But, do you see that neutral mutations can enter en masse into the pool of selectable mutations at any time? Your original point was a critique of functional intermediates. This is one way (networks and hierachies are another) in which the demand for functional intermediates is invalidated.
And you are clearly unable to have a discussion without behaving like a 15 year old.
Read the context of the threads. We weren't having a wide-ranging discussion of the probability of ANY beneficial somatic change. We were talking about a PARTICULAR unspecified beneficial somatic change, and whether that change could conceivably have been reached via N small mutations.
Yes, we were, but the point is that that sort of calculation is a fallacy. If you don't understand the relevance of my shuffled deck example, I'd be happy to help you with any part that you failed to grasp.
Twice a week in the Texas Lotto, a 16-million-to-1 event occurs, week after week, all year long. Should we thus conclude that the Texas Lotto is so astronomically impossible that it couldn't possibly be occurring? This is the flaw in your argument.
The point I was making was that bringing NONFUNCTIONAL mutations into the explanation doesn't help the evolutionists' argument, because natural selection by definition cannot operate on NUNFUNCTIONAL mutations.
Yes, that was your point, and the fact remains that it's a silly one, for exactly the reasons that I and others have explained. Nonfunctional mutations provide a pathway for the accumulation of changes until a workable modification is stumbled upon (at which point natural selection kicks in). The fact that evolution can't work on the nonfunctional mutations until/if they eventually come together in a useful combination is entirely beside the point, I don't know why you're so fixated on it. The fact remains that nonfunctional mutations "help the evolutionists' argument" by being one of the many ways that beneficial changes can be introduced into the population without requiring that every single-base-pair mutation be a beneficial one in and of itself.
Congratutlations on your high school math. Good work, boy. I have a bachelor's degree in math from Harvard. And you?
Sorry, I don't believe it. Your mathematical analysis here has been extremely simplistic. A math major, from even a state school, would understand the fallacy of ignoring the statistical universe, for example. You might wish to consult a book such as John Allen Paulos's Innumeracy: Mathematical Illiteracy and its Consequences, and then reconsider your argument. In short, you have confused the probability of a particular outcome with the probability of some outcome -- read the shuffled deck example again until you figure it out. I learned this in my first week in my first college probability class, what's your excuse? Are they really not covering such elementary concepts at Harvard any more?
Similarly, I highly doubt that Harvard would allow anyone to graduate with a math degree who was able to make such ludicrous declarations as P1*P2*...PN being, and I quote, "next to impossible", *without* first examining the likely values of "N" or "P(i)" to get an estimate of the actual results of the calculation. Hey, Harvard-boy, the outcome of four coin flips is also P1*P2*...PN, is that "next to impossible" too? *snort*