David: So how come you described yourself once as a Platonist? What does that mean?
MG: The notion of being a Platonist, and the fact that even Plato wasn’t as much a Platonist as the ones who followed him, this whole idea of Platonism simply means that there is truth in mathematics. That nature is mathematical. That if you want to understand the hidden code of nature, you have to do it through mathematics, and only through mathematics.
David: And did you used to believe that? Was that your philosophy?
MG: Yes, because it’s a very compelling idea. Because when you say 2+2=4, there’s some finality to that statement. You can hold that and say, ‘I know that,’ and that gives you a sense of safety, of security.
So you don’t want flakiness when you’re trying to pursue the quest of understanding everything. You want the most profound kind of truth that you can find. So if math can give you that, you embrace it with all your might.
David: And Ard has, I think!
Ard: Yeah…
MG: And lots of mathematicians and lots of physicists believe that. They believe that the fundamental core of nature is essentially pure mathematics.
David: And you’re saying you’ve moved away from that?
Ard: You don’t believe it anymore?
MG: No, I don’t believe that anymore. I think that mathematics is a human invention.
Ard: Oh!
MG: It’s a product of how we evolved in this very specific planet to make sense of things and to survive. So there are certain things in mathematics which are definitely true. So if you’re an intelligence that can count, you know, one, two, three, four, then you can develop the sense of a set of integer numbers, and from there you can go on and do other things. But there may be intelligences that do not count.
There’s this famous mathematician from England called Michael Atiyah who had this image of this intelligent blob that lived at the bottom of the ocean. It was dark. It didn’t move. It didn’t have to collect any food. The food just came to it from above, and all it sensed was the flow of currents. So this intelligence created a super-sophisticated hydrodynamics – the physics of fluids and how they move about – but it would not count because there was nothing to count, unless it could hear its own heart beat or something like that.
So the fact that you’re intelligent does not mean that you have to create the integers. It really depends on the context in which you evolved.
Ard: Would you say that’s a lack that it had?
David: I’m not convinced by that, because surely the prime numbers would still be prime, even though this creature hadn’t discovered…
MG: What if there are no primes? There are no numbers?
Ard: If you don’t experience numbers, you may or may not be able to count with them, but that doesn’t mean that they don’t exist.
MG: It exists to whom? I mean to that blob? It exists, and that’s all that matters, and it would know a lot about plasticity and shapes and the form of shapes, continuous…
David: That’s quite radical, isn’t it?
Ard: My dog doesn’t know about prime numbers, but that doesn’t mean they don’t exist.
MG: Right.
Ard: It’s because it lacks the intelligence, or maybe the experience of them.
MG: Where do they exist?
Ard: Who knows?
David: I asked this question and they laughed at me.
Ard: I think they’re non-empirical realities, but what’s wrong with that?
David: What’s a non-empirical reality?
Ard: Something you don’t need to measure in order to know that it’s true.
Ard: For example, in physics, Sir Roger Penrose gave us the idea of complex numbers, or imaginary numbers.
MG: Mm-hm.
Ard: So it’s very strange… it surely looks like an invented thing – the square root of minus one – but it turns out that it had all this surprising richness to it that eventually allowed us to formulate quantum mechanics in that language. So, the argument is that you have something that seems very abstract and made up, but then it turns out to have a life of its own, and not only does it have a life of its own, but it ends up being able to describe things about the physical world that you didn’t know about when you came up with it. That’s very surprising.
MG: It’s surprising to a certain extent.
Ard: Okay.
MG: Because physicists are really good at picking the bits of mathematics that are useful.
Ard: Sure.
MG: There are all sorts of mathematics that are completely useless. To physics, they’re not picked. So I wouldn’t jump to conclusions like that, because, I think, at the very bottom of this question is the following question: what comes before, mind or reality?
Ard: What does that mean? Mind or reality?
MG: So the people that say that mathematics is the language, is the code of nature, they’re basically saying that there is mind before everything else. There is sort of almost like some sort of metaphysical plan to reality, which is that mathematics is the fundamental blueprint of everything that exists, and we’re just discovering that stuff because it’s just there. We’re just plucking the fruit.
David: A lot of mathematicians we’ve talked to have said that.
MG: Yeah, the pure mathematicians.
David: ‘We’re not making this up. We are discovering it.’ And you don’t think that?
Ard: You don’t think it’s true?
MG: Well, I don’t know it’s true, but I don’t agree with that. I think that first comes reality. Not just reality, but the parts of reality that we can observe. Then our minds try to make sense of what’s going on, creating concepts which are useful to us.
So, for example, if you go way before mathematics, if you were a hunter-gatherer in some forest and you couldn’t distinguish between the brush and a panther, you die.
So, clearly pattern recognition was incredibly important to the survival of humanity way before there was mathematics. So our brains were moulded in such a way to favour certain things over other things so that we could thrive in an environment which was very hostile. One of them was the notion of pattern recognition. The other one was the notion of ordering. So you wanted to order things – you order space; you order time – so we created this mathematics and then the science based on this mathematics because it was very useful to us.
And so, to me, what we are trying to do, is we are trying to use our minds to describe the portions of reality that we can. And then, of course, as we evolve as a species and we learn more about reality, we pluck more math and more math and more math to do that job. And so there is a very productive, symbiotic relationship between our minds and reality.
But the notion that there is a grand plan in nature which is mathematical, and we’re just trying to uncover that, sounds to me very crypto-religious. It’s very much like some sort of medieval cult and that God was this supreme mathematician, and the job of scientists is essentially to uncover the Truth – with a capital T – which is reading the mind of God, so to speak.
Ard: And you don’t like that?
MG: I don’t like that.
David: I love the idea that you’re part of a medieval cult! This is great! This day is getting better and better.
Ard: That’s why you want to be careful around me late at night! But you don’t like it because you think it smacks too much of religion?
MG: I don’t think we need that. I don’t think that we need that in order to make sense of things…
David: Even if we, as you were saying, create the beginnings of mathematics, isn’t it that once you’ve created it, there are a whole load of consequences which flow from that first stuff? In some sort of theoretical sense, all of those consequences of what you started with, they’re already there, and you are now going to discover them.
So there is a process of discovery. In other words, we’re not free to make up the next bit of mathematics any old way. The next bit of mathematics is already decided because of the few things we invented at the beginning. So in that sense we really are. So you could forgive people for thinking, ‘My god! That was there before I got there. It was waiting for me.’ Because, in some sense, it really was. It didn’t need to be put there by God, did it? It was just a consequence of the first few ideas that we had.
MG: Could you argue the same way about music?
David: Precisely. I would say yes.
MG: Because, you know, music is… once you have the notes, everything else follows. So any species that is intelligent enough to understand that there are musical scales can come up with all the symphonies that… because they’re just waiting there to be discovered, right? And I think they are not. They are just being created by this very clever neuronal network that we have in our heads that allows us to do these wonderful things. I think… Let me put it another way…
David: Okay, go on.
MG: I think that to say that everything is out there…
David: I’m not saying everything.
MG: But it’s taking away from how amazing humans are.