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.
I wonder how much mass change of our planet there'd have to be to get the year to have 360 days in it?
There could be other reasons for the count being "off" by five odd days. Maybe the guy doing the counting was sick like a dog for two weeks, and by the time he got back to making his scritches on the stone, he misremembered a few days due to fever delirium. Or, maybe they counted accurately, but used an invalid endpoint, due to viewing the sun's yearly position from "Stone A" to "Crotch of Tree B", not taking into account that "Tree B" would be growing.
There are probably plenty of other reasons for getting the count wrong, I just pulled those two off the top of my head.
Or, maybe they said, "365.25? That's nuts, just round it down to 360, it'll work fine, and the math's a lot easier." (Or maybe some scribe copied it that way, thinking he'd be doing the world a favor.)
It doesn't necessarily mandate a change in the planet's mass.
Now, on the other hand, I've wondered about dinosaurs, whose bones weren't strong enough to support their weight, and flying dinosaurs, that didn't have the lift or bone structure sufficient to allow flight.
I'm thinking that two things may have been at play here, that I haven't read of anyone else considering. (Maybe they have, but I haven't read it.) If the world was spinning faster on its axis, then centrifugal force would make everything on the surface seem to weigh less than it does now. (Even today, you'll weigh less at the equator, where you're traveling at about a thousand MPH, than you will at the poles, traveling at 0 MPH.)
Also, if the air pressure was significantly higher, the air would be denser, which would of course make any lifting surface much more efficient.
"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."
The answer to the last paragraph is found in the first. 
I'm surprised no one has answered this yet. Think about it. Since the early days of commerce (and even within family units prior to that), people have needed to divide integral numbers of things into portions. To avoid inequity (or squabbles in the case of family units), one needs to group things in easily divisible quantities.
What is the smallest number of items that can be grouped into either 2 or 3 equal piles? The answer is 6. How about 2, 3 or 4 equal piles? The answer is 12. How about 2, 3, 4, or 5 equal piles? Of course, 60. How about 2, 3, 4, 5, or 6 equal piles? Also, 60. And how about 2, 3, 4, 5, 6 or 8 equal piles (we'll leave out lucky 7)? The answer is 360.
Though I have never read it anywhere, the answer always seemed obvious to me that selling things in groups of 12, 60 or 360 (wholesale) was to facilitate retail in smaller equal portions. It also makes figuring out what the subportion is worth easier.
It's all fractions!, which the schools think we no longer need.
Big Indian orOne little - two little - three little Endians -Little Indian???
four little - five little - six little Endians -
seven little - eight little - nine little Endian boys!
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