HENRI POINCARE NORDMANN. 759 



perhaps a millionth, as much smaller as you please, but nevertheless 

 smaller, which would verify a theorem of the Lobatschefskian geom- 

 etry, sometmies a little greater but sufficient to conform to a Riemann 

 geometry. Experiment, then, does not show the exclusive truth of 

 Euclidean geometry, which, like the others, is at the bottom an edifice 

 formed by logic. If the Euclidean method is innate to us, it is doubt- 

 less because of ancestral experiences, because the brain of man has 

 little by little been adapted to the exterior v/orld by natural selection 

 and because Euclidean geometry has proved to be ' ' the most advan- 

 tageous to mankind; in other words, the most fit." 



If in mathematics deduction is almost all, fact almost notliing, we 

 find the reverse in the observational sciences. Pure deduction can 

 teach us very httle about nature except in an indirect way, and then 

 only because our brain has httle by httle become harmonized to the 

 exterior world with the fewest clashes possible. In that sense, cer- 

 tainly, the study of our intellect teaches us indirectly of the universe 

 itself just as the appearance of a mortal wound indicates to the 

 mechcal expert the instrument employed and the gesture of the 

 assassin. But that evidence is not only indirect, but it is incom- 

 plete, for it teUs us notliing of those external conditions not involved 

 in the adaptation of the species. These latter are the more numerous. 

 Accorchngly, the discoveries due to the experimental sciences are 

 unlimited, whereas those from pure deduction are doubtless limited. 

 It is better to observe than to reason, and doubtless in that sense 

 Poincare is to be understood when he wrote in regard to the methods 

 of the physical sciences: ''Experience is the sole source of all truth. 

 It alone can teach us new tilings. It alone can give us certaint3^" 



But, then, should not the theorems of mathematical physics, 

 which are but the synthesis and expression of physical experiences, 

 furnish us with a definitive, although in a way dogmatic, imago of 

 the universe such as certain philosophies have promised ? We once 

 behoved so; but ha\ang observed how j)recarious was the fortune of 

 such theories and how rapidly and repeatedly the most brilliant gave 

 way to others, some have been pleased to call science futile and only 

 a source of error. But Poincare has shown that physical theories 

 deserve neither such excesses of honor nor of indignity and has 

 brought their bhnd adorers as well as their systematic detractors to 

 a more sane view. 



Observation and experience furnish the physicsd facts to the 

 physicist. Should he be content merely to accumulate them ? No, 

 for ''he must coordinate them. Science is built with facts as houses 

 are with stones; but an accumulation of facts is no more a science 

 than a heap of stones a house;" and, further, a physicist must 

 "predict" phenomena. So ho genorahzos what he has observed, 

 interpolating, connecting by a hue the isolated facts; then he pro- 



