BIOLOGICAL RELATIONSHIPS OF THE MATHEMATI- 

 CAL SERIES 1,2, 4, ETC. 



WITH A DESCRIPTION OP A NEW NEMA, TYLENCHUS CANCELLATUS 

 Contributions to a Science of Nematology. XV 



BY N. A. COBB 



The behavior of the components of matter, e.g., in chemical reactions, 

 appears to compel discontinuous variation in the evolution of organisms. 

 Organic evolution has been thought continuous, but mutation now suggests 

 that it is discontinuous. Must it not necessarily be discontinuous 1 from the 

 very ' nature of the composition of matter? Morphological changes in 

 organisms originate in chemical changes in the matter of which they are 

 composed. Now, a chemical change is one that either takes place or does 

 not take place; nothing intermediate is known. Hence it seems that the 

 fundamental changes in the evolution of organisms, so far as we can conceive 

 at present, i.e., chemical changes, must be saltatory. But we cannot con- 

 ceive of the greater and obvious (visible) changes, except as summations of 

 these minute changes. The visible changes then must per force be con- 

 sidered of the same character as that of their components, i.e., all visible 

 evolutionary changes in organisms must be of a saltatory nature. 



The mathematics of the morphology of organic evolution may therefore 

 be considered as, at least mainly, discontinuous, -arithmetical. 



The material basis of life is discontinuous, but is the only known form of 

 matter so organized as to grow and multiply by assimilation; in this lies the 

 fundamental difference between living objects and all others; not a mathe- 

 matical difference. 



Matter is dual r or, less abstractly, there exists in matter an exceedingly 

 widespread, probably universal, "bipolarity", exemplified, therefore, in organ- 

 isms. The universality of "bipolarity" is more or less understood and 

 generally admitted. Its universality might be assumed to prove, and at 

 least very strongly suggests, its necessity. Assuming its necessity, this 

 bipolarity determines that cells, as well as many of their components, multi- 

 plying, do so by binary division in a bipolar manner. 2 



1 Mathematics. Arithmetic and its derivatives arose through everyday problems 

 connected with matter, which is discontinuous. The Calculus, mathematics of con- 

 tinuity, arose through problems like those of astronomy, where the continuity of space 

 and time impress us most vividly. 



Quantity. It may be said we cannot conceive of anything so small that it cannot be 

 divided, or so large that nothing can be added to it ; but as the two opposite statements 

 seem just as true, we find ourselves within two limits at each of which we confront some- 

 thing that must be so, but can't be so. Between these two irrationalities lie quantities 

 we can handle rationally by mathematics. 



2 Thence "fore-and-aftness" and bilateral symmetry in organisms arose (doubtless 

 modified by gravity). Bilateral symmetry seems the invariable result of the growth of 

 what we may call, for lack of a better term, "untrammeled protoplasm." When proto- 

 plasm is "hampered," say by inorganic materials tending to produce other forms of 

 symmetry as, for instance, through the laws of crystallization then bilaterality may 

 be more or less masked; otherwise it is manifest. We readily recognize it in nearly all 

 animals and plants. 



.371 



