July 25, 2006

The Nobel Prize Winner as Neglected Genius

Cross-posted to Crooked Timber.

A staple of bad movies and trashy novels about scientists (i.e., the kind I read) is the neglected genius whose ideas are rejected with incomprehension by the scientific establishment during his life, because they are simply Too Far Ahead Of His Time to be grasped by lesser mortals, only for the scientific community to rediscover these insights decades later. This sort of thing can make for entertaining fiction (if dreary self-mythologization), but it simply doesn't happen all that often in real life, especially not when the hero is a part of the establishment, and indeed a much-honored one. It certainly doesn't show up, with documentary evidence, in the staid, reliable pages of Reviews of Modern Physics. Nonetheless:

Gregory L. Eyink and Katepalli R. Sreenivasan, "Onsager and the theory of hydrodynamic turbulence", Reviews of Modern Physics 78 (2006): 87--135; no free copy
Abstract: Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less well known is his ground-breaking work and lifelong interest in the subject of hydrodynamic turbulence. He wrote two papers on the subject in the 1940s, one of them just a short abstract. Unbeknownst to Onsager, one of his major results was derived a few years earlier by A. N. Kolmogorov, but Onsager's work contains many gems and shows characteristic originality and deep understanding. His only full-length article on the subject in 1949 introduced two novel ideas — negative-temperature equilibria for two-dimensional ideal fluids and an energy-dissipation anomaly for singular Euler solutions — that stimulated much later work. However, a study of Onsager's letters to his peers around that time, as well as his private papers of that period and the early 1970s, shows that he had much more to say about the problem than he published. Remarkably, his private notes of the 1940s contain the essential elements of at least four major results that appeared decades later in the literature: (1) a mean-field Poisson-Boltzmann equation and other thermodynamic relations for point vortices; (2) a relation similar to Kolmogorov's 4/5 law connecting singularities and dissipation; (3) the modern physical picture of spatial intermittency of velocity increments, explaining anomalous scaling of the spectrum; and (4) a spectral turbulence closure quite similar to the modern eddy-damped quasinormal Markovian equations. This paper is a summary of Onsager's published and unpublished contributions to hydrodynamic turbulence and an account of their place in the field as the subject has evolved through the years. A discussion is also given of the historical context of the work, especially of Onsager's interactions with his contemporaries who were acknowledged experts in the subject at the time. Finally, a brief speculation is offered as to why Onsager may have chosen not to publish several of his significant results. [My links.]

Nobody outside of statistical physics (and maybe physical chemistry) has heard of Onsager, but he was indeed a great physicist, albeit in a very technical, non-flashy way. By the time he did this work on turbulence, he was already well-known in statistical mechanics for the analytical solution of the Ising model, his theory of phase transitions in liquid crystals, and, perhaps most importantly, a pair of classic papers from 1931 which basically founded modern irreversible thermodynamics, for which he would eventually win the Nobel Prize. (Eyink and Sreenivasan give a fuller discussion of his accomplishments, including the Onsager-Machlup theory of non-equilibrium processes, on which Eyink himself has done important work.) We're definitely not talking about some marginal figure cut off from the scientific community.

Nonetheless, his attempts to get people to pay attention to these ideas on turbulence were singularly unsuccessful. The reaction of Theodore von Kármán, a deservedly great name in fluid mechanics, was to describe it (in a letter to his student C. C. Lin) as "somewhat 'screwy' "; Onsager also corresponded with Lin, who replied in the classic manner of someone wanting to put an end to a conversation (quoted on p. 117): "I am sorry to say that I have not made much progress, except that I desire still more to see something done in this line to bring your ideas down to my level of understanding." As for the statistical physicists, Eyink and Sreenivasan describe their reaction as one of "polite incomprehension" (except on the part of von Neumann — in an unpublished report). The fact that one of Onsager's letters describing his ideas (reproduced as Appendix A in this paper) is headed "The little vortices who wanted to play", and begins "Once upon a time there were n vortices of strengths K1, ... , Kn in a two-dimensional frictionless incompressible fluid" probably didn't help, either. Most of all, a combination of discouragement over this reception, a tendency to be a slow and perfectionist author, and having scads of major research projects going simultaneously kept Onsager from even trying to publish any of this material.

The moral, I hope, is clear: statistical physicists who wander into other areas of science, and find their ideas dismissed by the best experts on those subjects, should nonetheless publish in Physical Review, in a "Fools! I'll show them all!" spirit, provided they are Lars Onsager.

(It's interesting that this paper was written by two physicists active in this area, rather than by a historian of science. It seems doubtful to me that a historian, reading the relevant materials in the Onsager archives, would have realized that there was a story here, unless they were familiar with modern work on turbulence at a deeply technical level — unless they had "contributory" as well as "interactional" expertise. And if anyone had gone over those archives around 1990, before these ideas were re-discovered, what would they have made of it?)

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Posted at July 25, 2006 15:20 | permanent link

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