The following is an email I sent to a friend after watching a debate between William Lane Craig and Felmon Davis. To be clear, this is not an endorsement of secular humanism, which I think makes specious claims about the nature of morality in order to make it more palatable.

Edit: My references to large numbers in this email are very casual and I combine different notations without skipping a beat; for that, I apologize. For reference:

“1e10” = “1*10^10” = “10^10” = 10,000,000,000 (ten billion)

“5e10” = “5*10^10” = 50,000,000,000 (fifty billion)

Also, Craig’s specific claim to which I refer in the email can be found just after 33:00 in the linked Youtube video.

I’ve been thinking more about Craig’s arguments. In addition to what I claim is a false dichotomy between the “universe beginning to exist” in the classical sense of time and the universe “existing infinitely in the past” (following which he describes god existing timelessly but implies a temporal experience in the creation of the universe, thus contradicting himself — in addition to his failure to define the concept of “timelessness”), he makes the very interesting claim that the universe had only one chance in (1e10)^124 to be in its current state (he cites Donald Page). He offers this statistic without any quantitative explanation whatsoever.

I think I know what this comes from. It’s an expression of the size of the state space of a hypothetical box with all the elementary particles of the universe in it (about 1e80 of them, although more recently I think the estimate is 1e89). In other words, there are (1e10)^124 possible configurations of that box at the universe’s energy level. Therefore, the chances of the box taking on its exact current configuration is one in (1e10)^124. You can already see what’s wrong with this line of argument (confirmation bias, anthropic principle, that thing you called it — you get the point), but there’s a more subtle aspect to its wrongness.

Suppose I was to take a box filled with oxygen and sit it on a table and look at it for a very long time. Our every day experience dictates that the gas will simply fill the box, evenly distributed over the whole volume, and that this state (on a macroscopic level) will persist for all time. But the truth is that there is a chance, albeit extremely small, that weird macroscopic events will occur (such as all the gas being packed into one corner of the box). One way of explaining why we don’t see this happen is to consider the state space of the system (gas in a box) at its given energy level. Each “state” specifies the exact position/momentum of every particle in the box (the only constraints are the total energy and momentum). It helps if you think about these values as being discrete. So the macroscopic “gas evenly distributed” state corresponds to an enormous number of states (or microstates); you can interchange any pair of particles, move them around a little bit on a microscopic scale, whatever — the macrostate of things is still an even distribution. On the other hand, the macroscopic “gas concentrated in a corner” state corresponds to a comparatively tiny number of microstates. Therefore, if we are looking at the box without any information about its microstate, we say that the chance of us observing a macrostate other than the “gas evenly distributed” one is virtually nonexistent (http://en.wikipedia.org/wiki/Terasecond_and_longer).

Now, in the event that an incomprehensibly unlikely macrostate (gas concentrated in a corner) were to appear in that box, what would we expect to see immediately following it? Well, the same thing as if we were to inject a gas into the corner of an empty box: the gas spreading out and returning very quickly (over some finite time interval) to its classical macrostate (gas evenly distributed), but passing through numerous intermediate macrostates with probabilities much greater than “gas concentrated in a corner” and much smaller than “gas evenly distributed.” In other words, there’s a one-hundred-percent chance, given the prior occurrence of an unlikely macrostate, that the gas will pass through a macrostate of intermediate probability.

You can scale this up. The “gas concentrated in a corner” state is analogous to the state of the universe at or immediately following the big bang, and the “gas evenly distributed” state corresponds to the heat death of the universe (which is the current agreed-upon forecast for the ultimate fate of the universe). The intermediate macrostate corresponds to the current state of the universe. In other words, given the fact that at a point in the finite past the universe existed in an extremely unlikely macrostate, its current macrostate (which corresponds to some number of microstates, each with the same unconditional probability as any other microstate) is not at all improbable (also check out http://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem).

Again, I am not exactly certain what Craig meant with the number he mentioned, but that’s his fault because he didn’t explain it at all. I think his reasoning is flawed, but that’s what you get from misapplication and abuse of the concept of entropy and the second law of thermodynamics.