The American Spectator

In the current debate over “Intelligent Design,” the strongest argument offered by opponents of design is this: we have scientific explanations for most everything else in Nature, what is special about evolution? The layman understands quite well that explaining the appearance of human brains is a very different sort of problem from finding the causes of earthquakes; however, to express this difference in terms a scientist can understand requires a discussion of the second law of thermodynamics.

The first formulations of the second law were all about heat: a quantity called thermal “entropy” was defined to measure the randomness, or disorder, associated with a temperature distribution, and it was shown that in an isolated system this entropy always increases, or at least never decreases, as the temperature becomes more and more randomly (more uniformly) distributed. If we define thermal “order” to be the opposite (negative) of thermal entropy, we can say that the thermal order can never increase in a closed (isolated) system. However, it was soon realized that other types of order can be defined which also never increase in a closed system. For example, we can define a “carbon order” associated with the distribution of carbon diffusing in a solid, using the same equations, and through an identical analysis show that this order also continually decreases, in a closed system. With time, the second law came to be interpreted more and more generally, and today most discussions of the second law in physics textbooks offer examples of entropy increases (order decreases, since we are defining order to be the opposite of entropy) which have nothing to do with heat conduction or diffusion, such as the shattering of a wine glass or the demolition of a building.

It is a well-known prediction of the second law that, in a closed system, every type of order is unstable and must eventually decrease, as everything tends toward more probable states. Not only will carbon and temperature distributions become more disordered (more uniform), but the performance of all electronic devices will deteriorate, not improve. Natural forces, such as corrosion, erosion, fire and explosions, do not create order, they destroy it. The second law is all about probability, it uses probability at the microscopic level to predict macroscopic change: the reason carbon distributes itself more and more uniformly in an insulated solid is, that is what the laws of probability predict when diffusion alone is operative.

The reason natural forces may turn a spaceship, or a TV set, or a computer into a pile of rubble but not vice-versa is also probability: of all the possible arrangements atoms could take, only a very small percentage could fly to the moon and back, or receive pictures and sound from the other side of the Earth, or add, subtract, multiply and divide real numbers with high accuracy.

The discovery that life on Earth developed through evolutionary “steps,” coupled with the observation that mutations and natural selection — like other natural forces — can cause (minor) change, is widely accepted in the scientific world as proof that natural selection — alone among all natural forces — can create order out of disorder, and even design human brains with human consciousness. Only the layman seems to see the problem with this logic. In a recent Mathematical Intelligencer article (“A Mathematician’s View of Evolution,” 22, number 4, 5-7, 2000), after outlining the specific reasons why it is not reasonable to attribute the major steps in the development of life to natural selection, I asserted that the idea that the four fundamental forces of physics alone could rearrange the fundamental particles of nature into spaceships, nuclear power plants, and computers, connected to laser printers, CRTs, keyboards and the Internet, appears to violate the second law of thermodynamics in a spectacular way.

Anyone who has made such an argument is familiar with the standard reply: the Earth is an open system, it receives energy from the sun, and order can increase in an open system, as long as it is “compensated” somehow by a comparable or greater decrease outside the system. S. Angrist and L. Hepler, for example, in Order and Chaos (Basic Books, 1967), write, “In a certain sense the development of civilization may appear contradictory to the second law…. Even though society can effect local reductions in entropy, the general and universal trend of entropy increase easily swamps the anomalous but important efforts of civilized man. Each localized, man-made or machine-made entropy decrease is accompanied by a greater increase in entropy of the surroundings, thereby maintaining the required increase in total entropy.”

According to this reasoning, then, the second law does not prevent scrap metal from reorganizing itself into a computer in one room, as long as two computers in the next room are rusting into scrap metal — and the door is open. In Appendix D of my new book, The Numerical Solution of Ordinary and Partial Differential Equations, second edition, (John Wiley & Sons, 2005) I take a closer look at the equation for entropy change, which applies not only to thermal entropy but also to the entropy associated with anything else that diffuses, and show that it does not simply say that order cannot increase in a closed system. It also says that in an open system, order cannot increase faster than it is imported through the boundary. According to this equation, the thermal order in an open system can decrease in two different ways — it can be converted to disorder, or it can be exported through the boundary. It can increase in only one way: by importation through the boundary. Similarly, the increase in “carbon order” in an open system cannot be greater than the carbon order imported through the boundary, and the increase in “chromium order” cannot be greater than the chromium order imported through the boundary, and so on.

In these simple examples, I assumed nothing but heat conduction or diffusion was going on, but for more general situations, I offered the tautology that “if an increase in order is extremely improbable when a system is closed, it is still extremely improbable when the system is open, unless something is entering which makes it not extremely improbable.” The fact that order is disappearing in the next room does not make it any easier for computers to appear in our room — unless this order is disappearing into our room, and then only if it is a type of order that makes the appearance of computers not extremely improbable, for example, computers. Importing thermal order will make the temperature distribution less random, and importing carbon order will make the carbon distribution less random, but neither makes the formation of computers more probable.

What happens in a closed system depends on the initial conditions; what happens in an open system depends on the boundary conditions as well. As I wrote in “Can ANYTHING Happen in an Open System?” (The Mathematical Intelligencer 23, number 4, 8-10, 2001), “order can increase in an open system, not because the laws of probability are suspended when the door is open, but simply because order may walk in through the door…. If we found evidence that DNA, auto parts, computer chips, and books entered through the Earth’s atmosphere at some time in the past, then perhaps the appearance of humans, cars, computers, and encyclopedias on a previously barren planet could be explained without postulating a violation of the second law here (it would have been violated somewhere else!). But if all we see entering is radiation and meteorite fragments, it seems clear that what is entering through the boundary cannot explain the increase in order observed here.”

THE EVOLUTIONIST, therefore, cannot avoid the question of probability by saying that anything can happen in an open system, he is finally forced to argue that it only seems extremely improbable, but really isn’t, that atoms would rearrange themselves into spaceships and computers and TV sets.

Darwinists believe they have already discovered the source of all this order, so let us look more closely at their theory. The traditional argument against Darwinism is that natural selection cannot guide the development of new organs and new systems of organs — i.e., the development of new orders, classes and phyla — through their initial useless stages, during which they provide no selective advantage. Natural selection may be able to darken the wings of a moth (even this is disputed), but that does not mean it can design anything complex. Consider, for example, the aquatic bladderwort, described in Plants and Environment, by R.F. Daubenmire (John Wiley & Sons, 1947):

In a Nature Encyclopedia of Life Sciences (Nature Publishing Group, 2004) article on Carnivorous Plants, authors Wolf-Ekkehard Lonnig and Heinz-Albert Becker acknowledge that “it appears to be hard to even imagine a clearcut 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 (Free Press, 1996), 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 insects, and to reset the trap to be able to catch more than one insect, 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 pressurized 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 maybe even find one in Nature!), 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 insects. But I don’t know how to prove this. (Lest anyone imagine a lot can be accomplished by single random mutations, note that if a billion animals each typed one random character per second throughout the Earth’s 4.5 billion year history, there is virtually no chance any one of them would duplicate a given 20-character string.)

I am furthermore 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 insect 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. 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.