## Operationalization and Intuition in the Development of the Theory of Flight

Abstract:

This talk discusses operationalization in the development of fluid dynamics and the theory of flight in the early twentieth century, particularly by Ludwig Prandtl. Here, I mean operationalization in the sense of Chang (2004), that is, taking an abstract system and trying to connect it up with the real world in such a way that we can acquire knowledge about the real world. In particular, I will be attempting to answer the following questions: Exactly how is an abstract mathematical representation being used to extract knowledge about the world? What is the role of intuition, or visualization, in the use of the abstract representation?
The development of the theory of flight is a case where a well-developed but highly idealized mathematical theory existed, but it took a long time for scientists to understand how to apply this theory to the real world. The modern theory of flight was developed by Prandtl at the Unversity of Gottingen in the 1910’s, more than a decade after the Wright brothers’ successful flight. The Kutta-Joukowski theory of the wing, developed in the early twentieth century, showed how to relate the lift of an airfoil to the speed of the airfoil, the density of the air, and the circulation of the air around the airfoil. It is the circulation that generates lift. The Kutta-Joukowski theory, however, gives the lift for an abstract, two-dimensional wing, or equivalently, a three-dimensional wing of infinite span. The problem still remained of somehow applying the abstract representation to an actual wing, with a finite span, in order to extract information about the actual wing. Prandtl was able to apply the theory in an ingenious way, by viewing the finite wing as, in essence, a superposition of an infinite number of Kutta-Joukowski wings. I will examine the way in which the abstract representation was used, and what the successful use of the abstract representation implies with regard to what the world must be like.
A further issue that is of additional interest for philosophers is the role of intuition in finding out ways to connect up an abstract representation with the real world. In 1948, Heisenberg attributed Prandtl’s success to his ability to “see” the solutions of equations without calculation, but Prandtl denied having this ability, saying instead that he strives to “form the most penetrating intuition [Anschauung] I can of the things that make the basis of the problem, and I try to understand the processes.” What, exactly, does one gain from having this penetrating intuition, and how did it help in the development of the theory of flight? An attempt to answer these questions might also give us some perspective in understanding debates about “anschaulichkeit” in quantum mechanics, especially considering that the theory of flight was developed contemporaneously with, and even involved some of the same people, as those involved in the development of quantum mechanics.