MS#131. The Paleolithic Birth of Geometric Thinking
Abstract: Following a visit in the Winter of 2007 to the Alhambra — a Moorish palace built around 1300 CE in the South of Spain — I have been digging up the roots of the Alhambra Theorem, which says that Moorish craftsmen in the Middle Ages knew that there were exactly 17 crystallographic groups. This fundamental result of modern group theory emerged into the mathematical literature only in 1891. Digging back from the Alhambra, we found an Ur source for the motifs of the Alhambra in the earliest Turkish carpets of Catal Hüyük, around 10 KYA (thousand years ago). Digging deeper led to the cave paintings of Upper Paleolithic Europe, beginning around 35 KYA. In this article we tell the story of the earliest geometric motifs we have found. This reveals the birth of geometric thinking in the ambiance of psychedelic shamanism -- religion, art, and mathematics were born together in the youth of our species.
[PDF] 25 pages, 1.5 MB