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.