3. The quadrivium
The quadrivium -- arithmetic, geometry, astronomy, music
-- is generally credited to Pythagoras, and the
"Greek miracle" of the 6th century B.C.
The details of the musical arithmetic of the several scales,
in various intonations, has been recovered by various authors.
The encoding of this ancient numerology in the dialogues of Plato
has been analyzed. (Brumbaugh, 1954) The numerical methods of
the Pythagoreans have been graphically reconstructed. (McClain, 1978.)
On the other hand, Pythagoras was known (according to ancient
accounts) to have traveled and studied in Egypt, Babylonia,
and India. The discovery of (McClain, 1979) of the musical arithmetic
of Pythagoras encoded in the poetry of the Rg Veda pushed back
the dating of this sophisticated mathematics by a millennium.
We have applied the methods of musical arithmetic
to measurements of the Venus of Lespugue, a paleolithic
sculpture of about 23,000 B.C., and found them to fit very closely
the diatonic scale basic to the theory of the Rg Veda and the ancient Greeks.