Cosmic Apprentice: Dispatches from the Edges of Science (12 page)

In retrospect, Boltzmann’s common-language summary after four-hundred-odd pages full of mathematics clouded the issue far more than illuminating it. Adding to the confusion was the code-breaking physicist John von Neumann, who advised Claude Shannon, innovator of information theory, which was to become the basis of global telecommunications, to adopt the term
entropy
to describe information. “Nobody knows what entropy really is” anyway, counseled the troublemaker von Neumann, a heavy drinker who had so many car wrecks that they named an intersection in Princeton Von Neumann Corner.
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Shannon took the advice.

The notion that the key concept of entropy is a spontaneous change from order to disorder stems from this 1898 summary Boltzmann gave of his own work. But what is order? It certainly appears that a sparkling crystal of ice is obviously more “ordered” than an equal volume of water, but the difference in the numbers of energy states is totally beyond our comprehension. As Lambert writes, “If liquid water at 273 K, with its 10
^{1,991,000,000,000,000,000,000,000}
accessible microstates [quantized molecular arrangements] is considered ‘disorderly,’ how can ice at 273 K that has 10
^{1,299,000,000,000,000,000,000,000}
accessible microstates be considered ‘orderly’?”
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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,
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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.”
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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.”
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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.
”
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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
thermo
dynamic 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.”
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