In connection with this view of the scientist in his own domain, I desire to quote also from the preface of the recent second German edition of "Value of Science," which expresses his attitude towards industrial science:
Science has always had to contend with skeptics and scoffers who were quite ready to draw conclusions from relative failures and temporary inactivity, and to note the confessions of scientists who admit that the field of science is bounded, but fail to add that inside its own realm it is supreme.
He who views scientific work from the outside is often amazed to see yesterday's truth so easily become to-morrow's error. He believes then, that our conquests are over-confident, that the principles so proudly paraded are only novelties, and he does not see that beneath these necessary changes of form scientific truth is always one and the same. It remains eternally unchanged and only the clothing in which we deck it out changes with the fashion.
Fortunately science is needed in applications, and this silences the skeptic. If he desires to use some new discovery, and convinces himself of its success, he must indeed admit that it is more than an idle dream. We thus perceive the blessing which lies in the development of industry.
I do not wish to say that science is created for its applications, far from it; one must love it for its own sake; but the recognition of its applications protects us from the skeptic.
Poincaré's conception of science can be summed up in these terms: Science consists of the invariants of human thought.
In the field of investigation, the important thing for Poincaré was the discovery of the real relation between isolated facts. The important facts are those that suggest relations. We select facts from this standpoint. The world of relations was as real to him as the world of phenomena, and so far as we know the real relations, in whatever language we express these relations, just so far we know the actual world, the objective world. Even absolute space and absolute time do not exist, these two are relations furnished by our own minds.[1] Thus the term energy, and our notion as to the existence of energy, may change in the course of time, but the persistent relation that gives us our present notion of energy is real and does not change. It may be true, as Herschel said, that in the twinkling of an eye a molecule solves a differential equation which if written out in full would belt the globe, but the molecule knows nothing of the equation—that is created by the mind, and as the modern discontinuous physics develops, it may be that we shall have to use difference equations rather than differential equations. But the differential equation expresses certain persistent relations between phenomena, and is thus real, and is the replica of an objective reality. The differential equation means that the phenomenon is one such that each state is the result of the immediately preceding state; the new integro-differential equation of Volterra means that the state is due to all the preceding states; the difference equation means that the states follow each other
- ↑ Scientia, 12 (1912), 159-171 (posthumous).
