There's another aspect to this fallacy, or maybe it's a closely-related fallacy, and I'm working on what to call it. It's similar to a newly-named fallacy we were discussing a week or so ago -- quantizing the continuum. Tortoise named it. But the fallacy I'm now thinking of is almost the opposite -- wrongly assigning the characteristics of the entire continuum to an individual quantum. In this case, the supposed "odds" against some action happening.
I mentioned this (without trying to name it) a couple of days ago in a now-dormant thread, when someone trotted out, for the zillionth time, the business of "figuring the odds" against evolution. I said this:
The biggest problem with these computations that take all the mutations that ever happened and then whomp up some kind of factorial result by stringing together all the generations is simply that ... each generation is mathematically on its own!Whatever accumulated mutations you may have hanging around in your gonads, that's the initial state as far as your offspring are concerned. Either a mutation will happen or it won't, and all the generations before you, going right back to the proverbial pond scum, are irrelevant in "computing the odds."
Source: post 81.
How about: "incorporation of the continuum"?
I'm math impaired, but it sounds like a variation the coin toss fallacy. You've had five heads in a row. What are the odds of tossing heads again? I think the central misunderstanding is the assumption that we had to get here from there. We are here, but it wasn't foreseen. I think the inventors of ID know this and are consciously and deliberately perpetrating a fraud. What are the odds?
The biggest problem with these computations that take all the mutations that ever happened and then whomp up some kind of factorial result by stringing together all the generations is simply that ... each generation is mathematically on its own!
If I am reading you correctly, you're talking about Climbing Mount Improbable, to use Dawkins' colorful (or would it be colourful??) expression.
I've referred to it in the past as the "second-floor frog fallacy" The creationists' argument is the equivalent of saying that frogs could never get to the second floor of a building, as it is twelve feet above the first floor. They say, "no frog can jump twelve feet into the air, so there can be no frogs on the second floor." This ignores, of course, the staircase...
It is not so much a fallacy as it is a case of people being ignorant of math, and probability theory and statistics is something most people find difficult to get right generally. Heck, I have to think about some of these things very hard to make sure I'm applying the math correctly and I'm supposed to know this stuff.
This particular misapplication of math refuses to die on these threads. The most common invalid uses are the assumption of an isotropic probability space (doesn't exist really but it makes the math *much* easier, never mind the wildly invalid results), and what you allude to above, inverting the size of the phase space and calling it "statistical probability".
If one can get people to acknowledge that the probability space is not isotropic, it will follow from the math that many outcomes are astronomically more probable than the number arrived at by inverting the size of the phase space.