The reader may feel that he is overwhelmed by the possibility of this kind of calculation, but before he decides to take up farming instead of arithmetic let us for one moment consider the mental arithmetic which is sometimes done by a certain Lakeland shepherd. During the course of a day his dog may drive past him a flock of perhaps two thousand sheep. At the end of the day he knows not only how many sheep are missing, but which sheep are missing. Now even if one assumes for purposes of argument that a man can learn to tell the difference between one sheep and another, one must admit that even a shepherd requires and can exploit a skill in mental arithmetic which few of us could ever hope to achieve.
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* Mathematical Recreations and Essays. See also Common Sense and Its Cultivation, by Hanbury Hankin, and Mental Prodigies, by Fred Barlow.
* Kiyoshi Mastuzaki may have been a calculating prodigy, using his abacus as Mr. Klein might use his pipe - to occupy his fingers (see page 6).