40 GENERAL VIEW AND BASIS OF SCIENTIFIC RESEARCH. 



Many extraordinary instances have been recorded .of 

 extremely high degrees of innate sensitiveness to parti- 

 cular classes of ideas, especially those relating to numbers 

 and sounds. 



' The case of Zerah Colburn, the son of an American 

 peasant, is especially remarkable among these, not only 

 for the immediateness and correctness with which he 

 gave the answers to questions resolvable by simple but 

 prolonged computation such as the product of two num- 

 bers, each consisting of two, three, or four figures ; the 

 exact number of minutes and seconds in a given period of 

 time ; the raising of numbers up to high powers ; or the 

 extraction of the square and cube roots but, still more, 

 for his power of at once answering questions to which no 

 rules known to mathematicians would apply.' 



' On being interrogated as to the method by which he 

 obtained these results, the boy constantly declared that he 

 did not know how the answers came into his mind. In 

 the act of multiplying two numbers together, and in the 

 raising of powers, it was evident (alike from the facts just 

 stated and from the motions of his lips) that sortie opera- 

 tion was going forward in his mind ; yet that operation 

 could not (from the readiness with which the answers were 

 furnished) have been at all allied to the usual modes of 

 procedure, of which, indeed, he was utterly ignorant, not 

 being able to perform on paper a simple sum in multi- 

 plication or division. But in the extraction of roots and 

 in the discovery of factors of large numbers it did not 

 appear that any operation could take place, since he 

 answered immediately, or in a very few seconds, questions 

 which, according to the ordinary methods, would have 

 required very difficult and laborious calculations; and 

 prime numbers cannot be recognised as such by any known 

 rule.' 



