NATUKE 701 



capricious shapes, and plough their way through space in every direc- 

 tion. The result observable is Mariotte's simple law. Each individual 

 fact was complicated. The law of great numbers has re-established 

 simplicity in the mean. Here the simplicity is only apparent, and the 

 coarseness of our senses alone prevents us from seeing the complexity. 



Many phenomena obey a law of proportionality. But why? Be- 

 cause in these phenomena there is something which is very small. The 

 simple law observed is only the translation of the general analytical 

 rule by which the infinitely small increment of a function is pro- 

 portional to the increment of the variable. As in reality our incre- 

 ments are not infinitely small, but only very small, the law of pro- 

 portionality is only approximate, and simplicity is only apparent. 

 What I have just said applies to the law of the superposition of small 

 movements, which is so fruitful in its applications and which is the 

 foundation of optics. 



And Newton's law itself ? Its simplicity, so long undetected, is per- 

 haps only apparent. Who knows if it be not due to some complicated 

 mechanism, to the impact of some subtle matter animated by irregu- 

 lar movements, and if it has not become simple merely through the 

 play of averages and large numbers ? In any case, it is difficult not to 

 suppose that the true law contains complementary terms which may 

 become sensible at small distances. If in astronomy they are negligi- 

 ble, and if the law thus regains its simplicity, it is solely on account 

 of the enormous distances of the celestial bodies. No doubt, if our 

 means of investigation became more and more penetrating, we should 

 discover the simple beneath the complex, and then the com- 

 plex from the simple, and then again the simple beneath the 

 complex, and so on, without ever being able to predict what the last 

 term will be. We must stop somewhere, and for science to be possible 

 we must stop where we have found simplicity. That is the only 

 ground on which we can erect the edifice of our generalizations. But, 

 this simplicity being only apparent, will the ground be solid enough? 

 That is what we have now to discover. 



For this purpose let us see what part is played in our generalizations 

 by the belief in simplicity. We have verified a simple law in a con- 

 siderable number of particular cases. We refuse to admit that this 

 coincidence, so often repeated, is a result of mere chance, and we 

 conclude that the law must be true in the general case. 



Kepler remarks that the positions of a planet observed by Tycho 

 are all on the same ellipse. Not for one moment does he think that, 

 by a singular freak of chance, Tycho had never looked at the heavens 

 except at the very moment when the path of the planet happened to 

 cut that ellipse. What does it matter then if the simplicity be real 

 or if it hide a complex truth? Whether it be due to the influence of 

 great numbers which reduces individual differences to a level, or to the 



