640 ãThere can be no doubt that Fraas is correct in regarding this type (Procetus) as an annectant form between the Zeuglodonts and the Creodonta, but, although the origin of the Zeuglodonts is thus made clear, it still seems to be by no means so certain as that author believes, that they may not themselves be the ancestral forms of the Odontocetiã; Andrews, Tertiary Vertebrata of the Fayum, 1906, p. 235.
CHAPTER XVII ON THE THEORY OF TRANSFORMATIONS, OR THE COMPARISON OF RELATED FORMS
642 M. Bergson repudiates, with peculiar confidence, the application of mathematics to biology. Cf. Creative Evolution, p. 21, ãCalculation 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 mathôÙeôÙmatôÙiôÙcal treatment.ã
643 In this there lies a certain justification for a saying of Minotãs, of the greater part of which, nevertheless, I am heartily inclined to disapprove. ãWe biologists,ã he says, ãcannot deplore too frequently or too emphatically the great mathôÙeôÙmatôÙiôÙcal 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 until its results can be expressed mathôÙeôÙmatôÙiôÙcally. 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 experiences, which we make as very little children and of which no adult has any recollection.
The fact that from this basis men of genius have evolved wonderful methods of dealing with numerical relations should not blind us to another fact, namely, that the observational basis of mathematics is, psychologically speaking, very minute compared with the observational basis of even a single minor branch of biologyã....ãWhile therefore here and there the mathôÙeôÙmatôÙiôÙcal methods may aid us, we need a kind and degree of accuracy of which mathematics is absolutely incapableã....ãWith human minds constituted as they actually are, we cannot anticipate that there will ever be a mathôÙeôÙmatôÙiôÙcal expression for any organ or even a single cell, although formulae will continue to be useful for dealing now and then with isolated details...ã (op. cit., p. 19, 1911). It were easy to discuss and criticise these sweeping assertions, which perhaps had their origin and parentage in an obiter dictum of Huxleyãs, to the effect that ãMathematics is that study which knows nothing of observation, nothing of experiment, nothing of induction, nothing of causationã (cit. Cajori, Hist of Elem. Mathematics, p. 283). But Gauss called mathematics ãa science of the eyeã; and Sylvester assures us that ãmost, if not all, of the great ideas of modern mathematics have had their origin in observationã (*Brit. Ass.
Address, 1869, and Laws of Verse*, p. 120, 1870).