-■246 Ohio State Academy of Science 



Now to biology and sociology, having to do with single 

 individuals differing from one another, in biology cells, in soci- 

 ology human personalities, the continuity mathematics with its 

 universalism is so ill adapted by its nature that the discrete way 

 of thinking must here soon take the chief role, giving as it does 

 large and free play to the individual peculiarities of the elements 

 to be studied. 



The continuity thought-way strives to reduce all phenomena 

 of nature to a general mechanism with fate-determined move- 

 ment. Just contrary to this then is the view that living nature 

 is a rationally-correllated realm, in which everything is harmonic, 

 shows adaptation, strives toward perfection. 



Are not the mechanical form-phenomena of the living 

 organism only its most elementary properties, upon which are 

 built others higher, psychic? Now the psychic properties of a 

 living organism cannot be studied by observation and compari- 

 son of the accompanying mechanical properties unless they flow 

 from these mechanical properties. If these accompaniments be 

 unessential, the psychic properties cannot be concluded from 

 them. Here is even yet the battleground. 



Biologists are at present emphasizing the statistical method, 

 but upon this modern mathematics has for them another mes- 

 sage. They rely upon the method of least squares and mean 

 value. But Chebyshev has demonstrated that not the great 

 number but the independence of the metric phenomena plays 

 the chief part in the application of the theory of mean value. 

 This independence is the essential requisite, and it is the very 

 thing whose unwarranted assumption vitiates much biologic 

 research. 



An illustration may be drawn from fire insurance. From 

 the records of past conflagrations of single houses, if the burning 

 of each one is independent of that of every other, the theory of 

 mean value can get a number which can be counted upon to 

 recur with slight variation from year to year, and upon it can be 

 based the charges for insurance. 



To realize how completely this essential requirement may 

 be lacking, we have only to remember the Chicago fire, or the 

 Baltimore fire. 



Biologists have treated their combinations as if they were 

 simple summations of independent elements. 



More likely are the combinations composed of interdepen- 

 dent factors whose symbolization must be at the simplest a 

 -product. 



A tremendous illustration of variation under change of 

 stimuli is given by Japan. For centuries environment and 

 potential variability were in static balance; variation was zero. 



