Precocious Mental Calculation
A rare exceptional instance of this faculty being cultivated and matured for a highly-useful purpose, is presented in the case of Mr. Bidder, the eminent civil engineer, known in his childhood as “the Calculating Boy.” (See a portrait in the Boy’s Own Book.)
George Parkes Bidder, when six years old, used to amuse himself by counting up to 100, then to 1000, then to 1,000,000: by degrees, he accustomed himself to contemplate the relations of high numbers, and used to build up peas, marbles, and shot, into squares, cubes, and other regular figures. He invented processes of his own, distinct from those given in books of arithmetic, and could solve all the usual questions mentally more rapidly than other boys with the aid of pen and paper. When he became eminent as a civil engineer, he was wont to embarrass and baffle the parliamentary counsel on contested railway bills, by confuting their statements of figures almost before the words were out of their mouths. In 1856, he gave to the Institution of Civil Engineers an interesting account of this singular arithmetical faculty—so far, at least, as to show that memory has less to do with it than is generally supposed: the processes are actually worked out seriatim, but with a rapidity almost inconceivable. They are accomplished mentally by occupying the mind simultaneously with the double task of computing and registering. The first—computing—is executive, or reasoning, and is that portion of the process, which, whilst it is the most active, is not that which causes the greatest strain upon the mind. The result is recorded by the second faculty, registering, which is the real strain upon the mind, and that by which alone the power of Mental Calculation is limited.
Experience has shown that, up to a certain point, the power of registering is as rapid as thought; but the difficulty increases, in a very high ratio, in reference to the number and extent of impressions to be registered, until a point is reached, the registering of which, in the mind and by writing, are exactly balanced. Below that point, mental registration is preferable; above it, that by writing will be as quick, and more certain.
All the rules employed by Mr. Bidder were invented by him, and are only methods of so arranging calculation as to facilitate the power of registration: in fact, he thus arrives at a sort of natural algebra, using actual numbers in the place of symbols. When he first began to deal with numbers (in his 6th year), he had not learned to read, and certainly long after that time he was taught the symbolical numbers from the face of a watch.
A brief outline of Mr. Bidder’s method is given in the Year-Book of Facts, 1857, pp. 149-152. The paper, in extenso, has been edited and published by Mr. Charles Manby, F.R.S., Honorary Secretary to the Institution of Civil Engineers.