Banquet Comments by Prof. Hanoch Levi-Ari June 9, 2005
I have spent quite a few years at Stanford, first as a student, and later as a research associate. I would like to illustrate what the endowment brochure calls “TK-magic” by sharing with you some of my experiences “under the influence” of Tom Kailath.
As a student I used to come to his office whenever I felt I had a new idea or result. I would come without scheduling a meeting, and usually emerge 2-3 hours later, with my thinking in turmoil. You see, TK’s approach to research advising was to keep re-examining what may appear to be a complete result, look for new perspectives and hope to gain new insights in the process. After each meeting I would spend many hours reorganizing my thinking, and when I felt I had the problem licked, write a set of detailed research notes. Then the whole process would repeat again … In one case – the geometric derivation of the adaptive RLS lattice filter – I went through 4 or 5 sets of notes before reaching the simplest formulation. Tom still has copies of all these research notes.
As high school students most of us were conditioned to believe that once you present a proof of a mathematical result, it is immediately accepted as true and final. The idea that every proof must undergo a process of repeated examination and refinement is, however, finding its rightful place in the philosophy of science; read for instance the essay/book “Proofs and Refutations” by Imre Lakatos.
One of the important by-products of Tom’s emphasis on understanding new results from many different perspectives, is the construction of bridges between disciplines. As students, we used to joke that in TK’s eyes one unification or connection is more valuable than 2 or 3 new results. A typical example of the rich tapestry of interconnections that is revealed by applying TK’s research method is the Schur algorithm. Originally a result about bounded analytic functions, it has been connected over the years with: circuit theory/cascade synthesis, linear algebra/triangular factorization, transmission line models/inverse scattering, order recursive estimation/lattice filters, to name just a few. Some additional comments about Schur (but not the Schur algorithm) in my talk tomorrow.
My most endearing memories are of the special meetings/workshops that Tom has organized to inspire interaction between his students and associates. For example, after I formulated the main ideas of my thesis early in 1981, I found myself traveling to Holland together with Tom to explore connections with the earlier work of Dewilde & Dym. We spent 5 intensive weeks in Delft interacting with Harry, Patrick and Patrick’s research group. Our work would continue even after we left our campus offices – after dinner we took long walks, continuing our discussions into the night. The same experience repeated itself exactly 10 years later at the Chateau de Bonas in the South of France. This time it was Ali Sayed who was in the final stages of this Ph.D. research, and again we took long walks after dinner in the French countryside, building up a fruitful collaboration between the three of us.
Tom always took great pride in the successes of his students – this was also very evident in the Q & A session this afternoon. I would like to share with you one minor episode from my first year at Stanford which underscores this point. It so happened that that year I got an A+ in all my courses. (In fact, Tom Cover reminded me this morning that one of these was his Information Theory course.) At the time I did not realize how much this meant to Tom until my first A (instead of an A+) arrived. Tom’s reaction, and I believe only half-jokingly, was “what happened?”
Tom, you have every reason to be proud of your students – just look around you.
So in conclusion, Tom, thanks for the beautiful memories, Happy Birthday, and the best wishes to you, Sarah, and your wonderful family.