For example, it was believed—it was discovered— that motion does not affect the weight of a thing—that if you spin a top and weigh it, and then weigh it when it has stopped, it weighs the same. That is the result of an observation. But you cannot weigh something to the infinitesimal number of decimal places, parts in a billion. But we now understand that a spinning top weighs more than a top which is not spinning by a few parts in less than a billion. If the top spins fast enough so that the speed of the edges approaches 186,000 miles a second, the weight increase is appreciable—but not until then. The first experiments were performed with tops that spun at speeds much lower than 186,000 miles a second. It seemed then that the mass of the top spinning and not spinning was exactly the same, and someone made a guess that the mass never changes.

How foolish! What a fool! It is only a guessed law, an extrapolation. Why did he do something so unscientific? There was nothing unscientific about it; it was only uncertain. It would have been unscientific not to guess. It has to be done because the extrapolations are the only things that have any real value. It is only the principle of what you think will happen in a case you have not tried that is worth knowing about. Knowledge is of no real value if all you can tell me is what happened yesterday. It is necessary to tell what will happen tomorrow if you do something—not only necessary, but fun. Only you must be willing to stick your neck out.

Every scientific law, every scientific principle, every statement of the results of an observation is some kind of a summary which leaves out details, because nothing can be stated precisely. The man simply forgot—he should have stated the law “The mass doesn’t change much when the speed isn’t too high.” The game is to make a specific rule and then see if it will go through the sieve. So the specific guess was that the mass never changes at all. Exciting possibility! It does no harm that it turned out not to be the case. It was only uncertain, and there is no harm in being uncertain. It is better to say something and not be sure than not to say anything at all.

It is necessary and true that all of the things we say in science, all of the conclusions, are uncertain, because they are only conclusions. They are guesses as to what is going to happen, and you cannot know what will happen, because you have not made the most complete experiments.

It is curious that the effect on the mass of a spinning top is so small you may say, “Oh, it doesn’t make any difference.” But to get a law that is right, or at least one that keeps going through the successive sieves, that goes on for many more observations, requires a tremendous intelligence and imagination and a complete revamping of our philosophy, our understanding of space and time. I am referring to the relativity theory. It turns out that the tiny effects that turn up always require the most revolutionary modifications of ideas.

Scientists, therefore, are used to dealing with doubt and uncertainty. All scientific knowledge is uncertain. This experience with doubt and uncertainty is important. I believe that it is of very great value, and one that extends beyond the sciences. I believe that to solve any problem that has never been solved before, you have to leave the door to the unknown ajar. You have to permit the possibility that you do not have it exactly right. Otherwise, if you have made up your mind already, you might not solve it.

When the scientist tells you he does not know the answer, he is an ignorant man. When he tells you he has a hunch about how it is going to work, he is uncertain about it. When he is pretty sure of how it is going to work, and he tells you, “This is the way it’s going to work, I’ll bet,” he still is in some doubt. And it is of paramount importance, in order to make progress, that we recognize this ignorance and this doubt. Because we have the doubt, we then propose looking in new directions for new ideas. The rate of the development of science is not the rate at which you make observations alone but, much more important, the rate at which you create new things to test.

If we were not able or did not desire to look in any new direction, if we did not have a doubt or recognize ignorance, we would not get any new ideas. There would be nothing worth checking, because we would know what is true. So what we call scientific knowledge today is a body of statements of varying degrees of certainty. Some of them are most unsure; some of them are nearly sure; but none is absolutely certain. Scientists are used to this. We know that it is consistent to be able to live and not know. Some people say, “How can you live without knowing?” I do not know what they mean. I always live without knowing. That is easy. How you get to know is what I want to know.

This freedom to doubt is an important matter in the sciences and, I believe, in other fields. It was born of a struggle. It was a struggle to be permitted to doubt, to be unsure. And I do not want us to forget the importance of the struggle and, by default, to let the thing fall away. I feel a responsibility as a scientist who knows the great value of a satisfactory philosophy of ignorance, and the progress made possible by such a philosophy, progress which is the fruit of freedom of thought. I feel a responsibility to proclaim the value of this freedom and to teach that doubt is not to be feared, but that it is to be welcomed as the possibility of a new potential for human beings. If you know that you are not sure, you have a chance to improve the situation. I want to demand this freedom for future generations.

Doubt is clearly a value in the sciences. Whether it is in other fields is an open question and an uncertain matter. I expect in the next lectures to discuss that very point and to try to demonstrate that it is important to doubt and that doubt is not a fearful thing, but a thing of very great value.

We are all sad when we think of the wondrous potentialities that human beings seem to have and when we contrast these potentialities with the small accomplishments that we have. Again and again people have thought that we could do much better. People in the past had, in the nightmare of their times, dreams for the future, and we of their future have, although many of those dreams have been surpassed, to a large extent the same dreams. The hopes for the future today are in a great measure the same as they were in the past. At some time people thought that the potential that people had was not developed because everyone was ignorant and that education was the solution to the problem, that if all people were educated, we could perhaps all be Voltaires. But it turns out that falsehood and evil can be taught as easily as good. Education is a great power, but it can work either way. I have heard it said that the communication between nations should lead to an understanding and thus a solution to the problem of developing the potentialities of man. But the means of communication can be channeled and choked. What is communicated can be lies as well as truth, propaganda as well as real and valuable information. Communication is a strong force, also, but either for good or evil. The applied sciences, for a while, were thought to free men of material difficulties at least, and there is some good in the record, especially, for example, in medicine. On the other hand, scientists are working now in secret laboratories to develop the diseases that they were so careful to control.

Everybody dislikes war. Today our dream is that peace will be the solution. Without the expense of armaments, we can do whatever we want. And peace is a great force for good or for evil. How will it be for evil? I do not know. We will see, if we ever get peace. We have, clearly, peace as a great force, as well as material power, communication, education, honesty, and the ideals of many dreamers. We have more forces of this kind to control today than did the ancients. And maybe we are doing it a little bit better than most of them could do. But what we ought to be able to do seems gigantic compared to our confused accomplishments. Why is this? Why can’t we conquer ourselves? Because we find that even the greatest forces and abilities don’t seem to carry with them any clear instructions on how to use them. As an example, the great accumulation of understanding as to how the physical world behaves only convinces one that this behavior has a kind of meaninglessness about it. The sciences do not directly teach good and bad.