Zeno's Paradox and the Creationist Demand for Transitional
Forms
By Glenn R. Morton
Copyright 2001 Glenn R. Morton
This may be freely distributed so long as no chances are made and no monetary
charge is assessed.
http://home.entouch.net/zeno.htm
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One might not think of modern anti-evolutionary apologists as
having much in common with ancient Greek philosophers, but they do. What this
paper will suggest is that they, like Zeno, argued for a particular
viewpoint by creating an absurdity. Zeno believed his teacher Parmenides.
Parmenides taught that sense data was an illusion. What you see isn't real. He
taught that there was no change in the world, no multiplicity of objects. Being
was one and all being was unchanging.
Zeno (495-430 BC) is famous for
several paradoxes which he invented in support of Parmenides position. While they sound a bit odd to the
modern ear, they are in reality quite fundamental in the questions they raise
about reality. Take the paradox of the race. In this paradox, an
well-oiled, muscular Greek athlete is attempting to run from the starting line
to the finish line. In order to accomplish this, he must first run to the
half-way point of the course. And once there, he must run to the 3
quarters point of the race. And after that he must somehow arrive
successively at the 7/8ths, 15/16ths,31/32nd... point in succession.
Indeed, this poor athlete must traverse an infinity of points just to finish the
race. No matter how close our oily friend is to the finish line, he still
has to run half the distance remaining before he can finish the race. Big
problem--an infinity of points to traverse. But turning the problem around
leads to the difficulty that our racer can't even start the race. In order
to get to the 50 percent mark, he must first get to the 25 percent. And to
get there he must manage to crawl to the 12.5 percent mark. And so on. To
move the first angstrom, he must somehow be able to move the first half an
angstrom. Obviously our racer has a problem.
Now it is not difficult to see that Zeno's paradox doesn't
apply to real life. Why? Because the mathematical laws which are used in
Zeno's paradox--infinite divisibility of space--does not happen. It is
clear from the fact that Zeno's demonstration that infinite divisibility
requires no motion combined with the observation that athletes actually
finish races that there comes a point in the division process in which the
distance to the finish line is so small that it can no longer be divided. Thus,
this paradox hints at the quantization of space, the famous del X of
Heisenberg's uncertainty principle. While Zeno didn't come to that obvious
conclusion, it is one mathematical way out of the paradox.
Similarly, Zeno presented a paradox that said that our
athlete could not beat a tortoise. Give the tortoise a head start on our
swift athlete. In order to pass the tortoise, the runner must first reach
the point where the tortoise started from. But by the time our
muscle-bound but inept hero has gotten there, the tortoise isn't there anymore.
He has moved a bit. So in order to pass the tortoise, the muscleman must now run
to the place where the tortoise is now, but once again, the tortoise has already
moved and the athlete can continue this forever and never catch up with the
tortoise. Both of these paradoxes show that the continuum doesn't exist. Space
is not equally divisible.
But assume that a minimum divisible distance does apply (call
it a min), and we now have our slug, the athlete and a photon of light racing
across the distance of one min. Space is indivisible, if one has these
three objects moving a distance of one min, then how on earth can it be
said that the photon is faster than the athlete and the athlete is faster than
the slug? Afterall, the three racers must all start and end at across one
indivisible distance. Surely then, they all move the same speed!
This variation of Zeno's Achilles paradox clearly hints that time is not the
same for each of the three objects moving at three different speeds. Only in
that manner can the light get across the minimum distance in a faster
time. Alternatively, it could also hint at the fact that the minimum
distance isn't the same for the three objects moving at three different
speeds. One is amazed at how close Zeno was to leading the world to an
understanding of a quantized world with a dilatable time and
distance.
Now, what does this have to do with the creationist cry for
transitional forms? Lots. Zeno used these and other paradoxes to claim
that there was no motion, no change. All being was one. What is amazing is
that the young-earth creationists in their demand for an infinite series of
transitional forms are arguing exactly like Zeno, arguing that there is no
change in the history of the world because the biological world should be
infinitely divisible. And like Parmenides, the anti-evolutionists act as if
observational data which today we call scientific data, is illusory. This
is what the anti-evolutionists are doing. They are playing the same
kind of Zeno game only with biology. They cry for 'gradual' evolution with an
infinity of transitional forms. Henry Morris shows this Zeno-tendency when
he writes:
"There ought to be a multitude of transitional forms in the fossil
record-in fact they should all be transitional forms!
"
"The
creationist, on the other hand, expects to find transistional forms. He
expects to find essentially the same situation as in the present world--that is,
much variation within kinds but clear-cut gaps between kinds, with also much
evidence of atrophy and extinction. And
what is the actual case in the fossils? The fossil record confirms explicitly the predictions of the
creationist."(1)
So
when the creationists find that the the world is quantized, even biologically,
they, like Zeno, conclude equivalently, that there can be no change.
Phillip Johnson wrote:
"In
short, if evolution is the gradual, step by step transformation of
one kind of thing into another, the outstanding feature of the fossil record is
the absence of evidence for evolution.
(2)
Phillip
Johnson says:
"Fossil
experts like Stephen Jay Gould sometimes distinguish between
"evolution" and "gradualism," primarily because they are
trying to square the former with a the fossil record does not reflect a pattern
of gradual transformations, but evolution has to be gradual when it is employed
to explain how an unintelligent process assembled all that complex genetic
information." (3)
An
amazing contradiction to the infinite series argument advocated by these people
is found in teratology, the mutants and misdeveloped animals that occur all the
time. A toad was found with its eyes on the roof of its mouth. There was no
gradual series of toad ancestor where the eyes gradually got lower on its face,
finally reaching the lips and then being found successively on the inside of the
lip, on the outside of the teeth, on the inside of the teeth and finally to rest
on the upper part of the mouth of this toad. (And yes, the toad was found living
fat and happy in the wild. He wasn't bothered by his unusual placement of his
eyes.) The change from the eyes on the top of the head to the interior of the
mouth occurred in one generation. The change was a quantum jump. A creationist
might demand an infinite series of forms connecting this toad to normal toads or
claim that this toad was a direct creation because one can't connect him via a
gradual series as I described with other toads.(4)
Similarly,
it has been shown that only 8 mutations are required to change a species of
Monkeyflower which attracts hummingbirds into a form that has a totally
differently shaped and colored flower which attracts bumblebees. The article
says (a QTL is a quantitative trait loci on a chromosome):
"Our mapping experiments show that for each of
eight-floral traits likely to play a role in reproductive isolation there is at
least one major QTL accounting for more than 25% of the phenotypic variance.
This finding suggests that the evolution of reproductive isolation may involve
genes of large effect and therefore that speciation may occur rapidly.
"The floral syndrome associated with hummingbird
pollination is found in 18 families and 39 genera in the flora of western North
America, and in many cases has evolved from bee-pollinated ancestors. One
plausible scenario for the initial steps in the evolution of hummingbird
pollination in Mimulus would include a sequence of three major mutations
affecting pollinator attraction, reward and efficiency. A mutation at the yup
locus causes carotenoid pigment deposition through the flower, reducing
attractiveness to bumblebees by eliminating contrast between the petals and
nectar guides. A second mutation at the major 'reward' QTL leads to greatly
increased nectar volume and visitation by hummingbirds. A third mutation at the
major QTL for pistil length improves the efficiency of pollen deposition by
hummingbirds. This hypothesis for the evolution of hummingbird pollination is
testable in part by introgressing the M. cardinalis allele at each major QTL
into a M.lewisi genetic background (singly and in combination), followed by
assessment of pollinator visitation and its fitness consequences in
nature."(5)
The
fact that biological systems, like everything else, is quantized, undercuts
Michael Behe claim that complex systems can't develop gradually. He writes:
"An
irreducibly complex system cannot be produced gradually by slight, successive
modifications of a precursor system, since any precursor to an irreducibly
complex system is by definition nonfunctional. Since natural selection requires
a function to select, an irreducibly complex biological system, if there is such
a thing, would have to arise as an integrated unit for natural selection to have
anything to act on."
Of
course gradual things don't create complex systems. Zeno's paradox shows
that all things are quantized. What the creationists are missing is
quantization in nature that requires a certain jump between two states of
being. What the Creationists don't want their laity to realize is that
they are arguing in the same fashion as Zeno, who was also defending a lost-cause position--that there was no motion and that there was no multiplicity of
things in the universe. Today creationists use Zeno's argument to demand
something, equally false, that there was no change between species.
Creationists are Zeno's children, demanding a continuum of biological change which is nowhere to be found in nature.
This certainly would evade Zeno's paradox if distance were infinitely
divisible. But Zeno had no knowledge of infinite sums. It is most probable that
he was thinking in terms of an infinite set of actions, which would require an
infinite time. But as we know today space is not infinitely divisible.
Heisenberg's principle shows that if a particle is localized in a very, very
small area, one has no idea of its momentum which is related to velocity. To add
things up as suggested leaves the momentum undefined.
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References
1.
Henry
M. Morris, Creation and the Modern Christian, (El Cajon, California:
Master Book Publishers, 1985), p. 29
2.
"Darwinists Squirm Under Spotlight: Interview with Phillip E. Johnson
",Citizen
Magazine, January 1992 http://www.arn.org/docs/johnson/citmag92.htm
4. For
a look at the toad see Nature Feb. 2, 1995, p. 398
5. H.D. Bradshaw Jr., S. M. Wilbert, K. G. Otto and D. W.
Schemske, "Genetic Mapping of Floral Traits Associated with Reproductive
Isolation in Monkeyflowers (Mimulus)," Nature, 376 Aug. 31, 1995, p. 765
cited on the internet at http://nsmserver2.fullerton.edu/departments/chemistry/evolution_creation/web/