How Chaos Theory Pioneer Ralph Abraham Made His Way to Santa Cruz

It was a short strange trip.

PUBLISHED JUL 16, 2022 12:00 A.M.
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Ralph Abraham, irrational?

Ralph Abraham, irrational?   Portrait, Paul Schraub, 2000. Background courtesy   Contributed/public domain


I first met Ralph Abraham in 1997 or 1998 for an interview for a locally produced web ’zine called The Hawk. 

Ralph taught math at UCSC, and was an early pioneer in the development of Dynamical Systems Theory. The interview turned into a very basic lay explanation of that theory, and the closely related Chaos Theory. 

Portrait of Rupert Sheldrake, Ralph Abraham and Terence McKenna.
Rupert Sheldrake, Ralph Abraham and
Terence McKenna, 1990's.

I particularly remember Ralph casually noting in the interview that ‘Laplacian determinism is dead,” and pointing out that because dynamical systems are unpredictable, a long-held notion that the present and future are determined by causality going back to the Big Bang is false. These theories were world-shattering, and they made Ralph and his cohort famous.

Sadly, the interview is lost to the ravages of time and lack of backups. 

After the interview was published, we invited Ralph to put together and teach a series about ‘Sacred Geometry’ which was well-received, and Peggy and I were honored to attend the last Trialogue at the Edge of the Unthinkable held up at UCSC in which Ralph, the renowned psychedelic explorer Terence McKenna, and the cosmic biologist Rupert Sheldrake sat on stage and took turns blowing the minds of the audience. 

After serendipitously encountering his Hip Santa Cruz series of local oral histories, I reached out to Ralph, and we rekindled our multi-decade conversation.

This transcript with Ralph was recorded on a delightful June day at his home in Bonny Doon over tea and scones, and is lightly edited for length and clarity.

For decorative purposes.

I'd like to learn more about you and your life and what led you to tuning in and turning on. Because you're a math professor and math professors don't normally have a reputation for the deeds that you have done.

For the irrationals (laughing).

You were born in 1936. Where were you born?

Vermont. I love it. It's one of the best states. I lived there until I was 18.

And then you went to college?

Yeah. But first, I went to prep school toward the end of ninth grade. I hated it there. But toward the end I was rescued because I caught tuberculosis. It was a time when it was sort of a death sentence.

Ralph with a ham radio.

Antibiotics were invented by then?

Streptomycin came to my rescue. It was invented just in time. So I spent two years in bed and missed the whole of high school. And during that time, my mother was afraid that I'd miss socialization by missing high school—and she had this idea that if I were a ham radio operator, then I would be socialized on the air, as it were. Because we didn't have the internet, we didn't have the worldwide web and we didn't have social media. 

That was the original peer-to-peer network!

It was the original peer-to-peer network that had been going on for a century or something. So I thrived on ham radio, and derived from that, I decided I wanted to be an electrical engineer because I was, and I still am mystified and amazed by the electromagnetic field. 

We talk about the psychic field, the family field, the biological field, the morphic field. And so the electromagnetic field is the greatest mystery because we have no idea what it is. It fills the entire universe and we can send a message to the moon and back with less energy than a hundred-watt bulb. Which—we don't even know what electricity is.

So that led to my departure from the state of Vermont. I went to electrical engineering school at the University of Michigan in Ann Arbor. I stayed there for six years and then gravitated from engineering to experimental physics to pure mathematics—you know, a gradual progression.

It's a logical progression, and from what you've said, it seems you were chasing the magic.

Exactly. So I learned quite a bit about electrical engineers and I learned about experimental physicists. I was deeply embedded. And then I learned about pure mathematicians and the way they are is nothing like their reputation. They aren't — as individuals they're not rational. [Laughs.]

It's an alternative universe in which hardly anyone could feel at home. But some people just have a gift. How they are, who they are, what they are in that alternative universe—there's no correlation whatsoever to what they are, who they are, and how they are in this universe. That's why, if you read any biography of any mathematician, it's always amazing. It's not what you expect.

'It's very similar to your first psychedelic trip. When I was experiencing this [world of mathematics], I had no idea that psychedelics existed.'

Would you say that a fundamental aspect of what makes a mathematician is that they're comfortable in this alternative universe?

All these famous mathematicians, male and female, have biographies. I used to give a course called History of Mathematics, and it was fabulous. Students loved it. And I found this was the way to teach anything, through its history, its genesis, its creation, its development. 

And especially through the personal biographies and autobiographies of the individuals. You can read all this literature, and it is never clear how the person discovered the alternative universe, and how they were at home in it, and could navigate and explore and discover. And it's wondrous. 

It's very similar to your first psychedelic trip. When I was experiencing this [world of mathematics], I had no idea that psychedelics existed. They did, but they weren't part of the culture.

So you ended up teaching at the University of Michigan?

No, I got my PhD in mathematics in 1960, and then my first job was at UC Berkeley. And it was sort of an amazing serendipity, because I had had a not-very-well-known thesis advisor at the university of Michigan, although some superb, world-renowned mathematicians were there. They were sort of passing through. The University of Michigan did not have a reputation as a math breeding ground. So I ended up with only one job offer, and it was in some minor branch of the University of Minnesota or something. 

And at the last minute I was rescued by a surprise letter from UC Berkeley. They’d had a cancellation or something, and I got an offer there. And I thought that university was not very well known either, but the climate was better than Minnesota. So I accepted Berkeley. 

This was before Berkeley became the powerhouse that it is today.

Exactly. And so I had no expectations at all there. And when I got there, I made the discovery of this amazing revolution, in which Governor Pat Brown had decided that California was gonna become like Detroit unless they had a superb educational system for STEM.

And so a huge amount of money had just arrived. And UC Berkeley had hired all these mathematicians and physicists. I mean, it was incredible. 

It took me about a month or six weeks to discover who my colleagues were, and where they'd come from. And they had Fields Medals and Nobel Prizes. And it was just incredible that I just ended up in this, and I knew very little of the mathematics that they were expert in. 

And they had in the math department a tea hour in the afternoon, every single weekday. And the first one I went to, I met some of these people and said, ‘what do you do?’ And this one guy said, ‘well come to my office down the corridor and I'll show you what I'm doing.’ And what he was doing earned him the Fields Medal a couple of years later. 

'So I found myself in the alternative universe. I felt more at home there than anywhere I'd ever been.'

And I discovered that I was able to look at what he was doing and intuitively understand it completely.


And I began doing joint work with him immediately, and it was like a miracle. So I found myself in the alternative universe. I felt more at home there than anywhere I'd ever been. And within a year or two, I had my own reputation and other offers and so on. It was like, get on the elevator that goes to the top floor

All through serendipity.

Yeah. All through serendipity. So, I went from Berkeley to Columbia and then I went from Columbia to Princeton.

That was climbing the math ladder.

Princeton was probably the best math department in the world. Yeah.

And in all this, when did you first encounter LSD?

1967 at Princeton.

So you had colleagues or acquaintances that said, Hey Ralph…?

I was a junior professor, so I had to teach calculus and graduate courses and whatever they needed. And during the time that I was teaching a calculus course, the Beatles happened …


… and so I ended up going to class in a kind of a Beatle costume, where I wore different costumes every day. I was not cleverly trying to manipulate my relationship with students or anything—I just did whatever I wanted as a nut case. And I apparently had some talent for teaching.

Although I considered my work as doing creative mathematics, and teaching was the day job. So I didn't approach it with any kind of ambition. But there was something about the students in those days that they were seriously interested in the subjects of the courses they were taking. And so I felt rewarded for making an effort in teaching. 

Anyway, the result was that at Columbia I already became a little bit popular with the students. The young teacher—I mean, I was just a little bit older than my students,

So … do you remember your first trip?

Oh yeah. So I was getting to that. It happened because I had this relationship with the undergraduate students. My math colleagues were mostly older than I was, because I was 23.

You were 23 when you got your Master's?

When I got my PhD. 


I didn't waste time in school. I just went as fast as I could.

So at Princeton, the teaching assignment I was given on arrival was a course called Advanced Calculus. And that was for the freshmen, their first course in mathematics, but they were supposed to be gifted or something.

Because they were accepted into Princeton?

No … more than that. They had shown talent and interest in mathematics. So they had already been recognized for this special class.

These are a bunch of 19 year olds.

17 or 18. Yeah.

And so I had 15 students in this special class where I was encouraged to do whatever I pleased. And I taught them advanced, pure mathematics from the get-go. What was going on in the frontier, and so on. And I had this relationship with them. And then I was invited. 

They mostly lived in dormitories. Princeton was not yet co-ed—I participated in making it co-ed with sit-ins with students. So I was going into the dormitories to talk with students, and they were smoking dope and stuff. And they introduced me to LSD—my undergraduate students.

So that was...?

November of ’67.

One of the students was the son of a very famous professor. He was 15, and his father interceded with me so I would allow him into my course, even though he was still in high school. So Carl got the stuff and offered to be my guide. 

We went on a tour around the campus, and we went into the homes of two or three close friends who hadn't had LSD yet—but pretty soon they did. They were my acid buddies at Princeton—junior professors in philosophy and art history. 

Carl sounds like a very ... precocious kid.

Gosh, he was precocious and his father was really pushing him. And he got sort of screwed up by that process. Yes. But he got a PhD in mathematics at a young age and became a well-known professor.

Your career up to this point sounds like an impossible magic carpet ride.

I was very lucky. Yeah. And one of the luckiest things was deciding to come to Santa Cruz—to leave the Big Time. I could have stayed at Princeton.  

What compelled you to leave?

Well, I was really gonna stay. I had very good friends there. I loved everything about it. Except the city of Princeton was very staid and boring. And the restaurants were not inspirational. 

What kept me going was the social life. Professors would have dinner parties almost every night, once in a while you would eat alone at home. But it was just wonderful company, fabulous conversations about politics, and books and movies and music and so on. 

It was in the fourth year—it was a four-year appointment, so I could only continue there if they gave me a new appointment. Which they would, but I was not gonna be promoted to tenure right away, because it was too early. 

You were still so young!

My work was also kind of on the frontier, so it was all uncertain. And at that point I got a letter from Santa Cruz offering a position with tenure.

So it was proposed that I would fly out because that was, I think, year three. Every year, UCSC added a new college at that time. And each year they had to attract the faculty. In those days, the faculty was associated to the college, not to any departments. And so they were desperate to find 15 or 20 people who were going be the faculty of the fourth college. 

'There were 300 people dancing to the weirdest music I ever heard. And they were all stoned on LSD, and in costumes, and nude and kissing. And there I was—like I’d died and gone to heaven.'

I knew that I did not want to come to Santa Cruz [to practice mathematics], but I had some friends out here and I thought I could visit them and see what it's like. And so this is where the LSD comes in as the crucial bifurcating factor in my life. 

So, we're way back there in the sixties. And I flew in and I rented a car and went to the campus and had a program of interviews with different administrators. One of whom was the Dean of Science—although there was very little science and no engineering. 

His field was aeronautical engineering. And I had a discussion with him, which was very dissatisfying. I didn't have any ambition to stay in Santa Cruz, so I didn't care how I appeared in this interview. 

So I asked him, as a professor, about a story I'd heard that negative ions made you high. When you're at the beach and a breeze goes over the ocean, it produces negative ionization. And that's why everybody's so happy on the beach. 

He pooh poohed that right away. He said, “no, if there were a cloud of negatively and positively charged ions in the atmosphere, they would combine and neutralize instantly.”

Well, he was completely wrong. Anyway, I just had a very negative opinion and that reinforced my idea of not having anything to do with Santa Cruz or California.

After the day's work ended. I had these friends that I had wanted to see in Santa Cruz that I had to go and find. So I called Jim Houston, who was a student of Wallace Stegner’s at the Stanford writing program. I was looking for my friend Fred, and Jim said, “if you wanna find Fred, you have to go to this nightclub in Scotts Valley called The Barn.” So I drove my car to The Barn and it was maybe just getting dark. And I went in and my mind was blown. 

There were 300 people dancing to the weirdest music I ever heard. And they were all stoned on LSD, and in costumes, and nude and kissing. And there I was—like I’d died and gone to heaven. (Laughs.)

The Barn was in Scotts Valley?

Next to some Bible school where they were constantly being attacked. And there were these raids by the sheriff and arrests and legal cases. And I met a young woman named Cheryl, who introduced me to her brother whose name was Peter. 

I ended up going with her to this Peter's house in downtown Santa Cruz, where we had the most incredible conversation, and that was Peter Demma. And as a result of that conversation, I decided to accept the position and come to Santa Cruz. Because instead of having these very staid but interesting colleagues in Princeton, I'd have the whole hip culture in Santa Cruz. 

And since this was just three, four months after my first LSD trip, I wanted the benefit of hip culture. I didn't wanna be the only one. I was attracted by the like-minded. I mean, there were two or 3,000 people just like me, and who were having a wonderful time,

Like Leary said, “Find the others.”


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