I’m not sure what to do with this article about the Tracy-Widom distribution, but it seems like it might contribute to Boyd’s philosophy of conflict on several levels. I’ll offer it in the spirit that Boyd spent a lot of time mining physics and biology for parts to use in his snowmobiles.
The article is “At the Far Ends of a New Universal Law,” by Natalie Wolchover in the October 15th edition of Quanta Magazine.
Usually I’m skeptical about applying physical or statistical concepts to the problems of strategy because these laws assume that the particles don’t behave like participants in a conflict, i.e., that they don’t lie, engage in deception, try to panic the scientists, and so on. As Boyd put it, on chart 132 of Patterns, instead of choosing the alternative that you think will be the most effective, select the one that your opponent will least expect, ideally something your opponent thinks is impossible. Do this just for the panic effect if nothing else. Typically, particles obeying the laws of physics don’t do this.
This article, though, starts off with conflict:
[Biologist Robert May] wanted to figure out whether a complex ecosystem can ever be stable or whether interactions between species inevitably lead some to wipe out others.
Reminiscent of Boyd’s relying on the the theory of evolution as one of the foundations of his work.
The there’s the notion of orders of phase transitions:
Similarly, the physicists realized, the energy curves of certain strongly correlated systems have a kink at √2N. The associated peak for these systems is the Tracy-Widom distribution, which appears in the third derivative of the energy curve — that is, the rate of change of the rate of change of the energy’s rate of change. This makes the Tracy-Widom distribution a “third-order” phase transition.
Recall that Boyd (in “New Conception”) began by considering the state of an aircraft — its altitude, airspeed, and direction. Maneuverability was defined as the rate of change of the state, things like turn rate and rate of climb. Agility was the ability to change maneuver state, go from a 9 deg/sec turn in one direction to 9 deg/sec in another, for example. The F-16 is an example of a highly agile aircraft.
The third derivative of state is sometimes called the “jerk,”and this fits Boyd nicely because he often described his philosophy as “jerky and disorienting.” But there’s a deeper way to look at this.
Near the end of his life, Boyd floated the idea of Behendigkeit, which usually translates as “agility.” He regarded it as “mental agility,” however, and based his concept on the idea that you can get trapped in a pattern of ideas and ride it to the bitter end. Behendigkeit was the ability to change patterns, hop on a new snowmobile as it were. If you’re in a conflict, for example, and you see that agility (the second derivative) isn’t working, then Behendigkeit is the ability to come up with something else on the fly. In other words, we’re talking not so much about the aircraft’s ability to change states but our own ability to change how we think about things.
This can be fiendishly difficult to pull off, especially if you were the person who sold your organization the original snowmobile. So Behendigkeit really is a deep concept and will repay a lot of pondering and experimenting. You might find something useful in this article.