700 SCIENCE AND HYPOTHESIS 



said in a conversation with Laplace that Nature cares naught for 

 analytical difficulties, was compelled to explain his words so as not to 

 give offence to current opinion. Nowadays, ideas have changed con- 

 siderably; but those who do not believe that natural laws must be 

 simple, are still often obliged to act as if they did believe it. They 

 cannot entirely dispense with this necessity without making all gen- 

 eralization, and therefore all science, impossible. It is clear that 

 any fact can be generalized in an infinite number of ways, and it is a 

 question of choice. The choice can only be guided by considerations of 

 simplicity. Let us take the most ordinary case, that of interpolation. 

 We draw a continuous line as regularly as possible between the points 

 given by observation. Why do we avoid angular points and inflections 

 that are too sharp? Why do we not make our curve describe the 

 most capricious zigzags? It is because we know beforehand, or think 

 we know, that the law we have to express cannot be so complicated as 

 all that. The mass of Jupiter may be deduced either from the move- 

 ments of his satellites, or from the perturbations of the major planets, 

 or from those of the minor planets. If we take the mean of the deter- 

 minations obtained by these three methods, we find three numbers 

 very close together, but not quite identical. This result might be in- 

 terpreted by supposing that the gravitation constant is not the same 

 in the three cases; the observations would be certainly much better 

 represented. Why do we reject this interpretation? Not because it 

 is absurd, but because it is uselessly complicated. We shall only 

 accept it when we are forced to, and it is not imposed upon us yet. 

 To sum up, in most cases every law is held to be simple until the 

 contrary is proved. 



This custom is imposed upon physicists by the reasons that I have 

 indicated, but how can it be justified in the presence of discoveries 

 which daily show us fresh details, richer and more complex? How 

 can we even reconcile it with the unity of nature? For if all things 

 are interdependent, the relations in which so many different objects 

 intervene can no longer be simple. 



If we study the history of science we see produced two phenomena 

 which are, so to speak, each the inverse of the other. Sometimes it is 

 simplicity which is hidden under what is apparently complex; some- 

 times, on the contrary, it is simplicity which is apparent, and which 

 conceals extremely complex realities. What is there more complicated 

 than the disturbed motions of the planets, and what more simple than 

 Newton's law ? There, as Fresnel said, Nature playing with analytical 

 difficulties, only uses simple means, and creates by their combination 

 I know not what tangled skein. Here it is the hidden simplicity which 

 must be disentangled. Examples to the contrary abound. In the 

 kinetic theory of gases, molecules of tremendous velocity are dis- 

 cussed, whose paths, deformed by incessant impacts, have the most 



