Geometrical patterns in the pre-classical Greek area. Prospecting the borderland between decoration, art, and structural inquiry (Q2707790)

In many histories of mathematics the prehistoric ``geometric'' decorations along with counting and tally-sticks are considered as the earliest beginnings of mathematics, that a direct line of development links such decorations to mathematical geometry. The article confronts this persuation with a particular historical case: The changing character of geometrical decorations in the later Greek area from the Middle Neolithic through the first millenium BCE. This is made by analyzing a collection of photographs (all together 87 items), made by the author in the National Archaeological Museum and the Oberländer Museum in Athens in 1983-96, and reproduced in the article. The analysis is summarized as follows. The Old European Middle Neolithic confronts us with simple patterns: zigzag-lines, rhombs, etc. No effort is made to achieve geometrical coherence between the various parts of a decoration. From a start in pure decoration the geometrical pattern develops towards structural experiments. As the Middle Cycladic offspring of Old Europe falls under the influence of Minoan Crete (itself largely an Old European offspring), this dominance of artistic concerns undergoes a qualitative leap: instead of introducing figurative painting as a supplement to the old geometrical decoration, the geometrical design itself is changed and vitalized. The ``native'' Mycenean tradition is different. In the shaft-graves of Mycenae a high level of regularity developed into genuine mathematical structuring. Later Mycenean art becomes less mathematical. Nevertheless, the geometrical impressionism, through Protogeometric and Geometric art, never evolves into structural mathematical inquiry. For some reason Greek culture maintained an interest in circles, squares, hexagons and octogons for more than thousend years before theoretical geometry emerged. There is no path leading from the decorations of Geometric vases to theoretical geometry, since Geometric vases disappear long before anybody imagines theoretical geometry to have arisen.