The other day, Stephen Batzer commented here on a great article by Vincent Torley posted at Uncommon Descent (and that is indebted to David Berlinski), about the evolution of the vertebrate eye. Here I shall ignore the eye, and focus — no pun intended! — on something that Torley quoted in passing. He reminds us that Jerry Coyne once wrote:

When, after a Christmas visit, we watch grandma leave on the train to Miami, we assume that the rest of her journey will be an extrapolation of that first quarter-mile. A creationist unwilling to extrapolate from micro- to macroevolution is as irrational as an observer who assumes that, after grandma’s train disappears around the bend, it is seized by divine forces and instantly transported to Florida. (Nature 412:587, 19 August 2001.)

We do need to be reminded that Darwinism depends on extrapolation. According to Harvard’s longtime evolution expert Ernst Mayr [1904-2005], evolution across species “is nothing but an extrapolation and magnification of the events that take place within populations and species.”
Coyne’s comment shows us that this extrapolation has not yet been demonstrated. If it had been, believe me, we would never hear the end of it. He wouldn’t have needed to put grandma on that imaginary train.
Here’s the background: In The Origin of Species, Darwin discussed the work of animal breeders, pigeon fanciers in particular. They might vary in coloring or display, but at the end of the day, as Darwin well knew, they all remained pigeons. Dogs vary greatly in size, but dogs they remain.
Darwin said that varieties were “incipient species,” thereby staking his claim to the belief they were on their way to becoming something else. In short, he was extrapolating. But that was philosophy, not science. He lacked the evidence to claim that the extrapolation had actually been observed.
Ever since, evolutionists have assumed that it has been observed. But the Coyne quote reminds us that it hasn’t been. Grandma just keeps traveling on to Miami, he reassures us, and it takes a “creationist” to raise doubts about that.
Darwin wrote in his 1844 Essay (a preliminary version of the Origin):

That a limit to variation does exist in nature is assumed by most authors, though I am unable to discover a single fact on which this belief is grounded . . .

Well, I’m sorry, Charles, but it’s up to you to demonstrate that unlimited variation has been observed. It’s no good complaining that “most authors” won’t tell us why it hasn’t been. Almost 170 years later, it still hasn’t been.
In the Origin, Darwin wrote that “by the repetition of this process [of micro-evolution] a new variety might be formed, which would either supplant or co-exist with the parent form.”
Might be, yes. But we don’t know that yet.
Alfred Russel Wallace, the co-discoverer of natural selection, wrote in 1858 that his theory could be summarized as “indefinite departure from the original type.” “Indefinite departure” is in fact the central claim of the theory of evolution by natural selection. But it still hasn’t been observed.
Richard Dawkins, Jerry Coyne and others keep trying to bully us into accepting that it is a “fact.” OK. Maybe it is. So give us the evidence. We have to read their books carefully to realize how meager it is. They still haven’t shown us that extrapolation. To an amazing extent, their books are filled with tendentious anti-design arguments, not positive evidence of evolution as a demonstrated fact.
In Darwinism: The Refutation of a Myth (1987), Soren Lovtrup wrote: “Neither in nature nor under experimental conditions have any substantial effects ever been obtained through the systematic accumulation of micromutations.”
In his final book, What Evolution Is (2001), Ernst Mayr was evasive on the question of whether extrapolation had been observed. He persistently obscures our vision by his references to “population thinking.” This is another way of asserting that micro-evolution is a reality. No one doubts that. And from that premise he leads us to suppose that the observed variation is continuous; all the way to Miami.
As to Coyne’s metaphor about grandma’s train ride, several people made critical comments, in the replies to Torley’s article. Here’s just one:

It is really hard to know if grandma will ever arrive at Miami when she is laying the track, randomly directed, one rail at a time, as she goes.

Good point. When you are relying on random variation, the track that Coyne presupposes doesn’t even exist. And if such parallel tracks could be created, and laid, they might lead anywhere. Or nowhere.