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The Secret of Inca Maths

How does the mathematics of the Incas work?

An Italian researcher has managed, in record time, to decipher the mystery of the yupanas, which scientists have been studying in vain for years. Nicolino De Pasquale has just solved the enigma that kept entire generations of scientists awake for half a millennium: that of Inca mathematics.

Nicolino De Pasquale is Italian, he is 54 years old, has an engineering degree in aeronautics, he teaches at school, as well as at university, and lives in Pescara [on the Adriatic coast]. He has no particular sign: he does not drink, does not smoke. Homebody, worker, he wears glasses, has white hair, is married and has two children.

Also, the strange thing in this affair is that De Pasquale unveiled this secret without knowing anything either of the Incas, or of the existence of this secret, or even of the age-old attempts to decipher the mysterious calculators, called yupanas, and to which were already doing alluding to the Spanish conquistadors in the 16th century. These yupanas are blocks of stone about a foot by twenty centimeters, revealing numerous carved cavities in the upper part, with, in these cavities, white beans, seemingly arranged at random. One of these yupanas was on display at the Palazzo Strozzi in Florence, until February 22, as part of the exhibition of artistic treasures from pre-Columbian Peru.

It was Antonio Aimi, curator of the exhibition, who officially announced the resolution of the enigma. And it’s no coincidence: it was he himself who had the idea of ​​bringing together the engineer and the yupanas. Aimi explains that the riddle is nothing more than the fruit of a misunderstanding supported by several sources: that of the conviction that the Incas calculated with a decimal system similar to ours. In fact, Nicolino De Pasquale discovered that they counted in a quadridecimal [base 40] system, and he demonstrated this using two wooden yupana models. The simplest reveals five or six series of four superimposed basins.

The Inca Calculator

The Inca calculator works from right to left, starting from the first bowl at the bottom (bowl which, according to an old drawing, would be that of unity and therefore contains a ball which is worth 1). The next bowl contains two balls each worth 2, the third three balls each worth 3, the fourth five balls each worth 5.

The sum therefore corresponds to: 1 + 4 + 9 + 25 = 39. The basin on the right of the upper series is worth 40, that next to it 80, and so on to infinity. In other words, it is a geometric progression that, curiously, reproduces the phenomenon of cell multiplication. Some particularities, however: 0 do not exist and the same number can be written in different ways. The method works regardless of the calculation requested. De Pasquale has provided several proofs of this. He has thus trumped the pawn of the fine flower of Western researchers and anthropologists.

The disbelief was such that for more than two years the discovery was blacklisted. Impossible, said the other researchers. They were wrong. But how did he get this far? “At Christmas, I had received a book of mathematical puzzles as a gift, which I leafed through between two conversations at my sister’s house in Rome. I found there a yupana designed by a Spaniard in the 16th century. I thought a little, then I took a paper and a pencil, and I did some calculations. How long did it take me? Half an hour, maybe forty minutes. I got through it before the new year. I’m sorry if I bothered people. But the calculations fall right, what can I do? »

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