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be wrong.

Quantum mechanics was discovered in two independent ways, which is a lesson. There, again, and even more so, an enormous number of paradoxes were discovered experimentally. Things that absolutely couldn't be explained in any way by what was known. Not that the knowledge was incomplete, but the knowledge was too complete. Your prediction was this should happen, it didn't.

The two different roots were one by Schrodinger, who guessed the equations. Another by Heisenberg, who argued that you must analyze what's measurable. So it's two different philosophical methods reduced to the same discovery in the end.

More recently, the discovery of the laws of this interaction, which are still only partly known, had quite a somewhat different situation. Again, there was a– this time, it was a case of incomplete knowledge. And only the equation was guessed. The special difficulty this time was that the experiments were all wrong.

All the experiments were wrong. How can you guess the right answer? When you calculate the results it disagrees with the experiment, and you have the courage to say, the experiments must be wrong. I'll explain where the courage comes from in a minute.

Today, we haven't any paradoxes, maybe. We have this infinity that comes if we put all the laws together. But the rug-sweeping people are so clever that one sometimes thinks that's not a serious paradox.

The fact that there are all these particles doesn't tell us anything, except that our knowledge is incomplete. I'm sure that history does not repeat itself in physics, as you see from this list. And the reason is this.

Any scheme– like think of symmetry laws, or put the equations in mathematical form, or any of these schemes, guess equations, and so on– are known to everybody now. And they're tried all the time. So if the place where you get stuck is not that, you try that right away. We try looking for symmetries, we try all the things that have been tried before. But we're stuck.

So it must be another way next time. So each time that we get in this log jam of too many problems, it's because the methods that we're using are just like the ones we used before. We try all that right away. But the new scheme, the new discovery is going to be made in a completely different way. So history doesn't help us very much.

I'd like to talk a little bit about this Heisenberg's idea. But you shouldn't talk about what you can't measure, because a lot of people talk about that without understanding it very well. They say in physics you shouldn't talk about what you can't measure.

If what you mean by this, if you interpret this in this sense, that the constructs are inventions that you make that you talk about, it must be such a kind that the consequences that you compute must be comparable to experiment. That is, that you don't compute a consequence like a moo must be three goos. When nobody knows what a moo and a goo is, that's no good.

If the consequences can be compared to experiment, then that's all that's necessary. It is not necessary that moos and goos can't appear in the guess. That's perfectly all right. You can have as much junk in the guess as you want, provided that you can compare it to experiment.

That's not fully appreciated, because it's usually said, for example, people usually complain of the unwarranted extension of the ideas of particles and paths and so forth, into the atomic realm. Not so at all. There's nothing unwarranted about the extension.

We must, and we should, and we always do extend as far as we can beyond what we already know, those things, those ideas that we've already obtained. We extend the ideas beyond their range. Dangerous, yes, uncertain, yes. But the only way to make progress.

It's necessary to make science useful, although it's uncertain. It's only useful if it makes predictions. It's only useful if it tells you about some experiment that hasn't been done. It's no good if it just tells you what just went on. So it's necessary to extend the ideas beyond where they've been tested.

For example, in the law of gravitation, which was developed to understand the motion of the planets, if Newton simply said, I now understand the planet, and didn't try to compare it to the earth's pull, we can't, if we're not allowed to say, maybe what holds the galaxies together is gravitation. We must try that. It's no good to say, well, when you get to the size of galaxies, since you don't know anything about anything, it could happen.

Yes, I know. But there's no science here, there's no understanding, ultimately, of the galaxies. If on the other hand you assume that the entire behavior is due to only known laws, this assumption is very limited and very definite and easily broken by experiment. All we're looking for is just such hypotheses. Very definite, easy to compare to experiment.

And the fact is that the way the galaxies behaved so far doesn't seem to be against the proposition. It would be easily disproved, if it were false. But it's very useful to make hypotheses.

I give another example, even more interesting and important. Probably the most powerful assumption in all of biology, the single assumption that makes the progress of biology the greatest is the assumption that everything the animals do, the atoms can do. That the things that are seen in the biological world are the results of the behavior of physical and chemical phenomena, with no extra something.

You could always say, when we come to living things, anything can happen. If you do that, you never understand the living thing. It's very hard to believe that the wiggling of the temple of the octopus is nothing but some fooling around of atoms, according to the known physical laws.

But if investigated with this hypothesis, one is able to make guesses quite accurately as to how it works. And one makes great progress in understanding the thing. So far, the tentacle hasn't been cut off. What I mean is it hasn't been found that this idea is wrong.

It's therefore not unscientific to take a guess, although many people who are not in science think it is. For instance, I had a conversation about flying saucers some years ago with laymen.

Because I'm scientific, I know all about flying saucers. So I said, I don't think there are flying saucers. So my antagonist said, is it impossible that there are flying saucers? Can you prove that it's impossible? I said, no, I can't prove it's impossible, it's just very unlikely.

That, they say, you are very unscientific. If you can't prove it impossible, then how could you say it's likely that it's unlikely? Well, that's the way that it is scientific. It is scientific only to say what's more likely and less likely, and not to be proving all the time, possible and impossible.

To define what I mean, I finally said to him, listen. I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence, rather than the unknown, rational efforts of extraterrestrial intelligence.

It's just more likely, that's all. And it's a good guess. And we always try to guess the most likely explanation, keeping in the back of the mind the fact that if it doesn't work, then we must discuss the other possibilities.

Now, how to guess at what to keep and what to throw away. You see, we have all these nice principles and known facts and so on. But we're in some kind of trouble– that we get the inifinities or we don't get enough of a description, we're missing some parts. And sometimes that means that we have, probably, to throw away some idea. At least in the past it's always turned out that some deeply held idea has to be thrown away.

And the question is what to throw away and what to keep. If you throw it all away, it's going a little far, and you don't got much to work with. After all, the conservation of energy looks good, it's nice. I don't want to throw it away, and so on.

To guess what to keep and what to throw away takes considerable skill. Actually, it probably is merely a matter of luck. But it looks like it takes considerable skill.

For instance, probability amplitudes, they're very strange. And the first thing you'd think is that the strange new ideas are clearly cockeyed. And yet everything that can be deduced from the idea of probability– the existence of quantum mechanical probability amplitude, strange though they are, all the things that depend on that work throughout all these strange particles, work 100%. Everything that depends on that seems to work.

So I don't believe that that idea is wrong, and that when we find out what the inner guts of this stuff is we'll find that idea is wrong. I think that part's right. I'm only guessing. I'm telling you how I guess.

For instance, that space is continuous is, I believe, wrong. Because we get these infinities in other difficulties, and we have some questions as to what determines the sizes of all these particles, I rather suspect that the simple ideas of geometry extended down into infinitely small space is wrong. I don't believe that space– I mean, I'm making a hole. I'm only making a guess, I'm not telling you what to substitute. If I did, I would finish this lecture with a known law.

Some people have used the inconsistency of all the principles to say that there's only one possible consistent world. That if we put all the principles together and calculate it very exactly, we will not only be able to reuse the principle, but discover that these are the only things that can exist and have the [INAUDIBLE]. And that seems to me like a big order.

I don't believe– that's not like wagging the tail by the dog. That's right. Wagging the dog by the tail.

I believe that you have to be given that certain things exist, a few of them– not all the 48 particles or the 50 some odd particles. A few little principles, a few little things exist, like electrons, and something, something is given. And then with all the principles, the great complexities that come out could probably be a definite consequence. But I don't think you can get the whole thing from just arguments about consistency.

Finally, we have another problem, which is the question of the meaning of the partial symmetries. I think I better leave that one go, because of a shortage of time. Well, I'll say it quickly. These symmetries– like the neutron and proton are nearly the same, but they're not, for electricity, or that the law of reflection symmetry is perfect, except for one kind of a reaction– are very annoying. The thing is almost symmetrical, but not.

Now, two schools of thought exist. One who say it's really simple, they're really symmetrical. But there's a little complication, which knocks it a little bit cockeyed.

Then there's another school, which has only one representative, myself.

Which says, no, the thing may be complicated and become simple only through the complication. Like this. The Greeks believed that the orbits of the planets were circles. And the orbits of the planets are nearly circles. Actually, they're ellipses.

The next question is, well, they're not quite symmetrical. But they're almost circles, they're very close to circles. Why are they very close to circles? Why are they nearly symmetrical? Because of the long complicated effects of tidal friction, a very complicated idea.

So it is possible that nature, in her heart, is completely as unsymmetrical for these things. But in the complexities of reality, it gets approximately looking as if it's symmetrical. Ellipses look

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