Unadulterated Dice Nerding

This 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 tumours 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. And the impact of this collaboration is clear because over the last 50 years, the charity's pioneering work has helped to double cancer survival in the UK. That is more people who are living longer, better lives.

Fossils 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. Well, the holidays have come and gone once again. But if you've forgotten to get that special someone in your life a gift, well, Mint Mobile is extending their holiday offer of half-off unlimited wireless. So here's the idea. You get it now.

You call it an early present for next year. What do you have to lose? Give it a try at mintmobile.com slash switch. Limited time, 50% off regular price for new customers. Upfront payment required. $45 for three months, $90 for six months, or $180 for 12-month plan. Taxes and fees extra. Speeds may slow after 50 gigabytes per month when network is busy. See terms.

Welcome 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. Yeah, I haven't brought that up.

with the producers, I 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 um but anyway uh welcome this is field notes uh we're gonna be uh we're gonna be sharing some objects later michael you've got something to share with us i do i've got some 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. 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. 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. 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'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. 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 care for my country men and women, but ultimately I actually think it 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. You wouldn't say gyms, would you? We 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. 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 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. Here's a sentence from it, right, just to give you a sort of flavour of how it reads. The mood is influenced by the combination of loud, 130 decibels, fast beats exceeding 300 beats per minute, music synchronised with bright flashing lights and frequent intoxication.

Yeah. 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 behaviour that is common across sort of...

systems of fluids, essentially. Each person, effectively, is like a particle. They're propelled, they're constantly colliding, and they're reacting to what's going on around them locally, not the whole global system. 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.

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 tend to copy what people are doing around us, flocking behavior, which is what you get when you see big.

big flocks of birds where they're sort of copying the average speed and 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 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. 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 haven't organized any of these patterns.

That is just something that happens when you stop behaving like people and start behaving like particles. Have you ever been in a mosh pit, Michael? No, I never have. No, absolutely not. I am very much not a mosh pitter. Okay. One of the things, so I actually, this is 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, including things like crowd behavior. This is one of the things that I was doing, a 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 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 where they're 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, it's really difficult to control that flow. been in a really busy crowd. I've been in a couple of football games.

sort of people start shouting, like, stop pushing, stop pushing. And 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, 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. 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. And I was like, this is, it was very scary.

It's very scary because I think at that moment you don't feel like you have the autonomy of a person anymore because you don't.

But the thing that's really interesting about 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 door... way 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 really small opening, you would get these clumps where it clogs up for a bit and then maybe you 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. If 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, 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. I 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, 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.

But 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.

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. Like 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? 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. 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? Like 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 100%, 90%, 80%, and so on percent to decide that randomly. You rarely need a 3 or a 5 or a 7 or a 9, 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. 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. Again, it's because I don't have the friends. My friends are all Catan people, you know? They're snobby about Monopoly, right? 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 uh 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. 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 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? 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.

we had to have an actual factory make an entire set send them to us and then um 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? How thick does...

a shape need to be to land on its edge just as frequently as it lands on its, you know, top and bottom. So the four-sided die is just a tetrahedron. Triangle-based pyramid. 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. 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 because then you've got the other ends, right? If it falls on either of those, that's sort of, that's seven sides. So you've got... I mean, it's tricky. It'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. 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 like a triangle-based pyramid. Yeah. And then the five-sided diet, it's more like a chunk of Dairy 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. And there's a company, a restaurant, 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 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. 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 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? Obviously 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. 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.

like manager or owner, because people could game it. If you take a regular die and you just put it in 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. 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. 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. 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. I think that's just extra redundancy that I need. What I think you should have gone for instead, Michael, and, you know, good as your amazing curiosity box of tender and dye are, is like a wonky dye like this.

Oh 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 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? 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 die. the symmetrical. So this is like the, has the minimum amount of symmetry required to make the dice 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 much nicer much more pleasant well the seven uh 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. And 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 uh 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 um 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. It's an absolute page turner. Yeah, it's quite dinky. They come in larger sizes, but I've...

I'll be honest with you, I've got the cheap one. Shall I give away the ending for you? It's quite the pay to tell. The ending here is 53477 and then 43466. 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. 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 like actually really strong reasons for this. So particularly in the 1950s, when people were starting to do big calculations, right, for like the space program or where they were like trying to sample populations or. like 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, right? If you are like, 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 like make up that randomness then uh 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

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 like very, very small, you know, atomic properties. and use that to like collect the randomness that appears naturally in nature and then printed it for other people to use. And so, yeah, I mean, I'll be honest with you.

I haven't done it start to finish. I've just flicked in, 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 generate randomness by doing deterministic processes on a machine. 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. And I cannot tell you how it ends because this is just part one. Of 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? 2.0.

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 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 pollutions game. They want you to get mad at the little guy who's trying to teach math.

Well, they just deforest for fun. I take it back. But that's also what'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, right? You need an infinite number more copies in order to fully complete the square root of four. The square root of two. Yeah. I don't have enough precision. No. A million zeros and then what?

How does it end? Tell us. How does it end? I don't know. Do you remember when There was a friend of ours, Brady Haran and Matt Parker, the YouTubers, where they took a million digits of pi and they printed it out on a roll of paper. They printed it by hand though, right? No, no, they printed it. They constructed it by, you know, they cheated slightly. They went in and they annotated it. I think it still took them four hours. They had to go to a...

to an airport runway and unroll it. Took them ages. 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 say very much, I think, because I've got a nice watch that's like 120 quid. How nice of a watch, I guess. Yeah, how nice of a watch. But somewhere, somewhere out there, there is a person who owns... a mile of pie on brown paper. I also like the idea that this is a person who is carrying their mile of pie around with them at all times, just in case they bump into someone like Vsauce 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 Pie 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. Yeah, a life story.

Hey, why not? I want to hear about where you've been. A confessional even. A confessional even indeed. If you have something that you would like to contribute to Field Notes, then you can write in to us, the rest is science at goalhanger.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.