(Note: This is dedicated to my Dad, who taught me about entropy, and a thousand other wonderful things about the universe.)

I was just driving to work today, minding my own business, when the most remarkable thing occurred to me. What it amounts to is a sort-of proof of Creationism, which is something I never expected to find myself attempting to prove. I say "sort of" because a) I don't really believe it, even though it is compelling in its own way, and b) it does not necessarily require the existence of God to occur. Regardless of those caveats, I still imagine that it's thought-provoking enough to attempt to convey.

The key to understanding this "proof" is entropy. Perhaps you're aware of what entropy is, perhaps not. If not, I'll provide a simple analogy to explain it, that I'll expand upon in order to build the proof.

Imagine that you have, for some unknown and diabolical reason, broken into the studios of a television station and stolen the machine that spins the balls around for the lotto drawing. Maybe you think you can rig it to your advantage. Maybe you just want to pretend that you're the prom queen that stands idly by the machine while it does its thing. Whatever. The point is that you've got this machine. And just for fun, you open the hopper and take out all of the balls except for the numbers 1 through 6 (you're really bored) and push the balls out onto the little runway in numerical order: from 1 to 6. Then, you put all the balls back in the hopper, give it a twirl, and push the balls out randomly. What are the odds that they will come out in the same order? If you do the math, you find that the odds are one in 720. So what we've got here is a situation where one possible configuration is considered "ordered" and 719 configurations are considered "disordered." To say it another way, there is one and only one configuration of the balls (1, 2, 3, 4, 5, 6) that is considered ordered, but there are 719 configurations that are considered unordered. No matter which combination we pick out of those 719, it's still NOT ordered.

To put this in physics terminology, we would say that an unordered configuration has high entropy. That is to say, the number of possible configurations that are unordered is high. It doesn't matter which of these configurations we choose, because for our purposes they're not in the order 1, 2, 3, 4, 5, 6, and therefore aren't ordered. The ordered configuration, on the other hand, has low entropy, because there's only one possible way we can generate it.

Now. If we take the balls ordered 1, 2, 3, 4, 5, 6 and place them in the hopper in order, do you think they'll come out in order? Probably not, as we've just seen. This is a demonstration of something called the Second Law of Thermodynamics. The Second Law of Thermodynamics states that in a given physical system (such as a lottery hopper, or a planet, or an airplane, or a universe), entropy tends to increase. In case you're curious, the First Law of Thermodynamics is the old saw that energy is always conserved. Anyway, when energy is applied to the system in such a way to perturb it (such as cranking the handle on the hopper), they system will tend to increase its total entropy. This is sort of obvious in the situation of the balls; since the balls are far more likely to pop out in an unordered state after being cranked around, it's easy to see why entropy tends to increase. Of course--and this is important--the law does not state that entropy must increase, but that it has a tendency to do so in a given system. For instance, if we placed the balls in the hopper in a random order, there's nothing preventing them from coming out in the order 1, 2, 3, 4, 5, 6. There's a 1 in 720 probability that exactly such a thing will occur. It's just not the likeliest event. (In real systems, the tendency toward entropy is far more overwhelming--in the hopper example, for instance, the energy that you expended cranking the handle would turn some of your ordered bodily energy into heat (in the form of friction) and air motion with much higher entropy, and the total entropy of the system would have increased, far outweighing the decrease in entropy caused by the balls' spontaneous self-ordering. But whatever.)

So what you should have gotten out of all that is that a) entropy is, essentially, a measure of the disorder of a given system; b) that entropy tends always to increase; and c) that you need to get out more. Now we can move on to this insane proofesque of Creationism that so disturbed me when I was driving to work today.

To begin, let's go back to that lottery analogy for a quick moment, then abandon it forever. We can imagine an arrangement of balls that has more entropy than the ordered arrangement, but less entropy than complete disorder. For instance, the sequence 1, 2, 3, 6, 4 ,5 contains a subset (1, 2, 3) that is ordered. So the total entropy of the system is less than if the numbers were in the order 2, 4, 1, 5 ,6 3, for instance. Another way to say this is that it's partially ordered and partially disordered. We can easily show that a partially ordered configuration is more likely than a fully ordered arrangement, but less likely than a fully ordered arrangement. In this example, the odds of a fully ordered arrangement are 1 in 720, and the odds of an unordered arrangement are 719 in 720. But the odds of a partially ordered arrangement (say, where the first three numbers are 1, 2, 3, but the final three numbers are whatever we choose them to be), are 6 in 720. That's because there are six configurations that match the rule 1, 2, 3, followed by any configuration of the other three. The point of all this is that a partially ordered configuration is significantly more likely than a fully ordered configuration. In the situation with the balls, it's six times more likely. (Update: Bzzzt! My very clever father points out that I've forgotten to include the comination 1, 2, 3 as one of the elements in the "partially disordered" configuration. Thus, the actual number of configurations is not 3! = 6, but 4! = 24. So replace all those "6 in 720"s with "24 in 720" and everything goes on as before...)

Now we get to the real world. We know that we are living in a world where low entropy is continuously yielding higher entropy. We see this every time we act in the physical world. When a star burns, when an engine runs, when we walk, when pretty much anything happens, the total entropy of the universe increases. Even when we do things to specifically counteract entropy, like arranging all of the balls in the hopper in the order 1 through 50, the resulting entropy of ourselves is always greater. We convert the energy-storing molecules in our bodies into less-ordered molecules, generating energy to do work with, and thus the total entropy of the universe always increases.

This means that in the past, the universe always has lower entropy than it does in the present. Let's imagine a date, say October 23, 4004 BC, just to pick a date out of the air. The total entropy of the universe on that day was a great deal lower than it is today, because fewer things had happened to increase the entropy of the universe. Let's go back even further, say fifteen billion years ago, to a millisecond following the big bang. According to physics, the total entropy of the universe immediately following the big bang was extraordinarily low. The universe just after the big bang occurred was extremely ordered. And it is that order, say physicists, that we are siphoning away every time we do work in the physical universe. If the universe continues to expand indefinitely, as physicists tend to believe it will (barring some further discovery of dark matter, energy, or--heck--even dark entropy), eventually it will reach a state of maximum entropy in which all energy has been converted into heat and no more physical processes will be able to occur. This is referred to by physicists as the heat death of the universe. Hmm. An endless expanse of darkness and heat where nothing useful can ever happen--does this remind you of any religious concept? Oh hell, never mind.

The point is this. The entropy of the universe was much, much, much lower fifteen billion years ago than it was on October 23, 4004 BC. Vastly, uncountably lower. Now, remember how I said it was really important that the Second Law of Thermodynamics does not prevent disorder from producing order? It says that the increase in entropy is a tendency. A tendency that the universe almost unfailingly follows, but a tendency nonetheless. There is a chance, however small, that the entire universe was in a state of complete disorder on October 22, 4004 BC; a state resembling the heat death of the universe that I mentioned earlier, and that it spontaneously sprang, fully formed, into being on October 23, 3004 BC. Sprang into being with planets and stars and people and Adam and Eve and fossils buried in the ground and vast amounts of microwave background radiation bouncing around to fool us into thinking there had been a big bang. Now here's the crazy part: the odds of this happening, this spontaneous popping into being of the universe as it was described in Genesis is incredibly more likely than the state of the universe just after the big bang. And the reasoning is extremely simple. Our universe in 4004 BC had vastly more entropy than did the universe immediately following the big bang. Because there are almost infinitely more combinations of universes that meet the conditions for 4004 BC than there are combinations of universes immediately following the big bang, it follows mathematically that it is almost infinitely more likely that the universe simply sprang into existence six thousand years ago, than it did in the big bang fifteen billion years ago. The actual figures are beyond human comprehension because they must take into account the total entropy of the universe, which is impossible to calculate. But there's no disputing the relative entropies of the two situations.

To sum up, it is almost infinitely more likely, from the standpoint of probability, that the universe spontaneously came into being on October 23, 4004 BC, than it is that it began in the big bang. I don't know what to make of that information, except to point out that likelihood is not the same thing as proof, and that realities and probabilities are two very different things.

You may be wondering why I picked that particular date. October 23, 4004 BC, is the date that the notorious Bishop James Ussher decreed as the official date of creation back in the 1650's. Using the Bible, he calculated the dates backward using the Jewish calendar and genealogies given in the Old and New Testaments. How he arrived at the precise date of October 23rd, I have no idea. But hey, for all we know, he could have been right!

Let me state for the record, that I don't think that this reasoning proves anything at all. It seems to me totally weird that the universe would have simply sprung into existence in such an intelligible manner. It's simply a thought experiment to show that the universe is much more wild and improbable and neat than anything we could imagine. In reality, I'm much more inclined to think that God, in a primal act of creation, willed matter into being in the form of the big bang, having formulated the laws of nature in just such a way as to produce, well, us, while at the same time having formulated those same laws to be mathematically decipherable in such a way that people like Newton and Einstein could figure them out later. A tall order indeed; but hey, this is God we're talking about.