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.
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 Introduction, 2nd Edition_ (Addison-Wesley, 1998): "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 number 39. As additional help for reading the numbers, the knots 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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