his pro-creationism book, written by a physicist and biblical scholar, is highly regarded among creationists. After introducing some biblical concepts, the author goes on to describe how he believes Darwin's theory of evolution is compatible with the creation story in the Bible. His goal, which is a laudable one, is to effect a reconciliation between science and religion. But it must have been difficult to reconcile this goal with his overriding belief that the theory of evolution is mostly wrong.

Schroeder begins by quoting Steven Weinberg, the famous Nobel-winning physicist, as saying that the laws of physics are too finely tuned to be the result of chance. Although Weinberg's statement is usually taken to mean that there is some deeper structure behind the laws of nature, Schroeder interprets it to mean that a Supreme Being set the physical constants of nature to their present values. Like Roger Penrose, another physicist who believed (quite erroneously) that his genius as a physicist made him an expert in biochemistry, Gerald Schroeder believes that he understands biology and the Bible well enough to draw them together to create a grand unified theory of religion. He starts out well. In the first part of the book, he produces an entertaining reinterpretation of Genesis, where he says that the first day actually lasted 8 billion years, the second day lasted 4 billion years, and so on.

One problem with this idea is that it means there are one billion years between day three (when God created grass) and day four, when God finally got around to creating the sun. How did the grass survive so long without light? (I asked a creationist this question, and was informed that it was "a special kind of grass"--some kind of super-shade-tolerant grass.) It also creates a problem when we consider the lifespans of Adam and Eve. If we assume that the lengths of the days continued to decrease exponentially after the seventh day at the same rate as before, it is easy to calculate that Adam would have had to have lived for approximately two billion years.

Another uncomfortable detail: the Bible says that God created both heaven and earth. So before creation, God could not have been in heaven--in fact, he had no place to live. He was homeless!

Then there is the section (p. 96) where Schroeder claims that Archaeopteryx is mentioned in the Bible, in Leviticus 11:18 and 11:30, and dinosaurs are supposedly mentioned in Genesis 1:21.

(Leviticus 11:18 and 11:30 say, "And the swan, and the pelican, and the gier eagle," and "And the ferret, and the chameleon, and the lizard, and the snail, and the mole." Genesis 1:21 says, "And God created great whales, and every living creature that moveth, which the waters brought forth abundantly, after their kind, and every winged fowl after his kind: and God saw that it was good.") To paraphrase General Burkhalter from Hogan's Heroes: "There are noooo dinosaurs here!"

If the book continued like this, it would have been a thoroughly entertaining, if flawed, treatment of the Bible from a physicist's point of view. But when he gets to biology, Schroeder becomes more and more careless with the facts. From the start, the author misunderstands the thinking of biologists and their experiments, starting with Stanley Miller's experiment, which showed that amino acids could be formed naturally in a prebiotic atmosphere. Schroeder makes a big deal about Nobel laureate George Wald's statements about life occurring by chance having been "retracted". The actual "retraction" says this:

Although stimulating, this article probably represents one of the very few times in his professional life when Wald was wrong .... merely to create a bacterium would require more time than the Universe might ever see if chance combinations of its molecules were the only driving force.

There is only one problem: the "retraction" was actually written by Steven Weinberg. This means it is not a retraction, but a criticism. One can only retract one's own statements, not those of others. This may seem like a small point, but it is worth spelling out in detail because the entire section on evolution is constructed of arguments such as this, where Schroeder makes a big fuss about some biologist supposedly being proved wrong, yet upon examination, the fuss turns out to be something quite ordinary and unremarkable.

So what about Schroeder's main argument? Stripped of the obfuscation, Schroeder says that it is statistically impossible for single-celled life such as bacteria to have formed by a random combination of chemical reactions. In fact, science does not claim to know the precise mechanism by which the first cell, if there ever was such a thing, was formed. It is a field that excites far less interest among scientists than among creationists. Why? Because as creationists rightly point out, all the original evidence for the creation of life has long since been obliterated. At best, scientists could only demonstrate, as Miller did, that a particular mechanism is possible. But proving that something "could" or "could not" have happened is not very satisfying to a scientist.

Nonetheless, Schroeder persists in trying to use statistics to do just this: prove that in fact random mutations could not have produced life. Discussing the similarities between octopus and human eyes, he says (p. 93):

We refer to this remarkable similarity of organs in very different animals as convergent evolution .... [T]he likelihood of producing any particular sonnet of Shakespeare by random typing is about one chance in 26⁴⁹⁰ or one in 10⁶⁹⁰. Here we are asking for chance to produce the same "sonnet" twice. The statistical improbability ... has made a mockery of the theory that random choice alone gave us the biosphere we see.

In this argument, Schroeder acts as if he thinks that convergent evolution is somehow equivalent to the same organ evolving twice by chance. Such a thing obviously would be highly improbable. But that is not what convergent evolution says, and Schroeder knows it. Convergent evolution occurs when two species end up in a similar ecological niche, and develop along similar lines. There is nothing improbable or magical about it. Of course it does not occur by chance. The environment causes it to happen.

This points out the biggest weakness in Schroeder's argument (and that of most other creationists): massive confusion about the term "random chance". As quoted above, Schroeder uses "chance" to mean something random and unpredictable, as it is used in physics. For example, the point in time at which a particular radioactive particle decays is determined by the half-life of the radioisotope. The half-life defines a probability curve, under which the particle's decay is purely random. In biology, "chance" simply means "not pre-determined by genetics". A "chance" encounter of a garden slug with a fifty-pound rock is not really random in the physical sense, but it is "chance" in the biological sense--despite the fact that only one outcome, slug moosh, is possible. The probabilities of such "random" events cannot be calculated in the simple way that we would compute the probability of a photon having a particular polarization. That's because they are the product of a complex interaction of the slug and its environment. As soon as the population of slugs decreases, the environment changes in such a way that fifty-pound rocks no longer mysteriously fall from the sky at random times onto the garden. Such probabilities can be calculated, but the methods that Schroeder uses do not apply.

A second use of "random chance" is in point mutations of DNA, presumably caused by radioactivity or some transcriptional error. These are obviously two completely distinct meanings of the phrase "random chance", yet they are routinely confused and interchanged at random, so to speak, by creationists.

Even though Schroeder's calculations are based on random point mutations, Schroeder himself admits that mutations rarely occur as single point mutations, but rather often involve a complex reshuffling of genes. Genes coding for proteins are duplicated and their functions diverge over time. Some genes orchestrate an entire symphony of other genes. Molecular biology is not the simple point by point DNA sequence that Schroeder imagines. Nature "knows" how to create stuff, and has become darned good at it.

The statistics Schroeder uses are much like the infamous Drake equation that UFO aficionados often use to "prove" that aliens must exist. The Drake equation consists of a large number of probabilities multiplied together. Since each factor is guaranteed to be somewhere between 0 and 1, the result is also guaranteed to be a reasonable-looking number between 0 and 1. Unfortunately, all the probabilities are completely unknown, making the result worse than useless. Engineers even have a name for this type of calculation: WAG, or Wild-A**ed Guess.

Even if the simple statistical model used by Schroeder was appropriate, his own calculations show that random mutations can produce the observed phenomenon. Unfortunately, once proving himself wrong, Schroeder then goes back to convergent evolution, which he clearly does not understand, tosses in a few more orders of magnitude, and pronounces the result "statistically impossible."

Schroeder then starts taking potshots at biologists. Discussing an obscure 1967 conference on evolution, he says (p. 113):

Unfortunately, each time the mathematics showed the statistical improbability of a given assumption, the response of the biologists was that the mathematics must be somehow flawed since evolution had occurred and occurred through random mutations.

I have not been able to find the proceedings of this conference; but I wonder how much of the above statement is really true and how much is Schroeder's overactive imagination. I have never known a biologist to say something this patently ridiculous. However, I have seen hundreds of papers by mathematicians using assumptions about biology that are utterly unrealistic, and reaching equally unrealistic conclusions. The field of neural networks, for example, is full of such papers. My guess is that those biologists left the conference feeling much the same way about the mathematicians' wild-assed models.

Another point that Schroeder makes is that the fossil record clearly points to a "staccato" nature of evolution, where a species will remain unchanged for a time and then suddenly undergo a rapid burst of evolutionary change. Schroeder once again expresses surprise that science should be forced to modify its theories to accommodate facts such as this. In fact, what is more surprising is that Schroeder, who is supposedly a distinguished scientist, seems to be unaware that this is the very nature of science. It is religion, not science, that has great difficulty adapting to the discovery of new facts.

The current thinking about "staccato" evolution (expressed by the theory of punctuated equilibrium) is that entire ecosystems must evolve as a whole. It is like a gigantic linear equation of many thousands of variables that comprises a solution to the "problem" that is the environment. Change one parameter, and all the species may have to adapt to a new ecological niche to solve the new equation. Schroeder and other creationists either ignore the large literature of mathematical biology that attempts to address these questions, or they are unaware of it.

Because, as mentioned above, the probabilities in a biological ecosystem are not independent of each other, and because his numbers are little more than wild guesses based on questionable assumptions, Schroeder's simple statistical calculations, which he describes in detail in chapter 7 (p. 101), are meaningless at best. Schroeder's statistical arguments are very competently discussed and refuted at http://www.infidels.org/library/modern/richard_carrier/addendaB.html#Schroeder. The reviewer, Richard Carrier, says:

Schroeder must be one of the few cases in history where a man very competently proves himself wrong, then claims he is right.

I could not have said it better. This basically sums up most of Schroeder's arguments, such as his argument about convergent evolution. To be fair, the entire book is not about evolution. There are chapters on free will, and ample speculation from a Jewish perspective about the nature of God in the universe. The reader will learn more about Judaism than about biology from this book.

It would be inaccurate to say there's no place for God in science. But in my opinion, speculating about the nature and the intentions of God must rank as one of the most futile exercises imaginable. If only physicists would learn more about biology before jumping in and making themselves look foolish. Now that would be convincing proof there really are miracles.

Update (Jun 3, 2010): Since this book was written, Schroeder has expanded on his idea that the first seven days after creation actually occupied 13.75 billion years. He now explains this by invoking the slowing down of time that occurs when an object approaches the speed of light. Although this slowing down of time (known as the Twins Paradox) is a real phenomenon, it doesn't save Schroeder's theory. In fact, it makes it worse, because if the entire universe shares the same time frame, its true age would only be one week. If only the Earth shared the accelerated time frame, we are back to postulating some supernatural uniqueness to our planet. In either case, Schroeder's theory conflicts with observations.