Ard: There’s sometimes, I think, a stereotype of scientists trying to unweave the rainbow and trying to, you know… if we once we’ve understood something, then we can reduce it to its components, and then…

GC: That destroys it. That’s reductionist.

Ard: That’s reductionist.

GC: Yeah, we’re destroying the beauty of everything. We’re destroying the sacred and making it secular and prosaic by understanding it. I don’t feel that way. I feel that it’s absolutely inspiring that puny human beings are able to have such beautiful theories.

Ard: Four forces…

GC: Yeah, there’s general relativity, there’s quantum mechanics, there’s electromagnetism and there’s Newtonian physics. And these are… are tremendous landmarks. They’re like crystals. They’re places where you can see that the universe actually… that mathematics is relevant.

Mathematics is not relevant to everything. For example, I don’t think it’s relevant to biology, and in Proving Darwin I tried to think, what is possible? What kind of mathematical theories might be possible as fundamental theories for biology? So what I see biology is all about is tremendous creativity: where new ideas come from, biological ideas. And I see that connected with mathematical creativity.

I don’t believe that there is a direct mathematical biology, like there is… mathematical physics is deeply mathematical. I don’t think that biology will ever be that way. So I propose creating a theoretical biology at one remove from real biology. It’s a toy model working with a model of biology which I call meta-biology. And that’s the idea. Instead of studying what happens when you… the evolution of making random changes in DNA software, DNA programs. What happens if you make random mutations in computer software and subject it to selection? So this is much simpler than real biology and has some mathematical ideas and is mathematically tractable. I don't know how far this idea will go, but that’s the kind of thing which I think might be possible in biology.

Understanding it is a patchwork quilt. No one idea is enough to understand biology. Population genetics is splendid, but creativity has sort of gotten lost in all of this. And I wanted to bring the focus back to that, which for me is the central issue.

Ard: There’s a very famous quote by a Dutchman, Hugo de Vries, who said, ‘Natural selection explains the survival of the fittest, but doesn’t explain the arrival of the fittest.’

David: Yes, that’s nice.

Ard: Where do new species come from? Where does biological creativity come from? And that’s in the variation. And that’s what your book is trying to do.

GC: That’s what I’m trying to do.

Ard: You’re trying to say, where does that creativity come from in the first place?

GC: I’m trying to propose a possible framework where this question can at least be asked, because in conventional population genetics, it can’t even be formulated.

David: Which leaves out the very engine of natural selection.

GC: Well, it depends if you’re interested in micro-evolution, which is sort of small variations, or if you’re interested in taking a broad perspective on the sweep of things and the major transitions in evolution, which is like when you go from single-cellular to multi-cellular, when you go from plants to animals, where the brain comes from. Those are major transitions in evolution, and those are much more mysterious.

There’s this tremendous outburst of creativity that takes place in a relatively short period where you find nature seems to be trying out every possible body plan. It’s just fabulous, and it just seems to be too fast, perhaps.

But if you think of genomes, entire genomes as software, a small change in a program can make an enormous change in what it does, in its output. So from that point of view, I think abrupt change doesn’t seem quite so mysterious.

Ard: People often think about mathematics, and even science, as just being a closed machine. And so what science is telling us is that we’re just machines, and if we’re just machines then we’re predictable.

GC: I hate… I detest that point of view.

Ard: You detest that point of view because you think it’s wrong?

GC: Well, look at Euler. Look at Ramanujan. Look at… Let’s take my favourite mathematician, Cantor: his theory of infinite sets which is really mathematical theology.

GC: So the stuff I’m working on is like a lower-level version of this. It’s a little more down to earth than Cantor’s infinities, and greater and greater infinities. But the whole question – the whole issue in both cases – is creativity, an open system.

David: You contrast one view of mathematics with another. And we’ve talked about one kind of science: the let’s just take it all apart and reduce it and claim that we’re machines. Is there something at stake, do you think, for you? For us?

GC: Well, there’s definitely something at stake. I want to save the human soul. One has to save the human race. If we think of ourselves… maybe we are machines. What do I know? But I think the idea of thinking that we’re just machines is a destructive idea. Even if we are machines, I think it’s better to think we’re not machines. I’m not saying that we shouldn’t do science to understand as much as possible how the brain works, how the body works, but if the human brain is a machine, it’s quite an amazing machine. It’s a machine on a level so different from our current machines.

David: So if we imagine that we are a machine, we need to be very careful about what kind of machine we imagine ourselves to be?

GC: This is a radically different kind of machine. And it’s a concept of a machine that will end up being totally un-machine-like. So in the end the machine and the sacred may meet.