Skip to comments.Incan Counting System Decoded?
Posted on 02/03/2004 6:04:59 AM PST by vannrox
Learn how to add 9+7 on the yupana abacus.
Jan. 29, 2004 ? The Inca invented a powerful counting system that could be used to make complex calculations without the tiniest mistake, according to an Italian engineer who claims to have cracked the mathematics of this still mysterious ancient population.
Begun in the Andean highlands in about 1200, the Inca ruled the largest empire on Earth by the time their last emperor, Atahualpa, was garroted by Spanish conquistadors in 1533.
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 stored following a seven-bit binary code. Nobody, however, had been able to explain the meaning of these geometrical tablets known as yupana.
Different in size and shape, the yupana had been often interpreted as a stylized fortress model. Some scholars also interpreted it as a counting board, but how the abacus would have worked remained a mystery.
"It took me about 40 minutes to solve the riddle. I am not an expert on pre-Columbian civilizations. I simply decoded a 16th century drawing from a book on mathematical enigmas I received as a Christmas present," engineer Nicolino De Pasquale said.
The drawing was found in a 1,179 page letter by the Peruvian Felipe Guaman Poma de Ayala to the King of Spain. A simple array of cells consisting of five rows and four columns, the drawing showed 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 above rows.
According to De Pasquale, the circles in the cells are nothing but the first numbers of the Fibonacci series, in which each number is a sum of two previous: 1, 2, 3, 5.
The abacus would then work on a base 40 numbering system.
"Instead, all 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," Antonio Aimi, curator of the exhibition "Peru, 3,000 Years of Masterpieces" running in Florence, told Discovery News.
"Since we lack definitive archaeological evidence, we tested this claim on 16 yupana from museums across the world. De Pasquale's system works on all of them," Antonio Aimi, curator of the exhibition "Peru, 3,000 years of masterpieces" running in Florence, told Discovery News.
The Inca's calculating system (see an example of how it works in the slide show) does not take into consideration the number zero. Moreover, numbers do 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 unusual counting way is described in an account by the Spanish priest José de Acosta, who lived among the Inca from 1571 to 1586.
"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," Acosta wrote in his book "Historia Natural Moral de las Indias."
The claim has sparked a dispute among scholars.
Gary Urton, professor of Precolumbian studies at Harvard University, an authority on khipu research, told Discovery News: "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? This system is also attested in a mountain of early colonial documents that describe how the Inca organized their administrative system according to a base 10 counting system."
As Aimi concedes, the 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 a strong evidence the fact that the system works on all yupana examined," he said.
It couldn't be that the Spaniards might have understood the system incorrectly. After all, we know how interested they were in cultural understanding:
the Inca ruled the largest empire on Earth by the time their last emperor, Atahualpa, was garroted by Spanish conquistadors in 1533.
Brilliant mathematicians those conquistadors! Outsiders bring a fresh perspective to "intractable" issues. Never look to experts for novel ideas.
You have to imagine the [sarcasm] tags, then read it again. The comment is really an indictment of academia.
Sumeria. Also the 60 minute hour and the 360 degree circle.
And how well-developed could their civilization have been when they didn't know about wheels?
Wheels really don't have a great deal of utility without draft animals to pull a cart. Apparently, the wheel in all cultures was first used for chariots, carts or wagons. Some of its other uses, such as the wheelbarrow that is actually useful by man-power, didn't come along till thousands of years later. In western Europe the wheelbarrow wasn't used till the middle ages.
Well it couldn't have been very reliable.
Either that or they never divided 200 Spaniards into the Incan population and came up with extinction.
Always nice to see my boy Gary being quoted. Good guy. I gave a talk on Incan mathematics once. They did some pretty complex stuff, nobody really knows how. I'd have to read more about this theory to form an opinion.
They unearthed an Incan PDP-8. :)
(Yes, yes, I'm taking certain artistic liberties. Hey, it's a joke, man, a joke.)
Personally, I got the sarcasm, but Gary Urton is a highly intelligent, open-minded individual. He is indeed a scholar and has studied khipus, ethnomathematics, et al in great depth. He was was also awarded a MacArthur "genius" grant.
And he is most certainly NOT uppity! He's -- well, he's very laid back, let's just say.
I wonder why they didn't do what the scandinavians did with reindeer, and use deer for draft animals?
Madonna plus Brittany = ANOTHER gross!
Smooth roads or wheels??
Little-Indian. They were Intelligent, after all.
Throw out yer dead!
Throw out yer dead!
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