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Ralph Abraham

profession and to the individual mathematicians, which have not yet been seized. Many mathematicians have rejected the significance of computers, so far. But if we could say that experiments with computers represent mathematical research, you could see the evidence of my stay in India in the cave on my outlook on mathematics.

My computer experiments involve the concepts of vibration, harmony, resonance and mathematical models for these phenomena. We would like to understand how a person is in morphic resonance with a field, if these metaphors have any function from a perspective of pattern modeling, which is what I think mathematics is all about. The processes where this kind of metaphor is proposed–whether in the Indian Samkya philosophy or in Rupert Sheldrake’s theory–are always in a living, biological, mental sphere. So the data, if there are any data, would necessarily be chaotic.

So first of all we would have to extend or map the notion of resonance from the circular sphere where the concepts first evolved in the context of chaos. When you have two strings of a guitar, you pluck one and the other one vibrates by so-called sympathetic vibration. This vibration is understood as a non-chaotic phenomenon; it is just oscillation. Each point on the string vibrates, left, right, left, right, left, right. So from this, which I’11 call the circular or periodic domain, the concepts have to be extended to the chaotic. If the two strings were chaotic instead of periodic, which means they would sound raspy and noisy instead of harmonious and sweet, then could there still be a sympathetic vibration of one caused by the nearby chaotic vibration of the other?

I came back from India in January 1973. By January 1974 I was already involved in experiments with chaotic resonance, and this has dominated my research to the present day. For example, one discovery we made is that the Rossler attractor, which is one of the simplest of chaotic forms, does have sympathetic vibration as one of its characteristics. So after India I concentrated more on vibration and resonance, whereas before, we were involved with the general, skeletal structures of chaos. And they’re related in that the theory of chaotic resonance is based upon an understanding of the skeleton, the so-called homoclinic tangles, as I’ve tried to explain in my picture books.

RMN: Could you tell us about your experience with John Lilly’s dolphins?

RALPH:¬†Well, I think that people who live in cities are not much in tune with animals. Actual communication with an animal is a rare experience for most of us. And some people are more sensitive to animals than others. They have a favorite pet, or they just really like animals. In my case, I grew up on the edge of town in Vermont, where they have, as it is said, two seasons: winter and July. Winter is very long, and a lot of times I was outside playing in the snow, usually alone. I used to go on long treks after school and on weekends on my skis, communing with animals and trying to figure out where they had been by the study of their tracks. And to this day 1 have a special love for animals, which is one of the reasons that I’m a vegetarian. I’m not only a vegetarian, but vegetarianism has a very great importance for me. It’s a big thing, not just another habit.

Anyway, I like animals, and so I was very keen to swim with the dolphins. I had bought it, like most hippies, that dolphins are more intelligent than people. They had had the brilliance to flee to the sea a long time ago, and there they have lived in peace ever since, except for a few tuna fishermen. So I had a sort of double setup to have a good experience with these dolphins, and 1 had read a little bit about other people’s experiences swimming with them. I knew that they have a very strong connection to the Orphic trinity of Chaos, Gaia and Eros. They’re connected to Chaos most directly through the experience of hydro-dynamical turbulence, that is, white water.

Now white water is the most perfect chaotic thing we have: you hear it, you see it, you feel it–it’s chaos personified. Dolphins know Chaos. They also know Gaia. They can find their way over great distances in the sea, their playground is thousands of miles across, they explore it all, they know their

way around. They can sing and speak to each other over tremendous distances. Through their sonar communication apparatus they have a global sense which

transcends our own. And then as far as Eros is concerned it’s rumored that they’re loose, they’re sexy and they like to get it on in the water.

So that’s the background. I went to John Lilly’s place in Redwood City for a routine swim with Rosie and Joe and had a fantastic experience with them. They were very violently playful. I had communicated nothing, I was just there, and I wasn’t adequately prepared for what they actually do. They like to take your hand into their mouth and press, but not too hard. You

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