24. THE ANATOMY OF SCIENCE 



process of multiplication is division. We write 

 2-^2 = l,4!-^-2^2, but as soon as we have 

 done this our idiotic mathematical machine be- 

 gins stamping out l-f-S,2-f-2, 3-^-2, and so 

 on. We have suggested no operation of which 

 1 -^ 2 is the inverse. The symbol is nonsense, 

 but may it not be what Clifford calls "useful 

 nonsense" ? May we not employ in some way the 

 antics of our absurd machine? 



If we have a set of six things and cut it in 

 the middle we get two sets of three, and it seems 

 perfectly reasonable to express the process as 

 6 -^ 2 = B. Therefore when we split one apple 

 into two equal parts it occurs to us to use one 

 of the nonsensical symbols, 1 -f- 2. We thus find 

 an application for the new symbols, after which 

 they are no longer ridiculous. The new idea even 

 proves applicable to things which cannot be cut 

 in halves. The striking of a bell or the laying 

 of an eigg are events which can hardly be 

 divided. Yet if someone asks us the old conun- 

 drum, "If a hen and a half lay an egg and a 

 half in a day and a half, how many eggs will 

 seven hens lay in seven days.^" we may not be 

 able to give the answer offhand, but we know 

 what the conundrum means. So also vou know 

 what I mean when I say that throughout the 



