Last week, looking for some information about the mathematician Richard Bellman who, among other feats and achievements, developed dynamic programming, I came across a film called the Bellman Equation which you can watch on the internet. It was written produced and narrated by Bellman’s grandson, Gabriel Bellman and features among others, Gabriel’s father (Bellman’s son), Gabriel’s aunt (Bellman’s daughter), Bellman’s first and second wives, and numerous friends and colleagues. You learn how brilliant, driven, arrogant, charming, and difficult Bellman was, and how he cast a shadow over the lives of his children and grandchildren. Aside from the stories about his life, his work on the atomic bomb in World War II, his meeting with Einstein when he was a young assistant professor at Princeton, his run-in with the Julius and Ethel Rosenberg at Los Alamos, and, as a result, with Joe McCarthy. And on top of all the family history, family dynamics, and psychological theorizing, you also get an interesting little account of the intuitive logic underlying the theory of dynamic programming. You can watch it for free with commercials on snagfilms.
But I especially wanted to draw attention to the brief appearance in the video of Bellman’s colleague at Rand Corporation in the 1950s, Stuart Dreyfus, with whom Bellman collaborated in developing the theory of dynamic programming, and with whom Bellman co-wrote Applied Dynamic Programming. At 14:17 into the film, one hears the voice of Stuart Dreyfus saying just before he comes into view on the screen:
The world is full of problems where what is required of the person making eh decision is not to just face a static situation and make one single decision, but to make a sequence of decisions as the situation evolves. If you stop to think about it, almost everything in the world falls in that category. So that is the kind of situation hat dynamic programming addressed. The principle on which it is based is such an intuitively obvious principle that it drives some mathematicians crazy, because it’s really kind of impossible to prove that it’s an intuitive principle, and pure mathematicians don’t like intuition.
Then a few moments later, Dreyfus continues:
So this principle of optimality is: why would you ever make a decision now which puts you into a position one step from now where you couldn’t do as well as [if you were in] some other position? Obviously, you would never do that if you knew the value of these other positions.
And a few moments after that:
The place that [dynamic programming] is used the most upsets me greatly — and I don’t know how Dick would feel — but that’s in the so-called “quants” doing so-called “financial engineering” that designed derivatives that brought down the financial system. That’s all dynamic programming mathematics basically. I have a feeling Dick would have thought that’s immoral. The financial world doesn’t produce any useful thing. It’s just like poker; it’s just a game. You’re taking money away from other people and getting yourself things. And to encourage our graduate students to learn how to apply dynamic programming in that area, I think is a sin.
Allowing for some hyperbole on Dreyfus’s part, I think he is making an important point, a point I’ve made before in several posts about finance. A great deal of the income earned by the financial industry does not represent real output; it represents trading based on gaining information advantages over trading partners. So the more money the financial industry makes from financial engineering, the more money someone else is losing to the financial industry, because every trade has two sides.
Not all trading has this characteristic. A lot of trading involves exchanges that are mutually beneficial, and middlemen that facilitate such trading are contributing to the welfare of society by improving the allocation of goods, services and resources. But trading that takes place in order to exploit an information advantage over a counter-party, and devoting resources to the creation of the information advantages that makes such trading profitable is socially wasteful. That is the intuitive principle insightfully grasped and articulated by Dreyfus.
As I have also pointed out in previous posts (e.g., here, here and here) the principle, intuitively grasped on some level, but not properly articulated or applied by people like Thorstein Veblen, was first correctly explicated by Jack Hirshleifer, who like Bellman and Dreyfus, worked for the Rand Corporation in the 1950s and 1960s, in his classic article “The Private and Social Value of Information and the Reward to Inventive Activity.”