Exclusive Articles and Interviews

5-HTP 
Aharon and Amalia Barnea 
Albert Hofmann, Ph.D 
Alex Grey 
Alex Grey – 2 
Alexander and Ann Shulgin 
Allen Ginsberg 
Andrew Weil 
Annie Sprinkle 
Antioxidants Extend Life 
Arlen Riley Wilson 
Art and Psychedelics 
Aubrey de Grey 
Barry Sears 
Bernie Siegel 
Bruce Sterling 
Brummbaer 
Candace B. Pert 
Carolyn Mary Kleefeld 
Charles Tart, Ph.D. 
Chemo-Eroticism 
Clifford Pickover 
Colin Wilson 
Dan Baum 
Daniel Siebert 
David Jay Brown 
Dean Radin 
Dean Radin – 2 
Deepak Chopra 
Dennis McKenna, Ph.D. 
Douglas Rushkoff 
Dr. Motoji Ikeya 
Durk Pearson and Sandy Shaw 
Durk Pearson and Sandy Shaw – 2 
Edgar Dean Mitchell 
Elizabeth Gips 
Etho-Geological Forecasting 
Etho-Geological Forecasting 
Eugene Roberts Ph.D. 
Fakir Musafar 
Francis Jeffrey 
Garry Gordon 
George Carlin 
Hans Moravec 
Hans Moravec – 2 
Hydergine and Albert Hofmann 
Jack Kevorkian 
Jacob Teitelbaum 
James Berkland 
James Ketchum, M.D. 
Jaron Lanier 
Jean Houston 
Jeff McBride 
Jeremy Narby 
Jerry Garcia 
Jill Purce 
John Allen 
John C. Lilly 
John E. Mack – 2 
John Guerin 
John Mack 
John Morgenthaler 
John Robbins 
Jonathan Wright 
Joseph Knoll 
Julia Butterfly Hill 
Kary Mullis 
Kary Mullis – 2 
Larry Dossey 
Laura Huxley 
Leonard Hayflick, Ph.D. 
Marija Gimbutas 
Marios Kyriazis 
Marsha Adams 
Mati Klarwein 
Matthew Fox 
Michael Fossel, Ph.D., M.D. 
Michael West 
Motoji Ikeya 
Nick Herbert 
Nina Graboi 
Noam Chomsky 
Oscar Janiger 
Paul Krassner 
Penny Slinger 
Peter Duesberg 
Peter McWilliams 
Peter Russell 
Pregnenolone and Psoriasis 
Ralph Abraham 
Ram Dass 
Ram Dass – 2 
Ram Dass – 3 
Raphael Mechoulam 
Ray Kurzweil 
Ray Kurzweil – 2 
Reverend Ivan Stang 
Riane Eisler and David Loye 
Rick Strassman 
Robert Anton Wilson 
Robert Anton Wilson – 2 
Robert Trivers 
Robert Williams 
Robert Williams 
Roland Griffiths, Ph.D. 
Rosemary Woodruff Leary 
Rupert Sheldrake 
Rupert Sheldrake – 2 
Secrets of Caloric Restriction 
Sex and Cabergoline 
Sex and Cialis 
Sex and Damiana 
Sex and Deprenyl 
Sex and DHEA 
Sex and L-arginine 
Sex and Pheromones 
Sex and Salvia divinorum 
Sex and Tribulus 
Sex and Uprima 
Sex and Yohimbe 
Simon Posford 
Stanislav Grof. M.D., Ph.D. 
Stephen La Berge 
Terence K. McKenna 
Theories of Aging 
Timothy Leary 
Timothy Leary – 2 
Understanding Sex on Viagra 
Valerie Corral 
Valerie Corral – 2 
William Irwin Thompson 
William Kautz 
William Regelson 

Ralph Abraham

Chaos and Erodynamics

“Chaos is very much the same as the steady state; it’s not scary at all.”

with Ralph Abraham

Ralph Abraham is renowned for bringing a fresh perspective to mathematical thought. His study of dynamical systems as the building blocks of reality, has led him to extrapolate fundamental mathematical principles into his philosophical outlook . A professor of Mathematics at the University of California, Santa Cruz, he received his Ph.D. at the University of Michigan in 1960. He taught at UC Berkeley, Columbia and Princeton before moving to Santa Cruz in I 96S and has held visiting positions in such various locations as Amsterdam, Paris, Warwick, Barcelona, Basel, Florence and Siena.

He is the author of numerous mathematical books. Linear and Multi-Linear AlgebraFoundations of Mechanics was written with J.E. Marsden and Transversal Mappings and Flows with J.Robbin. He wrote Manifolds,Tensor Analysis and Applications with J.E. Marsden and T. Ratiu, and the highly successful four-volume Dynamics, the Geometry of Behavior with C.D. Shaw. His latest book entitled, Trialogues on the Edge of the West is a group of discussions with Terence McKenna and Rupert Sheldrake on the relationship between science, philosophy and religion.

Traveling through Europe in his twenties, living in a cave in northern India and working as a professional gambler in Las Vegas were all experiences which helped to shape Ralph’s philosophical outlook. He has been active on the research frontier of dynamics in mathematics since 1960, and in applications and experiments, since 1973. In 1975 he founded the Visual Mathematics Project at the University of California, Santa Cruz to explore the use of interactive computer graphics in teaching mathematics. He is the founding editor of Eagle Mathematics and Applied Global Analysis.

We talked with Ralph on March 4th 1989, in the cozy· living room of our dear and mutual friend Nina Graboi, who has often worked as his editor. We found him to be a soft-spoken, intensely thoughtful and down-to-earth character, with the gentle tone of a person who has become philosophically resigned to seeing further than others.

RMN

 

DAVID: Ralph, you’re recognized as one of the leaders in the mathematical study of chaos. Can you tell us what it was that originally inspired your interest in mathematics and the mathematics of vibrations and dynamical systems?

RALPH: Well, I didn’t get interested in dynamics and decide that’s what I was going to study. It was just left foot, right foot, or some series of miracles. It happened like this.

I was an engineer and worked in a physics project, so I became a student of physics. Then one day a physics professor said in class that if you want to understand physics you have to study mathematics. So I changed to mathematics at that point. And I found a mentor, somebody who took care of me and helped me out, a wonderful man, Nate Coburn. I started studying what he was doing because he was my only contact in mathematics. One reason I responded to his program was that it had to do with general relativity. Einstein had been a household word when I was growing up. My father respected Einstein very much. It was said that only eight people in the world could understand Einstein. My teacher apparently could and was writing in that field.

I had taken very few math courses during that period. I remember two or three very influential courses. One of them was a differential geometry course taught by Raoul Bott who became a very famous mathematician. Some concepts were included in that course that I later found useful in dynamics. So I had some math background, but not the kind of background I would have had if I’d done a Ph.D. under a famous professor of dynamics.

Then I was looking for a job. I had one offer for some place where I didn’t want to go and at the last minute, before the school year began, I got a letter from Berkeley offering me a job. In 1960 there wasn’t any big mathematical center there, but of course I took it.

After I got to Berkeley I was engaged in rewriting my thesis for publication. One day I discovered that they were having tea in some little room in the back of the building, and I had already been there for two or three months and hadn’t met anyone. So I went to the tearoom to meet some people and to find out what was going on. And in this way I discovered a couple of people who later

Pages: 1 2 3 4 5 6 7 8 9 10 11 12

Leave a Reply