Incan counting system as easy as 1,2,3,5
The Inca invented a powerful counting system that could be used to make complex calculations, according to an Italian engineer professor who says he has cracked the mathematics of this ancient population.
But one U.S. expert is not convinced, saying this latest claim conflicts with other evidence.
The Incan civilisation arose in the Andean highlands in about 1200 AD and by the time their last emperor, Atahualpa, was garrotted by Spanish conquistadors in 1533, the Inca had ruled the largest empire on Earth.
The Inca had long been considered the only major Bronze Age civilization without a written language. They left mysterious objects that, according to the latest research, would have been used to store units of information.
Recent studies are investigating the hypothesis that elaborated knotted strings known as khipu contain a hidden written language that follows a seven-bit binary code.
But until now nobody had been able to explain the meaning of geometrical tablets or yupana.
An ancient abacus?
Yupana come in different shapes and sizes. Some researchers thought they were stylised models of fortresses. Some thought they were counting boards. But how the abacus would have worked remained a mystery.
Italian engineer Nicolino De Pasquale thinks he has discovered how.
"It took me about 40 minutes to solve the riddle. I am not an expert on pre-Columbian civilisations. I simply decoded a 16th century drawing from a book on mathematical enigmas I received as a Christmas present," he said.
The drawing was in a 1179-page letter by the Peruvian Felipe Guaman Poma de Ayala to the King of Spain.
It showed a simple array of cells consisting of five rows and four columns. It had one circle in the right cell on the bottom row, two circles in the next cell, three circles in the other one and five circles in the last cell of the row. The same pattern applied to the rows above.
According to De Pasquale, the circles in the cells were the first numbers of the Fibonacci series, in which each number is a sum of two previous ones: 1, 2, 3, 5.
The abacus would then work on a base 40 numbering system.
Antonio Aimi, curator of the exhibition Peru: Three Thousand Years of Masterpieces running in Florence at the Palazzo Strozzi, explained how the base system worked.
"[Earlier] scholars based their calculations according to a base 10 counting system. But calculations made to base 40 are quicker, and can be easily reconverted to base 10," he said.
"Since we lack definitive archaeological evidence, we tested this claim on 16 yupana from museums across the world," Aimi said. "De Pasquale's system works on all of them."
The Inca's calculating system did not take into consideration the number zero. And numbers did not exist as graphic representations.
According to Aimi, in most cases the Inca made their calculations by simply drawing rows and columns on the ground.
The Spanish priest José de Acosta, who lived among the Inca from 1571 to 1586, described this unusual counting.
"To see them use another kind of calculator, with maize kernels, is a perfect joy ... They place one kernel here, three somewhere else and eight, I do not know where. They move one kernel here and there and the fact is that they are able to complete their computation without making the smallest mistake," de Acosta wrote in his book Historia Natural Moral de las Indias.
Not everyone agrees
The claim has sparked a dispute among scholars.
U.S. researcher Gary Urton, professor of Precolumbian studies at Harvard University is an authority on khipu research.
"The fact that an explanation can be constructed for one or even several yupana that conforms to this theory of a base 40 numbering system amongst the Incas is of some modest interest.
"How would one explain the many statements in the Spanish chronicles, both those written by Spaniards and by literate Andeans, who stated quite straightforwardly that the Inca used a base 10 counting system?
"[A base 10 system] is also attested in a mountain of early colonial documents that describe how the Inca organised their administrative system."
As Aimi conceded, the Italian engineer's claim has the limits of any interpretative system that isn't proven with definitive historical evidence.
"We would need to find a Rosetta yupana, something similar to the deciphering of Egyptian hieroglyphics from the Rosetta stone. Since we can't have it, I would consider it strong evidence the fact that the system works on all yupana examined," he said.