264 



CHAPTER XIII. 

 CALCULATING PBODIGIES. 



At rare intervals there have appeared lads who possess 

 extraordinary powers of mental calculation*. In a few seconds 

 they gave the answers to questions connected with the multipli- 

 cation of numbers and the extraction of roots of numbers, which 

 an expert mathematician could obtain only in a longer time 

 and with the aid of pen and paper. Nor were their powers 

 always limited to such simple problems. More difficult questions, 

 dealing for instance with factors, compound interest, annuities, 

 the civil and ecclesiastical calendars, and the solution of equa- 

 tions, were solved by some of them with facility as soon as the 

 meaning of what was wanted had been grasped. In most cases 

 these lads were illiterate, and usually their rules of working 

 were of their own invention. 



The performances were so remarkable that some observers 

 held that these prodigies possessed powers differing in kind 

 from those of their contemporaries. For such a view there is no 

 foundation. Any lad with an excellent memory and a natural 

 turn for arithmetic can, if he continuously gives his undivided 

 attention to the consideration of numbers, and indulges in 

 constant practice, attain great proficiency in mental arithmetic, 

 and of course the performances of those that are specially 

 gifted are exceptionally astonishing. 



* Most of the facts about calculating prodigies have been collected by 



E. W. Scripture, American Journal of Psychology, 1891, vol. it, pp. 1 — 59; by 



F. D. Mitchell, Ibid., 1907, vol. xvm, pp. 61—143; and G. E. Muller, Zur 

 Analyse der Gedachtnistatigkeit und des Vorstellungsverlaufes, Leipzig, 1911. 

 I have used these papers freely, and in some cases where authorities are quoted 

 of which I have no first-hand information have relied exclusively on them. 

 These articles should be consulted for bibliographical notes on the numerous 

 original authorities. 



