1030 THE THEORY OF TRANSFORMATIONS [ch. 



was round, Newton shewed that the forces at work upon it must 

 lead to its being imperfectly spherical, and in the course of time its 

 oblate spheroidal shape was actually verified. But now, in turn, 

 it has been shewn that its form is still more complicated, and the 

 next step is to seek for the forces that have deformed the oblate 

 spheroid. As Newton somewhere says, "Nature dehghts in trans- 

 formations." 



The organic forms which we can define more or less precisely 

 in mathematical terms, and afterwards proceed to explain and to 

 account for in terms of force, are of many kinds, as we have seen; 

 but nevertheless they are few in number compared with Nature's 

 all but infinite variety. The reason for this is not far to seek. 

 The living organism represents, or occupies, a field of force which 

 is never simple, and which as a rule is of immense complexity. And 

 just as in the very simplest of actual cases we meet with a departure 

 from such symmetry as could only exist under conditions of ideal 

 simplicity, so do we pass quickly to cases where the interference of 

 numerous, though still perhaps very simple, causes leads to a recultant 

 complexity far beyond our powers of analysis. Nor must we foi*get 

 that the biologist is much more exacting in his requirement^, as 

 regards form, than the physicist; for the latter is usually content 

 with either an ideal or a general description of form, while the 

 student of living things must needs be specific. Material things, 

 be they living or dead, shew us but a shadow of mathematical 

 perfection*. The physicist or mathematician can give us perfectly 

 satisfying expressions for the form of a wave, or even of a heap 

 of sand ; but we never ask him to define the form of any particular 

 wave of the sea, nor the actual form of any mountain-peak or hill. 



In this there lies a certain justification for a saying of Minot's, of the 

 greater part of which, nevertheless, I am heartily inclined to disapprove. 

 "We biologists," he says, "cannot deplore too frequently or too emphatically 

 the great mathematical delusion by which men often of great if limited ability 

 have been misled into becoming advocates of an erroneous conception of 

 accuracy. The delusion is that no science is accurate imtil its results can be 

 expressed mathematically. The error comes from the assumption that 

 mathematics can express complex relations. Unfortunately mathematics 

 have a very limited scope, and are based upon a few extremely rudimentary 



* Cf. Haton de la GoupiUiere, op. cit.: "On a souvent I'occasion de saisir dans 

 la nature un reflet des formes rigoureuses qu'etudie la geometrie," 



