Mnemonic - Articles

J . I N A U D I The most extaordinaire Calculateur of the modern time This article was publishes by THE ILLUSTRATION and POPULAR ASTRONOMY under the signature of CAMILLE FLAMMARION The eminent Astronomer Price : 1 f. 50

NOTE on JACQUES I N A U D I The most extraordinary Calculateur of the modern time This article was publishes by THE ILLUSTRATION and THE POPULAR ASTRONOMY under the signature of CAMILLE FLAMMARION the eminent Astronomer

- 3 - Curiosity                             Mathematics The prodigy Computer INAUDI I am delighted to give here my appraisal of Inaudi, as I have observed him for a long time in his marvellous feats of calculation, ever since he first aroused interest upon his arrival in Paris at the age of thirteen. Inaudi is comparable with a musician who charms us without ever having learned music, and without knowing a single note. When he arrived in Paris, he could neither read nor write and did not know a single figure. He had been unable to make an addition with a pencil. However, he gave almost instantaneously the solution to the most complicated problem. He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes - while amusing himself with another activity.

- 4 - He could not yet extract cube roots, and it was in one of our sessions that he carried out the first test of them, and flawlessly so. The question had been asked by a mathematician of the Academy of Sciences. The very term was unknown to him, because he had confused it with "public root", and, for more than a year, he knew it by this expression alone. His face was of a striking prominence. His head was malformed, resembling that of a child with meningitis, familiar from the Spanish postage stamps. The general shape of the head changed appreciably with age. His facial angle is normal and almost gives the Greek profile. But if the face is incomparably less bomb-??? than it was ten years ago, there remains on his skull a rather curious feature: at the top, along the line corresponding to the meeting on the two cerebral hemispheres, one sees, and feels to the touch, a rather deep furrow apparently separating the two hemispheres, and this area of the skull is covered only with a slight envelope very sensitive to the touch: the skull is not yet closed. Inaudi's capacity for calculation is truly extraordinary. As I write these lines, he is in my office, and, in order to analyse his method, I have just proposed to him an unspecified problem. A clock is in front of me. I first require the multiplication of two numbers of three digits, viz., 869 by 427. I look at the seconds hand; at the sixth second, he answers: 371,063. Here is the manner of his calculating; it is simple and natural, though contrary to our traditional practice, it begins with the left-hand side and ends with the units:

- 5 - 800 by 400 = 320.000 800 by 27 = 21.600 60 by 400 = 24.000 60 by 27 = 1.620 9 by 400 = 3.600 9 by 27 =       243 Total : 371.063 It is clear that he proceeds by groupings. His method does not resemble our computation formulae and looks embarrassingly simple. He multiplies by only one figure at a time. Ultimately, he did six multiplications and the addition of their products, all in six seconds... actually slightly less, because, at about the fifth second, he said: "I now make the proof while restarting." The most prodigious faculty here is the memory. The numbers given him are fixed in his thought. An hour, a month later, you ask him for them: he remembers without error. But other than for numbers, his memory is unremarkable. I ask him the multiplication of two numbers of five digits each: 70,846 by 88,875, and I look at my watch. He is appreciably longer. After 55 seconds, he answers: 6,296,438,250. And the detail of the operation? Here it is. This example is even more striking. He proceeds by round numbers and adds: 80.000 by 50.000 = 4.000.000.000 80.000 by 20.000 = 1.600.000.000 8.000 by 50.000 = 400.000.000 8.000 by 20.000 = 160.000.000 900 by 50.000 = 45.000.000 900 by 20.000 = 18.000.000

- 6 - He has therefore multiplied first 88,900 by 70,000, giving 6,223,000,000. Now he must subtract the product of 25 and 70,000, i.e. 1,750,000. The result of this subtraction gives 6,221,250,000. There still remains the multiplication of 88,875 by 846. Firstly: 80.000 by 800 = 64.000.000 80.000 by 56 = 3.680.000 8.000 by 800 = 6.400.000 8.000 by 46 = 368.000 And, while holding this result, he multiplies 875 by 846. This he does by first multiplying 900 by 846 and then subtracting 25 by 846. So first: 900 by 800 = 720.000 900 by 40 = 36.000 900 by 6 = 5.400 Then he subtracts 25 x 846 = 21,150. The stages can be summarised this: 6.221.250.000 74.448.000           761.000 6.296.459.000 Take off : 21.150 Total : 6.296.438.250 You can now understand why 55 seconds were necessary, even though the calculation involved only simple multiplications and additions of round numbers. It appeared interesting to present this analysis to our readers, because it gives the key of the method. Its capacity may be summarised thus: marvellous aptitude for calculation, extraordinary speed, and extraordinary memory for numbers. The root extractions and the other problems lead to the same psychological dissection.

- 7 - The other day, at the Institute, Mr Darboux wrote the two numbers: On the one hand, 4.123.547.238.445.523.831 and 1.248.126.138.234.129.310 on the other, and, after having stated the figures, requested that the calculator make the subtraction. Inaudi repeats the problem from memory, because he does not see the written figures behind him. "Is that right?" said he. One answers: "Yes." A smile passes on his lips: "I have the proof", says he, blinking his eyes, and, immediately, announces the correct solution. Mr. Darboux asks him another question: "What is the number whose cube and square sum to 3,600?". Less than two minutes later, Inaudi answers: "It is the number 15." After some other tests, covering a plethora of figures, Jacques Inaudi announces to the Academy that he can speak and calculate at the same time and perform two calculations at once. The following test takes place. Mr Poincare proposes to the calculator the following problem: "4,801 divided by the square root of 6". Mr. Bertrand raises, at the same time, the following question: "What day of the week was on 11 March 1822?" Inaudi answers immediately: "11 March 1822 was a Monday. A person born this day would have lived for so many hours, minutes, seconds." (All these figures were recognised as exact.) The result of the operation proposed by Mr Poincare is the number 1,960. A few days after, in the amphitheatre of the Sorbonne, above Paris, several professors of high standing proposed to him the most complicated operations. He made, with incredible speed, multiplications and divisions

- 8 - covering numbers of 24 digits, extracted the square and cubic roots with 17 decimals. With the calculations complete, he repeats all the numbers that had been written on the board (there were more than 400 figures and on which he had operated without them being visible to him, and that one hour later). The mnemonic capacities of Inaudi are exclusively turned towards the numeric operations and the algebraic problems. The young computer can barely read or write and is, moreover, not concerned with learning. But he is possessed by calculation. This amuses him a lot. His method is self-explanatory, and it is the simplest of all methods. Nobody slightly accustomed to mathematics, if questioned, for example, on the square root of 147, does not see instantaneously in their thought the figure 3 as a remainder and the number 12 as a root, because everyone knows only 12 times 12 make 144. And nobody who, questioned on the cube root of 1,103, for example, does not see, with the same spontaneity, the number 103 as a remainder and the number 10 as a root, given that everyone knows that 10 multiply twice by it-same-same gives 1,000. If one asks an astronomer how much there is of seconds in so many years, he sees immediatement in front of him numbers 864,000 and 365.25. Inaudi has had for a long time in memory all the numbers that return unceasingly in calculations. If you speak with a chemist of substances of carbon and of hydrogen, he sees in front of him a C2 H4 immediately O6 or a C4 H4 O5, as well as the parallax of a star does not appear to the mind without being accompanied by the number 206,265. A music type-setter can see the rules of the counterpoint, or a painter the association of the colours. Ask for Inaudi the fourth or higher (???) root of a number: he will find the solution more quickly in his head than

- 9 - a lesser calculator using log tables. The young computer has made major progress for ten years and can improve still further: His methods are improved continuously, and his keyboard becomes richer by new notes. He currently possesses a formidable knowledge of numbers, of operations performed previously, which serves him as a base, almost a springboard, to spring much further. One intended to say around him formerly: "He cannot survive... He will go mad..." Mistake, his constitution is robust and his head is hard. His life has not been an easy one, and his wisdom is uncommon for someone just forty years of age. His early upbringing was harsh. Born into a poor family in the mountains, he was accustomed more to being hit than being caressed. In his seventh year he tried his luck in the village with his dancing marmot. Sometimes a cold dinner was better than his previous misery. While on his travels, he counted the trees; by crossing the meadows, he saw the number of the poplars; while arriving above a village, he counted the houses, then windows, doors. He counted, counted, an obsession not without charms. One day, while he was in Beziers, he saw a merchant, who, at his table, was calculating what he had sold. With a wry smile, the marmot carrier challenged the merchant: "Would you like me to make you your calculation?" General astonishment! Everybody gathered around the table: "You know, boy, if you are making fun of me, then you should cover your ears!... but if you succeed, I will give you ten under.... "You sold so much, so much and so much. That makes so much." Less of a minute, the turn was done. The ten coins from the merchant fell into the young person's hand and never had the young chap taken so much pleasure from counting.

- 10 - It was the first step. He went from cafe to cafe, of city downtown, as far as Paris and as far as the other capitals, outshining his predecessor Henri Mondeux. Can this extraordinary capacity be exploited by the sciences? Apparently not. One day, ten years ago, I received a letter from his father asking me to take Jacques at my service and to direct him towards the conquests of astronomy. It had been an error, whichever way one looked at it. In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation. Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory. C. F.