…Not with mathematical prodigies like these…
Lets suspend judgement until we’ve looked at some of them. One of the most thoroughly documented calculators was Jedediah Buxton of Derbyshire ( b. 1707). Buxton’s specialty was interpreting the infinitely large in terms of the infinitesimally small: how many cubic eights of an inch in a rectangular block of stone 23,145,789 yards long by 5,642,732 wide by 54,965 thick? How many grains of corn ( dimensions given) in a bin whose volume is 202,680,000,000,360 cubic miles? He had never heard of billions and trillions, much less the still higher multiples of 1,000, so he made up his own names for two of them: the cube of 1,000,000 ( quintillion) he called a “tribe”; a tribe of tribes ( an undecellion- the figure 1 followed by thirty-six zeroes) was a “cramp.”When Buxton visited London to be examined by the Royal Society, his hosts took him to see Garrick in Richard III. The plot meant nothing to him; he focused his whole attention on counting the words each actor spoke and the number of steps each took. Unlike most eidetics, he found a practical application for his gift: he could glance at any field, whatever its shape, and announce a minutely accurate estimate of its acreage. “In this manner he measured the whole lordship of Elmeton and brought ( the owner) the contents not only in acres, but even in square inches.”
(see link at end)…JEDEDIAH Buxton was born in Elmton, six miles from Chesterfield, Derbyshire, England in 1702, and died in that same village 70 years later. His grandfather, John Buxton, was the vicar of Elmton and his father, William Buxton, was the schoolmaster there. Nonetheless, he was completely illiterate, unable even to write his name.
It is likely that Buxton was somewhat retarded (“Life” 1754:251): “his perpetual application to figures has prevented the smallest acquisition of any other knowledge, and his mind seems to have retained fewer ideas than that of a boy of ten years old, in the same class of life.” He was, however, able to support a family by his labors. A letter to Gentleman’s Magazine from George Saxe of Sherwood Forest, dated February 8, 1751, closes with a reference to Buxton as “this surprizing genius now cloathed in rags and labouring hard with his spade for the support of himself and a large family” (Saxe 1751). A later correspondent, T. Holliday (1751) of Haughton Park, mentions only a wife and daughter. (Buxton was nearing 50 at that time.)
Saxe (1751:61) remarks that he met Buxton by accident the previous summer and “proposed to him the following random question: In a body whose 3 sides are 23145789 yards, 5642732 yards, and 54965 yards, how many cubical 1/8ths of an inch?” Saxe then went about some necessary business, leaving Buxton among 100 or so of his fellow laborers. Saxe returned 5 hours later, having computed the answer in the meanwhile. Buxton said he was ready and asked whether Saxe would have the number forward or backward. Saxe chose the “regular method” and “found that in a line of 28 figures, he made no hesitation nor the least mistake.” Unfortunately, the answer to the problem as stated contains 27, not 28 digits. (Perhaps the last side should have six rather than five figures.)
Saxe (1751:61) also attributes to Buxton considerable surveying skill, being able to pace off a piece of land almost as accurately as could be accomplished with a chain. He had paced off the entire lordship of Elm-ton, and reported its extent to its owner, Sir John Rhodes, “not only in acres, roods, and perches, but even in square inches; after this, for his own amusement, he reduced them into square hairsbreadths, computing … 48 to one side of the inch, which produced an incomprehensible number, that instead of entertaining the mind with any sort of pleasure, serves more to amaze and distract it.” If Buxton erred, he would, in his terms “overhaul,” and search out the error for himself.
On a later but unspecified date, he was visited by T. Holliday of Haughton Park, at the request of the editor of Gentleman’s Magazine, to gather more particulars about Buxton and his calculations. Holiday (1751:347) found him to be “a very illiterate man,” though he had “a good notion of the square, oblong, triangle, and circle.”
The first question posed by Holliday was to give the area of a field 423 by 383 yards (answer: 162,009 square yards, given in two minutes). Holliday then asked Buxton for the acreage of the foregoing field. After 11 minutes he replied (1751:347), “33 acres, 1 rood, 35 perches, 20 yards, and a quarter just.”1 The answer is correct. Read More:http://stepanov.lk.net/mnemo/smith20e.html