norse hundred.

• 5:49Michael Stevens?

  Which was 120, though.

• 5:51Hannah Fry?

  Which was 120.

• 5:52Michael Stevens?

  This is such a British thing to do, Hannah, by the way. They're always like, yeah, you know, we're going to call a quarter note a crotchet.

• 6:00Hannah Fry?

  You know why? You know why it's a British thing to do? It's because, it's because we've got history. We've been around for a long time.

• 6:06Michael Stevens?

  That's right. It's always history. It's like, look, I know it doesn't have a hook on it, but we're going to call it the hook, the crotchet anyway. I think this is all pointing towards one answer, which is that 101 is better. Why? Because math is taught like, this is the answer, and it's true because the universe, or something unchangeable about it. When in reality, the fact that four times 10 is easy to do in my head is purely because of the decimal system. We've talked about this in a previous episode. I don't even remember which one it was. But I gave examples of problems in binary that would be just simple. Like someone who was a binary thinker would be like, well, that's just prima facie obvious, the answer to that one. But to us, it's weird.

• 6:45Hannah Fry?

  It's very easy for us to sort of think in clock terms that 13 is the same as 1, 17, you know, is the same as 5, because we're very used to this idea that you go all the way around and then you start again, right? And it's only because we're using the base 10 numerical system to represent a base 12 clock system that it sort of gets a little bit confused. If you instead had like some other squiggle, some other positional mark that told you how many, how many units of 12 hours you had, you'd gone through, actually, doing calculations in base 12 would be really, really simple. And I think there's a strong argument that base 12 is vastly superior in all kinds of ways.

• 7:26Michael Stevens?

  I completely agree.

• 7:28Hannah Fry?

  I mean, base 12, base 10, you can halve it, right? You can divide it by 5, and you can divide it by 2. That's about it.

• 7:36Michael Stevens?

  That's it. Yeah. You could break it into fifths and halves, but what can you do with 12?

• 7:41Hannah Fry?

  You've got, you've got halves, you've got quarters, you've got, you've got sixths.

• 7:45Michael Stevens?

  You've got thirds.

• 7:46Hannah Fry?

  Lovely. Thirds and quarters. Thank you very much. Yes, I will.

• 7:49Michael Stevens?

  It is so richly divisible.

• 7:51Hannah Fry?

  Isn't it? Yeah. If only we'd been born with two extra fingers.

• 7:55Michael Stevens?

  That's all it would have taken. And instead, we're stuck here in a world that is predominantly decimal, base 10. And so we're supposed to sit here and celebrate our 100th episode. Give me a break. All right? And you know what? I'm so grateful for Bilbo and for Tolkien writing about the 111st birthday because it allowed me to show my daughter how numbers work. I was like, 111st? Makes sense. Why don't we say it that way? Well, because we decided not to. But I think her appreciating the arbitrariness of the system allows her to go, aha, okay, well, I get it now. It's not a mean monster I need to submit to. It is a tool that we made and I can make, and I can handle and control.

• 8:37Michael Stevens?

  So here's the deal. We've, we've established right now that bases make everything murky and arbitrary. But there's something about 101 that makes it special, no matter what base we're in. What is it? Something 100 doesn't have. 101 is prime.

• 8:54Hannah Fry?

  Hmm. I mean, that's the opposite of the dividing by 3, divided by 4, divided by 6, divided by 2, isn't it?

• 9:03Michael Stevens?

  Yes. It is the opposite of what 12 gives us, which is this super rich amount of divisors. 101 is like, look, you got me and you got one. That's it.

• 9:10Hannah Fry?

  You've got nothing else. Are you allowed to do that? Are you allowed to simultaneously argue that you don't like base 10 because it hasn't got divisors and then argue that you don't like it because it's not prime? It feels like cheating.

• 9:20Michael Stevens?

  You tell us below in the comments if you think that my rubric is contradicting itself. But all I'm trying to say is that I think an alien, okay, who came from some other planet and had a different number of fingers would go, why is 100 special? If we told them 101, at least they could go, oh, I see, it's prime. Yes, I can recognize the specialness of this anniversary.

• 9:41Hannah Fry?

  All right. I, I accept that. I accept that that is, that is something. You're right that actually 101 is something much more fundamental, regardless of whatever you call it, regardless of whatever you, however you write it down, whether you're using Arabic numerals or not. Irrespective of what the number looks like, there is something innate about that number.

• 10:03Michael Stevens?

  Yes, by being prime, it transcends number systems.

• 10:07Hannah Fry?

  Yeah, it's not just in base 10.

• 10:08Michael Stevens?

  Yeah, it, it can transcend cultures, but even species and even intelligences.

• 10:14Hannah Fry?

  Right.

• 10:15Michael Stevens?

  And I haven't even rested my case yet.

• 10:17Hannah Fry?

  Okay, I, I, you know what? And my phone just dropped as a, as a sort of mic drop moment.

• 10:25Hannah Fry?

  You know what? Boom. You win. End of the episode.

• 10:27Michael Stevens?

  No, don't let me win. We've, we've got at least 40 more minutes.

• 10:31Hannah Fry?

  Here's, here's the thing though, right? Sure. Yes. To an alien species, fine. If we're talking about pistachios, fine. But I think that there's something psychological about the number 100. That's just

• 10:43Michael Stevens?

  Okay, I agree. Go on.

• 10:44Hannah Fry?

  That's nice. That's, it just feels nice. And I think that this isn't just sort of a hunch that I have. I think that you see this in the data. I think a really nice example of this is, uh, that there was a group of economists who looked at 22 million used car sales in sort of wholesale auctions. And what you would expect is that, that the price of a vehicle should fall smoothly as the mileage goes up, right? The more miles a car's done, the less it's worth. Not, not what happens. Not what happens.

• 11:15Michael Stevens?

  I think I see where you're going with this.

• 11:17Hannah Fry?

  Right. And with this sample size of millions and millions of cars, you can really clearly show that a car with 79,900 miles will sell on average for $210 more than one with 80,100 miles. So even though it's like 200 miles extra on the clock, it's nothing. Because it takes you over that threshold.

• 11:41Michael Stevens?

  That's right. It's threshold psychology. Yep.

• 11:44Hannah Fry?

  And actually, incidentally, uh, the, the car with 79,900 miles will only sell for $10 less than one with 79,800. So if you go the other way, it's like, it barely makes a difference.

• 11:58Michael Stevens?

  Yeah, yeah.

• 11:59Hannah Fry?

  And I think that that's a really clear indication of just how much we actually put value, as it were, in all of this.

• 12:07Michael Stevens?

  Yeah. And I don't want to underestimate that psychological value. Whether it is, is universally important or not, the fact that we have for so long peg numbers on this base 10 system means that they mean something to us. If a car has over 100,000 miles, there's that 100 again, that means something. It puts it in a whole different category. Even if to a base 12 person or a hexadecimal person, 100,000 is probably not going to be some nice round number that divides cars into two groups. So I'll admit that we could just embrace tradition and say 100 matters for that reason. But that's not my job today.

• 12:46Hannah Fry?

  Well, it is my job. I'm going to argue strongly in favor of that. It's a bit like, do you remember we were talking about rectangles? We, someone sent us in a photo of their, of their poster and it was a bit on a wonk on the wall. And we ended up on a very long conversation about their sort of history of rectangles and how they don't appear in nature. And yet wherever you look in every human made space, it is brimming. It is brimming with the shape of choice, the shape that we fundamentally created and have put literally everywhere. I think this is the same thing. You know, I, I think that rectangles are important by virtue of the fact that humans use them all the time. And I think that 100 is important by virtue of the fact that humans care about it.

• 13:31Michael Stevens?

  Well said. However, I'm looking beyond humans. I think that an intelligent life form from another solar system would also appreciate rectangles. Because we just don't see rectangles in any place in the universe, but where there's an intelligence that is rectilinifying things. However, I don't think 100 has the same kind of claim. Because the bases that other intelligence use, you could find it or you could not find it. It's not like a rectangle. That your numbering system isn't like a straight line. It doesn't immediately flash, this is something important. That's what I'm saying.

• 14:16Michael Stevens?

  Let's, let's leave that where it is and move on

• 14:19Hannah Fry?

  Go on.

• 14:19Michael Stevens?

  To arguments that don't depend on base.

• 14:23Hannah Fry?

  Go on.

• 14:23Michael Stevens?

  Or pro or against. 101 is also a palindrome in base 10. Okay?

• 14:31Hannah Fry?

  And there's someone called, someone called Hannah. I like that.

• 14:34Michael Stevens?

  As someone called Hannah with an H on the beginning and the end, there are some Hannahs that don't, and I am calling you out.

• 14:39Hannah Fry?

  The incorrect ones is wrong.

• 14:42Michael Stevens?

  Your name, it just clumps off at the end and I, I can't make it a circle. I still love you though. But 101 is a palindrome. And it's, it's pretty cool in base 10. It's like, it's not the first palindromeic prime, because technically I'd say 11 should get that. But it's the second one. And we don't know if there's an infinite number of them. There could be a point where there just isn't another one. Find, found out one way or the other yet.

• 15:09Hannah Fry?

  Hang on, what's the third?

• 15:11Michael Stevens?

  131.

• 15:12Hannah Fry?

  Okay.

• 15:13Michael Stevens?

  And then 151. Like down at the low numbers, they're not that rare.

• 15:19Hannah Fry?

  That is, it's an unsolved question whether there are, whether there are an infinite number of palindromeic primes. I like that.

• 15:26Michael Stevens?

  I'm going to throw a curve ball at you. Because I'm supposed to be here arguing for 101.

• 15:32Hannah Fry?

  Sorry, can I just, I'm so sorry. I'm just looking

• 15:34Michael Stevens?

  Please.

• 15:35Hannah Fry?

  Forgive me. I'm just looking at the Wikipedia page of palindromeic primes because I have never seen this page before. This is, I'm really, I'm delighted. Okay. The palindromeic prime, ready? 1 0 0 0 0 0 0 0 0 0 0 6 6 6 0 0 0 0 0 0 0 0 0 0 0 1. Oh, that's nice, isn't it?

• 16:01Michael Stevens?

  Yeah, it's a palindrome.

• 16:03Hannah Fry?

  Belphegor's prime.

• 16:05Michael Stevens?

  Yeah, it's named after a demon.

• 16:07Hannah Fry?

  It is. One of the seven princes of hell. I like that so much.

• 16:12Michael Stevens?

  Who was the guy who introduced me to that number? He's, he wrote like the, you know, the big book on math, very well-known, recognizable name.

• 16:20Hannah Fry?

  Clifford? Clifford Pickover?

• 16:22Michael Stevens?

  Yes, Clifford Pickover.

• 16:24Hannah Fry?

  That is a big math book.

• 16:25Michael Stevens?

  That is a big math book. And, and he, I think he's done a lot to, to popularize that prime. What is it called? Befalgars or something? I don't know all the demons.

• 16:34Hannah Fry?

  Belphegor. Befalgars probably.

• 16:37Michael Stevens?

  It's a, it's a, what is it? It's like a few ones, a bunch of zeros, and then the number of the beast, 666.

• 16:43Hannah Fry?

  13 zeros.

• 16:44Michael Stevens?

  13 zeros.

• 16:47Hannah Fry?

  Either side, 13 on either side.

• 16:49Michael Stevens?

  So it's 666, sandwiched between 13 zeros on either side and then a 1 at the beginning and the end.

• 16:55Hannah Fry?

  It's good.

• 16:55Michael Stevens?

  I love it. I love it. That's a great palindromeic prime. It's in base 10.

• 16:59Hannah Fry?

  So hang on a second. We're, you're trying to argue for 101. We don't even think 101 is the best palindromeic prime.

• 17:06Michael Stevens?

  No, it's not. It's not even the first one, because I think 11 should count.

• 17:10Hannah Fry?

  I'll get excited. I'll get excited when we get into our Belphegoric prime episode.

• 17:15Michael Stevens?

  Okay, let me throw you a bit of a curve ball. Let's, let's, let's ignore primes for a while and just talk about palindromeic numbers. Because again, whether a number is a palindrome, it's, it does depend on the base, but it doesn't always have to. Here's the thing. Let me throw in a different idea. Not 100, not 101, but 99. 99 is a palindrome. It's the same way backwards as, as it is forwards.

• 17:41Hannah Fry?

  Not prime.

• 17:42Michael Stevens?

  It's not prime, but it's a palindrome in base 10. It is also a palindrome in base 2.

• 17:49Hannah Fry?

  Is it?

• 17:50Michael Stevens?

  In base 2, 99 is 1 1 0 0 0 1 1.

• 17:56Hannah Fry?

  Oh, okay. That's not, yeah, that's nice. That's nice. So how many other numbers are, are palindromeic in both base 10 and base 2?

• 18:02Michael Stevens?

  I think the next one is 313. That is a palindrome in base 10.

• 18:08Hannah Fry?

  You nerd.

• 18:09Michael Stevens?

  313.

• 18:11Hannah Fry?

  I like this so much.

• 18:13Michael Stevens?

  And it's also a palindrome in, in binary. 1 0 0 1 1 1 0 0 1. So as you can see, I got pretty deep into this this morning.

• 18:22Hannah Fry?

  I love it.

• 18:23Michael Stevens?

  Okay. All right. Look, so can I find a number that is a palindrome in base 10, base 2, and hexadecimal?

• 18:32Hannah Fry?

  You're talking my language. Tell me.

• 18:35Michael Stevens?

  Such a number has never been found. So Rick Reagan, over at a website called ExploringBinary.com, became obsessed with finding a number that was a palindrome in base 10, 2, and 16. And he searched 2 to the 32 numbers. It taxed out his machine and he couldn't do it. Now, this was back in 2010. Maybe we can, we can start the adventure again. But he could not find one. It stressed out his machine. It took like 60 hours and he, he suspended the search. So

• 19:06Hannah Fry?

  I feel like there's a lot more data centers now than there was back then. I think, I think that we should put the might, the might of our collective compute as, as, as a planet onto this very important problem.

• 19:17Michael Stevens?

  All I'm saying is 101 is not a palindrome, um, in base 2 or 16. Neither is 100 though. But it's, it's also confirmed that there's no number around 100 that is a binary decimal and hexadecimal palindrome. So we're not going to be close soon to having an episode number that has that special property.

• 19:37Hannah Fry?

  No, no. Um, you're right. Should we go for a little break and then come back and continue this argument?

• 19:43Michael Stevens?

  Let's go for a break and I can't wait for what comes next.

• 19:59Speaker 04

  Hi, everyone. It's Cathy Kay here from The Rest is Politics US. The midterms are almost here. It's the biggest political moment of the year. And Anthony Scaramucci and I will be right there with you, making sense of every twist and turn as the results come in.

• 20:12Speaker 05

  Yo, that's right. We're going to be live on YouTube covering the midterms as we get the results. Will Donald Trump be a lame duck for the next two years? Or walk away with a mandate to do whatever he wants? We're about to find out.

• 20:27Speaker 04

  So join us from midnight to 3 a.m. Eastern Time on November the 4th. We'll be live reacting to all of the results as they come in. That's 5 a.m. to 8 a.m. if you're listening in the UK.

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• 21:49Michael Stevens?

  All right, we're back. And so far Hannah and I have been debating 100 versus 101. I think I'm going to let her go next because I'm so clearly winning this debate. I think it's almost unfair. What else do you have?

• 22:00Hannah Fry?

  Okay.

• 22:01Michael Stevens?

  That's pro 100.

• 22:02Hannah Fry?

  All right, here's the thing, okay? Everything you're talking about, right? All of this whole stuff about, you know, other numbers that you like. I think you're thinking too linearly here, Michael. That's what I think.

• 22:12Michael Stevens?

  Hmm.

• 22:13Hannah Fry?

  I want you to tell me, what number is halfway between 1 and 9?

• 22:17Michael Stevens?

  Halfway between 1 and 9?

• 22:19Hannah Fry?

  Mm-hmm.

• 22:19Michael Stevens?

  Uh, I guess that would be 5?

• 22:22Hannah Fry?

  No, I don't think it is. I think it's 3.

• 22:25Michael Stevens?

  Why?

• 22:26Hannah Fry?

  Because actually, a lot of the time, our brains don't think in linear scales. We think in terms of fractions. And actually, the fraction of 1 to 3 is the same as the fraction of 3 to 9. And you see this over and over again in the way that we react to different stimulus is stimuli.

• 22:48Michael Stevens?

  Stimuli.

• 22:49Hannah Fry?

  Stimuli, thank you. Okay, so if I handed you...

• 22:53Hannah Fry?

  Stim, you sit up and listen because 100 is better, all right? Okay, so if I gave you two weights, okay? And asked you which one of these weighs more? And the weights weighed, let's say, 10 grams and 30 grams, okay? You'd be like, oh, well, it's obviously this one. It's obviously the 30 gram one.

• 23:18Michael Stevens?

  Right.

• 23:19Hannah Fry?

  However, if I now handed you two weights and they were 1 kilo and 10 grams and 1 kilo and 30 grams, you'd be like, uh, I'm not really sure. I can't really tell between the two. The bigger the baseline number, the smaller that difference is as a fraction of the whole and thus the harder it is for you to tell the difference. And this is, I think, a really clear demonstration that actually our brains, that, you know, it's still the same 20 grams, right? It's still the same 20 gram difference, whether you're on teeny tiny weights or really big weights. It's just that our brains aren't, don't work like that, right? Our brains work in terms of fractions. It's the same thing if you send somebody to jail for three months or six months.

• 24:03Hannah Fry?

  It's, it is the sort of same extension of the sentence as if they're there for 25 years and three months or 25 years and six months. You're still in prison for the same amount of time. You're still deprived of your liberty for the same amount of time, still cost the same amount of money to the taxpayer. And yet you see this as evidence of the way that judges give out sentences is that they are so much more careful about extra days when they're down at the other sort of smaller end of the spectrum. So here is the reason why I think 100 is important. We think logarithmically, right? We think in fractions. That's how we experience the world. And the thing about 100 is that it's sort of the same distance as 1 to 10. It's from 10 to 100. So it's sort of the second number really in a lot of ways, isn't it?

• 24:49Michael Stevens?

  Yeah, no, I get it. You, you're making a very, very good point. I think what you're doing is you're taking the roundness of it that I was just considering was a consequence, a, an artifact of the base. And you're saying, no, no, no, it is very deeply in our bones. And you're right, I made a whole video about this whole logarithmic thinking. Not only logarithmic thinking, but logarithmic feeling and sensing. The world comes to us logarithmically and in fractions.

• 25:17Hannah Fry?

  I mean, think about how you, how you experience your life. Your childhood seems to go on forever because, because every new year is such a big fraction.

• 25:26Michael Stevens?

  A large fraction of what you've already lived, yeah.

• 25:28Hannah Fry?

  And as you go on and you're older and older and older, it's just, it starts to whisper. And like some of this is about, you know, the way that your brain processes the information. But part of it is because, again, this evidence that our experience of reality is fundamentally logarithmic is that it's just a much smaller and smaller, smaller fraction of what you've experienced thus far.

• 25:49Michael Stevens?

  Yeah. I mean, it's no accident that we use 100 to talk about fractions and completeness. We could be talking about completion amounts in per mil, you know? Per, per thousand or, or in per deck, I guess. But we use percent, cent meaning 100. Because it's just this like, it's a kind of a lot, but it's not too much. It's enough for us to kind of go, aha, I get it. If you talk about a 10th, two tenths, it's a little too rough. But 25%, 27%, it gives us just this perfect amount of human-sized specificity.

• 26:25Hannah Fry?

  Does, it really does.

• 26:26Michael Stevens?

  There's something very human about it. And I think if anything, you're making this really good point that we aren't trying to talk about how to impress an alien. We're talking about the only intelligent species we, we have, and it's us. So we should focus on what means something to us.

• 26:43Hannah Fry?

  If you are an alien listening to this, then I'm sorry for us excluding you, okay? But, but that's, that's the argument I'm fundamentally making here.

• 26:52Michael Stevens?

  However, Hannah, humans do like 101. According to books in print.

• 26:57Hannah Fry?

  Go on.

• 26:58Michael Stevens?

  More book titles begin with 101 than begin with 100.

• 27:04Hannah Fry?

  Do they?

• 27:05Michael Stevens?

  Why? Because they know I'm right. 101 is better. They do, yeah.

• 27:10Hannah Fry?

  Have you checked this?

• 27:11Michael Stevens?

  I'll caveat this by saying I do not have the original source for this fact.

• 27:16Hannah Fry?

  Okay.

• 27:16Michael Stevens?

  It has been repeated in a lot of different locations. Books in print is always the one credited. It's even on Wikipedia with no citation. So I could have to eat my words. This might not be true anymore. I haven't searched a database of all titles. But the, the thrust of the argument is that it makes sense because a book titled 100 Great Recipes is like, okay, but 101 great recipes psychologically feels like, man, there wasn't even enough to give me a round number. You had, there's one more, it's a bonus. And so more books begin with 101 than 100. 101 implies abundance. It applies, what do you want to say? That our show has done 100 episodes or more than 100 episodes? The latter sounds better.

• 27:59Hannah Fry?

  Is it also just because of the wording of it? Like room 101, you know? It's like there's something about the palindromic nature of the word. You know, that thing, the thing that you just described about 101 recipes sound so much better? It reminds me of a story about an advert in the paper selling 10 beautiful puppies. And they were really struggling to get any takers. So they changed the advert, reprinted it with nine beautiful puppies and one ugly one.

• 28:26Michael Stevens?

  Oh.

• 28:26Hannah Fry?

  And then, and then sold the ugly puppy 10 times over.

• 28:29Michael Stevens?

  Oh, because people felt so sympathetic to it?

• 28:32Hannah Fry?

  Yeah, it's just like a weird, there's something, you're right. There's like, it's, it's sort of the just noticeable difference, right? It's like, just there's something like a little bit weird about 101.

• 28:40Michael Stevens?

  A little bit weird, exactly. So I think. Even 101 has something psychological to it, too. It's not just about pure math. It's also a little bit more than 100. It's a little bit, we can't handle it all. Our, our round number system is overflowing with 101, but 100 just fits in there all boring and square, you know?

• 28:59Hannah Fry?

  I think sometimes you need boring and square, though. I mean, you've got to draw a line somewhere and, and 100 is the place to draw it. I, I'm thinking here about the, the Carmen line, which we have mentioned many, many times on this, that the, the official line of where space starts is 100 kilometers up into the sky. Only 62 miles, which I think is actually less. I mean, you could walk there.

• 29:24Michael Stevens?

  Yeah, you could easily walk there.

• 29:25Hannah Fry?

  If gravity wasn't in the way.

• 29:27Michael Stevens?

  Yeah.

• 29:28Hannah Fry?

  But the problem is with this, there was a bit of an argument about this, about where the edge of space should be drawn. Because the point at which lift really stops mattering is actually somewhere between 66 and 88 kilometers. It's not at 100.

• 29:44Michael Stevens?

  Oh.

• 29:44Hannah Fry?

  Right? It kind of depends a little bit on different latitudes, that kind of thing. Um, so there were some suggestions that it should be more like 80, right? Or give or take 10, which sort of matches the, the previous definition. The US had a definition of 50 miles before.

• 29:59Michael Stevens?

  Hmm.

• 30:00Hannah Fry?

  Also, by the way, satellites on elliptical orbits can dip to about 80 kilometers at their lowest point and be fine, carry on surviving and go back around again.

• 30:08Michael Stevens?

  Oh, interesting. I mean, I knew the Carmen line was a bit arbitrary.

• 30:12Hannah Fry?

  It is.

• 30:12Michael Stevens?

  But I didn't really know where lift really ceased to be a, a method of propulsion.

• 30:18Hannah Fry?

  It's, it's kind of around there. It is around there, but 100 is arbitrary. And they said that they actually, they, they chose 100 because it's nice and round. But, but, but they literally did. And in doing so, by the way, there were some people from the US Air Force. The US Air Force would give out astronaut wings to any pilots who flew above 50 miles, right?

• 30:41Michael Stevens?

  Yeah.

• 30:41Hannah Fry?

  And some astronauts, so there's one guy in particular, Robert White, who in 1962 flew to 95 kilometers up. But unfortunately, he doesn't count as, he doesn't, doesn't count as an astronaut. Sorry, hon, got to give them back. But incidentally, in 2018, there was a, a big discussion about moving the line to 80 kilometers instead, purely because of this, this point about it being the, the point at where, uh, where lift stops mattering.

• 31:10Michael Stevens?

  Okay, well, thank you, because I think that you are emphasizing why I'm right.

• 31:15Hannah Fry?

  No, I'm not. I'm emphasizing that it's standard practice in human nature to draw a line somewhere, and this is where you draw the line.

• 31:23Michael Stevens?

  Exactly. Okay, that's what Celsius did with his system as well. He's like, oh, 100, that's going to be where water boils. 100, fine, that's where space begins. Here's the deal, you, you're calling it standard. I'm saying that that's proof that 100 is overrated. Okay? It's just used, we always just, it's like a magnet and we get sucked towards it. And I'm saying we need to stand up for our own individuality in, say, 101. Gosh darn it.

• 31:49Hannah Fry?

  Mm hmm, okay. But then we've got to do all this episode all over again next time.

• 31:55Michael Stevens?

  Yeah, I know. I guess I didn't think about that. Um, what is our 101th episode going to be? It's going to be a Field Notes episode from you.

• 32:08Hannah Fry?

  Oh, no, damn. Damn. I think we need to work out a way that I win and then we, then we don't have to return to this topic. What else you got? Come on, come on, hit me.

• 32:18Michael Stevens?

  Okay, you can't talk about 101 without talking about its, like, slang usage to mean introductory, right? English 101.

• 32:27Hannah Fry?

  Right, right.

• 32:27Michael Stevens?

  Calculus 101.

• 32:29Hannah Fry?

  Yeah, where did that come from?

• 32:30Michael Stevens?

  People aren't exactly sure. The OED, which I wish I, I had my big OED right over here so I could, you know, show it off, floss my giant dictionary. But they say it began at the University of Buffalo, or at least the earliest known usage of 101. In like 1929? But then I read Buffalo University was like, no, no, no. We used it way back in like 1924. Here's the deal, before the twenties, a lot of college courses, or a lot of just school courses, would just be kind of given a, a, a label, a number, and it was really hard to know what those numbers meant. So it was standardized in the 20th century, according to a system that said, look, let's do it this way.

• 33:12Michael Stevens?

  Let's have the first number be the, sort of the level or the.

• 33:16Hannah Fry?

  Yeah, the year.

• 33:17Michael Stevens?

  Okay? And then the, the, the next number could be the actual course number. And since we might have more than, you know, nine courses, we'll need to have two digits for that. Other schools would say first digit is the, the year, second digit is the topic, third digit is the, a specific class. That's why we wound up with these three-digit numbers. And then, I don't know, I don't have a good answer to this, but people love to start counting with one and not zero.

• 33:43Hannah Fry?

  Incorrectly, yes.

• 33:45Michael Stevens?

  I mean, I, it, it doesn't really make a whole lot of sense. It, it turns into some confusing things. And it's why we have 101 as the beginning of a course. Because you'd have, okay, so the freshmen, the first people to be learning in this topic, they'll, they should be, you know, zero, but actually they start at one. So we start at one, we're already at a hu, at the, at the hundred level. And then the very first course at the hundred level isn't numbered zero, it's numbered one. So you get 101. If we were to say, okay, the first class at level one is class zero, then 100 would be the beginning class. But instead it's 101. And so, yeah, 101 has become like, like a, a, a thing that people use

• 34:29Michael Stevens?

  in all kinds of contexts, like, oh, that is such a baseball 101 kind of thing. Or here's everything you need to know about online gambling, 101. It's, it's, um, got a little bit of fame for that.

• 34:40Hannah Fry?

  Okay, you know what, right? That, I, okay, I actually really disagree with counting starting at one. Okay, I much prefer counting starting with zero. There's a few reasons for this. Some programming languages, by the way, are correct in, in starting at zero. Python, for example, is like structures where it's like, the first item in a list is the zeroth item. And then the, the, the next item is item number one, right? Because it's like, how many items have there been already? Right, it works really well. This, by the way, is the main reason why, um, I think America is going down the pan. Uh, and that is that you're, the way that you number the floors in your buildings starts incorrectly, right? We have ground floor, then we have the first floor.

• 35:24Hannah Fry?

  You start on the first floor and then have the second floor, which is the first floor. You're incorrect, okay? Start at zero, it's ground, then you start counting.

• 35:32Michael Stevens?

  I am sympathetic to this. I, I will say, as someone who grew up in America and still live here, it is just more natural to me to say, oh yeah, first floor is the ground floor. And then when I go to the UK, it's so confusing. We're on the first floor and I'm like, cool, let's go outside. Well, we have to go down first. And I'm like, the heck? Starting at zero, though, I do appreciate. So I will admit that 101, having this cool meaning of like introductory, it only has that because we start counting at one instead of zero. But I thought there was something kind of beautiful about when we, The Rest Is Science, hit our 101th episode, it's 101. And I, I like that the, the vibe of being a 101, where it's accessible to everyone, where you have to begin,

• 36:17Michael Stevens?

  you have to all begin together. Don't underestimate anyone's ability, that kind of a thing I like, so.

• 36:24Hannah Fry?

  I'm not buying it. I'm, I'm sorry, I'm not buying it, because we've been doing this stuff for a year. And if you're only starting at our 101, I'm afraid you've missed out on a lot of stuff. You've missed out on hu, you know, well over 100 hours of me and Michael talking.

• 36:38Michael Stevens?

  Yeah, I mean, look, I agree, I agree that, this is not my strongest argument, but I, I couldn't discuss 101 without discussing its meaning of introductory.

• 36:49Hannah Fry?

  Yeah, no, that's fair. That's absolutely fair. Okay, I've got one, I've got one argument of why 100 is important, that it isn't arbitrary. Okay, because I think actually, nature cares quite a lot about the number 100. And, and not in a base ten kind of way.

• 37:04Michael Stevens?

  Yeah.

• 37:05Hannah Fry?

  During the first successful hydrogen bomb in the fallout, uh, this is 1952, by the way, this is, uh, in the Pacific, at one of the atolls in the Pacific, like 10 megatons explosion. In the blast, some of the uranium-238 nuclei were hit by so many neutrons at once that they, uh, swallowed up 17 of them before decaying into sort of, into new elements. And, uh, these new elements, uh, were sort of picked over by scientists and they discovered all of these, these, these new elements. So element 99 was found first. Element 100 is, uh, thermium, it's known as.

• 37:50Michael Stevens?

  Named after Enrico Fermi?

• 37:52Hannah Fry?

  I would guess so, yes. They found it in contaminated coral at the site. This all, by the way, was like, uh, classified until 1955. So for, for a really long, you know, for a few years, anyway. They had found element 100, but as, as far as the world knew, it didn't exist. Meanwhile, over in Stockholm, there's another group who made thermium in 1954, without realizing that the Americans had already done it. The normal way that you build heavy elements is that you sort of, you stuff loads of extra neutrons into a nucleus and then it gets in, it's sort of unstable and then it will convert into the next element up. Okay? But thermium-257.

• 38:36Hannah Fry?

  Is the end of that road. So if you add one more neutron in there to get thermium 258, it will just tear itself apart. Its half-life is 370 microseconds. So the neighbors, thermium 259, 260, they end up doing the same thing. Okay, so there's like what they call a thermium gap here. So there is no known thermium isotope that will decay into element 101. So thermium, it's basically the heaviest element that you can make by just adding neutrons, right?

• 39:20Hannah Fry?

  So it might be in a reactor, might be in a bomb, but it's the end of the line for building elements with neutrons. Because after that, you have to then start smashing big nuclei together.

• 39:32Michael Stevens?

  Oh.

• 39:33Hannah Fry?

  Just, you know, by handfuls of atoms at a time. Can't just like, have a little bit more, have a little bit more.

• 39:38Michael Stevens?

  Oh, that is very cool. So 100 protons in the nucleus is like this kind of magical cliff.

• 39:44Hannah Fry?

  Yes.

• 39:45Michael Stevens?

  Okay, I will say that is pretty neat. I, I'm not saying I'm totally swayed. I like that you keep pointing to humans and the physical world. Whereas what I've got are these kind of like, oh, it's prime.

• 40:00Hannah Fry?

  How has it worked out this way that the mathematician is the one anchoring it in reality?

• 40:06Michael Stevens?

  Well, you just never know. After 100 episodes, Hannah, everything gets topsy-turvy.

• 40:11Hannah Fry?

  Maybe by osmosis, if we've swapped personalities.

• 40:13Michael Stevens?

  I'm nervous now because all I have left is an argument that actually helps out your side.

• 40:21Hannah Fry?

  Go on.

• 40:22Michael Stevens?

  There's something I love about the number 100. It's the only thing I like about it. And it's the fact that in the Roman numeral system, 100 comes first alphabetically.

• 40:35Hannah Fry?

  Go on.

• 40:36Michael Stevens?

  C.

• 40:37Hannah Fry?

  Yeah.

• 40:38Michael Stevens?

  In the Roman numeral system, where you start with, you know, 1 is I, and then you have III, IIII, and then IV, 1 before 5, which is V. We can alphabetize all the numbers. And 100 comes first alphabetically as a Roman numeral, C.

• 40:57Hannah Fry?

  Yeah. Of all of the numbers, of all of the numbers.

• 41:01Michael Stevens?

  Yeah, of all the numbers.

• 41:02Hannah Fry?

  No, it cannot be bigger than 100 because otherwise you've got to put something in front of it. It kind of be smaller than 100 because otherwise it doesn't have the C there. Of all of the, every single number alphabetically, it is the first. What's the first number in English?

• 41:16Michael Stevens?

  Alphabetically, the first number in English is 8.

• 41:20Hannah Fry?

  Hmm, I was thinking 11. Yeah, you're right.

• 41:23Michael Stevens?

  And now I found David Pearce, there's this whole 79-page PDF where he investigated alphabetizing the Roman numerals. And here's the list. Number 1 is C, 100. Number 2, CC, 200. Coming in in third place, CCC.

• 41:41Hannah Fry?

  CCC.

• 41:42Michael Stevens?

  300. Okay, so here's the list. Yeah, you guys can peruse this on your own. 101 is the 302nd Roman numeral alphabetically. Pretty poor performance there. Interestingly, not only can we figure out the first number alphabetically in Roman numerals, we can also figure out the last one. Alphabetically, the last Roman numeral is 38. Which in Roman numerals is XXX.

• 42:13Hannah Fry?

  XXX.

• 42:14Michael Stevens?

  V.

• 42:15Hannah Fry?

  VI.

• 42:17Michael Stevens?

  Yeah.

• 42:19Hannah Fry?

  But hold on, why can that, oh, because if you put, I was thinking, why can it not be a bigger number? Why can't you have XXXX? But then it wouldn't be because then it would be, what's 50? V, L, L, right?

• 42:30Michael Stevens?

  L, right. So 400 is going to get you into the XL, 10 before 50.

• 42:36Hannah Fry?

  Right.

• 42:37Michael Stevens?

  So.

• 42:37Hannah Fry?

  It really is the last one.

• 42:39Michael Stevens?

  Yeah, 38 is the last number alphabetically. Unless you use the non-standard Roman numeral for 9. Normally 9 is IX, 1 before 10. But sometimes you will see it, even in the ancient world, written VIII. So a 5 with 4 1s after it. In which case, XXXVIII would come last, which is 39. But using the most standardized Roman numeral system, 38 is last alphabetically. And 100, your number, comes first.

• 43:19Hannah Fry?

  I think we've reached a conclusion, don't you? From here on in, we're going to change our numbering system to the Roman one.

• 43:28Michael Stevens?

  I think that, yeah, wouldn't that be funny? We began debating 100 versus 101 and we ended with a petition to the World Mathematics Association to convert us to the Roman numeral system.

• 43:40Hannah Fry?

  To get rid of our big numeral system.

• 43:43Michael Stevens?

  Goodness gracious.

• 43:44Hannah Fry?

  Yeah, look, you know, it's not where I thought we'd end up, but I'm willing to back it all the way. Okay? Where do I sign?

• 43:51Michael Stevens?

  What a perfect opportunity for all of you out there listening to let us know in the comments below, what's better, 100 or 101?

• 44:00Hannah Fry?

  And we will see you next time for episode CI on the rest of science.

• 44:07Michael Stevens?

  CI, 101, CI, see you later. That's in the Michael numeral system. It's like the Roman one, but way worse, but funny.

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