Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Book Review: Worlds of Flow, published by remember on January 16, 2023 on LessWrong.

This work was written at Conjecture.

“Worlds of Flow,” a history of 19th and early 20th-century hydrodynamics by Oliver Darrigol, concludes:

What distinguishes the history of hydrodynamics from that of other physical theories is not so much the tremendous effect of challenges from phenomenal worlds, but rather it is the slowness with which these challenges were successfully met. Nearly two centuries elapsed between the first formulation of the fundamental equations of the theory and the deductions of laws of fluid resistance in the most important case of large Reynolds numbers.The reasons for this extraordinary delay are easily identified a posteriori. They are the infinite number of degrees of freedom and the nonlinear character of the fundamental equations, both of which present formidable obstacles to obtaining solutions in concrete cases. Moreover, instability often deprives the few known exact solutions of any physical relevance.

These difficulties have barred progress along purely mathematical lines. They have also made physical intuition a poor guide, and a source of numerous paradoxes. Hydrodynamicists therefore sought inspiration in concrete phenomena. Engagement with and challenges from the real worlds of flow were essential to the development of the above-mentioned strategies. The challenged theorists strove to find new solutions and to develop new methods of approximation. Experience indicated some general properties of the motion, such as the existence of boundary layers, the random character of turbulence, the sudden character of the Reynolds transition, or the formation of trailing vortices.Altogether, there were many ways in which practical concerns oriented theorists in the conceptual maze of fluid dynamics. The evolution from a paper theory to an engineering tool thus depended on transgressions of the limits between academic hydrodynamics and applied hydrodynamics.

This quote captures one of the most significant lessons in the book: the study of concrete phenomena was critical in overcoming many of the difficulties in hydrodynamics. Roughly two upstream problems required interacting with concrete phenomena to solve. The first is summarized nicely by the quote above: theorizing and abstract thinking alone was not enough to solve the problems posed by hydrodynamics. The second is a subtler point: early mathematical and theoretical tools weren’t adapted to understanding hydrodynamics. Much of the necessary mathematical machinery existed quite early in the 1800s, but people hadn’t built the physico-mathematical tools or intuitions to tell us what they physically meant. Contact with reality forced scientists to confront the inadequacies of their theories while guiding the adaption of physico-mathematical tools.

While the book is organized along rough problems that hydrodynamics faced (waves, viscosity, vortices, instability, etc.), this review will focus on broader scientific lessons. First on the two big themes I think are most important, then briefly on the other themes at the end.

Practice and theory in hydrodynamics

The first problem was that abstract thinking and theorizing proved unable to solve many of the problems of hydrodynamics. A great example of this comes from the discovery of Reynold’s number, which predicts whether flow is turbulent or laminar. Reynold’s number could have potentially been hypothesized as a consequence of Navier-Stokes, which describes viscous flow behavior. But Navier-Stokes is not analytically solvable, so Reynold’s number doesn’t come automatically. Making this more difficult is that turbulent flow, such as after submerged propellers, is generally invisible. Instead of reasoning his way there from first principles, Osborne Reynolds firs...