Biology and Mathematics 247 



Then came Commodore Perry, humiliations to the inordinate 

 pride of a hermit nation, defeats, contempt, a tremendous 

 response to the changes in stimuli, and today dark pagan Japan 

 is easily defeating the largest European Christian white nation: 

 variability unchanged, variation the greatest recorded in human 

 history. 



According to Quetelet's celebrated law of variability pub- 

 lished some years after Darwin's Origin of Species, it is subject 

 to the law of probability, and according to this law the occur- 

 rence of variations, their frequency and their degree of variation 

 can be calculated and predicted in the same way as the chance 

 of death, of murders, of fires. 



But such applications did not fit actual evolution, since the 

 law is to deal with different degrees of the same qualities, giving 

 a continuity production of species, while as De Vries has so 

 stressed, the origin may be by abrupt jumps, by sports, by 

 mutations. 



De Vries has said that a thorough study of Quetelet's law 

 would no doubt at once have revealed the weak point in Darwin's 

 conception of the process of evolution. It would have shown 

 that the phenomena which are ruled by this law and which are 

 bound to such narrow limits, cannot be a basis for the explanation 

 of the origin of species. 



It rules the degrees and amounts of qualities, but not the 

 qualities themselves. 



Species, however, as De Vries says, are not in the main dis- 

 tinguished from their allies by -quantities, nor by degrees; the 

 very qualities differ. 



How such differences of qualitative character have been 

 created is the burning question. They have not been explained 

 by continuous accretion of individual variations. 



The attitude "of the new mathematics strongly favors 

 attempts like the mutation theory, based on the abrupt, explo- 

 sive changes, wholly discrete, which under the name of "sports" 

 had long been observed and known in horticulture and animal 

 breeding, and of which DeVries has found a whole fusillade being 

 shot off by "Lamarck's evening primrose." 



Here he says there is no gradual, no continuous change or 

 modification, nor even a common change of all the individuals. 

 On the contrary, he says, the main group remains wholly unaf- 

 fected bv the production of new species. After eighteen years 

 it is absolutelv the same as at the beginning. It is not changed 

 in the slightest degree. Yet it produces in the same locality, 

 and at the same tim,e, from the same group of plants, a number 

 of new species diverging in different ways. '^^ ^^ 



The vastly vaunted natural selection, then, can only destroy 

 new species, never create them. 



