88 Kansas Academy of Science. 



by habit, so to say, into flesh and blood, and began to penetrate 

 and dominate in physiology, in psychology, in sociology, in biol- 

 ogy. ... So we have the doctrine of a fatalist causality, denial 

 of efficient freedom of the will, belittling of the idealistic endeavor 

 of mankind : hence the pessimistic attitude toward the whole of 

 human existence. . . . But the latest advances in mathematics 

 have rendered unnecessary for biology the wearing of this misfit 

 garment. 



"The new mathematics gives now a standpoint for the explana- 

 tion and treatment of natural phenomena from which the biologic 

 elements need not be suppressed. . . . 



"The continuity thought way strives to reduce all phenomena of 

 nature to a general mechanism with fate-determined movement. 

 Just contrary to this, then, is the view that living nature is a ration- 

 ally correlated realm, in which everything is harmonic, shows adap- 

 tation, strives toward perfection." 



This discovery that discontinuous variation in biology is in ac- 

 cord with non-Euclidian mathematics relieves students of life 

 problems from the necessity of declaring that the method of 

 studying the life sciences differs widely from the method of study- 

 ing the mathematical and physical sciences. Darwin tried to con- 

 form in his great theory of evolution to the Euclidian continuity 

 theory of mathematics; but the occurrence of sports among plants 

 and animals was fatal to his theory of continuous variation. Dar- 

 win's appeal to natural selection to account for wide gaps in the 

 ranks of plant and animal species also failed, for nature could se- 

 lect or reject only what life offered ; and life has always persisted 

 in offering those forms of individuals which contain parts possessed 

 by generations of ancestors, and rarely a form with a few parts, 

 found, perhaps, in one individual in a million, never before found 

 on earth. These individuals, those given the new structures, and 

 called sports or mutations, cannot be accounted for by peculiari- 

 ties of environment, for they and the environment may or may not 

 agree. 



Burbank's experiments in plant-breeding have demonstrated 

 that each species is the sum total of all past strains of heredity 

 more or less modified by their interaction. When several species 

 are crossed by pollination, no man knows what may be the out- 

 come. In 100,000 hybrids produced by such crossing, Mr. Burbank 

 found all shades of intermediate characters and many new ones. 

 Selecting from these hundreds of thousands of hybrids those that 

 possessed the qualities he desired, and destroying the rest, Mr. 



