Narrative Threads: Accounting and Recounting in Andean Khipu

4. Reading Khipu: Labels, Structure, and Format

Reading Khipu F O U R Labels, Structure, and Format Marcia Ascher Beginning some thirty years ago, my collaborator (an anthropologist) and I (a mathematician) began an extensive investigation of Inka khipu. Our work included firsthand study of over 215 khipu spread throughout thirteen countries , in thirty-four museums and private collections. Recognizing the fragility and importance of the artifacts, we recorded and published detailed descriptions, including knot types and placement, cord and space measurements , and colors, for each khipu we studied (Ascher and Ascher 1978, 1988). We analyzed the khipu as a corpus, as well as analyzing them individually. Building on previous studies of khipu and on our own findings, we came to see the khipu as richer and more significant than previously realized. In our numerous writings (e.g., Ascher 1983, 1986; Ascher and Ascher 1975, 1997), and particularly in our book Code of the Quipu (Ascher and Ascher 1981), we have characterized the khipu contents as a logical-numerical system and have also emphasized that, as such, it is a general recording system. We have placed emphasis on the significance of numbers used as labels combined with numbers used as magnitudes, and on the importance of format and structure in the encoding of information on the khipu. Still, however, in regard to khipu, many equate numerical with statistical and, what is more, overlook the importance and power of symbolic systems that do other than encode speech sounds. Here I elaborate further on numbers as labels, and on structure and format. First, a preliminary comment: as a mathematician, I have come to realize that a special clarification is needed about symbolic systems. The clarifica- 8 8 Marcia Ascher tion is that with any recorded symbolic system there is a difference between (1) what is recorded; (2) how we say it; and (3) what it means. For example, for the squiggles twenty-two, we say ‘‘twenty-two’’ when we read it aloud; for the squiggles 22, we say ‘‘twenty-two’’ when we read it aloud; and for XXII, we say the same thing. Similarly, when we see the configuration Öx, we say ‘‘square root of ex,’’ or for 3ò 6 x2dx, we say ‘‘the integral of ex squared dee ex from three to six.’’ And, of course, how squiggles are said depends not just on the individual items but on the others around them and how they are juxtaposed . For example, if I see 22.14, I say ‘‘twenty-two point one four,’’ but when it is preceded by $, that is, $22.14, I say ‘‘twenty-two dollars and fourteen cents’’: and, for 22'14" I say ‘‘twenty-two feet fourteen inches,’’ but for 10°22'14" I say ‘‘ten degrees twenty-two minutes and fourteen seconds.’’ In none of these examples have I mentioned meaning. I am not distinguishing between the signifier and the signified—I am distinguishing only between what is seen and what is said. The crucial point is that were I to say ‘‘he read ‘the square root of twenty-two’ from the blackboard,’’ you have no reason to assume that what was written was encoded speech sounds. In fact, because of the context, you probably would assume otherwise, but there is no justification for that either. The next crucial point is: What does twenty-two or any other number mean? For one thing, it can be a magnitude or a quantity, as in the cases just used. In these cases, one could, for example, double the number and add four and the result would be another magnitude. But a number can also be used as a label. Look, for example, at the following: 065-62-1803 14850 607-257-1011 3/24/35 0-472-06325-1 The first item, 065-62-1803, is my social security number. To the U.S. government and many other institutions, it stands for Marcia Ascher. These institutions could, if they chose, use letters encoding the sound of my name, but that would not be a unique identifier. The next item, 14850, is the zip code identifying where I live—namely, in the town of Ithaca in New York State. Many of us still write the letters encoding speech sounds for addresses (such as writing out Ithaca, New York), but we know it isn’t necessary. In fact, post offices disregard them. And, recogni- Reading...