Monthly Archives: March 2013

The Discontinuous Mind, Now and Then

Richard Dawkins trashed Darwinian evolution in an essay recently posted on his website (  Now, in 2013, he claimed that gradualism in Darwinian evolution generates the intermediates between species as a continuous spectrum, which no longer exists due to extinction of the intermediates.  Way back in 1991 he demonstrated that gradualism in Darwinian evolution generates gaping discontinuities between species; that due to gradualism most intermediates are never generated.  Dawkins was right back then in 1991, although he didn’t realize what he was demonstrating.  He is wrong now in 2013.  Throughout the intervening decades Dawkins never did understand the terminology of Darwinian evolution (random vs. non-random; efficiency vs. probability) and the role of gradualism in stages consisting of random mutation and natural selection.

In 2013, Dawkins identified many ordered sequences as differing in degree, not kind, including the ordered sequences of biological species.  He noted that it would be invalid to introduce an arbitrary discontinuity into such a sequence, labeling the resultant dichotomy as two kinds when differences are merely of degree.

Dawkins is legitimately expanding the narrow definition of a continuous variable.  An example of the narrow definition would be that of the continuous variable, improbability.  It would be invalid to identify a point within the continuous range of improbability, from 0 to 1, demarcating values greater than the arbitrary point, as prohibitive values, and values less than the point, as non-prohibitive.  There cannot be two kinds of improbability because improbability is a continuous variable over its range of definition, where values differ from one another by degree, not kind (See the DES Journal, link: Volume LVII Fall 2012 Number 2, pages 64-71, “What is modern in the new atheism? – The inference of probability”, the section entitled, ‘Imposing an arbitrary extra-mathematical numerical limit on probability’, page 67).

An example of a logically defined, ordered sequence to which Dawkins is expanding the concept of continuity is the set of integers from 0 to 29.  There are no gaps or discontinuities in the ordered set.  A point could be inserted between 9 and 10, demarcating single digit integers from double digit integers.  However, this would be superficial.  All elements of the set fundamentally differ from one another by degree, not kind.  The artificial character of the dichotomy can be seen in eliminating it by designating the integers, 0 to 9, as 00 to 09.  Even for the set of just two integers, 00 and 29, the two elements differ by degree and not by kind in spite of the gap or discontinuity in this set when compared to the logical set of all 30 integers.  If we came across a hat containing two ping pong balls, labeled, 00 and 29, there would be no reason to assume that ping pong balls of the logical intermediates, 01 to 28, actually existed.  Nevertheless, 00 would differ from 29 by degree, not kind, in spite of the gaping discontinuity of the 28 intermediates.

In his 2013 essay Dawkins suggests another example of a logical, ordered sequence, namely, that of two species and their biological intermediates.  He cites two such sequences: (1) modern man and his common ancestor with the modern pig and (2) that common ancestor and the modern pig.  Based on these logically ordered sequences, modern man and the modern pig differ by degree, not by kind.  According to Dawkins, the intermediates were generated due to the gradualism of evolution, but no longer exist due to extinction.  Dawkins does not criticize the Discontinuous Mind, for failing to acknowledge the logical intermediates.  He criticizes the Discontinuous Mind for failing to realize that the intermediates, as a continuous set, were materially generated due to the gradualism of Darwinian evolution.  By this stance, Dawkins thoroughly trashed Darwinian evolution.

Moreover, in 1991 (, minute 4:25) Dawkins had demonstrated that the gradualism of Darwinian evolution actually introduces gaping discontinuities into the materially generated set of intermediates when compared to the logical, ordered sequence of biological mutations.  For example, Darwinian evolution would virtually require the generation of all intermediates between man and his common ancestor with the pig, but only if the Darwinian evolution of man from that ancestor occurred in a single evolutionary cycle.  In a single cycle, not only would virtually all intermediates be generated, but man would be the direct offspring of the common ancestor.  Gradualism by stages in Darwinian evolution not only eliminates the direct generation from the common ancestor, but eliminates also the generation of most of the intermediates.  Gradualism in Darwinian evolution requires gaping discontinuities, or if you will, missing links.  Dawkins demonstrated this dramatic efficiency in mutations due to gradualism in 1991.

Dawkins chose to demonstrate this dramatic efficiency due to gradualism in Darwinian evolution using, for the sake of simplicity, a model non-random mutation.  For illustration, Dawkins chose three mutation sites of six mutations each.  A single cycle of Darwinian evolution with non-random mutation would require the generation of the entire ordered sequence of 216 mutations (6 x 6 x 6).   This would be the two endpoints and the 214 intermediates.  Dawkins then compared this with gradualism by stages in Darwinian evolution.  The replacement of one cycle, involving all three sites, with three cycles, each involving a single site, would decrease the number of different mutations generated from 216 to 18, i.e. six different mutations per site.  These 18 mutations would be the two endpoints and only 16 of the 214 different intermediates.  Thus, gradualism in Darwinian evolution introduces a dramatic efficiency in generated mutations, reducing the number in this illustration from 216 to 18.  It thereby introduces gaping discontinuities in the generated set when compared to the logical set of the 216 sequentially ordered intermediate mutations.

By Dawkins’ own demonstration it is not the Discontinuous Mind, which sees discontinuities where there are none.  Rather discontinuities do exist and are an essential attribute of Darwinian evolution due to its gradualism.  Gradualism produces dramatic discontinuities in the materially generated sequence when compared to the logical, ordered sequence of intermediate mutations.

How could Richard Dawkins demonstrate in 1991 that gradualism in Darwinian evolution increases the efficiency of mutation by riddling the ordered spectrum of intermediates with discontinuities and then in 2013 claim that gradualism generates the ordered spectrum of intermediates as a continuum without discontinuities?  The answer is that in the fog of Dawkins’ world there is no clear understanding of Darwinian evolution and its terminology.  Contradictions morph into compatibilities and vice versa.  In 2013 Dawkins analyzed the dictionary meaning of gradualism and concluded that gradualism in Darwinian evolution required the full spectrum of intermediates without discontinuities.  In 1991 he demonstrated, within the context of Darwinian evolution, that gradualism increases the efficiency of mutation by introducing discontinuities.  However, such was not the conclusion which he drew from his demonstration.  Rather than an increase in the efficiency of mutation, Dawkins drew the conclusion of an increase in the probability of evolutionary success.  Dawkins was oblivious to the fact that the probability of success was 100% in his illustration lacking random mutation.  That is 100% for the single cycle of 216 mutations and 100% for the series of three sub-cycles of 18 mutations.  In the fog of Dawkins’ world there is no distinction between efficiency and probability.  Similarly in Dawkins’ world, there is no understanding of the concepts of continuity and discontinuity in the context of Darwinian evolution.

A die is a cube of six faces that are marked with the ordered sequence of the six integers, 1 through 6.  The mutations of the face of a die are the six integers.  This set of mutations, which includes one copy of each of the six integers, is a set of non-random mutations.  The random mutation of a die is simulated by rolling it.  No matter how many rolls, the resulting set of random mutations cannot be guaranteed 100% to include at least one copy of any one of the integers, e.g. the integer 6.  The probability of including at least one copy of 6 in six random mutations is 66.5%, not 100%.

In 1991 for illustration, Dawkins used a lock dial of six positions, i.e. six non-random mutations, rather than a die of six non-random mutations.  Dawkins mistook the six non-random mutations for random mutations, calling them a maximum of six tries.  He did not identify, as efficiency, the efficiency of gradualism, which efficiently eliminates the generation of most of the intermediates.  He identified the efficiency as ‘smearing out the luck’.  He was unaware that his example of 216 mutations and 18 mutations were sets of non-random mutations.  Having confused non-random with random, Dawkins went on to confuse efficiency with probability or luck.  Then in 2013, he went on to make it evident that he completely misunderstands the role of gradualism in Darwinian evolution.  He did so by confusing the complete and ordered set of mutations defined by a single cycle of Darwinian evolution with the set of mutations defined by the equivalent series of sub-cycles.  He was totally unaware of the gaping discontinuities in the set defined by sub-cycles.

It is evident from his 1991 lecture, his 2006 book, The God Delusion, pages 121-122, and his 2013 blog post that Dawkins does not understand the role of gradualism in Darwinian evolution (In the book reference, he labels the gradualism of sub-cycles of evolution ‘natural selection’, when natural selection is also present in the main cycle being replaced!).  He does not understand the terminology of Darwinian evolution.  He does not understand Darwinian evolution.  Yet, it is not entirely his fault.  No doubt, throughout the course of his education, he was not taught the meaning of the terminology of Darwinian evolution.  The terminology was left in the fog of vague impression.  Consequently, when in 2012, Dawkins was asked, “Could you explain the meaning of non-random?” ( minute 38:55), Dawkins replied, “Of course, I could.  It’s my life’s work.”  However, he did not explain the meaning of non-random or random.  He merely used the terminology in the usual and adequate outlining of Darwinian evolution as random mutation (random selection) in the generation of variants and natural selection (non-random selection) in the differential survival of the generated variants.  He did not explain the meaning of the terminology because he has never given it a second thought.  Vague impressions of the concepts embodied by the terminology of Darwinian evolution were enough for his teachers.  Vague impressions are enough for Richard Dawkins and others of an impressionable mind.