Alpha Theory – Page 2 – God of the Machine

Tomorrow. Did I say tomorrow? I meant the last syllable of recorded time.

Now where were we? Oh yes: nowhere. Philosophy to date has yielded no explanations, no predictions, no tools unless we classify logic generously, and very little practical advice, much of it bad. And then from “cogito ergo sum,” or “existence exists,” philosophers expect to explain the world, or at least a good chunk of it. Tautologies unpack only so far. No matter how much you cram into a suitcase, you cannot expect to fill a universe with its contents.

I was a little unfair to the Greeks in Part 1. They didn’t have 300 years of dazzling scientific advance to build on. What they had was nothing at all, and as Eddie Thomas pointed out in the comments, you have to start somewhere. But 2500 years later, do we have to start from nothing all over again? In what follows I will take for granted that the external world exists, that we are capable of knowing it, and doubtless many other truths of metaphysics and epistemology that everyone knows but philosophers still hotly dispute. If you want to argue that stuff, the comments are still raging on Part 1.

I propose to begin with the First and Second Laws of thermodynamics. You can follow the links for some helpful refreshers, but in brief, the First Law states that energy is always conserved. It is neither created nor destroyed, merely transferred. And since we know, from relativistic physics, that matter is merely energy in another form, we conclude that everything that ever happens is an energy transfer.

This profound fact about the universe has gone almost entirely unnoticed by philosophers, whether from ignorance or indifference I cannot say. But it leads almost immediately to two other profound facts. First, all events are commensurable at some level. They are all instances of the same thing. Second, all events are measurable, at least in theory. We need only to be able to measure each thermodynamic consequence, and add them all up.

Now let’s set up a little thermodynamic system. Call it Eustace. Eustace need not be biological, or at all fancy; it is best to think of him as just a cube of space. Eustace would be pretty dull without a few things going on, so to liven up matters we will assume that at least something in the way of atomic state change is going on. Particles will dart in and out of our little cube of space.

To describe Eustace, we have recourse to the Second Law. As ordinarily formulated, it states that energy, if unimpeded, always tends to disperse. Frying pans cool when you take them off the stove. Water ripples outward and fades to nothing when you throw a pebble in a still lake. Iron rusts. Perpetual motion machines run down. Rocks don’t roll uphill.

Vast quantities of ink have been spilled in attempts to explain entropy, but really it is nothing more than the measure of this tendency of energy to disperse.

The Second Law is, fortunately, only a tendency. Energy disperses if unimpeded. But it is often impeded, which makes possible life, machines, and anything that does work, in the technical as well as the ordinary sense of the word. The lack of activation energy impedes the Second Law: some external force must push a rock poised atop a cliff, or take the frying pan off the fire. Covalent bond energy impedes the Second Law as well, which is why solid objects hang together. The Second Law has been formulated mathematically in several ways. The most useful for describing Eustace is the Gibbs-Boltzmann equation for free energy, which states:

Î”G = Î”H – TÎ”S

This is one of the most important equations in the history of science; it has been shown to hold in every context that we know of. The triangles, deltas, represent change. Gibbs-Boltzmann compares two states of a thermodynamic system — Eustace in our case, but it could be anything. As for the terms: G, or free energy, is simply the energy available to do work. The earth, for example, receives new free energy constantly in the form of sunlight. Free energy is the sine qua non; it is why I can write this and you can read it. It does not, unfortunately, necessarily become work, as no one knows better than I. Let alone useful work: this depends on how it is directed. I do work when I paint your car and work when I scratch it.

H is enthalpy, the total heat content of a system. We are interested here in changes (Î”), and since we know from the First Law that energy is neither created nor destroyed, that nothing is for free, any increase in enthalpy has to come from outside the system. T is temperature, and S is entropy, which can be either positive or negative. Negative entropy is, again, good; it leads to more free energy by subtracting a negative from a negative. Positive entropy is what you lose, and one of the consequences of the Second Law is that you always lose something.

To return to Eustace, we know from the First Law, in the terms of the equation, that Î”G >= 0. We will also assign Eustace a constant temperature, which isn’t strictly necessary but simplifies the math a bit. So we have:

Î”H – TÎ”S >= 0

We are dealing here with sums of discrete quantities here. Not one big thing, but many tiny things. Various particles are darting around inside Eustace, each with its own thermodynamic consequences. Hess’s Law states that we can add these up in any order and the result will always be the same. So we segregate the entropic processes into the positive and the negative:

Î£H – TÎ£S negative – TÎ£S positive >= 0

From here it’s just a little algebra. We take the third term, the sum of the positive entropies, add it to both sides, and then divide both sides by that same term, yielding:

Î± = (Î£H – TÎ£S negative) / TÎ£S positive >= 1

And there we have it. Alpha (Î±) is just an arbitrary term that we assign to the result, like c for the speed of light. The term TÎ£S negative (the sum of the negative entropy) is always negative, so the higher the negative entropy, the larger the numerator. And alpha is always greater than or equal to 1, as you would expect. One is the alpha number for a system that dissipates every last bit of its enthalpy, retaining no free energy at all.

Alpha turns out to have several interesting properties. First, it is dimensionless. The numerator and denominator are both expressed in units of energy, which divide out. It is a number, nothing more. Second, it is calculable, at least in principle. Third, it is perfectly general. Alpha applies to any two states of any system. Fourth, it is complete. Alpha accounts for everything that has happened inside Eustace between the two states that we’re interested in.

Which leaves the question of what Î± is, exactly. It can be thought of as the rate at which the free energy in a system is directed toward coherence, rather than dissipation. It is the measure of the stability of a system. And this number, remarkably, will clear up any number of dilemmas that philosophers have been unable to resolve. Not to get too far ahead of ourselves here, but I intend, eventually, to establish that the larger Eustace’s Î± number is, the better.

Next (I do not say tomorrow): From physics to ethics in one moderately difficult step.

Update: Edited for clarity. So if you still don’t understand it, imagine what it was like before.

Humans have suffered three thousand years of philosophy now, and it’s time we took stock.

Explanations. A successful explanation decomposes a complex question into its constituent parts. You ask why blood is bright red in the air and the arteries and darker red in the veins. I tell you that arterial blood has more oxygen, which it collects from the lungs and carries it to the heart, than venous blood, which does the opposite circuit. Then I tell you that blood contains iron, which bonds to oxygen to form oxyhaemoglobin, which is bright red. I can demonstrate by experiment that these are facts. I have offered a successful explanation.

Of course it is incomplete. I haven’t told you how I know the blood circulates, what oxygen is, how chemical bonding works, or what makes red red. But I could tell you all of these things, and even if I don’t you know more about blood than you did when we started.

The explanation succeeds largely because the question is worth asking. You notice an apparently strange fact that you do not understand. You investigate, and if you are lucky and intelligent, maybe you get somewhere. Philosophers, by contrast, when they sit down to philosophize, forget, as a point of honor, everything they know. They begin with pseudo-questions like “Do I exist?” (Descartes) or “Does the external world exist?” (Berkeley and his innumerable successors), the answers to which no sane person, including Descartes and Berkeley, has never seriously doubted. Kant, the great name in modern philosophy, is the great master of the showboating pseudo-question. The one certainty about questions like “how is space possible?”, “how are synthetic judgments possible a priori?”, and, my favorite, “how is nature possible?,” is that you will learn nothing by asking them, no matter how they are answered. Kant rarely bothers to answer them and such answers as he gives are impossible to remember in any case.

Explanations would seem to be philosophy’s best hope, but its track record is dismal. There has been the occasional lucky guess. Democritus held, correctly, that the world was made up of atoms. Now suppose you had inquired of Democritus what the world-stuff was, and he told you “atoms.” Would you be enlightened? In any case he couldn’t prove his guess, or support it, or follow it up in any way. Atoms had to wait 2500 years for Rutherford and modern physics to put them to good use. If you asked Parmenides how a thing can change and remain the same thing, he would have told you that nothing changes. It’s an explanation of a sort. But would you have gone away happy? Grade: Two C’s, two D’s, and an F. Congratulations Kroger, you’re at the top of the Delta pledge class.

Predictions. To be fair, predictions have been the Achilles’ heel of many more reputable disciplines than philosophy, like economics. Human beings have a nasty habit of not doing what the models say they should, and most philosophers retain enough sense of self-preservation to shy away from prediction whenever possible. Still, a few of the less judicious philosophers of history, like Plato, Spengler, and Marx, have taken the plunge. Spenglerian cycles of history take a couple thousand years to check out, fortunately for Spengler, but Plato’s prediction of eternal decline and Marx’s of advanced capitalism preceding communism were — how shall i put this politely? — howlingly wrong. The very belief that history has a direction is a prime piece of foolishness in its own right.

Brute matter is more tractable. Einstein’s equation for the precession of the perihelion of Mercury, which Newtonian mechanics could not explain, is a classical instance of a successful prediction. Although the precession was a matter of a lousy 40 seconds of arc per century, Einstein wrote Eddington that he was prepared to give up on relativity if his equation failed to account for it. Ever met a philosopher willing to throw over a theory of his in the face of an inconvenient fact? Me neither. Grade: No grade point average. All courses incomplete.

Tools. OK, there’s propositional logic, for which Aristotle receives due credit. But really that’s more mathematics than philosophy, Aristotle’s version of it was incomplete, and it took mathematicians, like Boole and Frege, to make a proper algebra of it and tighten it up. With this one shining exception philosophy has been a dead loss in the tools department. Probably its most famous contribution is Karl Popper’s theory of falsifiability, which turns real science exactly on its head. Where real science verifies theories, Popper falsifies them. Most of us consider “irrefutability” (not “untestability,” which is a different affair) a virtue in a scientific theory. For Popper it is a vice. Mathematics, which is obviously not “falsifiable” and equally obviously “irrefutable,” supremely embarrasses Popper’s philosophy of science, and Popper takes the customary philosophic approach of never mentioning it.

Far from supplying us with tools, philosophers have taken every opportunity to disparage the ones we’re born with. According to Berkeley things do not exist outside of our mind because we cannot think of such things without having them in mind. According to Kant we are ignorant because we have senses. I cite these arguments not because they are bad, which they are, but because they are the most influential arguments in modern philosophy.

To modern philosophy in particular also belongs the unique distinction of making the ad hominem respectable. According to Marx we reason badly about economics because we are bourgeois. According to the deconstructionists we are racist, being white; sexist, being male; and speciesist, being homo sapiens. Grade: Fat, drunk, and stupid is no way to go through life, son.

Advice. Moral advice from philosophers divides into two categories, the anodyne and the dangerous. Under the anodyne begin with Plato and “know thyself,” which is to advice what “nothing changes” is to explanation. Kant recommends that we treat our neighbor as we ourselves would be treated, which works well provided our neighbor is exactly like us, and sheds little light on the question of how we would wish to be treated, and why. Rand counsels “rational self-interest,” which might be helpful if she told us what was rational, or what was self-interested.

Under dangerous file Nietzsche’s “will to power,” just what a growing boy needs to hear. (Yes, he is tragically misinterpreted, and no, it doesn’t matter.) But utilitarianism, “the greatest good for the greatest number,” with its utter disregard for the individual, is the real menace. Occasionally some poor deranged soul actually tries to follow it, with predictable consequences. Ladies and gentlemen, I give you the consistent utilitarian, the unblushing advocate of infanticide and cripple-killing, Mr. Peter Singer. The sad fact is that your moral intuition, imperfect though it is, gives you better advice than any moral philosophers have to date. G.E. Moore, confronted with this fact, responded with “the naturalistic fallacy,” from which it follows that the way we do behave has nothing to do with the way we should behave. Well George, natural selection, which largely governs our behavior, has seen us through for quite a long time now, which is more than I can say for moral philosophy. Grade: Zero point zero.

One loose index of the value of a discipline is whether it helped humanity out of the cave. Mathematicians, scientists, engineers, and even a few economists have all made their contributions. As for philosophy — we programmers have a term to characterize a programmer without whom, even if he were paid nothing, the project would be better off. The term is “net negative.”

Is it too late to start over? Tomorrow we will consider a better approach.

(Update: Bill Kaplan notes in the comments that I had the Einstein-Eddington story backwards, which reflects no credit on Einstein but, alas, none on the philosophers either. Umbrae Canarum comments. Colby Cosh wittily points up my debt to David Stove, to whom I owe some, though not more than 95%, of the argument. The original draft contained an acknowledgement of Stove, which was inadvertently omitted in the final version thanks to a transcription error by one of my research assistants. I recommend Stove’s The Plato Cult to anyone with even a mild interest in the topic. You skinflints can find a few of his greatest hits here. Ilia Tulchinsky comments. Jesus von Einstein comments. Ray Davis comments.)

The Disconsolation of Philosophy, Part 2: Among the Ruins

The Disconsolation of Philosophy, Part 1