Michael Wrote Some Math Poetry

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For more information about Cancer Research UK, their research, their breakthroughs, and how you can support them, visit cancerresearchuk.org forward slash rest is science. Hello and welcome to The Rest is Science. This is Field Notes, a podcast expedition into the minds of michael stevens and hannah fry we've brought along some baggage some luggage some thoughts some things in these episodes we share stuff from the museum of our minds yeah then let's let's delve into that uh it's you know you sort of think this i think um as uh like the rest of sciences version of show and tell that's that's that's the sort of idea that we're going on for exactly but it's like an interactive show and tell because we want to hear and show and tell about you So send in your questions, your thoughts, your ideas, and you can be on the show, too, in a way. Your crazy inventions, the darkest depths of your mind, any of that stuff we would like. And you've got something for us this week, haven't you, Michael? Yeah. Later on, I'm going to be sharing something that represents the fusion or it doesn't represent. It is the fusion of math and poetry. Oh, it's poems about math. OK, but we'll get to that later. First, we're going to start with you guys. We've got some questions that have come in. I want to start with this one from Noor. This may sound ridiculous, but how do we know math is correct? OK, first of all, I see, Noor, that you've you've gone for math rather than maths, which is only adding to the conclusion that we drew a couple of weeks ago. All right. Also, second thing to say, not a ridiculous question at all. actually quite a deep and insightful question and one that there unfortunately isn't isn't really the sort of satisfactory answer that you or any of the rest of the world might be hoping for because the real answer is that we don't we don't know that it's correct and people have tried to to prove that it's correct and I mean basically failed failed to do so One thing I will say is that we are in a position where maths is either this like massive hallucination that all of us have come up with that just so happens to work perfectly or it really is the language of the universe. That's that's the sort of it's only one of those two things that can possibly be the case. It's one of those two things. Yes. What's that famous paper? The unreasonable effectiveness of mathematics. exactly it's like look we we came up with all these rules and then when you'd practice them in the real world it always works i mean what are the chances what are the chances that it always works but not just always works on the stuff you already know about always works about the stuff that you don't know about either so there's loads of examples in science of where there's been an equation everybody's liked the equation but there's been something weird that the equation has predicted. So for example, Dirac was messing around with an equation and there was one point where it showed that there could be sort of a negative sign where you wouldn't expect one. And that was really the birth of the idea of antimatter, which then went on to be demonstrated to be absolutely true. There was a group of astronomers who were looking at the path of Uranus in the sky and it was moving weirdly. And they were like, well, we like Newton's equations of gravity that we sort of feel like they do a good job and so without without looking at a single telescope they sort of worked out what could possibly be going on and predicted the existence of Neptune figured there must be another planet there that's sort of mucking up this path of Uranus and then indeed managed to find that planet as a result of it and there are I mean there are countless examples of these right over and over and over again equations showing us where to look or showing us something we didn't know about that that kind of couldn't be the case if math was absolute nonsense that's right so i think what we're doing here though is we are defining correct to mean effective works corresponding to reality if that's what we mean by correct then we do it through observation and experimentation and yeah i mean look we landed people on the moon we got it right you know those equations those ballistic trajectories They all worked out. But yeah, math can also explain things that we could never test. We can use math and logic to figure out that we'll never know the answer to something. Yeah. And that's a weird thing when you prove that like, oh, yeah, it's been proven that this cannot be known under the current framework. And that's really like what you're hinting at there is the sort of deep, dark secret lying in the very foundations of mathematics that everyone, I mean, basically tries to not look at too closely, which is that we have tried to prove that math is correct. I mean, we should definitely do at least one episode on this. Yeah, we will. Like, but in the 1900s, people tried very, very, very hard to prove that math is correct by saying, right, what is the most, the smallest kind of, what are the atoms of math effectively? What are the axioms, the smallest nuggets of truth that we can we can take as fact and then build up from there? And and the only thing that they managed to prove, as you hinted at, is that you can't prove that math is correct. Yeah. And they tried. I mean, we don't know. We're going to spend a bunch of time on your question or we're going to do a whole episode on it. But I just wanted to show now that I've got my full bookcases here. Who was it? It was Bertrand Russell worked with someone else or was it on his white head? Yeah. Whitehead. You got the book. Have you got their book? I've got the books. Have you? So Bertrand Russell and Alfred Whitehead decided we're going to just finish this once and for all. And we're going to prove that one plus one equals two. Yeah. OK. Without having to go. Well, look, if I have one thing and then I have a second thing, one, two, it's two things. they were like, let's do it purely with the mind. And here's how they did it. Now, while Michael is getting that book, I'm going to tell you some of the problems that they ran into, because for starters, to be able to prove that one plus one equals two, you sort of need to know what two is. And it's not enough to just say, oh, well, two is the number that follows one, because that requires you know what one is. So what they wanted to do was come up with a way to like define two-ness, as it were. Yes, you need to know what one is, and you also need to know what follows or comes after means. And so they wrote a book. And by book, I mean books. Oh, my God. This is the Principia Mathematica by Alfred North Whitehead and Bertrand Russell. And these represent all the characters and words and the new language they had to invent to prove that one plus one equals two. So they did all of this work. And then someone else came along, Girdle, and said, ah, but yet there's a little bit of a problem with all of this. And they just they said, screw it. And so now you can only get this in paperback. For people who are listening rather than watching, what Michael just picked up is, I mean, frankly, enough that you could skip a skip an arm day at the gym. Right. Just by picking up. These are these are tomes. There's three volumes of it. They are thousands and thousands of pages in total. There were supposed to be six volumes in the end. But even look at this, it's impenetrable. I know actual professors of logic who have never read these books because they are so. unbelievably dense. You know, I strongly suspect that only Russell and Whitehead are the people who have ever existed, who have ever worked their entire way through those books. Yeah, I tried to read it and I said, man, I have to learn a whole new language first. And sometimes you just have to embrace the religious aspect of math, which is that through faith alone, I accept that one plus one equals two. Now let's move on. And it sounds like you're being almost flippant or silly by saying that. But really, when it comes down to it, I mean, we're not lying. Honestly, there comes to a point where it really is just a matter of faith. Yeah. And so I think we should definitely do a full episode on this because I'm sure a lot of listeners are going, this sounds like the biggest waste of time in human history. Why would you need all of that work? All of these new symbols, all this new way of thinking to show, to prove that one plus one equals two. But it's actually extremely real. Yeah, I see. See, I think the other half of listeners is sort of saying, I'm sorry, what? What do you mean you don't know that math is correct? What are you talking about that once it comes down to it is all an act of faith? And both of those things are true. It's both pointless and terrifying. yeah but it's really effective okay so so working and corresponding to reality might be different than correct do you let me put you on the spot do you think that math is discovered and it's been really um coincidentally useful or do you think that it is something very fundamental in the universe's fabric discovered or invented i actually did um a few years ago i did a three hour documentary series on exactly this question. So, so you'd better believe I have, I have thought about this extensively. And I think that my, my final sort of conclusion that I came to is that the tools that we've built are invented, right? The way that we write numbers, the way that we, you know, structure equations, all of that stuff is invented. But what we're doing with those tools, there is no doubt in my mind that it is discovery and there's this really beautiful description by um andrew wiles who was the person who solved fermat's last theorem again we should definitely do an episode on that yep he describes doing mathematics that has never been done before right so if you sort of doing a phd if you you doing research mathematics which i done um this is a really i think the best description of what it feels like He said that it feels like you are clambering through an incredibly thick brush, right, through a sort of hedge. And it's incredibly dark. You don't know which way you're going. You're turning around. Everything looks exactly the same. And then if you're lucky enough, you will have one single moment where you will turn a corner and instantly before your eyes, you will realise that this entire time you have been navigating this perfectly manicured garden and you are in absolutely no doubt whatsoever that what you are seeing, all of the places that you visited, how they all fit together, you will be in no doubt whatsoever that it is not of your invention, that you are exploring a space that exists beyond the human mind. That's beautiful. Yeah. That's why people want to be mathematicians. The tools, the machetes you're using to chop through what feels like a dense jungle. We invented those. Yeah. The symbols, the theorems, the axioms. And yet they suddenly just become the frame through which you look and go, oh, shoot, it's it's wonderfully clear and manicured and was just waiting for these tools to fit into it yeah right we'll do more on that if you want if you want us to i mean look me and me and michael can uh can uh basically we could do an entire podcast series on like our love of deep philosophy and the philosophy of mathematics so you know maybe you should tell us whether that's something that you want but i've got another question in this one's for you michael this is from thomas who asked how difficult was it for the discoverers of germs to convince the world that something they couldn't see was harming us. Yeah, it was really difficult. I think a lot about the, and this might be what the question asker is getting at, a phenomenon in human psychology known as the Simmelweis reflex. Have you heard about this? No. So yeah, I mean, germ theory, first of all, germ theory is the idea that illnesses and disease are caused by real things, So not ghosts or spirits or curses, but real mechanical things, biological things that are just too small to see. OK, so if you can't see them, how do you know they're there? How do you know that an illness is caused by like a little organism and not just by bad air or your own sins? Right. Like it's hard to prove one way or the other. So one of the most famous stories of germ theory slowly being accepted was that 20 years before germ theory became a serious topic of discussion. Back in 1847, there was a Hungarian physician named Ignaz Semmelweis, and he worked at this hospital where autopsies were done on every person who died in the hospital. And the doctors did this without gloves, without proper antiseptic technology. because they didn't know. But it wasn't great to go to a hospital back then. You often left with brand new infections. You would get better and then you'd get worse. And his theory was that the problems they saw that seemed to only appear at the hospital were truly iatrogenic. That means an ill effect, something bad, a disease caused by medical activity. So caused by the doctors themselves, by the nurses themselves. Because wasn't that there was like a maternity ward there, wasn't there? Yes, there was a maternity ward there. And there was this disease known as child bed fever. And he said, maybe we shouldn't be doing gynecological exams with the same hands we've just performed autopsies with. And he didn't know that there was a virus or a bacteria, any kind of microbe on the hand. He thought maybe it was just the smell because he'd said, you know, after you do an autopsy, your hands smell. And if you wash all the debris off with soap and water, they still smell, right? So it must be this bad smell. And he thought that the smell was made of what he called cadaverous particles. But he found that if he used alcohol, the smell went away so he instructed everyone at his hospital to wash their hands in really strong high proof alcohol and the fatality rate of childbed fever improved by tenfold at only his hospital because of this procedure so of course he wrote about it he told doctors all over the world this is back in 1847 that late oh my goodness because there's the counter to that is that you You know, in other hospitals, people were I mean, it seems wild that you would like cut up a dead body and then immediately go and deliver a baby without washing your hands in between. Seems insane. Well, the prevailing theory at the time was that childbed fever was caused by miasma, bad air. And so it had nothing to do with the hands of the doctor. And I mean, it was so ingrained as a way of thinking that it couldn't be the doctor themselves. It must be something else. It can't be me. That when Semmelweis spread the results of fatality rates for Beaver in his hospital and how much of an improvement they found, no one accepted it. The experts felt personally insulted and they just could not change their paradigm. So Semmelweis's story has been studied profusely when it comes to understanding how people come to rational conclusions. because we don't, right? We have so many biases, confirmation bias and personal biases and authority bias. All the most famous doctors disagreed with Semmelweis and they always had. So who's this guy think he is coming in and saying, well, actually, I think that it might be some like particles that soap and water aren't getting off our hands. And they said, no, like, why would we believe you? For some reason, we have these barriers to accepting new information, even in light of convincing evidence. And so, again, it took 20 years for people to say, OK, let's start entertaining the idea of these things. We'll call them germs now. And let's do some experiments and take it seriously. So it was a slow process. And we still see that today with accepting new ideas. Like what? Like what kind of ideas? I realize I'm putting you on the spot here, but like, are there some ideas that scientists have been like, guys, seriously, this is a really big problem and it's just taking people time to accept. The 1850s, I mean, it wasn't that long ago, but it sort of feels like this is a lesson that we should have learned by now, have we? Or does this still happen? Well, yeah. I mean, really recently, how COVID-19 was transmitted, how the virus that caused it was transmitted, took a long time for a consensus to be reached, despite all the evidence. Believe it or not, it wasn't until December of 2021 that the World Health Organization finally recognized airborne transmission of the virus. So two years after the first sort of confirmed. Yeah, because for so long, the prevailing theory was droplet transmission. That's how they always kind of saw it. They thought, surely it can't waft through the air as well. And it just takes a long time to move something as big as modern science. You know, in the Centre of Mathematical Sciences, where I work at Cambridge, right? So you've got all of these incredible mathematical scientists, people who study how air flows and stuff. They've got like this one big lecture theatre there. And when the first reports were coming through that it was transmitted by the air, airborne disease, some of the fluid and amethysts, they took the dimensions of this room, of this lecture room, and decided to like run this mathematical model of the airflow of like what happens when you're standing at the front. And basically realised that the exact design of this lecture theatre was that anyone who was standing at the front was like in direct line of fire, that all of the people's air was like perfectly, perfectly funneled directly to them. so they um they then redesigned it and they're these like black flags that are up to sort of like disrupt the airflow in there still oh wow yeah they only want the knowledge to be contagious exactly exactly and also if there is any contagion i think they want it to go in the opposite direction from the professor to the audience rather than vice versa uh yeah yeah yeah right speaking of the dynamics of things moving like liquids um then asks in fluid dynamics the energy flows from large structures to smaller structures. In that case, why do hurricanes exist? If larger eddies break down into smaller eddies, then no large eddies should ever form, right? What a transition that was, Michael, from germs to frozen up. Don't thank me, thank Ben. Yes, I mean, that's true, right? If you think about stirring a coffee, you know, mixing milk into your coffee uh you put in your spoon and you're sort of injecting energy at the larger scale and then the little eddies the little vortices that come off go smaller smaller smaller smaller smaller um and that's uh it's known as the forward energy cascade basically it's sort of that friction's kind of turning into heat and in hurricanes it's the opposite way around that it's like the rich get richer the the you know sort of a winner takes all the kind of the little vortices that you get end up cannibalizing each other and growing and growing and growing until you get this like giant hurricane and the reason for that difference the reason why it's the opposite way around is uh it's basically because of depth so in your cup of tea or your cup of coffee it's like a three-dimensional fluid um but this may come as a bit of a surprise but in uh in the earth's atmosphere the earth's atmosphere is so thin in comparison to the size of the earth and in particular the spin of the earth the coriolis effect um that it basically acts like a two dimensional fluid right which is which sounds like the most crazy idea but that is basically how we know that it that it works is that if you just get rid of that third dimension and you just say okay it's a sheet of fluid that is moving around then suddenly everything works you can predict the path of hurricanes and so on. Oh, wow. I've heard that if the earth was the size of an apple, the atmosphere would be thinner than the skin of an apple. Right. Yeah. Basically not there. It's basically not there. Exactly right. The, I should tell you the equation that you need when you're trying to work out all of the stuff this sort of two dimensional flow of fluids on the surface of the earth It got my favourite equation name ever You know when you do you know when you watch like sitcoms with scientists in it and they try and make the scientists sound clever by using really complicated words? This is my fake sounding overly complicated favourite equation, which is the quasi-geostrophic potential of authenticity equation. You sound like you're smart when you're saying that, but basically it just means, you know, it's 2D on the earth. One more time. Quasi geostrophic potential vorticity equation. Quasi geostratic? Geostrophic. Yeah. Geostrophic. Vorticity. Potential vorticity. Potential vorticity. Vorticity is a great word, isn't it? It sounds both scientific and literary. Vorticity. The sound and the fury. Vorticity. There you go. um i should tell you actually if you want to see the quasi-geostrophic potential of autosity equation uh slash two-dimensional fluids on the surface of a planet in action right and the way that these storms build and build and build and build and build um it's jupiter that you should look to because uh there's no solid ground to stop the wind on jupiter so it can carry on going carry on building um its atmosphere is also very stratified so it's kind of effectively this 2d wrapping and the great spot on Jupiter, it is this hurricane that has been like feeding on these smaller storms for, we think, at least 300 years. And it's, I mean, it's the ultimate result of what happens in these situations. Thank goodness for mountains. Otherwise, we'd be in that situation, too. Yeah, but Jupiter has no mountains. It has no solid ground. But it's, it would seem that its atmosphere would have depth, though, right? But the whole thing is just a big gas giant. Or is it Stratified meaning there's just thin layers like an onion that that can't interact enough. Exactly right. They're thin layers that don't interact really enough to make a difference. So it's like exactly as you say, it's like an onion wrapped and wrapped and wrapped. Right. Well, that was quite a mathsy first half in the end, wasn't it? Yeah, it sure was. I mean, frankly, I'm happy with it. Let's go into the break and we'll see how mathsy we get in the second half, shall we? This episode is brought to you by Cancer Research UK. Radiotherapy is over a century old, but it is still changing. Cancer Research UK helped lay the foundations of radiotherapy in the early 20th century and has driven progress ever since. Radiotherapy 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 radiotherapy 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. And 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 forward 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. 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We had a very mathsy first half, as Hannah said, and we're going to continue to stay mathsy, but we're going to inject a little bit of rhyme, a little bit of art, a little bit of literature. What I've brought today, Hannah, is some mathematical poetry. Oh, delightful. And as I was looking through my math poetry books and my own brain, everything I found was a limerick. So very specifically, these are mathematical limericks. I wanted to share some that you've probably heard before. And then I wanted to show some that I've written just for today's episode. What a treat. OK, go on then. By the way, the chance of me having had these before is almost zero because I'm racking my brains and cannot think of a single one that I've ever encountered before. So I think this is going to be a treat. Well, let's see if you've heard this one. This one comes from the most famous palidromist ever, Lee Mercer. All right. You might know Lee Mercer from his most famous work, A Man, A Plan, A Canal, Panama. No, but the fact that you said that he was a palindrome is making me work out backwards in my head. It's a palindrome. A man, a plan, a canal, Panama. So the history of the Panama Canal being built can be a palindrome. Same backwards as forwards. But Lee Mercer also wrote this cute little limerick. And a limerick is a kind of poem that has a very specific kind of rhythm. The most famous limerick is, of course, there once was a man from Nantucket. And so on and so on. A lot of them end in a way that is not appropriate for this podcast. But there are clean versions of this Nantucket man. I don't know the Nantucket one, but I can I can imagine what rhymes at the end. Yeah. So if you look it up, you'll mainly find like clean versions that are pretty clever. But then if you want to find the dirty ones, you'll read them and you'll go, oh, my gosh, that is a lot dirtier than I expected. So here's what I want to share from Lee Mercer that is a mathematical limerick, not a palindrome. It's it begins with this equation. OK, everyone's looking at this looks like a normal old equation. And yet when we read it, we find the meter of a limerick, a dozen, a gross and a score plus three times the square root of four divided by seven plus five times eleven is nine squared and not a bit more. Hang on. Let me just work it out. It actually holds. It holds. It holds. Oh, that's nice. It's really nice. Gosh, can you imagine how long it took him to come up with that? I know. But now let me read you this one, which is from an unknown author. It's an anonymous limerick. I think that in a video I once credited it to a guy named Matthew on Stack Exchange. But I have since learned that he was just sharing it. He did not write it. So we had Lee Mercer's equation. Now look at this equation. the integral z squared dz from one to the cube root of three times the cosine of three pi over nine equals log of the cube root of e does it hold hang on it holds it's true it only works in american accent though because if you said dz then three you're sort of it falls it falls apart okay but let me tell you this it doesn't have to be zed it could be um t let me do a version for for the rest of the world. The integral t squared dt from one to the cube root of three times the cosine of three pi over nine equals log of the cube root of e. That is that is that is absolutely gorgeous. Isn't it gorgeous? I'm so genuinely impressed to get it to work so that it actually works as an equation i cannot even imagine how much time that takes i know because normally when you write a limerick you can go oh okay the meter or the rhyme isn't really working let me find a synonym but in math you can't always do that it needs to also work mathematically now it helps that things like dz or dt three and e all rhyme cosine and nine that's pretty nice yeah but you The score and not a bit more. I mean, I'll be honest with you. He might be good at palindrops. That is a tiny bit cheating. It's a tiny bit cheating. Yeah, I will admit that, too. It's nine squared and not a bit more. It's like, ah, that really it helped you. It could equal anything. And you could just put on the and not a bit more and finish the rhyme and the meter. OK, so here's one that's not about an equation. And this one is also from an unknown author. This is an anonymous limerick. A mathematician confided a Mobius strip is one sided. You'll get quite a laugh if you cut one in half for it stays in one piece when divided. That is delightfully nerdy. That's really delightfully nerdy. It's very fun. Also true. If anyone wants to cut a Mobius strip in half and have that joy for yourself, then then then off you go. Yeah, take a strip of paper, twist one end over, tape them together, cut it in half. It won't be cut into halves. It will just be one bigger loop. Okay, well, here's one. This is from Dave Morris from an issue of Wordways. This one is, if you're talking about cheating, this one, it's almost kind of like funny in the way that it works. Here it is. A one and a one and a one and a one and a one and a one and a one and a one and a one and a one equal ten. That's how adding is done. yeah that's my kind of guy still pretty good that is still pretty good i feel like it's that's the kind of limerick where once you come up with and a one and a one has the right rhythm then everything else falls together wait did you say that you wrote some yourself yes i did i did so um okay here's here's a geometrical one let's do some wait wait do any of the any of them as impressive as that integral one no none of them they are though because you wrote them thank you hannah okay so this one this one about shapes the rhombus was keenly aware that his side lengths were famously fair But when he brought in his neck all his angles were wrecked And then the poor guy was a square. And this plays on the pun that wrecked, R-E-C-T, means right, a right angle, a rectangle. You nerd. Rectangular square. That's amazing. Do you know what? I think I actually, it's got, you know, there's sort of an anthropomorphization to that. There's like, you know, it's cute sort of imagining it. In many ways, I prefer that to the other extremely clever ones. It's got a character in it. And, you know, I really debated whether I should gender the rhombus. Are his side lengths or its side lengths? Was the poor guy now a square or was the poor thing now a square? I guess you can make your own decision. I like the guy. you like yeah i think it's i think it's the kind of thing a guy would do bring in his neck and then oh my angles are all wrecked and now since my side lengths were the same on a square um and it's a great way to kind of teach i don't know if anyone's going to use it to remember the definition of a rhombus but you know a rhombus is any quadrilateral whose sides are all the same length yeah which means a square is a kind of rhombus but a square is a rhombus with all right angles wrecked angles so that's just a little one for the geometry nerds talking about using poems to remember stuff and we were talking about hurricanes earlier there was a guy called lewis fry richardson no relation um who was integral in lots of the um the modeling of hurricanes and weather systems and he had a little rhyme which was to remember how uh it all worked basically i mean quite literally talking about hurricanes he had uh big worlds have little worlds that feed on their velocity and little worlds have lesser worlds and so on to viscosity oh isn't that cute that's really cute yeah i mean your rhombus is on is better but no no there's no such thing as a better or worse poem you know maybe there's a a more or less successful uh communication of feeling but um I do feel for this rhombus. It should have been happy with what it was. It should have been happy with what it was. It wanted more respect, and so not knowing what to expect. There's different versions of it that I wrote, but that's the one that's – the first version of the rhombus limerick I wrote simply had his angles become wrecked. And I'm like, ah, but unfortunately, a rhombus with wrecked angles is exactly a square. It needed to be about a parallelogram. Yeah. It squares up its angles and becomes a rectangle. But parallelogram does not have the right meter to be in a limerick. Limericks have to have dactyls, which means a stressed syllable followed by two unstressed. Oh, yes. For example, there once was a man from Nantucket. OK, but parallelogram, it doesn't have that little triplet. Could you split it? Could you go parallelogram? Yes, you could parallelogram. Yeah. But then it doesn't scan and people go, oh, you're not very good. So I wanted to share these with you. These are more of like a work in progress. I'm really into division by zero, division involving zero. And so I've tried to write some limericks describing the three ways zero can be involved in division. And this first way is when you take some number that's not zero and you divide it by zero. Right. This is like, oh, my gosh, it's going to create a black hole and it's going to end the universe. And this is how I feel about it. Division by zero earns prison unless we agree with precision that math doesn't break if there's nothing you take because dividing by none ain't division. the idea here is that look if division is just is repeated subtraction and i ask well if you take away nothing from say five when will i have nothing left it's like well you're not dividing because you're not subtracting if you're not taking anything away each time like it's not a paradox or a weird you know singularity inciting event it's just not division no prison for you that's uh that's essentially where we're at now let's talk about when zero is the dividend okay zero divided by five zero divided by n well here's the limerick when zero's the number on top you don't need a logical cop if you aren't done till the total is none just scribble down zero and stop okay can i tell you the things i like about this right one i like that you are going through the different types of the ways that zero is involved and you're doing it logically and it's a progression and it's great too i like how both of those limericks are tied together by the insistence of there being some sort of maths police yes who are absolutely eager eager to catch people for these zero division crimes i'm absolutely loving it wait have you got one more there's one more because there's the special case where zero is divided by zero and this is different. So here's that limerick. Repeated subtractions are grind. But when you see zeros combined, any number will do, both a lot or a few. So we say the whole thing's undefined. Oh, that's good. I need a judge in there. And for our listeners at home, I think to appreciate it more, I'm just going to tell you that what's going on there is that we're saying zero divided by zero is asking many, you know, there's a lot of ways to parse what it means. But one thing it can mean is how many zeros does it take to have zero? And as it turns out, it could be none or five or 17 or a billion. That many zeros will always be zero. So it can be any number. And that's why zero divided by zero is undefined. Now, a lot of people say that a number divided by zero maybe is like infinite or something. But even an undeniable amount of nothing won't ever equal the the the dividend so like the quotient is just it's it's not division and then finally when you're when you're dividing zero by another number you're asking like zero divided by seven how many sevens will give me zero it's just none easy that whole thing about the number being undefined zero divided by zero i mean i also think we should do a whole episode on zero at this stage Michael and I really are just doing a whole podcast series on on the philosophy of mathematics. But zero divided by zero. It's sometimes there is actually an answer. Sometimes it's undefined. Sometimes it's infinity. Sometimes it's zero. Sometimes it has a finite answer. OK, so, yes, we're going to do an episode on this. You're going to teach me. I'll write some more lyrics. And then finally, the division involving zero limerick sonnet or, you know, a book of poetry will be complete. There's so much to say about zero. For example, my daughter likes me to count by twos when she's going to bed. And I always start at zero and she's like, is zero even? And I'm like, well, it is for a few reasons. It just helps the pattern work. But also like an even number is just two times some integer and two times zero is zero. So zero is even. And she still doesn't really believe it. So we'll we'll we'll set her right. Meanwhile, my two daughters asked their dad the other day, is zero a number? And he gave them an answer. But then when we were all together, he said, oh, you should really ask your mom that question because she'll have something much more interesting to say. Yeah. And and they they both declared that they deliberately didn't ask that question in front of me because I would give a boring answer. in fact because of my job right i know quite a lot of like the most amazing science people in the world right you michael being one of them brian cox being another i've met david attenborough like all of these people and i've tried over and over again to introduce my daughters to them and uh every time i'm like come on let's watch one of these programs it'll be amazing and every single time they say mommy why are your friends so boring uh-huh so yep you know hopefully you dear listeners will find it slightly more interesting than my children i hope so i mean like my daughter's young enough she hasn't quite like become a rebel so i can still tell her yeah look we're going to count by twos tonight um and she asks for that but that's because she doesn't know that there's anything else to talk about all right i've got i've got two more limericks i want to share and these are about us okay so they're not actually mathematical or scientific really um all right let's start with this one i'm not quite happy with this one but here it is a circle of chips was prepared but filling it nobody dared till she pointed out with no shadow of doubt that the areas just fry are squared i love it i love it yeah that's great also thank you for using chips as well rather than fries I know, right? I felt like the kind of like cross-Atlantic, the trans-Atlantic combo here deserves fry and chip. So they're both in there. It also meant that I didn't have to repeat the word fry over and over again. That was absolutely brilliant. I'm going to have that put on my wall. Go on, I want to hear your one, Michael. Go for your one. OK, well, this is this is actually about both of us. Deep thinkings, a kind of defiance. And so was their nerdy alliance. mike was the guy and the girl was named fry and the rest as they say is well science yeah they are so good they are so good we have found a new skill we have found a new skill from michael stevens um if you have any limericks that you'd like to share with us um any others i think michael you need your own one i'm gonna between now and the next episode i'm gonna i'm gonna furiously yeah i don't think i've ever written one in my entire life so um that we're going to really test your theory on whether it's possible for there to be a good or bad poem and once once i come back to you with that um but i think that concludes our uh episode for the day uh if you have anything you'd like to send us in limericks or otherwise send them to us the rest is science at goalhanger.com yes and please join our newsletter at the rest is.com slash science we'll be back next thursday with another episode of Field Notes and on Tuesday with our normal episode. See you then. See ya.