Ironick

Out of the Ruins

We do not so much "stand on the shoulders of giants" as we build out of the ruins of fallen giants.

Entropic Variations of Albert Einstein's Quote Regarding Entropy

See my post to the Albert Einstein Discussion Page in Wikiquote. Here's what I think the quote should be:

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore, the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown.

I blogged about this quote a while back. It just occurred to me that irony itself is yet another manifestation of entropy: a gap between intended meaning (macrostate) and possible meanings (microstates).

Neurath's Boat and Theseus' Ship are Dissipative Structures.

[This entry was edited on August 5, 2004 to remove the text of M.R.M. Parrott's email to me. See my comments for details.]

A while back, I made the connection between Neurath's Boat and the Ship of Theseus. I thought the lack of connection elsewhere on the Web was interesting. Only a site by M.R.M. Parrott mentioned both terms, but there is no mention of a connection.

I guess I forgot to post this discovery back in January (surprise). I'm posting it now because I've made another interesting connection, IMO. Both metaphors are examples of dissipative structures (aka dissipative systems): A dissipative [structure] is characterized by the appearance of stability, but is continually changing. A simple example is a whirlpool: a similar shape is maintained, while water is continually moving through it. More complex examples include lasers, Bnard cells, and even life itself. The term dissipative structures was coined by Ilya Prigogine.

Thus this seemingly paradoxical boat (or ship) is simply a dissipative structure whose compositional materials are continually flowing through it (albeit at a much slower pace than a whirlpool). Of course this means that it is both the crew and the boat that are the dissipative structure, unless the boat is imagined to be autonomic, i.e., self repairing.

As you philosophers are well aware, this coincidence of opposites (a term coined by Nicholas of Cusa -- see NICHOLAS OF CUSA (1401-1464): FIRST MODERN PHILOSOPHER?) for an excellent overview, "One can identify at least sixteen Cusan themes that have a peculiarly Modern ring to them and on the basis of which Nicholas has been deemed to occupy a special relationship to Modernity.") "stability and change" permeates all our concepts. For an excellent essay on the roots of this fundamental unity of opposing aspects and how it has been transformed and extended to myriad contemporary dichotomies see EARLY GREEK THOUGHT AND PERSPECTIVES FOR THE INTERPRETATION OF QUANTUM MECHANICS: PRELIMINARIES TO AN ONTOLOGICAL APPROACH. I am also in the process of connecting all of this to the concept of a limit (thanks to Keith), which is a kind of attractive fixed point (related to a fixed point), which is a kind of attractor, which comes full circle back to dissipative structures.

Crack's in the Second Law of Thermodynamics?

Just came across this fascinating issue of the open access online journal Entropy: Quantum Limits to the Second Law of Thermodynamics. Not sure what to believe here, but my gut tells me that the Second Law is on a shaky foundation. Here is a quote from the opening of the overview article: The Second Law Mystique:

Over fifty years ago Arthur Eddington wrote [1]: "The second law of thermodynamics holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation".

Although this is perhaps the most famous endorsement of the second law, it is certainly not the only one; in the works of Einstein, Planck, Maxwell, and other luminaries one can find similarly strong imprimaturs. Common to them is an almost mystical faith in the law's inviolability. Aside perhaps from the standard conservation laws, no physical axiom engenders more support from the scientific community. The reasons are not hard to list. No experimental violation of the second law has been recognized by the scientific community in over 150 years; meanwhile, it has been confirmed in countless experiments and natural phenomena. Absolute inviolability is intellectually satisfying. One should also not discount the power of peer pressure; like most paradigms, the second law is understood deeply by few and taken on faith by most. Such faith is cemented by many famous endorsements and is so deeply rooted in a century and a half of cultural legacy that it has put the second law nearly beyond the reach of serious scientific discussion. Taken together, these constitute what may be called the second law mystique.

Despite the deeply rooted belief in its absolute status, the second law has always had surprisingly shallow roots. Despite vaunted claims to the contrary, it does not have a fully satisfactory theoretical proof; therefore, its absolute status has always been questionable and contingent and, like all good laws, it is falsifiable in the Popperian sense. Second, since its discovery, physics has undergone multiple paradigm shifts - e.g., quantum mechanics, relativity, chaos - that have revolutionized our view of reality, and yet the second law has emerged essentially unchanged from its classical roots and has been inadequatedly tested in many new experimental regimes where it should apply. Lacking full theoretical or experimental support, it is epistemologically unsound to presume it at the level to which the scientific community has become accustomed. Third, there are more than a half dozen common statements of it - dating back to Clausius and Thomson and, in spirit, to Carnot 180 years ago - not all of which are equivalent. As quipped by Clifford Truesdell, "Every physicist knows exactly what the first and second law mean, but it's my experience that no two physicists agree on them". From a purely logical standpoint, this Babel-like understanding is intolerable - but this situation has not only been tolerated by the scientific community, it has been embraced. Sensing some of these difficulties, there have been some serious attempts to render the second law axiomatic in recent years [2,3].