Good evening ladies and gentlemen. By now it has become a tradition for the recipient of the Field Award to share with the community his past experiences, views on where the subject is going, and future prospects. Over the next 7 or 8 minutes, I too would like to continue this tradition by making a few remarks that are partly autobiographical and partly philosophical.
About forty years ago Andy Warhol said that “In future everybody will be famous for fifteen minutes.” This is my fifteen minutes of fame, but what with inflation and all that, my fifteen minutes have shrunk to eight minutes.
My first comment is: It is essential to have role models. While I have been influenced by several distinguished researchers during my adult life, undoubtedly my first role model was my father, who was a professor of mathematics. I was about eight years old when I first began to notice that our house in the South Indian city of Tirupati was always full of my father’s college students, who were constantly discussing what my father called “the subject.” I asked him what they were doing and he said “Oh, we are trying to find ‘results.’” I asked him what a “result” was and he said “Well, it is something new.” Within a few days I got my own first “result”, namely: If you square a number, and multiply the two numbers on either side, the difference is always one. Or in modern algebraic notation, (n+1)(n-1) = n^2-1. When I showed this to my father, he said “Well, a result is not something that you did not know before, it is something nobody knew before.” My first reaction was to be amazed that any human being could possibly find out something that nobody knew before, but my next reaction was that if he could do it, then I was also going to do the same thing – I was going to become a researcher and find lots of “results.” It was exactly the kind of thing a silly little kid would think, but it definitely did set me on the path to being a researcher.
At a time when many young people seem to be so confused about what they want to do, it was really a blessing for me to know so early in life exactly what I wanted to be, even if I had no idea how to go about it. My father was a most remarkable researcher. He published his first paper at the age of 21, and when he passed away at the age of 84, he had five or six papers under review. Mathematics is supposed to be a young person’s game, and I can’t think of anyone else who published steadily for more than sixty years. I would like to take this opportunity to acknowledge my debt to my father.
My second comment is: Don’t rule out the role of chance in life. Modern man suffers from the hubris that he can control nature, and therefore life is deterministic. But random events and arbitrary choices have unpredictable consequences. In my case, when I was finishing up my Bachelor’s degree in electrical engineering at the University of Wisconsin, I was pretty clear in my mind what I was going to do for my Master’s and Ph.D. I was simply fascinated by passive network synthesis, the relationship between positive real functions and energy dissipation, and such topics. So I had decided to study circuit theory for my graduate degrees. Now by the time I reached the final semester of my undergraduate degree at the University of Wisconsin, to graduate all I had to do was to take six elective courses in anything at all. So I chose six electrical engineering courses, which, as you can imagine, all met on Monday, Wednesday and Friday. So the result was that I had classes solidly from 9:30 until 3:30 on Monday, Wednesday and Friday, and no time for lunch. After doing this for one week, I realized that I wasn’t going to survive the semester with this kind of schedule. So I dropped my lunchtime course and looked for a course that met on Tuesday and Thursday. The only course I could find was an introductory control systems course. Believe me, that was the only reason I signed up for that course, not any interest in control theory. But somehow this chance deviation into the controls course had quite unforeseen consequences, as you can all see.
My third point is: If you aspire to success, you must work on entire areas, not just individual research problems. I got this advice from the late George Zames, back in 1975, and it really changed the way I do research. Until then I was like a gun-slinger, working on whatever problems caught my fancy, with no particular theme or coherence to my work. But after I got this advice from George, I consciously tried to work on entire areas, and it has definitely paid off in terms of the impact I have had on the field.
My fourth point is: Don’t be afraid to change research areas often. Changing areas requires a lot of courage, because you get pushed out of your comfort zone. But it has its own rewards. A related point is: When you do move into a new area, work out everything for yourself from scratch, and don’t always believe everything you read. This is the reason why I like to write a lot of books. It’s only when you start writing a book that you realize just how poorly you understand the subject. Writing a book forces you to develop a holistic view of the subject. The benefit is that if you do even a halfway decent job of explaining a particular subject, then pretty soon everyone begins to look at things your way.
In this connection I would like to acknowledge my debt to Charlie Desoer. When he invited me to join him and finish up our book on feedback systems, I was just 25 years old. It was his generosity that made him reach out to such a kid on such an important project. Working on that book made me realize the importance of making it easy for the reader to dip in and out of a book. Even thirty years ago, most people did not have the time to read a book in its entirety. They just want to look up something very specific, and the author has to facilitate that. I have consciously tried to make my books highly “modular” and I think this has caused them to be pretty popular.
Now here is the last and final point: The family comes first and foremost. Shakunthala and I have been married now for thirty six years, and without doubt I could not have achieved what little I did without her support over the years. Everyone who knows her is extremely fond of her, and indeed some of our relatives who come to Hyderabad stay with us, even if they have their own houses in the city. That’s how affectionate and universally well-loved she is. While our daughter Aparna was growing up, I always tried to be there when she needed me. In fact I would wait until she went off to sleep at 9 PM or so, and then start my “second shift” as I used to call it. Now she’s not “my little baby” anymore, and is going to get her own Ph.D. very shortly.
Let me conclude with a little attempt at crystal ball-gazing. What is the future of control theory and its applications? I believe the strength of control theory derives from two aspects: First, as engineers we are problem-driven, and not technique-driven. Second, we know bits and pieces of lots of branches of mathematics, which is the queen of all science to quote Gauss. Because of these two factors, we are able to look at each problem on its own merits, instead of forcing it to fit into a preconceived formalism. To illustrate just how widely applicable control theory really is, note that controls people are branching out into all sorts of areas like communications, mathematical finance, and even biology, but we don’t see people from those areas moving into control! In short, control theory is a “great place to be from” and I don’t see that changing in future. Fads may come and fads may go, but control theory will go on forever, because of its ability to adapt itself constantly.
When I was doing my Ph.D., the whole new vista of mathematical control theory was just opening up. Now, with all the doom and gloom of the financial meltdown all around us, paradoxically I think the current generation of young control theorists has at least two exciting opportunities, namely in mathematical finance, and in “in silico” drug discovery. I would like to describe, extremely briefly, these two opportunities.
I really think that we control theorists can play an important role in mathematical finance; indeed, we have already been doing it for the past decade and a half. Again to over-simplify grossly, I view option pricing as computing an expected value, and hedging as stochastic control. But the spectacular failure of all the pricing and hedging models, which is at the core of the financial meltdown, shows that it is necessary to incorporate human behavior into the models. The volatility of an asset, which is a key parameter in mathematical finance, is not a natural constant like the Young’s modulus of steel; rather, the volatility is what everyone thinks it is at a given point in time! Suppose everyone in the market place uses the same “incorrect” formula to compute the price of an asset-based derivative. Then will the formula gradually become “correct” over time, as a kind of self-fulfilling prophecy? What we really need is a new approach that may be called “flocking theory meets Black-Scholes”!
The current situation in drug discovery reminds me of VLSI synthesis about 30 years ago. Back then, “yields” in chip fabrication were about 3% to 5%, and every single fabrication facility had its own in-house design team. Over the past three decades, we have moved towards “virtual foundries” that can design a VLSI system purely using CAD tools, and design is now decoupled from fabrication. Interestingly, the “yield” on drug molecules is now between 1.5% to 2%, or about the same as for VLSI thirty years ago. But I see the emergence of “virtual” drug discovery companies, and indeed one of my research groups is working on precisely this area. Of course, the human body is a lot more complex than an inanimate silicon wafer, but I really do believe that by bringing the rigor of the “systems approach” to problems of drug discovery, we can make substantial contributions.
In conclusion, I feel privileged to join the ranks of the previous winners, many of whom are all-time greats of control theory. I wish everyone in the room the same success I have had if not very much more. Thank you and good night!
