212 THE POPULAR SCIENCE MONTHLY 



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 edi- 

 tion of " Value of Science/' which expresses his attitude towards indus- 

 trial 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 yester- 

 day'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 pro- 

 tects us from the skeptic. 



Poincare'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 Poincare was 

 the discovery of the real relation between isolated facts. The important 

 facts are those that suggest relations. We select facts from this stand- 

 point. The world of relations was as real to him as the world of phe- 

 nomena, 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 ob- 

 jective world. Even absolute space and absolute time do not exist, these 

 two are relations furnished by our own minds. 4 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 dif- 

 ference equations rather than differential equations. But the differen- 

 tial equation expresses certain persistent relations between phenomena, 

 and is thus real, and is the replica of an objective reality. The differen- 

 tial equation means that the phenomenon is one such that each state is 

 the result of the immediately preceding state; the new integro-differen- 

 tial equation of Volterra means that the state is due to all the preceding 

 states; the difference equation means that the states follow each other 



4 Scientia, 12 (1912), 159-171 (posthumous). 



