KNOTS and QUIPU

I would like to suggest the reader to pay a visit to the web-page by Luis Kauffman. His researches are fundamental for knot theory. Rather important objects in theory, knots are now quite studied in macromolecules science and biology (see the structure of the molecular Borromean rings reported by Stoddart et al. Science 2004, 304, 1308–1312, and the article “Intricate Knots in Proteins”, by Virnau et al. Computational biology).

Archaeologists have discovered that knot tying dates back to prehistoric times. Besides their uses in tying objects together, knots have interested humans for their aesthetics and spiritual symbolism. Knots appear in various forms of Chinese Arts dating from several centuries BC, in the Chinese knotting. An endless knot appears in Tibetan Buddhism, while the Borromean rings have made repeated appearances in different cultures, often representing strength in unity. Spirals and patterns are dominant motifs in Celtic art prior to the Christian influence on the Celts, which began around 450 A.D. These designs found their way into early Christian manuscripts and artwork. The Celtic monks who created what today are known as the Celtic knot-work. Mathematical studies of knots began in the 19th century with Gauss, who defined the linking integral (Silver 2006). In the 1860s, Lord Kelvin's theory that atoms were knots in the aether led to the creation of the first knot tables by P.G. Tait..

A thread with knots turns out to be as recording information: this is what Incas discovered.
Incas developed a recording/writing system based on threads and knots, named "quipu" ("knot" in quechua). Some scholars guess that quipus were simply recording media. Others believe that this is a true writing system. Quipus are rare and precious, because the main part was destroyed by Spanish conquerors. It seems to be possible that Incas had another recording system, using pottery in the shape of human heads with different face expressions.