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BOOK REVIEW

# String Theory

Eleanor Robson

Signs of the Inka Khipu: Binary Coding in the Andean Knotted-String Records. Gary Urton. xiv + 202 pp. University of Texas Press, 2003. \$45 cloth, \$19.95 paper.

Some 500 to 1,000 years ago, the Inka (or Inca) inhabitants of the Andean highlands of Peru ran a sophisticated urban civilization, apparently without the need of writing. Instead, their bureaucrats and accountants kept records by tying complex series of knots in string. A khipu (or quipu) was a long, thick "primary cord" to which many pendant strings were attached that themselves could have subsidiary pendants. Carefully spaced knots were tied in the pendant strings. Single knots marked tens, hundreds, thousands and tens of thousands; multilooped "long knots" recorded the integers 2 through 9 (the integer corresponding to the number of turns in the knot); and a figure-of-eight knot close to the loose end of a pendant cord indicated the integer 1. Inka khipu are amongst the most extraordinary and elusive communication systems that humanity has ever invented.

It was a system that baffled the Spanish conquistadors, who dismissed it for the most part as no more than a primitive mnemonic device. More recently khipu have perplexed archaeologists and historians too. The decimal system of numeration has been understood now since the early 1920s, but many questions remain to be answered. Why, for instance, did the khipu makers use strings of different colors, and how should we understand the many khipu which were clearly knotted according to nondecimal principles?

Harvard anthropologist Gary Urton is determined to crack this tantalizing code, and his book Signs of the Inka Khipu is a first step on that road. He draws on a painstaking analysis he made of more than 400 khipu in museum collections across the world, his many years studying and living with the Quechua-speaking descendants of the ancient Inka in modern-day Peru, and the best of anthropological and linguistic theory on writing and communication in other ancient cultures worldwide.

Urton's fundamental thesis is that to decipher the khipu we have to reconstruct the decision-making processes involved in their original construction—what archaeologists of the European Neolithic have termed the chaîne opératoire. He contends that the Inka record keepers were faced with a series of binary (either-or) decisions each time they made a new khipu: (1) Should it be made of llama hair or cotton? (2) Should the threads be chosen—or dyed—according to the predominantly red "Creator Rainbow" or the predominantly blue "Mourning Rainbow"? (Together they contain 24 colors.) Here Urton is using color terminologies and symbolism of dyes found among Bolivian weavers today and hypothesizing that in ancient khipu, the light and dark variations in the natural hues of largely undyed cotton and wool fibers had a binary organization "structurally and symbolically compatible, or homologous, with the two rainbow groupings." (3) Should a cord under construction be spun clockwise or anticlockwise (and thus plied in the opposite direction)? (4) Should an individual pendant cord face the front or back of the primary cord? (5) Should a decimal or a nondecimal knotting convention be used? (6) Should a knot be tied clockwise or anticlockwise? (7) Should the knot represent an odd number or its pair (the even number immediately greater than it)?

Urton further argues that each of these binary decisions had an "unmarked" (default) outcome and a "marked" one. The marked option tended to be chosen less often and to carry special significance, usually in relation to the unmarked choice. So, for instance, a nondecimal encoding would be the marked outcome of decision 5—only a third of known khipu do not obey the decimal principles outlined above.

Urton sees dualism as an important pillar of the Inka worldview: Inka objects, concepts and social structures naturally belonged in pairs, one part of which was dominant and extant in its own right, the other part subsidiary and complementary to the first. All together, Urton maintains, we should understand the khipu-making process as having the capacity to encode 26 x 24 (for the 24 colors) = 1,536 distinct information units, which gives the khipu a sign repertoire as large as that of the earliest cuneiform writing of ancient Iraq, and twice the size of the ancient Egyptian and Mayan hieroglyphic systems. Khipu are no mere knotted-handkerchief aide-mémoire then, but sophisticated repositories of complex data sets.

Compelling as this argument is—and Urton draws on a dazzling array of supporting evidence to back it up, from analysis of the technical color terminology of modern Quechua-speaking weavers to the structuralist theory of linguist Charles Sanders Peirce and his followers—some serious flaws remain. My comments here are restricted to failings in his description of the chaîne opératoire, which would have been greatly clarified by formally distinguishing between decisions at the level of khipu, cord and knot.

First, the list of seven decision-making steps is neither exhaustive nor exclusively binary. For instance, as Urton acknowledges, significant choices were made about the type and finish of primary cord to be used, although this is still badly understood. A single pendant string could be multicolored or could change color halfway along its length.

Second, not every step in the process was necessarily the outcome of a deliberate choice. According to modern ethnographic study, spin and knot direction closely correlate with the left- or right-handedness of the weaver. Further, the default choice of cotton or wool varied regionally, so it cannot be known of a khipu whose provenance is uncertain whether its material of manufacture was the result of a "marked" decision or not.

Third, the decision-making process continually narrowed down the range of options, so that by the time an individual knot was to be tied there were, following Urton's list, only a paltry eight different options available to the khipu maker. A scribe using any of the writing systems mentioned above, by contrast, had far greater freedom regarding which signs he deployed in any particular context.

Urton, it is clear, set out to be provocative. In that aim he has been enormously and engagingly successful. No doubt he will ruffle the feathers of many an Inka specialist, and some will perhaps dismiss him outright. But no future student of khipu, or any ancient communication system, will be able to ignore this hugely stimulating and exciting work. Even at his most conceptually challenging, Urton writes with a grace, clarity and openness that invite the nonspecialist to share the intellectual adventure of deciphering one of the greatest enigmas of the ancient world.—Eleanor Robson, History and Philosophy of Science, University of Cambridge