A not so short history of Universal Function

Acceptance speech - 1993 NKT Research Prize in Physics
Dansk Fysisk Selskab Årsmøde, Lalandia, Rødby, Maj 18, 1993

                                                                           Excerpted and edited July 5, 2019

[For A very brief history of universality in period doubling click here]
[For hyperlinks to some of the literature,  click here]

Among my friends at Cornell were two called Feigenbaum.  The first one moved to a factory town to do union organizing, and reached brief national fame when the Mafia bombed his house.  The other one was amazingly fast in solving New York Times crossword puzzles, but he published nothing. Hans Bethe dispatched him to Blackhole, Virginia, where he languished publishing nothing until Peter Carruthers rescued him and took him to Los Alamos on the risky presumption that the man seemed very smart.  In contrast to these good-for-nothings, I was advertised as the best thing since Roman Jackiw and sent off to Stanford, Princeton and Oxford with a mission to solve the QCD quark confinement problem.

[...]

Mitchell told me about existence of period doubling universality at 10pm on December 19 1975, in a bar in New York City, over a glass of good red wine and in presence of my Black Irish Poetess.

In spring 1976 he came  from Los Alamos to visit Princeton, having published even less than before.  He gave a seminar, but nobody understood a word. Starting point was a parabola, then things got incredibly complicated, and at the end it turned out that the theory might be applicable to fluctuations in forest moth populations.

During his graduate school years at MIT, the strongest intellectual influence on Mitchell was not his adviser Francis Low (of Gell-Mann--Low beta function), who by that time had lost faith in quantum field theory, but charismatic cognitive scientist Jerry Lettvin. So Mitchell and I were driven by a secret agenda - the thing was robust, you could make it very imperfect, and a universal superstructure would survive the imperfections. In other words, just what you need to build a brain - all parts imperfect, and the thing functions anyway.

But my first task was to help my friend, make his lecture comprehensible. My friend Betty Boop worked on a Hewlett-Packard assembly line, so I was able to acquire a discounted programmable pocket calculator (with [multiply] and  [divide] buttons interchanged) for a mere one-fourth of my monthly salary.  Mitchell needed no such display of dedication, Los Alamos was floating in money.

I started thinking about functional equations on May 1, 1976. I calculated away with such gusto that I was calculating even laying on my belly on an operating table, with a surgeon lancing a large bicycle-caused sore. Eventually I reduced the whole complicated mess to one equation, wrote down the period doubling fixed point function equation on May 3, 1976,

and went off to the math library to look it up.  The Institute has an excellent math library, but I did not find it.  As a matter of fact, we never found it to this very day - it had never been written down before.
             For the record: universality in period doubling and the functional renormalization theory that explains it were         Mitchell's discovery, my contribution was to recast what was an infinite tower of renormalization equations into a more concise form.

As one would expect, nobody wanted to hear about it.  To be fair, I remember that a total of four people did:  Freeman Dyson, John Milnor, Bill Thurston, and Donna Lee.  Donna Lee is a wonderful San Franciscan whom I love even more dearly than Dyson; the rest you should know.

Blott, AKA Donna Lee above us to the right. In front: following our friend Stephen Wolfram, Nordita purchased the first Sun-1 in Scandinavia (though this desktop is not it). On the keyboard is one of Mitchell's calculators, on which he did most of his early period-doubling computations.

Six years passed and I was laboring away at Nordita, Copenhagen, when the word arrived from USA; there is chaos, and in August 1981 I could muster an audience for my first talk about the period doubling universality. It was an after-dinner talk in the Perturbative QCD Nordita summer school, Yngsjö, Sweden. In long run, quantum field theorists became dismayed by this theory. Being as intelligent as they were, they should have understood it with no effort, but they did not. But this first evening talk, to innocent, budding theory graduate student was a resounding success.

I went around spreading the news. In those days it was impossible for most to access the literature in a field so new, with foundational publications spread across so many specialties, so a put together a book of source materials:

This was the 3rd of my heavily illustrated home-production books, with hand drawn covers that I called 'Classics Illustrated'. Here we have Graf von Chaos himself as Faust (he loved Goethe) in der Periodenverdoppelnde Wald, cigarette aflame, desirous of Black Irish Poetess, soul aflame with turbulent longings, Das Ewig-Weibliche Zieht uns hinan, eying Die Gleichung. I had just returned from California where it was not unusual that a woman would ask you about your Sign. Plus? Minus? I resent all those violent and horned animals, so I would have to explain that mine was Helix Vulgaris, or the Gentle Garden Snail, the not well known 13th Sign of The Zodiac.

Feigenbaum contemplating a cauliflower

It is true: Mitchell has gone live on the 7PM German TV news  contemplating a cauliflower (?)

Mitchell does prime time TV in Copenhagen

Mitchell has appeared in the leading Danish left-intellectual rag, (Mis)Information, holding a Wonder-bread-like blackboard sponge, pensively, to great merriment of our students who have the picture on our bulletin board, with a variety of captions emanating from his mouth, comic-strip style. It is a reasonable article, from Mitchell's angle the best thing about it is that it is in danish, so he is safe from understanding it, and I ask you only 3 brief stupid questions, so I'm also clean.

Mitchell is now a heartthrob of many a wo in this ducky kingdom. They aired him and Polyakov in prime time, and they re-aired him alone today. It is actually almost sensitively done, considering the foreign worker treatment I got on Danish DR televison.

Well, Mitchell does have his detractors. MargArethe says that he has a strange way of blinking into camera, and that neither he nor Polyakov are her man types. But many a less critical Valkyrie is wet to her knees just at one of those blinks.

Other than that, there is much ballooning around. The Eye's woman is supposed to burst any day or hour now, and Ulla and Natural Radiance bounce around like Venus of Milendorf fertility amulets.

How long is this seriousness going to continue (and this includes Mitchell)? It's deadening, the joy is gone if every act is supposed to be laden with meaning. I'll go home and bounce few balls on the HP - it's trivial childlike game, but it is making me euphoric. All the patriarchal and fessorial responsibility
is dry and dusty as old wood.

Hamlet, Feigenbaum constant and the fine structure constant

There is a Procaccian chapter in our Hénon epic that makes me go to Hamlet to cheer up - "... is it better to suffer the outrageous ..." etc etc  soliloquy.

The whole idea was building my Ruinofficio was to have a place big enough to absorb my friends with their nasty habits and still sustain life as we know it. Empty it is as insane as any Latin American deserted oversized hacienda from Marquez.

The madness persists - I am getting visa papers to fly in November to Bezerkley and deliver a single review lecture of profound wisdom to nuclear physicists at LBL. The man in charge is the selfsame person (Switezky) who has related Feigenbaum constant to the fine structure constant, a paper that baffles me even more upon rereading now.

UFO's neuroscience and E&M provocateur

During my visiting professor stint at Cornell, I subbed for Mitchell for one lecture - I told him that I could teach E&M without any formulas, only using birdtracks.eu notation, and I was lucky - got to teach kiddies Green's theorem. There might be someone out there who still wanders what happened that day.

I my clouds video I mentioned some brain related projects that didn't pan out. "Universality in chaos" AKA "period-doubling" does not care what particular system one starts with, and we were wondering how neurons - each one noisy and imperfect in every way - never-the-less build up a pretty robust brain. Could it be that the renormalized (?) composite neuronal system is more robust than all of its imperfect components? It was all very naive and totally wrong. That's not how computational neuroscience has developed since.

I actually spent that semester secretly (in an attic of the Math Department) coding my idea of how a passive observer (a frog on a rock) visually observes and then develops abstract concepts, i.e. learns. That bombed out in an spectacular way. I was using Barbie Burke's husband, John Hamal Hubbard's IBM workstation, and it 1) one day lost all the programs in its memory, and then 2) literally chewed up my back-up diskette when I tried to restore them, thus destroying without any trace (there were no printouts) months of work. That was the end of my secret foray into computational neuroscience. Looking today at ChatGTP billions of parameters, I was way too optimistic about how this would have worked.

In other words, you do not want to get any neuroscience advice from Predrag .