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Scientists untangle Inca number-strings

August 11, 2005 By Andreas von Bubnoff This article courtesy of Nature News.

Knotted threads carry signs of ancient accountancy.

Scientists have picked apart some 500-year-old calculations from the Inca empire.

The team deciphered the maths from a series of 'khipus': elaborate structures of coloured, knotted strings. Researchers have long known that the Inca, who lived along the west coast of South America from AD 1400-1532, used such cords to record numbers. But this is the first mathematical relationship found between khipu. And that may help to work out what kind of information they stored.

Khipus encode numbers as knots in strings hanging from a cord. The closer a knot is to the cord, the higher its value, just as the number 1 can denote 1, 10, or 100 depending on its position.

Sacrifices were very important to the Incas.
Bill Conklin
Textile Museum in Washington DC
Numerical value also depends on a knot's shape. Single overhand knots encode tens, hundreds or thousands. Single knots represent ones, and long knots with between 2 and 9 turns encode the numbers 2 to 9.

"The challenging thing is that, while we can read these numerical values that are knotted onto the strings, we don't know what they refer to," says Gary Urton, an anthropologist from Harvard University and lead author of the study, published this week in Science1.

Modern maths

Urton and his colleague Carrie Brezine used twenty-first century computer power to seek numerical relationships between different clumps of string.

They analysed a group of 21 khipus found all together in 1956, near an Inca palace at the archaeological site of Paruchuco, in the Peruvian capital Lima. These are the only khipus found so close to each other, Urton says, making it more likely that at least some of them served similar purposes.

Sure enough, seven of the khipu were numerically related. The summed values of all strings of the same colour of one khipu, for example, matched the sums on the corresponding strings of another khipu. The sums of that khipu, in turn, could be found on the corresponding strings of a third khipu.

The numbers didn't add up perfectly, but Urton thinks this may be because the Inca rounded numbers up or down, or took averages of their results.

Death or taxes?

Urton speculates that these sums might record tax payments. Incans paid their taxes by working a certain number of days per year on state projects. The knotted strings could represent such days, and the sums could represent totals for all work in a certain area, Urton says.

Bill Conklin, a textile archaeologist at the Textile Museum in Washington DC says the study is "terrific, careful and great". But he thinks the numbers are probably records of animal sacrifices. "Sacrifices were very important to the Incas," he says. "If they didn't make the proper sacrifices, it wouldn't rain."

"That could be," says Urton, adding that only further studies will solve the matter. The team has created a database of the numbers, colours and other features of 290 khipus - about half of the 600 found so far. They hope to mine this in search of further patterns.


  1. Urton G. & Brezine C. J. Science, 309. 1065 - 1067 (2005).


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