From Euclid into Chaos, Preface

From the beginning, Greek philosophy reflected a balance between the two principles: (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.)

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 <>