Smearing Out the Luck

My previous post (Ref. 1), may have given the false impression that no one agreed with Richard Dawkins’ explanation of smearing out the luck of Darwinian evolution. This post hopefully corrects that impression.

Dawkins has stated “. . . natural selection is a cumulative process, which breaks the problem of improbability up into small pieces. Each of the small pieces is slightly improbable, but not prohibitively so.” (Ref. 2) What does this mean? We can tell from his illustrations (Ref. 3 – 4).

It would seem that Dawkins is saying that the probability of the generation of a given number by a random numbers generator, is increased by the introduction of natural selection. This doesn’t fly. Natural selection doesn’t generate mutations. It culls mutations. It permits only copies of one particular mutation to survive. It doesn’t affect the generation of the survivable mutation from which arises its probability.

Consider a single mutation site defining six different mutations. The six faces of a die define six different mutations. In this example of a total of six defined mutations, the probability of the random generation of at least one copy of the number, 6, for a total of one randomly generated mutation is 1/6 = 16.7%, with or without natural selection. Similarly the probability of the random generation of at least one copy of 6 for a total of six randomly generated mutations is 80.6%, with or without natural selection. In Darwinian evolution natural selection has no effect on probability (Ref. 1). It merely eliminates superfluous mutations, whether the superfluous mutations have been generated randomly or non-randomly.

It is apparent that Dawkins is not assessing the role of natural selection, but analyzing the replacement of a single cycle of random mutation and natural selection with several sub-cycles. In Ref. 3, he compares a single cycle affecting three mutation sites of six mutations each to three sub-cycles, each affecting a single site. The replacement of a single cycle with a series of sub-cycles has no effect on probability. Rather, it increases the efficiency of random mutation. Yet, Dawkins does not identify this as efficiency in mutation due to sub-cycles. He calls it ‘smearing out the luck’, as if the probability of success changed from 1/216 to 1/18. Dawkins is comparing 216 non-random mutations to 18 non-random mutations at a probability of success of 100% (Ref. 4).

Some of Dawkins’ reviewers have agreed with him. The Wikipedia review says the comparison is between probabilities of 1/216 and 1/18 (Ref. 5). More remarkably, in referring to a set of twenty-eight mutation sites of twenty-seven mutations each, John Lennox cites a probability of 10^(-31) and one billion mutations for a single cycle compared to the probability and the number of mutations for a series of 28 sub-cycles (Ref. 6). A computer simulation of the sub-cycles reached a probability of 1 in a maximum of 43 mutations per sub-cycle. In accord with Dawkins, Lennox refers to this as drastically increasing the probabilities. Superficially, Lennox’ comparison appears to imply an increase in probability due to the introduction of sub-cycles.

However, the Darwinian algorithm with sub-cycles, as well as this example of it, does not increase probability. In fact, the comparison in Lennox’ example, implies efficiency in the number of mutations due to sub-cycling with no change to the probability. A more appropriate comparison would have been at a probability of 90% for both the single overall cycle and for the series of 28 sub-cycles. This would compare 2.3 x (27)^28, i.e. roughly 2.7 x 10^40 mutations for the single cycle to 4144 mutations for the series of 28 sub-cycles at the same probability of success, namely 90%.. The 4144 mutations are 148 mutations for each of 28 sub-cycles, where the probability of success for each sub-cycle is 99.6%. This yields a probability of 90% for the series of 28.

Contrasting non-random vs random mutation, within the algorithm of Darwinian evolution for a single cycle, also shows that natural selection has no effect upon probability. For non-random mutation, one mutation yields a probability of 1/n. This increases linearly to a probability of 1 as the number of non-random mutations reaches n. Natural selection merely culls the superfluous mutants. Similarly, random mutation starts out at a probability of 1/n with one mutation and asymptotically approaches 1 as the number of random mutations increases. When the number of non-random mutations is respectively, n, 2.3n, 4.6n and 11.5n, then the respective probabilities are 63%, 90%, 99% and 99.999%. Here too, natural selection merely culls the superfluous mutants.

Another common error in the evaluation of Darwinian evolution is to attribute temporal and material constraints to random mutation. Due to the fact that Darwinian evolution is strictly a logical algorithm of random mutation and natural selection, it is not subject to any temporal or material constraints. It is material simulations, not the logical algorithm, which can exceed such constraints. Also, in a material simulation, there is no increase in time or material due to a random mutation compared to a non-random mutation.

There are 52 factorial or 8.06 x 10^67 different sequences of 52 elements. The inverse of this is the probability of any sequence. In a material simulation, how many decks of cards and how long does it take to generate randomly any sequence, if shuffling for five seconds is granted to be a random selection? The answer is one deck and five seconds. Granted this, how many decks of cards and how long would it take to generate a pool of decks of cards containing at least one copy of a particular sequence at a probability of 90%? The answer is 2.3 x 8.06 x 10^67 decks and 5 x 2.3 x 8.06 x 10^67 seconds. If we apply the Darwinian algorithm of a single cycle of random mutation and natural selection, these paired numbers of decks and seconds are required for a probability of success of evolution of 90%. This exceeds by far any practical temporal and material limits. However, if we are content with any value of probability, then we would be content with one random mutation. Natural selection does not affect probability. It merely culls superfluous, randomly generated mutants. If we trust success to just one random mutation, then there is no need for natural selection, while the material and temporal requirements of the simulation are insignificant, namely one deck and five seconds.

Indeed, we must be content with any and every value of probability. I have argued that no value of probability represents a ‘problem of improbability’. To claim that ‘the probability of this outcome is so close to zero that it could not be due to chance’ is a self-contradiction. Of course, I am not claiming that probability is to be accepted as an explanation. Rather, if probability is accepted in any instance as an explanation, then in no instance can it be rejected as an explanation on the basis of its numerical value, irrespective of how close it is to zero. (Ref. 7). Similarly, the acceptance of probability as an explanation is not bolstered by a value of probability closer to 1.

References:
(1) https://theyhavenowine.wordpress.com/2014/04/04/dawkins-on-gradualism/
(2) “The God Delusion”, page 121
(3) “The God Delusion”, page 122
(4) http://www.youtube.com/watch?v=JW1rVGgFzWU minute 4:25
(5) Growing Up in the Universe, Part 3 http://en.wikipedia.org/wiki/Growing_Up_in_the_Universe
(6) “God’s Undertaker Has Science Buried God?” Page 165-167
(7) https://theyhavenowine.wordpress.com/2013/12/30/too-improbable-to-be-due-to-chance/

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