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 why they didn't do what the scandinavians did with reindeer, and use deer for draft animals?
Probably had almost everything to do w/ the mountainous terrain where the Incas lived (Andes). Pack animals are just more suitable for that sort of terrain. Annual aver. rainfall at Machu Picchu (lost city of Incas) is approx. 85 inches. Translation--lots of road & bridge maintainence; narrower roads & bridges require less effort to build & maintain. Also, a good deal of the farming was on narrow mountain terraces, not the ideal situ for draft animals & plows. Even today, the Sherpas rely extensively on the yak as a pack animal in the Himalayas.
The other thing is that when you live in the mountains, if you invent the wheel, you also gotta' invent brakes. Coulda' been a case where all the Incan mechanical genuises kept getting killed in cart crashes...
Translation: "Who does this smartass outsider think he is, solving problems we professionals have failed to figure out?"
The biblical Nefilim (those who from Heaven came). Read the 12th Planet. Some wacky stuff but other claims make more sense than a lot of the stuff we're fed today.
Also 12 is prevalent in religion, as in the 12 gods of the Greeks, 12 Holy Imams of Islam and the 12 Apostles. A little further afield are the 12 signs of the Zodiac, etc. etc.
All the more interesting since you'd think we'd have used 10 from the beginning (fingers on both hands probably the first calculators).
Why does our current numbering system go to 12 before we start using the "teens"? Why not an eleventeen and a twelveteen?
Finanally, veering off topic, just HowinL did the ancients know that the precessional period of earth (slow periodic wobble in the Earth's axis) was 26,000 years? Who is counting?
True. However, my point was that the invention of the wheel was a lower tech achievement than (apparently) the numbers system of the Incas and that it is short-sighted to measure a civilization's techonological worthiness soley on whether or not that civilization used the wheel.
Yes one must look at the big picture and clearly the wheel was not their sole technical or cultural lack else their civilization would not have been vanquished so quickly by a much smaller force at arms.
You can do base anything if you have a reason for it.
You can do base 37218934 if you want.
I wonder how much mass change of our planet there'd have to be to get the year to have 360 days in it?
Only recently (past 10 years IIRC) did we find out that the Maya understood and were using the concept of zero long before the Spanish knew about it. Most records were wiped out, those that remained were unreadable because the Spanish wiped out the readers when they killed off the upper class and religious class. Lots of things were lost forever.
But then the Spanish didn't come for mathematical exchanges or medicinal knowledge. They came for gold and conquest. And they got what they came for.
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