Relying on calculators and computers is a catastrophic loss of mental arithmetic. It is all the more surprising for many of us that there are human counters in the world who can perform the most complex calculations without the use of technical means.
THEY COULD REPLACE THE COMPUTER
One of the earliest miracle calculators, about which written evidence has been preserved, was Jedediah Buxton, who was born around 1707 in Elmton (Derbyshire, UK).
Although he was the son of a village teacher, no one was involved in his education, and he never learned to read or operate with numbers.
If you do not take into account his computing gift, then in all other respects he was distinguished by low mental abilities: absolutely devoid of ambition, he remained a simple agricultural worker all his life and did not derive any material benefit from his exceptional skill, except for the small sums that he occasionally received from those who forced him to demonstrate his art. Buxton died in 1772.
Buxton did not remember when and why he first became interested in oral calculations; there are no reliable details about his first performances. However, numbers seemed to have always worried him. When it came to the size of an object, he immediately began to count how many inches or "hair thickness" there were; if a period of time was mentioned, he counted how long it was in minutes; listening to the sermon, he thought only of how many words or syllables it contained.
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Through constant practice his natural qualities have undoubtedly increased; however, his ideas remained childishly naive and did not go beyond pride in his own ability to accurately perform such calculations. Buxton was slow-witted and spent much more time solving arithmetic problems than other miracle calculators. He found the only practical application of his abilities in the fact that, having walked over a field of irregular shape, he could immediately determine its area.
Englishman George Parker Bidder was born in 1806. His ability to count was manifested at an early age, but his father did not want to give him an education. There was a man who appreciated the boy's abilities, thanks to his help Bidder went to school. The boy's father wanted to send him to the circus to earn money from him. However, Bidder had patrons that gave him the opportunity to graduate from college.
In 6 minutes, George multiplied 257 689 435 by 356 875 649. He had a phenomenal memory, he could remember 43 numbers at once, pronounced only once. Bidder became a railroad engineer in 1834, and George's extraordinary ability helped his country quickly establish a railroad network. Bidder played the role of a computer, which did not exist at that time, with his help many projects were quickly and efficiently calculated.
Frenchman Henri Mondet worked as a shepherd from early childhood. Henri's favorite pastimes were counting the flints he had in rows and the following combination of the numbers they represented. Little by little, he reached such speed of counting that he began almost instantly to answer questions from people he met about the number of hours or even minutes representing their age.
Someone Jacobi gave him an initial school education, after which he presented him on November 16, 1840 to the Paris Academy. sciences, which for the study of the remarkable phenomenon presented by Monde appointed a special commission made up of academicians Arago, Cauchy, Serre, Liouville and Sturm. In a meeting of the academy before the election of the commission, Monde gave the correct answers to the questions: what is the square of 756 and how many minutes in 52 years.
In the report of the commission on the results of the research entrusted to it, presented at the meeting on December 14, 1840, Cauchy said: “At present, he easily performs in his mind not only various arithmetic operations, but in very many cases also the numerical solution of equations; he sometimes invents wonderful processes for solving many different questions, usually treated with the help of algebra, and determines, in his own ways, exact or approximate values of integers or fractional numbers satisfying the indicated conditions."
The negro Thomas Fuller was born in Africa in 1710. In 1724 he was sold into slavery and brought to Virginia (USA), where he lived until his death; Fuller died in 1790. Like Buxton, Fuller did not learn to read or write; all his abilities were limited to the ability to count in the mind.
He coped with the multiplication of two numbers, each of which contained no more than nine digits; could count the number of seconds in a given time interval; the number of grains in a given volume, etc. - in short, to solve standard problems usually offered to such calculators, if they did not contain anything more complicated than multiplication and the triple rule.
Jacques Inody was born in 1867 in Onorato (Italy). In his childhood he tended cattle, and in those long hours when work allowed, he liked to think about numbers; nor did he use any specific objects like pebbles.
Inody's ability to count first attracted attention around 1873. Soon after, his older brother went to Provence to try his luck as an organ grinder.
Accompanying him, young Inody found himself in the thick of life and managed to earn some coins, demonstrating his art on the streets. Variety entrepreneurs became interested in him - so in 1880 he came to Paris. During the performances, the op conquered the audience with modesty, honesty and spontaneity.
In those days he still could neither read nor write; he learned this later. There was nothing particularly remarkable in his first speeches compared to other calculators, but through continuous practice he was constantly improving.
So, speaking in 1873 in Lyon, he almost instantly multiplied two three-digit numbers. In 1874 he could multiply six-digit numbers. Nine years later, he was already very quickly coping with the multiplication of nine to ten-digit numbers.
Later still, in Paris, when Darboux asked him to cube 27, he spent only 10 seconds on it. In 13 seconds, he calculated how many seconds contain 18 years 7 months 21 days and 3 hours, and instantly calculated the square root of one-sixth of the difference between the square of 4801 and one.
He easily calculated the amount of wheat owed to Sethe, the inventor of chess, who, according to legend, demanded 1 grain for the first square of the chessboard, 2 grains for the second, 4 for the third, etc. in geometric progression.
Inody knew how to find integer roots of equations and integer solutions to problems, but he acted only by trial and error. A special quality inherent only to him was his remarkable ability to represent numbers less than 105 as the sum of three squares. He usually did it in one or two minutes. He often solved such problems in an informal setting, but not on the stage, since they required a lot of mental stress.
Let's remember another unique man-counter - a native of Denmark Willem Klein (1912-1986). It has been listed in the Guinness Book of Records for its ability to extract the 73rd root of a 500-digit number. This process took him only 2 minutes and 43 seconds. During the 1920s and 1930s, Klein demonstrated his unique abilities in the circus.
In 1958, he began to apply his gift at the European Organization for Nuclear Research, where he worked for 19 years. Then Klein moved to Amsterdam. Unlike Bidder, who died a natural death in 1878, Klein was stabbed to death in 1986 by an unknown assassin in his own home.
HOW DO THEY DO IT?
Such people were always very interested in psychologists and mathematicians, who tried to find out what the secret of their abilities was. But the explanations that the miracle counters gave, trying to reveal their skill, at first glance seemed strange, and even very.
For example, Urania Diamondi said that her color helps her to own numbers: 0 - white, 1 - black, 2 - yellow, 3 - scarlet, 4 - brown, - blue, 6 - dark yellow, 7 - ultramarine, 8 - gray blue, 9 - dark brown. The process of calculation seemed to her in the form of endless symphonies of color.
Some miracle counters have been scientifically examined. Inody was once invited to a meeting of the French Academy of Sciences. The meeting was reported by the mathematician Darboux. Scientists have come to the conclusion that Inody uses some of the classic techniques that he himself "rediscovered".
One of the commissions at the academy, which, in particular, included the famous scientists Arago and Cauchy, was investigated by Henri Monde. According to Cauchy, the semi-literate son of the woodcutter Modé used Newton's binomial. The academy came to similar conclusions during an experiment in 1948 with Maurice Dagber.
Monde and Kalbyurn clearly saw the rows of numbers drawn by an invisible hand before their eyes. Their "trick" was to read this "magic" record. Urania's brother, Perricles Diamondi, said: "The numbers seem to accumulate in my skull."
Inody's method is very "simple". It seemed to him that someone's voice was counting instead of him, and while this inner voice was doing the calculations, he himself either continued to talk or was playing the flute. Maurice Dagber makes dizzying calculations while playing the violin.
Several years ago in France, in Lille, in the presence of an authoritative jury of physicists, engineers, cyberneticists, mathematicians and psychologists, Maurice Dagber entered into a dispute with an electronic computer that produces about a million operations per second.
Dagber said that he would admit himself defeated only if the machine solved seven problems earlier than he ten … Dagber solved all ten problems in 3 minutes 43 seconds, and the electronic machine in only 5 minutes 18 seconds.
IS IT POSSIBLE TO “STAMP” SUPERVALUES?
From modern people-counters, one cannot but mention Alberto Coto Garcia, who was born on May 20, 1970. At the moment, he is one of the most famous "counters". In addition to his work as a financial advisor and accountant, Alberto often appears on popular television programs.
At the moment, he is considered the fastest-performing human counter on Earth. It costs him nothing to multiply two eight-digit numbers, it takes him 8 minutes and 25 seconds. But Alberto can add two 100-digit numbers in 19.23 seconds.
The study of the abilities of super-calculators, as people-counters are now often called, is of interest to science. Alfred Binet began to study such people in the laboratory of physiological psychology in Paris in the 19th century. He did not reveal the essence of the phenomenon, but made a number of generalizations concerning people-counters.
For example, Binet established the absence of heredity of this phenomenon, the manifestation of the ability to count in childhood, its development with constant exercise and extinction in the absence of use.
Now there are certain techniques that can greatly reduce the calculation in the mind. Through hard training, you can achieve significant success in this area, but no training will help you become a real human counter. It is still unclear how a supercomputing can be made of an ordinary person; it remains to be determined.