58 THEORETICAL BIOLOGY 



CALCULATING AND ESTIMATING 



Since it is possible to count up everything of which we 

 can so much as form a thought, the resulting confusion has 

 led to the development of the art of arithmetic, the first 

 principle of which requires that we shall reckon together only 

 those things that have the same denominator. Thus it is 

 inadmissible to add J and J ; } must first be transformed into 

 f, and then we may calculate that J and f = f. 



In the same way, we must not count up 3 apples and i pear 

 straight away. The apples and pears must first of all be 

 brought under the same conception of " fruit " ; then we may 

 calculate that 3 fruits and i fruit = 4 fruits. 



So it appears that calculation is not merely a summing-up 

 of the rhythms of the attention ; it also has regard to the 

 content of the things to which the attention, stimulated by 

 rhythm, is turned. Only by assuming like content can we 

 institute a calculation having any real sense. 



We take as the common denominator of regular movements 

 the direction-sign ; as the smallest magnitude of movement 

 that remains always constant. It is quite indifferent what 

 name we give to the direction-sign. 



The difiiculty is greater when we try to subject to cal- 

 culation regularly increasing intensity of a sensation. If, for 

 instance, we hold a pail under a tap, we feel the steady increase 

 in the weight ; we can estimate it approximately, but we are 

 quite unable to calculate it. Even if we let the water run in 

 intermittently, that does not help us, for, each time, the 

 estimation of the increase in weight is so uncertain that we 

 dare not use it as the common denominator for calculation. 



Weber has helped us out of this predicament in an in- 

 genious way, by employing as the common denominator the 

 feeling of just perceptible increase in weight and introduc- 

 ing for it the concept of " threshold." By so doing, he has 



