Can Mathematics Fuel Creativity? With Marcus du Sautoy (Part One)
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Welcome to Intelligence Squared, where great minds meet. I'm Head of Programming, Conor Boyle. I'm joined by our producer, Mia Sorrenti, to discuss what we've got coming up today. Mia, if people haven't seen Marcus de Sotoie's snazzy promo video on social media, what can they expect from today's episode? Yeah, we're huge fans of Marcus at Intelligence Squared. So previously, we hosted an event with him on

the workings of board games and around the world and how games are so important to humanity and our understanding of life and the world.

We had the honour of having Marcus back on the Intelligence Squared stage this May. He was in conversation with Dr. Shini Samara, and the two of them were speaking about the interaction between maths and creativity, which we think often of things, you know, maths and creativity feels like something completely separate. You know, when you're picking a GCSEs, you go down one route or the other. But Marcus argues that this actually isn't the case and that they're actually very closely interwoven. You know, whether we're searching for kind of

meaning in an abstract painting or finding patterns in poetry. You know, what he calls kind of mathematical blueprints are everywhere. Symmetry, prime numbers, the golden ratio and more. So this is a really fun discussion that was a pleasure to host. Absolutely. As a fan of creativity and someone who loathed maths, I'm excited to see if Marcus can convince me to the contrary. Well, let's get into the episode now. Let's join Marcus de Sautoy and Dr. Shini Samara now with more.

Hello and welcome to this event of Intelligence Squared. It's great to see such a packed audience. Now, I am Dr. Shini Samara. Clearly not Arsenal supporters in the audience. I wondered when you were going to get that in. Very quickly. Anyone who's got their phones, do a shout of Arsenal score, OK? We've actually got the score. We've got the score appearing on this little iPad. So if you see... Very bad planning on my part, but...

So I'm delighted to introduce Professor Marcus de Sautoy, who needs no introduction, but I will run through a few highlights. You are a professor of mathematics at Oxford University, where you hold the prestigious Simoni Chair for the Public Understanding of Science. You've presented numerous programs on television and radio, including the internationally acclaimed BBC series, The Story of Maths.

And your best-selling books include "The Music of the Primes," "The Number Mysteries," "Around the World in 80 Games," where we last met to talk about that book. And now your latest book, "Blueprints: How Mathematics Shapes Creativity."

which I finished last night, which is why I've got giant bags under my eyes, because I could not put this book down. I genuinely loved it. So I am thrilled to be able to talk to you about it. You'll see that I folded down the pages because there are so many things. It's doubled in size. It has. You've folded every page down. It has. So my first question to you is, what is your definition of creativity?

Yeah, that's one I actually had to encounter in a previous book because I actually wrote a book about whether AI could be creative with the complete explosions of AI. And so I actually took a definition...

that I quite liked that the cognitive scientist Margaret Bowden told me about. We were on a committee together at the Royal Society looking at the impact that machine learning was going to have on society about 10 years ago. And she has a nice definition which is kind of quite clean because she says it's something which is new, surprising, and has value.

which I quite like because novelty you can judge very easily, but the element of surprise, that's something which is about an emotional reaction to whatever it is. So that's something very, you know, some people will...

have an emotional reaction, others won't. It's very subjective. And value, again, I think something's going to be creative if it engages you in your emotions, but then leaves you with a kind of new way of looking at the world.

And you see, I think those second two qualities are things that people don't necessarily associate with mathematics so much. Maybe value, but the emotional side of the response. And so I think, you know, this is a book about creativity and mathematics. Creativity, especially in the creative arts. And I think for most people, those two things are just polar opposites. But actually, there's a lot of choice involved in the mathematics that we create. And

the things that we want to share with our audiences, both in our seminars or in our journals or more broadly, that mathematics is very often driven by an emotional response. You want to take your fellow mathematicians on a kind of journey of discovery where there will be twists and turns and surprises and, wow, I didn't think that was related to that or these things looked completely different and you're saying they're the same. Show me how that works. So mathematics,

I've always felt that mathematics is actually about storytelling. In fact, science more generally is about storytelling, trying to tell a story which helps us to understand our place in the universe. I think mathematics has the potential to be more creative because we can create worlds that don't necessarily match the universe that we live in. So while science is trying to explain a

mathematics is able to create sort of multiverses. We can, as long as they're consistent and they can, they're as interesting to me, even if they don't match up to physical reality, um,

Whilst I think science will throw away a theory that says, well, this isn't how our universe works, it suddenly becomes uninteresting. But if it's actually a theory which is consistent in its own right mathematically, it will still be interesting to the mathematician. So our stories have to be, you know, they're a bit more imaginative because they don't have to match reality.

And at some point in the book, and I was trying to find the quote on my notes, but at some point in the book you talked about how mathematicians are motivated by a beauty or aesthetic. You know, it's not about functionality. Yeah, you see, I fell in love with mathematics when I was at school because my math teacher in my comprehensive school gave me a copy of G.H. Hardy's A Mathematician's Apology. And this was a book that...

It was the first time I realized that mathematics is actually closer to the creative arts than the sciences. You know, mathematics is clearly the language of science, but

actually what drives the mathematician, and this is something I read for the first time in this book, which is an account of what it's like to be a mathematician, is that actually the drive is to... It's often beauty, aesthetics, but not necessarily just beauty. It's about narrative. It's about storytelling. It's something that is...

yeah, much more about the imagination and creativity. And so somehow the drive for the mathematician is to find some interesting new connections in the mathematical world, which you want to share that kind of strange discovery with your fellow mathematicians. So

I think the education system fails us because it just concentrates on utility, which is fair enough. We do need to know, especially if you're going to become an engineer, there are certain things that you need to learn on the mathematical side to facilitate doing things. But very often, the mathematician will make a discovery just for the pure joy of

um understanding some strange new connection and what's beautiful is because mathematics of course grew out of societies trying to understand the natural world how to build new cities you know where does mathematics start it starts in um egypt and babylon where suddenly they're building things they want to build a pyramid so suddenly they need to know the formula for a pyramid um but uh

So as civilization developed, mathematics develops to sort of control and understand the environment around us. But then somehow we became free to just start thinking about mathematics for its own right. But because it starts in something somehow practical,

in trying to understand the world around us. That's why very often we get these amazing surprises of a discovery of new symmetrical objects just for the beauty of these new symmetries.

Then suddenly the thing that an engineer wants in order to be able to make a new code to make a JPEG, for example, how to encode pictures in an efficient way. Or we discover something amazing about prime numbers in the 17th century with Pierre de Fermat. And then amazingly, this is absolutely what was needed to create codes that could be used on the internet. So, you know, there is...

although the drive for the mathematician is often something very creative, what we make is because of that connection to the real world around us is very often something that turns out to be useful, but it's not our motivation.

And that's what I love about the book, is that you talk about the function of maths in creativity. So you talk about music and dance and poetry and the kind of structure of those creative pursuits. But then towards the end of the book, you talk about randomness again.

and chance and the Dada art movement, which actually is, you know, screwing all of that up and kind of, well, tearing it up into pieces and throwing it into the air. Yeah, literally. Yeah, exactly. But I think this is a kind of contradiction I want to sort of address in the book, which is, you know, we've talked about mathematics actually being quite emotional and storytelling, and that's something we generally associate with the arts, right?

But actually what I want to illustrate in this book is that if you actually talk to an artist, and this book really grew out of the decades I've spent with artists. I've been invited into their studios, into the rehearsal room for theatre companies, the concert hall with musicians. This is very much a lot of my passions because I suppose I actually secretly wanted to be all of these people, and I ended up being a mathematician. But I found actually, I think that mathematics was my bridge between actually wanting to be a scientist and being a

wanting to be an artist, I found actually this language was useful for both. And here's the thing, you see, I think most...

people have this impression that artists are just emoting, you know, they're just expressing themselves through paint or music. And clearly there's a lot of emotion, emotional response that comes out of encountering art. But if you talk to any artist, and this is, you know, there are many stories of the people I've talked to, they will say, yeah, the emotion comes much later. I start with structure. Mm-hmm.

And those structures are things, why I wrote this book is all that time I spent with artists from all of these disciplines, those structures that they enjoy doing

creating within are ones that I recognize from a mathematical perspective and they don't understand quite often that it is mathematics. A lot of the musicians say, "Oh, I'm terrible at maths." And then I explain to them, "Yes, but look at what you're playing. It's full of mathematical structures." They say, "Well, if that's maths, then I'm good at that." I mean, I like this quote of Stravinsky who said, "I can only be creative under huge constraints."

If you're faced with a blank piece of paper, it's terrifying. Or a blank stage, just improvise. You freeze and nothing happens. But the theatre companies, I work a lot with Complicite, the way they devise their theatre is they do a lot of improvisation, but under very controlled rules, and they enjoy seeing what emerges out of those rules.

Now, the interesting thing is, so I've structured the book as a lot of these structures that I recognize mathematically and then showing, I mean, the interesting thing was seeing how they get used in different ways, in different art forms, in music or literature or architecture. But the last one, we're sort of starting at the end because it's a structure which most people think is almost like an anti-structure, which is randomness. And I think for many people,

years, mathematicians felt that randomness was the opposite of mathematics. But actually it's not. I mean, we can produce and have produced a mathematics of randomness. I mean, the idea of probability theory allows us to make predictions about what you would expect from a random process. So it's very interesting seeing that moment in

in the beginning of the 20th century when somehow almost there'd been too much structure and artists felt they needed some way to break out of that. And they chose the idea of, you know, where would we be taken if we actually gave up agency and let ourselves be led by what randomly could appear. And then seeing each different artist's

relationship to that when they they they just can't stop getting involved and you know okay that's a really interesting idea you've thrown me but i like to do this thing i have to say talking about randomness i love the personal anecdotes to really stick out in my mind on the topic of randomness it was you trying to randomly tile your kitchen

And so coloured tiles, trying to avoid three in a row that were the same colour and your wife saying... No, you see, I was... So I did this talk for the Serpentine Gallery about Gerhard Richter's amazing exhibition. I don't know whether anyone went to it a few years ago. It's quite a difficult exhibition because basically he produces these canvases which are five by five grids

And he just randomly chooses from 25 colors, the entries for each of these. And I was kind of intrigued. And he has 196 of these canvases. And I was very intrigued. So Serpentine asked me to come and give a talk. And I was like,

"Gosh, what am I going to talk about?" And then I thought, "Well, that's interesting. He claims that these are chosen randomly." So, and I know what we... It's quite a lot of data with 196 canvases. If I could actually do a test to see whether he genuinely had been random, because randomness does strange things. As you say, it clumps things together. With randomness, you'll expect to see three red squares together.

when people go to that exhibition, they start to think there are messages inside there because they see patterns emerging because of this kind of clumping. So I did a statistical analysis and sure enough, Richter was, it matches absolutely what you would expect from a random process. So he didn't

And now it was at the same time, I was doing some work with an artist. We made something called the Pattern Foundry. He really enjoyed making tiles. He had an old, one of the oldest tiling factories in England was making tiles based on graphic patterns that he was curating from different people. And he had this lovely pattern that he curated from a Dutch artist,

which was just a graphic, but he made them into tiles. And my kitchen was the first place where we actually put these tiles into operation. And of course I wanted to do it randomly. So I laid them, I used the decimal expansion of pi. I'm a nerd. Okay, so to choose all of the colours. 2.0. But you see, my wife is an artist and she said,

can't have that in my kitchen there are three reds together there and i said yeah that's what randomness um she says no no and she started moving them around so so anyone comes to my kitchen will be able to tell that we did not do it randomly because there are no colors um which are together well that was the question that was provoked is how random is randomness yeah so um you know the throwing of the dice you know the actual action well does that interfere it

Yes, so it's very, you know, that's a really interesting, deep philosophical question. You know, is anything genuinely random in this universe? Because as you say, a dice is just following the, you know, Newtonian laws of physics. If you know exactly how it's set up, you launch it, you should be able to just work out how it's going to land. So that doesn't sound random at all. But of course, what rescues randomness is the mathematics of chaos theory.

because a very small change in the initial conditions can cause it to land on a completely different side. And so we never know the exact setup. So Laplace had this statement that if we knew how the universe was set up, we just run Newton's equations and we can predict the future.

but that didn't take into account two things, chaos theory and start with that we can never know exactly. And so that's why things can go very different ways with this almost an unnoticeable change.

But the second revolution, and this is what I think is very interesting about the Dada movement and all the artists being interested in randomness, because this is what's happening in the science of the time. Because what is the science of the early 20th century? It's quantum physics, which actually says that science, by its very nature, has randomness at its heart, that we can never... So actually, Laplace is wrong. If you know how something is set up,

Quantum physics says that the wave equation can randomly collapse in different ways. So it seems like randomness is part of the way we must do science. And that is something that comes up time and again, that often a change in an artistic movement will reflect often the science that's happening at the time. So look at the Baroque. The Baroque kind of breaks from a very sort of static movement

Renaissance kind of art to trying to capture things in motion. You know, you've got people falling off horses, architecture of the Baroque, you have to move through a building. You can't understand it from just standing in one place. It's a dynamic art form. And what's the science that's happening at that time? It's the calculus. It's suddenly a mathematical technique to understand a world in flux.

the two things are running alongside each other. You've got science trying to understand a world in flux and art also being interested in trying to capture moments of movement. - There are so many questions.

There's so many things in this book. It's just, I mean, it was kind of... It's honestly... I wrote a dramatis personae at the front of the book because when I was talking to my editor, he said, wow, you take us everywhere on this. And so doing that list kind of makes you realise...

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Eczema isn't always obvious, but it's real. And so is the relief from EBCLS. After an initial dosing phase of 16 weeks, about 4 in 10 people taking EBCLS achieved itch relief and clear or almost clear skin. And most of those people maintain skin that's still more clear at one year with monthly dosing. EBCLS, labricizumab, LBKZ, a 250 milligram per 2 milliliter injection is a

Prescription medicine used to treat adults and children 12 years of age and older who weigh at least 88 pounds or 40 kilograms with moderate to severe eczema. Also called atopic dermatitis that is not well controlled with prescription therapies used on the skin or topicals or who cannot use topical therapies. Ebglus can be used with or without topical corticosteroids. Don't use if you're allergic to Ebglus. Allergic reactions can occur that can be severe. Eye problems can occur. Tell your doctor if you have new or worsening eye problems.

You should not receive a live vaccine when treated with Epglys. Before starting Epglys, tell your doctor if you have a parasitic infection. Searching for real relief? Ask your doctor about Epglys and visit epglys.lily.com or call 1-800-LILY-RX or 1-800-545-5979. So let me ask you this question before I lose it. Mathematics and the structures and laws that are devised within mathematics are considered to be perfect. And nature...

it's said in your book is the imperfect interpretation of perfect mathematics. Expand.

- Yes, I am a Platonist at heart and I am a kind of, why do we see so much mathematics in the natural world around us? I think because we are a physicalized piece of mathematics that things in nature have a moment of creation, the first cell, the first atom that came together, the first star, the first universe, a moment of, but mathematics, which I define in this book as a study of structure,

Those structures do not need a moment of creation.

they might have a moment when a mathematician recognizes, a human mathematician creates or discovers them for the first time. But I believe that mathematics is outside of time. And therefore what we're seeing is that the universe is, you know, just as Plato kind of expressed in that image of us sitting in the cave and watching the shadows, I believe that what we see around us are sort of shadows of what could exist in the structural realm, the platonic realm, the realm of mathematics.

But the very curious thing is that physicalization, as you say, is not perfect. So one of the structures I talk about is the circle. You know, the circle is something which artists have explored in lots of interesting different ways. James Joyce, for example, starts,

Finnegan's Wake in the middle of a sentence and you finish the sentence at the end and you realise the whole thing's looped up. The Goldberg Variations is basically a circular structure that Bach uses. It got me thinking that, you know, we often think of the moon as circular or even planetariums

planet Earth as being circular, but actually after the statement that nature is not perfect, maybe the Earth is like this crumpled odd shape. Crumpled odd shape is also elongated, if I get my physics right, I think it's elongated equator-wise. It's one direction. So yes, I mean, it's interesting because the circle becomes such a fundamental object for the humanity because we see it

In the night sky, we see it change and become a full moon. The Earth ripples in the water. The circles of time in the year, we measure time because of circles. But if you think about it, as you say, the Earth's certainly not a perfect sphere. Neither is the moon. Those ripples in the water are also...

they might look circular, but as you zoom in, you see a lot of imperfection. And here again, if we come back to quantum physics, quantum physics says there's no way, even if you have like a perfect bit of kit to try and draw a circle on a page. I mean, there's the story of which artist? Leonardo and the pricks in the pages. Is there a picture? Which one is it?

Yes, he's asked to prove his worth as an artist for the Pope and all he does is to freehand draw a circle. Yeah.

And that's meant to be impressive enough and he gets the job. But if you think about it, quantum physics says that our universe is actually quantized. Every space comes in small little units. We are basically pixelated. If we zoom in close enough, actually we will come down to a fundamental unit of space.

which actually means that a circle, suppose you tried, okay, I'm gonna use a whole universe to draw a circle so I can do it. At some point you will get down to these pixelated points and you will not be able to see the difference between. So this circle is actually never ever perfect according to quantum, but you could never see the perfection.

This is also interesting in relation to another structure, which are fractals, because fractals mathematically, here's another example of where mathematically we can create a structure which has infinite complexity as you zoom in on it.

And we see that coming up again and again, that nature uses fractals to grow things. A tree is basically a big branch followed by the trunk, and then the branch, and then a twig, and then smaller twigs. I love your example of you could pick up a twig and it looks like a tree. Yeah, I mean, that's... This idea of scale, fractals. Scaleless. So, you know, nature uses... But at some point, you're going to hit things which show that...

the sort of basic unit, either the cell or some sort of pixel. Whilst in mathematics though, the Mandelbrot set, one of the first kind of psychedelic fractals that people were dancing in the clubs to in the 90s, you can just send that zooming in and in and in, and it will never simplify. But that is something that physically, there's a limitation to that in the natural world.

But then the interesting thing is where you see it in art as well. So the fractal chapter, I start with an artist who didn't, I mean, this is the other interesting, I think, theme is when does an artist know what they're doing mathematically and when do they intuitively predict

produce a mathematical structure without even realizing the mathematics and Jackson Pollock is an example of an artist who you know you think of first sight oh gosh that should be easy to do you everyone should be able to fake Pollock's and there are a lot of fake Pollock's out there where people just flick paint around but it turned out mathematics was the key to revealing these as fakes because what Pollock was doing was was something quite unique he was creating with these dripped

dripping paint method a fractal quality to the canvas. So if you zoom, if you take a Pollock and you zoom in on a section and zoom in on the zoomed in section, zoom in again and put them side by side, it's impossible almost to tell which is the original painting and which is the closest image. And that's the magic of a Pollock is that when you come up in front of one, they're huge, yet you somehow, because of this scale, this property, you lose yourself inside them.

But what he's doing is replicating the natural world around him. That is an abstract form of where is this studio? It's the middle of a forest.

And so I went to visit his studio and you realize he's looking at fractals every time he walks into the studio and he's representing them, although he doesn't understand that that's actually a mathematical structure. Well, I love the fact that he was not mentioned in the randomness blueprint. Well, he was mentioned, but he was mentioned because you said you were not going to mention him.

in this chapter because there was nothing random about it. Very meta. But actually, yes, because he was doing something very deliberate. He wasn't... And he always said, I know exactly where I'm going to put the paint. I mean, there is no randomness to this. However, actually, what he was tapping into, how he managed to do it, was that...

fractals are the geometry of chaos, this idea of having a system which a very small perturbation will send it off in a very different direction. So what he did was to make himself into a chaotic pendulum.

So his style of painting was, I think most of us when we flick paint, if we were trying to pretend to be Jackson Pollock, is that we would stay quite static and we would just move our arm from our elbows. And we would flick, flick, flick, flick, flick. But that's not how he painted. Now there's some conjecture that he painted very often when he was drunk.

I mean, he did drink a lot and unfortunately that's how he died, I think in a car accident. But I think the evidence is that the periods when he was most productive were not the periods when he was drinking. But he was creating what looks like a rather unbalanced, staggered, as if he was drinking. So when you see videos of Pollock painting, what he did was to create... So a pendulum is very regular, but if you have a double pendulum, which is kind of a two-jointed system...

that is very chaotic and very unpredictable. So if you have a piece of metal pins with another piece of metal on the end and you let this thing go. So what Pollock was creating was this chaotic pendulum. And then the geometry that emerges is this chaos. And that's,

quite hard to replicate until you know that that's what you do and then you create a chaotic pendulum and you start faking Pollock's which I tried to do but my faked Pollock didn't sell very much on eBay so I don't know. It was in Pollock's studio that you talked about taking pictures of the floor around the canvas. Yeah, there's a secret Pollock which nobody knows about and I took a picture of this

Because, of course, all the paint comes off the canvas. And so the whole floor looks like... So I took a picture of this and it's actually my desktop on my laptop computer. So I sit watching Jackson Pollock's... You know, the Pollock that nobody knows about every day. I show you a love of Pollock. I just love his work. So I've got just under 10 minutes to ask you a very big question about the mysticism. I mean...

There are so many references in the book about the number three, the triangle, unity, 12 being a very important number, prime numbers. In fact, that was the other personal anecdote, wanting to call your twin daughters 41 and 43.

Do you want to expand on that? I actually start with the first structure in the book. We talked about the last structure. The first structure is somehow... I mean, I'm wearing tonight my Fibonacci golden ratio T-shirt in honour of the book. And so I suppose, you know, the most obvious structures are things like Fibonacci and golden ratio. And they're in there, the way Le Corbusier uses them. But I actually really wanted to talk about unexpected ones. And so, for me, prime numbers is part of my research, these indivisible numbers. And I think I...

it's beautiful how artists have also been drawn to these numbers, creating music, architecture, even literature. And so these indivisible numbers, there are some special pairs because the closest that two primes can be, except for two and three, is two apart because obviously the number in the middle is even. So like 41 is...

and 43 is prime, 42 is the answer to life, the universe, and everything is even. So there are these twin primes. Now, we know primes go on forever. There are infinitely many of them, but we still do not know, we still haven't finished this story. It's an unsolved mystery whether there are infinitely many twin primes.

So that's why, you know, I have identical twin daughters and I wanted to call them 41 and 43, but my wife wouldn't let me. So they're my secret names for Magalie and Ina. Thanks for listening to Intelligence Squared. This episode was produced by Mia Sorrenti and edited by Mark Roberts. If you want to join us live, be in the audience and ask your questions yourself. Why not see what we've got coming up on intelligencesquared.com slash attend. This is an ad by BetterHelp.

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