THE AESTHETICS OF THE IMPERFECT

David: You are not one of those who think that mathematics is woven into the fabric of the universe?

MG: So, the question of mathematics being the language of God, so to speak, or, sort of, the blueprint of reality, right? There is no question that there are patterns in nature. They are repetitive and they can be described through mathematics in beautiful ways.

You have not just symmetric patterns, or almost symmetric patterns – I like to make that distinction because nothing in nature is perfect. You have periodicity in the orbit of planets, and things like that. Clearly there is order, but I think to just say that this sort of symmetry in nature is the hidden code, so to speak – that all you have to look for is that symmetry – is missing half of the story.

David: What’s the other half?

MG: The other half is the role of asymmetry in nature. There is a lot of imbalance in nature, and it’s really through the complementary roles of symmetry and asymmetry that nature creates. A lot of stuff happens because of this imbalance between the two.

Ard: Give an example.

MG: I have lots of examples. One good example is in life. It turns out that proteins, which are made of chains of amino acids, like big molecules, and these amino acids they are basically molecules and they have a carbon in the centre, and then they have four sticks coming out of it. And it turns out that they come in two ways. They can be what we call left-handed and right-handed, jby the way in space they look like. And it turns out that if you go and you synthesise an amino acid in the laboratory – it was Pasteur that discovered this – you get 50/50: fifty percent with the left-handed shape and 50 percent with the right-handed shape. When you look at the amino acids in all living creatures, from bacteria to a sequoia, they all come only in the left-handed shape.

Ard: So, why…?

MG: The right-handed shape just is not there. So there is a fundamental asymmetry between the two, and without that asymmetry, the lock-and-key mechanism that proteins need to, kind of, fold and split and create, be part of reproduction, etc., wouldn’t work.

David: Hm!

MG: And we do not know why this is true, okay? We just know it’s true. It’s there. It’s fundamental for life. So that’s an asymmetry which is very important, for example.

Ard: How about matter and antimatter?

MG: Exactly, so there you go. You know, that’s the good physics example: the fact that Dirac’s equation predicts that there should be as much matter as antimatter in the universe. And antimatter is nothing so esoteric that goes up instead of down, or anything like that. It just means a particle that has an opposite electric charge but the same mass. So, for example, the electron, which is negatively charged, has an antimatter particle called the positron, which is positively charged.

In principle, they should come in equal amounts, but when you look out, you find out that there is no antimatter out there – very, very, very little. And that’s good because if there were as much matter as antimatter in the universe, we wouldn’t be here.

David: We’d have all gone, pfft!?

MG: Exactly, because matter and antimatter, when they come together, they disintegrate into a puff of gamma rays – very high-energy radiation. So if you find your anti-person walking around, don’t shake hands. And so that’s the story, and we do not know. I spent a long time trying to understand what sort of causal processes may have happened early in the history of the universe that would have biased one form over the other, and there are all sorts of ideas – none of them is very compelling right now.

Ard: Okay. That’s a big mystery.

MG: So you need both. And I think it’s this yin and yang kind of thing, you know? You can’t just look at this reverential perfection, symmetry, as, kind of, the language of God, where nature is showing you that you really need both to make sense of things.

Ard: But there is some beauty to this combination between symmetry and broken symmetry.

MG: I think so. I have been proposing that there is what I call the aesthetic of the imperfect.

Ard: Okay.

MG: Physics is a little old-fashioned, in a way, in thinking that it’s really the perfection that counts. It’s truth, right? The arts and music, they moved away from that in the early 20th century, and I think we’re still stuck in it.

Of course, symmetry’s fundamental: you cannot be a serious scientist, and physicist in particular, without having deep respect and veneration for symmetry. But symmetry is often an approximation to the real thing.

There’s this joke about the physicist that looks at a cow, and he says, ‘Consider a spherical cow as the first order approximation to what a cow is.’ And it works quite well for many things, right? If you want to collide cows at high speed, it’s a good approximation. But it’s not a good approximation if you want to milk the cows and things like that.

Ard: So do you think that when we understand biology better, that this aesthetic of symmetry won’t be the right way of thinking about it?

MG: Yes. I think life is a great example of the importance of asymmetry. You know, I have another example, which is Marilyn Monroe. So, Marilyn Monroe had a beautiful little mole. Imagine if she had two equidistant moles, how ugly she would look. So symmetry is not always beautiful. There is this breaking of symmetry, and I think we should embrace a combination of both.

Truth and Beauty in Art and Science

Ard: I liked the way you said, ‘the crystalline part of mathematics’. So mathematics has a certain austere beauty. I was just curious whether you think that narrative has a different kind of beauty sometimes, or maybe richer forms of beauty than just mathematics. A lot of mathematicians talk about beauty in mathematics, and you've spoken about this as well.

BO: What do you think mathematicians mean when they talk about beauty in mathematics?

Ard: Well, I think I recognise beauty in mathematics, and the interesting thing is we all, all of us mathematically orientated people, tend to agree on the beauty, and we tend to think this is more beautiful than that. But when you say to me, define it exactly, it's hard to put. I can recognise it without necessarily always being able to define it.

BO: Okay, I have a question for you then. Can the beauty in mathematics, in an equation, can it be there even when the mathematics is wrong?

Ard: Sometimes it can be. So sometimes we speak about a very beautiful theory which is ruined by experiment: an ugly fact. But in general, this is definitely true... there are very beautiful theories that are wrong, but, in general, if I have two competing theories for the same bit of nature I need to explain, the more beautiful theory is more likely to be the true one.

BO: But have there been cases where the ugly theory has turned out to be the truth?

Ard: Unfortunately it has.

BO: Because you have quite a few of that in literature. You do. Things are ugly. The first people who read Moby Dick didn't see its beauty. The first set of people who saw Demoiselles d'Avignon didn't see its beauty. We still don't see the beauty in a lot of cubism. A lot of modern music we still think of as being too fractured for us. So sometimes something can seem ugly.

Ard: But there are mathematical things that seemed ugly or seemed trivial at the time but ended up being very profound later, so part of that is just our inability to perceive.

BO: It's the same with literature, absolutely the same with literature.

Ard: There are mathematicians whose work was forgotten while they were alive, and then after they died we realise there was something unbelievably profound.

BO: I think it's also the nature of perception that we're only capable of seeing that which we've seen before. We're only capable of perceiving that which we've perceived before, and when a slightly new order of perception comes along, we can't see where it diverges. We can't see what it is. And because it doesn't conform to what we've seen before, we think it's either trivial, unimportant, insignificant or not beautiful at all.

You think of the great works that people did not understand at first. You think of something like Waiting for Godot, or you think of many Shakespeare plays that people didn't understand, didn't think beautiful at first, but which we've come to learn to perceive its correct inner beauty.

Ard: Is there a logic to narrative or to poetry that has to be conformed to or...?

BO: The best poetry and the best novels, the best narrative, absolutely. You can almost create a divine logic. What you're struck by, more than anything else, is the shocking clarity of thinking. You read Dante and from one line to another there are no absurd leaps. Everything has to come; it has to add up. Let’s just say there's a great rigor to the best parts.

You can always tell when a writer is faking it because the images don't add up. The narrative doesn't add up. It makes like sudden leaps that are not prepared for meticulously.

Ard: As if it's less beautiful somehow? Is that what you're saying? It's less beautiful, less aesthetic? Or is that the wrong way...?

David: Or is it less truthful?

BO: It always feels less truthful, and it is. Sometimes something can be wrong in its inner logic and still have beauty, and I think that's because beauty partially transcends logic. I think it's implied in it. I think beauty is implied in logic. I think that which we find to be beautiful is something which is logical to our aesthetic sense.