From Euclid into Chaos, Preface
From the beginning, Greek philosophy reflected
a balance between the two principles:
- Dionysus (aspect of Osiris, Bacchus, feminine,
son of Persephone, grandson of Demeter,
the Earth Mother Goddess in the Orphic theogony) represented by
Pythagoras, Empedocles, Archytas, Plato, and the Neoplatonists, and
- Apollo (masculine) represented by
Aristotle, Alexander the Great, Euclid,
and later, the early Christian and Muslim authors.
(Nietzsche and Ruth Benedict also utilized this dichotomy.)
As Euclid's Elements travelled from Alexandria to Europe,
big events followed: Christianity, Islam, the Renaissance, etc.
The balance shifted, and the Apollonian tendency prevailed.
The most recent of these major social transformations
clearly discernable in cultural history,
the Enlightenment,
followed from the work of Newton,
sometimes described as the greatest intellectual
contribution ever made by a single individual.
We refer to this sequence of erosions at the flattenning
of the ancient world view. The progessive flattenning
was relieved from time to time by an archaic revival,
such as the Renaissance, or the Chaos Revolution.
In my book, Chaos, Gaia, Eros,
I have made a case that the Chaos Revolution
of our own times belongs on this list of "shortwave
crises" along with the Renaissance.
Even more, I have made a case that the Chaos Revolution
belongs on a shorter list of the "longwave crises",
the three largest social transformations
of the Holocene Interglacial (that is, the past several millenia.)
- agriculture, ca 10,000 B.C.,
- the wheel and writing, ca 4,000 B.C., and
- the Chaos Revolution, ca 2,000 A.D.
In the model of cultural transformation deduced
by Sir Flinders Petrie from his excavations of
Ancient Egypt, mathematics and philosophy play
a special role, spearheading a domino sequence of
catastrophic events in different layers of
society. Is this model followed by our current
transformation, the Chaos Revolution?
In From Euclid into Chaos,
a book-in-progress with philosopher Paul A. Lee,
we present a legal brief for this claim, and a microscopic analysis
of the transformation, during the last century,
from ancient (Euclidean)
to postmodern (chaotic and fractal) geometry.
We show that the shift began in the mathematical
sphere, then progressed into philosophy, long before
the domino sequence began within the sciences.
Revised 05 February 1996 by Ralph Abraham
<abraham@vmi.vismath.org>