Feynman on Understanding

transcription of excerpt of video lecture of Richard Feynman


Suppose you have two theories, A and B. Both completely different psychologically, different ideas and so on. But all the consequences they computed are exactly the same. They may even agree with the experiments. The two theories, although they sound different at the beginning, have all the consequences the same. It’s usually easy to prove by doing a little mathematics ahead of time to show that the logic of this one and this one will always give corresponding consequences. Suppose we have two such theories: how are we going to decide which one is right?

No way. Not by science. Because they both agree with experiments there’s no way to distinguish one from the other. So two theories, although they may have deeply different ideas behind them, may be mathematically identical, and usually people say then in science ‘one doesn’t know how to distinguish them’. And that’s right.

However, for psychological reasons, in order to get new theories, these two things are very far from equivalent. Because one gives a man very different ideas than another. By putting a theory in a certain kind of framework you get an idea what could change. Which in theory A would talk about something, you say I’ll change that idea here, but to find out what corresponding things you’re going to change in B could be very complicated. It may not be a simple idea. In other words, a simple change here makes maybe a very different theory than a simple change there. In other words, although they are identical before they’re changed, there are certain ways of changing one which look natural, which don’t look natural in the other. Therefore psychologically, we must keep all those theories in our head. Every theoretical physicist that’s any good knows six or seven different theoretical representations for exactly the same physics, and knows that they’re all equivalent, and that nobody is ever going to be able to decide which one is right – at that level – but he keeps them in his head, hoping that they’ll give him different ideas.

Incidentally that reminds me of another thing, and that is that the philosophy or the ideas around the theory: a lot of ideas, ‘I believe there is a space-time’ or something like that in order to discuss your analyses… these ideas change enormously when there are very tiny changes in the theory. For instance, Newton’s ideas about space and time agree with experiment very well. But in order to get to get the correct motion of the orbit of Mercury, which is a tiny tiny difference, the difference in the character of the theory with which you started with is enormous. Reason is, these are so simple, so perfect. They produce definite results. In order to get something that produces a little different results, it has to be completely different. You can’t make imperfections on a perfect thing, you have to have another perfect thing. So the philosophical ideas between Newton’s theory of gravitation and Einstein’s theory of gravitation, their differences, are enormous.

What are these philosophies? These philosophies are really tricky ways to compute consequences quickly. A philosophy, which is sometimes called an understanding of the law, is simply a way a person holds the laws in his mind so as to guess quickly at consequences.

Some people have said, and it’s true for instance in the case of Maxwell’s equations and other equations, ‘Nevermind the philosophies, nevermind anything of this kind, just guess the equations. The problem is only the compute the answers so that they agree with experiment, and it is not necessary to have a philosophy, or worry about the equations’. That’s true. In a sense. Yes, and no. It’s good in the sense if you’re only guessing at the equations, you’re not prejudicing yourself and you’ll guess better. On the other hand maybe the philosophy helps you to get it. It’s very hard to say.

For those people who insist however that the only thing that’s important is that the theory agrees with experiment, I would like to make an imaginary discussion between a Mayan astronomer and his student. The Mayans were able to calculate with great precision the predictions, for example, for eclipses and the position of the moon in the sky and Venus and so on. However it was all done by arithmetic. You count some numbers you subtract certain numbers and so on. There was no discussion of what the moon was. There wasn’t even a discussion of the idea that it went around. There was only calculate the time there would be an eclipse or a time when it would rise full moon and when it would rise half moon. Just calculated, only.

Suppose that a young man went to the astronomer and said, I have an idea. Maybe those things are going around, and they’re balls of rock, we could calculate how they move in a completely different way, rather than just what time they appear in the sky.

So of course the Mayan astronomer would say Yes, how accurate can you predict eclipses? He says I haven’t developed the thing very far. He says But we can calculate eclipses more accurately than you can with your model and so you must not pay any attention to that, this mathematical schema is better.

There’s a very strong tendency in people to say against some idea, if someone comes up with an idea, says let’s suppose the world is this way, and you say to them what would you get for the answer for such and such problem, and he says I haven’t developed it far enough, and you say well we have already developed it much further and we can get the answers very accurately.

So it is a problem as to whether or not as to worry about philosophies behind ideas.

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