WILLIAM McDOUGALL 155 



powers from such rudiments as we find in the animal 

 world. 



One of these is the mathematical capacity. If we 

 see a dull boy labouring with the principles of elemen- 

 tary arithmetic or geometry or algebra, his mathe- 

 matical capacity inspires in us no respect and no won- 

 der. But sometimes we find a boy, in all other respects 

 dull and commonplace enough, who displays a most 

 astonishing and wholly inexplicable capacity to solve 

 (to return true answers to) almost instantaneously, 

 most difficult arithmetical problems, such as extracting 

 the cube roots of high numbers or raising numbers to 

 the nth powers. In some such cases a quite unusually 

 vivid visual memory seems to be involved. But in 

 some cases even the assumption of such memory raised 

 to an unknown degree of vividness and accuracy leaves 

 the achievement utterly inexplicable. And, mysteri- 

 ously enough, this strange capacity in some cases fades 

 away, as mysteriously as it came, leaving its erstwhile 

 possessor a very ordinarily endowed human being. 

 Put alongside these facts the facts of mathematical 

 genius of a high order, such as that of Pascal, of 

 Newton or of Kelvin, and the problem assumes deeper 

 mystery and deeper significance. 



That the human race should have evolved from its 

 ancestral foundations of animal capacity the power of 

 simple counting, measuring and calculating seems of 

 no exceptional significance. Such powers are of ob- 

 vious biological utility; and, if the Lamarckian prin- 

 ciple be valid, may well have improved greatly through 

 use in the civilized races of mankind. But neither 

 natural selection nor the Lamarckian principle can in 

 the least account for the genesis of either the talents 



