Speeches, James Clear, Wolves Forever [best ereader manga TXT] 📗

almost like circles, it's another possibly. Nobody knows, it's just guess work.

Now another thing that people often say is that for guessing, two identical theories– two theories. Suppose you have two theories, a and b, which look completely different psychologically. They have different ideas in them and so on. But that all the consequences that are computed, all the consequences that are computed are exactly the same. You may even say they even agree with experiment.

The point is thought that the two theories, although they sound different at the beginning, have all consequences the same. It's easy, usually, to prove that mathematically, by doing a little mathematics ahead of time, to show that the logic from 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 experiment to the same extent, 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 guess new theories, these two things are very far from equivalent. Because one gives a man different ideas than the other. By putting the theory in a certain kind of framework, you get an idea of what to change, which would be something, for instance, in theory A that talks about something. But you say I'll change that idea in here.

But to find out what the corresponding thing you're going to change in here may be very complicated. It may not be a simple idea. In other words, a simple change here, may be a very different theory than a simple change there.

In other words, although they are identical before they are 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 the theories in our head.

And 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's 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 for guessing.

Incidentally, that reminds me of another thing. And that is that the philosophy, or the ideas around the theory– a lot of ideas, you say, I believe there is a space time, or something like that, in order to discuss your analyses– that these ideas change enormously when there are very tiny changes in the theory.

In other words, for instance, Newton's idea about space and time agreed with experiment very well. But in order to get the correct motion of the orbit of Mercury, which was a tiny, tiny difference, the difference in the character of the theory with which you started was enormous. The reason is these are so simple and so perfect. They produce definite results.

In order to get something that produced a little different result, 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 are enormous. Their difference is rather 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 that 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, never mind the philosophy, never mind anything of this kind. Just guess the equations.

The problem is only to compute the answers so they agree with experiment, and is not necessarily to have a philosophy or words about the equation. That's true, in a sense, yes and no. It's good in the sense you may be, if you only guess the equation, you're not prejudicing yourself, and you'll guess better. On the other hand, maybe the philosophy helped you to guess. 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, the position of Venus, and so on.

However, it was all done by arithmetic. You count certain numbers, you subtract some 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. It was only calculate the time when there would be an eclipse, or the time when it would rise– their full moon– and when it would rise, half moon, and so on, just calculating, only.

Suppose that a young man went to the astronomer and said, I have an idea. Maybe those things are going around, and there are balls of rocks out there. We could calculate how they move in a completely different way than just calculate what time they appear in the sky and so on.

So of course the Mayan astronomer would say, yes, how accurate can you predict eclipses? He said, I haven't developed the thing very far.

But we can calculate eclipses more accurately than you can with your model. And so you must not pay attention to this, because the mathematical scheme is better. And it's a very strong tendency of people to say against some idea, if someone comes up with an idea, and says let's suppose the world is this way.

And you say to him, well, what would you get for the answer for such and such a problem? And he says, I haven't developed it far enough. And you say, well, we have already developed it much further. We can get the answers very accurately. So it is a problem, as to whether or not to worry about philosophies behind ideas.

Another thing, of course, I wanted you to guess is to guess new principles. For instance, in Einstein's gravitation, he guessed, on top of all the other principles, the principle that correspondent to the idea that the forces are always proportional to the masses. He guessed the principle that if you are in an accelerating car, you couldn't tell that from being in a gravitational field. And by adding that principle to all the other principles was able to deduce correct laws of gravitation.

Well, that outlines a number of possible ways of guessing. I would now like to come to some other points about the final result. First of all, when we're all finished, and we have a mathematical theory by which we can compute consequences, it really is an amazing thing. What do we do?

In order to figure out what an atom is going to do in a given situation, we make up a whole lot of rules with marks on paper, carry them into a machine, which opens and closes switches in some complicated way. And the result will tell us what the atom is going to do.

Now if the way that these switches open and close, with some kind of a model of the atom– in other words, if we thought the atom had such switches in it– then I would say, I understand more or less what's going on. But I find it quite amazing that it is possible to predict what will happen by what we call mathematics. We're just simply following a whole lot of rules, which have nothing to do, really, with what's going on in the original thing. In other words, the closing and opening of switches in a computer is quite different, I think, than what's happening in nature. And that is, to me, very surprising.

Now finally, I would like to say one of the most important things in his guess compute consequences compare experiment business is to know when you're right, that it's possible to know when you're right way ahead of computing all a consequences– I mean of checking all the consequences. You can recognize truth by beauty and simplicity. It's always easy when you've got the right guess and make two or three little calculations to make sure it isn't obviously wrong to know that it's right. When you get it right, it's obvious that it's right. At least if you have any experience.

Because most of what happens is that more comes out than goes in, that your guess is, in fact, that something is very simple. And at the moment you guess that it's simpler than you thought, then it turns out that it's right, if it can't be immediately disproved. Doesn't sound silly. I mean, if you can't see immediately that it's wrong, and it's simpler than it was before, then it's right.

The inexperienced and crackpots and people like that will make guesses that are simple, all right, but you can immediately see that they're wrong. That doesn't count. And others, the inexperienced students, make guesses that are very complicated. And it sort of looks like it's all right. But I know that's not true, because the truth always turns out to be simpler than you thought.

What we need is imagination. But imagination is a terrible straitjacket. We have to find a new view of the world that has to agree with everything that's known, but disagree in its predictions, some way. Otherwise it's not interesting. And in that disagreement, agree with nature.

If you can find any other view of the world which agrees over the entire range where things have already been observed, but disagrees somewhere else, you've made a great discovery. Even if it doesn't agree with nature. It's darn hard, it's almost impossible, but not quite impossible, to find another theory, which agrees with experiments over the entire range in which the old theories have been checked and yet gives different consequences in some other range. In other words, a new idea that is extremely difficult, takes a fantastic imagination.

And what of the future of this adventure? What will happen ultimately? We are going along, guessing the laws. How many laws are we going to have to guess?

I don't know. Some of my– let's say, some of my colleagues say, science will go on. But certainly, there will not be perpetual novelty, say for 1,000 years. This thing can't keep on going on, we're always going to discover new laws, new laws, new laws. If we do, it will get boring that there are so many levels, one underneath the other.

So the only way that it seems to me that it can happen– that what can happen in the future first– either that everything becomes known, that all the laws become known. That would mean that after you had enough laws, you could compute consequences. And they would always agree with experiment, which would be the end of the line.

Or it might happen that the experiments get harder and harder to make, more and more expensive, that you get 99.9% of the phenomena. But there's always some phenomenon which has just been discovered that's very hard to measure, which disagrees and gets harder and harder to measure. As you discover the explanation of that one, there's always another one. And it gets slower and slower and more and more uninteresting. That's another way that it could end.

But I think it has to end in one way or another. And I think that we are very lucky to live in the age in which we're still making the discoveries. It's an age which will never come again. It's like the discoveries of America. You only discover it once. It was