It may take dictionaries twenty years to change, but already disorder is dead as shorthand for entropy in most first-year collegiate chemistry texts. It is being replaced with the idea that energy dispersal is the essence of the change described by the second law. Energy, if unhindered, spreads out in space and on a greater number of energy levels. This tendency of energy to disperse is the essence of the second law that Snow neglected to mention. A loud sound spreads out through the air from a speaker, a crashing car spews metal and heat in all directions, potential becomes kinetic energy if we fall from a tree. This dispersion tendency does not have to happen right away, however. It can be dammed or blocked. Indeed such complex damming and blocking is crucial to living systems, whose energetic molecules are safeguarded from immediate dispersion by their structure. Like a boy being pushed before he falls out of a tree, life’s molecules require higher energy levels, so-called activation energies, before they disperse their stored energy. The meta-stable molecules of organisms are protected from energy dispersion, as are their evolved networks of repair mechanisms. They do not defy the second law but block its immediate action. The reason we don’t burst into flames is because of Ea, the energy of activation, usually stated in units of kilojoules per mole.
We often lament our lot, crying why me? Our cultural stories about why things go wrong in our lives include Satan, karma, and Murphy’s law, which states that everything that can go wrong will go wrong, with many comic variations, such as Roberts’s axiom, “Only errors exist.” But our acute awareness of problems, pains, and errors is itself part of living systems’ protective feedback systems. Chemical kinetics in physiology continuously safeguards life from spontaneous combustion and other forms of destruction that would occur if the second law mandate of dispersion were immediately fulfilled. On the other hand, life’s organized systems, chemically and cybernetically (because of cyclical, sensitive feedback loops) protect it from immediate breakdown and allow it to prolong its “entropy production.” In animals, that involves the recognition of and oxygen-aided breakdown of energetically concentrated chemical substrates—food—which we continue to take in to maintain our body and mind acting in the world around us. Bacteria have greater diversity in the concentrated energy sources and chemical substrates that they can use to run their metabolism. Fungi produce enzymes that digest food outside their bodies before they ingest it. Plants, generally considered inferior to animals, in fact are metabolically superior. We learn in grade school that plants produce oxygen that we breathe, and breathe carbon dioxide that we exhale, suggesting an essential equivalence and a nice ecological match between plants and animals. But plants not only photosynthesize, producing oxygen; they also use oxygen. They do it at night when sunlight is not available as a source of energy. They do so using mitochondria, former respiring bacteria, the same inclusions we have in our cells.
All these life-forms, however ordered and protected they are from immediate gradient breakdown, are actively and profoundly engaged in energy dispersal. We do not burn up like a sparked piece of paper, but while alive we seek concentrated sources of energy such as food, methane, and oil. We pay attention when things go wrong, as in Murphy’s law, but we miss the fact that at the unconscious biochemical, cellular, and physiological levels things continuously go right, protecting us as natural machines to spread energy in accord with the second law. Each of us is the result of 3.8 billion years of evolution of highly organized, actively metabolizing, energy-dispersing systems that are protected by chemical kinetics and molecular barriers. We store energy the better to disperse it. Our damming and delaying of the effects of the second law locally allow us, as open thermodynamic systems, to maintain and increase our personal realm of active gradient reduction. Rather than bemoan our lot, we should be continuously amazed at the exquisite artistry of life that has used chemical kinetics to keep us going and growing with nanotechnological precision since shortly after Earth’s origin. Murphy was wrong. And although Neil Young said it’s better to burn out than fade away, better still is what life has been doing, growing its domain of controlled burning to protect itself even as it finds new gradients, new concentrated sources of energy to its organized, ordered, energy-dispersing selves.
More confusion stems from entropy’s status as a ratio in its original definition. A “low entropy (ordered)” state, in a typical expository article by a highly competent physicist in a New Scientist article,10 illustrates the situation. The New Scientist article befuddlingly labels both an illustration of the big bang—indicating that in its first instant our cosmos was a seething mass containing the entire energy of the present universe but in a relatively small volume with an extremely high temperature—and also, three pages later, a panther who stalks a cage as “low entropy.” An arrow, marked “Ordered energy and matter,” enters the cage. But clearly the zoo environment and panther’s food are not billion-degree seething masses of quarks and gluons. The phrase does not add to clarity, especially when the “low entropy (ordered)” state also describes a smallish box of indolent molecules at a very low temperature.
Clearly, a great advantage of introducing “entropy increase as due to molecular energy spreading out in space,” if it is not constrained, begins with the ready parallels to spontaneous behavior of kinds of energy that are well-known to beginners: “the light from a light bulb, the sound from a stereo, the waves from a rock dropped in a swimming pool, the air from a punctured tire.”11
The physicist Harvey Leff, coeditor of definitive anthologies on Maxwell’s demon, writes in a pedagogical note in The Physics Teacher, “It is a remarkable, fortuitous coincidence that entropy’s traditional symbol S can be viewed as shorthand for ‘Spreading function.’ Using the interpretation of spreading over space and time, entropy might become more meaningful to you and your students.”12
In the Woody Allen film Whatever Works, an attractive young woman from Mississippi persuades a retired physicist (and chess teacher) from Greenwich Village to let her live with him. Her mother finds her and lets her know that she is unhappy with the daughter’s choice of mate, encouraging a handsome British actor to pursue her instead. After initially resisting the young man’s advances, the young woman finds herself on his houseboat, happily pushing him away after a passionate kiss. Overcome by a moment of reflection—she is still under the intellectual influence of her grumpy string theorist benefactor (who is now her husband)—she returns from her mental ruminations to gaze into the actor’s eyes. What is it? he asks.
“Entropy,” she murmurs, explaining that what happened was like a “tube of toothpaste,” by which she means that life, like toothpaste squeezed from its tube, can never return to the way it was.
Molecules of perfume speeding at hundreds of miles per hour but constantly colliding with equally rapidly traveling air molecules will move from one side of an absolutely quiet-air room to the other. Cream molecules, totally unstirred, independently and inevitably, similarly collide and slide from the top of a cold coffee cup throughout that cup. They will always move, disperse, and thereby delocalize and disperse their energy by spreading out in simple three-dimensional space if they are not constrained. S—the spreading function: This simple formulation beautifully generalizes much of the ordinary phenomena in our lives. If you place a hot piece of iron on another, cooler piece of iron, “heat energy” flows to the cooler iron until the two become exactly the same temperature. Technically, the “heat energy that flows” is actually the vibrational energy of atoms dancing in place in the metal that, on average, are moving faster in the warmer iron bar than in the cooler. At the surfaces of contact, the vibrations of the warmer bar interact with slightly slower vibrations in the cooler bar, and over time the surplus energy of the warmer bar disperses. It spreads out, so the vibrations of atoms held in place are at the same energy levels in both bars.
PROTOSEMIOSIS
Simple as it is compared with the more sexy, obscure term entropy, the S function has major implications for philosophy. If
we didn’t know better, we might be tempted to risk the hypothesis that the bar was heated on one end and wanted its warmth to spread to its cool parts. That might not be its goal in any conscious human sense, but that is clearly its direction, its unconscious orientation.
Spreading comes before meaning, before discrete sense. We are reminded of Georges Bataille’s writing that his ink is like blood, the slow spill of a lifelong intellectual suicide or sacrifice. Energy’s delocalization sets the stage for teleology, because it has a natural end, equilibrium, and will find ways, sometimes complex ways, of getting there.
The brute reality of this protoconscious, protosemiotic process ultimately poses Copernican inferiority problems for a certain not-so-hairy prodigy and problem-child great ape species; let’s not mention any names. The main problem seems to be that we like to congratulate ourselves for being the sole full possessors of a certain sort of truly teleological purposiveness. Some see glimmers of sign making and purposive behavior in other creatures, and biosemioticians may grant the power to all life, even considering it its distinctive feature. But in general we conflate purposiveness with human consciousness—not noticing that it is implicit in the telic substrate of a thermodynamic universe “prior to” or “irrespective of” life. The phenomenologically observed tendency of things to go from being concentrated to spread out demarcates a natural telos, and the relative end-state of “being spread out” (thermal or chemical equilibrium) seems to select for, tug, or pull random aggregates to become more organized to accomplish that natural end.
It is no coincidence that plants, animals, fungi, and bacteria spread as they grow or that, even if they are not growing or reproducing but merely metabolizing, they put more entropy, mostly as heat, out into the local environment than would be the case without them. The organism itself, from όργανον—organon in Greek, meaning “instrument” or “tool”—seems to be a kind of natural device, a kind of cosmic organ for the degradation of the ambient concentrated energy sources that it craves. At least unconsciously, organisms must recognize the ambient gradients that support them and that they degrade.
BOLTZMANN’S SLEIGHT
In Isabelle Stengers’s judgment, “Boltzmann was forced to recognize that his theorem did not describe the impossibility of an evolution that would lead to a spontaneous decrease in entropy and would, therefore, contravene the second law of thermodynamics, but only its improbability.”13 Spreading occurs as radiation, as the big bang, as change that does not return in linear time. But this is confounding to the mathematical mind, which imagines eternities, symmetries, and geometrical perfection. Boltzmann’s trick of deriving experiential, time-flowing thermodynamic spread from time-reversible, symmetrical dynamics is a kind of mathematical sleight. But just because there are more ways in which things can be disordered than ordered does not mean that they have to go in that direction, as over infinite time even the most orderly combinations will recur an infinite number of times. So, too, assuming that the past is ordered and the future as disordered, as Boltzmann did, when the difference between past and future is precisely what we are trying to explain, is problematic. The problem is so difficult that apparently Albert Einstein and Kurt Gödel gave up on improving upon Boltzmann’s derivation of linear time from time-independent mechanics after which the former devoted himself to more tractable pursuits, developing the special and general theories of relativity.
Many times in the history of science there has been a fatal disconnect between the insular certitudes of the mathematical realm explored by theorists. The unifier of electricity and magnetism, James Clerk Maxwell, had a name for such idealism: he called it “the Queen of Heaven,” meaning roughly that what his German mathematical colleagues wanted they would never have. The term is from a letter in December 1873 from Maxwell to his friend Peter Guthrie Tait, in which Maxwell derides the attempts of Clausius and Boltzmann to reduce irreversible nature (as described by entropy, the second law of thermodynamics) to the reversible equations of mathematics: “The Hamiltonsche Princip [i.e., the Hamiltonian Principle, a mathematical formalism that is applied also today in quantum mechanics], the while soars along in a region unvexed by statistical considerations while the German Icari [i.e., Clausius and Boltzmann] flap their waxen wings in Nephelococcygia [Νεφελοκοκκυγία, Cuckoo Cloud Land—referring to Aristophanes’s play The Birds in which the trusting and naive characters, done with Earth and Olympus, plan to build a perfect city in the clouds] amid those cloudy forms which the ignorance and finitude of human science have invested with the incommunicable attributes of the invisible Queen of heaven.”14
For Maxwell these German physicists were seeing the mathematical equivalent of animals in the clouds—they saw them all right, but they weren’t really there. Mathematics, for example in Newton’s theory of gravity, which ultimately allowed the Earth to be reflected as faces in the visors of cosmonauts, can sometimes be spectacularly successful. But despite the power of math on its own, its application to physics is not a lock. Richard Feynman quipped that mathematics is to physics as masturbation is to lovemaking. (He also said physics is like sex: it gives results but that’s not why we do it.)
“You are a magician,” an admirer tells the ballet impresario in the 1948 film The Red Shoes, complimenting him for putting together a great show based on the Hans Christian Andersen fable on a shoestring budget in so little time.
“Ah, yes,” says Boris Lermontov, “but even for a magician to pull a rabbit from a hat, the rabbit must already be in the hat.” In the case of the road from time-reversible dynamics to the lived world of thermodynamic spreading, there doesn’t seem to be a way to get from there to here, where we always end up except in our mathematical abstractions, geometric projections, and imagined infinitudes.
ISABELLE STENGERS
Isabelle Stengers crosses the two cultures, scientific and human, the mechanical-reversible and the irreversible-real. A student and colleague of Ilya Prigogine, who won the Nobel Prize in physics for inroads in the problem Einstein abandoned, she and Prigogine wrote Order out of Chaos, a book that attempted to introduce temporal irreversibility into the heart of physics and that developed the very important notion of dissipative structures, real “live” (i.e., not computer programs) three-dimensional systems that appeared in energy flows. If they continued their access to energy and matter substrate, they could continue to grow, producing entropy and spreading energy. In Prigogine’s descriptions they were “far from equilibrium,” and the farther they evolved or diverged from an equilibrium state, the more sensitive to external conditions they became. Eventually, they could undergo bifurcations, separating to new, perhaps higher-energy meta-stable energy regimes.
I met Stengers briefly in passing twenty years ago, at the annual festival of Spoleto. I didn’t know anything about her except that she was a scientist. Spoleto, with its small, crooked cobbled streets and outlying fields of giant sunflowers showered by rays of Renaissance master light, is a beautiful, picturesque villa. My son was a toddler at the time, and a tricycle-possessing pixie with big blue glasses, the grandson of a fascist, was showing my son how to ride. My mother introduced me to Stengers as summer air wafted over the stone balcony. Not long after, Umberto Eco could be seen in the corner, smoking a cigar and surrounded by Italian reporters as if he were Marcello Mastroianni beleaguered by paparazzi in a Fellini movie. Eco had just published Foucault’s Pendulum, which was everywhere in the airports. And although we had just met her, Stengers suggested my son, Tonio, might want to spill some water on Eco.
As luck or Gaia would have it, a few years after meeting her I began working, at the behest of the Montana ecologist Eric Schneider, on popularizing the thermodynamics of complex systems—especially as applied to life, which was not Prigogine and Stengers’s focus. Two decades later I found myself at a small conference celebrating her philosophical work Cosmopolitics: In Place of Both Absolutism and Tolerance. I was invited by Eben Kirksey, it was put on by the Mellon Committee for
Science Studies at the Graduate Center of CUNY, and my offering was “Time Tricks, or Lure of the Retrocausal: Isabelle Stengers’ Delicate Operations on the Body of Science.”
A week before the conference, I was reminded of the strange interweaving of the threads of our lives in the folding tapestry of time by an e-mail, which I forwarded to Stengers, reminding her also of our original meeting when she advocated that my son douse Eco. I also forwarded it to other experts in thermodynamics.
The e-mail was from a Dr. Graf in Germany.
“This April 17th,” it announced, in what could pass for a digital-age version of a broadside for a traveling medicine show, “Dr. Graf will be demonstrating his suitcase-sized gravity machine, a perpetual motion machine of the second kind.” Curious, because I knew the U.S. Patent Office no longer even accepted applications for perpetual motion machines, I fired an e-mail off to Frank L. Lambert. Lambert e-mailed me back to say that Dr. Graf was no mountebank. He had looked at Graf’s calculations, and his valise-sized gravity machine looked like it worked. It did collect energy from gravity. But it was impractical. Lambert calculated that it would require a tube of 90 trillion miles to produce enough energy to light one 100-watt lightbulb.
AROUND 1990 I started working with Schneider, who had already been studying the intersection between nonequilibrium thermodynamics and life for twenty years. This led in 2004 to the University of Chicago Press book Into the Cool: Thermodynamics, Energy Flow, and Life. It is a post-Prigoginian work. And it focuses on life, how characteristic patterns appear in and as organisms and ecosystems, on the specifics of life itself—which was not Prigogine’s focus, although some, such as the Austrian astrophysicist Erich Jantsch, who dedicated his book The Self-Organizing Universe to Prigogine, saw immediately a relationship between Prigogine’s work and James Lovelock’s description of Earth’s surface as physiological.
Cosmic Apprentice: Dispatches from the Edges of Science Page 11