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In its recent decision in Derwin v. State U., the State Supreme Court ordered the State University to award Charles Derwin the degree of doctor of philosophy. Derwin admitted that his case, which he lost in all the lower courts, depended upon one sarcastic statement made in writing by Prof. Stickler of the faculty panel, which heard his defense of his graduate thesis. The bylaws of the University in awarding the degree of doctor of philosophy require unanimous approval of the faculty panel by written yes or no voting. The members of the panel are free to offer verbal or written criticism during and after the defense, but must mark their ballots simply yes or no. However, in casting the lone negative vote, Prof. Stickler wrote in addendum to his ‘No’, “If Derwin and his major advisor were to submit an article for publication reporting the experimental results of Derwin’s thesis, I suggest they submit it to The Journal of Random Results or to The Journal of Darwinian Evolution.”

Derwin’s legal team argued that Stickler violated the university bylaws by adding the written addendum as well as academic decorum by its sarcasm. Further, and most importantly, they argued that Prof. Stickler exposed his own incompetence to judge the thesis by his attempt to belittle Darwinian Evolution. By this Stickler had disqualified himself as a judge of the thesis panel. The State Supreme Court agreed and ordered the State University to award the degree in accord with the university bylaws requiring unanimous approval by the thesis panel. The Court noted that the university bylaws allow for a panel of six to eight faculty members. The panel, which heard the defense of his thesis by Derwin, consisted of seven, including Prof. Stickler. The Court also ruled that the academic level arguments presented in the lower courts by both sides regarding ‘random results’ in general and ‘random mutation’ in the particular case of Darwinian evolution, were simply of academic interest and irrelevant to the legal case.

For their academic interest those arguments are presented here.

Prof. Stickler stated that random experimental results are of no scientific value and that Derwin conceded the results he reported in his thesis could be characterized as random. Stickler argued that even those, who contend that genetic mutation is random, claim that Darwinian evolution is non-random, and therefore scientific, even though their claim is erroneous. Stickler attributed the following quote to Emeritus Prof. Richard Dawkins of Oxford University as his response to the question, “Could you explain the meaning of non-random?” Dawkins replied, “Of course, I could. It’s my life’s work. There is random genetic variation and non-random survival and non-random reproduction. . . That is quintessentially non-random. . . . Darwinian evolution is a non-random process. . . . It (evolution) is the opposite of a random process.” (Ref.1).

Stickler stated that Dawkins’ argument that Darwinian evolution is non-random and therefore, scientific, does not hold water. He noted that the pool of genetic mutants subjected to natural selection in Darwinian evolution is formed by random mutation. The pool’s containing the mutant capable of surviving natural selection is a matter of probability. Consequently, the success of natural selection cannot be 100%. Evolutionary success is equal to the probability of the presence of at least one copy of the survivable mutant in the pool subjected to natural selection and is therefore random.

In his rebuttal, Derwin agreed with Stickler that Darwinian evolution was indeed characterized by probability and randomness. However, the universal scientific acceptance of Darwinian evolution indicates that random results are indeed scientific, which he noted was the pertinent issue in the case.

Stickler’s counter argument was to note that Darwinian evolution is based on data consisting of a series of cycles, each cycle consisting of the proliferation of genetically variant forms and their diminishment to a single form. Darwinian evolution explains such cycles by the hypothesis of the random generation of genetic variants and their reduction to singularity by natural differential survival. Stickler claimed the data could also be explained by what he called ‘The inverse Darwinian Theory of Evolution’. The inverse theory explains the same cyclic data of the standard theory, but as the non-random, natural generation of genetic variants by scientifically identifiable material processes and the reduction of this pool of genetic variants to singularity by random, differential survival.

Deciding which hypothesis, if either, was valid would require some ingenuity beyond the stipulated data of the proliferation and diminishment of variant genetic mutations. He noted, however, that the inverse hypothesis would be rejected a priori by the claim that we know at least some of the scientific factors affecting differential survival, so it could not be hypothesized that differential survival was random. This, Stickler claimed, demonstrates that randomness and probability cannot be proffered as a scientific explanation. He said, “If randomness is rejected a priori as scientifically untenable as an explanation of variant survival because differential survival is due to scientific material processes, then randomness must be rejected a priori as scientifically untenable as an explanation for the generation of genetic variants for the same reason. If randomness is sauce for the goose of scientifically variant generation, randomness must potentially be sauce for the gander of scientifically variant survival. In fact it is sauce, i.e. the mathematics of randomness and probability is a tool of ignorance to cover a gap in scientific knowledge. It is in the context of the absence of the scientific knowledge of genetics in the mid-nineteenth century that made it seem plausible at that time to propose ignorance of the scientific knowledge of material processes, that is, to propose random changes, as part and parcel of a scientific theory.”

In response, Derwin noted that quantum mechanics, perhaps the most basic of the sciences, is recognized as founded on probability and therefore randomness. (Ref.2).

References:
1) http://www.youtube.com/watch?v=tD1QHO_AVZA (minute 38:56)
2) https://theyhavenowine.wordpress.com/2014/03/26/quantum-or-wave-dilemma-of-the-imagination/

I was impressed with the lucidity of an essay at Strangenotions.com attributed to one, Chana Messigner (http://www.strangenotions.com/venn-diagram/). She was identified as graduating from the University of Chicago, having majored in mathematics and soon to commence teaching mathematics in high school. I now believe such a person to be purely fictitious.

The essay critiqued the proposal that science and religion cover disparate areas of human knowledge and therefore, by definition, cannot be in conflict. She noted that there are indeed areas of overlap. There would be no means of reconciling even apparent conflicts between science and religion, if the two disciplines have mutually exclusive epistemologies in accord with the premise that they cover disparate areas of knowledge. The epistemological basis of science is admittedly empirical evidence and obviously rational. The epistemological basis of religion is apparently faith and seemingly arational. In the absence of a common epistemology, any conflict must be resolved in favor of science.

This lucid essay was followed by an interview of the alleged Chana Messinger conducted by Brandon Vogt (http://www.strangenotions.com/messinger/). In it the interviewee claimed to be an atheist since reading The God Delusion by Richard Dawkins. A college math major can certainly be an atheist, but not by having read The God Delusion. That book is chock full of mathematical errors some of which are hilariously comical. Here are two.

The core argument of The God Delusion is that there is a mathematical solution to the improbability of evolution in a one-off event, but there is no mathematical solution to the improbability of God. When Dawkins discusses probability in the context of evolution, he is referring to mathematical probability, the fractional concentration of an element in a logical set, where the range of its definition is zero to one. When he discusses probability in the context of the existence of God, he is referring to the subjective numerical ranking on a scale of zero to one of an individual’s subjective certitude of the truth of a premise. Dawkins’ argument is based on equivocation in use of the word, probability.

Dawkins thinks his argument is mathematical. The mathematical probability of God is nearly zero and the mathematical probability of non-God (the improbability of God) is nearly one. However, when he “take(s) the idea of a spectrum of probabilities seriously” (p 50, The God Delusion), he rates theism at a probability of one, i.e. 100%, and atheism at a probability of zero! Throughout the rest of his book it is the other way round. The central thesis of his book is that the improbability of God is nearly 100% and the probability of God is nearly zero. Apparently in the rest of the book, in which he argues in favor of his thesis, Dawkins is not taking “the idea of a spectrum of probabilities seriously”.

More hilariously, having identified theism at a probability of plus one, he places its opposite, atheism, not at minus one, but at zero. Consequently he has no place in his spectrum for agnosticism, which should be zero, half-way between the plus one ranking of theism and the opposite ranking of atheism at minus one. When Dawkins realizes that there is no place for agnosticism in his spectrum, he says that if it is practical agnosticism, it can be shoehorned it in at +0.5. Dawkins identifies agnosticism in practice as having a middling opinion on the existence of God. The midpoint +0.5, is labeled a ‘temporary zero in practice’. However, he says this won’t do for agnosticism in principle. Agnosticism in principle would be the claim that the existence or not of God is humanly unknowable or that the premises, that ‘God exists’ and that ‘God does not exist’, have no meaning. Dawkins, to his credit, refuses to identify +0.5 as a ‘permanent zero in principle’. Even after discussing the fact that there is no true zero (no permanent zero in principle) in his spectrum of zero to one, poor Richard could not figure out the reason why. He doesn’t realize that his spectrum lacks a true zero due to his high school level mathematical blunder of identifying zero as the opposite of plus one.

Dawkins’ spectrum of probabilities has nothing to do with mathematical probability or with the objective truth or falsity of the premises. It is a scale for expressing the degree of certitude of one’s personal opinion. Perhaps Dawkins should be excused, because it is not easy to keep these distinctions clearly in mind due to the terminology employed. When Dawkins refers to the improbability of God, he considers it comparable to the improbability of the assembling of a Boeing 747 by a hurricane sweeping through a junkyard. (p 113, The God Delusion). Such improbabilities have nothing to do with mathematical probability or objective truth. These improbabilities do not identify a logical set of elements in which one or more of the elements is tagged ‘God’ or tagged ‘Assembling of a Boeing 747 sweeping through a junkyard’. In context, these probabilities apply solely to a scale for ranking the certitude of one’s personal opinion of the truth of premises. Yet, Dawkins claims, “I can’t get excited about personal opinions” (p 108, The God Delusion).

Of his many other blunders in math, another hilariously comical one is his claim that a big piece of improbability can broken up into smaller pieces (p 121, The God Delusion). That means that the complementary little piece of probability is thereby broken up into bigger pieces! Tied into this is his inability to see the distinction between an increase in the probability of success of natural selection and an increase in the efficiency of random mutation. That, however, is a more subtle mathematical error than indicating that a little piece of probability can be broken up into bigger pieces.

Mathematical probability is the fractional concentration of an element in a logical set. The probability of the total of elements in a set is one. A set may be divided into nested subsets. Consequently, the probability of one for the entire set can be broken up into smaller probabilities, which can be broken up into smaller probabilities corresponding to the nested subsets. A deck of playing cards would serve as an example. The probability of a card is 52/52 = 1. The thirteen probabilities of rank, each of 1/13, add up to one. That doesn’t hold for the thirteen improbabilities of rank, each of which is 12/13. Nested within rank, the probability of rank and suit is 1/52. These four probabilities of 1/52 within each rank add up to 1/13. In contrast, the probabilities with which Dawkins is dealing in Darwinian evolution are factors which are multiplied to form a product, the overall probability. They are not parts which are added to form a sum, the whole probability. Darwinian ‘pieces’ of probability don’t add up. Similarly, their product can’t be broken up into bigger ‘pieces’. Of course, I should not refer to Darwinian ‘pieces’, but rather to Dawkinsian ‘pieces’ of probability and Dawkinsian ‘pieces’ of improbability.

Except for those who plan to teach biology to university students and/or philosophy to the general public, high school students should learn:
1. The opposite of +1 is -1, thereby defining a range of which the mid-point is 0.
2. The arithmetic operations of addition and subtraction are distinct from those of multiplication and division.
3. The word, probability has several disparate meanings two of which are:
a) The fractional concentration of an element in a logical set. The probability of rolling 7 with a pair of dice is a material analogy of the mathematical concept of probability, i.e. the fractional concentration of 7’s, among the logical set of integers consisting of the sums of the outputs of two random numbers generators to the base, 6. That is a probability or fractional concentration of 6/36.
b) The ranking by an individual of the certitude of his opinion of the truth of a premise. For example, consider the premise ‘Grant is buried in Grant’s Tomb’ and its negative form, ‘Grant is not buried in Grant’s Tomb’. Let these have ranks of +1 and -1, respectively. An individual may then express the certitude of his opinion of the truth of these premises. Typically this would consist of two ranks, one for each premise. One individual may be fully convicted that Grant is not buried in Grant’s Tomb. He would place one of his two ranks at -1 for full conviction of the truth of the negative form of the premise and the other at 0 for the null conviction of the truth of the positive form. An individual who was half persuaded by each premise, would place one rank at +0.5 and his other at -0.5. An individual who had no interest and, therefore no opinion, would place both his ranks at 0, indicating temporary indifference in practice. Another individual, who claimed that both premises lacked meaning, would place both his ranks at 0, indicating permanent indifference in principle.

I can readily believe in the existence of an Oxford University Professor of biology as incompetent in high school mathematics as the author of The God Delusion. I cannot believe in the existence of a clear headed essayist named Chana Messinger, who graduated college as a math major and yet who found The God Delusion something other than a comedy of mathematical errors. Chana is purely fictitious.

For other mathematical errors by the author of The God Delusion, see earlier posts on this web site as well as (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/DES_Winter_2010.pdf), “Richard Dawkins’ problem of improbability in The God Delusion: A valid argument for atheism or an error in mathematics?”

For an assessment of the central philosophical concept of the new atheism, see Part 1 (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/1DES_Journal_FALL12F.pdf) and Part 2 (http://deltaepsilonsigma.org/media/delta-epsilon-sigma/Volume-LVIII-Spring2013-Number1.pdf) of “What is modern in the new atheism? – The inference of probability”.

It is not logic, but the bravado of presentation, along with ridiculing those who disagree, that wins arguments.  In arithmetic the probability of a series is the product of the probabilities forming the series.  Nevertheless, e.g., it would be naïve to apply such simple arithmetic to evolutionary biology thereby misunderstanding the power of accumulation of natural selection.  Logic must be crafted to fit the argument.  It is the desired conclusion of an argument, which determines the logic.

Argument One

“The point is that every single one of us is lucky to be alive against hyper-astronomical odds.” http://newsweek.washingtonpost.com/onfaith/panelists/richard_dawkins/2010/02/the_great_tim_tebow_fallacy.html

A human fetus cannot be identified in foresight as the person after birth.   Prior to birth its identity is that of a hyper-improbability indistinguishable from every other hyper-improbability.  Also, it would be illogical to view any event in the series of probabilities in isolation from the overall series of which the end product develops into the eventual person.  Included in the series of events is the decision of the mother not to abort the hyper-improbability.  To point to that decision as determining the existence of the end product in its eventuality as an individual historical person is illogical.  To identify the end product of gestation as anything other than a hyper-improbability, i.e. the arithmetic complement of the arithmetic product of a series of probabilities, is scientifically illogical.

Argument Two

“What is it that makes natural selection succeed as a solution to the problem of improbability where chance and design both fail at the starting gate?  The answer is that 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.  When large numbers of these slightly improbable events are stacked up in a series, the end product of the accumulation is very very improbable indeed, improbable enough to be far beyond the reach of chance.  It is these end products that form the subjects of the creationist’s wearisomely recycled argument.  The creationist completely misses the point, because he (women should for once not mind being excluded by the pronoun) insists on treating the genesis of statistical improbability as a single, one-off event.  He doesn’t understand the power of accumulation.”,The God Delusion, page 121.

The problem of improbability of the mammalian eye as the end product of Darwinian evolution is solved by ignoring the hyper-improbability of the end product of the series of Darwinian events and by focusing on the probability of each Darwinian event in isolation from the probabilities of the other Darwinian events in the series.  By so doing, one is dealing with individual probabilities which are not prohibitively improbable in contrast to the hyper-improbability of the end product.  To identify the end product of evolution as a hyper-improbability, i.e. the arithmetic complement of the arithmetic product of a series of probabilities, is scientifically illogical.