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### Incan Quipus

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Date: 09/30/1999 at 14:51:51
From: Ann Marie J.
Subject: Quipus

I need to know where I can find what the Incas used for numbers. I
know that they are colored ropes, but we need more specifics.

Thanks.
```

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Date: 10/03/1999 at 22:10:26
From: Doctor Twe
Subject: Re: Quipus

Hi Ann Marie!

According to Victor J. Katz in his book _A History of Mathematics: An

"A quipu is a collection of colored knotted cords, where the colors,
the placement of the cords, the knots on the individual cords, the
placement of the knots, and the spaces between the knots all
contribute to the meaning of the recorded data. Every quipu has a main
cord, thicker than the others, to which are attached other cords,
called pendant cords, to each of which may be attached further cords,
called subsidiary cords. Sometimes there is a top cord, a cord placed
near the center of several pendant cords and tied so that when the
quipu lies flat it falls in a direction opposite to the pendant cords.
Data are recorded on the cords (other than the main cord) by a system
of knots. The knots are clustered together in groups separated by
spaces and represent numbers using a base 10 place-value system with
the highest value place closest to the main cord. Thus the cord with
three knots near the top and nine knots near the bottom represents the
representing units are generally larger knots than those representing
higher powers of ten. The largest number so far discovered on a quipu
is 97,357. Zeros are generally represented by a particularly wide
space."

"The pendant cords on quipus are themselves generally clustered in
groups, sometimes with each group consisting of the same set of
distinct colors. It is assumed that each color refers to a particular
class of data being recorded on the quipu. In addition, one often has
a top cord associated to a group of cords on which is recorded the sum
of the numbers on the individual cords of the group. Sometimes certain
of the pendant cords record sums of the numbers on other such cords.
Sometimes it appears that the knots on a particular cord do not
represent data at all but are simply labels. In any case, the quipus
are not calculating tools, but only records. The calculations on which
these records are based must have been done elsewhere, probably with
some sort of counting board."

"What is not generally known is exactly what kinds of data a given
quipu records, but one particular quipu is known to be a record of
census data for a region of seven provinces. In this case, the people
of each province were classified in one of two groups, each of which
was further divided into two subgroups. Thus the individual pieces of
data recorded on certain of the cords were the number of households in
each province belonging to each of the subgroups. Other cords then
represented the sums of the various pieces of this data, with one cord
finally giving the grand total of the number of households in the
entire region."

Katz references _Code of the Quipu: A Study in Media Mathematics, and
Culture_ by Marcia Ascher and Robert Ascher, (University of Michigan
Press, 1981), and says that the book has recently been reprinted under
the title _Mathematics of the Incas: Code of the Quipu_ (Dover
Publications, 1997). According to Katz, this work "provides a
mathematical analysis of various techniques of quipu making and also
provides exercises to help students learn the relevant mathematical
ideas."

As to Web sites, I used a few search engines and came up with the
following:

This site has lots of historical info, and lots of other links:

The Incas and their Descendants on the Web
http://www.uiuc.edu/unit/lat/19outreach_Incas.html

These sites have information on quipu. The last one has a good
diagram.

Talking Knots of the Inka
http://www.archaeology.org/9611/abstracts/inka.html

The Quipu
http://www.nasm.edu/nasm/dsh/LDC/ldc_part2.html

The Quipucamayu
http://ripley.wo.sbc.edu/departmental/spanish/www/MMLatAm/Quipus.html

I hope this helps. Write back if you have any more questions.

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
Elementary Math History/Biography
Middle School History/Biography

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