Unadulterated Dice Nerding

0:00This episode is brought to you by Cancer Research UK. Dinosaurs walked the earth 180 million years ago. But, you know, cancer was part of their story too. Scientists have found tumors in ancient fossils. Well, that is part of the reason why cancer is a big, big part of our story, right? It's the other side of evolution. It's the most complex disease that we face. There are more than 200 types of cancer in total, each with distinct characteristics, challenges and mysteries. And that complexity demands scale. Cancer Research UK is the world's largest charitable funder of cancer research, with more than 4 ,000 scientists, doctors and nurses working across more than 20 countries in the search for answers, and then sharing their discoveries beyond borders.

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1:21Welcome to The Rest is Science. This is Field Notes, a kind of podcast expedition diary where Michael and I, we trade stories about objects, 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. I mean, 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 mean, I think ultimately it's you and I chatting about stuff. Like, yeah, I haven't brought that up with the producers.

1:54I don't mind. I mean, 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 that these ones, we just have a load of fun. These are different. Just have a load of fun and it 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. Things, yes. But first, what we thought we would do is we would empty our science mailbag because we've had some really interesting questions in.

2:29One 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. Didn't you? I don't think it's a thing that Americans confront all the time. Like, oh, that's the British word for mathematics. Aluminium. 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, it just gets the American version and they get it.

3:10They'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 that's what some people say. Okay, so then I take that back. 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.

3:50It feels like it's one unified thing. Also, people say maths is, they don't say maths are. Oh, that's right. You know? That's right. The plural thing doesn't work for me at all. So what is your feeling about it? I say it because I want to be patriotic and care for my country men and women. But ultimately, I actually think it probably should be math. Fascinating. Now, look, 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?

4:35We don't say math. I'm doing some math, specifically 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 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. Speaking of language, I'm going to use some more to describe a question from Max Sebastian.

5:11And 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 by some proper good mathematicians and 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 um here's a sentence from it right just to give you a sort of flavor of how it 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 what a way to distill the joy of a good night out with your friends um 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 some systems of fluids essentially and and each person effectively is like a particle right they're they're propelled they're constantly colliding and they're reacting to what's going on around them locally, not the whole global system.

6:46They're not sort of all following a series of rules. 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, adorably good 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 uh tend to copy what people are doing around us flocking behavior which is what you get when you see big um big flocks of birds where they're sort of copying the average speed and direction of their neighbors 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 um 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.

7:43And what they found is that actually these mosh pits, they do have this gas-like state. 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 disordered way. But then when you get more people going in, people organise 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 with the audience. And this is like something, these circle pits that emerge from nowhere.

8:29It'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 start behaving like people and start behaving like particles have you um have you ever been in a mosh pit michael no i never have no no absolutely not this is uh i am very much not a mosh pitter okay um one of the things so i actually um this is one One of the things that I did after, so my PhD is in fluid dynamics, but after that, I then started working on complex social systems.

9:09Right. So including things like crowd behavior. This is one of the things I was doing, 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, 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 sand in a sort of collapsing. Yeah, right.

9:45Okay, so there's a lot more squeezing and cleaving. Exactly, exactly. Exactly. And this is the fact that people turn into that state where they're acting like granular flow. That's one of the reasons why crowd crushes are so 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, 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.

10:24And it's not that people are pushing. It's that the movement sort of ends up driving itself. You end up getting 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 going to push everybody. 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.

10:59And 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 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.

11:31you 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 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 behaviour when you have humans all pushing through towards getting through a small opening but one way that you can solve it, right which is something that was discovered by mathematical modelling and then demonstrated in experiments since, is that it's completely counterintuitive.

12:05If you put a bollard immediately in front of the doorway, so where the crowd would be standing, you have your doorway and then a couple of steps backwards, you have a bollard, 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 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.

12:48I was 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 bollard in front of an exit because it sort of feels like you're doing something quite dangerous. Yes, it does. It sounded dangerous. But 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 or they'll have railings in particular way or curved approaches.

13:34But 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 dice.

14:19I 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.

15:09Like 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 okay 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 and so 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, right? What is wrong with just normal, a normal dice?

15:48Like 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 likelihood of having a critical strike. And that should be out of 100. So you could use a 10-sided die to do, you know, 100%, 90, 80, and so on percent to decide that randomly.

16:24You 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. Are you a 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 disappoint. I have played it, but I wouldn't say that it's a regular occurrence in my life.

17:04Again, it's because I don't have the friends. My friends are all Catan people, you know? They're snobby about Monopoly, right? But But not snobby about Catan. They're just, they're not the extreme end of the spectrum. Well, we've got to find some better friends, Hannah, because Dungeons & 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 though, right? I mean, in your day-to-day life, anytime you come across, I don't know, a crossroads, you can get out the three-way die to choose which path you're going to go in.

17:41Who'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 weren'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 these are fair? Have you checked whether you are equally likely to get a one, two or three?

18:23Yes. 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 writer, 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?

18:59How 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 dice shop the five-sided die that's the oddball and there's a lot of different ways to do it do have you ever seen it done five-sided no i mean it's really tricky right because you can't do well you can't just use a pentagon um because then you've got the other ends, right? That if it falls on either of those, that's sort of, that's seven sides. So you've got, I mean, it's tricky.

19:39It's tricky. And the cop out, the one I don't like is to just keep making barrel dice, 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.

20:20If 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 whereas the four-sided die is like a triangle-based pyramid. Yeah. And then the five-sided die, it's more like a chunk of Derry Lee, you know, laughing cow. That's where we're talking. That's right. A little bit of squeezy cheese. Yeah. 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 switching over all your decision-making to dice rolling rather than actually making any choices.

21:04And there's a company, a restaurant in the UK that has gone for this approach. They're called Dishoom. They're like 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 are qualified to be given a teeny tiny little die, right, with, you know, standard six size, the standard, you know, 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, that's smart, that's kind of like a cute idea.

21:46But 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 diet? Okay, so if you rolled a one, two, three, four or five, you paid full price. Full price. But there's a one in six chance that you are walking away free and easy. Yeah, so would you rather have 15 % off every time you went or a one in six chance of getting it for free?

22:20Obviously the latter. Obviously the last one, though in the long run, they're the same thing. You'll wind up spending the same amount. But in the short term, you could roll a six three times in a row. You could. And, you know, that's good. And, you know, 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 sucker who's rolled a one many hundred times in a row is the one that's struggling and effectively paying for your meal. Do you know what the dice were made of? I don't. I don't. Because I wouldn't do that as a store manager or owner because people could game it.

22:54If you take a regular die and you just put it in 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 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.

23:35Oh, 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 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. I think that's just extra redundancy that I don't need. What I think you should have gone for instead, Michael, and, you know, good as your amazing curiosity box of tender and die are, is like a wonky die like this.

24:15Oh, my gosh. Have you seen these before? The wonky die. Can I – let me go look in 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 an Alice in Wonderland version of a normal die. That's right. 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 a one or one to six, right?

25:01Any 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 dyes are symmetrical. So this is like the has the minimum amount of symmetry required to make the dyes fair and no more. Oh, wow. Which makes me think that these are superior. I've 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 have the minimum amount of symmetry needed for six choices. Yeah, there's no rotational symmetry on it at all. Much nicer, much more pleasant.

25:37Well, the seven, we got to use our little trick. We made a pentagonal prism that's just thick enough that it's likely to 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 heptagonal prism. with just the right thickness. I like those a lot. I like those a lot. I also just like the idea of you wandering around your day-to-day life and using them at all opportunities. That's the thing I like the most. Yeah, it impresses people.

26:14And if it doesn't impress them, well, then they're just not for me. Then go and play Dungeons and Dragons on their own, Michael. Some people call it people repellent. I call it a friend finder. All this dice 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 show you. 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.

26:52It's an absolute page turner. Yeah, it's quite dinky. They come in larger sizes, but I'll be honest with you, I've got the cheap one. um i uh shall i give away the ending for you it's uh it's it's quite the page 10 yes the ending here is um 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 whoa spoiler alert spoiler it is quite literally just an entire book filled with pages and pages of nothing but random numbers um one of the reviews on Amazon for this book said that it relies too heavily on 10 characters, which I quite enjoyed.