A Mathematician Explains the Irreducible Complexity of Metamorphosis

Granville Sewell

The new documentary Metamorphosis presents, as ENV readers will know, the case for intelligent design in a powerful way. The metamorphosis from caterpillar to butterfly is a spectacular example of “irreducible complexity,” and here is one way of explaining why that’s so.
In my 2000 Mathematical Intelligencer article “A Mathematician’s View of Evolution,” I compared the development of the genetic code of life with the development of a computer program, such as my finite element code PDE2D. I pointed out that the record of PDE2D’s development would be similar to the fossil record, with large gaps where major new features (new orders, classes and phyla) appeared, and smaller gaps where minors ones (new families, genera or species) appeared (see also this short video). I argued,

Whether at the microscopic or macroscopic level, major, complex, evolutionary advances…also involve the addition of many interrelated and interdependent pieces. These complex advances, like those made to computer programs, are not always “irreducibly complex” — sometimes there are useful intermediate stages. But just as major improvements to a computer program cannot be made 5 or 6 characters at a time, certainly no major evolutionary advance is reducible to a chain of tiny improvements, each small enough to be bridged by a single random mutation.

In the real world of biological evolution, or of computer programs, “climbing up Mount Improbable” involves not just taking large numbers of tiny steps upward, but scaling many steep cliffs. You not only have to explain how the giraffe’s neck grew longer, but how the bacterial flagellum developed, with dozens of parts (each essential for function) similar to those of an outboard motor, or how aquatic bladderworts developed their carnivorous traps. 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.

The problem with making this argument, as all who have tried it know, is that Darwinists have very fertile imaginations, they can imagine some alternative uses, some selective advantages, for the individual parts of a bacterial flagellum, or for a partially constructed vacuum chamber before it could catch small animals. No matter what example of irreducible complexity is set before them, they will propose far-fetched functions for 2 or 3 intermediate stages and consider the problem solved. Sometimes they can actually find the intermediate stages in Nature.
But metamorphosis is different. The process of transforming a caterpillar into a butterfly is surely far more complex than anything ever accomplished by man. The information needed to control this process, stored somewhere in the caterpillar’s cells, must be far greater than that stored in any man-made computer program. And explaining how this enormous program arose through many “5 or 6 character” improvements is even more challenging here, because now the intermediate stages are not just useless, they are fatal. Metamorphosis involves the destruction of the caterpillar: the butterfly, with an almost completely new body plan, is constructed from dissolved and recycled tissues and cells of the caterpillar. Now we are not talking about climbing Mount Improbable, we are talking about building a bridge across an enormous chasm, between caterpillar and butterfly. (Ann Gauger and Paul Nelson use this metaphor in the free companion e-book to Metamorphosis.)
Until construction of this extremely long and complicated bridge is almost complete, it is a bridge to nowhere. Unless a butterfly (or another organism capable of reproduction) comes out at the end, the chrysalis only serves as a casket for the caterpillar, which cannot reproduce. Now we do not have to simply imagine uses for not-quite-watertight vacuum chamber traps, we have to imagine a selective advantage for committing suicide before you are able to reproduce, and that is a more difficult challenge!
Of course, if Darwinism fails to explain metamorphosis, we just have to wait for science to come up with an alternative theory; there is no need to resort to intelligent design, which, we are told, is not scientific. Well, we can define science to exclude intelligent design and wait as long as we want, but intelligence will still be the only force of Nature that can look ahead to see a desired function and keep adding useless lines of computer code until the code can perform that function, and it will still be the only force that can guide the development — gradual or not so gradual — of new organs through their initial useless stages.
And it will still be the only thing that can imagine a butterfly as the final product and develop a gigantic code for metamorphosis, through intermediate stages that would produce nothing but the destruction of the caterpillar.