Nervously unstable children are, as Burt has pointed out, often deficient in arithmetic, even when in general intelligence they are not deficient. This follows from the same causes of failure as were set forth under discussion of nervous instability and special difficulty in reading. To build up little by little the intricate hierarchy of arithmetical habits, each habit in its essential sequence, is a task uncongenial to the flighty, uncontrolled, or negativistic neurotic.
Individual instruction is here, again, the solution of the problem. The neurotic can learn arithmetic within the limits of his intelligence, by means of patient individual instruction, given preferably at rather brief sittings.
VIII. ARITHMETICAL PRODIGIES
Extremely great ability to perform feats of mental arithmetic excites popular wonder and admiration to a degree far beyond that excited by most other manifestations of mental gifts. This may be due to the fact that in calculation each individual has a rather definite standard of performance, namely his own ability to calculate. When another goes far beyond him and his friends, in so definite a performance, he can see for himself that the typical has been phenomenally exceeded. The gifted person who exceeds the typical to an equal extent in perception of the fine shades of meaning in words, or in the detection of absurdities and contradictions in demagogy, creates no sensation among his fellow townsmen; for there is no way whereby the average man can “check up” in the performances, to show himself how phenomenally he has been exceeded in capacity for them.
Bidder, the famous English calculator, is recorded in history because he could perform mental arithmetic perhaps fifty times as well as typical persons. The facts that he also became one of the most successful civil engineers of his time, and made a large fortune, are noted as of merely incidental interest, and would not have given him a place in the history of unusual persons. A man may make fifty times as much money as the average man does, by meeting with fifty times as much acumen and energy the intricate, subtle, and difficult situations offered by modern economic life. Yet he is not so very likely to be regarded as prodigiously gifted. His fellowmen can and will explain the difference between him and themselves as due to luck or circumstance. But a gift for “lightning calculation” is obviously peculiar to the person, and makes of him an object of wonder.
The same general considerations hold in the case of children. Many children of extraordinary intelligence are found, because they have attracted attention to themselves by excellence in arithmetic; and upon examination show themselves to be equally excellent at those tests which measure IQ, excellence in which is not necessarily conspicuous except to the trained psychologist.
Accounts of prodigious calculators go back to ancient Greece, in Lucian’s reference to Nikomachos of Gerase. The word “calculation” means literally “pebbling,” coming from the Latin calculi, pebbles. Records of lightning calculators have been collected by Scripture and by Mitchell.
Jedediah Buxton (b. 1702) appears to be the first calculator on record in modern accounts. He lived at Elmton, England. “He labored hard with a spade to support a family, but seems not to have shown even usual intelligence in regard to ordinary matters of life.... In regard to matters outside of arithmetic he appeared stupid.” In 1754, when he was taken to London to be tested by the Royal Society, he went to see King Richard III performed. “During the dance he fixed his attention upon the number of steps; he attended to Mr. Garrick only to count the words he uttered. At the conclusion of the play, they asked him how he liked it.... He replied that such and such an actor went in and out so many times, and spoke so many words; another so many.... He returned to his village, and died poor and ignored.” It is said that he could give an itemized account of all the free beer he had had from the age of 12 years.
Tom Fuller, “The Virginia Calculator” (b. 1710), seems to be another case of highly specialized ability. He came from Africa as a slave when about 14 years old. He is first heard of as a calculator at the age of 70 years, when it is stated that he reduced a year and a half to seconds in about two minutes, and 70 years, 17 days, 12 hours to seconds in about a minute and a half, correcting the result of his examiner, who had not taken leap years into the reckoning. He also calculated mentally the sum of a simple geometric progression, and multiplied mentally two numbers of nine figures each. He was totally illiterate.
Other prodigious calculators, who are not known to have had superior general ability, are Zerah Colburn (b. 1804), Henri Mondeux (b. 1826), Jacques Inaudi (b. 1867), and Ugo Zaneboni (b. 1867). None of these individuals achieved eminence in any other respect, but this does not necessarily prove that they were not of superior intelligence. It would have been impossible, for instance, for the slave, Tom Fuller, to achieve intellectual eminence in a profession.