[Dan Day]

You are a doofus (sp?).

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*

[maro]

You poor confused sap. Let's say your lottery involved picking a number from 1 to 6, in an (ordered) sequence of 10, with replacement. The odds of any single 10-tuplet are about 1 in 60 million. That is calculated as 6 raised to the tenth. When you say suggest that the odds are certain that someone will win (actually, not quite certain, because there could be no match, and a rollover of the jackpot), you are implicitly defining the universe of successes as the universe of all 10-tuplets, the probability of which will be 60 million times 1 divided by 60 million, or one. The probability of any one 10-tuplet is still 1 in 60 million. Let's say you wanted to figure the odds that all the winning numbers are even. That's 1/2 raised to the tenth, or 1 in a thousand in rough numbers. Both computations are figured as P1*P2*P3...PN. You can get from the first computation to the second by figuring the number of 10-tuples in which there are only even numbers (3 to the tenth, or about 59,000, and multiplying by the probability of each 10-tuplet. Thus, it is seen that is useful to separate the question of what the probability is of one 10-tuplet from the question of how many are in the set A for which one is determining P(A). One practical reason why this approach makes sense is the difficulty of determining how to count all functional DNA computations. Because we are talking about bitflip mutations, it seems obvious that PN << 1, and we have assumed some significant minimum size of N, so in our case P1*P2*P3...PN is pretty small. As to how dense in our probability space are the functional DNA sequences--by intuition it seems likely to be not dense at all. In logic, well-formed sentences form a small fraction of all sentences. In all programming languages I have been exposed, the fraction of working programs in the space of all possible binary combinations of a certain set size is also small. I would think that if the density of successful DNA combos in DNA space were high, we would irradiating our sperm and ova rather than avoiding high radiation--or at least doing that to our livestock. I think the onus is on the evolutionary camp to show that things are different when it comes to DNA. And by the way, math majors at Harvard don't take "probability" in their freshman year. They take Math 55, or 22, which used to be the advanced calculus classes, which are preparatory to other classes.