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.