Granville Sewell is Professor of Mathematics at the University of Texas El Paso, and visiting professor at Texas A&M University.

He has two new books released last summer, Computational Methods of Linear Algebra, and The Numerical Solution of Ordinary and Partial Differential Equations, both published by John Wiley & Sons, 2005. The latter includes an Appendix entitled, "Can ANYTHING Happen in an Open System?" which contains material referred to below.

He argues that the theory of creation of species through natural selection violates the second law of thermodynamics:

    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 answer] requires a discussion of the second law of thermodynamics.

    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 (more random) 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.