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Episode 71 - Emily Howard Kevin Knudson & Evelyn Lamb Download Evelyn Lamb: Hello and welcome to my favorite theorem, a math podcast with no quiz at the end. I'm Evelyn Lamb, a freelance math and science writer based in Salt Lake City but currently podcasting from my parents’ house in Dallas, which is actually not any warmer than Salt Lake City right now, unfortunately. This is your other host. Kevin Knudson: I’m Kevin Knudson, professor of mathematics at the University of Florida. I'm in my faculty office. I'm usually — I'm the chair of the department. But I'm hiding out in the faculty office today. Actually, I was looking for better wireless. And it seems to be working a little better in here. But it's so weird because I have nothing in this office, like nothing. It's very strange. So anyway, how are things going for you? EL: Not too bad. Yeah, seeing my family, which is nice, and very excited about today's episode. So let's get right to it! We're happy today — both of us are music lovers, and we're very happy to introduce our guest, Emily Howard, a composer. Emily, do you want to tell us a little bit about yourself? Emily Howard: Yeah. So I'm based in the UK, in Manchester. I'm originally from Liverpool. And I'm a composer. I love writing for large ensembles, large acoustic ensembles, such as the orchestra. I also write vocal music, choral music, and also chamber music. So a lots of different areas. And I suppose probably the reason that you've got me on here is that I've got a real interest in mathematics. And actually, I have a degree in mathematics and computer science, my undergraduate is in mathematics and computer science. And I suppose that, you know, definitely it's one of the key influences on my work. EL: Yeah, I was listening to — it might have been the BBC Proms a few years ago — I was listening and saw this piece that I think was called Torus. And I thought, “You don't accidentally name something Torus.” So I decided to try to find out more about this person who had named her composition Torus. And so yeah, I found out that you had a math background, and thought it would be just really fun to talk to you on the podcast. So yeah, can you talk a little bit about the — I know, you've done some collaborations with mathematicians, you know, written pieces, like kind of in conversation with mathematicians in the composition process, and I would love to hear about that. EH: Yeah, so I mean, I suppose actually, in 2015, I had I think it was a Leverhulme fellowship at the University of Liverpool, working within the mathematics department. I had been invited by Lasse Rempe-Gillen. He's a professor in dynamical systems. And I think he'd been in touch because he had himself played the violin in an amateur orchestra in Liverpool, and they had performed a piece of mine called Mesmerism. Actually, it was after Ada Lovelace. Ada Lovelace used to dabble in all types of things, including mesmerism, sort of a form of early hypnosis. And the piece, I mean, that piece was a piece for solo piano and orchestra, and he was playing in it. And I think he thought it will be great to invite me as someone with a mathematics background back — after 15 years away in the music world— actually back into the maths department. And, I'm so glad that this happened, because going back in and speaking to lots of different mathematicians in a different way, rather than, I don't know, having to take exams and study, I was more being an observer, having amazing conversations about people's research. Regularly I'd speak to someone in one area of mathematics and another, and I suppose I felt — what I realized was that mathematicians often don't understand what each other are speaking about. So I didn't feel so bad about it, that I could sort of dip in and I suppose it helped me to take a more global approach, or to take in more general ideas, because I think that's one thing, perhaps, you lose if you don't practice mathematics regularly, you know, you lose this very detailed approach, and that's kind of annoying. It’s really annoying in many ways, but I also find it annoying when you can’t completely understand something because you'd have to spend quite a few years really thinking about it in depth. But then something is also gained from sitting back and taking a look at everything and absorbing it in a very different way. So anyway, we worked together on a set of chamber pieces. You can find them on my website. One’s called Leviathan, another is called, well, these are all pieces, exploring ideas from lattice research in dynamical systems. And I suppose they're all based on thinking about perturbations, and thinking about — I’ve got some etudes as well, they’re called Etudes in Dynamical Systems — just trying out very particular things with datasets, but also conceptual ideas about reaching stasis and loops from something. I also spoke a lot with colleagues in mathematical biology and also in topology. And I remember, I think this is where, kind of, talking about Torus, it was kind of born, the idea, because this period of time gave me more confidence to actually do something with mathematics. Just to go back back a bit, after my undergraduate in mathematics, I'd spent a couple of years doing a Masters at the Royal Northern College of Music in composition, and then more years at Manchester University doing a PhD in composition as well. And I suppose, when I was doing this, I really wanted to use these ideas or concepts from mathematics, but I didn't really have a musical technique to do that. I suppose that grew. And at this point, it sort of all merged, and I was able to perhaps achieve something that I wanted to achieve with these mathematical ideas through music. And so yeah, just to go on, you mentioned Torus. And I'm immensely proud of Torus. It's a big orchestral work, it's like 23 minutes long, based on the mathematical shape, a torus, a doughnut. And this is when I had actually just met a mathematician, Marcus du Sautoy, who I’ve worked with quite quite a lot. He's based at Oxford, and we met because of this thing. And when we spoke first, actually, he was writing about, no, he’d written a play about a torus. And I was sort of saying, “Well, actually my piece is about a torus,” so we really bonded on this. And one of the things that interested me most was, you know, the, the BBC Proms are held at the Royal Albert Hall in London. And the first thing he said was, “Well, that is a torus.” And I just thought, How funny. It really is, because you can run round and round it, you know, it's just just really nice to, you know, hear this. KK: So I'm especially fascinated here, because my son is a composer. Well, he just finished his undergraduate degree, and now he's in graduate school for composition. And so I'm always — first, I'm encouraged that composers can actually make a living, right, because whenever I would tell a mathematician, one of my friends, “Oh, my son's studying composition,” they say, “Well, how’s he going to live?” And I say, “Well, I don't know,” but clearly it’s possible to figure it out. So I'm super encouraged. Yeah, so Evelyn, you had a real question, though. EL: Oh, well, I was just saying this is an existence proof then for your son. KK: Yeah, that's right. That's right. EL: Yeah, well, I was — you know, music is a very non representational art form, unlike a canvas where you could — I mean, it's still hard to represent mathematical ideas on a painting. But can you say anything about how you do use the form of music to represent mathematical ideas? EH: I suppose — it's really interesting that you say that, because I completely agree with you actually, that it is very difficult to do that. And I wonder if, even if I, especially in abstract music, if we take aside — you know, if it has text in it, that's a very different thing — but in an abstract form, actually, I wonder if I ever tried to absolutely represent something from mathematics within music, whether in fact, anyone would know. And I suspect, actually, there are cases when I've worked very closely with people and they really know what I'm doing. I think they can certainly tell, but actually, I don't think that that's necessarily happens. And also, it's definitely not what I'm trying to do. Absolutely not. So I suppose my aim is not to represent mathematics. My aim is to — I mean, I love hearing about mathematics, and I'm completely inspired by processes and systems and patterns. And I suppose what I'm doing is taking them, and that’s a catalyst for my creative process. And so I do think something comes through, but I think it's more that I couldn't make what I'm making without doing this. And it's more that something new is occurring that came from thinking about these things. But it's definitely not a representational thing. I mean, that's definitely the case for maybe the more large-scale pieces we could talk about, like Torus. But I think also there have been a couple of pieces when I have tried my very best to represent ideas, and one of them would be this set of dynamical system etudes. That was one of them. And then another one would be the music of Proof, which is, I wrote a string quartet because Marcus and I were discussing proof and different ways you can prove things: proof by contradiction, by induction. He wanted to, to put those to me, and then I would create responses to different kinds of proofs. And so I suppose that’s as representational as I've been, and actually, it was really useful, because in doing that, then I gained a whole set of like, I thought about — I've never tried to write music before as though I'm solving a mathematical proof. But actually, in doing that, that led me to new places. So that's kind of what I'm trying to do, find new ways to do things and make new sounds. EL: Yeah, maybe respond more than represent you? EH: Definitely. KK: I mean, certainly, some music is sort of, you can tell, it's not deliberately mathematical, I don't think. I think of like, like Steve Reich's minimalism percussion pieces, right? EH: Clapping Music. KK: Yeah, they’re so cyclical. And you know, you can kind of, if you think about it as a mathematician, you can kind of imagine, well, if I saw this on the page, it would almost look like — our listeners can't see my hands doing this — but you can imagine sort of, you know, intersecting sine waves and things like that. So I can see how you could do that. EH: And to take that further, I wonder if all music in some way can be — well, I say reduced, and I don't like to reduce — but you could certainly represent ideas in very complex music, I think mathematically probably. Not that anyone necessarily has. But perhaps the secret to lots of things is in really complex music represented. I mean, I don't know. KK: Well, there’s a whole journal of mathematics and music. I mean, you could you could certainly, I sat on a PhD committee for composer on campus here, who really was trying to do these very strange time signatures that were sort of approximations of pi and things like that. EH: Wow. KK: And I put the question to him. I said, “Okay, I mean, you can make a machine do these. But, you know, can a human do this?” And he said, “Well, no, not really.” But it was interesting. EL: Can humans do math anyway? KK: This is not a philosophy podcast. I don't know. EL: Yeah. Thankfully,. EH: Just to say on that on that subject. I mean, I've got certain things — there are certain things you do put in notation that are absolutely beautiful mathematically, you know, but in fact, yes, they're not really possible. But they they do make a performer think in a certain way, and it will give you certain results. So I mean, I think there can be, I think they're beautiful, and they can be there. But you just can't expect perfection, perhaps. EL: Yeah. All right. So we always like to ask our guests, what is your favorite theorem? EH: I mean, we've kind of been speaking about it. That's, that's the main problem with this. I mean, actually, I would say, rather than a theorem, it's definitely these shapes. So I mean, let's take the torus, but I've got this fascination, I'd say, with thinking about mathematical shapes and thinking about, you know, them being far away, and also thinking about being on them. And I suppose, I mean, so you've got a torus. I mean, so, if you think about the difference between, say, flat geometry and a sphere with the spherical geometry, and then, I mean, there's a pseudosphere, and then I would call, like a negatively curved geometry, I've got a piece actually called Antisphere because I've worked out that an antisphere, there's a word antisphere, which is the same as the pseudosphere, and the word antisphere is a lovely word, and I don't like the word pseudosphere. So I called the piece Antisphere. And I suppose I've just got this — because, you know, my music is usually notated. So I find it very interesting as a process to be in my mind wandering around these shapes. And I suppose, I also think it’s very useful for music because they don't necessarily need to be 3d, I mean music, potentially, you could perhaps hear really high-dimensional mathematics. Because, you know, you could be traveling around and you're not necessarily visualizing it. So my answer to your question is that I like these mathematical shapes. And I've been thinking about them and really studying them and using them to influence these large-scale orchestral work. So that's Torus, Sphere, and Antisphere. And going forward, I'm now looking at, well, I'm trying to look at Thurston’s eight geometries and pushing myself in this direction with the aid of a number of very kind mathematical friends, because they're very difficult. And yeah, so that's kind of the direction where I’m going. And I find, you know, I suppose that's what we were saying earlier about the representation thing. So there are a number of stages. So I'm thinking about this tours, I'm thinking about traveling around it. Shall I give an example of the compositional process for writing Torus? KK: Sure, please. EL: Yeah. EH: Okay so Torus is a piece, yes, it was for the BBC Proms. It was performed first in 2016, by the Royal Liverpool Philharmonic Orchestra with Vasily Petrenko. Now I’d say, I wrote it over at least a year or so. And I'd also been thinking a lot about this just previously, thinking about traveling on this torus. And what I was thinking about when I wrote it was the idea that you're traveling round and round one direction of the torus, you know, and I took these very consonant chords, see, I've got major sixths. If you hear it, they’re a very constant chord. And I start with this major sixth, and I travel up one and down one and up another — they're going up in semitones, and down, and they reach a point and they come back again. So that the harmony is very much also shaped like a torus all the way through. And it's skewed, when you hear it, it's more complex than just listening to it timed because I've got a real combined fascination with exponential functions and the idea of really big things becoming absolutely minuscule, but also kind of being related. So, you know, this kind of journey around the torus, the first loop in this orchestral work is about five minutes long. And if you do listen, you'll hear it in the strings. And to my mind, I've got this sort…
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