XVII] THE COMPARISON OF RELATED FORMS 1029 



than the features in which it agrees; and even that the pecuUar 

 aesthetic pleasure with which we regard a living thing is spmehow 

 bound up with the departure from mathematical regularity which 

 it manifests as a peculiar attribute of life. This view seems to me 

 to involve a misapprehension. There is no such essential difference 

 between these phenomena of organic form and those which are 

 manifested in portions of inanimate matter*. The mathematician 

 knows better than we do the value of an approximate resultf. The 

 child's skipping-rope is but an approximation to Huygens's catenary 

 curve — but in the catenary curve lies the whole gist of the matter. 

 We may be dismayed too easily by contingencies which are nothing 

 short of irrelevant compared to the main issue ; there is a jyrinciple ' 

 of negligibility. Someone has said that if Tycho Brahe's instruments 

 had been ten times as exact there would have been no Kepler, no 

 Newton, and no astronomy. 



If no chain hangs in a perfect catenary and no raindrop is a perfect 

 sphere, this is for the reason that forces and resistances other than 

 the main one are inevitably at work. The same is true of organic 

 form, but it is for the mathematician to unravel the conflicting 

 forces which are at work together. And this process of investigation 

 may lead us on step by step to new phenomena, as it has done 

 in physics, where sometimes a knowledge of form leads us to the 

 interpretation of forces, and at other times a knowledge of the forces 

 at work guides us towards a better insight into form. After the 

 fundamental advance had been made which taught us that the world 



* M, Bergson repudiates, with peculiar confidence, the appHcation of mathe- 

 matics to biology; cf. Creative Evolution, p. 21, "Calculation touches, at most, 

 certain phenomena of organic destruction. Organic creation, on the contrary, 

 the evolutionary phenomena which properly constitute life, we cannot in any way 

 subject to a mathematical treatment." Bergson thus follows Bichat: "C'est 

 peu connaitre les fonctions animales que de vouloir les soumettre au moindre 

 calcul, parceque leur instabUite est extreme. Les phenomenes restent toujours 

 les memes, et c'est ce qui nous importe; mais leurs variations, en plus ou en moins, 

 sont sans nombre" (La Vie et la Mort, p. 257). 



t When we make a 'first approximation' to the solution of a physical problem, 

 we usually mean that we are solving one part while neglecting others. Geometry 

 deals with pure forms (such as a straight line), defined by a single law; but these 

 are few compared with the mixed forms, like the surface of a polyhedron, or a 

 segment of a sphere, or any ordinary mechanical construction or any ordinary 

 physical phenomenon. It is only in a purely mathematical treatment of physics 

 that the "single law" can be dealt with alone, and the approximate solution 

 dispensed with accordingly. 



