Michael Wrote Some Math Poetry

Can mathematics ever truly be proven? And can Michael's poetry help you remember some tricky equations? In this episode, Professor Hannah Fry and Michael Stevens answer your questions and take a look at what it means for something to be true in mathematics. Starting with a grand attempt to prove that one plus one equals two, and into Gödel’s theorem that no system of maths can ever fully prove itself, they explore how maths connects to the real world, from an equation that predicts antimatter to the calculations that led to the discovery of Neptune. After the break, Michael shows off a set of limericks written and read by himself. The Rest Is Science: Field Notes is released every Thursday, with Hannah and Michael exploring questions where mathematics, science, and human behaviour meet. ------------------- For more information about Cancer Research UK, their research, breakthroughs and how you can support them, visit ⁠⁠https://cancerresearchuk.org/restisscience⁠⁠ Cancer Research UK is a registered charity in England and Wales (1089464), Scotland (SC041666), the Isle of Man (1103) and Jersey (247). A company limited by guarantee. Registered company in England and Wales (4325234) and the Isle of Man (5713F). Registered address: 2 Redman Place, London, E20 1JQ. ------------------- Find The Rest Is Science all over the internet by ⁠⁠clicking here.⁠⁠ ------------------- Video Producer: Adam Thornton + Oli Oakley Video & Social: Bex Tyrrell Assistant Producer: Imee Marriott Senior Producer: Lauren Armstrong-Carter Head Of Digital: Samuel Oakley Exec Producer: Neil Fearn Learn more about your ad choices. Visit podcastchoices.com/adchoices

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Hannah Fry?

  This episode is brought to you by Cancer Research UK.

• 0:02Michael Stevens?

  So when most people think of naked mole rats, their unusual relationship to cancer probably isn't the first thing that comes to mind.

• 0:10Hannah Fry?

  But maybe it should be because it is incredibly rare for them to develop cancer, which could be partly down to their unique immune system, or it might be the way that their cells respond to damage.

• 0:22Michael Stevens?

  So scientists are studying their biology for its cancer-fighting secrets. It's a reminder that discoveries can sometimes come from places you don't expect.

• 0:31Hannah Fry?

  Cancer Research UK is the world's largest charitable funder of cancer research. Thousands of scientists, of doctors and nurses, work across more than 20 countries to help turn discoveries in the lab into new tests, new treatments and new innovations.

• 0:46Michael Stevens?

  And the impact is clear. Over the past 50 years, the charity's pioneering work has helped double cancer survival in the UK, meaning more people living longer, better lives, free from the fear of cancer.

• 0:59Hannah Fry?

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

• 1:10Speaker 02

  Observe: The North American Dad. 50s, great polo collection. He enters his vehicle information on Carvana. An offer appears in minutes. Remarkable. He squints, reads it again, smiles and says, "Dang, that's a good offer." The highest form of approval. No haggling, no hassle. No one called him "boss." He's still on the couch. Astonishing. Sell your car today on carvana.com. Pickup fees may apply.

• 1:41Speaker 03

  This episode is brought to you by Google Chrome. You think you know a browser, but Gemini and Chrome, that's new. It can help you with practically anything on the web, like restoring a vintage motorcycle from a 50-page restoration block or finally break down that long article you've had open for weeks. Gemini and Chrome is here for it. Ready to make anything online make sense? There's no place like Chrome. Check responses set up required. Compatibility and availability varies. 18+

• 2:13Michael Stevens?

  Hello and welcome to The Rest Is Science. This is Field Notes, a podcast expedition into the minds of Michael Stevens and Hannah Frye. We've brought along some baggage, some luggage, some thoughts, some things. In these episodes, we share stuff from the museum of our minds.

• 2:30Hannah Fry?

  Yeah, and let's delve into that. You sort of think this, I think, as like the Rest Is Science's version of show and tell. That's the sort of idea that we're going up for here.

• 2:40Michael Stevens?

  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.

• 2:51Hannah Fry?

  Your crazy inventions, the darkest depths of your minds, any of that stuff we would like. And you've got something for us this week, haven't you, Michael?

• 3:00Michael Stevens?

  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.

• 3:08Hannah Fry?

  Oh.

• 3:09Michael Stevens?

  It's poems about math. Okay, 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?

• 3:22Hannah Fry?

  Okay, first of all, I see, Noor, that 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, Noor, actually quite a deep and insightful question, and one that there unfortunately 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 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

• 4:06Hannah Fry?

  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 the it's only one of those two things that can possibly be the case.

• 4:20Michael Stevens?

  It's one of those two things, yes. What's that famous paper, The Unreasonable Effectiveness of Mathematics?

• 4:26Hannah Fry?

  Exactly.

• 4:27Michael Stevens?

  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.

• 4:34Hannah Fry?

  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 and that was really the birth of the idea of antimatter, which then was went on to be 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.

• 5:19Hannah Fry?

  And they were like, well, we like Newton's equations of gravity. 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.

• 5:56Michael Stevens?

  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.

• 6:29Hannah Fry?

  Yeah.

• 6:30Michael Stevens?

  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.

• 6:38Hannah Fry?

  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 maths is correct. There's this, I mean, we should definitely do at least one episode on this.

• 6:59Michael Stevens?

  Yeah, we will.

• 6:59Hannah Fry?

  Like, but in the 1900s, people tried very, very, very hard to prove that maths is correct by saying, right, what is the most, the smallest kind of, what are the atoms of maths 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 maths is correct.

• 7:24Michael Stevens?

  Yeah, and they tried. I mean, we don't, yeah, we're gonna spend a bunch of time on your question, Nora. We're gonna do a whole episode on it. But I just wanted to show, now that I've got my full bookcases here.

• 7:34Michael Stevens?

  Who was it? It was Bertrand Russell.

• 7:35Hannah Fry?

  Mm hmm.

• 7:36Michael Stevens?

  Worked with someone else, or was it on his own?

• 7:38Hannah Fry?

  Whitehead.

• 7:39Michael Stevens?

  Yeah, Whitehead.

• 7:39Hannah Fry?

  Have you got the book? Have you got their book?

• 7:41Michael Stevens?

  I've got the books.

• 7:43Hannah Fry?

  Have you?

• 7:44Michael Stevens?

  So Bertrand Russell and Alfred Whitehead decided, we're gonna just finish this once and for all, and we're going to prove that one plus one equals two.

• 7:52Hannah Fry?

  Yeah.

• 7:52Michael Stevens?

  Okay. Without like 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.

• 8:02Hannah Fry?

  Now, while Michael is getting that book, I'm gonna 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.

• 8:23Michael Stevens?

  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.

• 8:33Michael Stevens?

  And by book, I mean books.

• 8:36Hannah Fry?

  Oh, my God.

• 8:37Michael Stevens?

  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, Gödel, 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.

• 9:05Hannah Fry?

  For 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 that 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.

• 9:47Michael Stevens?

  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.

• 10:01Hannah Fry?

  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.

• 10:15Michael Stevens?

  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, it's actually extremely real.

• 10:35Hannah Fry?

  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, what, what are you, what are you talking about that once it comes down to it is all an act of faith? And, and both of those things are true. It's both pointless and terrifying.

• 10:52Michael Stevens?

  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 coincidentally useful? Or do you think that it is something very fundamental in the universe's fabric?

• 11:14Hannah Fry?

  Hmm, discovered or invented? I actually did, 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, and I think that my, my final sort of conclusion that I came to is that, that the tools that we've built are invented, right? The way that we write numbers, the way that we, you know, structure equations.

• 11:39Michael Stevens?

  Sure.

• 11:39Hannah Fry?

  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 Andrew Wiles, who was the person who solved Fermat's Last Theorem. Again, we should definitely do an episode on that.

• 11:58Michael Stevens?

  Yep.

• 11:58Hannah Fry?

  He describes doing mathematics that has never been done before, right? So if you're sort of doing a PhD, if you're, you know, doing research mathematics, which I've done, this is a really, I think, the best description of what it feels like. He said that it feels like you are, you are clambering through 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.

• 12:34Hannah Fry?

  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've 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.

• 13:01Michael Stevens?

  That's beautiful.

• 13:02Hannah Fry?

  Um, yeah, that's why people want to be mathematicians.

• 13:06Michael Stevens?

  The tools, the machetes you're using to chop through what feels like a dense jungle, we invented those.

• 13:12Hannah Fry?

  Yeah.

• 13:12Michael Stevens?

  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.

• 13:27Hannah Fry?

  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 asks, how difficult was it for the discoverers of germs to convince the world that something they couldn't see was harming us?

• 13:53Michael Stevens?

  Um, yeah, it was really difficult. I think a lot about the, and this might be what the the question asker is getting at. A phenomenon in human psychology known as the simulvice reflex. Have you heard about this?

• 14:08Hannah Fry?

  No.

• 14:09Michael Stevens?

  So, 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. Okay, so if you can't see them, how do you know they're there? Uh, how do you know that um an illness is caused by like a little organism and not just by bad air or your 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

• 14:50Michael Stevens?

  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, you know, gloves, without proper antiseptic technologies 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

• 15:31Michael Stevens?

  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.

• 15:46Hannah Fry?

  Because wasn't there, there was like a maternity ward there, wasn't there?

• 15:49Michael Stevens?

  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 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,

• 16:31Michael Stevens?

  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 child bed 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 eighteen forty seven.

• 16:54Hannah Fry?

  That late. Oh, my goodness. Because there's because the counter to that is that, 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.

• 17:10Michael Stevens?

  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 fever in his hospital, and how much of 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

• 17:55Michael Stevens?

  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, you're 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 twenty years for people to say, okay, let's start entertaining the idea of these things. We'll call them germs now. And let's do some experiments

• 18:39Michael Stevens?

  and take it seriously. So it was a slow process. And we still see that today with accepting new ideas.

• 18:45Hannah Fry?

  Like what? Like, like, what kind of ideas? I'm realized 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 to accept the eighteen fifty s. I mean, 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?

• 19:07Michael Stevens?

  Well, yeah, I mean, really recently, how covid nineteen 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 twenty twenty one that the World Health Organization finally recognized airborne transmission of the virus.

• 19:31Hannah Fry?

  So two years after the the first sort of confirmed.

• 19:35Michael Stevens?

  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.

• 19:52Hannah Fry?

  You know, in the Center of Mathematical Sciences, where I work at Cambridge, right? So you've got all of these 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 the first reports were coming through that it was that was transmitted by the air airborne disease. Some of the fluid dynamicists, 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 realized that the exact design of this lecture theatre was that anyone who was standing at the front was

• 20:32Hannah Fry?

  like in direct line of fire, that all of the people's air was like perfectly, perfectly funneled directly to them. So they they then redesigned it and there are these like black flags that are up to sort of like disrupt the airflow in there still.

• 20:48Michael Stevens?

  Oh, wow. Yeah, they only want the knowledge to be contagious.

• 20:52Hannah Fry?

  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.

• 21:00Michael Stevens?

  Ah, yeah, yeah, yeah, right. Speaking of the dynamics of things moving like liquids, 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?

• 21:23Hannah Fry?

  What a transition that was, Michael, from germs to floating.

• 21:28Michael Stevens?

  Don't thank me, thank Ben.

• 21:30Hannah Fry?

  Um, yes, I mean, that's true, right? If you think about um, 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, it's 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.

• 22:15Hannah Fry?

  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.

• 22:58Michael Stevens?

  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.

• 23:04Hannah Fry?

  Right, yeah.

• 23:05Michael Stevens?

  It's basically not there.

• 23:07Hannah Fry?

  It's basically not there. Exactly right. The um, I should tell you the uh, 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, on the surface of the earth. It's got my favorite equation name ever. You know, when you do, you know, when you watch like um, 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 favorite equation, which is the quasi geostrophic potential vorticity equation.

• 23:37Michael Stevens?

  Ooh.

• 23:37Hannah Fry?

  You sound, you sound like you're smart when you're saying that, but basically it just means, you know. It's it's 2D on the earth.

• 23:44Michael Stevens?

  One more time.

• 23:45Hannah Fry?

  Quasi geostrophic potential vorticity equation.

• 23:47Michael Stevens?

  Quas- quasi geostratic?

• 23:50Hannah Fry?

  Geostrophic, yeah.

• 23:51Michael Stevens?

  Geostrophic. Vorticity.

• 23:54Hannah Fry?

  Potential vorticity.

• 23:56Michael Stevens?

  Potential vorticity. Vorticity is a great word.

• 23:59Hannah Fry?

  Isn't it?

• 24:00Michael Stevens?

  It sounds both scientific and literary. Vorticity, the sound and the fury, vorticity.

• 24:07Hannah Fry?

  There you go. Um, I should tell you, Ashley, if you want to see the quasi geostrophic potential vorticity equation slash two dimensional fluids on the surface of a of a planet in action, right? And the way that these storms build and build and build and build and build. 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. It's 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 of of what happens in these situations.

• 24:52Hannah Fry?

  Thank goodness for mountains, otherwise we'd be in that situation too.

• 24:55Michael Stevens?

  Yeah, but Jupiter has no mountains. It has no solid ground. But it's, it 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?

• 25:13Hannah Fry?

  Exactly right. They're they're thin layers that don't interact really enough to to 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?

• 25:23Michael Stevens?

  Yeah, it sure was.

• 25:25Hannah Fry?

  Um, I mean, frankly, I'm happy with it. Let's go into the break and um we'll see how mathsy we get in the second half, shall we?

• 25:41Speaker 03

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• 27:10Michael Stevens?

  All right, welcome back. We had a very maths-y first half, as Hannah said, and we're going to continue to stay maths-y, 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.

• 27:28Hannah Fry?

  Ooh, delightful.

• 27:30Michael Stevens?

  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.

• 27:48Hannah Fry?

  What a treat. Okay, go on then. By the way, the chances of me having heard 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.

• 28:00Michael Stevens?

  Well, let's see if you've heard this one. This one comes from the most famous palindromeist ever, Lee Mercer. All right. You might know Lee Mercer from his most famous work, A Man, a Plan, a Canal, Panama.

• 28:15Hannah Fry?

  No, but the fact that you said that he was a palindrome, this is making me work out backwards in my head.

• 28:19Michael Stevens?

  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.

• 28:47Hannah Fry?

  I don't know the Nantucket one, but I can imagine what rhymes at the end.

• 28:52Michael Stevens?

  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 begins with this equation. Okay, 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 11, is nine squared and not a bit more.

• 29:30Hannah Fry?

  Hang on, let me just work it out. It actually holds. It holds?

• 29:34Michael Stevens?

  It holds.

• 29:35Hannah Fry?

  Oh, that's nice.

• 29:37Michael Stevens?

  It's really nice.

• 29:38Hannah Fry?

  Gosh, can you imagine how long it took him to come up with that?

• 29:41Michael Stevens?

  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 1 to the cube root of 3 times the cosine of 3 pi over 9 equals log of the cube root of e.

• 30:10Hannah Fry?

  Does it hold? Hang on.

• 30:12Michael Stevens?

  It holds. It's true.

• 30:15Hannah Fry?

  It only works in an American accent, though, because if you said dz, then 3, you sort of falls, it falls apart.

• 30:22Michael Stevens?

  Okay, but here, let me tell you this. It doesn't have to be z. It could be t. Let me do a version for the rest of the world. The integral t squared dt from 1 to the cube root of 3 times the cosine of 3 pi over 9 equals log of the cube root of e.

• 30:42Hannah Fry?

  That is, that is, that is absolutely gorgeous.

• 30:46Michael Stevens?

  Isn't it gorgeous?

• 30:47Hannah Fry?

  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.

• 30:58Michael Stevens?

  I know, because normally when you write a limerick, you can go, ooh, 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, 3 and e all rhyme. Cosine and 9, that's pretty nice.

• 31:17Hannah Fry?

  Yeah, but you need the cosine and 9 to be in the e bit.

• 31:21Michael Stevens?

  I know. I know.

• 31:23Hannah Fry?

  The score and not a bit more. I mean, I'll be honest with you. He might be good at palindrome. So that is a tiny bit cheating.

• 31:28Michael Stevens?

  It's a tiny bit cheating. Yeah, I will admit that, too. It's 9 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. Okay, 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.

• 32:03Hannah Fry?

  That is delightfully nerdy.

• 32:05Michael Stevens?

  That's really delightfully nerdy. It's very fun.

• 32:07Hannah Fry?

  Also true. If anyone wants to cut a Mobius strip in half and have that joy for yourself, then, then, then off you go.

• 32:13Michael Stevens?

  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 a one bigger loop. Okay, well, here's, here's one. This is from Dave Morris, um, from, uh, an issue of Wordways. This one is, uh, if you're talking about cheating, this one, it's almost kind of like funny in the way that it works.

• 32:33Hannah Fry?

  Cool.

• 32:34Michael Stevens?

  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 equal 10. That's how adding is done.

• 32:46Hannah Fry?

  Yeah, that's my kind of guy.

• 32:48Michael Stevens?

  Still pretty clever.

• 32:49Hannah Fry?

  It's still pretty good. That is still pretty good.

• 32:51Michael Stevens?

  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.

• 32:59Hannah Fry?

  Wait, did you say that you wrote some yourself?

• 33:01Michael Stevens?

  Yes, I did. I did. So, um, okay, here's, here's a geometrical one. Let's do some geometry.

• 33:07Hannah Fry?

  Wait, wait, did any of the, any of them as impressive as that integral one?

• 33:12Michael Stevens?

  Uh, no, none of them.

• 33:13Hannah Fry?

  They are though, because you wrote them.

• 33:15Michael Stevens?

  Thank you, Hannah. Okay, so this one, this one's 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 rect, R E C T, means right, a right angle, a rectangle.

• 33:38Hannah Fry?

  You nerd.

• 33:40Michael Stevens?

  Rectangular square.

• 33:42Hannah Fry?

  That's amazing. Do you know what? I think I actually, this, it's got, you know, there's sort of an anthropomorphization to that. There's like, you know, it's, it's cute sort of imagining it. In many ways, I prefer that to the other extremely clever ones.

• 33:56Michael Stevens?

  It's got, yeah, it's got a character in it. And you know, I, 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.

• 34:10Hannah Fry?

  I like the, I like the guy.

• 34:12Michael Stevens?

  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. 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.

• 34:32Hannah Fry?

  Yeah.

• 34:33Michael Stevens?

  Which means a square is a kind of rhombus. But a square is a rhombus with all right angles, rect angles. So that's just a little one for the geometry nerds.

• 34:44Hannah Fry?

  Talking of using poems to remember stuff, and we were talking about hurricanes earlier. There was a guy called Louis Fry Richardson, no relation, who was integral in lots of the the modeling of hurricanes and weather systems. And he had a little rhyme, which was to remember how it all worked, basically. I mean, quite literally talking about hurricanes. He had, "Big wells have little wells that feed on their velocity, and little wells have lesser wells, and so on to viscosity."

• 35:15Michael Stevens?

  Oh.

• 35:16Hannah Fry?

  Isn't that cute?

• 35:17Michael Stevens?

  That's really cute.

• 35:19Hannah Fry?

  Yeah. I mean, your rhombus is on is better, but.

• 35:22Michael Stevens?

  No, no, there's no such thing as a better or worse poem, you know? Maybe there's a more or less successful communication of feeling. But I do feel for this rhombus. It should have been happy with what it was.

• 35:37Hannah Fry?

  It should be with what it was.

• 35:38Michael Stevens?

  It wanted more respect. And so not knowing what to expect. There's different versions of it that I wrote, but I thought that's the one that's. The first version of the rhombus limerick I wrote simply had his angles become rect. And I'm like, ah, but unfortunately, a rhombus with rect angles is exactly a square. It needed to be about a parallelogram.

• 35:59Hannah Fry?

  Yeah.

• 36:00Michael Stevens?

  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.

• 36:13Hannah Fry?

  Oh.

• 36:14Michael Stevens?

  Yes. Uh, for example, there once was a man from Nantucket.

• 36:21Hannah Fry?

  Hmm.

• 36:21Michael Stevens?

  Okay, but parallelogram, it doesn't have that little triplet.

• 36:27Hannah Fry?

  Could you split it though? Could you go par-a-low-a-gram?

• 36:32Michael Stevens?

  Yes, you could. Parallelogram.

• 36:36Hannah Fry?

  Yeah.

• 36:36Michael Stevens?

  But then it doesn't scan and people go, oh, you're not very good. So. Um, I wanted to share these with you. These are more of like a work in progress. I'm really into um, 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 gonna, you know, the create a black hole and it's gonna end the universe. And and this is how I feel about it. Division by zero earns prison unless we agree with precision.

• 37:17Michael Stevens?

  That math doesn't break if there's nothing you take, cuz dividing by none ain't division.

• 37:27Michael Stevens?

  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.

• 37:52Hannah Fry?

  No prison for you. That's uh, this is essentially where we're at.

• 37:56Michael Stevens?

  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.

• 38:18Hannah Fry?

  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 as a progression, and it's great. Two, I like how both of those limericks are tied together by the insistence of there being some sort of maths police.

• 38:35Michael Stevens?

  Yes.

• 38:36Hannah Fry?

  Who are absolutely eager, eager to catch people for these zero division crimes. I'm absolutely loving it. Wait, have you got one more?

• 38:45Michael Stevens?

  There's one more because there's the special case where zero is divided by zero. And this is different. So, 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.

• 39:04Hannah Fry?

  Oh, that's good. I need a judge in there.

• 39:07Michael Stevens?

  And for, 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, 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 undying amount of nothing won't ever equal

• 39:50Michael Stevens?

  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.

• 40:04Hannah Fry?

  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, the philosophy of mathematics. But zero divided by zero, it's, uh, sometimes there is actually an answer. Sometime, sometimes it's undefined, sometimes it's infinity, sometimes it's zero, sometimes it has a final answer.

• 40:29Michael Stevens?

  Okay, so yes, we're going to do an episode on this. You're going to teach me, I'll write some more limericks. 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.

• 41:07Hannah Fry?

  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 will have something much more interesting to say.

• 41:20Michael Stevens?

  Yeah.

• 41:21Hannah Fry?

  And, um, and they, uh, they both declared that they deliberately didn't ask that question in front of me because I would give a boring answer.

• 41:31Hannah Fry?

  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 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?

• 41:54Hannah Fry?

  So, you know, hopefully you, dear listeners, will find it slightly more interesting than my children.

• 41:59Michael Stevens?

  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.

• 42:16Michael Stevens?

  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. 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 R squared.

• 42:44Hannah Fry?

  I love it. I love it. Yeah, that's great. Also, thank you for using chips as well rather than fries.

• 42:50Michael Stevens?

  I know, right? I felt like the kind of like cross Atlantic, the transatlantic 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 uh over and over again.

• 43:04Hannah Fry?

  That was absolutely brilliant. I'm I'm gonna have that put on my wall. Go on, I want to hear you on, Michael. Go for you on.

• 43:09Michael Stevens?

  Um, okay. Well, this was 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.

• 43:25Hannah Fry?

  Yeah.

• 43:29Hannah Fry?

  They are so good. They are so good. We have found a new skill. We have found a new skill for 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.

• 43:44Michael Stevens?

  Yeah.

• 43:44Hannah Fry?

  dribbling. I don't think I've ever written one in my entire life. So um that we're gonna 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 episode for the day. Uh, if you have anything you'd like to send us in, limericks or otherwise, send them to us, [email protected].

• 44:06Michael Stevens?

  Yes, and please join our newsletter at therestis.com/science.

• 44:11Hannah Fry?

  We'll be back next Thursday with another episode of Field Notes and and on Tuesday with our normal episode. See you then.

• 44:19Michael Stevens?

  See ya.

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