Page 97 - J. C. Turner "History and Science of Knots"

The Peruvian Quipu 87

Conclusion
The Incas met their vast bureaucratic tasks with the help of the quipus, cords
which were tied together to form a meaningful structure and in which knots
were tied that represented integers. These were not simply in one-to-one cor-
respondence to the objects, but a base ten positional system was used. From
the chroniclers who came to Peru during the Spanish conquest we know for
what and how the quipus were used. Analysis of surviving specimens allows
reconstruction of Incan mathematical ideas, which are far from primitive. Un-
fortunately for us, the Incas had no writing in the usual sense of the word.
Their culture was completely destroyed by the Spanish conquerors before they
could make contact with writing cultures, which was intensive enough to pro-
vide us with the equivalent of a rosetta stone. Therefore the only things we
know for sure is what the single signs mean, and that there is in fact some
profound meaning behind the Incan knots. We can reconstruct some of the
ideas which stand behind the quipus, but not with any certainties. We cannot
be sure that our interpretations are right; and we cannot say anything about
the concrete meanings of the ancient quipus which we find in the museums.

References

1. M. Ascher, `Mathematical Ideas of the Incas', in: Michael P. Closs,
ed., Native American Mathematics. (University of Texas Press, Austin,
1986) 261-289.
2. M. Ascher, Ethnomathematics. A Multicultural View of Mathematical
Ideas. (Brooks/Cole Publishing Company, Pacific Grove, 1991).
3. M. Ascher and R. Ascher, `Code of Ancient Peruvian Knotted Cords
(Quipus)', Nature 222 (1969) 529-533.
4. M. Ascher and R. Ascher, `Numbers and Relations from Ancient An-
dean Quipus', Archive for History of Exact Sciences 8 (1971-72) 288-
328.
5. M. Ascher and R. Ascher, Code of the Quipu: Databook. (1978) and
Code of the Quipu: Databook II. (1988): available on microfiche from
Cornell University Archivist, Ithaca, NY, USA.
6. M. Ascher and R. Ascher, Code of the Quipu. A Study in Media, Math-
ematics and Culture. (University of Michigan Press, Ann Arbor, 1981).
7. F. H. Cushing, `Manual Concepts: A Study of the Influence of Hand-
Usage on Culture-Growth', The American Anthropologist V No. 4
(1892) 289-316.
8. C. L. Day, `Knots and Knot Lore: Quipus and Other Mnemonic Knots',
Western Folklore (1957) 8-26.
9. C. L. Day, Quipus and Witches' Knots. (University of Kansas Press,