On my seventieth birthday, my former postdoc, frequent coauthor, and friend Carl C. Evertsz organized a meeting on the island of Curaçao. His family’s prominence there greatly helped, as did the lure of February in the Caribbean. While this meeting was memorable, many speakers came just before their talk and left just afterward. I concluded that the days of the truly interdisciplinary fractals meetings were over. When I was nearing eighty and another meeting started being discussed, I strongly urged my friends not to all meet together but instead to have specialized sessions for each discipline. Some friends heeded my request, and a conference on finance was held at the Deutsche Bundesbank in Frankfurt for my eightieth birthday. Others did as they pleased and organized an interdisciplinary international meeting in Paris, also for my eightieth birthday. In each case we had a marvelous time.
(Illustration Credit 26.1)
Riding the Coattails of a Best Seller from Bremen
Essential “promotional” help for the 1982 book came from an exhibit at the University of Bremen and a mass-market book. They revived a tradition of high-class expository books that had long lapsed but used to be practiced by the likes of the great Henri Poincaré.
During the summer of 1984, I was making arrangements to replace our black-and-white graphics with color. Everything was in place when a popular German magazine published an article by Heinz-Otto Peitgen and his colleagues from Bremen featuring precisely the kind of color pictures I was about to undertake. Throughout my life, it had been my principle never to compete frontally with anybody. Therefore, I stopped my work on color and instead wrote to congratulate the authors and suggest that we get together. An exchange of letters followed, culminating with an invitation in the spring of 1985. The Bremen group was preparing a big exhibit of fractal art, to be shown first at home and then to travel around the world. They wanted me to visit Bremen for the vernissage and a lecture. I was delighted to accept. The exhibit catalog was magnificent, became wildly popular, and soon sold out. A foretaste made the cover of Scientific American. It was expanded into an extraordinarily beautiful book by Peitgen and Peter Richter titled The Beauty of Fractals, for which I was flattered to be asked to write a historical chapter.
I became close to the Bremen group and took part in many of their activities. Some were of a kind I would have hesitated to initiate myself but was happy to participate in. They wrote several textbooks that continue to be basic to the teaching of fractals and chaos. They also organized—both in Germany and in Broward County, Florida—a forward-looking program that uses fractals to help teach mathematics in high schools.
I Become Known as the Father of Fractal Geometry
Let me first mention an overflow that occasioned a shower of papers. U.S. publishers believe that thin books are more attractive. Therefore, The Fractal Geometry of Nature was made thinner by printing on high-quality (“Bible”) paper and keeping the length under five hundred pages. I was left with a mountain of “cuttings.” Papers mentioned in The Fractal Geometry of Nature remained to be finished and published. They propelled my publications from a low rate while I was concentrating on The Fractal Geometry of Nature to a high rate that lasted several years … and has not yet been exhausted.
The Fractal Geometry of Nature generated a formidable wave of interest. The word “formidable” has several meanings—often implying something either promising or threatening—and all those were strongly felt. Invitations of every kind started coming and—amazingly—continue to come. Only a handful could be accepted, but every aspect of my life changed in one way or another. Fads come and go and include best-selling books that soon vanish from shelves and minds. New styles begin slowly but are long-lived.
One reason The Fractal Geometry of Nature took off was that an amazing variety of journals reviewed it—in glowing terms. Every time I stopped by the library at IBM Research, or so it seemed, one of our librarians would hand me a new journal, often in a field that I did not expect would know or care about my work. Most unexpected, as I try to think of it, was a periodical put out by the French Royalist Party. Its review began by saying that they found themselves surprised to feel that my book had to be reviewed.
And the book did not become that nightmare of publishers: one that reviewers love but readers avoid. For years, friends who visited bookstores more than I do commented that the science section displayed a few scattered works and a big pile of The Fractal Geometry of Nature. It paid for my sons’ college tuitions and is still in print.
A Shower of Awards
Are awards important? Having sat on a number of committees, I know all too well that their decisions are not divinely inspired but disconcertingly human. For colleagues pursuing a normal career, awards are one of many other indicators of their progress. Those other indicators being absent in my case, awards took on an altogether different importance, especially those coming as a surprise.
The first two, to IBM’s credit, came from inside: an Outstanding Innovation Award at the research division level in 1983 and at the corporate level the next year. Being named an IBM Fellow in 1974 might also be viewed as an early award.
My first outside award was the 1985 Barnard Medal for Meritorious Service to Science. It used to be granted every fifth year by Columbia University, in memory of its longtime president, Frederick Barnard, on the recommendation of a committee of the National Academy of Sciences. Earlier laureates included the likes of Albert Einstein, Niels Bohr, and Enrico Fermi. The previous laureate had been the founder of Bourbaki, my nemesis André Weil! When Ralph Gomory, my manager at IBM, called to announce this forthcoming event, he first asked whether I was sitting down, then read the list of my predecessors. He added that winning this award guaranteed that it would not be my last. Indeed, it was not, and in 1986 I received the Franklin Medal for Signal and Eminent Service in Science, followed by the 1989 Harvey Prize in Israel and the 1994 Honda Prize in Japan.
The Steinmetz Medal, awarded in 1988, was heartwarming because Charles Proteus Steinmetz had been a special hero of Father. Crippled by polio, he rose to be a great inventor and also—as a German liberal who had fled the Second Reich—a great civic reformer.
Particularly exotic was the Science for Art Prize, also in 1988. It was awarded by LVMH Moët Hennessy Louis Vuitton. I was entitled to wonder: Is a provider of booze, even a high-class one, sufficiently respectable, especially given that IBM was still dry at that time? So I responded that I must take a night to consult with my wife. The check was small, but a whole week of festivities in Paris and the provinces was arranged as a public relations effort by a skilled purveyor of luxury. For us, it was unforgettable.
Another not purely scientific award, the Médaille de Vermeil de la Ville de Paris, was supposed to be presented in grand ceremony by the mayor of Paris, Jacques Chirac. But in 1995 Chirac was campaigning to become president of France. As a result, appointments were postponed repeatedly, and finally the medal was handed to me by his successor in one of the grand halls of the Hôtel de Ville. I was asked to prepare both a formal speech for the mayor and my own response. I had passed by the Hôtel de Ville millions of times, and although I should have, I never did suspect that its grand halls were extreme examples of the flamboyant academic style that the Impressionist painters famously rebelled against.
A specialized award in mathematics is the annual Sierpiński Medal of the University of Warsaw and the Polish Mathematical Society. Being selected for this award in 2005 and accepting it in Warsaw marked my belated “closure” with Poland.
The most prestigious award was the Japan Prize for Science and Technology of Complexity, which I received in 2003.
It was a full week of varied and entertaining events, a most enlivening glimpse of cultural Japan. One funny moment: at the gala awards dinner, I was given a translator so I could speak to Her Majesty the Empress of Japan, who sat next to me. The translator, who stayed kneeling down behind the table for the entire meal, had a very easy job. As it turned out, Her Majesty and I were both fluent i
n English, and we had a lovely conversation on our own.
(Illustration Credit 26.2)
My most memorable award was the 1993 Wolf Prize for physics, which apparently was triggered by the 1989 Saint-Paul de Vence conference Fractals in Physics. It was memorable for two reasons. First, it was presented to me by Ezer Weizman in his first public function after he became president of Israel. Second, although IBM was ecstatic about the award, I received it at the precise moment in 1993 when pure research was being dismantled.
Full disclosure forces me to report that at Yale, where I would become Sterling Professor, this prize did not impress my physics colleagues. They kept absolutely mum.
Awards Accompanied by Backlash
Sudden success is almost always problematic. The success of The Fractal Geometry of Nature failed to make my fledgling discipline intellectually, financially, and organizationally strong. However, it sufficed to make it potentially threatening. The physicist Hans Bethe welcomed an unfair advantage in his scientific work; in my case, it was a keen eye.
But unfair competition from an outsider is something that no group faces rationally. So the worst outcome for The Fractal Geometry of Nature would have been that it failed to be noticed. The second worst would have been universal dislike. The third worst, which is what happened, was an uncanny split I had to learn to live with.
On the one hand, it made me a world-renowned scientist, and not by moonlighting as a media personality. Apparently, my solo scientist’s work has features that are widely attractive.
On the other hand, I have continually faced strong hostility and criticism. In addition to the continuing flow of glowing reviews there was a trickle of dismissive comments and virulent diatribes.
The Balzac-Bohr-Bialik Syndrome: The Tongue, the Pen, and the Eye
Being an agile writer can be a great asset. Mozart could compose a full opera in his head and know it by heart before sitting down to write it. An opposite extreme case is that of the great writer Honoré de Balzac. He became infamous among typesetters for his peculiar hot-type anticipation of word processing. Having penned a few pages of incomprehensible scribbles with corrections all over, he would send them by messenger to the printer and expect to receive the next morning a galley of what he had written the previous day. To that he proceeded to add further corrections and “bubbles” in the margins, leaving almost nothing untouched, and the process continued several times. Rumor has it that printers assigned to his jobs set up an early trade union to escape spending more than a certain number of hours a day on his demanding work. Once, having seen in a museum in Paris a page of Balzac’s proofs—and feeling bubbly and flush—I tried to buy a corrected proof for myself. No such luck, not because—as I feared—they cost too much, but because I could not locate a supplier. The many elite dealers in old books and manuscripts that I consulted didn’t know what I was talking about: “Sorry, can’t help. Perhaps you should follow the auctions.”
The great physicist Niels Bohr is reputed to have been almost as bad—with the added problem that being both wealthy and powerful, he was not much in a hurry. He had to be urged by colleagues to stop revising and publish, and his earlier drafts continue to be viewed as better than the last and to circulate in a kind of samizdat. Yet another sufferer was the Russian poet Bialik, so this extreme style of writing might perhaps be called the Balzac-Bohr-Bialik syndrome.
(Illustration Credit 26.3)
I suffer from that syndrome in an acute form. I never begin with a table of contents and then write chapters, sections, and sentences in the order in which they appear. Instead, I start with several already available pieces that can be counted upon to provide the structure of the whole, and I keep adding here and there. Every so often, I wake up in the morning with the overwhelming feeling that a chunk of the book is in the wrong place and had better be brought forward or back. Quite literally, a book does not approach completion until I know it by heart. As a young man, I had no access to a typist or time for careful successive handwritten texts. So I often sent the printer something that in truth was an immature early draft. Galleys required extensive Balzacian changes and sometimes made it preferable for my text to be reset from scratch—leading to very stiff bills. Word processing has made this syndrome incomparably easier to live with but has not cured it. One day, my programmer, watching my assistant suffer with an especially messy draft, asked how I had managed before electronics and without an assistant. My answer: “Extremely painfully.”
Let me elaborate by expanding on the distinction I see between “seers,” who favor pictures—as I do—and “hearers,” who favor language. Written or printed material is a hybrid that came late in human evolution and some otherwise advanced cultures never produced it at all. Hearers like Mozart and Homer put to paper one or several linear sounds heard in the mind’s ear—without need for much iteration. I think that Balzac must have been a seer, having simultaneous multidimensional thoughts that demanded being linear during the writing process. My handwriting is poor, and I wonder whether dictation would have helped. The result is seen best after it is set in type. It then becomes subjected to a mental process that resembles metallurgical annealing, where metal dissolves after being kept under fixed conditions. In metaphorical annealing, I find that type reveals unsuspected relationships between words, phrases, paragraphs, or chapters. Once I can see these, I am able to adjust them as needed. The paper becomes a new crucible for creativity, a crutch for lesser Mozarts.
Many scientific articles are completely flat because they are written for people who do not have to be convinced. Their authors are part of a small circle within a well-established domain; they know everybody, or are introduced by their thesis supervisors or mentors, and they write for one another. As a result, style is secondary and unimportant for them. In my case, the fact that I write for an unknown public influences and shapes my style. Whether it is opera or Greek drama, one must know how to enter into a subject quickly because one cannot assume that the audience will wait to understand. One has to be able to speak to people in their style, to motivate and even amuse the reader a little.
This syndrome has caused my scientific productivity to be overly dependent on circumstances that made a helper available. Gaps in my productivity resulted not from a lack of imagination but from a lack of assistance. And I must confess harboring a sharp regret. Had I been able to get more assistance in the early years, I would have moved faster, and The Fractal Geometry of Nature would have appeared when money for scientific research was flowing, well before 1982. This would have made a big difference.
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At Yale: Rising to the University’s Highest Rank, Sterling Professorship, 1987–2004
THE ART OF RECEIVING new offers and fast promotions has always baffled me, but I have been lucky on a few occasions. One in particular was landing a job at Yale University.
Adjunct Professor of Mathematical Sciences at Yale
The indispensable intermediary who started the process that led me to Yale was a self-described “institutional economist,” Martin Shubik. We had met while I was John von Neumann’s postdoc at the Institute for Advanced Study and he was at Princeton University with Oskar Morgenstern (1902–77), Johnny’s coauthor on the book Theory of Games and Economic Behavior. For a short period in the sixties, we were colleagues at IBM Research, but he soon left for Yale.
Out of the blue, Shubik called me when I was in transit to Harvard in 1964 and again early in 1967. The first time, I must have rebuffed him. The second, I must have sounded more open. Shortly afterward, a call came from the mathematics chairman, Ronald Raphael “Raphy” Coifman. “We know that you have a position at Harvard but keep strong links at IBM and a house in Scarsdale. Both places are far closer to Yale. Could we convince you to join us?” “But what about Serge Lang?” I asked. Lang (1927–2005) was a distinguished mathematician, widely feared for his strong and strongly expressed opinions. “Yes, Serge does have clear opinions of departmental colleagues but keeps them to
himself. If you are concerned about what he thinks, this department is the best place to be.” “But at this point, I know no mathematician at Yale.” “Actually, you met Peter Jones in Stockholm, at Mittag-Leffler.” “But he is in Chicago.” “Not anymore, he has now moved to Yale. We have not met, but I know your work very well. Plus, Shubik, several economists you know, and other colleagues are working hard to bring you here. Come over. Let’s meet and talk.”
I went, saw, and was won over. Key attractions were Yale’s proximity to our house in Scarsdale and that this would be part of a long-term project. The Yale mathematics department disliked being ranked below Princeton and Harvard, and they had decided to replace “lesser” with “different”—in particular, by expanding less abstract topics. The idea was to first appoint senior people with high name recognition.
The dean of (undergraduate) Yale College was Sidney Altman, a noted biochemist who would soon receive the Nobel Prize. Funds had been collected in memory of Abraham Robinson (1918–74). I happened to have met him, so I knew that he had a good reputation in three distinct fields: aeronautics, symbolic logic, and mathematics. At the time of his death, he was Sterling Professor of Mathematics and Philosophy. Therefore, the kitty was constrained to prospects of exceptional versatility, and I qualified. There was not enough money for a full-time permanent chair but enough for aging me to become—on half-time—the first (and so far only) Abraham Robinson Adjunct Professor of Mathematical Sciences. “Adjunct” contradicts holding a chair, but nobody cared. The negotiations went smoothly because I was helped by experience drawn from my Harvard adventure and was not thinking beyond the original five-year contract. As it turned out, I stayed for seventeen.
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