Zeno's Paradox and the Creationist Demand for Transitional Forms

Copyright 2001 Glenn R. Morton. This may be freely distributed so long as no chances are made and no monetary charge is assessed. (home.entouch.net/dmd/zeno.htm)

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.”

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.

Objections Appendix: Some of the initial readers suggested summing the distances as seen at mathacademy.com/platonic_realms/encyclop/articles/zeno_tort.html

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.

Another reader in Feb 2009 who works with continuous systems, at least occasionally disagreed that my conclusion about gradual things not creating complex systems. While I replied to him, he didn't reply back to me, so I will post his objections as best as I can. In some sense he is right because due to the atomization and quantization of every known system, continuums don't actually exist--they are a mathematical item. Fields are quantized, fluids are atomized etc. He did say that continuum math can become chaotic, so in that, I probably do stand corrected above. But if such systems don't exist in nature, one could make the statement more firm.

He more substantively suggested that I was using circular reasoning. He says correctly that an infinitude of events take an infinitude of time if and only if time has a finite lower limit of duration. This runs smack dab into the problem of the reality of time. If time doesn't have a lower limit of duration, then a quite logical argument can be made that time is unreal. The existence of a lower limit of duration is a quite well known quantum effect. It can be seen in the Heisenberg Uncertainty Principle. Del Energy x Del Time <= Planck's constant. Time has a lower durational limit because the energy of the universe is not infinite. Thus, one is not using circular reasoning.

One final criticism is that one should be able to see 3 transitional forms. I would suggest looking at home.entouch.net/dmd/micro.htm where smooth transitional forms are found in plankton.


  • Henry M. Morris, Creation and the Modern Christian, (El Cajon, California: Master Book Publishers, 1985), p. 29
  • “Darwinists Squirm Under Spotlight: Interview with Phillip E. Johnson”, Citizen Magazine, January 1992 http://www.arn.org/docs/johnson/citmag92.htm
  • Phillip E. Johnson, The Storyteller and the Scientist, First Things, Oct. 1996, http://www.arn.org/docs/johnson/behedawk.htm
  • For a look at the toad see Nature Feb. 2, 1995, p. 398
  • 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
  • Michael Behe, “Molecular Machines: Experimental Support for the Design Inference” http://www.arn.org/docs/behe/mb_mm92496.htm
  • cited on the internet at nsmserver2.fullerton.edu/departments/chemistry/evolution_creation/web/

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