Unadulterated Dice Nerding

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Bossils can show us the past, but research is shaping the future. And for more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit cancerresearchuk.org-forward-slash-rest-is-science. This episode is brought to you by Project Hail Mary, the new spectacular space adventure coming to cinemas. Okay, hypothetically, imagine that there's this mission to save our world. Only you can do the job. As this expert in mathematics and science, how do you think you would do? Terribly. But not because I love teaching and learning, because I'm a scaredy cat. But what about yourself, Hannah? I'm back myself, Michael. I think I'd be good. I just, I'd just be very slow. I think the point is that no one should rely on Hannah or I to save the world. In Project Hail Mary, Ryan Gosling stars as science teacher Ryland Grace, who is sent unexpectedly on an impossible mission to space to discover why the sun and stars are dying. He teams up with an unimaginable ally to defy all odds and save the universe from extinction. See Project Hail Mary in cinemas and IMAX from Thursday the 19th of March. You can also catch it early on Saturday the 14th of March, Pi Day and a Sunday the 15th of March. Welcome to the rest of science. This is Field Notes. A kind of podcast expedition diary where Michael and I, we trade stories about objects. It's thrilling discoveries. Big questions. Anything that's been occupying our minds. Yeah, each week one of us is going to bring in something to either show or tell. That's what it is. It's the rest is science's very own version of show and tell. Do you think people have noticed yet that the two episodes that we put out a week are not the same thing? I don't know. I think ultimately it's you and I chatting about stuff. I haven't brought that up with the producers. I don't mind. I mean, it's obviously it's very fun. I still feel like we put so much more effort into the main ones and then people haven't even noticed these are the things we just have a load of fun. These are different. Just have a load of fun. This takes a tenth of the amount of time to work. But anyway, welcome. This is Field Notes. We're going to be sharing some objects later, Michael. You've got something to share with us, haven't you? I do. I've got some things. Thingazoo. Yes, but first what we thought we would do is we would empty our science mail bag because we've had some really interesting questions in. One from Lou Fern, who wants to know, Michael, is it Math or Maths? I don't know. I don't know. Math or Maths. You guys across the Atlantic call it Maths, plural with an S. And I didn't even know that until I moved to the UK. Ding-ee. I don't think it's a thing that Americans confront all the time. Like, oh, that's the British word for mathematics. Aluminum. Yeah, exactly. I think a lot of Americans don't experience aluminium either because the way the whole world of entertainment especially is like made for the American local audience. And then the rest of the world just gets the American version and they get it. They're aware of these differences. I mean, I'm only really speaking for myself and as a child, I never confronted. Oh, it's an elevator or a lift. It's a truck or a lorry. It's a it's math or maths. But I am curious to know because I've heard the justification from people like you going, but there's more than one kind. It's maths. I don't. You don't say that? No. I mean, I agree that that is what some people say. Okay, so then I take that back. I feel I feel very bad that I put words in your mouth. But it's definitely a thing that I've heard as a justification for maths. And then I'm thinking I get it. There's geometry, trigonometry, group theory. But they're all mathematics. It feels like it's one unified thing. Also, people don't say, people say maths is, they don't say maths are. Oh, that's right. You know, that's right. It just the plural thing doesn't work for me at all. So how is what is your feeling about it? I say it because I want to be patriotic and and yeah, for my my country men and women. But ultimately, I actually think it's probably should be math. Fascinating. Now look, I don't I don't think one's more right than the other. So, you know, I don't have a dog in the fight. I'm not like, no, Americans are right. But it's interesting to hear that take from you. I mean, gymnastics. Like, you wouldn't say gyms, would you? We don't say math. I'm doing some math, specifically, or trigonometry right now. That's why I said math. But if I was doing trigonometry and a little bit of algebra, then of course, I'd have to say that I'm doing maths. I'm absolutely fine with it. What I normally do is I write math and then put a little S in the brackets. Sure. Yeah, I mean, what I like to do is just, just elongate it to mathematics and then everyone's happy. Anyway, you'll hear both from us. And we're not ashamed of it, okay? No, not at all. I think we all know what we're talking about. And that is the point of language. Absolutely. Speaking of language, I'm going to use some more to describe a question from Max Sebastian. And by describe, I mean verbatim read it. Max asks, can you talk a bit about mosh pits and fluid dynamics and how that links to crowd safety at large concerts? Absolutely, I can, Max. When this question came in, I had completely forgotten that there was a paper that was published in about mid-2010s, which was the most wonderful paper. And it was called collective motions of humans in mosh pits and circle pits at heavy metal concerts. It was a bicembal proper good mathematicians of physicists. And what they did is they attended a number of heavy metal concerts and also watched videos of them on the internet. And it is written as a proper academic paper would be. Here's a sentence from it, just to give you a sort of flavor of heart reads. The mood is influenced by the combination of loud 130 decibels, fast beats exceeding 300 beats per minute. Music synchronized with bright flashing lights and frequent intoxication. Yeah, all right, it's a physical system and they're describing it properly. I appreciate that. What a way to distill the joy of a good night out with your friends. Anyway, here's the thing, if you stop thinking of people as people and you start thinking of them as particles, actually what you see in mosh pits is this behavior that is common across systems of fluids, essentially. And each person effectively is like a particle, right? They're propelled, they're constantly colliding, and they're reacting to what's going on around them locally, not the whole global system. They're not sort of all following a series of rules, they're just they're just reacting to what's going on around them. So these physicists, what they did is they made this mathematical model, this computer simulation. I mean, a door of bleak sense of humour here. They called it the mobile active simulated humanoids model, otherwise known as mashers. Cute. There are two different tendencies that people have when they're in this sort of crowd situation. Either we tend to copy what people are doing around us, flocking behaviour, which is what you get when you see big, um, big, uh, flocks of birds, um, where they're sort of copying the average speed in direction of their neighbours. And humans are doing the same thing, right? If the crowd is moving in a particular direction, we tend to copy what's going on immediately around us. But then we also, you have sort of more random movement, unpredictable movement, when we're acting as an individual, you know, say somebody spots a friend or whatever it might be. And what they found is that actually these mosh pits, they do have this gas like state. They, they essentially form the same patterns that you would see if you were looking at a box of atoms, right? This sort of disordered gas. This Maxwell Boltzmann distribution is what it's known, but people are sort of pinging around from each other in this, in this disordered way. Um, but then when you get more people going in, people organize into this vortex like state, this sort of circular motion that you see precisely as you do in fluids, where people are sort of rotating, um, with the audience. And this is like something, these, uh, these circle pits that, that emerge from nowhere, it's this emergent property. Nobody ever says like, okay, off you go, start rotating in this direction. These are people with their own personal wills. And they're not, they haven't organized any of these patterns. That is just something that happens when you stop behaving like you won't start behaving like particles. If you, um, if you've been in a mosh pit, I'm like, no, I never have. No, no, absolutely not. This is, uh, I am very much not a mosh pitter. Okay. One of the things, so I actually, um, this is one of the things that I did after, so my PhDs in fluid dynamics, but, um, after that, I then started working on, uh, complex social systems, right? So including things like crowd behavior, this is one of the things that I was doing, you know, mathematician modeling this stuff. And the thing that's really interesting about crowds is that you get this, you know, this behavior, like a box of atoms or a fluid that's moving around. But there comes a point where crowds become so dense, and it's normally when you get about five to six people per square meter. Okay. When they start to actually become quite dangerous, when it stops flowing like a fluid, and instead becomes, it's called granular flow. So it's much more like, um, sand in a sort of collapsing. Yeah. Right. Okay. So there's a lot more squeezing and cleaving. Exactly. Exactly. And, and this is the fact that people turn into that state, whether acting like granular flow, that's one of the reason why crowd crushes are so, um, are really dangerous, because they're quite hard to stop once they begin. If you think about trying to control a pile of sand, sort of move it effectively, and apart from making it less dense, you, it's really difficult to control that flow. It's also, I don't know if you've ever been in a, in a really busy crowd, I've been in a couple, you know, football games, and sort of people start shouting like, stop pushing, stop pushing. And it's not that people are pushing is that the movement sort of ends up driving itself. You end up getting these, these dynamics that flow through the crowd. Oh, interesting. Yeah. That's happened to me one time in New York City on New Year's Eve. Oh, right. We were all waiting to get into Times Square. And I found myself being moved just by the people around me moving. But you're right. No one was pushing. Like it's, it's, no one was on the outside going, I'm gonna push everybody. Yeah. It was an emergent property of everyone's motion together. And I was like being lifted and moved like this, like I was in an ocean. And I was like, this is, it was very scary. It's very scary because you, because I think at that moment, you don't feel like you have the autonomy of a person anymore. I mean, because you don't. But the thing that's really interesting about this using these fluid dynamics and physics equations and models to, to look at crowd behavior is that you end up getting really counterintuitive results. So for example, one of my favorites is if you imagine that you have a doorway, right? And a huge number of people who are trying to get through it. So you have this sort of granular flow where people are kind of, like, bunched in together and pushing everyone desperately trying to get through. You, you would expect to see that clumping that you would have if you were, you know, if you're trying to push, kind of grains of wheat through a, through a really small opening, you kind of would get these clumps where it clogs up for a bit. And then maybe you kind of release the pressure and then you get a big burst and then it stops again. You get the same pattern of behavior when you have humans or pushing through towards and getting through a small opening. But one way that you can solve it, right? Which is something that was discovered by mathematical modeling and then demonstrated in experiments since is that it's completely counterintuitive. If you put a ballad immediately in front of the doorway. So where the crowd would be standing, you sort of, you have your doorway and then a couple of steps back, would you have a ballad, right? Effectively, kind of blocking the doorway in a way. What that actually ends up doing is it forces people, rather than bunching around that, that single opening. It forces people to form these lanes around the side. And then if you think about it as though it was sand or grains of wheat or whatever it might be, if you stop that clogging from happening immediately above the opening, actually, you would get this much faster flow, this much smoother flow of people. I'm going to ask, is that possible with pouring grain? Yeah, exactly. It absolutely is with pouring grain. If you stop the clogging by kind of creating a little barrier immediately in front of the exit, then yeah, you get much, much smoother flow. The only problem is that even though it works mathematically and in experiments, no one wants to put a ballad in front of an exit, because it sort of feels like you're doing something quite dangerous. Yes, it does. It sounded dangerous. So in the context, I'm like, oh, I see how this is a safety mechanism, actually. Yeah. So what you have instead, with newer designs of stadiums and buildings that deal with large crowds, they do things like they'll have offset barriers, although have railings in particular way or curved approaches. The general idea is think of lots of humans together as though they are grains of rice or wheat or whatever it might be, and the way that it will clog up and design the system so that they can flow as smoothly through as possible. That is all really cool. I love that. I love knowing that I'm a human with a conscious will, but at the same time, I can also become a piece of sand or a molecule of gas. Thank you for that question, Max. Coming up after the break, we're going to look at some other bizarre behaviors and see what emerges. That's right. I'm talking about... This episode is brought to you by Cancer Research UK. Radio therapy is over a century old, but it is still changing. Cancer Research UK helped lay the foundations of radio therapy in the early 20th century and has driven progress ever since. Radio therapy remains one of the cornerstones of cancer treatment today. Every year, millions of people worldwide benefit from cancer research UK's work to make it more precise. Scientists are still refining how radio therapy is delivered, and one example is an experimental treatment called flash radiotherapy, which delivers radiation in fractions of a second up to a thousand times faster than standard radiotherapy. An early studies suggest that speed could make a real difference. Flash radiotherapy may cause up to 50% less damage to healthy cells. But scientists don't yet know why healthy cells seem to be spared, so cancer research UK are working to answer that. Understanding it could be key to reducing side effects in the future. For more information about cancer research UK, their research and breakthroughs, and how you can support them, visit cancerresearchuk.org slash the rest is science. This episode is brought to you by Thriver. Most of us tend to think of blood as something slightly clinical, linked to illness or bad news. But in reality, it has been quietly keeping a record of what's going on inside our bodies, almost like a biological diary. It holds clues about how everyday choices shape our health, sleep, stress, food, movement, and without access to that information, staying healthy can feel more complicated than it needs to be. Thriver is a proactive health platform, though, unless you check in from home using regular at-home blood testing, with clear guidance to help you understand what your body is telling you. That sense of clarity changes how health feels. Instead of juggling advice, rules, and trends, you get a simpler sense of direction, what looks consistent, what's shifted a little, and what's actually worth paying attention to. It just makes health feel calmer and simpler to think about today today. Head to Thriver.co to get started. That's THRIVA.co. And use code TRIS for 20% off your first test. This episode is brought to you by our wonderful friends ATIO, the AI CRM. William here from MPa, briefly crossing the GoalHanger network borders. In this AI era, software doesn't just store information, it understands how everything connects. Work now happens across meetings, messages, and calls, information is there, but the shared volume of it can hide what actually matters. Most CRM's capture activity, but rarely turn it into insight. ATIO is the next generation CRM built with AI at its core. It reflects our modern team's operate fast, lead, and interconnected. Sink your email and calendar and you're up and running in minutes. From there, teams simply ask ATIO what they need to know. It's about deals, customers, or what's moving across the pipeline. Powered by universal context, ATIO's intelligence layer, it connects what's happening across your meetings, messages, and data, and it turns into answers you can actually act upon. With ATIO, you are seeing what's gaining momentum, what's stalling, and what needs attention next. In an accelerating world, clarity is the real competitive edge. Try ATIO for free at ATTIO.com slash MPa. DICE. I have my 10 dice, a D1 to a D10. I'll show this off later when I've earned my turn, but here's a two-sided die. It's basically just a coin. It's rounded enough that it will not land on its edge. I'm going to flip and or toss this. I need you to pick a number. Do you want to be one or two? I want to be number two. Okay, here we go. Okay, I'll flip it, catch it, it's over, and the answer is one. It's number one. You are up first. What on earth possessed you to make a die that was just a coin? We had to, because we wanted to do a D1 to a D10, and D1 means a die that allows you to make one decision. This die right here, I'll pull it out of the foam. It's a D1. It's not a one-sided die because it has more than one side, but because of the way it balances, it can only ever fall on one. This is its shape. It looks like a piece of penne. It looks like a piece of penne, and it only has one stable equilibrium point, which is this way with the one facing up. It's perfect for if you have no choice, but still can't make up your mind. Okay, if it rolls a one, I'll do it. It's always going to be one. Hang on, I need to ask more questions about this. What is wrong with just normal and normal dies? What is wrong with the six sides? You know, you know where you stand. This wasn't enough for you. Nothing's wrong with it. It's perfect. I love these things. We all know them. This is a version with numerals instead of Pips, the little dots, but sometimes you've got more than six decisions you need to make. Sometimes you're working with a percentage, right? You're playing some tabletop game where you need to figure out, okay, what's my, you know, likelihood of having a critical strike? And that should be out of a hundred. So you could use the ten-sided die to do, you know, a hundred percent, 90, 80, and so on percent to decide that randomly. You rarely need a three or a five or a seven or a nine, but that's what we do. The rare, the unnecessary stuff. The stuff that's a conversation piece. Presumably, you can use these in situations that don't just involve tabletop games like Dungeons and Dragons or whatever it might be. You Dungeons and Dragons fan, by the way. I'm a fan, but I have never played. You've never even tried to play a game. I've never had any friends who played. Michael, I'm sorry. What about yourself? I bet you went through a phase that's still going on. I'm really sorry to this point. I have played it, but I wouldn't say that it's a regular occurrence in my life. Again, it's because I don't have the friends. My friends are all cattan people, you know? They're snotty about monopoly, right? But not snotty about cattan. They're just, they're not, they're not the extreme end of the spectrum. Well, we've got to find some better friends, Hannah, because Dungeons and Dragons, I think, would be fantastic for us, especially armed with all this randomized mathematical knowledge and tools. You could use this beyond just board games there, right? I mean, in your day to day life, anytime you come across, I don't know, across roads, you can get out the three-way die to choose which path you're going to go in. Who's going to pay the bill? Well, there are five of us, so I will use the five-sided die. You can't use a regular six-sided for that. Now, I don't want to get ahead of myself. I'll show off the three. Now, the three is basically a kind of barrel die. And I'll explain that for those who aren't watching the video. It's basically just a barrel with rounded tops and bottoms, so it won't land on its top or bottom. And then the sides are faceted. So there's three sides. And it can fall on them to get a three or a two or a one. Have you checked whether they's a fair? Have you checked whether you are eating or not? Yes, it's get a one, two or three. Yes. And that's why they took so long because we 3D printed all of the prototypes and then realized that the weight was different than it was going to be when they were injection molded. So we had to have an actual factory make an entire set, send them to us. And then I didn't do it. I had our science writers Scott do it. I said, today you're going to be rolling these die and making tally marks. And we actually found that they were all fair right off the bat. But that was because of all the prep we had done. And when I say we, I mean Scott, he did all the mathematics behind, okay, how is this going to be fair? How thick does a shape need to be to land on its edge? Just as frequently as it lands on its top and bottom. So the four-sided die is just a tetrahedron. Triangle base pyramid standard. You can find these in any game shop, any die shop. The five-sided die, that's the odd ball. And there's a lot of different ways to do it. Have you ever seen it done? Five-sided? No, I mean it's really tricky right because you can't do, oh well, you can't just use a pentagon because then you've got the other ends right? If it falls on either of those, that's sort of seven sides. So you've got, it's tricky. It's tricky. And the cop out, the one I don't like is to just keep making barrel dyes where you take a cylinder. You round the top and bottom so it won't stay on them. And then you just slice a regular pentagon around the side. So it's got five facets there. And now you roll it and it rolls like a log. And it's going to wind up with one of those facets down, one of them up or whatever. You know, I thought that was boring. It was just too easy. So instead, we took a triangular prism and we made it thick enough that it will land on its edge, one of its edges just as often as it lands on its top or bottom. If it lands, say, with this edge down, the two is at the top. So you've rolled a two. See that? So hang on. So where is the four-sided die? Is it's like a triangle-based pyramid? Yeah. And then the five-sided die, it's more like a chunk of derrily, laughing cow. That's where we're talking. That's right. A little bit of squeezy cheese. The six is just the standard cube. A cube gives us six sides and it is a regular platonic solid. Okay. I've got a couple of things to say about the six-sided die if I may. Right. The first thing is I'm extremely in favor of of switching over all your decision-making to dice rolling rather than actually making any choices. And there's a company, a restaurant in the UK that has gone for this approach. They're called Dishoom. They're like this, this Indian restaurant. They're really popular. But there was one point where they decided they wanted to get more people to come during the day. So they ran this promotion where if you, like, ate enough times in their restaurant, you qualified to be given a teeny tiny little die, right, with, you know, standard six size, the standard cube-based die. And what happens is if you go in and you eat a meal between, I think, it's one and six, something like that, and you roll the die, right? If you land on a six, you get your whole meal for free. Okay. Which is like, hmm, that's smart. That's kind of like a cute idea. But the thing is, is that when you actually work out the sort of mathematics of this, it would have been exactly the same as if they had just said, if you're a regular customer, if you eat between one and six, you get 15% off your meal, right? It's exactly the same thing. But how much more fun is it to do it where it's based on the role of a die? Okay. So if you rolled a one, two, three, four, or five, you paid full price. Full price. But there's a one and six, so you are walking away free and easy. Yeah. So would you rather have 15% off every time you went or a one and six chance of getting it for free? Obviously. Obviously the last one. Though in the long run, they're the same thing. You'll might have spending the same amount. But in the short term, you could roll a six, three times in a row. And, you know, that's good. And you know, it's, it only needs to average out, like, I mean, if you're the one individual, you could only go once and then just, you know, never pay them some other poor suckers rolled a one. Many hundred times in a row is the one that's struggling and effectively paying for you. Do you know what the dice were made of? I don't, I don't, because I wouldn't, I wouldn't do that as a store, like manager or owner, because people could game it. If you take a regular die and you just put it in a, like a warm oven, like a 200 Fahrenheit oven for a few hours, it'll soften and gravity will cause it to get imperceptibly, but truly a little bit heavier on the bottom. So you put it in there with the six side up, and the one side will fatten in a way that you cannot see. But it's so much denser there that you're going to roll a six, I mean, not all the time, but much more often than you should. Well, anyone who's got a tissue, little dice knows how to game the system now. I have, I have a second thing to say about the six sided die, if I may, which is a critique of your decision to go for the bog standard boring die. Oh, well, what else should I have done? So here's the thing I think there's redundancy, I think there's more going on in the standard six sided die than you need, because it has like extra levels of symmetry that are just totally irrelevant, right? You take a die, yeah, of course, you want it that it lands on the numbers one to six. You know, there's equal chance of landing landing on each one, but you don't really care that you can rotate it on the number one, and the number one still come up, right? Right. I'm not interested in that. Nothing lasts just extra redundancy that I need. Well, I think you should have gone for instead, Michael, and you know, it gives you an amazing curiosity box of tender and die. It's like a wonky die, like this. Oh my gosh. You seen these before? The wonky die. Can I, let me go look at my dice collection and see which kind I have. I have some like that. I may not have them, but that, so that looks like a regular cubic D6, and yet it's all slanted and skewed, but it's still fair. Still totally fair. So this is like exactly right. It looks like a normal die, but it looks like someone sat on it or left it in the oven for too long and kept turning it, basically. It's sort of like, it's sort of like an Alice in Wonderland version of a normal die. That's right. And it's like modern art meets a regular die. Exactly. But the thing is, is that when you roll this, you still are equally likely to get one or one to six, right? Any of those numbers are equally likely to come up. But what this is doing is it is removing all of the redundant ways that the original dies the symmetrical. So this is like the, has the minimum amount of symmetry required to make the dies fair and no more. Oh wow. Which makes me think that these are superior. Got to be honest with you. I didn't know that about them. I just thought they were like novelties. I knew they were probably fair, but they had the minimum amount of symmetry needed for six choices. Yeah. There's no rotational symmetry on it at all. Much much nicer, much more pleasant. Well, the seven we got to use our little trick. We made a pentagonal prism that's just thick enough that it's likely that land on any of its edges just as much as it is its top or bottom. So it's five. Five is the weird one then. Well, five, seven and nine are all weird. They're all prisms that have to have a certain thickness. The nine is a pentagonal prism with just the right thickness. I like this a lot. I like this a lot. I also just like the idea of you wondering around your day to day life and and using them at all opportunities. That's that's the thing I like the most. Yeah. It impresses people. And if it doesn't impress them, well, then they're they're just not for me. They can go and play Dungeons and Dragons on their own, Michael. Some people call it people repellent. I call it a friend finder. Or this die stuff, you know, using it to generate random numbers to help you make decisions is all well and good, right? But what if you need more? What if you need more randomness? What if you need more than just six digits? And for that, Michael, I've got something to say you can turn to this book that I have very proudly had on my show for a number of years. It's called a small book of random numbers. It's an absolute page turner. Yeah. It's quite it's quite dinky. I think they come in larger sizes, but I'll be honest with you. I've got the cheap one. I should I give away the ending for you? It's quite the page turner. Yes. The ending here is five three four seven seven and then four three four six six. I know what you're thinking. You didn't see that coming, right? I did. Wow. Spoiler alert. Spoiler. It is quite literally just an entire book filled with pages and pages of nothing but random numbers. One of the reviews on Amazon for this book said that it relies too heavily on 10 characters, which I quite enjoyed. But it is totally unbiased. And I know you might be thinking why on earth would anybody ever want to have an entire book of random numbers? But there are actually really strong reasons for this. So particularly in the 1950s when people were starting to do big calculations for the space program or where they were trying to sample populations or come up with military routes to travel across terrain that might be attacked by other people. In all of those situations, having random numbers genuinely random numbers was really, really important. If you are crossing enemy territory and there's a route that you want to go in, you want to make yourself as unpredictable as possible. So you might want to add in a certain random amount of noise. If you try and come up with that yourself, if you try and make up that randomness, then you are going to fall into the trap that humans are very, very, very bad at coming up with random numbers. You need something like this small book of random numbers in order to help you. So in the 1950s and many, many times since, scientists have sat down with processes that create genuine randomness. So things like the static on a television or a wall full of lava lamps or looking at the radioactive decay of very, very small, atomic properties and use that to collect the randomness that appears naturally in nature. And then printed it for other people to use. And so yeah, I'll be honest with you, I haven't done it start to finish. I've just flicked in and flicked out. Have you used it for anything, even like a game? No, I haven't. I have used because now you can get computer, if you're like programming. So, you know, from my PhD and in my young years, I used to build a lot of mathematical models. And there are pseudo random number generators that you can get that sort of do this job for you. They're called pseudo random because they're not totally, perfectly random. Like nothing is apart from physical processes. You can't sort of generate randomness by doing like, you know, deterministic processes on a machine. But I, so I've used lots of random numbers. I've never used the actual book. I'm cheating, really. All right. Well, you showed off a book. I've got a book of digits that are not random. You can easily calculate them. One million digits of pi. This book contains pi in order, right? So it starts with three, but it's got a million digits. Here's some in the middle there. Oh, man. Amazing. I'm not telling you how it ends because this is just part one. Oh, I'm an infinite number. So this is beautiful. And related is a book that is quite controversial. But I own it because I'm not afraid. This is the square root of four to a million places. Hang on. Square root of four. Yeah. It's just two. The first million digits of the square root of four right here. Show it to me. Okay. So square root of four, it also begins in the way that we would all expect. Do you see the two point zero? Is it just zeros? Yeah. And then it's just a million zeros. The whole way through a million zeros. Michael, how many trees had to die for the purposes of that joke? Well, when I had it made, I said just one tree, but make it painful. And so that tree suffered. No, here's the way I feel about it. I think that this is much less than one tree. The trees are replanted twofold when they're cut down. And I've used this so many times to get people excited about math that I think that that tree died with honor. I think that's great. And if you if you think there's a problem with printing a million zeros and you get mad at me for it, I get it. But you are playing big pollution's game. They want you to get mad at the little guy who's trying to teach math. Well, they just deforest were fun. But that's also it's beautiful about the book. It's a funny joke. It's a cool mathematical teaching tool, but it's also a philosophical lesson about the rights of plants. It's also an incomplete series. You need an infinite number more copies in order to fully complete this query for the script of two. Yeah. I don't have enough precision. No, a million zeros. And then what? How does it end? Tell us. How long does it end? I don't know. Do you remember when there was a friend of us, Brady Haran and Matt Parker, the YouTubers, where they took a million digits of pi and they printed it out on a roll. They printed it by hand though, right? No, no, they printed it. They constructed it by hat. They cheated slightly. They went in and they annotated it. I think it still took them four hours. They had to go to an airport runway and unroll it. Took the majors. Something fun to do in an afternoon. Roll out a million digits of pi. It was actually a really interesting video if you want to go and watch it. But I do remember Brady telling me that once they rolled up that sheet of paper, he got a message from someone on the internet asking to buy it. And he sold it to them and used the money to buy himself a very nice watch. I mean, that doesn't really save very much, I think, because I've got a nice watch that's like 120 quid. How nice of a watch, I guess. How nice of a watch. But somewhere out there, there is a person who owns a mile of pi on brown paper. I also like the idea that this is a person who is who's carrying their mile of pi around with them all times just in case they bump into someone like V-Saw's in a museum and can use it as an opportunity to make a friend. Well, yeah, so that person might be listening to this podcast. I'd love to know what they're doing with it. Do they have it shoved in the back of a closet? Is it on display? If you own the mile of pi, reach out because I want to meet you and I might even have an offer to make you. A mile of pi annotated by Matt Parker, I mean, that's Smithsonian stuff right there. That's the big dog. So there we are. That was an episode of Field Notes where every week Michael and I are going to bring something to show and tell the other. It might be a little object. It might be a riddle, it might be a thought experiment, it might be a question or a story even. Yeah, life story. Hey, why not? I want to hear about what you've been a confessional even indeed. If you have something that you would like to contribute to Field Notes, then you can write into us the rest of science at gohanger.com with your ideas, with your thoughts, with your stories, with your questions. Yes, please do. I cannot wait to read those and experience what you guys send over. And until next time, see you later.