On October 26th, 2015, I received an email from a colleague of my former dissertation supervisor, Leo Kadanoff, informing me that Leo had died that morning. It’s now some time since his passing, but I still would like to pay my respects to him.
I came to know Leo when I was a math graduate student in 1987. It was an uncertain time in my mathematical education. I had finished my qualifying work and spent a semester doing research in probability at Cornell in the fall of 1986. Back at the University of Chicago at the start of 1987, I was looking for a dissertation problem with which to get my PhD and move on.
Patrick Billingsley, who was the main probabilist in the UofC math department at the time, was no longer at the top of his game, having, as he put it to me, “run out of steam,” and then turned to acting as what appeared to be his primary interest (he was quite accomplished locally in the Chicago theater, and one can see him with small roles in various Hollywood films from the 1980s, notably The Bodyguard and Somewhere in Time).
Given my interest in probability theory, I was therefore looking for someone at the University of Chicago to supplement my work with Billingsley, someone who was at the top of his game and used probability as an essential component in a cutting-edge research program. That, as it turned out, proved to be Leo Kadanoff. When I defended my dissertation in the spring of 1988, Patrick Billingsley and Leo Kadanoff were joint dissertation supervisors.
I came to know of Leo on a lark, or by providence, depending on one’s view. My good friend at the time Chris Bishop (for many years now a math professor at SUNY Stonybrook) had departed the University of Chicago in the middle of his graduate studies to follow his advisor, Peter Jones, to Yale. Chris would come back periodically because he intended to get his degree from the University of Chicago rather than Yale.
At one of the afternoon math teas (late afternoons at the University of Chicago math department always included a spread of hot beverages and cookies in Eckhart Hall), I was talking to Chris, and he told me about this supergenius physicist who had an amazing quickness of mind, anticipating key results and insights of entire doctoral dissertations merely by attending their defenses.
So a few days later I walked past the Fermi Memorial on the UofC campus and entered the James Franck Institute, where Leo had his office. As it is, he was working on chaos and nonlinear dynamics, and I had previously spent six months intensive study in ergodic theory, so when I approached him and described some of my interests, he handed me a bunch of papers that he and his group were working on and asked me to get back with him.
Soon I got to know some of his graduate students and postdocs and to hang out with his research group. It was a warm and high-powered group. I enjoyed the people very much, and Leo treated everyone well, from the secretaries right up to his main collaborator at the time, Albert Libchaber.
With dissertations in math, two happy things can happen: (1) an advisor proposes a problem and the student solves it, writes it up, and gets his degree; (2) the student comes up with a problem, solves it, and the advisor deems it worthy of a dissertation. Other things can happen, but they are less happy, such as the inability to solve a problem (whether given by advisor or self-inspired), or solving the problem and then finding out it’s been solved already.
From my vantage, it is a credit to Leo and the intellectual ferment in his research group that I was able to devise my own problem, solve it, and have both Leo Kadanoff and Patrick Billingsley deem it worthy of a dissertation (titled “Chaos, Uniform Probability, and Weak Convergence”). In this connection I’d like also to mention another physics grad student, who worked not with Leo’s group but with Bob Geroch, for inspiring in me the the confidence that students can figure out interesting research problems worthy of dissertations if they keep their eyes open to currents that are driving their field.
As it is, I started working with Leo’s group in March 1987 and by August I had solved the two key problems that I had set myself in the dissertation. An intensive six weeks followed on various Mac computers to pull together the details and write up the dissertation. I was thoroughly exhausted at the end of this, but it was also one of the most satisfying experiences in my life. Both Leo and Patrick signed off on it immediately, though to stay on as a student through the academic year 1987-88, I didn’t defend until March 1988.
I think Leo was surprised how quickly the dissertation came together. As I was applying for postdocs in early 1988, he cautioned me that proper recognition for my work may lag behind its intrinsic merit. At that time, I had done nothing on intelligent design. I therefore pondered his words and wondered at the time if they might in some way be prophetic.
I stayed in touch with Leo sporadically over the coming years. Occasionally, he would comment on intelligent design. He was never a convert, to be sure. But he was always respectful to me, even when we disagreed. Early in 2014 I sent him the manuscript for Being as Communion: A Metaphysics of Information. He wrote back the following:
I read the first bunch of pages of your book and found nothing with which I could disagree, except perhaps the conjunction of science and material [matter] or rather the disjunction between science and information. As you well know, information is the primary topic in 21st century science. Even my own work on phase transitions is often phrased as how one part of a material communicates with another. Like matter, information flow can in some situations be guided by intelligence and in others can flow without the aid of a guiding thought.
Shortly thereafter I received an invitation through Leo to speak at the University of Chicago’s Computations in Science Seminars. The talk I gave was titled “Conservation of Information in Evolutionary Search” and it was given August 13, 2014 (click here and scroll down). A friend used his Mac to record the talk and the talk itself is available on YouTube (click here).
Leo also shared with me a correspondence between him and Jerry Coyne, where Coyne was taking him to task for giving me a platform at the University of Chicago. Leo stressed to Coyne that he thought I had some ideas and mathematical techniques to share with grad students that would be of value to them regardless of Coyne’s ideological concerns. As always, Leo was friendly and unflappable.
After my talk, Leo, a postdoc, and I had dinner at a Vietnamese restaurant on 55th Street. We had a good time and a photo of us at the restaurant is above. My last memory seeing Leo is him riding away from the restaurant on his bicycle.