| In 1987 I was in the mathematics department of Union College, in Schenectady, NY. There physicist David Peak and I developed a course on fractals and chaos as a general introduction to quantitative thinking, eventually writing a book to support that course. |
| In 1989, Benoit Mandelbrot received an honorary doctorate from SUNY Albany. Mandelbrot's host, the late physicist James Corbett, organized a minisymposium on fractals in the morning, before Mandelbrot's commencement address. Corbett had arranged for several people to give half-hour presentations of current research topics on fractals, but hadn't found anyone to give a general introduction to the subject. He asked Peak, who declined because on commencement day he had another meeting that he could not skip. Peak suggested Corbett ask me. |
| As it turned out, that day I also had a meeting, one I did not want to miss, but did not have to attend. On the other hand, I'd not heard Mandelbrot talk, and that certainly sounded interesting. What to do? I flipped a coin. No, really, that's what I did. It came up "Mandelbrot." So my giving the introductory talk at Corbett's fractals symposium was the result of a coin toss. A coin landing one way or another is a pretty small change in initial conditions. |
| The morning of the symposium I arrived in the back of an already crowded room, with a dean making deanish noises in the front of the room. "Our first speaker of the morning is Prof. Michael Frame from Union College. Are you here?" Carrying a box of overhead transparencies (this was 1989, before computer projection systems were common) I walked to the front of the room, turned to face the audience, and sitting right in the middle of the front row I saw ... Mandelbrot! |
| My heart skipped a few, or maybe it was a few dozen, beats. These other people were talking about new things, but I was going to give a compressed version of the introduction to fractals that I give to freshmen. Mandelbrot will be bored out of his mind. I knew he was a tremendously busy guy, and hadn't expeted him to sit through the morning program. At the very least, he'd skip my talk, because what could he learn from me? I felt like I was giving a general introduction to the Ten Commandments, with Moses sitting in the front row. |
| But what can you do? I gave my simple talk, as planned. Then the other sumposium speakers gave their talks, then there was a break before Mandelbrot's commencement address, in a much larger auditorium. Between the symposium and commencement, Mandelbrot circulated around, talking with all the other speakers. To my surprise, he made a point of talking with me, complimenting my ability to give clear explanations of complicated ideas and saying he hoped we could work together sometime. OK, he was much more polite and (at least in my case, 'way too) generous with compliments than I had expected, but surely he wasn't serious about our working together. We live in entirely differnet worlds. Different galaxies, as far as I could tell. |
| A few years later, Mandelbrot called and invited me to spend the year working with him at Yale. I had sabbatical from Union, so went to Yale, introduced a fractal geometry course there, and eventually this led to an offer of a permanent position at Yale. |
| So, I wound up at Yale, Mandelbrot and I got a $1.6M NSF grant to run summer workshops on fractal geometry for several hunderd high school and college teachers, wrote a book, wrote the webapges you're reading now, I developed an advanced fractals course, two courses on the geometry of nature, and redesigned the Yale calculus curriculum and premed math classes, all because of the outcome of a coin toss. |
| That particular butterfly had pretty powerful wings. |