Hypotheses In Physics

The Role of Experiment and Generalisation

Experiment is the sole source of truth. It alone can:

• teach us something new
• give us certainty.

If experiment is everything, what is mathematical physics for, but just an auxiliary which can be useless or even dangerous?

However, mathematical physics exists and has rendered undeniable service.

We should not merely observe. We must use our observations. For that, we must generalise.

Every age has scoffed at its predecessor, accusing it of having generalised too boldly and too naïvely.

Descartes used to commiserate the Ioni-hypotheses in physics.

ans. Descartes in his turn makes us smile, and no doubt some day our children will laugh at us. Is there no way of getting at once to the gist of the matter, and thereby escaping the raillery which we foresee?

Cannot we be content with experiment alone? No, that is impossible; that would be a complete misunderstanding of the true character of science. The man of science must work with method.

Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.

Most important of all, the man of science must exhibit foresight.

Carlyle has written somewhere something after this fashion.

“Nothing but facts are of importance. John Lackland passed by here. Here is something that is admirable. Here is a reality for which I would give all the theories in the world.” 1

Carlyle was a compatriot of Bacon, and, like him, he wished to proclaim his worship of the God of Things as they are.

But Bacon would not have said that. That is the language of the historian. The physicist would most likely have said: “John Lackland passed by here. It is all the same to me, for he will not pass this way again.” We all know that there are good and bad experiments.

V. Past and Present, end of Chapter I., Book 2

The latter accumulate in vain.

Whether there are a hundred or a thousand, one single piece of work by a real master—by a Pasteur, for example—will be sufficient to sweep them into oblivion. Bacon would have thoroughly understood that, for he invented the phrase experimen- tum crucis; but Carlyle would not have understood it. A fact is a fact.

A student has read such and such a number on his thermometer. He has taken no precautions. It does not matter; he has read it, and if it is only the fact which counts, this is a reality that is as much enti- tled to be called a reality as the peregrinations of King John Lackland. What, then, is a good experiment?

It is that which teaches us something more than an isolated fact.

It is that which enables us to predict, and to generalise. Without generalisation, prediction is impos- sible. The circumstances under which one has operated will never again be reproduced simultaneously. The fact observed will never be repeated. All that can be affirmed is that under analogous circumstances an analogous fact will be produced. To predict it, we must therefore invoke the aid of analogy—that is to say, even at this stage, we must generalise. However timid we may be, there must be interpolation. Experiment only gives us a certain number of isolated points. They must be connected by a continuous line, and this is a true generalisation. But more is done. The curve thus traced will pass between and near the points observed; it will not pass through the points themselves. Thus we are not restricted to generalising our experiment, we correct it; and the physicist who would abstain from these corrections, and really content himself with experiment pure and simple, would be compelled to enunciate very extraordinary laws indeed. Detached facts cannot therefore satisfy us, and that is why our science must be ordered, or, better still, generalised.

It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so eas- ily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas. Only they are unconscious preconceived ideas, which are a thousand times the most dangerous of all. Shall we say, that if we cause others to intervene of which we are fully conscious, that we shall only aggravate the evil? I do not think so. I am inclined to think that they will serve as ample counterpoises—I was almost going to say antidotes. They will generally disagree, they will enter into conflict one with another, and ipso facto, they will force us to look at things under different aspects. This is enough to free us. He is no longer a slave who can choose his master.

Thus, by generalisation, every fact observed enables us to predict a large number of others; only, we ought not to forget that the first alone is certain, and that all the others are merely probable. However solidly founded a prediction may appear to us, we are never absolutely sure that experiment will not prove it to be baseless if we set to work to verify it. But the probability of its accuracy is often so great that practically we may be content with it.

It is far better to predict without certainty, than never to have predicted at all. We should never, therefore, dis- dain to verify when the opportunity presents itself. But every experiment is long and difficult, and the labourers are few, and the number of facts which we require to predict is enormous; and besides this mass, the number of direct verifications that we can make will never be more than a negligible quantity. Of this little that we can di- rectly attain we must choose the best. Every experiment must enable us to make a maximum number of predic- tions having the highest possible degree of probability.

The problem is, so to speak, to increase the output ofhypotheses in physics. the scientific machine. I may be permitted to compare science to a library which must go on increasing indefinitely; the librarian has limited funds for his purchases, and he must, therefore, strain every nerve not to waste them. Experimental physics has to make the purchases, and experimental physics alone can enrich the library. As for mathematical physics, her duty is to draw up the cat- alogue. If the catalogue is well done the library is none the richer for it; but the reader will be enabled to utilise its riches; and also by showing the librarian the gaps in his collection, it will help him to make a judicious use of his funds, which is all the more important, inasmuch as those funds are entirely inadequate. That is the rôle of mathematical physics. It must direct generalisation, so as to increase what I called just now the output of sci- ence. By what means it does this, and how it may do it without danger, is what we have now to examine.