[In physics] you have to have some understanding of the connection of the words with the real world: it’s necessary, at the end, to translate what you figured out into English – into the world, into the blocks of copper and glass that you’re going to do the experiments with – to find out whether the consequences are true.
This is a problem which is not a problem with mathematics at all.
[…] If you say I have a three dimensional space – an ordinary space […] – and you begin to ask [the mathematician] about theorems. Then they say, “Now look, if you had a space of n dimensions, then here are the theorems.”
“Well, yeah, but I only want the case 3.”
“Well, substitute n = 3”
and then it turns out that very many of the complicated theorems they have are much simpler, because it happens to be a special case.
Now, the physicist is always interested in the special case; he’s never interested in the general case.
He’s talking about something; he’s not talking abstractly about anything; he knows what he’s talking about: he wants to discuss the gravity law; he doesn’t want the arbitrary force case; he wants the gravity law.
And so there’s a certain amount of reducing because the mathematicians have prepared these things for a wide range of problems, which is very useful.
And later on, it always turns out that the poor physicist has to come back and say, “Excuse me, when you wanted to tell me about the four dimensions…”
