246 OuIo 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 lhving 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; variat‘on was zero. 
