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.