Notebooks

Ilya Prigogine

11 May 2010 13:03

Ilya Prigogine was a Belgian-American scientist, working mainly in physical chemistry and statistical mechanics. (He's of white Russian descent, hence his rather un-Belgian first name.) As part of the "Brussels School" of thermodynamics, he did important and valuable work on irreversible processes in the 1950s and 1960s. In the 1970s he began to work on what he called "dissipative structures" (q.v.). He also began to dispute the orthodox ideas of statistical mechanics, according to which the fundamental laws of physics are reversible, and the irreversible phenomena of everyday life and physical chemistry arise statistically. (The usual example is that it's not impossible for every molecule of glucose from a sugar-cube dissolved in water to find its way back to just the right place to re-assemble the sugar-cube, any more than it's impossible to get a million heads in a row tossing a fair coin, but both are damn unlikely. Statistical mechanics lets us quantify the damn unlikelihood.) Partly his rejection of statistical mechanics rests on technical grounds; partly on an unwillingness to see irreversibility originated in reversibility, as merely a statistical effect; partly it comes from his early and enduring devotion to the philosophy of Henri Bergson. This led to a good deal of controversy within physics, which pretty much consisted of the rest of the profession versus Prigogine.

After winning the Nobel Prize in chemistry for '76, Prigogine began writing popular books about his work. But he wasn't (he said) just trying to popularize some fairly esoteric material in statistical physics; this stuff was profound, he said. The old timeless soulless mechanistic drab and cold sciences of being were giving way, on their last legs; supplanting them were new sciences of becoming, with lots of room for "human time" (Bergson again), spiritual values, kind words for Heidegger's grousing about technology --- generally a much more clubbable and more poetic and more elevating sort of thing, a whole <<nouvelle alliance>> with nature. The study of dissipative structures and self-organization (the two are hardly distinguished in his writings; I cannot speak for his mind) is, we are told, a prime example of the sciences of becoming. This led to him becoming, all at once, the patron scientist of New Age twinks, of post-modern I-know-not-whats, of some anti-post-modern I-know-not-whats (like Frederick Turner), and of Alvin Toffler. (The English translation of La Nouvelle alliance, titled Order Out of Chaos, boasts a foreword by Toffler, associating it with his own lower and distorted form of historical materialism.)

Clearly, I am hostile to all this; but in the interests of fairness, before consigning From Being to Becoming and its kindred to the flames, I should enumerate Prigogine's intellectual benefactions. First, he really did do excellent work on non-equilibrium thermodynamics in the early days; his Thermodynamics of Irreversible Processes is a model of lucidity, and while inevitably dated (the last revision was in 1967), suffers for the most part from the omission of new results, not the commission of definite errors. Second, he tried to push forward a rigorous and well-grounded study of pattern formation and self-organization almost before anyone else. He failed, but the attempt was inspiring. Third, and related to the previous item, his example encouraged many people to take up the same problems, and do better than he had. Fourth he helped inspire some of the earliest and most mind-bending of Bruce Sterling's science fiction. (I am not being frivolous when I say this; frivolity would be suggesting that this was because they both lived in Austin.)

Reading accounts of Prigogine's work by non-physicists, a number of mis-understandings crop up much more often than chance alone would suggest. These all flatter him, but I do not believe he deliberately encourages any of them.

Perhaps the most significant is that his ideas about dissipative structure are actually of use in the experimental study and theoretical analysis of pattern formation. In fact, they are not. His supposed criteria for predicting the stability of far-from-equilibrium dissipative structures fails --- except for states very near equilibrium (Keizer, pp. 360--1). The Brusselator-type models of chemical oscillators and other excitable media are quite incompetent to handle many important and easily-observed experimental phenomena; and so on. As Pierre Hohenberg put it, "I don't know of a single phenomenon his theory has explained." Perhaps for this reason, in the just under five hundred pages of his Self-Organization in Nonequilibrium Systems, there are just four graphs of real-world data, and no comparison of any of his models with experimental results. Nor are his ideas about irreversiblity at all connected to self-organization, except for their both being topics in statistical physics. Self-organization is usually modeled in such a crude way that working in any sort of microscopic dynamics, reversible or otherwise, isn't worth the bother, but it's perfectly possible to have a reversible system, of just the kind Prigogine dislikes, which nonetheless self-organizes quite nicely. (See, if only because a little citation of friends never hurt anyone, Raissa D'Souza and Norman Margolus, "Reversible Aggregation in a Lattice Gas Model Using Coupled Diffusion Fields," cond-mat/9810258, for such a model.)

Next after this is the claim that Prigogine played a big part in the origins of chaos theory. His advances are easily summarized: Prigogine made no significant contributions to nonlinear dynamics. He employed results achieved by mathematicians, which is a very different thing.

Nor did Prigogine found non-equilibrium and irreversible thermodynamics; that honor doesn't even go the Brussels School of which he is a member. As far back as 1872, in the course of mating the kinetic theory of gases to thermodynamics, and so spawning statistical mechanics, Boltzmann produced an equation --- Boltzmann's Equation, naturally --- for the evolution of the distribution of the position and velocity of particles in a fluid, which not only handles non-equilibrium situations but is quite non-linear. His disciples Paul and Tatiana Ehrenfest went on to produce an influential "urn model," a kind of caricature of the approach to equilibrium. (The Ehrenfests extended their imitation of the master to killing themselves.)

This work, and its relatives, is all at the level of statistical mechanics; but even at the coarser and more abstract level of thermodynamics, the breakthrough to treating non-equilibrium, irreversible processes was made, not by Prigogine in the 1950s and 1960s (as one reads in far too many books), but by Lars Onsager in the 1920s, and published in 1931 in that obscure journal to which unacceptable ideas are condemned by the scientific establishment, The Physical Review. [One e-mail from an irony-impaired reader later: The Physical Review is the official organ of the American Physical Society; nowadays it's the premier journal in physics, and even in 1931 it was a coup.] This work was recognized as being absolutely brilliant, and when Onsager was decently aged he got the 1968 Nobel Prize in chemistry for initiating non-equilibrium thermodynamics. Nobody outside of physics and chemistry has ever heard of Onsager, even though this is one of at least four fundamental contributions he made to statistical physics (the others being a solution of the Ising model of magnetic phase transitions, the first model of the nematic order of liquid crystals, and the independent discovery of the statistical theory of turbulence first found by Kolmogorov). The reason is, of course, that Onsager did not claim any profound cultural, metaphysical significance for his work. (It has none.)

Finally, it must be said that much of what outsiders take to be novel in Prigogine's work on statistical mechanics and the origins of irreversiblity --- probabilistic treatments, abandoning individual trajectories of particles for statistical ensembles, writing off Laplace's Demon as a loss --- is in fact part of orthodox statistical mechanics, and, again, has been so ever since Boltzmann. (Recall that Laplace argued, in his Philosophical Essay on Probabilities, that if a sufficiently "vast and considerable intellect" knew the complete laws of microscopic physics, and the physical state of the universe at any one moment, it could calculate the state of the universe at all subsequent times; all prior ones, too, if the laws are reversible. But of course not even Laplace thought such a thing was anywhere near the bounds of practicality, of real possibility, since we could never know the exact state of anything, much less the whole universe. That's why Laplace wrote books on probability theory, after all.) The true disagreement between him and us (and it is between him, or at any rate himself and his students, and the rest of us), has to do with the origins of irreversiblity. Now, it's a simple matter of brute fact, demonstrable mathematically and visually, on a computer, that reversible small-scale dynamics can lead to large-scale effects which are irreversible on any reasonable time-scale. (Demonstrable, but I've seen a statistician who thought otherwise refuse to believe that a computer running such a demonstration really was programmed as claimed.) The question is then whether real dynamics, the ones actually operative in this universe, have the necessary properties. The equations of motion we've found to work very nicely in most applications --- whether Newtonian or quantum-mechanical --- are reversible, but led to irreversible phenomena in aggregate. An excellent critique of Prigogine's arguments, including an exposition of the traditional views, is Jean Bricmont's polemically titled "Science of Chaos or Chaos in Science?"

In addition to these technical doubts about his science, I find myself completely unpersuaded by his philosophy. (What follows is taken from one of my letters: if I can't steal from myself, who can I steal from?) The difference between a universe with deterministic, reversible physical laws and one with stochastic, irreversible laws interests scientists, philosophers working on the foundations of physics, maybe even epistemologists, but I don't see how it has any bearing at all on ethics or metaphysics --- certainly it's only his say-so that the latter has room for spirituality, cosmic purpose, etc. and the former doesn't. In fact it sounds like a scene out of Candide:

"The earthquake in Lisbon has destroyed the work of centuries in the city, plunged the country into chaos, and killed thousands, guilty and innocent alike. My entire family was wiped out when the cathedral collapsed upon them, and I will shortly expire from this infected wound caused by falling masonry. Where is the justice? What is the point?"

"But consider, friend, that the bacteria in your swollen and suppurating arm are prodigiously complicated creatures, assembling themselves from that continual and far-from-equilibrium flow of energy and material which you are; that the leveling of this great city provides a splendid opportunity for urban morphogenesis; that the death of the innocents was not the outcome of blind deterministic laws, an always-fated condition of being, but open and stochastic, a moment of pure becoming; that the earthquake itself was a fluctuation in an open system, a strongly non-linear phenomenon leading to a more stable geophysical state; in short all this devastation you see around you is manifestation of the reality of time, of lived experience, of our own integration into the universe."

"Ah! Thank you, Dr. Prigogine! All is for the best in the best of all possible vortices." With that, he coughed up blood and died.

Since writing that, I've read Horgan's description (in The End of Science) of an interview --- one almost says audience --- with Prigogine. I'm pleased to see that he agrees with my evaluation of Uncle Ilya; but would be more pleased if his over-all take on science wasn't so wrong-headed.

Note, 17 April 2003: I've just discovered a Turkish creationist (and anti-Masonic conspiracy theorist) has linked to this page, and mined my quotations here, to try to make it sound like self-organization is a "myth", and evolution is thermodynamically impossible. For the record, this is repugnant and I have nothing to do with it. His arguments about evolution and thermodynamics are century-old fallacies. And to go from the failure of Prigogine's theories to explain self-organization, to claiming that self-organization doesn't happen, is just (forgive me) bullshit. Self-organization can be demonstrated in the lab and in nature to anyone with eyes to see.

Note, 18 September 2006: If you sent me e-mail about this page in the last few days, please re-send; your letter was deleted in a system crash.

[Thanks to Pedro Fonseca for pointing out an HTML bug, to Olivier Pelletier for reminding me about Onsager's work on liquid crystals, and to "Dougie" for typo-catching.]

See also: Nonequilibrium Statistical Mechanics and Thermodynamics; Foundations of Statistical Mechanics; Self-Organization; Pattern Formation


Notebooks:     Hosted, but not endorsed, by the Center for the Study of Complex Systems