I'm bumping this to the top of the queue: 1) on general principle, and 2) because I was going to include some of this material in a paper that goes up on 3 Quarks Daily, but then I decided not to use it. So here it goes. Moreover (3), it's a good antidote to the all too frequent and casual use of the concept of "emergence," which more often than not is used as a sophisticated synonym for "magic." We don't really know what's going on so we'll call it emergence. Well, in this case, the appearance of convection cells, we know what's happening:
The tumbler was sitting on a window sill during the morning and mid-day on a sunny day. Sunlight came through the window and heated the water, just a bit. But the black carbon particles in the ink absorbed energy faster than the water molecules, making them warmer than the water in which they were immersed. That’s what supported the formation of those convection cells, which began dissipating within an hour after they had formed. No violation of the Second Law of Thermodynamics. You can download this discussion as a PDF from this link.
With a Note on What to do When You are Fascinated by Technical Concepts but Lack the Math: Call the Plumber!
Matter is not given. In the present-day view it has to be constructed out of a more fundamental concept in terms of quantum fields. In this construction of matter, thermodynamic concepts (irreversibility, entropy) have a role to play.
–Ilya Prigogine and Isabelle Stengers, Order Out of Chaos, 1984
I’ve been thinking a lot about entropy lately.
It is, of course, one of the foundational concepts of modern thought, haunting our dreams with the prospect of the universe grinding to a halt in heat death, but also animating our hope of understanding how life arose in the universe. In a Latourian context one might even speculate that entropy is the concept that, more than any other (except perhaps biological evolution, with which it has become richly intertwined), gives the lie to the Modern’s conceit that they are here and nature is somewhere over there, separated from one another by a sharp line of clear and distinct ideas. For the concept of entropy, unlike relativity and quantum mechanics, has arisen from deep within the world of classical physics.
According to
the Wikipedia the term was coined in 1865 by Rudolf Clausius, but the work leading to the concept originated earlier in the century with the research of Lazare Carnot, a mathematician whose
1803 paper Fundamental Principles of Equilibrium and Movement proposed that in any machine the accelerations and shocks of the moving parts represent losses of moment of activity. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire which posited that in all heat-engines whenever "caloric", or what is now known as heat, falls through a temperature difference, work or motive power can be produced from the actions of the "fall of caloric" between a hot and cold body.
There you have it, the machine, a mechanical device with moving parts. We have Newtonian mechanics with its three laws of motion and the grand suggestion that the universe
works like a clock, a vast device of many parts all ticking away in perfect order, except when they don’t. And there’s La Mettrie’s 1748 treatise,
Man a Machine.
Oh! how easy our intellectual life would have become if only the universe were nothing but a clock and we but little tick-tocks within it.
But it is not, nor are we. The mechanistic vision ground to a halt in the analysis of fire and we became but especially clever monkeys through Darwin’s elucidation of a pattern he traced though the geological, paleontological, botanical and zoological records.
Chasing Molecules
Though my interest in entropy is long-standing, my recent thoughts have been occasioned by various and numerous remarks the philosopher Levi Bryant has made at Larval Subjects, his blog. The post
Entropy and Me is a representative example. Or, consider this passage from his book,
The Democracy of Objects (pp. 227-228):
Entropy refers to the degree of disorder within a system. Suppose you have a tightly closed glass box and somehow introduce a gas into it. During the initial phases following the introduction of the gas into the system, the gas will be characterized by a high degree of order or a low degree of entropy. This is so because the particles of gas will be localized in one or the other region of the box. However, as time passes, the degree of disorder and entropy within the system will increase as the gas becomes evenly distributed throughout the box. In this respect, entropy is a measure of probability. If the earlier phases of the gas distribution indicate a lower degree of entropy than the later stages, then this is because in the earlier phases there is a lower degree of probability that the gas will be localized in any one place in the box. As time passes, the probability of finding gas particles located evenly throughout the box increases and we subsequently conclude that the degree of entropy has increased.
This seemed a bit, well, “off” to me. For one thing Bryant doesn’t say just how the gas gets introduced into the box. Surely he doesn’t mean that it gets magically whisked there through a Star Trekkian transporter. But what DOES he mean?
Well, he probably meant something like poking a small hole somewhere in the box and letting the air rush in. So that’s what I did. Not physically, of course, as I have no convenient source of high-vacuum boxes, but in my imagination.
I began imagining lots and lots of tiny tiny air molecules going in through the hole. Does that first cohort march in formation like a highly trained marching band or drill team, or do they twist and tumble every which way, pushed by the molecules behind them, and those behind them, and so forth? How fast do they move? Who’s the first to make it to the other side? And how do you measure their positions?
It seemed reasonable to think, as Bryant more or less stated (except, remember, he said nothing about a hole), that they’d be bunched up near the hole at the beginning and that, at the end, they’d be scattered evenly throughout the box. But how’d they get from one state to the other? Getting from New Jersey to New York is easy, there’s the Holland Tunnel, the Verrazano-Narrows Bridge, and so forth. But the kind of states we’re talking about aren’t geographical regions and moving from one to the other is not like getting in a car, turning the key (or pushing the button) and driving away.
And, by the way, just what does “evenly” mean? It might mean that they’re at the vertices of a cubic lattice, or some other regular structure, but I suspect that that’s not what Bryant meant. If not THAT, though, then just what? Perhaps he was, in his imagination, dividing the box into lots of tiny cubes. We then count the number of molecules in each cube. It doesn’t matter just where they are in the cube, just so they’re inside it. Some place. And when we’ve done our count we find that there’s approximately the same number in each imaginary cube.
Now we’re getting somewhere, says I to myself, we’re making progress.
But no, we’re not, we’re just getting deeper and deeper into the quicksand. What’s the size of our imaginary cubes? Does it matter? And those molecules, they’re moving, right, always moving. Since we can’t possibly examine all these imaginary cubes at one time, but have to look at one after another, how do we keep those molecules inside their proper imaginary cubes? And, since the little critters are identical to one another, how can we be sure that some of them aren’t sneaking about from cube to cube just to mess up our count?
Now, you might say, this is all nonsense, this stuff about imaginary cubes and pesky molecules who are unwilling to sit still for the count. Well, yes, you’re right, it’s nonsense in a way. But, if Bryant’s talk about order and probability is to have any substantive meaning, then we really do have to have some way of locating and counting those molecules. We need some way of taking measurements and my imaginings, some of them anyhow, are aimed at the informal notion of evenness. If we're going to measure it, well, what does it mean? Without measurements we’re just talking gibberish.
Still, it’s clear that something isn’t working. My thinking was at an impasse, that’s clear. I’m in over my head. What to do?
Call the Plumber
My plumber is Tim Perper. Though he’s not a plumber, he’s not even a physicist. He was trained as a molecular biologist and geneticist, worked in industry for a bit, worked in academia for a bit, and then decided that he was really more interested in human courtship than in complex molecules. So he spent a couple years hanging out in bars, night clubs, church socials and such and wrote down what he saw people doing—all courtesy of the Guggenheim Foundation. He wrote that work up in a book, Sex Signals (1985), that work and, of course, a lot more, including Ovid and Durkheim.