Remembering Benoit Mandelbrot

Benoit Mandelbrot burst upon the public stage with his extravagant work of genius: Benoit Mandelbrot, Fractals: Form, Chance and Dimension (W. H. Freeman, San Francisco 1977). As Mandelbrot himself might put it, "I know of very few books … in which so many flashes of genius, projected in so many directions, are lost in so thick a gangue of wild notions and extravagance."

(He made this remark about George Kingsley Zipf's book, Human Behavior and the Principle of Least Effort. The Mandelbrotian word "gangue," more commonly used in French, refers to otherwise worthless material in which valuable ores or gems may be found. It's pronounced like "gang" in English.)

Detail of the MandelCubicWhoopDiDoo Cubic Mandelbrot Set.

Today's illustrations and videos are recycled from my rather long post from April and May, 2010, "Rudy Set as Ultimate Cubic Mandelbrot Set. Quartics & Quintics Too!" That post contains explanations of how the images were computed.

I went to Mandelbrot's house early in 2001, when I was involved in an abortive project to try and make a large screen (IMAX) science movie featuring some huge, prolonged zooms into the Mandelbrot set.

The movie, which was to be about fractals, had the working title Search for Infinity, a title which was dictated by the producer, Jeff Kirsch, director of the San Diego Space Center Museum. Jeff was committed to presenting the film as being about infinity instead of being about fractals, as he felt many more people would be interested in the former than the latter. And in a mathematical sense, fractals are indeed infinite, in that you can zoom into them, forever finding more levels of detail. It's an infinity in the small, rather than an infinity in the large.

Detail of MandelCubicInvasionOfTheHrull

The very talented film maker Ron Fricke (Konaequaatsu and Baraka) was committed to shooting the film, and I was going to write the script. Ron and Jeff were also bent on including Arthur Clarke in the movie as a character. And Ron wanted the movie to star a computer-brained space probe who was afraid to fly off into the endless void of interstellar space. Jeff had scored a development grant for the project from the National Science Foundation and we worked on preparing a final proposal over a couple of years.

Taking all the story constraints into account, I put together ten or eleven successively more refined treatments for a film script, resulting in a fairly reasonable treatment, The Search For Infinity, which you can read online.

But, like so many films, the project was never realized. The sticking point was that we failed to get the needed the million dollar grant from the National Science Foundation. One reason I visited Mandelbrot was in fact to try and win his support in case the NSF were to ask his opinion about the project, but he was unenthused about it, I don't know exactly why. One of his issues was that it was wrong to bill the film as being about infinity, when in truth it was about fractals  I agreed with him on this point, but this wasn't something that I could get Jeff and Ron to go along with.

Detail of MandelCubicPacMan

The rest of this post consists of excerpts of my journal entry of January 14, 2001, regarding my meeting with Benoit. I published this as an endnote to my tome on the meaning of computation, The Lifebox, the Seashell, and the Soul, but I thought I'd post it on my blog today as well.

RudyMars

Mandelbrot is waiting for me at the end of his driveway, he's worried I might not find the house as the address on the curb is covered by snow. A white-haired balding man, stocky, somewhat diffident, he sees me, I wave, he doesn't wave back, not sure yet I'm the one he's waiting for, when I'm closer he says "Are you Rudy Rucker?" We introduce ourselves, shake hands, I tell him I'm thrilled to meet him. In the house his wife Adèle greets us, Mandelbrot disappears to take a pee I suppose, then we sit in a cold room with some armchairs. They don't seem to really heat their house. He sits on an odd modern chair with parts of it missing, a collection of black corduroy hotdogs. He wears a jacket, a vest, a shirt, trousers with a paperclip attached to the fly to make it easier to pull up and down, I guess he's 75. Rather rotund and, yes, a bit like the Mandelbrot set in his roundness and with the fuzz of hairs on his pate.

He starts talking almost right away, an incredibly dense and rich flow of information, a torrent. Fractal of course, as human conversation usually is, but of a higher than usual dimension. It's like talking to a superbeing, just as I'd hoped, like being with a Martian, his conversation a wall of sound paisley info structure, the twittering of the Great Scarab.

His wife listens attentively as we talk and from time to time she reminds him to tie up some loose thread.

RudyHorse

Mandelbrot doesn't seem overly vain  as I'd heard him described by some rivals. Certainly he has good self-esteem, but I think it's well-earned and justified.

I repeatedly feel a great urge to go out and have a cigarette. The firehose-stream of information in his strong French accent  I have to cock my ear and listen my hardest to process it. Conscious of his wife watching me listen to him. I imagined she's judging how well I seem to listen, and when once I smirk as he says something a bit self-aggrandizing, she catches my expression and I imagine her giving me a black mark.

He isn't clear exactly what Jeff is trying to do with the movie, how Jeff plans to fund it, what his (Mandelbrot's) role is supposed to be, etc. I explain it as best I can; we don't really expect Benoit to do much more than to say that that he doesn't find our project totally absurd. He seems to want to exact some kind of concession; at the end I have the feeling that he considers Jeff's emphasis on "infinity" to be a deal-breaker, to the extent that there might have been a deal.

RudyRockets (detail of the Rudy Set). Lower down in this post is an animated YouTube zoom to the Rockets.

I mention how much he's affected my view of the world. I mention also that I'm as excited to meet him as I was to meet Gödel. Mandelbrot says, "Oh Gödel didn't talk much, I saw him at the Institute, I was von Neumann's last student." I rejoinder, "Well, Gödel talked a lot when I saw him, I was working on something he was interested in," and Benoit is impressed.

In the event, it's not really like meeting Gödel because I'm not so young and starry-eyed that I see Mandelbrot as a mythopoetic guru. Yet it is like meeting Gödel in the sense that for these two special oasis hours midway in the long caravan of my life I'm talking to someone whom I feel to be smarter than me. An ascended master.

YouTube movie of a "Rockets" zoom into the Rudy Set.

I've been thinking some more about ways in which Mandelbrot resembled the Mandelbrot set, it's a conceit I'm bent on playing with. As I mentioned yesterday, he was rather round about the middle, even bulbous, and his clothes and his head were indeed adorned with any number of fine hairs. He appeared and disappeared from my view several times; he'd get up and leave the room and then return. Perhaps each time it was a different bud of him that came back in!

A key point in perceiving his multi-budded nature is that his wife in many ways resembles him: accent, age, attire, knowledge about his work. She was in fact a mini-Mandelbrot set hovering near the flank of the larger bud I was talking to. The two of them were connected, of course, by a tendril of love and attention, rather hard to physically see.

[Y MandelQuinticLeopard.]

At times I felt a bit of menace from Mandelbrot, as when he was repeatedly asking that we not bill the movie as being about infinity. I felt some anxiety that he might somehow do something against us if we didn't accede. He has, one imagines, a wide range of influences. What was going on here was that I was sensing the presence of the stinger at the tip of the Mandelbrot set. A stinger so fine as to be all but invisible, a stinger that, as he grew somewhat agitated, was twitching with rapid movements that made it yet harder to see. But nevertheless I could feel its whizzing passages though the air near me. Palpable menace.

RudySanskritBud

The world will miss you, Benoit. Thanks for making it a better place.