My Favorite Theorem by Kevin Knudson & Evelyn Lamb

July 20, 2023 Episode 86 - Sarah Hart

Evelyn Lamb: Hello and welcome to My Favorite Theorem, the math podcast with no quiz at the end. Or perhaps today we should say the maths podcast with no quiz at the end. My name is Evelyn Lamb. I'm a freelance math and science writer in Salt Lake City, Utah. And this is your other host.

Kevin Knudson: Hi, I’m Kevin Knudson, professor of mathematics at the University of Florida. It's Juneteenth.

EL: It is, yeah.

KK: And I'm all alone this week. My wife's out of town. And yesterday was Father's Day and I installed cabinets in the laundry room. This is how I spend my Father's Day, something we've been talking about doing since we bought the house.

EL: That’s a dad thing to do.

KK: 14 years later, I finally installed some cabinets in the laundry room. So it looks like you had a good time in France, judging from your Instagram feed.

EL: Yes, yeah. And I'm freshly back, so I'm in that phase of jetlag where, like, you get up really early. And so it's 9am and I already went for a bike ride and did some baking and had a relaxing breakfast. At this point, I'm always like, “Why don't I do this all the time?” But eventually my natural circadian night owl rhythms will catch up with me. I'm enjoying enjoying my brief, brief morning person phase.

KK: Yeah. Never been one, won’t ever be one as far as I can.

EL: Yeah. Just keep moving west, and then you’ll be a morning person for as long as you can keep jetlag going.

KK: That’s right. That's right. Yeah.

EL: So yeah. Today we are very happy to have Sarah Hart on the show. Sarah, would you like to introduce yourself? And tell us a little bit about, you know, what you're all about?

Sarah Hart: Ah, yes. So my name is Sarah Hart. I'm a mathematician based in in London in the United Kingdom. I'm a professor of mathematics, but my true passion is finding the links and seeing them between mathematics and other subjects, whether that's music or art or literature. And so I think there's fascinating observations to be made there, you know, the symmetries and patterns that we love as mathematicians are in all other creative subjects. And it's fun to spot them and spot the mathematics that's hiding in all of our favorite things.

EL: Yeah. And of course, just a couple of months ago, you published a book about this. So will you tell us about it?

KK: Yeah,

SH: So this book, it's called Once Upon a Prime: The Wondrous Connections between Mathematics and Literature. And in the book, I explore everything from the hidden structures that are underneath various forms of poetry, to the ways that authors have used mathematical ideas in their writing to structure novels and other pieces of fiction and the ways that authors have used mathematical imagery and metaphor to enrich their writing, authors as diverse as you know, George Eliot, Leo Tolstoy, Marcel Proust, Kurt Vonnegut, you name it. And then I also look in the third section of the book at how mathematics itself and mathematicians are portrayed in fiction, because I think that's very, very interesting and shows us the ways in which those things at the time the books are written, how is the mathematics perceived? How has it made its way into popular culture? And how mathematicians are perceived as well, that tells us something fascinating, I think, about the place of mathematics in our culture.

EL: Yeah, definitely.

KK: We’re always portrayed as either mentally ill. Or just, like, absurd geniuses, you know, when really, you know, we're all pretty normal — most of us are pretty normal people, right?

SH: Yeah. Well, we are, as everybody, there's a range. There's a range of ways to be human. And there's a range of ways to be a mathematician. But yeah, we're not all tragic geniuses, or kind of amoral beings of pure logic, or any of those things that you find in books. So yeah, and there are some sympathetic portrayals of mathematicians out there, and I know I talk about some of those, but yeah, it's very interesting how these these tropes, these stereotypes can creep in.

EL: I must confess I'm about three quarters of the way through, I haven't quite finished that last section. But the first few sections that I've read, I've definitely — I keep adding books to my “Want to Read list,” so it’s a little dangerous.

SH: Oh yeah, it should have a little warning, the book, saying “You will need a bigger bookcase.” Unfortunately, you know, you will want to go and read all of these books. And yeah, “Sorry, not sorry,” I think is the phrase.

EL: Yes, definitely. I downloaded — so I don't need a bigger bookshelf because I put this one on my ereader — but I downloaded The Luminaries, which sounds like a really interesting book and excited to get to that, you know, in the neverending list of books that I'd like to read.

KK: Right, we were talking about talking about our tsundoku business before [tsundoku is a Japanese word for accumulating books but not reading them]. So I actually I did, with a friend in the lit department, or in the language department, we taught a course on math and literature a few years ago.

SH: That’s fantastic.

KK: It was. It was so much fun. It's the best teaching experience I've ever had. But I was glad to read your book because we missed so much. Right? I mean, of course, we only had 15 weeks, you know, we and we talked about Woolf, like To the Lighthouse is kind of an interesting one. And yeah, I did finish the book. So sorry, Evelyn, I won. But no, it's it's actually, you know, it is spectacularly well written and, and I'm glad you're having success with it. Because it's — again, I like this idea, that you're sort of humanizing mathematicians and mathematics and showing people how it's everywhere. Isn't that part of your job? Aren’t you the Gresham professor, is that correct?

SH: Yes, I’m the Gresham professor of geometry. So Gresham College is this really unique institution, actually. It was founded in 1597 in the will of Sir Thomas Gresham, who was a financier at the Court of Queen Elizabeth I in Tudor times. And in his will, he left provision for this college to be founded that would have seven professors, and their whole job was to give free lectures, at the time to the people of London. Of course now it's all livestreamed and it goes out and is available all over the internet. And anyone could go and it was just, you know, if you wanted to learn these subjects — and he thought there were seven most important subjects at the time that he said, I still say, geometry and mathematics more broadly, very important — but it was geometry, music, astronomy, law, rhetoric, physic, which is the old word for medicine, and I perhaps I’ve forgotten one. But yeah, these subjects, and so still today, this is what Gresham College does, free public lectures to anyone who wants to come. Now, you used to have to give them once in Latin and once in English. Now, you do not have to do it, thank goodness.

KK: Yeah. Who would come?

SH: I don’t know. Yeah, if I had to suddenly give my lectures in Latin, that might be slightly more of a challenge. My role there is to communicate mathematical ideas to anyone who wants to listen, so a general audience. And some of them will have mathematical training, but many will not. And they they're just kind of interested people who find things in general interesting, and mathematics is part of that. I love that idea, that mathematics is part of what a culturally interesting person might want to know about. And that is something that perhaps used to be more so than it is today. And I really would like mathematics to somehow be rehabilitated into what the cultural conversation involves, rather than it seems to be perhaps in a little bit, sometimes it's pigeon holed or put to one side, you have to be a geek to like mathematics. You have to be unusual. And it's really not true. It's not the case.

EL: Yeah. Wow, that sounds like a dream job. I’m writing that down and putting it on my dream board? It's yeah.

KK: I seem to remember, so I read the review of your book, I think by Jordan Ellenberg, who's also been on.

SH: Yes.

KK: It mentioned that the first person who held your chair invented long division. Is that right?

SH: It’s true.

KK: That's what used to get you a university job, is you invent long division.

SH: Yeah. So that's, you know, what a lineage to be part of. I really feel honored and humbled to be in that role. And, actually, I'm the first woman to do this job in its 400 and whatever year history which, yeah, okay, you could say, yes, we might be a bit late with that one. But I feel it's a real privilege to do it.

EL: Yeah. Well, that's wonderful. So we have invited you on this show to tell us what your favorite theorem is. So have at it.

SH: Okay, so, my favorite theorem, I guess it's could be called a collection of theorems really, but the properties of the cycloid. So the cycloid is, it’s my favorite curve. And it's my favorite curve that probably unless you're a mathematician, you may not have heard of it. So people have heard of ellipses and circles and parabolas. And they've heard of shapes like triangles and things, but cycloids, people tend not to have heard of. And for me that's a surprise because they're so lovely. And the history of the study of the cycle of which, you know, we can we can talk about, is so fascinating and fun, and so many of the most famous mathematicians that people have heard of, like Isaac Newton, and Leibniz, and Mersenne, and Descartes and Galileo, and Pascal and Fermat, all of those people worked on the cycloid and were fascinated by it. And so there are these beautiful properties that it has, which we can bundle up into a theorem. And that would be my favorite thereom.

EL: That’s great. And yeah, in case anyone listening to this doesn't know about the cycloid, it’s a cool curve. And it's actually, you know, it's a curve that a lot of people haven't seen as such, but it's one that does kind of arise sort of in everyday life, kind of. So yeah, do you want to describe what a cycloid is?

SH: You can make a cycloid quite easily. It’s a fairly natural idea, I would say. Imagine a wheel rolling along the road. And now somewhere on the rim of the wheel, you paint the put a little blob of paint, or something like that, or if it's in the dark, you can put a little light. And then and then as the wheel rolls along, that blob of paint or little light will be following a particular path, as the wheel rolls.

EL: Going up and down.

SH: Kind of up and down. And eventually, sometimes it'll touch where the ground is. And then we'll go up and down again. And what you get is a series of arches, they look like arches. And that's what the cycloid is, normally you take one arch and call that the cycloid.

KK: Right.

SH: So this is quite a natural idea, what kind of shape will that be? And what is this arch shape? And the first thing you can say is, yeah, is it something I already know about? So early on in the study of this curve, which is first written down as a question, what is this shape? About 1500. Marin Mersenne, who is famous for Mersenne primes, among other things, so he thought maybe it's half an ellipse. And that's not too bad an approximation, but it isn't quite that. And so that's sort of question one. Is it something we already know? And it wasn’t. So then, people like Galileo started to ask, well, what do we what do we like to know about shapes and curves? So there are two questions really, at the time, they were called the quadrature question and the rectification. So quadrature is what's the what's the area? So if you make this arch, what's the area underneath this arch, between the arch and the road, I guess. That's question one. And the other one is the rectification: what's the length? So how long is this arch in terms of the circle that makes that makes the arch, the cycloid. And Galileo didn't know how to calculate either of those things. But he actually made, he physically made a cycloid. So he got a piece of sheet metal, and he rolled a circle along it, and he got the path. And then he cut it out and he weighed, he weighed the bit of metal that he had.

EL: Oh wow!

SH: To find an estimate for the area. Okay? So this is a real hands on thing.

EL: Yeah, that’s commitment.

SH: Because he did not know. So he physically made it and weighed it. And he got an answer that was around about three times the area of the of the circle that makes it, roughly speaking, and he said, Okay, if we all think, what’s a number that's roughly three, that's to do with circles, right? And so he wondered, could it be pi times the area of the circle? It isn't. It isn't pi times the area of the circle! Galileo never managed to work out exactly what it was. But this guy Roberval, Gilles de Roberval, did manage to work out what the area is. He didn't tell anyone how he'd done it because at this time in history, there were all these priority disputes, who sorted this thing first, who has done what first? People would sometimes go to the length of writing their solutions in code. So Thomas Hooke, who was another Gresham professor, when he worked out what we call Hooke’s law now, he wrote Hooke’s law down as an anagram in Latin, before he told anyone else. And then if anyone else came up with it, he could say, look, here's my anagram that I did earlier to prove that I thought of it first. So there were all these weird and wonderful things that people did at that time to establish priority. But Roberval, he had this incentive for not telling that he knew the area under a cycloid. And the incentive was this — it was not a good idea for them to do this — the job he had at the time, Roberval, was renewed every three years. And to get the job every three years, there were some questions that were set. And if you could answer those questions the best out of all the people who tried to do it, you could get that job for the next three years. But the person setting the question was the incumbent professor. So if you're the incumbent professor, you need to set questions that only you know the answer to, and then you get to keep your job. So for a few years, Roberval could say, you know, what's the area under this cycloid, and no one else knew. So he worked it out. And his proof was quite nice, but it wasn't published until 30 or 40 years after his death. But it actually — and this is the first lovely thing about the cycloid — the area, if you have a circle that's making this cycloid by rolling along road, the area underneath one of these arches is exactly not pi times, exactly three times the area of the generating circle. So a lovely whole number, simple relationship between the arts.

EL: What are the odds? It’s almost miraculous.

SH: Fantastic. So here's another equally miraculous thing that kind of adds to the first one. Then people try to work out what's the length of this cycloid? And the person who managed to solve that was, in fact, Christopher Wren. So he's well known as an architect, and he designed St. Paul’s, the wonderful dome of St. Paul's in London, and many other churches in London. But he was also a mathematician among many other things. So he solved the rectification problem, what's the length, and if the circle that makes this, the cycloid has diameter d. So we know that the circumference of that circle, the length around the circle would be pi times d. Well, another beautiful whole number relationship, the length of the cycloid arch is exactly four times the diameter. A beautiful whole number relationship. It's fantastic. So you've got these two lovely properties of the cycloid. And people were fascinated by it. So it had this nickname, the Helen of geometry, as in Helen, you know, face that launched a thousand ships.

KK: Right.

SH: It was a very beautiful curve with beautiful properties. But there's another reason why it was called the Helen of geometry. And it was because, like Helen of myth, it started lots of squabbling. So I mentioned Roberval, who had proved the area formula for the cycloid. Someone else came along a few years later, and found out this this result, and Roberval immediately accused him of plagiarism. And this guy was like, No, I didn't do that. But they argued about it. I think it was Torricelli. And and When Torricelli died a few years later, team Roberval said he's died of shame because of being a plagiarist. He may have died of shame. But he also happened to have typhoid at the same moment. So you know.

KK: Sure.

EL: Shame-induced typhoid?

SH: But you know, so that was one squabble, but then Fermat and Descartes had an argument because they both proved something about the tangents to the cycloid. And they hated the way each other done this. So I think it was Fermat did have a particular method. Descartes said that this method was ridiculous gibberish. So you know, he's not mincing his words, he’s not saying “I prefer my method” but “Fermat is speaking gibberish nonsense.” So they argued. But, you know, this beautiful curve has other exciting properties. And this is where it goes for me from, “Okay, nice whole number relationships, cute.” But then one of the things that we all love in mathematics is where something you've studied over here, reappears in a completely different context. And this is what happens with the cycloid. So it comes up to in connection with trying to make a better clock. So there's this mathematician, Christiaan Huygens, who is trying to make a better clock. And he comes up with a pendulum clock. And so pendulum clocks improved timekeeping dramatically. Before the pendulum clock came along, basically, it was a sundial or nothing, really. There were no good mechanical clocks. And the ones that existed would lose about 15 minutes a day or something of time. The pendulum clock comes along. And so you can do kind of the mathematics of a swinging pendulum, and if you make a little approximation, so the approximation that you make is that for a small angle, theta, the sine of theta is approximately theta. So you can make that approximation. And it's pretty good for small angles. And if you do that, then when you work out what the forces are acting on the pendulum, you find that, roughly speaking, it'll take the same time to do its swing wherever you release it from. So it has this kind of constant period, basically. And that's why pendulum clocks are useful for telling for time. But they're not perfect, because we had to use an approximation to get to that point. So Christiaan Huygens is wondering, is there actually a curve that I can make, that will really genuinely have this constant period property, that wherever I release a particle from on this curve, it will reach the bottom in the same time?

KK: Right.

SH: Because that's what the pendulum almost does, but doesn't quite do. And so he said — and this problem is known as the tautochrone problem, because it's “the same time” in Greek. And it turns out, guess what, the cycloid solves the tautochone problem. It's precisely — so we have an arch, you've got to turn the arch upside down. So now you can roll, your particle can roll down. And wherever you release a particle from on the cycloid, it will reach the bottom in exactly the same time.

KK: Remarkable.

SH: I mean, assuming you know, it's smooth, no friction or whatever. It's just rolling down under gravity. And I mean, it's not even clear that such a curve could exist, right? It's quite a thing to ask. And yet, the cycloid has this property, and it's fantastic. So that's an amazing thing. And few years later — so Huygens worked this out. A few years later, a different problem was posed. It's kind of a related question, or it's something to do with particles anyway. And the question here is called the brachistochrone problem. And it was proposed by Johann Bernoulli, one of the Bernoulli brothers. And he posed this kind of publicly in a journal saying, Okay, if you now have two points A and B, A is above B, and you want to have a curve such that when a particle rolls down that curve from A to B, it will reach point B in the quickest time, so what might that be? Is it sort of a parabola, maybe a straight line, what's it going to be like? And this problem was posed to the mathematicians of Europe as a challenge, and quite a few big names enter this competition to see if they could do this. So Leibniz was one, Gottfried Leibniz, Bernoulli himself solved it, his older brother solved it, and then they got this anonymous entry. And it was so beautifully done, and elegantly produced, the solution to this, that, even though it was anonymous, when Bernoulli he saw it, he said this famous phrase, “I recognize the lion by his claw.”

KK: Right.

SH: And it was Isaac Newton, who had solved this problem. And guess what? It's the cycloid again. The cycloid solves this problem as well. So you've got this amazing curve, which is a natural idea. It's got these lovely whole number relationships about its length and its area, and then it suddenly also can solve these totally different questions about particles rolling down in the quickest time or constant time. And so that is why I love the cycloid so much. Everybody’s worked on it. It's got this amazing history, it's really beautiful.

KK: This sounds like a good public lecture.

EL: Yeah.

SH: I just get really.

EL: The cornucopia of the cycloid.

KK: Yeah, so question, the original area calculation that Roberval did, did he use calculus? Or was this a geometric argument?

SH: So he used something that isn't quite calculus yet, Cavalieri’s principle. If you're comparing areas, if you have got two shapes where if you slice through, the length of those slices is the same at every point, then the areas are the same. So he used that principle, which you can extend to volumes as well. And he kind of did a particular, so he managed to do this. And he had the curve that you make for the cycloid, he made it up from three different pieces. And he did this sort of slicing argument to compare it to with things he already knew, one of which was the sine curve, although I don't think he noticed it was a sine curve at the time, but we can now see that. So now, you would make that argument with calculus. But it's the same basic idea. You're slicing something very finely.

KK: Right. You could almost imagine Archimedes figuring this out.

SH: Yeah. Yeah, exactly.

EL: Yeah. So I mean, you've made a very compelling case that this is a very cool curve that has all these properties, So like, why is this your favorite? Or I know it's hard to pick a true favorite. But yeah, can you talk a little bit about, like, how you encountered it and what makes it so appealing to you?

SH: Well, there's at least two things. There might be three. One is, I love the simplicity of the results about the area and the length, that they are just lovely, simple relationships there comparing to the circle that makes this this curve, which itself is easy to think about what it is. So it's not contrived at all. It arises fairly naturally from just thinking about wheels rolling along roads. You get this curve, and then these relationships are very simple. The second reason I love it so much is because of this unexpected appearance of the cycloid in this totally different context from from how you imagined it. When it's generated by just, you know, a wheel, but then a curve that has these other properties, that’s very surprising. There are other things we could talk about to do with it. involutes, and other kinds of things where it crops up, but that for me, it encapsulates why it's such an exciting thing. And it's like when you first encounter pi or something, or you see the e to the i pi plus one equals zero, it gives you that same kind of feeling, that thing's from over here, and this other constants from over there, you know, that they're linked together seems really surprising. But the final thing, I suppose this kind of links in again with what we were saying about mathematics and literature, is how the cycloid has caught people's imagination over time. And it's both of mathematicians, but outside. And there are several books that mention cycloids. So Moby Dick is one. That's got a lovely little passage about cycloids. But also, Gulliver’s Travels mentions cycloids, Tristram Shandy by Laurence Sterne, this amazing, crazy 18th century book talks about cycloids. And those are just three that are really classic books. It was in the air at the time, and perhaps we don't necessarily — like, a modern and modern person may not have heard of cycloids. But certainly if you were educated in the 18th, 19th century, you may well have heard about cycloids. And that, to me, is very interesting too.

EL: Yeah, do write a little bit about this in your book that Moby Dick part, I have gotten to that part. And apparently, did you say that Melville apparently had some amazing math teacher in high school. And so, you know, kind of was able to really capture his imagination about math and then bring that into literature later, which is just kind of a cool thing to think about as math teachers, people who teach math. It's like, yeah, even if your your students don't end up in math or something, they might, you know, hopefully bring some of what you teach them that direction.

SH: Yeah, absolutely. I mean, it’s the value of having a great inspirational teacher. Just look at with Melville. So he had a teacher. He went to a school called the Albany Academy, and he was good at school in some areas, mathematics was something he was particularly good at. And he actually won a prize for being the first best at ciphering, was what it was for. Cipher, the old word for calculation.

KK: Right.

SH: His prize was a book of poetry, which I liked, because for me, that's absolutely a natural prize, but it wouldn't necessarily be thought so. But his teacher was a man called Joseph Henry. And Joseph Henry was no ordinary schoolteacher. He was a very good scientist in his own right, he went on to become the first secretary of the Smithsonian. So you know, pretty impressive. But physicists will know the name Henry, because the Henry is the scientific unit of inductance. And that's for Joseph, that is Herman Melville's maths teacher at school. So he was by all accounts an exceptionally good teacher, to the extent that some of his classes were actually, members of the public were allowed to come in and attend as public lectures. So there's a record that says, a request of his that he wants to have additional books for the more advanced students to entertain them beyond the normal curriculum. And so I don't know, and we can't know for sure, how Herman Melville learned about cycloids. But I could very easily imagine that a lesson on Friday afternoon, let's just talk about this fascinating curve because it's really interesting. And Melville did have a love, then, of mathematics, which just comes out in his writing. You can just see it, the way he chooses metaphors and imagery, they're often mathematical. And you can just see it's, it's not thinking “I must include some mathematics.” It's just the sheer pleasure of it. The delights, the joy of mathematics just comes out in his writing, which is wonderful to see.

EL: Well that was such a cool story that I read in there. And I have loved to revisit this. I don't think I've actually thought about cycloids since I taught calculus, right, which, it's been quite a while since I taught calculus. It is a fun, it’s a very common example in calculus books now. You'll kind of go through and solve some of these, these things. And I think, when you do parametric curves, maybe?

SH: Yes.

EL: So yeah, lots of fun, but I don't think I had really appreciated it as this whole whole thing before. So the other thing we like to do on this podcast is ask our guests to pair their theorem, or their bouquet of cycloid facts, with something else in life. So what have you chosen for your pairing?

SH: Well, so I've chosen Moby Dick.

EL: Okay.

SH: Because, I mean, he does talk about cycloids in the book. It’s not just because of that, but with the cycloids is this lovely passage where Ishmael, who is, you know, traveling as a deckhand on a whaling ship with Captain Ahab, who perhaps is not entirely sane, and we discovered that through the book, but there are many — Ishmael sort of has these wonderful meditations, he's just thinking about things. And some of them are mathematical, and some of them aren't. But there's one particular point where he is cleaning the the try pots. A try pot is something you had on a whaling ship, where there's great cauldron like pots where they kind of render the whale blubber down, and then you have to clean them. And so he says, you know, this is a place for wonderful mathematical meditation. And he and he talks about, as his soapstone is circling around the inside of the try pot, he says, I was struck by the fact that in mathematics, the cycloid is the curve where you can you can release something and it falls to the bottom in a constant time. And so he's just sort of drops in, the cycloid, just mentions it while he's daydreaming about something else. But Moby Dick, it's full of mathematical ideas. And it’s, you know, they are interested in numbers, to the extent that Ishmael keeps, he has the data or information about whales, measurements and statistics about whales, he has them tattooed onto his body, because as he says, you know, I didn't have a pen to hand, kind of thing, there was no other way to record. So he just has them tattooed on his body. Ahab is doing calculations on his ivory leg, you know, there are all these discussions about number. But there are lovely pieces of imagery around the infinite series of ripples in waves in the sea. There's a metaphor about loyalty where Ahab says to the cabin, boy, you are loyal as the circumference to the center, you know, the circumference always stays the same distance from the center. And it's just lovely little pieces of mathematical imagery throughout, and throughout all Melville's work. So I thought, yes, Moby Dick would be a very good pairing.

KK: Yeah. And so you actually have a paper about this in the Journal of Humanistic Mathematics, right?

SH: Yeah.

KK: Ahab’s arithmetic?

SH: Yes. And that itself is a little bit of a reference to a discussion that happens in Moby Dick, which is where two of them were talking about a book called Daboll’s Arithmetic, which was the kind of classic text in American schools, I think, at the time, which had all these rules about how to do calculations. And you could do mysterious things with with this book because, you know, if perhaps the mathematics hadn't been taught by a teacher like Joseph Henry, perhaps you learnt you've learned these rules off by heart, you don't quite understand them. And so they talk in the book about cabbalistic contrivances of producing these things. And at one point, someone says, “I have heard devils can be raised with Daboll’s arithmetic.” So, you know, this is the other side of mathematics, where people sort of hold it in or but also, perhaps, they have some suspicions around what do all these symbols mean? And it's very interesting, if you look at that book, Daboll’s Arithmetic, it isn't like a mathematics book would now be. So when he talks about how to find the areas of circles, for instance, pi is not mentioned at all. He says, you square the radius, and you multiply it by 22/7, or if you want a more accurate thing, you could multiply it by what's that other approximation right? 355/113? But he doesn't say “because these are approximations to pi,” it's just like, you can do this or you can do that.

EL: Here’s a number.

SH: Tust where's that come from? So that's a very interesting thing. And so there are mathematics books discussed or mentioned in Moby Dick as well. And if you know a little bit about them, so Euclid, of course, is mentioned a little bit. Yeah. So the book is full of mathematics. And I really wanted to think about in the article I wrote, why — how did Herman Melville know all this stuff? Why, you know, where does it come from? Because, you know, he's not a mathematician. And this is why, you know, nowadays, we're sort of taught to believe, or somehow we come to believe, quite often, that you're either a mathematics personal, or you're not. And if you're not, then you don't know any and you don't care. But this is absolutely not the case for one of our greatest writers, Herman Melville. And so you know, yeah, where did that come from? And, you know, it was just lovely to, to find out a little bit more about what he knew and how he knew it, and where it all came from.

KK: Very cool.

EL: Yeah, that's great. I have confessed to you already, but I will confess to our listeners that I have not read Moby Dick, but it is on my list that I hope to get to this year. It's a little daunting.

KK: You’d better get cracking.

EL: I know. I’ve only got six months.

KK: I read it at bedtime. That's when I tend to read, and so I read it, you know, maybe 10 or 12 years ago, and it took me quite a while. Yeah, yeah. It's pretty dense too.

SH: It is. I mean, I didn't read it till I was older. Because, you know, you hear this is the “great American novel,” and you should, everyone should have read this book, and then you feel bad that you haven't read it, and then you feel annoyed that you feel bad that you haven't read it. So there's all these barriers that you put up for yourself. And, you know, I'm so glad that I did eventually read it, because I loved it. It's so rich. And there is, you know, many many, many layers of interpretation and depth in the writing, but it is a great book. So yeah, I hope you will enjoy it when you read it.

EL: Yeah.

SH: You know that there are books that we all — I haven't yet read, I don't know if I will ever read, maybe one day, Finnegans Wake. I do mention it in the book because James Joyce, I talk about Ulysses a little bit and Dubliners in the book. But Finnegan’s Wake for me, I tried and I didn't quite quite get there. All I can say is in the middle of Finnegans Wake, there is a picture which could have come straight out of Euclid’s Elements. It's got equilateral triangles, two circles intersecting. But yeah, that for me, maybe one day, maybe I'll have a sabbatical one day and that will be what I do in that sabbatical.

EL: There just, there is so much. There's so many good books published now, you can't you can't read them because you’ve got to read last year's good books. But I mean, it's just you — Yeah, anything you read is great. And you’re never going to get to all of it. Enjoy what you read.

SH: Exactly. Amnesty of all our unread books. It's fine. We forgive ourselves.

EL: Yeah. Thank you so much. for joining us. This has been a lot of fun. You know, we do like to give our guests a chance to plug things but we've already talked about your book quite a bit. Is there anything else that you'd like to to mention about what you're working on or other things that you've published that you'd like us to share?

SH: Oh, no, I think I'm alright. So coming up. I mean, not for US listeners, but I've got an event coming up in a couple of weeks is going to be really fun because we're going to watch a classic B movie from the 1950s, which is this film about giant ants terrorizing the New Mexico desert. It’s called Them! with an exclamation point.

KK: Yeah, I've seen the posters.

SH: Yeah, right. Yeah. Which is super fun. But that's about, yeah, something has happened. Who knows? But there are giant ants. They have a lot of fun with it. But we're going to watch the film at the Barbican Centre in London. And then we're going to talk about, yeah, what does mathematics tell us about what life is like? Could giant ants exist, could giant spiders exist? Or giants, or tiny people like Lilliputians. And so that's a kind of fun thing that's coming up. But yeah, you've already, if you look at my book, you will already have a reading list that’s like 100 new books that are gonna be fun, fun to read and explore. So yeah, there's plenty to go on.

EL: Great.

KK: Thanks so much, Sarah, this has been great fun.

SH: Thank you for having me. Yeah. I’ve loved it.

EL: Bye.

SH: Bye.

[outro]

In this episode, we were delighted to talk with Sarah Hart, the Gresham Professor of Geometry at the University of London, about the serendipitous cycloid. Below are some links you might enjoy as you listen.
Hart's website and Twitter profile
Her book Once Upon a Prime and its review in the New York Times
Hart's article Ahab's Arithmetic about mathematics in Moby-Dick
The Wikipedia entry for the cycloid, which has links to many of the people we discussed

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