StarTalk Radio - The Hidden Science of Music, with Eric Whitacre

Episode Date: November 2, 2020

Did you know there’s hidden science in music? Neil deGrasse Tyson sits down with Grammy-award winning composer Eric Whitacre, co-host Chuck Nice, neuroscientist Heather Berlin, PhD, and mathematician and concert pianist Eugenia Cheng, PhD, to investigate. NOTE: StarTalk+ Patrons can watch or listen to this entire episode commercial-free here: https://www.startalkradio.net/show/the-hidden-science-of-music-with-eric-whitacre/ Thanks to our Patrons Julia Zeikowitz, Cory Ricci, Sridev Pawar, Mark Hachem, Michael Gessner, Roderic E Hairston, Chuck Betlach, and Riyam Al-Sammarraie for supporting us this week. Shown: Neil deGrasse Tyson and Eric Whitacre, before the pandemic. Photo Credit: Stacey Severn. Subscribe to SiriusXM Podcasts+ on Apple Podcasts to listen to new episodes ad-free and a whole week early.

Welcome to StarTalk, your place in the universe where science and pop culture collide. StarTalk begins right now. This is StarTalk. I'm your host, Neil deGrasse Tyson, your personal astrophysicist. I serve as the director of New York City's Hayden Planetarium at the American Museum of Natural History. And today's topic, the hidden science and math in music. Ooh, the music of the spheres. You got to love it. And we're going to feature an interview with composer Eric Whitaker. We'll get more on that in just a moment. But let me introduce my co-host, Chuck.

Chuck, nice. Hey, hey, hey, hey, Neil. How are you, buddy? Good. Always good to have you, Chuck. Always good to be here. You're a comedic man about town. And we're going to also bring in, for this, because if the science of music affects us emotionally, we can't do that without sort of bringing in our emotional case. We got to check up on emotions. Definitely, Heather Berlin. Heather, welcome back to StarTalk. Pleasure to be your emotional case, Neil. Pleasure to be here. You are everything neuro for us. Yeah, exactly. So for you, it's a compliment to be the emotional case, or even as a professor of psychiatry, maybe the head case. Oh, the head case.

Right. Oh, that's great. That's great. Yeah, I get that. Put that on your office door. Yes. I'm just going to have Dr. Heather Berlin, head case. Right.

Yeah, head case. So, Heather, you're assistant professor at the Icahn School. Not I can't, but the Icahn School. Icahn. Icahn. Icahn, indeed. Not the Icahn School, but the Icahn School of Medicine at Mount Sinai. Icahn, I-C-A-H-N.

And he's a wealthy donor, I think. Is that correct? Carl. Carl Icahn. Thanks to him, we changed the name of our whole medical school. Sorry, I'm not on that correct? Carl, Carl Icahn. Thanks to him, we changed the name of our whole medical school. Okay, sorry, I'm not on a first name basis. Sorry. No, yeah. Carl and I, you know, we go way back. You go way back. You and other billionaires go way back. Right, right. And so today we're going to talk about how science and math influences

music. And we're featuring my interview with the composer and conductor Eric Whitaker. He's got a huge fan base. He won a Grammy in 2012 for his album Light and Gold, best choral performance. And he's a graduate of the Juilliard School of Music. Who wouldn't want to be a graduate of that place? He also created a short film called Deep Field, the Impossible Magnitude of the Universe, in collaboration with the Space Telescope Science Institute down in Baltimore, Maryland. They're the caretakers, if you will, of the Hubble Space Telescope. And one of the Hubble Telescope's most famous images of the universe is called the Hubble Deep Field. So I caught up with Eric Whitaker when he was visiting New York, and I invited him by, and I thought, you know, I got to get an interview with him for StarTalk.

And this is a few years ago, but I wasn't really ready for that. And I grabbed like a microphone off the shelf, and I put it on the table between us, but I got the interview. And so with your forgiveness, you will hear our interview, and it's the content that matters, of course, not the audio quality. And we're going to learn how Eric put off getting formal training in music for a long time. Here it goes. I played music by ear, but I didn't read music.

Now, who does that? Is it one in a hundred, one in a thousand? I actually think more kids than not do it, and it's kind of squeezed out of them at an early age. Ooh, one of those things where the school system just beats it out of you. Or even worse, the parents, like what happened with my parents is we had a piano in the home. And they encouraged me to play piano, but then they tried to give me lessons. And thank God I resisted the lessons because for me it would have just squeezed the life.

Ooh. Is there deep insight there into how to stimulate creativity? I think so. I think that what happens is you try to codify it too early and those kids just— Then it's a chore. That's right. It's a chore. And also it gets—yeah, the aspirational quality of it gets totally taken out and it becomes virote.

And that's good for a very specific kind of personality for a kid. But most kids, they just turn off. They don't want to do it wrong. Oh, yeah. So the kids rather just explore. That's it. That's my word, explore. Explore.

So I had the kind of personality where I wanted to explore and was stubborn enough that I wouldn't take to the lessons. Chuck, Heather, did either of you get forced piano lessons or music lessons when you were a kid? Absolutely. Oh, really? Oh, God, yeah. You say that like, of course. It was just what had to be done. And I hated them. Yeah. How about you, Heather? I actually, I did violin and I was in the choir and I loved it. So I don't know, maybe I'm just a nerd. I just, I loved the, it was like math to me in a way, the patterns of the music. And so I really just appreciated it. And I felt like I was part, I guess I was, again, I was a nerdy kid. So I felt

like I was part of history. Like I loved playing classical music and like thinking about times gone by, like things. So I enjoyed it. Well, now I feel bad about hating it, but guess what? I still hated it. So Chuck, Heather loved it so much, she didn't become a musician. So let the record show. You can't do everything.

Eventually you got to choose one thing. Music fell by the wayside. Yeah, but my brother is a musician now so it it worked out you know does that count for you do you get points for that of course as far as i'm concerned you know we're we're our dna is close enough where i could just take like if he commits a crime i will be a suspect so i i had forced piano lessons. I mean, it wasn't forced where I was kicking and screaming, but I had piano lessons for a couple of years,

and I still remember three things. I can play three short musical pieces from that period, but that's it. But I appreciated what it did for me, giving me a bit of sensitivity and awareness of what other people are doing when they play music that's all that's what i did what i loved about it is learn is reading music um which is very hard now because i haven't done it in so long but it is a language and learning that language is fun. The rote. So back when I took lessons, it was rote.

That's how you learn. And the lessons were highly structured. And I couldn't take sitting there doing those same exercises over and over and over again. That just drove me crazy. All right. So that means it was a formal training that stuck with you. But Heather, comment on what Eric Whitaker said about the contrasting rote learning and formalized learning with creative learning where you just might train yourself. Do we know anything about what role that plays in creativity? Absolutely.

Absolutely. Just what Chuck said, actually, what we see, what happens to the brain when people are learning or playing music is that the language area of the brain, Broca's area, is actually activated. And so, as he was saying, it is like a language. It is like learning a language. And those same language areas of the brain and having to do with language comprehension and language creation are also active when you're either listening to or playing music. The other thing is that one of the positives of learning a musical instrument as a child is that studies show that children's brains actually develop faster with musical training. So they did an experiment actually with the Los Angeles Philharmonic and they had children, a couple of them got lessons with them and some just had soccer lessons and other afterschool activities and they followed them for five years and found that particular parts of the brain, like the auditory cortex, developed much quicker. And the auditory cortex is also involved in things like language and reading. So they actually were doing better. They had an advantage in those

other areas. So you're learning to read the language of music, but that kind of has a knock-on effect to other areas. So it's very positive. But the idea of creativity, so another study showed, and they measured areas of brain activation and creative music ability, and they found that people who were trained still had an advantage when it came to actually being spontaneously creative or improvising. And the idea is that… So it didn't squash that part of it? still had an advantage when it came to actually being spontaneously creative or improvising. And the idea is that... So it didn't squash that part? Oh, interesting. Okay.

It didn't. And so I think that's sort of a subjective sense that it does. And maybe because of the rote and maybe if it was taught in a different way, it would be taken in differently. But the actual fact of learning the basics, in many cases, gives people more tools to use to be more creative. Oh, very good point. Yeah.

So could it be true? I mean, I have to say, you know, now that you mention it, I don't know very many inarticulate musicians. inarticulate musicians. If they're both in the same part of the brain, does one help the other, force the other, nurture the other? Yeah, I think, and that's the whole argument, I think, for, you know, the arts, you know, in school, talk about cutting the arts, right? But actually, the arts can enhance your abilities in the other more traditional academic areas. So they find that, you know, students who take and have art, whether it's painting or music or theater, tend to do better in the other disciplines. Because if you think creatively in the arts and outside the box, you can also use that to think creatively in the sciences and come up with novel theories and ideas.

So they really do, these skill sets can enhance, you know, can bleed over into other areas. So when you're enhancing musical ability, you can be enhancing your language ability as well. Well, Eric was also interested in science when he was young, but he didn't think he had the right stuff for it. And let's check out what he meant by that in this next clip. At age, I'd say probably nine or 10, I was given a telescope for Christmas. Ooh. Yeah. Nice. Much like you. Nice. And it changed my world. And where did you live? I lived in Northern Nevada. So in retrospect, the perfect place. Oh, my gosh. In the middle of nowhere.

We lived in the sticks, a dirt road. So my childhood was huge, open night skies. So you could say that the – did you even know that there was a universe to discover at the time you got that telescope? No. Okay. So it was a toy at the time. Yeah, that's right. It was just a thing that somebody thought a nine-year-old would want, right?

Yeah, and it blew my mind. And I'd say, I mean, still, frankly, if they somehow needed me, I wanted to be an astronaut from the earliest age I could remember. Wow. And I was fascinated by physics. I love math. I don't really have the brain or personality to be a mathematician. And then I found my way into music.

All right, so let me get on your case. So you ended up studying music instead of science. Where did we go wrong? Was it a teacher? What was it? Yeah, it was ultimately a teacher. So I had in, I'd say, in my junior year, I had a fantastic physics teacher. I loved him, Mr. Patterson. We always remember the names of our teachers.

Don't we? Yeah. The most important ones. Right. And in fact, when I graduated, you'll love this, I'm not Mormon or religious, but my best friend in high school was Mormon. So when we were seniors, we went to Brigham Young University to observe classes. And the only class we could find... So you were seniors in high school?

Yeah, that's right. The only class that was open to us at the time that we could go and observe was this graduate-level astrophysics class. Really? I will never forget this. This is probably the moment I knew I wasn't going to be a physicist.

So at that point, I'd had calculus, or I was in calculus. I'd done trig. I'd done some advanced algebra. But we sat and listened to five students sit alone in a room. And, you know, they're talking about the velocity of a photon as it passed through a star or something. And there were no numbers on the board. It was all, right, symbolic and representational math.

And I remember just thinking, oh, it turns out that there's no way. I mean, I was so fascinated by the concept, but the nuts and bolts, I realized I'm not sure. Okay, so most people in that situation are inspired to do what it is they just saw happened. You were inspired to not do what you just saw happened. Yeah. Yeah, I mean, so, Heather, yeah i mean so heather do you think there was a left brain right brain

war going on in his head yeah i mean so just to debunk the myth of the left brain right brain myth which is no let's keep it i like it it's so helpful i mean it's okay how about this okay so so whether or not it's left or right, there are parts of the brain that specialize in analytic thinking and other parts that specialize in, I guess, abstract thinking. Is that a fair characterization? I think that is fair, yes. That is fair. Okay.

Whether or not it's left or right. So, okay, go ahead. No, no. Debunk it. Back brain, front brain. Back brain. Is your head in your ass? Your ass brain, head brain.

The brain's all over specific parts of your body. No, so go ahead, Heather. So, you know, I think that is a bit of, you know, when he says, you know, I just wasn't a math person. I don't think that's necessarily true. I mean, the problem is when you jump into math or physics and you jump in at a very late stage before you've gotten all the basics, it can look just completely like another language and very, you know, you think you have no control over it. But if you start people young and train them and to understand the basics, this is what this symbol stands for and et cetera,

you can build up, right? So I think people have this sort of irrational fear of like math and science, just because if they haven't learned the basics, it feels very foreign to them. So I guess I'm going against that idea that there's some people that are math people and some science people and some that are, you know, let's say artistic and music. There is a difference though, between people who can think more creatively and outside the box. And that could be applied either to the sciences or to the arts. And so creative people can be in any discipline. So as educators, we have to be cautious about what could completely bomb someone out of the water in a one-time encounter with a subject?

If you get turned off at an early age, let's say from math, you think, oh, I just can't do it, or you had a bad teacher, then it's very difficult to catch up years later once you haven't picked up the basics because it builds upon, it builds on each other. And the same with music. It's years of practice. And if you miss those early years of training and brain development where your brain is still plastic and easily malleable, you're at a disadvantage later on. And just one other thing, it's the same thing with language. If you're learning a second language and you don't learn it within these critical periods of development, you'll never be able to speak it without an accent. So there are certain critical periods where you learn music or math or language. And

if you don't learn it in those periods, it becomes more difficult to learn it later in life. Well, we got to take a quick break. And when we come back, we're going to talk about how science might inspire the artist on StarTalk. We're back. Star Talk. I got Chuck Nice. Chuck. Hey, Neil. Tweeting at Chuck Nice Comic.

Thank you, sir. Yes. And I follow you, just so you know. And I follow you, too. Okay, that's very sweet of you. To the ends of the universe, Neil. Of the social media universe, wherever the hell that is. Even the deep field universe, okay?

We're talking about creativity and science and music and art in general and the neurological components of that. And of course, we have our longtime friend of StarTalk, Heather Berlin. Heather, you tweet it. What's your handle? Heather underscore Berlin. The underscore is very special. The underscore makes me very unique. Yes. Underscore Berlin. Yeah. I hate underscores. I know that. Yes. So is that why you don't follow me, Neil? Because, uh... As soon as you get rid of that underscore,

you got one more follower. That's right, we got that. Well, we've been discussing how science and math might be embedded in music, or at least in musical creativity, and we're featuring my interview with Eric Whitaker when he had just come through New York and a friend of a friend knew him.

And he agreed to come by for an interview, but it was like on the spot and I had to like grab a microphone off my shelf and set it up on a table between us. So forgive the quality of the recording, but the content is all there. And ultimately that's what really matters. So I asked if he drew musical inspiration from the science that he embraced.

So let's check it out. So I've written this piece called Deep Field. And it's based on the Deep Field image. And for years, I've been looking for the right way to write this piece. For me, when I'm composing a piece of music, it always starts with, God, wouldn't that make a great movie? And then I musicalize the movie version of it, I suppose, the dramatic version of it.

And what happened for me was that I knew the image. I'd known it since I was, God, when was it released? 94, 95? Yeah, yeah, 90s, yeah. But I didn't really know the story behind it. So as I started to think about, maybe I should write this piece, I just started researching it. And the human drama to get that image,

that's the thing that tipped it over the edge for me. Whoa. Right, so the fact that they launched the Hubble. So it's not just that it's a cool image. You like the story behind it. Because it speaks to who we are as human beings. It speaks to the sense of adventure and exploration. And specifically, the NASA can-do spirit, where they send the telescope up there.

They open up the lens, and it turns out it's got that aberrated mirror, right? There's that aberration on the end. And then NASA, you know, they just, I can just see these guys sitting around a conference table saying, okay, what do we do? All right, well, send somebody up there and fix it. So they send three or four missions up. They do a hardware fix on it.

They do a software fix, right, to basically put a contact lens on the thing. And that, to me, is as extraordinary as the image that comes back because it just says so much about who we are. So it's the access to the universe through our technology. Yeah, that's it. And building tools.

And this is what I love about NASA. I'm sorry I'm all over the place, but what I love about NASA is I feel like it's just this crazy collection of artists. It's so pure what they're doing. All they want to do is just build these machines and so we can get up, so we can find out, discover. Yeah. So, yeah. So let me give some backstory on the Hubble Deep Field. Before you do, Neil, if I may, I just, you know, he made the fixing of the Hubble such a big, big deal. But I just want to show people, anybody listening won't be able to see this, but if you're watching, this is all that really happened. Chuck is...

There you go. Chuck just cleaned the lens on his camera. Yeah, we went up there and, like, went, ha, ha, ha. Just took out a kerchief. Squeak, squeak. So just a couple of things, and this might be too much inside baseball here,

but so you know, even if you don't know why, that if you look at the iris in your eye and you watch what it does as you go from a bright, if you move from a bright, well-lit room to a darker room, right? The iris constricts when you're in light and it opens up when you're in darkness. And the act of opening up tries to bring in as much light as it can. And so physiologically, you are responding to the absence of light. Well, if you want to measure something that is way dimmer than even that you can detect with your eyes, you can do one of two things. You can make your iris even bigger.

No, you can't really do that. But the physics of this is if you had an eyeball the size of your head, you can't really do that, but the physics of this is if you had an eyeball the size of your head, you can see into much dimmer places. All right? If your eyeball were the size, were 100 inches across, okay, 94 inches across,

you could see out to the edge of the universe. That's the size of the Hubble telescope. Sweet. Okay? It's a 94-inch iris, if you will. Wow. And it's taking in light, much more light than the iris of the human eye. Not only that, the detectors are much more sensitive to light than our retina is.

Okay? Hundreds of times more sensitive. So not only is it getting more light, it's detecting it better than your eye would have even done so if it were that big. Not only that. Oh, sweet. Okay? There's an effect...

Oh, wait, there's more. There's an effective shutter speed of your eyeball. And Heather, correct me if I'm wrong, from what I've read, it's about a tenth of a second. Like it's, you collect that much light before you send a coherent signal to your brain,

which is why you could show frames at 10 frames a second, 20 frames a second, and it looks like a movie, right? Because you can't see the individual frames, even though a second, and it looks like a movie. Yeah. Right? Because you can't see the individual frames. And no one thinks about this. If aliens come to visit, let's say they have like 1,000 frames per second time resolution in their seeing.

If we showed them a movie, they would find it completely annoying. They'd say, why are you showing us these still images? This is annoying. It'd be a flip book. It'd be a flip book. It'd be a flip book. Exactly. Exactly.

So not only is the iris bigger, not only is the detector better, but it's not limited by a tenth of a second exposure. You could take a long exposure and continue to accumulate as provided you stayed locked and tracked on your star, you can take a continuous exposure. Now you don't want to do it too long because then if something goes wrong with that image, then you lose the whole thing. So what we did was take many, many, many, many exposures and then added them together. So that way you get the deepest, deepest as in the dimmest things in the universe will show up in that image, even if you don't even see them when you point the telescope.

That's what's so amazing about it. In fact, that region of the sky that was picked was picked for how empty it was. They said, let's pick the emptiest part of the sky we can and then aim the telescope there, our most potent, powerful telescope in the world. That was a big gamble. It was a gamble. Now, okay, who would agree to this? Why would anyone say, yeah, I want to look in the emptiest part of the sky? No one would. No one did. So how did the picture get approved? We build, we, my people, my people, my astrophysics people. We build into our system the modes of serendipity, modes of where you override what might be prevailing sentiment.

So for every telescope in the world, there's something called director's discretionary time. And normally we compete for time on the telescope and it's got to be peer-reviewed and everything, but there's a percentage of the time that the director says, I choose to do this with it and no one can tell me no. Oh, it's the way I make my children compete for my affection. Okay.

no one can tell me no. Oh, it's the way I make my children compete for my affection. Okay. Heather, you got to, you know, work on him. We're getting a list of things that Chuck needs help on. Yeah. But can I just say what, this is so fascinating, what it really sheds light on, so to speak, is just how limited our sensory capacity is, how we're limited by the physical structures that we have, like our eyes and our ears and even our brain. Your human physiology, right. And so what we did is we used our ingenuity to build a better eye, let's say, a better functioning eye. Now imagine if we could build a better brain, you know, how much could we understand about the universe i mean unfortunately

the brain is much more complex than understanding how the you know the physiology of the eye and how that works but ultimately that's the ideal right because look what we did when we just said we built a better eye i would love that a better well that's just ai building on itself yeah yeah saying there well when that day comes chuck they just the ai makes us their pets that's just AI building on itself. Yeah. That's what you're saying there. Well, when that day comes, Chuck, AI makes us their pets. That's what I'm about to say. Who wants that? I want a better brain. I don't want to build a better brain.

What good does that do? No, I want the brain. No, we can just plug you into the big brain, and you can just become sort of a part of it. We can all just plug in. No, because the big brain would you can just become sort of a part of it. We can all just plug you in. No, because the big brain would say, I don't want Chuck. I don't want Chuck. Exactly. Why do I want dumbass Chuck as a part of my brain?

That brain don't need Chuck. Big brains don't need Chuck. Exactly. So I'm almost done with this. Okay, sorry. Go ahead. I digress. What happens is the director.

So the director. Okay. Okay, sorry, yeah. Go ahead. I digress. What happens is the director, okay, his name is Bob Williams, he said, I want to do this. And there was some criticism, and he was going to use a lot of telescope time, and on peer-reviewed, he said, I just want to see what's out there. And so he did it,

and it became the most famous picture taken by the Hubble telescope. Yeah. In this tiny patch of the sky. Right. of galaxies right there going out to the edge of the universe. And you might say, well, maybe you just looked on a patch of the sky that's that filled with galaxies. We don't think so because the universe is really... That's what I was about to ask you.

Has there been any extrapolation done to see whether or not we just hit a galaxy-dense portion of the sky or... Right, right. That would be like really unlucky-lucky if that were the case. So we say, alright, just to... Let's look like over in the opposite direction in another place. And we did that and so

there's several deep fields and they all are statistically equivalent in how rich the universe is. And so the story of fixing the telescope, the story of getting the time to even obtain the Hubble deep field mattered to Eric Whitaker. And so let me ask you, Heather, he likes stories. Why? We know stories are important. So I'm not going to ask you are stories important. I'm going to ask you why. There's a number of reasons. I mean, one is that it's ancient.

It allows us to predict things, right? Stories are a narrative, and it's a sequence of events, and it allows you to predict the next event. And it's a way to transfer information, right? And memory is tied to emotion, and often these stories are illicit emotions right so but i mean you're going way back to caveman's you know either we went over to that that pond over there but there was like no fish in it so don't go over there you know like that's a very simple story with the but but over time they've evolved and they also teach morality in many cases as well. So there are moral lessons. There are ways to predict sequence of events.

But I think... So it's a way of connecting what would otherwise be disparate information into a narrative that then makes sense in your head. Yes. And then often they have some moral to them or they're conveying information, then often they have some, you know, moral to them or they're conveying information, but they elicit some sort of emotion that, again, helps us track the information and we remember things better. So does music help with storytelling? Absolutely, because music is, I mean, one of the reasons why it's so potent is that it really directly activates these emotion centers in the brain, things like the nucleus accumbens and the

reward centers. And so when you tie music into stories, it's just another way to kind of help us not only remember, but appreciate. You even get things like oxytocin, which is a kind of neurochemical that has to do with bonding and love. And so when you elicit those emotions, I mean, that's what every commercial is trying to do. They're trying to help elicit an emotion and a catchy jingle and help you remember it. So in that case, you buy the product. I remember jingles that I don't want to remember. That's the other thing. There's certain patterns that stick in your head that you don't necessarily want sticking your head like baby shark baby i just had to do that so that everybody can enjoy that now for a moment but yeah that's thanks for the earworm right but

you know so certain things we don't want to remember but music is such a powerful way and if you notice in the best kind of musicals right when there's an emotional crescendo in the storyline that's when the music comes in and it just accents that. And so it's so emotional. You can't even use words. You need to break out into song and dance. Right. And so it's another. Yeah. So, so, so, so can storytelling help inspiration? Yes.

Yeah. I think it helps with, so we all want to solve problems and we like, we like mystery and uncertainty to a point, but when we feel that there's a possibility of solving something that excites us. And I think that's what inspiration comes from and motivation. And that's part of the human condition. All right, we got to take another break. When we come back, we're going to talk about Patreon shout out to the following Patreon patrons. Julia Zajkiewicz and Corey Ricci. Guys, thank you so much.

Without you, there's no way we could make it across the cosmos and do this show. And for those of you listening who would like your very own Patreon shout out, please go to patreon.com slash StarTalk Radio and support us. We're back. Star Talk. We're talking about the hidden math in music in a larger program about what role science literacy, music literacy, art literacy plays in our creativity. And I'm inviting back our guest, Heather Berlin. Heather.

Hey. All right, Chuck. I'm inviting back our guest, Heather Berlin. Heather. Hey. All right, Chuck. I'm here. Hey. And, of course, we're featuring my interview with Eric Whitaker, who had just wafted by my office a few years ago, and I was unprepared for that. I had to grab a microphone off my shelf,

and so the audio quality isn't good, but the content is most excellent. But what I want to do in this segment is introduce yet another guest, Eugenia Kang. Eugenia, welcome to StarTalk. Hello. Thank you so much for having me. Yeah, so you're a mathematician and a concert pianist. Mm-hmm.

So that's the whole—so we're done here. You did it. That's what we're trying to wonder if that could happen. And you did it. You got a PhD in pure mathematics from the University of Cambridge. That poses the question, is there such a thing as impure mathematics? But that's you. That's a whole different topic. That's a whole different topic. Okay. You're also a scientist in residence at the School of the Art Institute of Chicago. And this is that famous museum there that has all the paintings that we saw in Ferris Bueller's Day Off, isn't it?

Yes, we did. Yes, okay. And you're also the author of X plus Y, A Mathematician's Manifesto for Rethinking Gender. Ooh, you're getting all into all kinds of stuff. All right. So tell me something. You teach a course called The Mathematical Secrets of Music.

So we want to know all the secrets. Just tell me right now. Right, how long have we got? Well, I try to demystify math and music at the same time because many of the students, they're all art students, and many of them were really put off by math education in the past. And so I try to gently show that math can help us be creative and also to demystify classical music

because classical music is another thing that puts a lot of people off, unfortunately. Well, because there's snooty people. Yeah, exactly. It's a whole culture that you might be put off by the culture even if you're not put off by the music. Right, and unfortunately, both math and classical music sometimes have a culture of keeping people out rather than bringing people in.

And I prefer to bring people in. And there are ways in, in lots of ways. So here's an example that just uses, it's not, so sometimes people say to me, well, music has counting and math has counting. And I think that's the most boring part of math. That's the most boring part of music together. I can count a four, eight, you know.

But here's an example. So if we go, like, here's a piece by Ravel. And so this is going one, two one two three one two one two one two one two three one two three one two and this is the same rhythm that's in um west side story i want to be in america okay we're in america everything free in america for a small fee in america and this is going one two three one two three one two one two one two what that is, is it's saying that two times three equals three times two, which is otherwise known as the commutativity of multiplication in math. And it's that commutativity that is giving us this little catchy rhythm.

And so that's just one example. And the thing is that you don't have to know that's the math that's going on to just enjoy the music. And I always say that's kind of true about a lot of the math around us in the world. You don't have to know it's there to get on with your life. And loads of people say, well, I get by perfectly fine without math. And sometimes I say, yes, you do, but I get by better. So you're saying if I just know what two times three is,

I can play the piano like you do? Yeah. Absolutely. You just said that. I think you just said that. I just said that. Yeah, yeah. Heather, she just told me that.

It's just that if you understand the structures inside things, I think you can get more understanding out of it. Would you say is this a trend that there's more math being put into music, musical pieces? It has happened for a long time. So Bach did tons of it. He used a lot of symmetry in his music, which I think is really amazing

because you don't have to know it's there. Like this theme from a Bach fugue. He then just completely turns it upside down, which turns into this. just completely turns it upside down which turns into this which still sounds sounds really nice and there's another example where rat mananoff so rat mananoff is a couple of hundred years later and there's the theme of of paganini where he writes a set of variations and the theme goes like this but then right so this is da-da-da-da-da. And then he turns it upside down.

He just, that's a reflection. He goes... And it becomes this beautiful... And you don't have to know that that's how he made that theme. You can just go, wow, that's a beautiful piece of music. And then when you know that he wrote the theme, I'm kind of like, wow, that's kind of cool. And what I do with my students is I let them write pieces of music for themselves using those mathematical principles. And then there's a contemporary composer, John Tavener, who used the same principles. All the possible symmetries are rectangle.

So you can rotate, you can reflect vertically, you can reflect horizontally. And he wrote this piece called The Lamb, where the theme is this. Little lamb who made thee. And then it's harmonised by flipping that upside down. So I can't sing two lines at the same time yet, but if I play the other one on the piano, it goes like this. And it's kind of eerie and then goes... It sounds like there's some dissonance in the very middle of that. Is that me or is that the way that's written? No, that's right.

It goes dissonant and then it converges. And then it comes back together. Right. And it's just a mathematical formula. He's supposed to tell Chuck it is in his head, the dissonance. In your head. Stop it! Get out!

Eugenia, is it fair to say that, of course, when you mentioned rectangles and the multiple symmetries of it, because you can put a mirror in the middle and it's the same, and horizontally it's the same, that you're not only getting sort of arithmetic infusion in the creativity there, but also geometric infusion. So could it be so that if a musician does learn math, they come with more tools in their utility belt to possibly invent new forms of music. I think that's true. But I think that's true of everything in life. I think that anyone who understands, if you understand more math, then you just have more tools to understand and create anything in basically any aspect of life. Well, I asked Eric Whitaker, how does he introduce math into his own music?

And he gave an interesting answer. Check it out. Here it is. For instance, I play endless number games, math games, in the pieces themselves. From the most basic, I wrote a piece called Equus, which simply means horse in Latin. But because it had five letters, E-Q-U-U-S, then the entire piece is based on the number five, which means that they leap up a fifth, they leap down a fifth. There are five-bar phrases. There's two plus three over four in terms of time signatures.

There's just this endless game where things are, and that's on the micro level and then on the macro level. So big sections add up and equal five. Okay, I'll grant you that, but is it pleasant to listen to? Okay, so. Go there. I don't have a problem. You go there.

But at the end of the day, am I listening to this music? Okay, so this is the best question ever. So I think for a lot of the 20th century, music was written where it was only about that process, and it is not pleasant to listen to. You can break it down. You can go, how elegant is this math? And, you know, I also use the Fibonacci sequence often.

People love them some Fibonacci numbers. Yeah, well, it sort of makes the perfect dramatic structure. You know, where the climax is, where that middle is, it's just a little bit further than center. And so for a piece of music, oftentimes the climax comes right at the Fibonacci number, at the golden mean, and then finds its way back down. And artists have been doing this for centuries without having any idea what they're doing. Bach does it all the time.

So they were led there because it worked. Intuitively. Eugenia, tell us about the Fibonacci sequence. Well, like you say, people love them some Fibonacci. They really do. So it's a sequence of numbers

that begins with one and one, and then you produce the next number by adding together the previous two numbers. So you add one and one, and that makes two. And then you take the previous two numbers, which are now one and one, and that makes two. And then you take the previous two numbers, which are now one and two, and you add those, and you get three. And then you take the previous two numbers,

which are now three and two, and you add those together, and you get five. And then you add the previous two. So each time, you stick another number on the end, and then you shift up, add the last two, and that makes the next number. Frankly, this sounds like the activity of a bored mathematician.

Kind of, yeah. But it goes on forever. It's an infinite, there's no end to it. And this sequence comes up in some places, but I think the reason it captures people's imagination is because there is this longstanding, well, honestly, it's a myth that it's very fundamental and that the golden mean is some magical number. So the golden ratio, or golden mean, is if you take consecutive numbers in the Fibonacci sequence, their ratio gradually stabilizes. And it never completely stabilizes, but it gets closer and closer to this particular number,

which is the golden ratio. And the golden ratio has a geometric interpretation as well. So it kind of makes some number stuff match up with some geometric stuff. And I think that often to non-mathematicians, that seems like magic. And that's wonderful. And I love the fact that math seems like magic, except that math isn't magic, it's logic. And that's slightly different. And I like the fact that logic seems mysterious, but it's not really mysterious because it's logic. It's only sort of mysterious if you don't understand it in a way. Yeah, if you don't understand it, it's mysterious, period.

Right, right, right. And the golden mean is not really a very, it's not a terribly, extremely special number. There are loads of numbers that come up by, if you like, magic, that's not really magic, it's really logic. There are loads of numbers that come up by, if you like, magic, that's not really magic, it's really logic. There are loads of numbers like that. And so there's this idea that the golden mean is inherent in beauty, and that it's the perfect ratio, and that artists have been using it forever without even realizing what they were. And the thing is, there isn't really any evidence for that.

You can find pieces that seem to have something happen at the golden ratio. But then the trouble is, that's awfully like confirmation bias. Yeah, you look for it and you find it. Yeah, right. And you can take any piece, find the golden ratio, and then declare that you've decided that something really dramatic happened there. This is great when you talk about it from a mathematical standpoint, but I'm trying to kind of audiolyze it as music. Is there an example you can give us

for those of us who are uninitiated that we might be able to know exactly what you and Neil are so gleefully talking about. So the idea often is that some dramatic climax happens, the golden ratio proportioned through the piece. And the golden ratio is approximately 0.618 something. And so what they're saying is that a bit more than halfway through, something dramatic happens. And the thing is, I think it's a bit, I think it's a bit fishy, honestly, because, because it's, it's also very close to two-thirds. And all it's really saying is that approximately two-thirds of the way through a piece, something interesting happens. And if a piece is interesting, then something interesting will always happen approximately two-thirds of the way through a piece, you know, and you can find examples. And something interesting probably happened a quarter of the way through as well. Well, exactly, also halfway through.

Right, and, you know, and the climax is right, yeah. So, regardless, the Fibonacci sequence is a pattern, all right, and if there's a repeat, if it's two thirds or the golden ratio, that's still kind of a recurring thing. Heather, why are we so quick to notice patterns sort of neurologically? Do we innately like patterns? Yes. And if so, why? So again, it has, you know, goes back, there are evolutionary reasons for it. So if you could predict what's going to come next, you're at an advantage, right? You save time, you save resources. So those who were able to do so had a higher chance of surviving. And so the brain evolved in a way to like discovering patterns. Even in ambiguous information, we try to come up with

patterns. And that's why often people see bases and clouds. They see those patterns. Yeah. Right. Right. But that's just because our brain is so adept at finding these patterns and we get dopamine when we do. And also when there's some uncertainty and then we can resolve that uncertainty. So we figure out either the pattern or the solution. We actually get rewarded for that. We like patterns, but we like a little bit of uncertainty. And I think that's what comes up with like, you know, oh, there's like this climax and a thing. And how is it going to resolve? And that sort of draws us in. Right. There's a little bit of uncertainty. And I think that's what comes up with like, you know, oh, there's like this climax and a thing and how is it going to resolve? And that sort of draws us in, right? There's a little bit of mystery, but, but, and then when it does resolve, we feel this like satisfied and gratified. If it doesn't, you know, some of that very disparate kind of like jazz music, maybe that doesn't have so much of a pattern or that doesn't resolve. Some people

don't enjoy it as much. I mean, maybe they enjoy it more on an intellectual level, but not so much on that basic basal emotional level. So Heather, you mentioned something I hadn't fully appreciated that the fact that we so quickly recognize patterns is because we're actually intellectually lazy, right? So if you know a pattern and something has happened before or it's repeating, then you don't have to have a whole fresh new thought to know what the next thing is going to be because the pattern gives it to you. By the way, we can get into trouble. So it's a heuristic, you know, it's a shortcut to save time. But this is also the same mechanism that's related to unconscious biases, right? Because when you notice certain things are happening over time,

you start to make these quick assumptions, which aren't always correct in the individual case. So Eugenia, does music have to have patterns in it to be enjoyable? Everyone's different. You know, we all enjoy different things. And I think that I like trying to explain why I enjoy particular pieces of music. Because to me, that is a more interesting discussion than just yelling backwards and forwards with people saying, no, you idiot, this piece is better. No, this piece is better. And there's enough arguments like that.

You idiot. And so I personally enjoy music that has really interesting structural patterns. enjoy music that has really interesting structural patterns. But just like Heather was saying, not exact repetitions, because then that wouldn't be any uncertainty and excitement of the possibility of resolution. And so, for example, there's this piece of Chopin where... And that theme comes back over and over again, but it's slightly different each time. So the next time he does something nuts with it and goes... Which is basically the same theme,

except that he's stuffed 11 notes in. And because 11... Just crowbarred it in yeah right and so 11 11 is well it's various things it's a prime number it's there has no common factors with six the left hand is going one two three four five six and so you have 11 and six happening at the same time and you kind of can't tell whether it's going to land i mean when i'm playing it i never know if i'm going to land them both at the same time either. And then each time something else. So the next time it goes.

And so it's the same thing, but with a slight twist on it. And it's the same with really huge pieces of music where there's often what's called a recapitulation, which is where the beginning section recapitulates. It comes back, but different. And then there's a little twist in it. Then it goes off into a different key or something. And I love seeing those big structural patterns.

There are other types of pieces where the same thing just happens over and over again without changing. Okay, but we call that rap music. Wait, wait, Eugenia, dare I even say this, that you like that kind of music because you're bringing an intellectual component to the underlying melodies to it. But if you don't go all intellectual on it, then you get a very, or if the music doesn't have

that extra dimensionality to it then it just becomes a simple melody and isn't that what a lullaby is to lull children asleep i mean so so you aren't you agreeing that pleasant music has to have patterns but interesting music needs to be to have the the dynamicism that you describe well different people like different kinds of music you know and so some people really rebel against patterns and actually that's how the development of classical music happened across the last several hundred years that there was a lot more rigid structure that was demanded just like in society was a lot it was a lot more rigid unfortunately society is still quite rigid. But I think we've become a bit more flexible

and people gradually broke rules in music and said things like, well, in the olden days, you had to write everything in four or three, like one, two, three, four, because we're all in the military. And then composers started going, no, I want to write things in five, like Eric Whitaker was saying, or I want to write things in 13 or

something. And then we gradually break rules. And that's how math develops as well. People say, well, there's this rule saying you can't take the square root of a negative number. And then mathematicians go, wait, but I want to take the square root of a negative number. And so they invent imaginary numbers and complex numbers. And we keep sort of wanting a framework with patterns but then also rebelling against it at the same time that's really deep and of course art the best art is breaking some rule and taking you to a new place but whether you're using math or not to compose a piece of music it still takes some investment of creative thinking. And I asked Eric Whitaker. I don't want to hear any more Eric Whitaker.

Let's keep talking to you, G. This is the last clip. It's the last clip and it's 90 seconds. So ask Eric Whitaker, how does he approach creating a new piece of music? And here it is. I did my master's degree at the Juilliard School. Okay. Here in New York.

That's right. And studied with a man named John Corleano. And John is brilliant, and he's a brilliant teacher. And he taught me this technique where you take a large piece of paper and you draw, before you write a note of music, you draw the emotional architecture of the piece. How do you want the piece to play out emotionally from start to finish? And you can use whatever you need,

you know, colors, pens, cut things out. And I use descriptive words. I'll write, you know, like that bit in Debussy that I want to steal, or that film score by Thomas Newman, or this is the big, grand, luscious, dense, and just whatever it takes to kind of get the lumpy shape of it.

And then from there, always, there's this little, what I call a golden brick. Some truth reveals itself in those doodles. The idea is that you're just freeing yourself from the tyranny of detail, just writing, writing, writing. And then somewhere there's a little golden brick, and that's the motive that becomes the DNA for the entire piece. And so that's how I always start. Does that golden brick somehow bring it all together?

Or does it emerge and take you yet to a different place? That's very perceptive. So in some pieces, in the best pieces, it's like Beethoven's Fifth. The entire symphony, all four movements are based on those four notes. So it gives it a cohesion and a coherence that, again, I think just reflect the laws of the natural universe. In chemistry terms, it would be a substrate. A substrate, yeah.

Okay, I have to learn about this. A substrate is good. There's already a piece of you. It's a thing in which everything else happens, so it's a substrate. Oh, it is? Yeah, yeah, yeah. Okay, that's it. Yes, exactly. Okay.

I didn't hear a word he said after he said he was taught by John Corleone. All I heard was, you come to me on the day of my daughter's wedding. Yeah, close cousin of Don Corleone. Yes, yes. That's right. So, Heather, I probably know the answer to this, but if you're going to create something new, is it better to start with the big picture

or the little picture? Assemble it from ground up or start from the large and unpack it from there? Yeah, it's always good to have a framework so you don't get sort of stuck in the details or the minutiae. You know, it's all about contextualizing and then editing yourself, right?

And so often if you get stuck in a pattern, per se, you can break free by thinking about the larger concept or having a larger kind of scaffolding or structure. But, you know, the thing that I just want to hark back to in terms of, you know, these patterns that we're talking about is how important novelty is, again, in the brain to keep our attention. So when you're talking about, you know, that's what Eugenia was talking about. Yeah, there's these themes, but then each one, they're slightly varied. It's almost like pressing the refresh button. So your attention comes back because it's like the same, but different. Now, our brain doesn't want it to be too abstract, too, you know, so there's this repetitive sort of pattern, but slightly different every time to keep our interest, to keep us engaged.

And all that, again, is happening at a very unconscious level. And while, yes, there are subjective individual differences in terms of like what kind of music we like or don't like, I do think there are sort of commonalities across humans, one of them being liking novelty or attending more to novelties. And I think with creativity, part of it is being able to break the rules. First, you have to learn the rules. You learn the structure, you learn the patterns, and only by then, then you can learn how to break them

in ways that are interesting. Because it's not just about smashing everything apart, but it's almost like breaking them in a sort of controlled way, you know, little by little, to get to these interesting creative places. So there's an old saying with IBM, if it, if it,, then break it so that you can reassemble it and have it work even better. It's like the opposite of what you might think in that.

Eugenia, how do you solve a math problem that you've never seen before? Well, it's actually very similar. So first I'd like to say that the research I do isn't really involved with solving problems. It's really involved with building new structures that illuminate things that other people are thinking about. very similar to me to how I start doing math research, which is definitely not to get bogged down in the details. The details are crucial when you're doing math, because the logical detail is how you write a proof. But when you start, you need a big, soaring structure of where you want to go, and where you might be able to go in your wildest dream. And you don't know if it's going to work. And you don't know how you're going to put it together. And it really reminds me of the story of how Sir Christopher Wren built St. Paul's Cathedral in London, where he had this dream of building this huge dome, and he just didn't know how he was going to do it. And he just started anyway. And eventually it came to him how he was going to make a structure that was going to be big enough to dominate the London skyline, but not so big that it would overwhelm the inside. But he didn't know how he was going to do it when he started. And that's how I think math

proofs start for me. I have a dream of how I want this overarching structure to be. And I sketch it out just to sketch out the broad. And then just like Eric said, there's often a golden brick or some one idea where you think, oh, maybe that's the one idea that's going to hold everything together. And then you go back and start filling in the details. And then usually 99% of the time it completely fails. But that 1% that it works. You're right. And then it's so exciting that it really, in that moment, it makes it all worth it. Well, Eugenia, we got to bring this to a close, but I'm delighted to have you on,

and we'd love to get you back again for another show. Oh, I'd love to come back. It's been so interesting. Oh, my gosh. We will build a show around you. We have no hesitation to do so. But, Heather, always good to have you. Great being here.

Thanks for having me. Chuck, I'm a man. Always a pleasure. Excellent. Now you have to have Eugenia play us out, as they say. Play us out. Can't leave the show without doing that. Okay, Eugenia, keep playing us out.

As I say, I'm Neil deGrasse Tyson, your personal astrophysicist, bidding you to keep looking up....