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Frank Wilczek is a theoretical physicist from the US. He was jointly awarded the Nobel Prize in Physics in 2004, along with David Gross and H. David Politzer, “for the discovery of asymptotic freedom in the theory of the strong interaction”; research that helps us understand how some of nature’s smallest building blocks – quarks – work together.

Your new book, A Beautiful Question, argues that some of nature’s fundamental laws mirror artistic ideas of beauty. How does that work?
The kinds of beauty that are most embodied in physics are symmetry on the one hand and exuberance on the other. Symmetry gives us mathematically ideal building blocks and exuberance means that these rules can be stacked up on one another to make very elaborate structures. These are themes that people for centuries have embodied in their art, especially decorative art.

Why is symmetry so important?
The word symmetry in general use is fairly vague and has connotations of balance and harmony. In science and mathematics a definition of symmetry is “change without change”. That could apply to objects like circles where you can rotate them on their centre and every point moves but the circle as a whole doesn’t, or to equations where you can change the different quantities in the equation without changing its ultimate content. More and more in the 20th century, especially with the development of quantum theory, symmetry has been our guide to formulating the laws of fundamental interactions. We have to guess the patterns in advance and then see if the evidence bears them out. So aesthetics of that kind has been a blessing, because it’s worked.

And how does symmetry lead to “exuberance”?
In decorative art, typically the elements are symmetric things like triangles and circles. But you move them around to make bigger patterns and vary them. Think of mosque interiors, where they put together patterns that are very large in scale and play with colours. That’s something that is very reminiscent of the fundamental structure of the world. In the physical world you can have simple rules for electrons and quarks and gluons, but if you have lots of electrons and quarks and gluons then you can make elaborate molecules; you can make Large Hadron Colliders; you can make people.

You also argue that a search for beauty in nature motivated the “heroes” of science throughout the ages. Who’s your favourite?
I have many heroes and heroines, but if I had to choose one, I would say it was James Clerk Maxwell. He’s famous for fundamental discoveries in physics, especially the laws of electromagnetism, but he also did work that greatly clarified the nature of colour perception, or work on the stability of the rings of Saturn, where he proved they couldn’t be solid. He had this extremely playful approach; the combination of power and purity and at the same time lightness – all that is what I aspire to.

Does this “search for beauty” mirror religious faith in any way?
I like to say, “Trust but verify.” I don’t think that religion at its best necessarily contravenes that principle. If you really have faith you should look for confirmation in the world, not be afraid of it.

Can religious believers be good scientists?
One thing I’ve come to treasure is Niels Bohr’s concept of complementarity. This is a theorem in quantum mechanics where you can ask about the position of a particle or the momentum of a particle and get sensible predictions for both, but you can’t ask both questions at the same time. The more general principle is that there can be different ways of regarding the same system, but each is valid in its own terms and gives insights that aren’t available to the other. I think it’s possible for people to have rules they live by, codes of behaviour, traditions and so forth that are valuable in themselves, have an inner coherence, add to their experience of life and make good communities that are different from ways of organising the world scientifically; each can be applied in a useful way to reality and life but it’s not necessarily the case that you can apply them at the same time. Scientists like Maxwell and Isaac Newton were very religious people, but when they came to do science they engaged the world objectively.

Are you saying there are some areas science shouldn’t enter?
David Hume insisted that there’s no way of getting from statements of the form “is” to statements of the form “ought”. That looks pretty convincing to me. If we want to discuss goals, to discuss morals, principles, we need something else than just learning facts about the world. Learning facts about the world can help us make intelligent choices, if we want to know what actions will cause what effects, but I don’t think it can set the ultimate principles. That has to come from somewhere else.

Has the search for beauty ever led scientists to the wrong conclusions?
Yes, one was Plato’s early theory of atoms based on the most symmetrical solids; the ones now called the Platonic solids. There are only a few kinds, so it was natural to propose those as building blocks. It was a brilliant idea and in a very broad sense anticipates modern ideas, the kind of guesswork I mentioned. But from a modern perspective Plato didn’t do a very good job of “trust but verify” and the details of the theory are just wrong.

What about ugliness in nature?
At present there are loose ends that don’t have any apparent beautiful pattern in them. The pattern of quark and lepton masses, and details of how they decay into each other, is very complicated. So that doesn’t look beautiful. We don’t understand what the dark matter or dark energy in the universe is.

I think the dark matter might have a beautiful resolution and I think I know what it is, actually, but the dark energy looks very obscure at present and may take a long time to clarify. So at any time there are frontiers where things haven’t yet become beautiful and, who knows, maybe never will. But we can only try.

A Beautiful Question: Finding Nature’s Deep Design is published by Allen Lane