METHODS OF SCIENCE; NUMBERS 17 



convention or mere definition. These processes 

 of abstraction go on without our knowledge or 

 control. So the formidable machine of mathe- 

 matics is no sooner created to be our servant 

 than, like the "Universal Robots" of a recent 

 play, it develops a will of its own, and when 

 once started cannot be stopped. We begin writ- 

 ing a for the first number, /3 for the second, and 

 when the alphabet is done we proceed with aa, 

 /3/3, and later aaa. But having taken these timid 

 steps we are suddenly appalled by the monster 

 of infinity, for having set up the rules nothing 

 can prevent our minds from hurrying on 

 through an endless series of alphas and betas. 

 We have no sooner begun our set of integers 

 than it has become endless. 



We might go back to the meditations of the 

 little lame boy when a new class is added to the 

 school and he has to distinguish between Eeny 

 and Meeny of the big room and Eeny and 

 Meeny of the small room, and I might relate 

 how when the two classes were joined together 

 he formed the notion of addition and called to 

 his mother with the cryptic remark, "Miny and 

 nigger make toe." But I cannot enter here upon 

 a discussion of the fundamental operations of 

 addition and multiplication, which have been 



