Lots of people wanted to tell me that the sort of super-complex molecules found in living things could not possibly have arisen by random chance in a universe a mere 13.7 billion years old, as the probabilities concerned are so immense — 10 to the power of 40,000, according to one reader.
There are several things wrong with this line of reasoning. In the first place, it is based ultimately on a common statistical fallacy — one so common that it has a name: "the fallacy of numerators without denominators." (The numerator is the top number in a fraction; the denominator is the bottom one.) Consider, for example, the New York State lottery. I believe the probability of any one ticket winning the lottery is around one in twelve million. And yet, most weeks, someone wins it. How? The answer, of course, is that twelve million is merely the numerator here. The denominator is the several million people who buy lottery tickets every week. Divide the numerator by the denominator, and you have a reasonable-sized number: 1, or 30, or 0.5, or something similar.
The probability of any particular thing happening is microscopically small. The probability that I flicked my eyes away from the screen to glance out of my study window just then, rather than a millisecond sooner or a millisecond later, is very tiny. However, in a busy universe, something must happen. In fact, untold trillions of things are happening all the time — that's the denominator. The physical universe is a far, far bigger assemblage than the population of New York State (it may in fact, for all we can prove to the contrary, be infinite!) so that extremely, extremely, extremely unlikely things are happening all the time.
A second problem arises from the term "random chance." In fact, even the most materialist of scientists does not believe that the universe is governed by random chance. There are organizing principles everywhere: subatomic particles organize themselves into atoms and molecules, interstellar gas organizes itself into stars and planets, and so on. Science consists of the search to understand how these organizing principles do their work. Why they are present is a very interesting question, but outside the scope of science. However, no thoughtful scientist, not even the most materialist atheist, thinks that the universe is the result of purely random processes.
A third problem is the one raised by the so-called "anthropic principle." However improbable you may think it was that human intelligence arose from inanimate matter, if it hadn't happened, we wouldn't be here to discuss it! Possibly the Big Bang happened 10 to the power of 40,000 times before we showed up. Now that we have shown up, we can sit around and discuss the whole business. The other (10 to the power of 40,000, minus 1) occurrences of the universe were — as an atheist friend of mine likes to say about the Afterlife — very quiet.
