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Ralph Abraham

have to have some sort of faith that they’re not going to bite you, because they have very strong jaws and sharp teeth. So I was kind of scared of this mouthing game. And then they had the flying body game. They would go down to the bottom of the tank, which was pretty deep, turn around, get ready and let go with their maximum acceleration and velocity, heading straight toward you, turning aside only at the last minute to brush gently against your side. It was kind of heavy; they were very heavy with me.

I was trying to figure out what to do. Should I grab on and go for a ride? I tried that; they slowed down and became more gentle. If I played with one, the other one appeared to be jealous, but it was all a game. There were a lot of interesting things, very much like playing with people, or at least children. But J was a little scared because I’m not that great a swimmer and they were very good swimmers. My faith had flaws that day, I suppose.

Then I decided to try a mental experiment. We know they’re mental–they have memory and intelligence and language and so on. So I proposed an experiment in telepathy. I swam out of the tank into a little nook or cranny to regroup. I had this fantasy of lying still in the water, and they would both lie still as well, and one of them would face me in the water so that we were co-linear, head to head on a straight line, and then we would just exchange thought without any further ado. They were thrashing around in the water. So keeping this picture in my mind I swam out again, and they both became totally still, just as I had visualized.

I believe it was Rosie who got into position: on a line, still, head to head and so on. And then I thought, “Okay, let’s exchange a thought.” Boom! Loud and clear came a thought. She said, “Do you think it’s nice in this tank? Would you like to live in this tank? It’s too small; it’s ugly; it’s dirty. We want out!” So I said, “Wow, yeah, I can understand that; I’m certainly going to get out pretty soon and I wish you could too.” Then we played a little bit more and I got out. I wrote in the log book about this experience just as I told you. Later there was a revolt of John Lilly’s crew over the question of conditions in the tank.

DAVID: Have your experiences with psychedelics had any influence on your mathematical perspective and research?

RALPH: Yes. I guess my experiences with psychedelics influenced everything. When I described the impact of India and the cave on my mathematics I could have mentioned that. There was a period of six or seven years which included psychedelics, traveling in Europe sleeping in the street, my travels in India and the cave and so on. These were all part of the walkabout between my first mathematical period and all that has followed in the past fifteen years. This was my hippie period, this spectacular experience of the gylanic revival ( G.R. wave), -after Riane Eisler-of the sixties.

I think my emphasis on vibrations and resonance is one thing that changed after my walkabout. Another thing that changed, which had more to do with psychedelics than with India, was that I became more concerned with the application of mathematics to the important problems of the human world. I felt, and continue to feel, that this planet is really sick; there are serious problems that need to be faced, and if mathematics doesn’t have anything to do with these problems then perhaps it isn’t worth doing. One should do something else. So I thought vigorously after that period about something I had not even thought about before: the relationship of the research to the problems of the world. That became an obsession, I would say.

DAVID: Why do you think it is that the infinitely receding, geometrically organized visual patterns seen by people under the influence of psychedelics resemble computer generated fractal images so much?

RALPH: I don’t know if they do, really. You know there’s a theory of the geometric forms of psychedelic hallucinations based on mathematics by Jack Cowen and Bard Ermentrout. It has to do with patterns of biochemical activity in the visual cortex which is governed by a certain model having to do with neural nets. This model has geometric patterns in space-time, dynamical patterns, which are patterns that any structure of that kind would have. So these two mathematicians see psychedelic hallucinations as mathematical forms inherent in the structure of the physical brain. Now I’m not very convinced by that, but I think it’s kind of an unassailable position. One cannot just argue it away on the basis of one’s personal experience.

What I think about psychedelic visuals is not so different, except that I would not locate them in the physical brain. I think that we perceive, through some kind of resonance phenomenon, patterns from another sphere of existence, also governed by a certain mathematical structure that

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