In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.
There are scientific and mathematical objections to such reasoning, my favourite being that there's a finite limit to how low the sequence can go (can't get smaller than Plank time). But to me, the paradox serves as an apt analogy to the reasoning methods justifying intelligent design.
The analogy is as follows. The tortoise is God, it has the head start in the race. While science is Achilles, starting from scratch and rapidly progressing. While playing the role of Zeno is the intelligent design advocate, creating a "paradox" by which science will never overtake God as an explanation.
The pattern goes as follows. Define pattern X. Explain how X cannot come about by the current accepted processes. Point to instances in nature that fit pattern X. Therefore current accepted processes are bunk, conclude God did it. A proof by definitions, so who needs evidence?
A good example is irreducible complexity, it's a proof by definitions. Much like Achilles can't ever overtake the turtle because of the infinite series needed to overtake the turtle, natural selection can never explain how system which requires all components could be built gradually.
One can see that Achilles could overtake the turtle in a matter of seconds, but the paradox remains! Can irreducible complex systems evolve? Of course, and it has been known how for around 90 years now. In Behe's efforts to make a proof by definitions he neglected the scientific literature showing just how such systems could evolve.
Intelligent Design proponents are sitting on the sideline, yelling whatever they can to invalidate the obvious fact: Achilles overtook the tortoise long ago. So while mountains of papers are pouring into the scientific literature showing with more and more certainty that we evolved, the cdesign proponentsists are looking for a paradox of their own by which they can dismiss the volumes of evidence.
So much time is spent trying to talk about the inadequacies of natural selection, it's disbelief that Achilles could possibly overtake the turtle. That way, all they have to do is reject natural selection and design wins by default. No mechanism, no testing a hypothesis against evidence or making predictions, but that evolution can't explain it therefore God did it.
Every accumulated piece of scientific evidence in favour of evolution propels the theory further and further in the metaphorical race. Even when science starts from the null hypothesis and God from a presupposition, there hits a point where the accumulated evidence "outruns" the presuppositionist position. The evidence for evolution is overwhelming, so much so that all the cdesign proponentsistscan do is try to downplay it as "not enough evidence for me". Achilles has past the tortoise long ago...