CH. XIII] CALCULATING PRODIGIES 281 



fessional calculator these problems are not particularly difficult. 

 As each number is announced, Inaudi repeats it slowly to his 

 assistant, who writes it on a blackboard, and then slowly reads 

 it aloud to make sure that it is right. Inaudi then repeats 

 the number once more. By this time he has generally solved 

 the problem, but if he wants longer time he makes a few 

 remarks of a general character, which he is able to do with- 

 out interfering with his mental calculations. Throughout the 

 exhibition he faces the audience : the fact that he never even 

 glances at the blackboard adds to the effect. 



It is probable that the majority of calculating prodigies rely 

 on the speech muscles as well as on the eye and the ear to help 

 them to recollect the figures with which they are dealing. It 

 was formerly believed that they all visualized the numbers 

 proposed to them, and certainly some have done so. Inaudi 

 however trusts mainly to the ear and to articulation. Bidder 

 also relied partly on the ear, and when he visualized a number 

 it was not as a collection of digits but as a concrete collection 

 of units divisible, if the number was composite, into definite 

 groups. Ruckle relies mainly on visualizing the numbers. So 

 it would seem that there are different types of the memories 

 of calculators. Inaudi can reproduce mentally the sound of 

 the repetition of the digits of the number in his own voice, and 

 is confused, rather than helped, if the numbers are shown to 

 him in writing. The articulation of the digits of the number 

 also seems necessary to enable him fully to exhibit his powers, 

 and he is accustomed to repeat the numbers aloud before 

 beginning to work on them — the sequence of sounds being 

 important. A number of twenty-four digits being read to 

 him, in 59 seconds he memorized the sound of it, so that he 

 could give the sequence of digits forwards or backwards from 

 selected points — a feat which Mondeux had taken 5 minutes 

 to perform. Numbers of about a hundred digits were similarly 

 memorized by Inaudi in 12 minutes, by Diamandi in 25 minutes, 

 and by Ruckle in under 5 minutes. This power is confined to 

 numbers, and calculators cannot usually recollect a long sequence 

 of letters. Numbers are ever before Inaudi : he thinks of little 



