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The following section of quotes is from Alexander Mebane's 
"Darwin's Creation Myth", which I regard as the best and most easily read
book on evolution currently available.  What is being discussed is the
rationale for viewing macroevolutionary jumps (not abiogenesis) as flatly
impossible on probabilistic and statistical grounds.

"There is an obvious analogy here to the observed impossibility of 
"transmuting" one element into another by chemical
reactions- a process that those old chemical Darwinists, 
the alchemists, too optimistically imagined to be feasible. 
We now know that what is crucially lacking in that case Is energy: 
reaction temperatures even of thousands of degrees can only knock about the
outer electrons of an atom, they are far too feeble to perturb 
its nucleus. In the genetic case, however, the energy of
microevolution does suffice to perturb and alter the DNA code, 
which is the reaction required to bring about inheritable genetic
changes; what is lacking this time is not force, but coordlnadon.

"Although gross bodily alterations of many kinds certainly can be
induced by even a single accidental mutation, the resulting new varieties
will hardly ever be viable ones. To produce a viable new life-form
that is more radically distinct than a variety, a single mutation
will not suffice: a whole group or "ensemble" of cooperative changes,
in several genes, must be simultaneously introduced, so as to ensure
that the novelty will prove to be a workable one.   *

"And these coordinated changes are just what accidental knocking-about
is inherently unable to provide, because chance events are subject
to stringent probability limitations, which make any appreciable
degree of workable complex change essentially impossible for them
to achieve.

"To see for yourself how readily these improbability barriers arise,
let us inspect, as a concrete example, some very simple imaginary
case. We will posit the existence of some simple organism whose meaningful
DNA totals only 10^4 (ten thousand) units (no real one is that short);
and we will take it as known that a certain set of only five base-
changes in that genome will be sufficient to generate a new, viable species.
What is the chance of producing that set by microevolution-that is,
by purely random mutations?

"Easy enough to find the answer: For the first "shot", there are 5
chances in 10,000 of hitting one of the five required base-positions;
when that has been achieved, the next shot must hit one of the four
remaining target-positions. and so on: thus, to get all five correctly,
the chance is     5x4x3x2x1 / (10^4)^5 , or 120/10^20,
slightly more than one chance in 10^18 (a billion billion.) - However,
we have not yet allowed for the fact that, at each of the five sites,
three different base-substitutions are possible; and since it seems
reasonable to believe that only one of these three will be "workable",
we should multiply the above result by 1/3^5, or 1/243, so that the true
probability of success is only "one in 200 billion billion".

"Now, how many years would it take to achieve this result by mere
chance, if we assume that in every second, somewhere on earth, a "
trial" zygote of the organism is produced that "just happens" to
carry 5 random mutations? (To make the task an easier one, let us
unrealistically forbid any duplications to occur, so that each trial
will test a different combination.) Since there are 60x60x24x365< =
about 32 million seconds in a year, we divide "200 x 10^18 seconds"
by 32 x 10^6, obtaining "200/32 x 10^12 years": so, trying all the
possibilities at the rate of one per second would be certain to bring
success before 6 x 10^12 (six trillion) years had elapsed. (In reality,
no doubt, about 3 trillion years would probably be found sufficient.)

"Of course, it should be added that a good deal more than one combination
capable of producing some sort of viable new species might in reality
be expected: supposing there were a thousand different possibilities
of success, chance might hope to hit on one of them in only three
billion years. This artificially-simple~ example demonstrates how
very easy it is for prohibitive improbabilities to appear, once we
begin to look a bit more closely at Darwin's airy suggestion that
all observed transformations of life "must have arisen by mere chance".

"But there is something quite vital to this matter that we have not
yet touched upon. The crushing disproof of Goldschmidt's proposed "
natural macromutations" (p- 7 above) is, in fact, valid against any
proposed natural transmutation that is supposed to produce, in one
step, a new form different enough to be unable to breed with its
progenitor (which, it should be recalled, is the usual criterion
of what distinguishes a different species from a different variety.)

"For, if a new-born species is not to perish immediately, a mating
pair of specimens-an "Adam and Eve" must somehow be supplied-and
this requirement squares the improbability! Any such natural. or
chance, sudden species-origin, is by this unfulfillable requirement
rendered not merely improbable but impossible.   *

"Darwin had originally circumvented this formidable obstacle by postulating
that all changes must be quite small ones, so that intersterility
will develop only gradually, never all at once: new varieties must "
pass insensibly into a (viable) new species. We can now perceive
that-because of the intersterility problem-these Darwinian "gradual
transitions" must, in fact, be a necessary and indispensable feature
of any theory of species-origin by natural means.

"Now, doesn't it seem, at first sight, that this now-recognized necessity
for dividing the transition to a new viable species into several
short jumps, rather than one long one, might resolve the difficulty
of the prohibitive improbability of the single long jump? It does,
indeed, alter the case: for it makes the transition not merely improbable,
but impossible. In our simple example of the five required mutations,
let us propose to acquire them seriatim, in three "easy stages":
first, just one (and let us grant that this small change actually
produces a viable new variety); then two (any two) of the four still
needed, and finally the two remaining-so there we are! But we aren't; 
for the second step leads to non-viability. Suppose you had to
jump a chasm eight feet wide, and said to yourself "No problem! I'll
just make it a gradual transition, by taking two four-foot jumps"?

"If a certain properly-coordinated set of five mutations will succeed
in producing a viable new organism, does that imply that a set of
just three of them - 3/5 of the way to the goal-will also be viable?
At this point the faithful Darwinist will explode in rage, declaring
that "of course" it must be "solid ground" all the way from one viable
species to another! But that is just where he parts company with
reality, for it is not. As Cuvier foretold, as the dog-breeders told
Darwin, and as the Drosophila-breeders confirmed in the twentieth
century, a "half-finished" new species is simply not a viable organism.
It is for that fundamental reason-not merely because of the Jenkin
effect-that, in the real world, species are found to remain "fixed":
because Darwin's gradual microevolutionary route to macroevolution
is simply not a passable one.