28 SCIENCE AND METHOD. 



not true, but it is symbolical, so we will treat it as if 

 it were true. Well, we must suppose that before 

 Newton's day many men had seen apples fall, but 

 none had been able to draw any conclusion. Facts 

 would be barren if there were not minds capable of 

 selecting between them and distinguishing those which 

 have something hidden behind them and recognizing 

 what is hidden — minds which, behind the bare fact, 

 can detect the soul of the fact. 



In mathematics we do exactly the same thing. Of 

 the various elements at our disposal we can form 

 millions of different combinations, but any one of 

 these combinations, so long as it is isolated, is ab- 

 solutely without value ; often we have taken great 

 trouble to construct it, but it is of absolutely no use, 

 unless it be, perhaps, to supply a subject for an exer- 

 cise in secondary schools. It will be quite different 

 as soon as this combination takes its place in a class 

 of analogous combinations whose analogy we have 

 recognized ; we shall then be no longer in presence of 

 a fact, but of a law. And then the true discoverer 

 will not be the workman who has patiently built up 

 'sdme of these combinations, but the man who has 

 brought out their relation. The former has only seen 

 the bare fact, the latter alone has detected the soul of 

 the fact. The invention of a new word will often 

 be sufficient to bring out the relation, and the word 

 will be creative. The history of science furnishes us 

 with a host of examples that are familiar to all. 



The celebrated Viennese philosopher Mach has said 

 that the part of science is to effect economy of thought, 

 just as a machine effects economy of effort, and this is 

 very true. The savage calculates on his fingers, or 



