David: We’ve been talking about the notion that some ideas are just there, like mathematics is an idea.
DN: Ah, that’s very interesting, mathematics. Where is that?
David: Yes, thank you. Precisely!
DN: Where is it?
Ard: I just think, ‘Where is it?’ is the wrong question.
DN: Exactly. It’s the wrong question.
David: The wrong metaphor?
DN: The where question is the wrong question.
DN: There is a sense in which it exists, because mathematicians discover, they don’t invent.
Ard: We sense very deep in our bones that we discover. We were talking about Paul Dirac earlier who used mathematics to look at the electron, and what happens if the electron goes fast, and from the mathematics came anti-matter: that’s something that you discover, it’s not something that you…
DN: Exactly so.
David: But then this notion of discovering makes me think, in my metaphorical misery over here, that you discovered this realm of ideas. Where are these ideas?
DN: Okay. Realm is okay, provided we don’t think it is a where.
David: No, okay.
DN: I cannot go to the realm where ideas are.
David: Okay. But exist in what way then? Because conkers exist as conkers and plants exist as plants, in a reductionistic, material world.
DN: But the square root of minus one does not exist.
David: Yes! How does that exist?
DN: Now, you see, that’s a lovely example, because go back to my rhythm in the heart: if you want to describe that, interestingly enough, one of the ways of describing that is to use in your mathematics the square root of minus one. Now the square root of minus one clearly does not exist, but the idea has a fantastic utility in mathematics. So I think you’ve got to see those ideas as tools.
Ard: Yeah, it’s a nice example. Because the square root of minus one…
David: It’s an imaginary number.
Ard: .It’s an imaginary number, and yet in oscillations it’s incredibly helpful and useful.
DN: Absolutely, yes.
Ard: And, actually, it has a kind of explanatory power that allows us to peer much more deeply into the universe than we would have been able to without it. And yet, there it is.
David: But you can see my problem, though, can’t you? How do ideas exist? Because they don’t exist in the same way that reductionists like.
DN: Indeed so. But doesn’t that, as it were, induce a sense of humility?