1. Introduction.
In Pacific Shift (Thompson, 1985) world cultural history
is divided into four periods called cultural ecologies.
Associated with each is a characteristic mathematical style,
or mentality. These, with approximate beginning dates, are:
- 4,000 BC, the riverine cultural ecology, with the arithmetic mentality
- 500 BC, transcontinental, geometric
- 1700 AD, oceanic, dynamic
- 1972, biospheric, chaotic
While the theory of dynamical systems and chaos theory are
new branches of mathematics, arithmetic and geometry are ancient,
and reach back into remote antiquity. Nevertheless, the cognitive
style of prehistoric cultures is arithmetic, while the geometric
style was an innovation of the ancient Greeks, sometimes credited
to Thales or Pythagoras.
As mathematics has evolved from astronomy and music,
we may regard archeoastronomy and archeomusicology as
the foundation stones of archeomathematics. And these two
foundation stones were eventually combined in the idea of the
music of the spheres, in which the zodiacal constellations were
mapped onto the tone circle of the twelve-tone chromatic scale.
This development goes back to the Pythagoreans, 400 BC, at least.
(See Part III of Godwin, 1987. See also Mountford, 1920.)
This paper is an exercise in archeomusicology,
demonstrating the existence of the arithmetic mentality
long before the beginnings of the riverine cultural ecology.