Braid Math Article

Summary

This month’s topics: Quipus and quantum computing Frank Wilczek’s column in the the Wall Street Journal (April 14, 2022) had the title “A Quantum Leap, With Strings Attached; The Inca system of quipu—tying a series of knots to record information—is providing a surprising model to modern physics and quantum computing.” Left, a quipu from the American Museum of Natural History, image taken from L. Leland Locke’s The Ancient Quipu (AMNH, 1923). Here the main cord supports 24 pendants, tied off in groups of four by the top cords. Right, Locke’s analysis of the third 4-cord group, image adapted from his book. Overhand knots, represented by circles and crosses, represent 10 or 100 depending on their position on the cord. The other symbols represent the special knots used to record the numbers from 1 to 9. In this quipu each top cord records the sum of the numbers encoded on the four corresponding pendants. This textile document is a typical quipu in that its data is numerical and recorded in a decimal system. (For another example and more details, see Nicole Rode’s YouTube video from the British Museum). While they were used by earlier pre-Columbian Andean cultures, most of the surviving specimens date from the period of Inca domination, c. 1400–1532 CE. (We can only guess what the numbers recorded on quipus were actually counting —these civilizations left no written records). Wilczek compares quipus with the information storage and transmission systems we encounter today: “written human language, the binary code of computers and the DNA and RNA sequences of genetics,” and remarks that the Andean system involves “something unique: topology, the science of stable shapes and structures.” In fact the difference between one knot and another, which is contrastive in quipus, to borrow a term from linguistics, is one of the most basic examples of a purely topological concept. The connection between quipus and “modern physics and computing theory” comes precisely through topology...