EVIDENCE PROVING THE STATEMENT OF THE CASE 39 



simply a calculating machine. It is a physiological 

 phenomenon. This misfortune arises from the physicist's 

 allowing metaphysical ideas, i.e. mathematical ideas, to 

 be his master instead of his servant. 1 In the latter 

 capacity the science of mathematics is very useful ; in 

 the former capacity, it is absolutely mischievous and 

 prevents progress. The physicist has departmental 

 ideas which may be illustrated thus : he conceives that 

 he has the power of multiplying groups of objects- 

 masses of atoms or molecules, by groups of similar 

 objects. Also to multiply forces by forces and inversely 

 to divide them. 



Let us illustrate the conception. An apple is a 

 group of molecules, and so is an orange. Let us take six 

 apples and six oranges and attempt to multiply them 

 together to produce a " numerical value " of 36. Then 

 take eight apples and eight oranges and try to 

 multiply them and obtain a " numerical value " of 64. 

 Of course we can do this on paper, but we cannot do it 

 practically. Now these two "numerical values," viz. 

 36 and 64, are very useful because they are proportional 



1 " This method," i.e. the mathematical method, "when rigorously 

 pursued, is the most powerful and satisfactory of all, and results 

 in an ordered province of science far superior to the fragmentary 

 conquests of experiment. But few indeed are the men who can 

 handle it safely and satisfactorily : and none without continual 

 appeals to experiment for verification. . . . For, observe, that the 

 mathematical study of Nature, the discovery of truth with a piece of 

 paper and a pen, has a perilous similarity at first sight to the straw- 

 thrashing subtleties of the Greeks, whose methods of investigating 

 nature by discussing the meaning of words and the usage of language 

 and the necessities of thought, had proved to be so futile and unpro- 

 ductive." (" Pioneers of Science," Prof. 0. Lodge, F.E.S., 1893, 

 p. 157.) 



