The Rôle of Hypothesis

Every generalisation is a hypothesis.

Hypothesis therefore plays a necessary rôle, which no one has ever contested. Only, it should always be as soon as possible submitted to verification.

If it cannot stand this test, it must be abandoned.

The physicist who has just given up one of his hypotheses should rejoice, for he found an unexpected opportunity of discovery.

His hypothesis had not been lightly adopted. It took into account all the known factors which seem capable of intervention in the phenomenon.

If it is not verified, it is because there is something unexpected and extraordinary about it, because we are on the point of finding something unknown and new.

Has the rejected hypothesis been sterile?

Far from it. It may be even said that it has rendered more service than a true hypothesis.

Not only has it been the occasion of a decisive experiment, but if this experiment had been made by chance, without the hypothesis, no conclusion could have been drawn; nothing extraordinary would have been seen.

Only one fact the more would have been catalogued, without deducing from it the remotest consequence.

Now, under what conditions is the use of hypothesis without danger?

The proposal to submit all to experiment is not sufficient. Some hypotheses are dangerous,—first and foremost those which are tacit and unconscious.

And since we make them without knowing them, we cannot get rid of them. Here again, there is a service that mathematical physics may render us. By the precisionhypotheses in physics.

which is its characteristic, we are compelled to formulate all the hypotheses that we would unhesitatingly make without its aid.

Let us also notice that it is important not to multiply hypotheses indefinitely. If we construct a theory based upon multiple hypotheses, and if experiment condemns it, which of the premises must be changed?

It is impossible to tell.

Conversely, if the experiment succeeds, must we suppose that it has verified all these hypotheses at once? Can several unknowns be determined from a single equation?

We must also take care to distinguish between the different kinds of hypotheses.

First of all, there are those which are quite natural and necessary.

The influence of very distant bodies is quite negligible. Small movements obey a linear law. Effect is a continuous function of its cause.

I will say as much for the conditions imposed by symmetry.

All these hypotheses affirm, so to speak, the common basis of all the theories of mathematical physics. They are the last that should be abandoned.

There is a second category of hypotheses which I shall qualify as indifferent.

In most questions the analyst assumes, at the beginning of his calculations, either that matter is continuous, or the reverse, that it is formed of atoms. In either case, his results would have been the same.

On the atomic supposition, he has a little more difficulty in obtaining them—that is all.

If, then, experiment confirms his conclusions, will he suppose that he has proved, for example, the real existence of atoms?

In optical theories, 2 vectors are introduced, one of which we consider as a velocity and the other as a vortex.

This again is an indifferent hypothesis, since we should have arrived at the same conclusions by assuming the former to be a vortex and the latter to be a velocity.

The success of the experiment cannot prove, therefore, that the first vector is really a velocity.

It only proves one thing—namely, that it is a vector; and that is the only hypothesis that has really been introduced into the premises.

To give it the concrete appearance that the fallibility of our minds demands, it was necessary to consider it either as a velocity or as a vortex. In the same way, it was necessary to represent it by an x or a y, but the result will not prove that we were right or wrong in regarding it as a velocity; nor will it prove we are right or wrong in calling it x and not y.

These indifferent hypotheses are never dangerous provided their characters are not misunderstood. They may be useful, either as artifices for calculation, or to assist hypotheses in physics.

our understanding by concrete images, to fix the ideas, as we say.

They need not therefore be rejected. The hypotheses of the third category are real generalisations.

They must be confirmed or invalidated by experiment.

Whether verified or condemned, they will always be fruitful; but, for the reasons I have given, they will only be so if they are not too numerous.