Mathematics and the Psychedelic Revolution

[mu!]

abraham MS#124.Maps, cr 09 mar 2008

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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, where I was given a bottle of DMT in 1969. A chemistry graduate

student verified that it was pure DMT, and I smoked up a large quantity of it.

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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Mathematics and the Psychedelic Revolution (by Ralph Abraham).pdf

Mathematics and the Psychedelic Revolution (by Ralph Abraham).pdf

Mathematics and the Psychedelic Revolution (by Ralph Abraham).pdf

[Seldom]

after reading through that OP I have to ask, what am I missing ? .. where's the relation ? how do the two fit together ? this article explains nothing - "new definition of mathematics as the study of space/time patterns" ? - this sounds like Einstein, not Ralph Abraham ..

What's the connection ?

[paradox]

isn't he talking about mathematically analyzing vibrational patterns in spacetime as a means of understanding consciousness in terms of patterns of (probably 'nano') vibration in the human nervous system/brain. perhaps sounds a bit flakey unless you're a fractal mathematician, which i certainly am not.. i assume he's referring to these vibrational fractal patterns being extremely prominent, amplified experiences while on psychedelics & so the use of psychedelics can potentially very much help one to experientially understand this process which can follow on to developing more accurate mathematical models.

[Seldom]

isn't he talking about mathematically analyzing vibrational patterns in spacetime as a means of understanding consciousness in terms of patterns of (probably 'nano') vibration in the human nervous system/brain.

.. if so then it makes little sense, and contributes nothing to consciousness studies .. modelling 'vibrational patterns in spacetime' can't afford priveledged access to understanding how the nervous system relates to consciousness because the nervous system is itself of coarse, according to this idea, also made of space time. it crashes into the same wall as most other empirical theories of consciousness .. the only conclusion could be the wet blanket of panpsychism, which would never be proved, only implied by the assumed identity between the stuff of the world and the stuff of consciousness

vibrational fractal patterns being extremely prominent, amplified experiences while on psychedelics & so the use of psychedelics can potentially very much help one to experientially understand this process which can follow on to developing more accurate mathematical models.

.. and yet empirical constucts like the notion of phosphenes possess a much higher level of experimental reliability and validity than the trip report phenomenology of 'wow the shiny colours are like fractals' .. even if hallucinated patterns were fractals, I don't see how tripping could provide 'experiential understanding' that would help to mathematically model vibrations, any more than taking a shower would help an uneducated person to understand the chemical composition of water ..

p.s - i love you, paradox

[ThunderIdeal]

he meditated throughout the night on small doses of acid, 25mg doses. heheh.

hmmmm, i didn't think he was claiming to have made solid headway in understanding consciousness. all of the details just build a case for his main point: maths and computer graphics were carried forwards thanks in no small part to hippie culture and hippie drugs.

some of the details were fascinating though. its bizarre to think that a maths professor would focus on the spiritual for five whole years. the events he describes in india are trippy, as though events were orchestrated and accomplished through psi abilities, or fate, or whatever. that is, unless he's describing sophisticated trickery to make it appear that mystical forces were guiding him.

[Optimystic]

Math and Sacred Geometry stuff is only for the advanced spiritualist

Science itself is really just and extension of mathematical studies, advanced equations, atomic weights and

chemistry type studies... .

I'll admit its mostly way over my head inspite of the fact that I did naturally well with math... Pretty much I always got

an A in math but I struggled with all the boring subjects... but I was never encouraged but rather discouraged from

going through the advanced classes in skool and so whatever advanced mathematics i've picked up over the years

was bits and parts that I picked up off the internet

I have picked up on where spirituality and math cross paths... I really I thought I understood that for years

but more recently I came to an even deeper, yet vague understanding and its kinda mind bogglings but

math is essentially the basis for every other study, every vibration, every color, every sound, every shape, every pine

cone and every breath of fresh air... there is a whole nudder world beyone skool & el universidad

if that bores you, draw a fucking picture or something <laff>

if you like mysteries and shit, join a secret society and if your one of the lucky geniuses to climb to the top of the

totem pole, a shadowy figure will introduce you to some sacred math and ur life will change forever....

now run boy

 

Edited March 23, 2014 by Spine Collector

[Optimystic]

http://www.amazon.com/The-God-Game-Series-ebook/dp/B008H540EM

these folks are really into mathematics for anyone who may want to explore this avenue

"This is the introductory text of a series of books called "the God Series" in which the most ancient secret society in the world - the Pythagorean Illuminati - reveal, for the first time in the public domain, the "answer to everything".

Pythagoras provided a glimpse of the answer 2,500 years ago when he declared, "All things are numbers". The God series fully reveals what Pythagoras meant. Mathematics - built from numbers - is not an abstraction but is ontological: it actually exists. Numbers are real things. Specifically, they are the frequencies of energy waves. (Moreover, energy waves are simply sinusoidal waves: sines and cosines, meaning that the study of energy is the study of sinusoids). There are infinite energy waves, hence infinite numbers. No numbers are privileged over any others, so negative and imaginary numbers are as ontologically important as real numbers (upon which science is exclusively based).

Real numbers correspond to space and imaginary numbers to time. Negative numbers are "antimatter": a mirror image universe.

The two most powerful numbers of all - and the ultimate basis of Illuminist thinking - are zero and infinity, which are harnessed together ontologically (opposite sides of the same coin, so to speak). The existence of zero and infinity is vehemently denied by the ideology of scientific materialism. In Illuminism, these two numbers not only exist, they are the "God" numbers: the origin of all other numbers. Zero and infinity comprise the Big Bang Singularity itself from which an infinitely large universe emerged: "everything" literally came from "nothing".

Moreover, zero is also the "monad" of Leibniz (an Illuminati Grand Master). It is therefore the number of THE SOUL, and it has INFINITE capacity. Being dimensionless - a mathematical point - the soul is outside the dimensional, material domain of space and time, hence the soul is indestructible, immortal and cannot be detected by any conventional scientific experiment.

What we are describing are the necessary, analytic, eternal truths of mathematics - they have no connection with Abrahamic religious faith. There is NO Creator God but, astoundingly, each soul is capable of being promoted to God status, just as the pawn in chess can become the most important chess piece, the Queen, if it reaches the other side of the battlefield (the board). In Illuminism, if you reach gnosis - enlightenment - you become God.

Mathematics is literally everything. Unlike science, mathematics offers certainty: 100% true and incontestable knowledge. Mathematics unifies science, religion and metaphysics. Mathematics is the true Grand Unified Theory of Everything that science pursues so futilely. Science can never deliver truth and certainty because it is inherently a succession of provisional theories, any of which can be overturned at any time by new experimental data. Science is based on ideas of validation and falsification. Mathematics is based on absolute analytic and unarguable certainty. No experiment can ever contradict a mathematical truth.

Mathematics is the ONLY answer to everything. Mathematics is the ONLY subject inherently about eternal, Platonic truth. As soon as existence is understood to be nothing but ontological mathematics, all questions are ipso facto answered.

The God series, starting with The God Game, reveals the astonishing power of ontological mathematics to account for everything, including things such as free will, irrationalism, emotion, consciousness and qualia, which seem to have no connection with mathematics.

Read the God series and you will become a convert to the world's only rational religion - Illuminism, the Pythagorean religion of mathematics that infallibly explains all things and guarantees everyone a soul that is not only eternal but also has the capacity to make of each of us a true God.

Isn't it time to become Illuminated?"

....

Again lots of this stuff is way over my head but I thought id post incase someone wants to explore

some of the more advanced stuffs.... I figure someday I might get rich and be the oldest geezer

in college and when I graduate I can try and read that book again lol

[Optimystic]

I really like this vid..

http://www.dailymotion.com/playlist/x1cbyd_xSilverPhinx_bbc-dangerous-knowledge/1#video=xdoe8u

as it relates to the mathematical side of things I guess... not that this has anything to do with psychadelics

other than how math can be sort of drug for mathematicians... they also seem to be crazy types who might

be prone to having nervous breakdowns ...

when I see "Psychadelic Revolution" the first image i get in my mind is a bunch of hippies looking for

a radical experience to boast about later but I think what the OP is getting to in the beef of it all is how

its all intricately related perhaps to inspire some studies into psychadelic use but from the perspective

of mathematics.. so I gathered what Paradox mentioned but not that im a fractal mathematician either lol

Ultimately I believe that psychadelics somehow or another, opens up a different perespective for some ppl

at least I gather that much from reading such stories...

I don't have much of a psychedelic background but i've had some personal experiences where my entire life and perspective has changed.. once when i was laced, another time when I did nothing hallucinogenic but I had what I guess was a nervous breakdown

but which was much like what I remember the psychadelic experience, minus the huge red spide and the shadow

people eh... the 3rd and only other time I tried psychadelics was when I was losing my home after losing

several other huge things in my life and well I self medicated after reading john hopkins research, w/some

shrooms... after that my perspective changed dramatically and thats why im into plants today intstead

of the superficial lifestyle I used to lead... not that im a mathematician but I got into some of that math stuff

after these experiences and they made alot more sense to me after these experiences whereas before that

I would have just considered it all useless info... and thus I believe mathematics can be perceived in a more

spritual manner and I can see how from that perspective might lead to one looking under a proverbial stone that they

otherwise might have passed up

i personally as well as what i've read from others have been inspired by experiences i've had that

were very out of this world and well its not stuff that would be ez to put on paper in laymans terms

but considering that thoughts and emotions are forms of energy too, well then mathematics must be able

to play a role in measuring these aspects and pschadelics, very likely have a place in the study, not that

they could or would provide experiential understanding but there certainly could be some experitiantial

inspiration and perhaps some outside of the box creativity inspired that might someday lead to advancements

or greater understanding as to what all these fractals have to do with , um , everything around you!

I think the most important study of all is the study that which happens internally and I believe that once one

has figured out their internal state of being, that their perspective of EVERYTHING else forever changed radically...

at least so far for me anyhow... so for a mathematician having a spiritual experience through psychadelics, I can

see how it might inspire something or other... but it can be said that one can have an psychadelic experience

without having ingested any substances.... I believe so but I suppose in my case, that could have been a flashback from

whatever I was laced with several years ago but maybe not... after all the brain is the ultimate drug factory

im done trying to be smart about this tho... back to simple equations eh

Edited March 23, 2014 by Spine Collector