Wesley R. Elsberry
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Posts: 4991 Joined: May 2002
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Gordon Mullings:
Quote | We must observe that the above 1986 Weasel shows a sample of 300, with 200 being in runs [thus a dominant feature of the output . . . and being of so large a number odf samples that if there is a reasonable chanve of a flick-back it should appear at least once], where never once a run appears do we see reversion away from the run. This contrasts with the 1987 outputs, which show frequent winks away from the correct letter.
These observed stable characteristics of the processes — whether explicitly or implicitly latched — tell us a lot.
So, again, we are simply looking at selective hyperskepticism.
Perhaps, we should put it this way:
Mr Kellogg you are in a dice game. Somehow the roll keeps on coming up 6’s 2/3 the time. After 200+ out of 300+ rolls, are you going to say maybe this is not a loaded die? [If so, can we meet for a little dice game; I could do with a fatter bank account.]
Onlookers, see the point?
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Mullings apparently doesn't know how to do a probability analysis of the phenomenon at issue. What, precisely, 300 rolls of a 6-sided die have to do with the output of "weasel" is something Mullings doesn't explain.
Mullings ignores the fact that one can analyze the probability of the phenomenon in question. I have already done so. The situation analyzed is the likelihood that the best candidate in a generation's correct characters are retained in a succeeding generation. That, in turn, is the complement of the probability that a generation will have all of its candidates change at least one correct base from the parent to an incorrect one. As I put it before:
Probability of a candidate changing a parent's correct base to an incorrect base = PCandidate_C2I =
(1 - (1 - (u * (K - 1) / K))C)
Probability that a population will have at least one candidate that preserves all the correct bases from the parent of the previous generation = PPopulation_C2C =
1 - (PCandidate_C2I )N
Notice the power of N in there. As the population increases, the chance that the best candidate in each generation will change a correct base to an incorrect one falls off sharply, achieving the teensy-tiny reaches of small probability otherwise beloved of IDC advocates very quickly. We don't see changes of correct characters in the output of best candidates per generation in Dawkins' "The Blind Watchmaker" because it is by far the most probable outcome of a run of an accurate (and thus non-latching) "weasel" with a reasonable population size and a reasonable mutation rate. For the case where N=50, u=0.05, and the best candidate from the previous generation had 27 correct bases, the probability that the best candidate in the new generation still has all those bases correct is
= 1.0 - (0.73614)50
= 0.999999777
That number means that we would expect to see one dropping of a correct base from the best candidate per generation in about 4,487,000 generations at the 27 correct bases level. How many generations were represented in the book? Even if all 43 best candidates per generation were there, the odds would still be less than 1 in 100,000 that we would expect to see a correct base changed to an incorrect one in the best candidate from any of those generations, and that is being generous by using the C=27 case for all generations. So anytime Mr. Mullings wants to play a betting game related to his misjudgment of probabilities for "weasel", I think I could also do with a fatter bank account.
For earlier generations with fewer correct bases, the odds are even higher that the best candidate of each generation still has all the correct bases inherited from its parent intact. Here is the run showing this fact:
Quote | 2000 runs, 00 correct : candidate p_c2c calc = 1.00000, MC = 1.00000; p_c2i calc = 0.00000, MC = 0.00000
2000 runs, N=50, u=0.05000, K=27, C=0, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.00000, MC = 0.00000 p_pop_c2c = 1.0 - (0.00000)^50
2000 runs, 01 correct : candidate p_c2c calc = 0.95185, MC = 0.95100; p_c2i calc = 0.04815, MC = 0.04900
2000 runs, N=50, u=0.05000, K=27, C=1, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.04815, MC = 0.04872 p_pop_c2c = 1.0 - (0.04815)^50
2000 runs, 02 correct : candidate p_c2c calc = 0.90602, MC = 0.89850; p_c2i calc = 0.09398, MC = 0.10150
2000 runs, N=50, u=0.05000, K=27, C=2, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.09398, MC = 0.09456 p_pop_c2c = 1.0 - (0.09398)^50
2000 runs, 03 correct : candidate p_c2c calc = 0.86240, MC = 0.86600; p_c2i calc = 0.13760, MC = 0.13400
2000 runs, N=50, u=0.05000, K=27, C=3, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.13760, MC = 0.13723 p_pop_c2c = 1.0 - (0.13760)^50
2000 runs, 04 correct : candidate p_c2c calc = 0.82088, MC = 0.81950; p_c2i calc = 0.17912, MC = 0.18050
2000 runs, N=50, u=0.05000, K=27, C=4, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.17912, MC = 0.17961 p_pop_c2c = 1.0 - (0.17912)^50
2000 runs, 05 correct : candidate p_c2c calc = 0.78135, MC = 0.79100; p_c2i calc = 0.21865, MC = 0.20900
2000 runs, N=50, u=0.05000, K=27, C=5, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.21865, MC = 0.21848 p_pop_c2c = 1.0 - (0.21865)^50
2000 runs, 06 correct : candidate p_c2c calc = 0.74373, MC = 0.74850; p_c2i calc = 0.25627, MC = 0.25150
2000 runs, N=50, u=0.05000, K=27, C=6, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.25627, MC = 0.25472 p_pop_c2c = 1.0 - (0.25627)^50
2000 runs, 07 correct : candidate p_c2c calc = 0.70792, MC = 0.70850; p_c2i calc = 0.29208, MC = 0.29150
2000 runs, N=50, u=0.05000, K=27, C=7, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.29208, MC = 0.29111 p_pop_c2c = 1.0 - (0.29208)^50
2000 runs, 08 correct : candidate p_c2c calc = 0.67384, MC = 0.68300; p_c2i calc = 0.32616, MC = 0.31700
2000 runs, N=50, u=0.05000, K=27, C=8, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.32616, MC = 0.32278 p_pop_c2c = 1.0 - (0.32616)^50
2000 runs, 09 correct : candidate p_c2c calc = 0.64139, MC = 0.64150; p_c2i calc = 0.35861, MC = 0.35850
2000 runs, N=50, u=0.05000, K=27, C=9, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.35861, MC = 0.35874 p_pop_c2c = 1.0 - (0.35861)^50
2000 runs, 10 correct : candidate p_c2c calc = 0.61051, MC = 0.61850; p_c2i calc = 0.38949, MC = 0.38150
2000 runs, N=50, u=0.05000, K=27, C=10, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.38949, MC = 0.39320 p_pop_c2c = 1.0 - (0.38949)^50
2000 runs, 11 correct : candidate p_c2c calc = 0.58112, MC = 0.55650; p_c2i calc = 0.41888, MC = 0.44350
2000 runs, N=50, u=0.05000, K=27, C=11, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.41888, MC = 0.42112 p_pop_c2c = 1.0 - (0.41888)^50
2000 runs, 12 correct : candidate p_c2c calc = 0.55314, MC = 0.55850; p_c2i calc = 0.44686, MC = 0.44150
2000 runs, N=50, u=0.05000, K=27, C=12, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.44686, MC = 0.44896 p_pop_c2c = 1.0 - (0.44686)^50
2000 runs, 13 correct : candidate p_c2c calc = 0.52650, MC = 0.53400; p_c2i calc = 0.47350, MC = 0.46600
2000 runs, N=50, u=0.05000, K=27, C=13, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.47350, MC = 0.47845 p_pop_c2c = 1.0 - (0.47350)^50
2000 runs, 14 correct : candidate p_c2c calc = 0.50115, MC = 0.50350; p_c2i calc = 0.49885, MC = 0.49650
2000 runs, N=50, u=0.05000, K=27, C=14, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.49885, MC = 0.49732 p_pop_c2c = 1.0 - (0.49885)^50
2000 runs, 15 correct : candidate p_c2c calc = 0.47702, MC = 0.46900; p_c2i calc = 0.52298, MC = 0.53100
2000 runs, N=50, u=0.05000, K=27, C=15, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.52298, MC = 0.52338 p_pop_c2c = 1.0 - (0.52298)^50
2000 runs, 16 correct : candidate p_c2c calc = 0.45406, MC = 0.44350; p_c2i calc = 0.54594, MC = 0.55650
2000 runs, N=50, u=0.05000, K=27, C=16, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.54594, MC = 0.54723 p_pop_c2c = 1.0 - (0.54594)^50
2000 runs, 17 correct : candidate p_c2c calc = 0.43219, MC = 0.42750; p_c2i calc = 0.56781, MC = 0.57250
2000 runs, N=50, u=0.05000, K=27, C=17, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.56781, MC = 0.56722 p_pop_c2c = 1.0 - (0.56781)^50
2000 runs, 18 correct : candidate p_c2c calc = 0.41139, MC = 0.39800; p_c2i calc = 0.58861, MC = 0.60200
2000 runs, N=50, u=0.05000, K=27, C=18, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.58861, MC = 0.59006 p_pop_c2c = 1.0 - (0.58861)^50
2000 runs, 19 correct : candidate p_c2c calc = 0.39158, MC = 0.38800; p_c2i calc = 0.60842, MC = 0.61200
2000 runs, N=50, u=0.05000, K=27, C=19, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.60842, MC = 0.60830 p_pop_c2c = 1.0 - (0.60842)^50
2000 runs, 20 correct : candidate p_c2c calc = 0.37272, MC = 0.35550; p_c2i calc = 0.62728, MC = 0.64450
2000 runs, N=50, u=0.05000, K=27, C=20, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.62728, MC = 0.62587 p_pop_c2c = 1.0 - (0.62728)^50
2000 runs, 21 correct : candidate p_c2c calc = 0.35478, MC = 0.36650; p_c2i calc = 0.64522, MC = 0.63350
2000 runs, N=50, u=0.05000, K=27, C=21, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.64522, MC = 0.64732 p_pop_c2c = 1.0 - (0.64522)^50
2000 runs, 22 correct : candidate p_c2c calc = 0.33770, MC = 0.35800; p_c2i calc = 0.66230, MC = 0.64200
2000 runs, N=50, u=0.05000, K=27, C=22, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.66230, MC = 0.66115 p_pop_c2c = 1.0 - (0.66230)^50
2000 runs, 23 correct : candidate p_c2c calc = 0.32144, MC = 0.30050; p_c2i calc = 0.67856, MC = 0.69950
2000 runs, N=50, u=0.05000, K=27, C=23, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.67856, MC = 0.67947 p_pop_c2c = 1.0 - (0.67856)^50
2000 runs, 24 correct : candidate p_c2c calc = 0.30596, MC = 0.30750; p_c2i calc = 0.69404, MC = 0.69250
2000 runs, N=50, u=0.05000, K=27, C=24, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.69404, MC = 0.69426 p_pop_c2c = 1.0 - (0.69404)^50
2000 runs, 25 correct : candidate p_c2c calc = 0.29123, MC = 0.29400; p_c2i calc = 0.70877, MC = 0.70600
2000 runs, N=50, u=0.05000, K=27, C=25, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.70877, MC = 0.70712 p_pop_c2c = 1.0 - (0.70877)^50
2000 runs, 26 correct : candidate p_c2c calc = 0.27721, MC = 0.27650; p_c2i calc = 0.72279, MC = 0.72350
2000 runs, N=50, u=0.05000, K=27, C=26, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.72279, MC = 0.72154 p_pop_c2c = 1.0 - (0.72279)^50
2000 runs, 27 correct : candidate p_c2c calc = 0.26386, MC = 0.25950; p_c2i calc = 0.73614, MC = 0.74050
2000 runs, N=50, u=0.05000, K=27, C=27, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.73614, MC = 0.73585 p_pop_c2c = 1.0 - (0.73614)^50
2000 runs, 28 correct : candidate p_c2c calc = 0.25116, MC = 0.25250; p_c2i calc = 0.74884, MC = 0.74750
2000 runs, N=50, u=0.05000, K=27, C=28, p_pop_c2c calc = 1.00000, MC = 1.00000 Proportion of candidates w/C2I bases calc = 0.74884, MC = 0.74540 p_pop_c2c = 1.0 - (0.74884)^50
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The 1987 video showed all the candidates, not just the best candidates per generation, which is why it is obvious that there never was any "latching" going in in the program: the complete set of candidates shows no "latching", and there is no expectation that the best candidates would show a change of a correct base.
Onlookers may note the weaseling of Mullings in trying to evade the clear conclusion that he cannot bring himself to admit error.
ETA: slight clarification and a little snark.
Edited by Wesley R. Elsberry on Mar. 20 2009,13:15
-------------- "You can't teach an old dogma new tricks." - Dorothy Parker
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