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Recollections of the impact of the psychedelic revolution on the history of mathematics and my personal story. [Ralph Abraham, Ph.D.]

1. Introduction

In 1972 I met Terence McKenna and we became close friends. Ten

years later we were joined by Rupert Sheldrake in a special triadic

bond. We developed a habit of conversing on common interests

in a style that evolved into a form we called a Òtrialogue,Ó and

eventually we performed public trialogues. These occurred sporadically

from 1989 until 1996. The Esalen Institute was very

hospitable and helped us organize and record these trialogue

events, which led to our two volumes of published trialogues.

In a typical trialogue, one of us would lead off with a trigger

monologue of Þfteen minutes or so. My conversation starter

for one of our trialogues in 1996 is the basis of the next section,

on my supposed revolutionary role in the psychedelic history

of mathematics in the 1960s, and the origin of chaos theory.

2. Math in the 1960s

One day I was sitting in my office

with my secretary, Nina, when there was a

knock on the door. Nina said, ÒThis is a

friend of a friend of mine, who wants to

interview you.Ó I was very busy with the

telephone and the correspondence, so he

came inside and I answered his questions

without thinking. After a month or so,

when a photographer arrived, I began to

realize that I had given an interview for

GentlemanÕs Quarterly (GQ) magazine. I

called my children and asked them what

was GQ magazine. They live in Hollywood

and know about such things. I was in Italy

when the magazine finally arrived on the

stands. I was very proud, in spite of my

style of dress, that I had been the first one

in our circle of family and friends to

actually be photographed for GQ.

But I was shocked in Firenze to open

the first page of the magazine, and see my

picture occupying a large part of the first

page, with the table of contents, with the

heading: ÒAbraham sells drugs to mathematicians.

Ó There were some other

insulting things in the interview, that as

far as I can remember, were largely Þction.

I didnÕt mention it to anybody when I

came back to California, and was very

pleased that nobody mentioned it. Nobody

had noticed. There were one or two phone

calls, and I realized that nobody after all

reads GQ. If they do look at the pictures,

they overlooked mine. I was safe after all

at this dangerous pass.

Suddenly, my peace was disturbed

once again by a hundred phone calls in a

single day asking what did I think of the

article about me in the San Francisco

Examiner, or the San Jose Mercury News,

and so on. All the embers in the Þre left by

GQ had ßamed up again in the pen of a

journalist. A woman who writes a computer

column for the San Francisco Examiner

had received in her mail box a copy of

the GentlemanÕs Quarterly article,

in which Timothy Leary was quoted as

saying, ÒThe Japanese go to Burma for

teak, and they go to California for novelty

and creativity. Everybody knows that

California has this resource thanks to

psychedelics.Ó Then the article quoted me

as the supplier for the scientific renaissance

in the 1960s.

This columnist didnÕt believe what

was asserted by Timothy Leary and others

in the GQ article, that the computer

revolution and the computer graphic

innovations of California had been built

upon a psychedelic foundation. She set out

to prove this story false. She went to

Siggraph, the largest gathering of computer

graphic professionals in the world,

where annually somewhere in the United

States 30,000 who are vitally involved in

the computer revolution gather. She

thought she would set this heresy to rest

by conducting a sample survey, beginning

her interviews at the airport the minute

she stepped off the plane. By the time she

got back to her desk in San Francisco sheÕd

talked to 180 important professionals of

the computer graphic field, all of whom

answered yes to the question, ÒDo you take

psychedelics, and is this important in your

work?Ó Her column, finally syndicated in a

number of newspapers again, unfortunately,

or kindly, remembered me.

Shortly after this second incident in

my story, I was in Hollyhock, the Esalen of

the far north, on Cortes Island in British

Columbia, with Rupert and other friends,

and I had a kind of psychotic break in the

night. I couldnÕt sleep and was consumed

with a paranoid fantasy about this outage

and what it would mean in my future

career, the police at my door and so on. I

knew that my fears had blown up unnecessarily,

but I needed someone to talk to.

The person I knew best there was Rupert.

And he was very busy in counsel with

various friends, but eventually I took

Rupert aside and confided to him this

secret, and all my fears. His response,

within a day or two, was to repeat the

story to everybody in Canada, assuring me

that itÕs good to be outed. I tried thinking

positively about this episode, but when I

came home still felt nervous about it and

said ÒnoÓ to many interviews from ABC

News, and the United Nations, and other

people who called to check out this

significant story. I did not then rise to the

occasion, and so IÕve decided today, by

popular request, to tell the truth.

It all began in 1967 when I was a

professor of mathematics at Princeton, and

one of my students turned me on to LSD.

That led to my moving to California a year

later, and meeting at UC Santa Cruz a

chemistry graduate student who was

doing his Ph.D. thesis on the synthesis of

DMT. He and I smoked up a large bottle of

DMT in 1969, and that resulted in a kind

of secret resolve, which swerved my career

toward a search for the connections

between mathematics and the experience

of the logos, or what Terence calls Òthe

transcendent other.Ó This is a hyperdimensional

space full of meaning and

wisdom and beauty, which feels more real

than ordinary reality, and to which we

have returned many times over the years,

for instruction and pleasure. In the course

of the next twenty years there were

various steps I took to explore the connection

between mathematics and the logos.

About the time that chaos theory was

discovered by the scientific community,

and the chaos revolution began in 1978, I

apprenticed myself to a neurophysiologist

and tried to construct brain models made

out of the basic objects of chaos theory. I

built a vibrating ßuid machine to visualize

vibrations in transparent media, because I

felt on the basis of direct experience that

the Hindu metaphor of vibrations was

important and valuable. I felt that we

could learn more about consciousness,

communication, resonance, and the

emergence of form and pattern in the

physical, biological, social and intellectual

worlds, through actually watching

vibrations in transparent media ordinarily

invisible, and making them visible. I was

inspired by Hans Jenny, an amateur

scientist in Switzerland, a follower of

Rudolf Steiner, who had built an ingenious

gadget for rendering patterns in

transparent fluids visible.

About this time we discovered

computer graphics in Santa Cruz, when

the first affordable computer graphic

terminals had appeared on the market. I

started a project of teaching mathematics

with computer graphics, and eventually

tried to simulate the mathematical models

for neurophysiology and for vibrating

fluids, in computer programs with computer

graphic displays. In this way evolved

a new class of mathematical models called

CDs, cellular dynamata. They are an

especially appropriate mathematical object

for modeling and trying to understand the

brain, the mind, the visionary experience

and so on. At the same time other mathematicians,

some of whom may have been

recipients of my gifts in the 1960s, began

their own experiments with computer

graphics in different places, and began to

make films.

Eventually, we were able to construct

machines in Santa Cruz which could

simulate these mathematical models I call

CDs at a reasonable speed, first slowly, and

then faster and faster. And in 1989, I had a

fantastic experience at the NASA Goddard

Space Flight Center in Maryland, where I

was given access to, at that time, the

worldÕs fastest super computer, the MPP,

the Massively Parallel Processor. My CD

model for the visual cortex had been

programmed into this machine by the only

person able to program it, and I was

invited to come and view the result.

Looking at the color screen of this super

computer was like looking through the

window at the future, and seeing an

excellent memory of a DMT vision, not

only proceeding apace on the screen, but

also going about 100 times faster than a

human experience. Under the control of

knobs which I could turn at the terminal,

we immediately recorded a video, which

lasts for 10 minutes. It was in 1989 that I

took my first look through this window.

To sum up my story, there is first of

all, a 20-year evolution from my Þrst DMT

vision in 1969, to my experience with the

Massively Parallel Processor vision in

1989. Following this 20-year evolution,

and the recording of the video, came the

story with GQ and the interviews at

Siggraph in the San Francisco Examiner that

essentially pose the question, ÒHave

psychedelics had an influence in the

evolution of science, mathematics, the

computer revolution, computer graphics,

and so on?Õ

Another event, in 1990, followed the

publication of a paper in the International

Journal of Bifurcations and Chaos, when

an interesting article appeared in the

monthly notices of the American Mathematical

Society, the largest union of

research mathematicians in the world. The

article totally redefined mathematics,

dropping numbers and geometrical spaces

as relics of history, and adopting a new

definition of mathematics as the study

of space/time patterns. Mathematics has

been reborn, and this rebirth is an outcome

of both the computer revolution and

the psychedelic revolution which took

place concurrently, concomitantly,

cooperatively, in the 1960s. Redefining

this material as an art medium, I gave a

concert, played in real time with a genuine

super computer, in October, 1992, in the

Cathedral of Saint John the Divine, the

largest Gothic cathedral in the world, in

New York City.

3. Conclusion

There is no doubt that the psychedelic

revolution in the 1960s had a

profound effect on the history of computers

and computer graphics, and of mathematics,

especially the birth of postmodern

maths such as chaos theory

and fractal geometry. This I witnessed

personally. The effect on my own history,

viewed now in four decades of retrospect,

was a catastrophic shift from abstract

pure math to a more experimental and

applied study of vibrations and forms,

which continues to this day. ¥

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