Sunday, May 3, 2009


This is a fascinating and insightful book. It is off the mainstream topic of what is now called complexity science (then called chaos theory), but an amazing piece of work. What Abraham, a world renown chaos theorist and professor emeritus of mathematics at the University of California, Santa Cruz, noticed was the apparent parallels between recent developments in physics and the history of consciousness and the rediscovery of the three forces that drive it: chaos, gaia and eros.

The characteristic features of this tradition are the trinity:

* Chaos, the creative void, source of all form
* Gaia, the physical existence and living spirit of the created world
* Eros, the spiritual medium connecting Chaos and Gaia; the creative impulse

According to the author: “One of the main goals of this book is to introduce the concept of dynamical historiography, the application of the mathematical theory of dynamical systems, chaos, and bifurcations to the patterns of history. It is hoped that from the future development of this mode of inquiry we may evolve a better understanding of ourselves and our evolutionary challenges.”

Abraham writes in the introduction, “Since 1960, I've been working in the area of dynamical systems theory, a classical branch of mathematics created by Isaac Newton in the seventeenth century. In the midst of the cultural upheavals of the 1960s, great inroads were made in the field of dynamical systems, due in part to the computer revolution. Dynamical systems theory deals with moving systems, such as the solar system, and the patterns they trace in space and time. Newton discovered mathematical laws that such systems obey, and constructed mathematical models that are abstract analogues of their space-time patterns. His discovery has been credited as one of the greatest intellectual contributions ever made by a single person.

About a century ago, dynamical systems theory was revolutionized by Henri Poincare, the great French mathematician, when he discovered models for highly complex motions (which later came to be called strange attractors).l By the late 1960s, numerous examples of strange attractors had been discovered in computer simulations.

In 1972 I traveled to the Institut des Hautes Etudes Scientifiques, in France, to visit with Rene Thorn. In his book on morphogenesis, the study of pattern formation, Thorn introduced a new language for the application of dynamical systems theory, which included the terms attractor; basin of attraction, and catastrophe. I was interested in pursuing these ideas with him, but when I arrived, Thorn was onto something new. He showed me a book of photographs by Hans Jenny, an amateur scientist from Basel. The photographs showed forms created by sound vibrations in sand, powder, and water. They were suggestive of galaxies, plants, brain waves, memories, hallucinations, and abstract works of art. A theory of morphogenesis, in which the mysteries of creation were seemingly revealed, was projected wordlessly by the book. My mind reeled with new possibilities for the application of dynamical systems theory to nature and society.

That summer I went to India on holiday and soon found myself living in a cave in the jungle of the Himalayas, a mile above sea level. The cave had been inhabited for centuries by jungle yogis, and in it I experienced a number of illuminations on the concepts of vibration in Hindu philosophy, and on harmony and resonance concepts in mathematics, music, and mysticism.

When I returned to California in 1974, I began a program of research and teaching on vibrations, chaos, computation, and computer graphics, delving deeply into the histories of these subjects, going ever backward-to the Baroque, to the Renaissance, to ancient Greece, and beyond. Soon after my return, I found other people who shared these interests, including Terence McKenna and the late Erich Jantsch. Erich was a missionary of general evolution theory, a whole systems theory evolving from the work of a number of twentieth century scientists interested in conceptualizing a science of the all-and-everything. The theory offered a strategy by which to understand the structure of history through the kind of mathematical model introduced by Rene Thom. Here, my Himalayan cave illuminations could be abstracted and applied to society, to the history of consciousness (and unconsciousness), and therefore to the future.

I've spent the last twenty years exploring a broad range of applications for these concepts, on which this book is a meditation. It offers a conceptual model for history, constructed from the mathematical tools conceived by Rene Thom and applied in the style of Erich Jantsch. Such a model may be crucial for understanding our history and as an aid in creating our future.

The Chaos Revolution, Gaia Hypothesis, and Erodynamics
During the 1970s paradigm shifts within the sciences began to emerge into public view. Around 1973 new dynamical models were applied to turbulent fluid motions (for example, boiling water, and a dripping faucet), but it was not until 1975 that these models were connected with the word chaos. The terms strange attractor and dynamical systems theory were replaced by chaotic attractor and chaos theory. The new theory swept through the sciences in a wave of renewal. The Chaos Revolution was underway.

Journalists began calling me to ask: "What is chaos theory? Does it have anything to do with chaos in ordinary life? What is the theory good for? Why are scientists so excited about it?"

These questions, which I could not easily answer, drove me deeply into the literature of myths and cultural history. I found that the word Chaos first appeared in a book called Theogony, by Hesiod, one of the early Greek poets. His poem is a creation myth telling stories of the origins of the gods. Here the word chaos does not mean disorder. Instead, it represents an abstract cosmic principle referring to the source of all creation. It also appears in connection with the two other fundamental concepts: Gaia (the created universe) and Eros (the creative impulse).
I was amazed to realize that this same trinity, which preceded the creation of the gods and goddesses of the usual pantheon of early Greek paganism (also called Orphism), is also associated with three revolutionary movements underway in the sciences:

* The Chaos Revolution was named in 1975 for a new branch of mathematics that provides models for many intrinsically irregular natural processes.
* The Gaia Hypothesis, named in 1973, proposes a self-regulation capability of the complex system composed of earth, ocean, atmosphere, and the living ecosystems of our planet. According to Gaia theory; which views Earth as a living system, the biosphere acts to create and maintain favorable conditions for life.
*Erodynamics, named in 1989, applies dynamical systems theory to human social phenomena.

What strange synchronicity, I wondered, led to three different recent innovations in the sciences, in apparently independent developments, sharing a common mathematical basis, bearing names (Chaos, Gaia, Eros) that are associated in Hesiod’s trinity almost three thousand years ago?”

The book races the development of the concept of the orphic trinity – chaos, gaia and eros – through the three parts of the book:

1. Dynamics and the Orphic Trinity in History
2. The Orphic Trinity in Myth
3. The Orphic Trinity in the Sciences

I encourage all readers interested in understanding the bigger “picture” of complexity and the future to study this book.

Ralph Abraham, Harper, 1994, 263 p

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