No doubt you've heard the venerable Darwinian dogma that given enough time and enough monkeys banging away randomly on a typewriter keyboard one of them would eventually produce Hamlet purely by chance.
The claim is designed to illustrate that even though life on earth is unimaginably improbable on the naturalistic hypothesis, it's not impossible. Given enough time and enough molecular combinations even the improbable becomes probable, and the probable becomes actual.
Unfortunately for this argument, however, its persuasiveness does not survive an actual look at the math.
Bill Dembski directs us to a decade-old site where the math is actually worked out. It happens that even if we hypothesize 17 billion galaxies, each containing 17 billion habitable planets, each planet with 17 billion monkeys each typing away and producing one line per second for 17 billion years, the chances of the phrase "To be or not to be, that is the question" not being included in the results are:
In other words, even given parameters unimaginably more lenient than those which actually obtained in the real world, it's about 99.999999999995% sure that the monkeys would fail to produce just a single sentence of Hamlet by random pecking.
The Darwinian objects, however, that this extraordinary improbability assumes that the monkeys have to get the whole sequence right or else they have to start over as soon as they make a mistake. What if there is a mechanism, though, which conserves any letters that come up correctly so that if, say, a TO is typed by some monkey somewhere it's preserved until a BE is typed and then that's saved, etc? If so, the target sentence would appear in no time at all, relatively speaking. The rest of Hamlet would then eventually follow on in like fashion.
This is essentially the argument made by Richard Dawkins in the Blind Watchmaker, and it's intended to send the doubter scurrying away in abject embarrassment at having had the temerity to challenge scientific orthodoxy. The problem with it, though, is that it must assume the very thing that Intelligent Design has been asserting ever since its inception. It assumes that there is some goal toward which life is striving. It assumes that somehow life knows to preserve combinations that "work" until they can be incorporated into the sequence of letters. It assumes that nature has the ability to see a goal and to strive toward it. In other words, it assumes that nature is somehow programmed to produce life.
Such a teleological aspect in nature is precisely what the Darwinian vigorously denies. There is no need to introduce purpose, he avers, since natural selection acting with no conscious purpose selects combinations on the basis of their survival value and thus acts as if it were intelligent. But again this answer won't work. The reason is that natural selection acts only on reproducing populations of organisms. What needs to be explained is how information far more complex than our target sentence (a strand of genetic material, for example) emerged before it developed the ability to replicate itself and thus be subject to the pressures of natural selection.
We suppose that technically speaking it could have happened, just as it's possible that a blind-folded man might select a single marked atom out of all the atoms of the universe just by luck, but it takes faith far greater than the size of a mustard seed to believe that it actually did happen in the few million years between the time the earth cooled sufficiently to allow bio-molecules to form and the appearance of the first living organisms. Of course, when one is a priori committed to the notion that only mechanistic, unintelligent forces were at work in the production of life, then one is constrained to accept the most outlandish and implausible of stories.
It took an intelligent writer to produce Hamlet. There is no basis for believing that any conceivable combination of chance, luck, and blind, impersonal force could accomplish it. Likewise, neither is there any basis for believing that blind, impersonal forces built DNA. The conviction that such mechanisms did indeed accidentally achieve this astonishing miracle is an article of faith that only true believers in the church of Materialism can convince themselves to embrace.