Griffith had, from the age of 3, a passion for counting and made fair records in all studies. He entered school at 10, and attended school seven years. In scope and tenacity of memory, and in rapidity at calculation, he ranked with the best recorded cases, according to the investigators who examined him. Memory was described as very systematic; and rapidity was seen to depend on the great number of numerical relations committed to memory, and upon reduction in number of operations through short-cut methods.
These three examinations were all conducted more than twenty years ago, before standardized methods of measurement had been developed. It is difficult to glean from them, and from the biographical material compiled by Scripture and by Mitchell, what the truth is, as regards the extent to which this gift for calculation was special in these persons. Many of them, as we have seen, were certainly men of genius, with general capacity for selective thinking. Several others probably were not of superior general intelligence, but in no case can we be certain, on the basis of anecdotal evidence alone. Some of them were peasants or slaves, born to manual toil, in the absence of free schools, and in the presence of rigid class distinctions. It is not inconceivable that a child of IQ over 170, condemned by unavoidable environment to herd sheep or pick cotton through his youth, might find relief from the monotony of his work by calculating. As Mitchell, himself a lightning calculator, says, “Given a knowledge of how to count, and later a few definitions, and any child of average ability can go on, once his interest is accidentally aroused, and construct, unaided, practically the whole science of arithmetic, no matter how much or how little he knows of other things.” This statement is probably true, if we change one word, and substitute for “child of average ability,” “child of great ability.”
All who have examined lightning calculators, or searched their biographical records, are agreed that the secret of their power lies in highly developed mechanics. Special habits of combining and recognizing numbers are formed, which differ from ordinary calculation comparatively in somewhat the same way as the method of the child who added 7 + 5 by adding 7 + 2 + 2 + 1, the latter being analogous to the usual method.
The lightning calculator memorizes combinations far beyond those ordinarily memorized, so that he is, for instance, able to add 2581 + 1763 as quickly as an ordinary person can add 15 + 8. He learns multiplication tables up to 100 × 100, whereas we learn only through 12 × 12. He devises and uses many “short cuts,” e.g. multiplying by two easy numbers and taking the difference, instead of multiplying by an awkward number. Multiplication is probably used as the fundamental operation.
This specialization in and perfection of arithmetical connections, by a person of original aptitude for and interest in numbers, results in the prodigious calculator. As Scripture concludes, “These persons had enormous ability to learn calculation, not to calculate without learning.” The rôle played by practice is seen in the fact that if interest in counting wanes, and practice at calculation ceases, the skill acquired deteriorates through disuse. Whatley, and others, who became distracted from calculation by other interests as they grew up, lost the power they had possessed. However, by resuming practice, the skill can be regained by those who have acquired it, as is the case with skills in general.
Satisfaction in mental activity for its own sake is expressed by those calculators who have given introspections. After Safford had lost the power of lightning calculation through disuse, he continued to take pleasure in factoring large numbers, or in satisfying himself that they were prime. The younger Bidder said, “With my father, as with myself, the handling of numbers or playing with figures afforded a positive pleasure, and constant occupation of leisure moments. Even up to the last year of his life,[[16]] my father took delight in working out long and difficult arithmetical and geometrical problems.”
All who have studied material relating to prodigious calculators have especially stressed the very early age at which the gift has shown itself. This is especially true of those who achieved greatness in science, as adults. Gauss, Whatley, and Ampère were all first noted at the age of 3 years, and Safford and Bidder at the age of 6 years. It appears to the present writer to be probable that any child of IQ over 180 could be taught to be a lightning calculator. This inference comes from observing such children, as they master numbers.
IX. ARITHMETICAL ABILITY OF TWO CHILDREN OF IQ 184 AND IQ 187 (STANFORD-BINET)
To illustrate mathematical aptitude in children of high IQ, a brief account is herewith given of two boys, both known professionally to the present writer since early childhood. These children are both of a degree of general intelligence so rare as to be scarcely ever found, and both are especially interested in mathematics.
The boy D, of IQ 184, was described first by Terman, in The Intelligence of School Children. His achievements are most remarkable in every kind of intellectual activity, including music and drawing. Among his favorite pastimes since infancy has been the manipulation of numbers. His calculations, dating from the time his hand could wield a pencil, have covered hundreds of pages. As a child of 7, 8, and 9 years, D found the keenest satisfaction in deriving formulæ to render himself unbeatable at family games based on number. At the age of 12 years he has completed the mathematical curriculum of the elementary and secondary schools, through arithmetic, algebra, geometry, and trigonometry. (It should be added that he has also completed the curriculum of the elementary and secondary schools in all other respects, and is ready at 12 years to enter college.)