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Carnivorous Plants, and Why 0 Really Is Not Equal to 1

Granville Sewell


There is a little mathematics game that people sometimes play. You start with x=0, do some long, complicated algebraic manipulations, and end up with x=1. Since 0 is not equal to 1, you know there must be errors somewhere in the algebra, even before you find them, and before you even look at the mathematics. The game is to find the errors, which are hidden as well as possible.

I have frequently tried to make the point that to not believe in intelligent design, you have to believe that a few fundamental, unintelligent forces of physics alone could have rearranged the fundamental particles on Earth into computers, jet airplanes, science texts, and Apple iPhones, sometimes relating this to the more general statements of the second law of thermodynamics.

Materialists have theories as to how unintelligent forces alone could, over a long period of time, construct Apple iPhones, but there seems to me to be nothing in all of science that is more clear and more obvious than that unintelligent forces cannot construct iPhones. So we can be sure there are errors in their theories, before even looking at the details.

But I have been disappointed to discover that only other mathematicians seem to be impressed by such simple arguments. Mathematicians are trained to value simplicity. When we analyze a complicated problem, we often try to find another perspective from which things are much simpler and clearer. But, understandably, few in the biological sciences seem to accept that it is possible to draw any important conclusions about evolutionary theory without looking at the details of the theory. Most seem to be interested only in more complicated arguments, which require more knowledge of biology and biochemistry to understand.

So in Section 5.3 of my book In the Beginning: And Other Essays on Intelligent Design, I tried to point out some of the problems in the details of the Darwinists’ proof that 0 really is equal to 1:

Consider, for example, the aquatic bladderwort, described in Plants and Environment (Daubenmire 1947):

“The aquatic bladderworts are delicate herbs that bear bladder-like traps 5mm or less in diameter. These traps have trigger hairs attached to a valve-like door which normally keeps the trap tightly closed. The sides of the trap are compressed under tension, but when a small form of animal life touches one of the trigger hairs the valve opens, the bladder suddenly expands, and the animal is sucked into the trap. The door closes at once, and in about 20 minutes the trap is set ready for another victim.

In a Nature Encyclopedia of Life Sciences article on carnivorous plants, authors Wolf-Ekkehard Loennig and Heinz-Albert Becker acknowledge that “it appears to be hard to even imagine a clear-cut selective advantage for all the thousands of postulated intermediate steps in a gradual scenario…for the origin of the complex carnivorous plant structures examined above.”

The development of any major new feature presents similar problems, and according to Lehigh University biochemist Michael Behe, who describes several spectacular examples in detail in Darwin’s Black Box, the world of microbiology is especially loaded with such examples of “irreducible complexity.”

It seems that until the trigger hair, the door, and the pressurized chamber were all in place, and the ability to digest small animals, and to reset the trap to be able to catch more than one animal, had been developed, none of the individual components of this carnivorous trap would have been of any use. What is the selective advantage of an incomplete vacuum chamber? To the casual observer, it might seem that none of the components of this trap would have been of any use whatever until the trap was almost perfect, but of course a good Darwinist will imagine two or three far-fetched intermediate useful stages, and consider the problem solved. I believe you would need to find thousands of intermediate stages before this example of irreducible complexity has been reduced to steps small enough to be bridged by single random mutations — a lot of things have to happen behind the scenes and at the microscopic level before this trap could catch and digest animals. But I don’t know how to prove this.

I am further sure that even if you could imagine a long chain of useful intermediate stages, each would present such a negligible selective advantage that nothing as clever as this carnivorous trap could ever be produced, but I can’t prove that either. Finally, that natural selection seems even remotely plausible depends on the fact that while species are awaiting further improvements, their current complex structure is “locked in,” and passed on perfectly through many generations (in fact, errors are constantly corrected and damage is constantly repaired). This phenomenon is observed, but inexplicable — I don’t see any reason why all living organisms do not constantly decay into simpler components — as, in fact, they do as soon as they die.

When you look at the individual steps in the development of life, Darwin’s explanation is difficult to disprove, because some selective advantage can be imagined for almost anything. Like many other schemes designed to violate the second law, it is only when you step back and look at the net result that it becomes obvious it won’t work.

For more, see my recent article at Evolution News, “Why Should Evolutionary Biology Be So Different?” — an excerpt from my new book, Christianity for Doubters.
Photo: Traps of aquatic bladderwort, by Michal Rubeš [CC BY 3.0 cz], via Wikimedia Commons.

Granville Sewell

Granville Sewell is professor of mathematics at the University of Texas El Paso. He has written four books on numerical analysis, most recently Solving Partial Differential Equation Applications with PDE2D, John Wiley, 2018. In addition to his years at UTEP, has been employed by Universidad Simon Bolivar (Caracas), Oak Ridge National Laboratory, Purdue University, IMSL Inc., The University of Texas Center for High Performance Computing and Texas A&M University, and spent a semester (1999) at Universidad Nacional de Tucuman on a Fulbright scholarship, and another semester (2019) at the UNAM Centro de Geociencas in Queretaro, Mexico.