NA TURK 



7Z 



PSYCHOLOGY OF MEXTAL ARITHMETI. 

 CIANS AND BLINDFOLD CHESS-PLAYERS. 



Psychologie des Grands Calctilateurs et Joiteurs d'Echecs. 

 Par Alfred Binet. (Paris : Hachette and Cie., 1894.) 



WHOEVER may hereafter write about mental im- 

 agery will be imperfectly equipped for liis task unless 

 he has mastered the contents of this curious and instruc- 

 tive volume. It analyses the mental processes of two groups 

 of remarkable men — those who possess extraordinary 

 powers of mental arithmetic, and those who are capable 

 of playing eight or more games of chess, blindfold and 

 simultaneously. The idea of making the inquiry is due 

 to the late Prof. Charcot ; its prosecution has been 

 conducted almost wholly by M. Binet, and principally at 

 his laboratory in the Sorbonne. The prosecution of such 

 an inquiry with the accuracy needed by modern rjsycho- 

 logy is exceedingly difficult, and it is also very difficult 

 to express such results as may be obtained from it, in 

 unambiguous language. The author has, however, suc- 

 ceeded in the latter as well as in the former, and he has 

 framed many happy turns of expression which will 

 contribute to the much desired evolution of psychological 

 language. 



The book begins by quoting the series of historical 

 cases of mental arithmeticians, that was published by 

 Scripture in iSSi, in the American Journal of Psycho- 

 logy. They suffice for making useful generalisations, 

 though few of the cases were tested with much precision. 

 Then the original work commences. It refers to two 

 remarkablecalculators, whoare now living, both of about 

 the age of twenty-six, but whose mental processes entirely 

 differ in their most obvious characteristics. The one is 

 Inaudi, a Piedmontese, who performs his mental sums 

 wholly, or almost wholly, by imagined sounds, one, tiuo, 

 three, &.z. ; the other is Diamandi, a Greek, who attains 

 the same end almost wholly by imagined figures, as 1,2, 

 3, &c. The careful testing of these two men, and the 

 analyses and comparisons of the results, show the 

 strange unlikeness of human minds in the above well- 

 marked features, accompanied, it may be, with a nearer 

 likeness in those deeper and more obscure qualities, 

 which are exceedingly difficult to grasp. I, myself, had 

 the pleasure of testing Inaudi at my own house, in com- 

 pany with a few scientific friends. Even the small 

 number of experiments that there was then time to 

 make, rendered it clear to my own mind that the con- 

 clusions which had been arrived at, after prolonged and 

 careful experiments in France, were i.|uite justified, 

 namely, that he performs his long sums almost wholly by 

 his auditive imagination, supplemented possibly by the 

 motive, or gesture sense, but that the visual form of imag- 

 ination was practically absent during the calculations. 

 His case is an extremely rare one, and proportionately 

 valuable for study. On the other hand, Diamandi is an 

 excellent example of the common type of mental calcu- 

 lators, who work almost wholly by the visual imagination. 

 A comparison between the achievements of Inaudi aiid 

 NO. I30S, VOL. 51] 



Diamandi under similar tests, is the main feature of the 

 first half of Binet's volume. He succeeds in distinctly 

 negativing the assertion that the visual memory, even of 

 a man who is so exceptionally gifted in that way as 

 Diamandi, resembles actual vision either in its accuracy 

 or in its completeness. Thus if a small square table of 

 twenty-five figures, five figures in breadth and five in 

 height, is shown to and learnt by Diamandi, he takes 

 only nine seconds to repeat them in successive lines, 

 but if he is asked to repeat them in the order of the 

 columns, he is just four times as long in doing so, whether 

 the columns are mentally read from their tops downwards, 

 or from their bottoms upwards. He does not therefore 

 read the figures as if they were written on a mental 

 blackboard, which could be done as easily in any one 

 direction as in any other, but he has, in some obscure 

 way, to puzzle the figures out. When another table of 

 twenty-five figures is taken, in which the figures are 

 variously coloured, Diamandi's power of re-presenting 

 colours being about as strong as that of re-presenting 

 form, he has no difficulty in learning them, but he does 

 it by two successive operations, first learning the figures 

 and then the colours, and he is consequently twice as 

 long over his task. This could hardly be the case if the 

 visualised schedule had the completeness of an " after- 

 image " or of a photographic plate. 



A great difficulty in the way of testing the power 



of the memory of professional calculators is caused by 



their habit of accumulating large stores of mnemonic 



; helps, which produce results that simulate those of 



j a direct memory. It is indeed difficult for any one 



to free himself wholly from the use of such helps, 



j which arise unbidden, more or less consciously, certain 



runs of figures, or accidents of position in the page, being 



; more readily fixed in the memory than others. Binet's 



chapter on this subject is very instructive. 



The most famous calculating boys had their calculating 

 faculties developed very early in life. Many began to 

 calculate of their own accord before they could read or 

 write, and for the most part they were born in humble 

 circumstances. It is found, so far as present information 

 goes, that they did not inherit their gifts, except in a few 

 cases, of which the Bidder family is a conspicuous in- 

 stance. For my own part, I hesitate for awhile to accept 

 the above negative result as a fact, and on the following 

 grounds. Two mental peculiarities have to concur in 

 the making of a calculating boy : the one is a special 

 capacity for mental calculation, and the other is a passion 

 to e.xercise it. Both of these peculiarities are rare, and 

 they are not necessarily coordinated, therefore the chance 

 of their concurrence in full force may be very small ir.- 

 deed. I have, however, reason to suppose that the 

 capacity for mental calculation is more common than is 

 usually believed, but that it does not commonly interest its 

 possessor, and may even be unknown and consequently 

 neglected by him. Trustworthy evidence for or against 

 its hereditary transmission could hardly be obtained under 

 these conditions. I may quote the case of a deceased lady 

 of remarkable ability, which I indirectly verified to my own 

 satisfaction at the time. She told me, and her husband 

 confirms my recollection, that one night, while travelling 

 I to the south of France, she could not sleep,' so she 



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