Beauty and truth in science

Frank Wilczek

A beautiful puzzle

'This exploration of how it comes to be that our perception of the world at a deep level matches our perception of beauty – it’s a puzzle.'

Transcript

A BEAUTIFUL PUZZLE

David: Why the title of the book? It’s such a lovely title. What was it that drew you to that title?

FW: Well, the more I thought about what I was doing in the book – this exploration of how it comes to be that our perception of the world at a deep level matches our perception of beauty – it became… it’s a puzzle. And the more I thought about it, the more it resonated, and the more I realised that, first of all, I have been worrying about the beauty of quantum theory and the beauty of the deep descriptions of nature all my adult life, and even before. So it was coming to terms with myself and what I had been doing all of those years.

David: You used the word ‘worry’: ‘I had been worrying about this.’ Why would beauty be something that would be a worry to a physicist?

FW: Well, because it’s not accomplished. We have a lot of beauty in our description of the world but also a lot of loose ends. Also it poses a deep mystery. Why should it be that way? Beauty is one thing and the way the world works is quite another. In fact, often when I start discussing this with people, they’re very puzzled. Beauty is this subjective feeling that people have, whereas science is objective: they couldn’t be more different, and yet many physicists and philosophers, for that matter, and artists, who have come into deep relationships with the natural world, have been delighted at its beauty. So it’s a common experience, and almost universal among modern physicists working on fundamental physics that they feel the structure they find is beautiful. So why should that be?

Ard: I think that’s a common view, isn’t it, that beauty is merely subjective? It’s in the eye of the beholder, and so what I find beautiful might be different to what you find beautiful, and so what’s really surprising is that this subjective feeling has traction on the physical world.

FW: Yes, well I think beauty is a word that is used for many things. I think what they have in common is that beautiful things, beautiful experiences, are things we want to come back to: they are things we find rewarding.

Much of my anticipation of what the laws might look like, and guessing of new laws, was based on an instinct for a kind a beauty, and it’s worked, so far. There’s some cases still out to jury, but some cases have definitely worked, and so it’s changed my life.

Ard: Is that what drew you to physics in the first place? That sense of beauty? Do you think that’s what made you interested in it?

FW: Ah, well, when I first was drawn to it, I didn’t really know how beautiful it was going to be, but if I think back on my childhood, my earliest memories have to do with taking things apart and putting them together. I was very much a student of mathematics, so I always had a feeling for that kind of beauty. The fact that it was abstract, which turns off many people, it didn’t turn me off because it allowed more freedom in manipulation, so to speak. And the fact that this particular kind of thinking is actually what gives you a deep understanding of the physical world: that’s a tremendous gift I can only be grateful for and sort of contemplate in awe. But that leaves a different question, which is: why are the laws comprehensible?

David: Yes, why can we understand them at all?

FW: If they weren’t beautiful, we wouldn’t find them. But why did we have to find them? Well that one I’m still working on… I don’t know. It’s just a gift.

John Cottingham

Is beauty subjective or objective?

‘Beauty is not entirely in the eye of the beholder: it’s in the object. The key there is that there’s something in reality which calls forth that response.’

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Is beauty Subjective or Objective?

David: In your essay, that lovely essay that I read, you chose truth, morality and beauty. So, truth, good and beauty. Why did you choose those three above anything else?

JC: Well, there’s a sort of traditional Platonic trio, I suppose. It’s difficult to explain, but they call forth a response from us.

David: They call us on in some way?

JC: In some way they call forth from us a response and we may be disinclined, if you like, to hear it. We may be disinclined to orient ourselves towards it, but nonetheless the pull still remains I think a lot of people are accustomed to think of beauty as just a matter of subjective taste, but it’s surely more than that. When we are overwhelmed by some great work of art, or by some stunning natural beauty in the world, of course there is a subjective reaction, but we’re responding to something in the object: something which calls forth our delight, our admiration. But there’s something real, there’s something true in the object, which generates that response, and which is also, I think, good.

Wordsworth in some of his poetry talks about those ‘spots of time’. These are quite ordinary experiences, but they are moments when the mundane, drab, routine of reality somehow gives way, and we see through it to something richer, something which, as Wordsworth puts it, ‘lifts us up’, which raises our spirits. And the key there is that there’s something in reality which calls forth that response. It’s not just him subjectively musing about it, though, of course, he’s doing that, but he’s describing a response to a reality that’s already there.

Ard: So, one critique of some of that would be that people clearly view beauty differently. There are things that some people think are beautiful and things that are not. Different cultures have different moral systems. So there’s a lot of diversity in our perceptions of beauty or our perceptions of what’s ‘the good’. And I think it’s a natural step sometimes to say, ‘Well, given that there’s diversity, perhaps we should just agree that that’s all that there is’. But you’re saying that’s not quite good enough somehow?

JC: I mean obviously there are wide variations in taste and fashion from culture to culture, but to believe in certain objective standards of beauty is to believe that, despite those divergences, there are core values which remain in place, which are common to these culturally variable differences.

So, to be beautiful, a work of art must have some harmony, rhythm, form, which intrinsically is valuable irrespective of cultural and social preferences. And we can’t, as it were, violate that. Well, of course you can make certain moves in the cultural game: you can create a disordered pile of bedclothes and put it in an art exhibition, and it may have a perfectly valuable function to shock people out of their complacency. I’m not, as it were, knocking it, but I’m saying you can’t make something which is messy or ugly, beautiful, just by an act of will. Beauty is not entirely in the eye of the beholder: it’s in the object, and so with goodness.

David: There’s something that bothers me about that.

Ard: Okay?

David: In the sense that I’m not sure I want to live in a universe where it can all be summed up, eventually, by the top ten in everything. I’m more attracted to a universe where we it continues to change rather than converging on a set of truths – whether those truths are ones laid down by scientists or God.

JC: But surely there can be creativity and variety? It needn’t be monolithic, surely?

David: Well, I hope not. But it sounds a bit that way – either monolithic or whittled away.

JC: If you think of music, there are many rich and varied and wonderful forms of music. There’s no reason why they should be whittled down to a single pattern. But it surely makes sense to say that they all exhibit certain structural features, symmetries of form or rhythm, which call forth our admiration – not identical in each case.

David: Yeah… maybe I’m putting it badly. To go back to mathematics is always the easiest one. I’m happy that there would be mathematical truths which are just true, and one set of truths opens up another. The question is whether that set of truths opens up new ones and new things emerge and it becomes… and the horizon broadens and makes up new things out of itself. Or whether it becomes a closed system, that eventually you’ve got all the answers. So, it’s whether it’s open and creative or just, sort of, finite: big, but finite.

JC: Yes.

David: I don’t want a prison house of certainties.

JC: No.

David: I’d rather live in…

JC: I totally agree with you, but I think this connects with what we were talking about, the transcendent urges that human beings have, not to rest content with the boxed set. So, something could be flowering every outward, if you like, in innumerable ways, always reaching forward, but informed by, infused by goodness and beauty, rather than degenerating into ugliness.

Alex Rosenberg

A beautifully simple universe

'Beauty alone is not going to be a substitute for, or treated as an invariable guide to truth: it’s just a general feature of many of the best scientific theories. Now, ask yourself why?'

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THE BEAUTIFULLY SIMPLE UNIVERSE

Ard: Many of the scientists that we speak to – in fact, I myself in my own research – think that beauty is a guide to truth in science. So, historically, many of the great scientists, like Dirac…

AR: Elegance.

Ard: Elegance and truth…

AR: Well the Dirac case is quite interesting if you’re thinking about the positron, but go on.

Ard: It was just… we interviewed Frank Wilczek, who has a whole book on this topic.

AR: Yes.

Ard: And there’s a classic argument that beauty is in some sense a guide to truth. What do you make of these arguments?

AR: So to begin with, where does our sense of beauty come from? It’s actually very interesting. There’s been some very nice studies about this, and our sense of beauty and of symmetry actually comes from the very bucolic, pleasing character of the sunset on the African savanna, or something rather like that.

But, for me, beauty, like simplicity, and other features of scientific theory are important, and they’re importance is justified largely by our inductive practices. That is to say, it has turned out in the past that those theories that are the simpler have proved to have been more well confirmed than the more complicated theories. And so we have a conviction in science that simpler is better than complicated, and we seek simpler theories.

Beauty alone is not going to be a substitute for, or treated as an invariable guide to truth: it’s just a general feature of many of the best scientific theories. Now, ask yourself why? That’s going to require an explanation, and that explanation may or may not be beautiful.

Ard: I’m wondering why. What do you think?

AR: I don't know the answer to that question. Probably because the universe… I’m inclined to think it’s because of reductionism. It’s because the universe is simple at its basement level, and because the principles of aggregation, of putting things together, are relatively simple, and so the outcomes tend to be simple.

Why is the universe simple? That’s a question for science too. We don’t even have a good metric for simplicity, still less a good metric for beauty, for us to actually be confident that more beautiful theories are, in fact, more well confirmed.

Ard: And do you think this question, of why is the universe simple, leads quickly to the kind of famous questions about why is there something…

AR: Rather than nothing? I don’t think that it does, but that’s an interesting question to which I think the sciences give an answer.

Ard: Which is what?

AR: No reason at all.

Ard: No reason at all?

AR: Quantum mechanics tells us that constantly, in this room, at every fire detector in this room, events are happening with no cause whatsoever, millions of times a second. Why shouldn’t the universe have come into existence on the same basis?

Ard: So you’re saying, why shouldn’t quantum mechanics itself have come into existence on the same basis?

AR: Quantum mechanics doesn’t come into existence. It’s a set of laws about reality. Are they the only set of laws about reality? Are they the set of laws at this universe as opposed to other universes in the multiverse? Well, let’s wait until we have established superstring theory.

Ard: Sure.

AR: And then we’ll be able to answer these questions. And until we do, anything else is just theology or speculation.

Semir Zeki

Beauty and truth in mathematics

'One mathematician described one of the beautiful equations as the equivalent, the mathematical equivalent, of the soliloquy in Hamlet. So you see how impressed they are. And indeed, when we did the experiments on mathematics, some of the subjects were in tears.'

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BEAUTY AND TRUTH IN MATHEMATICS

David: Why did you get interested in beauty? Because it’s not the normal thing that neuroscientists get interested in.

SZ: Well, it’s part of a more general question, which is I’m interested in the visual brain: how the visual brain functions, how we see. So the next step, really, is to ask, how does a visual input arouse an emotional state? And one of these is beauty. In a sense, what is the point of learning all about the visual brain and not being able to say what happens in your brain when you experience something which is visually beautiful? So that was the inevitable next step.

David: And what were you expecting when you started? Were you expecting that beauty would be a separate thing?

SZ: No, I think in this instance we just did not have any hypothesis. We just thought that it would be interesting to see what happens when you experience something which is visually beautiful: not only beautiful portraits, beautiful landscapes, but also beautiful abstract art. And then you go and say, well, philosophers have spoken of beauty in the abstract, so I must look at musical beauty as well. And then you reach the ultimate question, which is mathematical beauty, because mathematical beauty is one of the reasons why mathematicians speak of mathematical beauty in poetic terms. One mathematician described one of the beautiful equations as the equivalent, the mathematical equivalent, of the soliloquy in Hamlet. So you see how impressed they are. And indeed, when we did the experiments on mathematics, some of the subjects were in tears.

David: Really?

SZ: Yes, yes.

David: So, wait a minute, tell me what you did in this experiment.

SZ: Well, all we did was to give them sixty equations to classify as to how they experienced them as beautiful. We gave them a scale from one to nine: one was very beautiful and nine was very ugly. And each one classified them according to their own subjective experience, and then they came into the scanner and looked at these same equations and reclassified them. So, we now knew that they had a category of equations which to them were beautiful, ones that were ugly, and ones that were indifferent. And the experience of mathematical beauty correlates with activity in the same part of the brain as experiencing musical beauty or visual beauty.

David: Can you show us?

SZ: This is part of the emotional brain. So this is a brain looked at in mid-section.

SZ: This is the front of the brain. This is the back of the brain. So you’ve bisected the brain, and you’re looking inside there, and this shows you the area of activity in the medial orbitofrontal cortex, which correlates with the experience of mathematical beauty.

David: So when your mathematicians said, ‘That’s beautiful’, that’s the bit that lit up?

SZ: Yes, yes, exactly. Not when they said it, when they experienced it was beautiful. Then if you look at the regions of the brain which are active with musical and visual beauty, now you’ve got the same area. You see this area in yellow is common to both. There’s a huge area of overlap, but it’s the same area of the brain that’s active when you experience mathematical beauty.

David: So what does that tell you, Semir?

SZ: Well it tells you a number of things. First of all, as a neurobiologist, let me just rephrase this question, ‘What does it tell me?’ You have to understand what am I looking for. I’m not looking to explain beauty or to tell you what art is, nothing like that. I am really trying to only find out, because I’m a scientist, what are the areas of the brain which are engaged when you experience beauty.

So the first thing that it tells me is that the experience of beauty, regardless of source, correlates with activity in a given part of the brain, number one. Number two, it is part of the emotional brain. Number three, that the activity there, I have not shown you this, but the intensity of activity is related to the intensity of the experience. In other words, if you find something extremely beautiful, then the intensity of the activity is much higher than if you’re indifferent to it or something.

But it also raises questions which inevitability make us trespass into other fields which do not properly belong to us, which is, what is the use of beauty? What does it indicate? And why is there a common area in the brain for the experience of beauty from such diverse sources?

And this question especially imposes itself in respect to mathematical beauty. What is it about mathematical beauty that people experience? Now, this part of the brain is also part of the reward centre of the brain and pleasure. But then, you see, beauty is never divorced from reward and pleasure: beauty is a rewarding experience, it’s a pleasurable experience, so the two are mixed. And if one was to read the philosophies of aesthetics, they are always talking of the three – of pleasure, reward and beauty – almost synonymously.

So the question I would ask is, what is it about mathematics that people find so beautiful? It’s a very difficult question, and the answer I would give is that they find something in the logical deductive system of mathematics that makes sense. It’s entirely based on the logical deductive system of the brain, and where did this logical deductive system develop? It developed in the universe.

So it’s an interesting question to consider: if you take a very sophisticated mathematical equation, for example, quantum mechanics, and you have an equation which does not make sense to the logic of the brain – the brain’s deductive logical system – will that ever be considered as beautiful? And if not, will it ever be considered as true?

What’s his name? Eh…

Ard: Dirac?

SZ: Paul Dirac, thank you. Dirac did say that the guide to the credibility and the truth of a mathematical equation lies, above all, in its beauty before its simplicity. If it is beautiful, then chances are higher that it will be true. But ‘beautiful’ implies that there is something in it that satisfies the brain. In the case of mathematics, I would say you’re satisfying the logical deductive system of the brain.

Ard: I have experience myself of studying physics, learning about the Dirac equation, and just being blown away by its beauty. And part of the reason was because Dirac took this theory of quantum mechanics, of small things, and special relativity of fast things, put them together for the electron, and out popped the positron. You know, that was anti-matter that was predicted by taking small things and fast things and putting them together. So he took two unrelated things, put them together and a third, completely unexpected, unanticipated, unimaginable thing happened, which was you predicted a new particle, which was anti-matter.

SZ: Now, there is another story of Hermann Weyl. Hermann Weyl and his attempt to reconcile the theory of relativity with James Clerk Maxwell’s electro-magnetism led to mathematical formulations which were rejected at the beginning. He accepted them only because they were beautiful. Einstein objected to them, and it was only after they were published – ten years after they were published or so – and the event of quantum mechanics, that people began to see that these were true. So the guide to the veracity of the equation was its beauty.

Ard: So that’s a really surprising thing.

SZ: Yes, indeed, extremely surprising.

David: It’s more than surprising, it’s just mysterious. Why should it be that way?

SZ: Well, I’m still surprised by it. You know, I’ve got the authority of people like Paul Dirac and Hermann Weyl and Michael Atiyah and others who speak about these things. It is shocking in a way that you find something… You said you were ‘blown over by it’. That’s a dramatic turn of phrase, but apparently it is true.

Now, in the same way, I think there are people who are extremely moved, and indeed are blown over, by the first sight of the Pietà of Michelangelo. It’s a very deep, emotional experience which is very difficult to recapture outside this frame of actually seeing it. So these are the sort of things which lead you to ask the question, what is the use of beauty? Darwin saw it as only a question of sexual selection, which of course it is, but that’s not the only thing. It’s doing a lot more.

David: But isn’t there something strange that the bit of the brain that says that bit of mathematics is beautiful is the same bit that says that this sculpture is beautiful. Why should that be?

SZ: I don’t think that bit of the brain says anything about this bit of mathematics is beautiful. I think all that happens is that when the Michelangelo Pietà, or the mathematical equation, satisfies something in the brain, then you experience beauty, and then you have activity that correlates with the experience of beauty. I don’t think there is an area which… It’s a question of satisfaction and pleasure and reward.

Frank Wilczek

Beauty and evolution

‘One form of beauty that goes really deep, and is closely related to the beauty that we find in the deep structure of the world, and the reason we find that beautiful, is the beauty of making successful predictions.'

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BEAUTY AND EVOLUTION

Ard: So in your book you ask the question, is the world a work of art? Or you phrased it differently: is the creator an artist? So is the creator an artist?

FW: Well, I’m a little bit hesitant to say that there is a creator because that gets all tied up with all kinds of issues with people having prejudices about what the creator is. We can talk about that, but let’s not start that way. But for purposes of elucidating this question of does the world embody beautiful ideas, I think it’s very useful to think about a case where beautiful ideas do get embodied: that’s what artists do; that’s sort of their characteristic activity they have. And so rephrasing the question, ‘Does the world embody beautiful ideas?’ Is, ‘Can the world be fruitfully considered as a work of art?’

Ard: And the answer is…?

FW: And then if it is a work of art, is it a good one? And I think the answer is yes. That’s how I try to think about it and make the case in the book that that is a fruitful way of thinking about it. If you think about it in that way, you are led to very interesting perspectives and ideas both on the world and an on art and perception and what beauty is. It’s a very fruitful question.

David: When you talked about beauty, you talked about it in terms of we have expectations, and if I understood you right, it’s something to do with… we develop theories, we don’t have enough data and so that leads us to have expectations. Would you explain that to us?

FW: I think one form of beauty that goes very deep, and is closely related to the kind of beauty that we find in the deep structure of the world, and the reason we find that beautiful, is the beauty of making successful predications.

I think beauty in general, plausibly, is the way humans describe things that they find rewarding and want to go back to, so it’s things that stimulate their reward system. And one important thing that evolution would want our reward system to reward is making successful predictions about how the world is going to work. There are many other things that beauty can be and that our reward systems respond to, but that’s one.

David: And you think it’s an important one for science?

FW: I think it’s the important one for science. The idea that you get rewarded and you find it beautiful to make successful predictions about how the world works, and the strategies for making successful predications match the way the world works, like they have to, that’s what they are.

So I think the most primitive version of that has to do with perception. We have to learn how to see when we’re children. So we have to learn how, if we see something from one vantage point, we have to be able to anticipate how it’s going to look from another vantage point. Just by solving problems like that, unconsciously, we get lessons in symmetry and geometry. In music when we sense harmonies, we are finding patterns in the tonal excitations, the vibrations that are arriving in our inner ear.

David: So you think harmony in music is like this as well? You get some sense of how you expect the music will unfold?

FW: Yes, very much so. The first great discovery in science, I believe, was Pythagoras’ discovery that the musical tones that sound good together are tones whose frequencies are in small whole number ratios. Those are the ones whose patterns of vibrations follow simple regularities and allow us to predict, knowing part of the signal, what the rest of it is going to look like, successfully.

David: Is that the one where he says that will give you one note, and then if I half it, it will give me another note and they will sound good together?

FW: Yes, that’s an octave. They will sound good together because they make a predictable pattern, and we can predict from seeing a little bit of it how it’s going to unfold. But, if it’s a little bit off, that’s the worst because then you make predictions, but they’re wrong.

David: Sometimes, a piece of music, you’re following it along, and part of your brain is thinking it will be like this; now you’re right, if it goes like this [makes a strange honking noise] and it’s sharp, that’s awful. But sometimes they do something which isn’t what I expected… so they break a rule, but somehow they do it…

FW: But they do it in a very special way, just a little bit, in a way that’s interesting, not an arbitrary way, not just hitting a sour note. And I think that is also consistent with these ideas, because what’s rewarding is not only making successful predications, but learning how to make successful predictions.

So once you’ve learned about simple harmonies, you’re not learning from that anymore; you’ve mastered that, so now you can add something that you would have thought was not harmonious before, but you’re ready for it, and you’re becoming more sophisticated in your predictive abilities. And you want that because you want not only to be making successful predictions, but making a wider expanse of one of them to learn how to make successful harmonies.

David: I can see that works both science in and music.

FW: In music and in art, generally. I think novelty is a very important part of any sophisticated experience of beauty.

In the advanced forms of physics now which applies to sub-atomic realms, super-duper cosmic scales, these are things very far removed from everyday life, and this evolutionary drive to understand our interaction with the world better doesn’t really apply. Nowadays we reverse the process: we guess on the basis of what would be a pretty description, what would be a beautiful description, what would bring things into orderly patterns.

And of course it’s science, so you have to derive consequences from these guesses and check them. But what we found in several remarkable cases over the course of the late 19th, 20th and now 21st centuries, is that that procedure works. It’s not a matter of wishful thinking: there are mountains of quantitative data with very precise experiments that show you that it does actually work – that beautiful concepts that we hope will work, sometimes actually do work.

Frank Wilczek

Examples of beauty and truth in science

‘Dirac, in trying to find an equation, was led by an instinct for simplicity and beauty, and when he found the trick that made it go.’

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EXAMPLES OF BEAUTY AND TRUTH IN SCIENCE

Ard: Could you give me one or two of your favourite examples of someone making a theory about the world guided by beauty that then turned out to be empirically true?

FW: Paul Dirac was faced with the problem of devising an equation for electrons that satisfied both the principles of quantum mechanics and the requirements of the special theory of relativity. This was a difficult problem that several people were trying to solve. Dirac, in trying to find an equation, was led by an instinct for simplicity and beauty, and when he found the trick that made it go, it was so compelling that he knew he was on the right track.

He tells a story that he didn’t dare… He didn’t want to work out the consequences because he was afraid it might be wrong. So it took him a while to actually take it out of his desk and do the calculations, but it turns out that that’s correct: that’s called the Dirac equation.

So it solves the problem that you’re trying to solve, but also it has more solutions than he was looking for, of a different character. And what these solutions represented was a new kind of thing, an anti-electron, now called the positron, and that particle was duly found about a year later.

Ard: That was the first time they found anti-matter?

FW: Yes, that was the first example of anti-matter.

David: You said you had a second example.

FW: Well okay, for my second example, thrusting modesty aside, I’m going to talk about my own work, my own early work on the strong force – this is the work for which I got the Nobel Prize.

David: And the strong force is?

FW: There are four basic forces of nature according to our current understanding. There is gravity and electromagnetism, which are the classic forces for which there have been beautiful theories for quite a while. And of course electricity and gravity have been known as forces for a very long time, going back to the Ancient Greeks or even further. People have been falling down for a long time.

But in the 20th century, when physicists started to examine the interiors of atoms, especially what happens inside the cores of atoms, the atomic nuclei, they found that electricity and gravity weren’t sufficient to account for what was going on at all. You needed two, not one but two, distinct new forces, and those were imaginatively called the strong and weak force.

The strong force is what is responsible for holding atomic nuclei together, and at a deeper level, when we learn more about it, we learn that the building blocks of atomic nuclei, protons and neutrons, in fact aren’t the elementary particles: the elementary particles are quarks and gluons out of which the protons and neutrons are built.

So the strong force is the force that is the most powerful force in nature that acts between quarks and gluons. It’s what they do most of the time, and when I was a graduate student, there was no decent theory of the strong force. There was nothing that could remotely be compared with Newton’s equations for gravity or Einstein’s general relativity or Maxwell’s equations for electromagnetism.

Now, you could imagine dreaming up all kinds of equations, but we focussed on equations that were beautiful: equations that had a certain simplicity and mathematical elegance.

David: And you decided to do that?

FW: We decided to do that; it was also all we could do. The calculations aren’t easy to do, first of all, and, secondly, if you start to consider complicated theories, there was not enough experimental information to sort that out.

So the only hope, really, in retrospect, was to follow the principle I discussed earlier in this anthropic explanation of beauty: that is guess that the description is going to be beautiful, work out the consequences, and check whether nature agrees. So in a nutshell that’s what we did. We guessed a particular kind of equation, which is an equation of extraordinary beauty that generalises the Maxwell equations of electromagnetism, in a very… I call it the Maxwell equations on steroids.

David: Was that a joy to discover?

FW: It was a great joy to discover. It was also nerve-wracking because, first of all, gluons at that time were just a word. There had to be some kind of glue that held the quarks together, and quarks were kind of a shadowy notion, too.

David: So this was quite an amazing experience because there is all this vague data around, and what you’re saying is that you took the equations and focussed on what you thought was beautiful, that made completely counter-intuitive predictions that then ended up being true. That must have been an amazing experience, even as an emotional experience just to see that.

FW: Yes, it was quite something.

Ard: And beauty played a big role?

FW: Beauty played an absolutely crucial role because we could only try equations that were beautiful, basically, and if the answer had been complicated, messy, not beautiful, we never would have found it.

Semir Zeki

Can you measure beauty?

'I don’t think you can experience beauty unless you have a brain. At least I am convinced of that. And, given that, I don’t think you can have a complete theory of aesthetics without taking into account the way the brain handles such experiences.'

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CAN YOU MEASURE BEAUTY?

David: Was there some significance to you, beyond what you’ve said, of finding that it’s the same part of the brain that’s linked to the emotional brain that lights up for mathematical beauty and other kinds of beauty? Is that what people expected before? Is it what you expected?

SZ: No, no, no, no, no, no. I had no such expectation. There were any number of possibilities. There was the possibility that this part of the brain did not light up. There was the possibility that the regions of the brain which are critical during the working out of mathematical equations would be lighting up. It could be, perhaps, the audio-visual area is lighting up. So there were no expectations, but it just happened to be same area, which actually mildly surprised me because the experience of mathematical beauty is derived from a highly cognitive source, whereas visual beauty is a very elementary visual source.

And the other thing which had been a critical issue in the philosophy of aesthetics, is can aesthetic judgement ever be quantified? And the answer is yes, in the sense that when you declare something is more beautiful, and these are all declared in writings after the experience, then the activity there is higher than when you find something less beautiful.

So, in a sense, philosophers should be the last people to be upset by these things because they have always spoken about beauty in abstract terms. If you look at John Locke or Hume or any of these people, or Plato or Aristotle, they don’t talk about visual beauty or assimilable beauty, they talk of poetic beauty, beauty in drama, beauty in music, beauty in, in painting and so on.

David: So they’re saying that beauty of itself is a part of the universe. It’s an abstract thing but…

SZ: Well, I wouldn’t put it like that. I would say that activity in a given, specific part of the brain correlates with the experience of beauty. So, if you were to sit down and say to me, you know, ‘Look, I know that you’re only a neurobiologist, and I know I shouldn’t be addressing this question to you, but it’s late in the night. Let me ask you, what is beauty?’

So I would say to you, ‘Look, I can’t tell you what beauty is, but I can tell you a characteristic of beauty which every time you are going to experience it, you’re going to have your medial orbitofrontal cortex increase its activity.’

I’m not even going to say it’s because of something beautiful, but it correlates with it. So I can give you a definition of beauty. I can tell you that when you experience beauty in Hagia Sophia or in the windows of a church, in Mexican sculptures, or the paintings of Cézanne or Poussin, then I can predict for you that you will have activity in the medial orbitofrontal cortex while you experience beauty. So that, I think, is progress.

Ard: Yeah, it is progress, but all you’re saying is it correlates. Beauty is infinitely more than the bit of my brain lighting up.

SZ: It is infinitely more. It’s infinitely more than the beauty of your brain lighting up. It’s infinitely more than a particular part of your brain lighting up. But I don’t think you can experience beauty unless you have a brain. At least I am convinced of that. And, given that, I don’t think you can have a complete theory of aesthetics without taking into account the way the brain handles such experiences.

Now, these are shocking words to many people, but it doesn’t matter. I think many people would say it’s got nothing to do with the brain, beauty exists outside. I’m happy with that statement. I don’t necessarily agree with it, but I would not care to spend time challenging it.

But what I’m saying to you is if you want to have a complete theory of aesthetics, then you must take into account the organ which is responsible for experiencing something that’s beautiful.

Ard: What you’re saying is not that this is the whole of beauty in the brain, this bit lighting up?

SZ: Now this is an important issue you’re raising. These are the usual criticisms directed at us: ‘You are a reductionist, and you are this and you are that. You’ve discovered the pleasure centre; you’ve discovered love centre’. All of this is not true.

David: Or the God Spot, that’s a favourite one.

SZ: Yes, the God Spot. And all of this – the ‘Moral Molecule’ – is not true. I mean, all you’re saying is there is one area of the brain which is especially active when you experience something. You do not say if you cut that bit out and put it in a Petri dish that you would experience beauty. So you’re not saying that it works on its own. But I think that science cannot proceed without reductionism. It’s out of the question. I mean, you cannot ask, what is the structure of this table? You’ve got to ask about the molecules, the subatomic particles.

David: But it’s not the whole story, is it?

SZ: Of course it’s not the whole story. But in order to proceed, one has to do a bit of reductionism. I mean, I find this a very, very trite and silly sort of stone to throw at you, and in a way, it shows a bankruptcy of ideas. You don’t know what else to throw so you throw that.

Ard: But you can imagine the kind of emotional sense somebody has. They see this and they think Professor Zeki has taken beauty and broken it apart and put it into the brain.

SZ: Yes, well, look, Professor Zeki hasn’t done anything of the sort. What Professor Zeki has done is to say to you, ‘Look, you are experiencing beauty and it’s interesting to me to know what happens in your brain when you experience beauty.’ He’s not trying to explain beauty: he’s just trying to understand the brain, which is a different thing. But people, for reasons I do not understand, are afraid of anything that probes into more complex human characteristics.

I think that there is a fear, which I can’t explain, in any attempt to try and explain things like the experience of beauty, or the experience of desire, or the experience of love. I don’t know why people fear this. They think it is too reductionist. They think you are always trying to explain a very complex phenomenon, and they put words into our mouths which are not there. I mean, nobody, no scientist I know, said that they’ve seen the love centre in the brain, or the beauty centre, or anything like that.

Frank Wilczek

Simplicity and symmetry

‘If I take a circle and rotate it, it doesn’t change. And some of the most beautiful things in physics and mathematics have exactly that symmetry property that makes them especially unique and compelling.’

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SIMPLICITY AND SYMMETRY

David: When you say beauty, what do you mean, because obviously there are different kinds? What is it in physics and science that you think this is what is beautiful?

FW: There is a phenomenon that lots of people agree on what is beautiful. First of all, professional mathematicians and physicists have largely overlapping intuitions and feelings about what they find beautiful.

David: And what is that?

FW: It’s easier to experience than to describe. I think it has to do with structures that have much more consequence than you might have thought. You get out much more than what you put in, and also that have a kind of inevitability that you can’t change them very much without either ruining them or not changing them.

An aspect of symmetry is that if you try to change a symmetrical object, like take a circle and rotate it, it doesn’t change. And some of the most beautiful things in mathematics and physics have exactly that symmetry property that makes them especially unique and compelling: if you try and change them, they refuse to change.

David: So it’s sort of telling you that this thing must be really important. It’s fundamentally down there, you can’t just...

FW: It’s like the circle of equations, which is a very special kind of equation. Equations for quantum chromodynamics, this theory of the strong attraction, are very much that way. So I can point to aspects of what beauty is.

David: So symmetry?

FW: Symmetry and productivity, or I call it exuberance sometimes: the idea that you get much more out than what you put in. These equations, or material structures, atoms, that can be put together in ways that are compelling and very productive, and a very small number of laws. You can write the laws of fundamental physics, as we understand them, easily on a T-shirt, in an honest way.

David: And the universe pops out?

FW: The universe pops out.

Ard: From these beautiful equations.

David: And simplicity. You talked about simplicity.

FW: Well, simplicity has to be understood in a special sense. It’s simple in this sense that you can describe it, in principle, in a computer code, for instance, that’s very definite and that’s not very large.

David: In the book you used the example of Mandelbrot set. Is that what you mean? Because to generate the Mandelbrot set is just a few lines of code, isn’t it?

FW: Yes, that’s a very nice example, where you have just a few lines of code that can spin out these marvellous structures and consequences, and that’s the case where you can really see it at work. And if you have the patience you can watch the computer build up the Mandelbrot set before your eyes.

David: I have one last question which relates to that because you have a lovely quote from Hertz which I loved in the book, and I thought it was just… I was fascinated by the fact that you obviously loved this quote where he says you get this sense that the ideas...

FW: They are wiser than their creators.

David: Can you quote it?

FW: [Reading quote]: ‘One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.’

That was Hertz describing the Maxwell equations, and he was entitled to because he did crucial experiments that got more out of the Maxwell equations than was put into them – things we now call radio and electro-magnetic waves – but it expresses his own experience. But it’s got much better since then in terms of the strategy of guessing beautiful equations and finding that those actually describe the world. That reached new heights in the 20th century with the two theories of relativity, and especially in quantum mechanics, and even more especially in the theory of the strong and weak interactions where beauty was absolutely necessary to find those equations in a practical sense.

Ard: And then the equations, would you say they were wiser than us?

FW: Oh, by far.

Ard: What does it mean that the equations are wiser?

FW: That means that you devise the equations to explain one thing, and then you find that they spin out consequences that you weren’t thinking about and had no way to anticipate.

David: And that must be a joyful experience.

FW: Oh, it’s the most joyful. It’s an extraordinary experience. It’s one of the highest experiences there is. I guess the thing that it could be compared to is when you have a baby: the baby is attractive, but the baby will unfold in ways you can’t possibly anticipate. This is like that, but there are lots of babies and we learn to anticipate how babies behave. When it happens with equations and concepts it’s somehow less familiar.

David: Well, it’s extraordinary that it should be so, isn’t it?

FW: And it’s sort of on a larger scale. A baby is one person, and that’s fantastic in its way, but when you find suddenly you can understand how the universe was made, or predict how unexpected new particles are going to come out, by doing very elaborate and tricky experiments and analysing them in particular ways, you’re getting out much more than you put in.