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?)
{ 26 comments }
vkri 07.25.06 at 3:50 pm
I think part of the problem was that Onsager was notoriously hard to understand, at least according to local reputation. Even his very well known papers are not the easiest to read, partially due to reasons of exposition. And I think it is always a little difficult for an outsider (even someone as famous and respected as Onsager) to convince fellow bigshots in other fields about their ideas (for often very human reasons). He should have just published his work instead.
Sebastian Holsclaw 07.25.06 at 4:05 pm
I’ve vaguely wondered if scientists in one field often labor for years on a problem that has been solved in another field because the fields were just distinct enough to make cross-pollenation of ideas unlikely.
Sebastian Holsclaw 07.25.06 at 4:07 pm
In a vaguely related note, I suspect in the future we will discover useful medicinal therapies that were first seen in the last 30 years but which were excluded from further testing by an overcautious toxicity standard.
John Emerson 07.25.06 at 4:33 pm
Well, when Ilya Prigogine finally did succeed in bringing turbulence into the awareness of the general educated public, he was on the one hand accused of New Age thinking, and on the other hand was told that Onsager had gotten there first.
As far as that goes, some related concepts (the three-body problem and the impossibility of its solution) were worked out by Poincare around 1900, and Poincare’s fame did not keep his thinking from sitting on the shelf for three-quarters of a century.
And then, when Mandelbrot started working with the mathematics behind these weird kinds of things, he was told by his elders that these particular mathematic objects were perverted and disgusting, or something like that. (Don’t have an exact quote here, but the actual language was similiarly disapproving).
Heisenberg was interested in these questions, though he thought that they were impossible to answer, but while he remains famous, he was a Nazi.
It seems to me that up until very recently the realities behind fractals, turbulence, non-equilibrium thermodynamics, and non-linear systems violated standard average scientific common sense, and for that reason were resisted and ignored, for common-sense rather than for scientific reasons. (It’s true that relativity and quantum mechanics also violate common sense, so I guess I have to add that turbulence, etc., violate common sense in a way which is more discouraging than exciting for working scientists.)
I’m an outsider in this game, but I read Prigogine’s “Order Out of Chaos” with great interest, and think that some but not all of its revisions of scientific common sense are valid and powerful.
Robert P. 07.25.06 at 5:14 pm
John, Prigogine is the dual to Onsager – while he made some important contributions to nonequilibrium thermodynamics early in his career, his popular reputation considerably exceeds his reputation within the field. His purported general stability condition for dissipative structures far from equilibrium turned out to be simply wrong. (I believe that he eventually conceded this.)
Poincare’s results in nonlinear dynamics didn’t “sit on the shelf” – they were taken up and continued by several generations of mathematicians and celestial mechanicians – Siegel, Kolmogorov, Arnold, Moser, Sinai … What is true is that most “mainstream” theoretical physicist ignored it, until Joe Ford began translating KAM into the language that is spoken at Physical Review in the early 1960’s.
John Emerson 07.25.06 at 5:26 pm
I’m really talking about scientific common sense, or about the general public’s understanding of reality based on the available science as they understand it. On the face of it, Poincare’s work had enormous though imperfectly understood consequences for scientific common sense, but as far as I understand Poincare’s work really didn’t go anywhere.
I really am not defending Prigogine’s specific technical contributions to science, but I learned a lot of things from his book which may have been decades old, but which I hadn’t seen before. And as far as I can tell, based on your report and Cosmas’, it wasn’t just me who hadn’t gotten the word, but a lot of high-powered scientists.
Prigogine seems to recieve surplus criticism beyond whatever amount he actually deserves, probably because people like me read him.
Rich Puchalsky 07.25.06 at 6:42 pm
Parenthetically, I was interested in the linked article on levels of expertise, until I got to footnote 3 of their “periodic table”:
“The success of lawyers suing firms such as MacDonald’s for selling over-hot coffee, and the consequent growth of warnings and safeguards surrounding every consumer good, is patronising — treating the public as incapable of learning the rules of ordinary living through the normal processes of socialisation.”
That much rightwingery instantly makes their science suspect, I think. The MacDonald’s case involved third-degree burns, and is the subject of endless corporate propaganda.
Jim Harrison 07.25.06 at 7:30 pm
Many professional mathematicians with whom I have spoken are not very impressed with Mandelbrot. They think of as something of a fraud, the author of books with lots of pictures instead of papers with lots of theorems. They point out that much of the mathematics involved in fractals goes back to Poincare and Julia. I partly agree; but if Mandelbrot’s fame owes more to computer graphics than formal math, that may just mean that the promotion of intellectual fads is also a worthwhile activity under certain circumstances.
John Emerson 07.25.06 at 7:52 pm
It’s starting to seem that a lot of stuff is reaching the “We knew it all along” stage. When I read about Poincare decades ago, what I could understand of his stuff fascinated me, but I couldn’t find anyone talking about the broader significance of his ideas.
Then Prigogine and Mandelbrot came along and did start talking about that, and now Poincare is being used against them. I don’t have documentation handy but I’m absolutely confident that Mandelbrot and Prigogine gave full credit to Poincare. Not sure about Onsager.
Mathematicians thought that calculus was an engineer’s kludge for over a century.
I’m just an outsider here, trying to figure out what the lessons of physics are for non-physicists.
otto 07.25.06 at 7:55 pm
What Onsager needed was a blog, of course.
theturbulenthydrodynamicist.typepad.com ?
If he’d thrown in some thoughts on Jennings and Middle East politics, there’s no way that his contributions would have been overlooked.
Tom T. 07.25.06 at 8:07 pm
We’re just lucky that Onsager didn’t build an orbiting laser death ray to get attention.
Walt 07.25.06 at 10:55 pm
I think Prigogne and Mandelbrot are distinct cases. It’s clear to an outsider what Mandelbrot did: he applied already-existing mathematics to real-world problems. Professional pure mathematicians might downplay the significance of this, but that’s what makes them pure mathematicians. If someone used the Thue-Siegel-Roth Theorem tomorrow to cure cancer, pure mathematicians would probably downplay that too. (I don’t know what applied mathematicians think of Mandelbrot; I’d be curious to hear what.) But it’s clear from reading Mandelbrot that he didn’t invent Cantor sets, or Sierpinski gaskets, or Hausdorff dimension, or Julia sets, but that he did suggest applying these to the coastline of Britain.
Prigogine is much murkier, since its harder for an outsider to separate out his ideas from others. He also proposed a specific narrow research program that has not been particularly successful. There is also reputedly a cult of personality around him that as far as I know does not exist for Mandelbrot.
I think it’s true that the significance of Poincare’s work was not fully appreciated by physicists at the time, and that the main conclusion they drew was just that the n-body problem was not analytically solvable. It was certainly understood by mathematicians in the relevant fields, though, and there was much subsequent work. From their point of view, I can see how irritating it would be for people to tell them they didn’t know something they knew for years. At the same time, mathematicians are in general terrible popularizers, so it’s not surprising that they had never managed to get the message out.
Mathematicians never thought calculus itself was an engineer’s kludge. The modern era of mathematics practically begins with calculus, and the use of intuitive but non-rigorous arguments didn’t really end until the turn of the century, at which point calculus was already on a firm footing. There were certain further developments, such as the Heaviside calculus and Green’s functions that mathematicians thought were kludges, but that’s a lot more specialized.
Chris 07.25.06 at 11:11 pm
Actually, that’s an odd thing about mad scientists – they never seem to have scientific demands, like “Unless every single paper in nature for the next ten years cites at least two of my papers, I’ll vaporize New York!” or “I want the physics Nobel every year for the next twenty!” or, I suppose, something to do with parking.
cosma 07.25.06 at 11:27 pm
Let me echo Walt’s remark about mathematicians’ opinions of calculus. It’s true that there was a long interval between Newton and Leibniz’s invention of calculus, and the work of Cauchy, Weierstrass &co. which produced “analysis”, during which the foundations of calculus did not meet modern standards of rigor. But, prior to their work, next to no mathematics met those standards. Vanishingly few mathematicians back then thought calculus was just a hack. The people who had problems were the philosophers: Bishop Berkeley thought it was a fallacious hack, Hegel and Marx had some exceedingly strange ideas (expounded — I am not making this up — in a little book called Marx Demystifies Calculus, apparently still in print), etc.
Maynard Handley 07.25.06 at 11:43 pm
I must admit to being somewhat unsympathetic to Onsager in this case. The fact of the matter is that the other scientists in the world don’t have years of free time to slowly work their way through incomprehensible papers in the hope that maybe, just maybe, they are worthwhile. You, the author of the paper, have a responsibility to make your ideas comprehensible. If the first method you choose to explain them fails, then you listen to what people say about where they lost all track of understanding and write a new paper — with NEW explanations, not the same explanations that failed last time only renumbered.
Science has a policy, and I think most scientists would agree that it is a fine policy, that if you come up with some fantastic idea, but refuse to publish it, then you’re not going to get much sympathy, in your lifetime or afterwards, when this effect/theorem/discovery is named after someone else who also wins the Nobel Prize. Science does *not* have a similar *stated* policy when it comes to comprehensibility. There is, to some extent, an informal such policy, in that if no-one can understand you they’ll just ignore you, but it’s not something that is drilled into young scientists; that it is YOUR responsibility to make your ideas clear to others, not their responsibility to try to figure out what you are talking about. As science grows ever larger and ever more complex, I think it is time for all scientists to be much more explicit and much more ruthless on this point.
vkri 07.26.06 at 1:46 am
I don’t completely agree that Poincare’s work on chaos was neglected in the Physics community. Historically, the many failures of classical mechanics took centrestage in physics for the early decades of the 20th century, so work on classical mechanical problems at that time seems correspondingly neglected. From what I gather, his ideas were of tremendous interest to the Russian school, and this culminated in the KAM theorem. His work also had an impact on Edward Lorenz in Meteorology.
Poincare’s case is quite different from Onsager. Poincare was known to be a very clear and good expositor of his work. On the other hand, this was not true of Onsager. Also, I dont think Onsager ever worried about the lack of recognition that his ideas received. It is also true that for most people, poorly written stuff gets ignored more often than not. I think though, that for people like Onsager, a lot more benefit of the doubt would be given even today, (in my opinion deservedly so) since a person with the depth of insight he had, is hard to find.
John Emerson 07.26.06 at 6:34 am
16: Lorenz’s work was 60 years later, though. The 60-year lag is what I meant. Prigogine gave a prominent place to and the KAM theorem and the Russian school, but apparently they were pretty isolated. Prigogine’s argument was that science was very resistant and slow to recognize the wider consequences of thermodynamics, the three-body problem, etc.
Very little of Prigogine’s book was about his own original work. It was mostly a history of thermodynamics and related questions.
I do remember reading that calculus was resisted at Oxford and Cambridge as late as 1800, but I can’t document that.
Peter Erwin 07.26.06 at 7:42 am
john emerson said: I do remember reading that calculus was resisted at Oxford and Cambridge as late as 1800, but I can’t document that.
Might you be thinking of 18th Century British opposition to Continental calculus, based on the fact that the latter gave at least some credit to Leibniz and used his notation instead of Newton’s?
John Emerson 07.26.06 at 9:05 am
I remember it as calculus per se.
This is not a very good point, and I should probably drop it unless someone comes along to support me.
tzs 07.26.06 at 11:39 am
There’s also WHERE stuff gets published and WHAT language it gets published in. A heck of a lot of stuff stayed on the Soviet side of the border for a lot longer than one would have wished because it wasn’t translated.
Wasn’t there a mathematician who took delight in publishing his discoveries in the most obscure mathematical journals he could find?
And then there’s how stuff gets written. Witten’s articles are a delight to read; undoubtedly one reason why his ideas in superstring theory spread so quickly at the beginning of the field. Then there are other scientists (I’m sure we all have our own examples to fume about) who link obscure and dense thickets of turgid prose with indecipherable mathematics.
bob 07.27.06 at 10:55 am
The article on Onsager, by H. C. Longuet-Higgins and Michael Fisher, Biographical Memoirs of the National Academy of Sciences vol. 60 (1991), pp. 183-232, is well worth reading. By the way, for Onsager’s opinion of Prigogine, see pp. 219-220:
About a certain Belgian theoretical chemist: “He’s a bright fellow. But there are a lot of folks, some quite talented, who arm themselves with methods and then go hunting for vulnerable problems; but to accept a problem on its own terms and then forge your own weapon—now that’s real class!” (Experts, beware!)
S. A. Jordan 07.27.06 at 3:39 pm
Cosma writes:
Not “all that often”, perhaps, but too often.
In astronomy, the proponents of the heliocentric model come to mind — not only Copernicus and Galileo among others during the Renaissance, but also Aristarchus of Samos about two millennia earlier.
In the biological sciences, take for examples the neglected genetic studies of Gregor Mendel, and the ridiculed contagion/hygiene ideas of the heartbroken Ignaz Semmelweis, both in the 19th century.
Granted, these were too early to be “Nobel Prize Winners”.
S. A. Jordan 07.28.06 at 5:55 am
Also see the Wiki on “scientific consensus”:
Comment on the last item: helicobacter pylori was actually observed (though not so named) a century earlier.
S. A. Jordan 07.28.06 at 6:06 am
My apologies for the poor formatting of the list items above (each beginning with “the theory of…”). I’d kept the source’s HTML tags (UL and LI), which displayed properly in the preview box but were stripped out by the posting software. I should have text-formatted the items, instead.
John Emerson 07.28.06 at 9:57 am
J. Harlan Bretz’s 1920s theory that the “channeled scablands” of E Washington were created by water action is another example of a rejected true theory.
John Emerson 07.28.06 at 10:04 am
J. Harlan Bretz’s 1920s theory that the “channeled scablands” of E Washington were created by water action is another example of a rejected true theory.
This link is sympathetic to Bretz’s skeptics:
http://www.geo.ucalgary.ca/~macrae/t_origins/bretz_re.html
Comments on this entry are closed.