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.
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.
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.
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.
David: Running through our conversation has been this sense, listening to you, that ideas, in your example ideas, that you find beautiful, are very powerful: they can guide what you think and what you do next. Do you think that ideas really do have that power? That they are as much a force in the world as the basic forces you are thinking about?
Because non-scientists tend to think physicists are always going to say that everything that happens is just these particles bumping into each other. And here you’ve been talking about it as if thoughts themselves shove the particles around: it was the thought which led you to the next idea. Do you see what I mean?
FW: Yes, I think I do.
David: It’s saying the radical reductionism that says everything that happens is determined by the bumping of the elementary particles, taking Laplace to the extreme…
FW: There’s a concept that Niels Bohr elaborated that I’ve fallen I love with that I think is very profound: it’s called complementarity. It’s something that’s just a true fact about quantum mechanics but is much more general. It’s the idea that you can have different descriptions of the same thing that are both valid, and both important for answering different kinds of questions, but they are mutually incompatible. It’s closely connected to wave particle duality. There are different ways, mathematically, of processing the wave function. I think that’s a much more general principle. Well I know it’s a much more general principle, and I think that it even applies to things like the problem of free will versus determinism.
There’s one description based on physics that tells you that, for practical purposes, in principle, the brain, for instance, is a pretty nearly deterministic, noisy, but deterministic system. Whereas if we want to deal with our own experience, if we want to interact with other people, if we want to have sensible systems of law, we need to use this concept of free will. And they are both valid descriptions, but they are meant to address different aspects.
David: But you think they are both genuine? Because listening to you, it was on the tip of my tongue to say there’s the rejoinder which says, ‘Yes, but that stuff about free will: that’s just a place-holder until we’ve really worked out the physics, and really, ultimately, there’s no such thing.’
I’ve talked to scientists who have said there is no such thing as free will; there is no such thing as the self; there’s no such thing as consciousness. I’ve had all those things said to me in the last five or six years, and the answer is always the same: ‘I know you think you’re conscious, but actually it’s just the chemicals in the air and they’re buzzing around and that’s why you’re laughing, it’s not because anything is funny.’
FW: This reminds me very much of Dr Johnson after hearing Bishop Berkley’s sermon about the unreality of matter, and famously Boswell said that this seems crazy but it’s impossible to refute. And Johnson kicked a stone and said, ‘I refute it thus.’ So when people say there’s no such thing as consciousness, come on!
David: I’m with you on that, but there is that sense that…
FW: Okay, we can illuminate it. It’s like saying there is no such thing as life because we can understand it on a molecular level. Life! There are useful concepts that are necessary in describing large domains of experience that aren’t going to go away. They may have alternative complementary descriptions.
David: But you think they’re real?
FW: Yes, I think they’re as real as anything can be. They are useful. They describe actual things in the world.
David: And ideas would be one of them? That realm of ideas?
Ard: And I think what you’re saying is that they may be contradictory if you try to have them at the same time?
FW: Yes, if you try to apply them at the same time, they can lead to contradictions.
Ard: But, nevertheless, they are both true if you are asking the right kind of question?
FW: They are both useful and necessary, I think, in addressing different kinds of questions.
Ard: In your book you say, for example, objects and persons are complementary.
FW: This is very much relevant to the discussion of free will. When we are trying to predict what they’re going to do, how we should interact with them, we are thinking of them in one way. If we are thinking about them as what their height is; what their mass is; what they are as physical objects; am I going to run into this object? If I’m diagnosing a disease, I want to analyse the chemistry. That’s a different way of thinking.
Ard: And those two ways are complementary to each other?
FW: They’re complementary. They’re both valid, but there’s a lot of tension if you try to apply them at the same time.
Ard: That’s really interesting. That’s a profound point that they’re both valid ways, so the world of the person is the world of intentionality, and the world of ideas as well. And then there is the world of the human being as a wet computer, a bag of chemicals, and they’re both useful. They may even illuminate one another, but if you try and apply them at the same time, or if you say that one is superior to the other, you’re missing something.
FW: Yes, that’s a good way to put it: you’re missing out. It’s not that you’re wrong in some sense, well I think actually that you are wrong, but at the very least it becomes very awkward to express concepts of intentionality, of emotion, of ideas in physical terms.
David: So are you sympathetic then to people like George Ellis who think emergence is something that’s a useful idea?
FW: The general concept, I think, is very much in line with these ideas about complementarity: that different levels of description can be useful, and if you’re describing the same thing in different ways, it’s also important, if you can do it, to make those consistent and get a rich interconnection between the two. So yes, I have a lot of sympathy for that. But where I don’t go is, I think our description of the world based on what Newton called analysis and synthesis – and I would like to call it that, but many people call it reductionism – the idea that the way you build up the description of the physical world is by understanding very small parts thoroughly and getting a complete description of those and then building out from there. That’s been extremely fruitful, extremely successful, and I don’t see any sign that it’s open to influence from higher levels. So specifically, for instance, at an accelerator, I don’t believe that no matter how hard you think about it, you’re not going to change how the protons collide.
David: It does sound a little bit like you’re trying to have your cake and eat it too. Obviously the accelerator, you chose the example because it works for what you were just saying, but then let’s take the mind again: does that mean the next word I’m going to say is forced upon me by the particular configuration of all of those particles? Or was it that I was having a thought and the logic of the thought dictated what I would say next?
FW: If you are discussing thoughts and how they evolve, then the appropriate language is cognitive language. That’s the way that people have found useful and have developed to express and analyse the development of thoughts. If you want to know about brain events, especially at a microscopic level, then you want to use quite a different description. Those can both be valid descriptions.
David: They have to be, in a sense.
FW: I think they are, but for different questions. If you want to use thought patterns to predict how chemical reactions and atoms are going to behave, I don’t think you can get very far. There are many, many different chemical reaction patterns and things that could correspond to the same thought, and conversely only slightly different chemical patterns could lead to grossly different thoughts. So it’s not a stable, simple mapping. It’s very complicated at best, and practically useless. So that’s why you have complementary descriptions of these different phenomena that are used in very different terms and superficially incompatible – and maybe not only superficially but just plain incompatible – but, in any case, appropriate for answering different kinds of questions.