September 24, 1915] 



SCIENCE 



401 



perhaps requires qualifying, becaiise it re- 

 calls a buyer to whom one offers a large 

 number of samples which he examines be- 

 fore making his choice. In our case the 

 samples would be so numerous that a life- 

 time would not suffice to complete the ex- 

 amination. That is not the way things are 

 done. The sterile combinations never pre- 

 sent themselves to the mind of the inventor, 

 and even those which momentarily enter 

 his consciousness, only to be rejected, par- 

 take something of the character of useful 

 combinations. The inventor is therefore to 

 be compared with an examiner who has only 

 to deal with candidates who have already 

 passed a previous test of competence." 



All those who have attempted to add 

 something to knowledge must recognize 

 that there is a profound truth in these re- 

 marks. New ideas may float across our 

 consciousness, but, selecting the wrong ones 

 for more detailed study, we waste our time 

 fruitlessly. We are bewildered by the 

 multitude of roads which open out before 

 us, and, like Poincare when he tries to play 

 chess, lose the game because we make the 

 wrong move. Do we not all remember how, 

 after the announcement of a new fact or 

 generalization, there are always many who 

 claim to have had, and perhaps vaguely ex- 

 pressed, the same idea? They put it down 

 to bad luck that they have not pursued it, 

 but they have failed precisely in what, ac- 

 cording to Poincare, is the essence of in- 

 ventive power. It may be bad luck not to 

 have had a good idea, but to have had it and 

 failed to appreciate its importance is down- 

 right incapacity. 



An objection may be raised that before 

 a selection can be made the ideas them- 

 selves must appear, and that, even should 

 they arrive in sufficient numbers, the right 

 one may not be among them. It may even 

 be argued that Poincare gives his ease 

 away by saying that "the sterile combina- 



tions do not even present themselves to the 

 mind of the inventor, ' ' putting into a nega- 

 tive form what may be the essence of the 

 matter. Moreover, a fertile mind like that 

 of Poincare would be apt to place too low a 

 value on his own exceptional gifts. Never- 

 theless, if Poincare 's more detailed ex- 

 position be read attentively, and more 

 especially the description of how the discov- 

 eries which made him famous among mathe- 

 maticians originated in his mind, it will be 

 found that his judgment is well considered 

 and should not be lightly set aside. New 

 ideas seldom are born out of nothing. They 

 most frequently are based on analogies, or 

 the recollection of a sequence of thoughts 

 suggested by a different branch of the sub- 

 ject, or perhaps by a different subject alto- 

 gether. It is here that the memory comes 

 in, which is not a memory of detail, but a 

 memory of premises with their conclusions, 

 detached from the particular case to which 

 they were originally applied. Before we 

 pronounce an adverse opinion on Poin- 

 care 's judgment, we must investigate what 

 constitutes novelty in a new idea, but the 

 subject is too vast to be dealt with here, nor 

 can I attempt to discuss whether an essen- 

 tial distinction exists between mathematical 

 invention and that more practical form of 

 invention with which, for instance, the 

 engineer has to deal. 



If Poincare, by this introspective analy- 

 sis of his own powers, has dimmed the 

 aureole which, in the eyes of the public, 

 surrounds the mathematician's head, he re- 

 moves it altogether by his definition of 

 mathematics. According to him, "mathe- 

 matics is the art of calling two different 

 things by the same name." It would take 

 me too far were I to try to explain the deep 

 truth expressed in this apparently flippant 

 form : physicists, at any rate, will remember 

 the revolution created in the fundamental 

 outlook of science by the application of the 



