Mathematics and the Psychedelic Revolution
Ralph Abraham
Professor of Mathematics
University of California at Santa Cruz (USA)
www.ralph-abraham.org

Recollections of the impact of the psychedelic revolution on the history of mathematics and my personal story.
Contents
1. Introduction
2. Psychedelics, computers, and visual mathematics
3. Vibrations and forms
4. Conclusion
References

1. Introduction
In 1972 I met Terence McKenna and became close friends, and 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 trialogue, and eventually we performed public trialogues. These
occurred sporadically from 1989 until 1996. The Esalen Institute was very
hospitable and helped us organise 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 fifteen 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. The following section,
based on an invited lecture in Calcutta in 2006, describes the change in my
own mathematical history wrought by the psychedelic revolution of the 1960s.
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, “This is a friend of a friend of mine, who wants to
interview you.” 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 Gentlemanʼs 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: “Abraham sells
drugs to mathematicians.” There were some other insulting things in the
interview, that as far as I can remember, was largely fiction. I didnʼt 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 100 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 fire
left by GQ had flamed 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 Gentlemanʼs Quarterly article, in which Timothy Leary was quoted
as saying, “The 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.” Then the article quoted me as the supplier for the scientific
renaissance in the 1960s. This columnist didnʼt 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
sheʼd talked to 180 important professionals of the computer graphic field, all of
whom answered yes to the question, “Do you take psychedelics, and is this
important in your work?” 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 couldnʼt 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 itʼs good to be outed. I tried thinking
positively about this episode, but when I came home still felt nervous about it
and said “no” 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 Iʼve 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 “the
transcendent other.” 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 20 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 fluid 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,1 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 worldʼs 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 first
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, “Have psychedelics had an
influence in the evolution of science, mathematics, the computer revolution,
computer graphics, and so on?” 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. Vibrations and forms
My main goal in this section is to give an idea, especially a visual idea, of my
experiments with vibrations and forms in consciousness, over the past thirty
years. The visual representations, computer graphic animations, may be best
understood in the context of my personal experiences in actual consciousness
exploration during the years 1967 to 1972 which motivated the work, and the
philosophical frames, or maps of consciousness, in which I am trying to
understand my experiences. These maps are based jointly on my own
experiences, and on the philosophies of Greek, Jewish, and Indian origin. I
must thank Dr. Paul Lee for his tutelage on the Platonic and Neoplatonic
philosophies of the Greek tradition, and Dr. Sen Sharma for his explanations of
the Kashmiri Shaivite or Trika philosophy and other features of the Indian
tradition.
My story begins in 1967, when I was a professor of mathematics at Princeton
University. This is a wonderful university, especially for mathematics, and I was
privileged to have colleagues and undergraduate and graduate students, whom
I remember fondly to this day. Also, the 1960s was the time of student political
unrest, and concomitantly, the time of the Beatles, and the Hip Subculture, or
"sex, drugs, and rock and roll", as they used to say. My wonderful students were
involved in both of these popular movements, and through them, I also became
involved.
In 1967, the three notorious and defrocked psychology professors of Harvard
University -- Timothy Leary, Richard Alpert (later aka Baba Ram Dass), and
Ralph Metzner -- were barnstorming about the USA plumping the powers of
LSD as an agent of spiritual growth. Leary, under the influence of Vedanta and
Gayatri Devi of Los Angeles, used to affect Indian dress, and hold forth on
Eastern philosophies. I heard their performance in the Lower East Side of New
York City, and decided to try LSD and see for myself. One of my undergraduate
students helped me onto the path, and my first experience was an epiphany
indeed.
Through this epiphany, I became fascinated with the exploration of
consciousness, as we called this path, and continued the work in irregular
episodes as I followed my career to the University of California at Santa Cruz in
1968, and subsequently to Amsterdam, to Paris, and to Nainital in the
Himalayan foothills. In 1973, I returned to Santa Cruz, and migrated from
personal explorations back to academic research on consciousness, chaos
theory, and other concerns. My walkabout of five years was over, but was to
have a lasting effect on all aspects of my life. I had had hundreds of meditations
of the sort practiced in Yoga Nidra, that is, lying prone through the night, in the
so-called fourth state of consciousness, and amplified by small doses (eg, 25
mg) of LSD. (Saraswati, 1998) Like Yoga Nidra meditation, the LSD experience
provides a trip to the fourth state lasting typically about eight hours, during
which sleep is held at bay. These sessions were usually done alone, but
sometimes in teams of from two up to a dozen or so others, flying, so we
thought, in group formation like a flock of birds. Marijuana use was ubiquitous
during this period, but in my experience it made no important contribution to my
research, and, generally, I avoided it.
At one time, around 1969, we used large doses of DMT, and this period was
crucially important to the whole evolution of my mathematical understanding of
consciousness, based on geometry, topology, nonlinear dynamics, and the
theory of vibrating waves. For in these experiments, although lasting only a few
minutes, the reciprocal processes of vibrations producing forms and forms
producing vibrations were clearly perceived in abstract visual fields.
Our perspective during this time and later, was gnostic. That is, we rejected
teachers and teachings, and sought to discover cosmology for ourselves.
Throughout this period, most of us in the Hip Subculture were apprenticing
ourselves to teachers of ancient traditions from East, Mideast, and the West,
sharing our experiences, traveling to faraway lands to find teachings, and so on.
Teachers travelled through California, and we circled the globe in search of
them. Personally I experienced yoga, martial arts (judo and aikido), prehistoric
moon rituals, musical meditations, fasting and strict diets (eg, macrobiotics), and
Native American ceremonies. This was the background of my interest in
vibrations and forms in the field of consciousness.
This final year of my walkabout was blessed with two special learning
experiences, one in Paris at the beginning of the year, the other in the
Himalayan foothills, in the Summer and Fall. This was the final year of my
walkabout, following which I returned to ordinary reality and my post at the
University of California at Santa Cruz, an arduous process taking about a year. I
began 1972 as a visiting professor at the University of Amsterdam, teaching
catastrophe theory. At the same time, I had a visiting position at the Institut des
Hautes Etudes Scientifiques (IHES) at Bures-sur-Yvette outside Paris. I used to
commute weekly on the train, which I loved. At this time, IHES was newly
formed, and had only two permanent professors, David Ruelle and Rene Thom,
both of whom were superb. Thom was one of the great mathematicians of the
20th century, and had received the Fields Medal at the International Congress
of mathematicians in 1956 for his work in differential topology. I had met him in
1960 in Berkeley, where we began working together on the foundations of
catastrophe theory. During 1966, I had written my first books, Foundations of
Mechanics, Transversal Mappings and Flows, and Linear and Multilinear
Algebra, while Rene had written his foundational work on catastrophe theory,
Structural Stability and Morphogenesis, which I arranged to have published by
my publisher, Bill Benjamin.
Early in 1972, Rene and I were both stymied in our work and were browsing the
borderlines of science looking for clues. I had been reading Kurt Lewin on
topological psychology, and on arriving at IHES one day, I asked Rene what he
was working on. He pulled a book from his desk and began showing me photo
after photo of familiar forms from nature: spiral galaxies, cell mitosis, sand
dunes, and so on. These forms, he said, had been photographed in vibrating
water. The book was Kymatik, by Hans Jenny, a medical doctor from Dornach, a
suburb of Basel, Switzerland. I was thunderstruck to see images from my
meditations on the pages of a book, especially in support of the vibration
metaphor of the Pythagoreans.
I immediately called Jenny in Dornach, and he agreed to meet me. I took the
train to Basel, and was met at the station by Jenny's son-in-law, Christian
Stutten, who drove me to Dornach. Along the way I learned that Dornach was
the world headquarters of the Anthroposophy movement founded by Rudolf
Steiner, the esoteric Christian follower of Madame Blavatsky's Secret Doctrine,
around 1900. Jenny was a follower of Steiner, and lived in Dornach along with
many other Anthropops. Jenny greeted me in his home, showed me part of his
lab, and an animated film of some experiments in progress. I collected his
papers and books and went home to Paris and Amsterdam inspired.
As the winter progressed, I thought much about morphogenesis and the
mathematics of coupled systems of vibrating membranes and fluids, while
continuing to teach catastrophe theory in Amsterdam, and giving many lectures
on these subjects at universities all over Europe. Also, my chemically assisted
meditations continued, and in them, I pursued the vibration metaphor in
conceptual space, and simultaneously, in experiential space.
These experiences were dominated by rapidly vibrating patterns of brightly
colored abstract forms, somewhat like the video art and rock concert light shows
of the 1960s. The scintillating light caustics projected by the bright sun on the
bottom of a swimming pool also give an intimation of the visual aspect of these
meditations. An excellent computer simulation has been achieved by Scott
Draves in his art works called Electric Sheep, and may be seen on his website.
(www.draves.com)
Suddenly, the spring semester in Amsterdam was over, grades were recorded,
and I had a small savings account. It occurred to me to pay India a brief visit
before school began again in the Fall of 1972. Here I was influenced by the
ambiance of Amsterdam culture, in which I met so many people who had just
returned from, or were about to go again to, India. One young man just returned
told me how he organized his explorations of the Himalaya: just sit in a tea shop
until somebody offers you an experience, then accept it, he said. Just go with
the flow. This was my plan. One day at the Kosmos, a psychedelic and
meditation hall run by the Dutch government (bless it), I looked up and saw my
old friend Baba Ram Dass. The former Richard Alpert, he was among the
Harvard trio of professors who had encouraged my decision to experiment with
LSD in 1967. Then he had lived briefly in my house in Santa Cruz, California.
He had stayed for a time in Nainital, near the western border of Nepal in the
Himalayan foothills, where he became attached to a guru called Neem Karoli
Baba. I told Baba Ram Dass about my plan to visit India and he gave me
instructions for connecting with Neem Karoli Baba. Find your way to Nainital, he
said, then hang out at this particular hotel, and if I was supposed to meet Neem
Karoli Baba, somebody would approach me and take me to the ashram outside
Kainchi, a small village.
And so, late in June, 1972, it came to pass. I went to the ashram with a group of
western devotees in a taxi. But on arrival I felt a bit disappointed by the
amplified music and carnival atmosphere. I saw the devotees sitting in darshan
formation in front of Neem Karoli Baba on his tucket, all in silence. Something
seemed to be going on but I was blind to it. Someone would give him prasad, a
fruit for example, and he would immediately toss it to someone else. I went back
to the hotel in Nainital determined to go on with whomever next approached
me.
This process took no time at all. Once back at the hotel, I meet a young barefoot
Canadian dressed in a simple smock. He introduced himself as Shambu. As I
had been on the road for a long while with a highly evolved travel kit that fit into
a small shoulder bag, I was greatly impressed by his kit, which required not
even a bag. Shambu explained that he had been living in a cave in the jungle
for several months with two other saddhus. There were three small caves by a
stream in the jungle, two miles from the nearest town. One of the saddhus had
just left, and the village had dispatched Shambu to find a replacement.
Apparently the villagers felt their prosperity was only possible with all three
caves occupied by appropriate persons engaged in full-time spiritual practice.
Smoking ganja apparently counted as spiritual practice, worship of Shiva it
seems. Shambu was sure that he had been guided to me as I was the chosen
person.
Shambu put me on a bus with the usual sort of instruction: ride the bus to the
end of the line at Almora, from there I would be guided somehow. This was
monsoon season, and there had been heavy rain. After a short while the bus
was firmly halted by a major road washout. Everyone climbed out of the bus.
Looking down the slope, I was surprised to see Neem Karoli Baba's ashram for
the second time. What a coincidence! Then someone came out to say I should
come in at once, as Neem Karoli Baba was asking for me. Was this really
happening, or was there some mistake? Neem Karoli Baba gave me a bag of
breakfast cereal. He said I was going to need it in the jungle. Two young Indian
devotees were told to guide me on a trek through the jungle around the
washout, and put me on a bus for Almora on the other side. By this time I was
losing my Western mind, and all this seemed more like paranormal phenomena
than conspiracy theory.
It was midnight when finally the second bus arrived in Almora. The village was
dark, but moonlight through a clearing in the clouds showed the shops in
silhouette. A man descended from the bus after me. He had a bearer with a long
box balanced on his head. I asked him where he was going, hoping for a clue
for my next steps. He said that he was a student of Jim Corbett, the famous
hunter of man eating tigers. I had just read Corbett's book, Maneaters of the
Kumoan. Actually, we were now in the Kumoan Hills. The man said the long
package was his rifle. There was a maneating panther on the loose nearby, and
he was about to spend the night in a tree overlooking a fresh human kill, hoping
to shoot the panther. This was his job, he had been sent by the government. I
decided not to follow him into the jungle.
I followed some other people who descended from the bus. They seemed to
know where they were going, on a footpath into the jungle. One by one they
vanished into side paths, and then I was walking alone into the dark unknown,
following this single-track footpath. I could not stop to sleep, for fear of the
panther. As long as the path continued, and looked like it was used by humans,
I would continue, until I found where it went. Another village or whatever.
Seemed like a plan, for an hour or so, until there was a fork in the path. In the
dark I could see no indication which way to go. Just then I was startled by a
rustle very close by. I could see only grey on grey in the darkness. Then a voice
said in clear English, "Good evening saheb, I am from the Wisdom Garden
School. I have been waiting for you. You are to go this way". Then he pointed to
the left fork, and vanished. So on I went, until I heard voices. Following the
sound, I came upon a group of Western hippies in a house, who offered me a
place to sleep. Apparently this was the Kasa Devi Ridge, where the German
Lama Govinda had established himself some years ago, after going totally
native in the Himalaya. In the morning they showed me the way to a village
nearby, which was Dinapani, my destination. The headman interviewed me in
his chai shop, approved me for cave service, and asked his young son to guide
me into the jungle to the cave.
Indeed there were three caves and two jungle babas, who were muni, that is,
they did not speak. Not out loud at least. But voices in my head made me
welcome, and spelled out the rules. I must keep a fire going in my cave every
night, or a panther would come to claim the space. I must go to the stream every
morning to wash, and worship Shiva in an underwater grotto that has been
used for centuries and has a polished lingam. The dhuni (small ritual fire) must
be kept going. Food would be brought by villagers every morning on their way
into the forest to tap turpentine trees.
All went well for a week or so. I thought of writing my mother to say I had found a
place where I should stay for a few months to further my education, but I could
not manage to write. Every night I practiced my yoga nidra, and explored further
the vibrational realms. There seemed to be instruction regarding the use of
'tools of light" for self-defense and self-maintenance. I practiced, according to
these instructions, during the day, while sitting meditation by the dhuni after my
bath with Shiva and the daily meal of dhalbhat (rice and lentils), gor (raw sugar),
and the mandatory chillum (straight pipe) of hashish.
Then the trouble began. I had some unwelcome orders during the night. I was to
leave this place immediately. I resisted. Then the orders were repeated with
physical discomforts, which would go away as soon as I agreed to leave in the
morning. But in the morning I changed my mind. And so on, in a cycle.
Until one day, around my 36th birthday, July 4, while the other two yogis were
away on mysterious missions and I was hard at work meditating by the dhuni, I
saw a person approaching, far down the jungle path. This figure got larger and
larger, and eventually resolved into a vision from hell, a wild man with a spear,
clothed primarily in ashes. He sat down by the fire and accepted a toke from my
fully loaded chillum. My paranoia subsided, as apparently he meant no harm.
After an hour or so staring into the distance, he turned to me and spoke in
unaccented American, "Don't you understand, you are supposed to leave here. I
am going to get up and leave now, and you are to follow me". Which he did. And
I did, after collecting my small bag from the cave. After a walk of a mile or so
down a path I had not seen before, he said, "I am going this way, you go that
way", and disappeared around a bend. I followed the indicated jungle path, I am
not sure how far, and it led directly to Neem Karoli Baba's ashram. Again, the
old fellow was apparently expecting me, bellowing, "Where is that professor
from California? Bring him here." And so, reluctantly, began my relationship with
Neem Karoli Baba.
I was setup with a house, a library of Sanskrit classics in English translation,
and a few devotees for company -- including one with Sanskrit skills, Kedarnath,
his partner, Uma, and their baby, Ganesh, born during one of our meditations. I
was informed by Neem Karoli Baba that I had a mission to relate my meditation
experiences to the Sanskrit classics, and transmit the understanding somehow
to my colleagues in the USA. These sources included the Vedas, a few
Upanishads, works by Sri Auribindo, and the Yoga Vasishta, a primary text for
the Trika philosophy of Kashmiri Shaivism.
I became known at Veda Vyaasa. I remained in this setup for six months, most
of the time with Ray Gwyn Smith, now my wife, who had arrived from California
in the meanwhile. The night meditations amplified by microdoses of LSD
continued, as I had brought a supply with me from Holland right from the start.
Yoga Vasishta was a great inspiration and support for my ideas of vibrations
and maps of consciousness.
Neem Karoli Baba and the entire satsang departed for warmer climes to the
south, after the thermometer in Nainital dropped below freezing in October. Ray
and I departed in December for a Himalayan trek in Nepal, where I donated my
library to a local university. We walked about 400 miles and returned to
California early in 1973. And thus ended my miracle year,1972, and also the
five year period of one-point focus on spiritual exploration. After returning to
Santa Cruz and my job as math professor at UCSC, I reinterpreted the mission
given me by Neem Karoli Baba as a program of academic research on
vibrations and forms in mathematical models, and in physical fluids as well.
What I learned about cosmos and consciousness during this final year of the
five-year project cannot be said in words, perhaps mathematics will be helpful. I
imagined this as my task intended by Neem Karoli Baba. But I had to go on
alone, as both Neem Karoli Baba, and Hans Jenny died at this time.
4. Conclusion
There is no doubt that the psychedelic evoluti in the 1960s had a profound
effect on the history 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.
References
Ralph Abraham, Consciousness: A Deeper Scientific Search
Proceedings of the 3rd Int'l. Conf. on Science and Consciousness.
Kolkata: Ramakrishna Mission Institute of Culture, 2006.
Ralph Abraham, John B. Corliss, and John E. Dorband.
Order and Chaos in the Toral Logistic Lattice.
Int. J. Bifurcation and Chaos, 1(1), March 1991: pp. 227-234.
Rupert Sheldrake, Terence McKenna, Ralph Abraham.
The Evolutionary Mind: Conversations on Science, Imagination, and Spirit.
Rhinebeck, NY: Monkfish Books, 2005.
Rupert Sheldrake, Terence McKenna, Ralph Abraham.
Chaos, Creativity, and Cosmic Consciousness.
Rochester, VT: Inner Traditions, 2001.
Hans Jenny, Kymatic. Basel: Basileus Press, 1967.
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