| | Wrong. 1/216 is the probability of getting 3 6's.
That's what we've been talking about. The chances of getting a target sequence of 3 sixes. It matters not if the tosses are sequential or simultaneous. It also doesn't matter, by the way, if it's three sixes, or three anything else; just as long as the sequence is a specified target.
No one has argued that there are no mutations in living organisms. The argument is that most of them are either neutral (they do nothing) or they are harmful (they kill the organism or make it sterile). There's no particular law, mathematical or otherwise, preventing beneficial mutations from occurring; it's simply an empirical fact that beneficial mutations rarely, if ever, occur.
Guessing, Ed's point about simultaneous trials is that correctly computing the probability of a successful mutation must consider the population of the species.
Thanks, but we've gone into this issue already. To update you: in playwriting and storycrafting, there's a form of cheating (i.e., cheating your audience out of their money's worth for a good story, well told) called the "deus ex machina", or "God of the machine." In antiquity, it took the form of an actor, dressed as some Olympian god, lowered onto the stage in a basket on a pulley. Once lowered, the "god of the machine" would proceed to solve all the plot problems for the characters, the audience, and especially the writer, who was too damned lazy to figure out how to unravel the plot complications and resolve the storyline himself. Audiences hated it then; they hate it now.
In Darwinism, the equivalent of the deus ex machina is the "Sewall Wright Effect" or "Genetic Drift." In this scenario, mutations are supposed to have no problem taking over a population because -- voila!-- the populations are by definition always small enough for the small number of beneficial mutations that might conceivably occur to overwhelm them and thus becomes fixed. What causes this "voila!"? Easy. Just be certain to lower the god of the machine onto the stage of academia and instruct the actor in the basket to say these lines: "In all cases of speciation, the big population became fractured, splitting off a small subsection of itself. In all cases of speciation, this small subsection became geographically isolated from the original parent population. In all cases of speciation, this small subsection managed to survive the sorts of natural disasters that normally wipe out small populations: predators, hurricanes, drought, earthquakes, volcanoes, etc. Statistically speaking, a rare beneficial mutation has a much greater chance of becoming fixed in a very small population than it does in a large population, where it would simply get drowned out (this was shown to be so by the population geneticists back in the 1930s)."
(The god of the machine makes a dramatic pause and continues):
"Then this small, lucky population mutates into either an independent species, or a superior form of the original species. It then rejoins the original parent population, which it can now overwhelm because it has had chance to grow strong, 'far from the madding crowd.'"
The audience -- made up of a friendly mix of academics, Darwinians, members of a local Objectivism Discussion Group, and journalists -- applauds loudly, shouting "Encore! Author!" A few persons sitting in the back -- I among them -- give the raspberry, like this "pppppppppppp" -- because the author promised to tell a great story about the Origin of Species -- you know, a scientific story with evidence, experimental proof, empirical evidence from field work, mathematical calculations -- but unable to resolve the plot and tell us how species originated, he resorted to this gimmick that just happens to come along in the nick of time -- every time -- to help species evolve.
I accept the Sewall Wright Effect as THE great deus ex machina that solves all the problems of speciation: everything -- butterflies, porcupines, whales, giraffes, birds, man -- all found safe refuges in geographical isolation from a go-nowhere parent population; free of predators (which can gobble up a small population a lot easier than it can a large one); free of storms; etc. Then in each case, they all had those rare beneficial mutations that became fixed, they became new and/or better species, and then they rejoined their original population.
Extending this to evolutionary questions is not so simple, since reproductive rates must be considered.
Yes, they certainly must be considered. In millions if not billions of generation of bacteria, and in hundreds of thousands if not millions of generations of fruit flies, there has emerged not ONE "non-bacteria" or "non-fruit-fly." It's all just more bacteria and more fruit flies.
But the main point holds. Population size is very relevant. Also, computations should be for one or more successful mutations, not simply one.
Already taken into a account. That's what SV is: "Selection Value." It applies (by definition) only to successful mutations.
I don't know about Claude Shannon, but I have seen creationists asserting probabilities based on "junk math", not taking into account these other factors.
I have seen almost no math by Darwinians, junk or elegant. But since you seem to have a handle on the problems involved, and since you seem to understand how to take into account these other factors, why don't you perform a calculation for us and show us how it's done?
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