Michael J. Behe's book Darwin's Black Box (Simon and Schuster, 1996) subtitled "The Biochemical Challenge to Evolution," is one of the most popular polemic publications arguing against Darwin's theory of evolution.

Behe's book is aimed at providing an argument in favor of the so-called "intelligent design" theory. Briefly, that theory states that the universe, and, more specifically, life, is not the accidental outcome of a spontaneous chain of random events but the result of a deliberate design by an intelligent mind. Usually the proponents of the intelligent design theory do not discuss the question of who the designer is. Sometimes they indicate (see, for example, part 3 of W. Dembski's book Intelligent Design, InterVarsity Press, 1999) that clarifying who the designer is, must be a task for theology. However, there is little doubt that the designer implied by the theory in question is a supernatural mind, i.e. God.

The popularity of Behe's book is evident, for example, from the inordinately large number of reviews submitted by readers to the Amazon.com web site. While other books of the same genre rarely invoke more than a couple of dozens reviews, hundreds of readers expressed their views in regard to Behe's book, and the flow of reviews shows no sign of abating.

Another manifestation of the strong splash made by Behe's book can be seen, for example, in a voluminous collection of articles titled Mere Creation edited by William A. Dembski (InterVarsity Press, 1998) in which almost every paper contains a reference to Behe's book. The level of discourse in that collection is uneven, but it includes some fairly sophisticated and insightful papers in which numerous references are made to Behe's book as an allegedly revolutionary step toward proving the intelligent design.

We read on the cover of Behe's book opinions of some prominent supporters of the intelligent design concept, who extol the virtues of Behe's breakthrough on the way to the complete defeat of Darwinism and Neo-Darwinism. For example, David Berlinski, a mathematician known as an outspoken adversary of Darwin's theory of evolution says: "Mike Behe makes an overwhelming case against Darwin on the biochemical level. No one has done it before. It is an argument of great originality, elegance, and intellectual power."

A similar view of Behe's book is evident from some of the references made to that book by the mathematician and philosopher Dembski in his books The Design Inference (Cambridge University Press, 1998) and the already mentioned Intelligent Design. Professor of law Phillip E. Johnson, who is one of the most prolific propagandists for the intelligent design theory, touts Behe's book in equally enthusiastic terms in several of his books (for example, in Defeating Darwinism by Opening Minds, InterVarsity Press, 1997). Hence, there seems to be a widely shared view by people of various professional backgrounds who are all believers in "intelligent design" and opponents of Darwin's theory of evolution, that Behe's book provides an indisputable argument in favor of "intelligent design" and thus against all the versions of Darwinian hypotheses and theories.

Behe's book, while highly acclaimed by many proponents of the intelligent design, was rather strongly criticized by the opponents of his thesis, including prominent biologists, such as professors Kenneth Miller and Russell Doolittle. This criticism does not seem though to have impressed Behe who continues to publish papers in which he shows no sign of any intention to modify his views. He repeats exactly the same arguments time and time again, despite very serious objections to those views from many critics.

Behe is a biochemist and his book reveals his wide knowledge of that subject. Since I am not a biochemist, I will not try to delve into Behe's detailed descriptions of biochemical systems; he is in his domain there whereas I am not. I shall accept Behe's biochemical discussion as flawless, even assuming that some other critics, possessing a wider ken in biochemistry and related fields, could possibly argue about some details of those biochemical descriptions. (A review of Behe's book from a biochemical viewpoint, which, in my view, is a devastating, clearly presented and highly convincing rebuttal of Behe's entire approach, was given by a professor of biology at Brown University Kenneth Miller at KR Miller's review of Darwin's Black Box.)

While the biochemical descriptions take up a considerable part of Behe's book, in his determination to offer a strong rebuttal of the evolution theory he ventures rather far outside biochemistry, invoking certain mathematical and philosophical concepts, and it is these excursions beyond biochemistry that are the target of this critical review. My intention is to show that Behe's principal concept is poorly substantiated and in no way proves his thesis.

Before discussing in detail Behe's main concept, it seems proper to point out that when Behe ventures beyond biochemistry, he sometimes looks more like a dilettante than an expert. One of the examples of Behe's dilettantism is how he discusses probabilities. Calculations of probabilities, for example, for the spontaneous origin of life, are very common in books aimed at disproving the theory of a natural emergence of life. More often than not, these calculations produce exceedingly small probabilities which lead to the conclusion that, for example, the spontaneous emergence of life was too improbable to be taken seriously. There are also some opponents of the natural emergence of life who realize that the small probability alone is irrelevant. For example, Dembski, who is better versed in probabilities, correctly points out, more than once, that a small probability in itself is not a proof. Therefore Dembski suggests more elaborate criteria to decide whether an event was the result of chance or of design. I will discuss Dembski's theory later in this paper.

I will discuss Behe's treatment of probabilities for two reasons. One reason is to support my earlier statement that Behe's excursions beyond biochemistry reveal his dilettantism in certain areas which are relevant to the discussion of his main thesis. The second, and more important reason is the fact that Behe's main thesis, his acclaimed irreducible complexity, inseparably includes a certain probabilistic foundation.

2. Behe calculates probabilities

Unfortunately, Behe's discussion of probabilities is just a recital of many other similar calculations, based on an insufficient understanding of probabilities. On pages 93 through 97 of his book, Behe criticizes Professor Doolittle's explanation of the blood clotting sequence. The discussion is about the probability that Tissue Plasminogen Activator (TPA) could have been produced by chance rather than by design. Behe suggests some calculations. On pages 93-94 we read: "Consider that animals with blood-clotting cascades have roughly 10,000 genes, each of which is divided into an average of three pieces. This gives a total of about 30,000 gene pieces. TPA has four different types of domains. By 'variously shuffling,' the odds of getting those four domains together is 30,000 to the fourth power, which is approximately one-tenth to the eighteenth power."

First, let us note the imprecision of Behe's statement. Obviously, 30,000 to the fourth power is a very large number, while one-tenth to the eighteenth power is a very small number, so these two numbers are not even "approximately" close to each other.

Probably Behe meant to say one in 30,000 to the fourth power. This is a small mistake, but it hints at Behe's possible discomfort with mathematics. Indeed, he continues, as follows: "...if the Irish sweepstakes had odds of winning of one-tenth to the eighteenth power, and if a million people played the lottery each year, it would take an average of about thousand billion years before anyone (not just a particular person) won the lottery."

Behe's statement is flawed in several respects. Let us briefly discuss them.

First, Behe's example is contrived, artificially and drastically decreasing the chance of winning, and in this way makes his example irrelevant. The trick used by Behe is in his selection of the numbers he discusses. On the one hand, he estimates the probability of an event in question (winning the Irish lottery) as one in ten to the eighteenth power. On the other hand, he assumes that only one million people play that lottery. One million is ten to the sixth power, which is just a tiny fraction of ten to the eighteenth power. In this way Behe artificially and drastically decreases the chance of winning for anyone (not just a particular person). To clarify that observation, let us discuss a small lottery where there are only 100 possible sets of numbers to be chosen by players, and, accordingly, only 100 tickets are available for sale. The probability of winning is the same 1/100 for each ticket. If all tickets are sold and no two players have chosen the same set of numbers, one of the tickets (we do not know in advance which one) will necessarily win. Therefore, if all tickets are sold, the probability that some set of chosen numbers is the winning one is close to 100%. (If we account for the possibility of more than one player choosing the same (losing) set of numbers, the probability of someone [not a specific player] winning is less than 100%. The proper calculation shows however that that probability is at least 37%. Such a calculation is given in the appendix to the article at Improbable probabilities). Now assume that out of 100 available tickets, only ten have been sold. Each ticket has the same chance to win, regardless of its being sold or not. Therefore, if no two players chooses the same set, the probability that at least one of the sold tickets will win is now 10% instead of 100% (which it was were all tickets sold). This example shows that the exceedingly small probability of anyone (not just a particular person) winning in the imaginary lottery described by Behe is due to his deliberate choice of numbers – only one million tickets sold while the number of potentially available tickets is immensely larger.

Obviously, Behe's example has nothing to do with a real lottery. In every real lottery the number of tickets sold is usually close to the total number of available tickets and the coincidental choice of the same numbers by more than one player is very rare, therefore the probability that someone (not just a particular person) wins is always close to 100%, and in any case not less than 37%.

Second, Behe's discussion is irrelevant if the probability of a particular person winning is considered. This probability does not depend on the number of tickets sold. If the total number of available tickets is 100, then each ticket, whether sold or not, has the same probability of winning, namely 1/100. If, as in Behe's example, the total number of possible events is ten to the eighteenth power, then the probability of a particular event happening is one in ten to the eighteenth power. It is exceedingly small. However, it is equally small for all possible events. If no two players chose the same set, one set of six numbers must necessarily win despite its probability being exceedingly small. Therefore the exceedingly small probability calculated by Behe for the case of TPA in no way proves his thesis and in no way rebuts Professor Doolittle's discourse.

Third, Behe seems to assume that an event whose probability is 1/N, where N is a very large number, would practically never happen. This is absurd. If the probability of an event is 1/N it usually means that there are N equally possible events, of which some event must necessarily happen. If event A, whose probability is very low (1/N), does not happen, it simply means that some other event B, whose probability is equally low, has happened instead. According to Behe, though, we have to conclude that, if the probability of an event is 1/N, none of the N possible events would occur (because they all have the same extremely low probability). The absurdity of such a conclusion requires no proof.

The assertion that events having very low probabilities do not occur was suggested by the prominent French mathematician Emile Borel (see, for example, his book Probability and Life, 1962). Borel suggested what he labeled The Single Law of Chance which stated that "Phenomena with very small probabilities do not occur." He estimated that the events that cannot reasonably be attributed to chance are those whose probability does not exceed one divided by ten to the power of fifty. Since Borel was a very influential mathematician who contributed many fruitful ideas to the field of probabilities, the quoted law gained wide acceptance often extending its meaning far beyond its legitimate implications. A little later we will discuss some facts illustrating that Borel's law, if interpreted literally, is absurd.

These paragraphs in Behe's book may seem to be of minor importance, as they appear to be beyond the main theme of his discourse. However, this item is actually closely connected to the core of Behe's main idea, his "irreducible complexity." The concept in question comprises two elements, one complexity, and the other irreducibility, both being necessary parts of Behe's idea. The question of exceedingly small probabilities calculated for the emergence of biological structures by chance is just another facet of the concept of complexity. Complexity of a biological system is a necessary component of Behe's scheme, because, as Behe's idea implies, a system of low complexity has a much better chance of emerging spontaneously as a result of a chain of random events. In order to build a bridge from irreducible complexity to intelligent design, Behe must assume that the probability of his system being the result of a random unguided process is exceedingly small.

Consider a simple example (which has actually been given by Behe, and will be again discussed later). Imagine we see on a table a piece of paper covered with letters. Viewing the written text we see that it is gibberish. We don't know who wrote all those rows of letters which make no sense, or why. Then we notice that somewhere within the gibberish text a whole word appears, say "love." The question is, has this word appeared in the gibberish text by chance or did whoever wrote all those letters insert that word deliberately, i.e. by design. There is a reasonable probability that the word in question did not result from design but happened within the gibberish text by chance. Now let us imagine that within the meaningless text we see a whole meaningful sentence containing some forty letters. We estimate the probability of its occurrence by chance as very small. The reason for that estimate is the much larger complexity of the sentence compared with a single four-letter word. The high complexity, according to Behe, means a low probability. This example shows why the small probabilities calculated by Behe are crucial to his main idea of irreducible complexity and that is why I had to analyze the deficiencies of Behe's treatment of probabilities.

3. Additional remarks on Behe's use of probabilities

This section which is meant to complement the above discussion of the treatment of probabilities by Behe, is based on the comments made by Dr. B. McKay, whose contribution is thankfully appreciated.

Suppose that, according to Behe's assertion, there is indeed only one sequence of proteins that can perform a specific function (for example, to clot blood). Suppose further, again according to Behe's approach, that there are no other, simpler, biological processes that could perform those functions. Also suppose that it can be somehow proved that higher organisms could not evolve without those particular mechanisms (like blood clotting).

Following Behe's discourse further, suppose also that a spontaneous emergence of the protein's sequence which is necessary to perform the function in question, by randomly joining individual proteins, is extremely unlikely (i.e. assuming that the probability of such an outcome of random events is too low to expect that it could have occurred during the time of the Earth's existence).

In other words, grant Behe all his assumptions.

The conclusion that seems to follow from all Behe's assumptions is that the "protein machines" were not created by joining proteins at random. This is the first part of Behe's conclusion. However, even if we accepted that, highly disputable part, the next part of his discourse which asserts that therefore those "machines" must be the products of intelligent design, would pose very serious problems.

One of the problem in question is that Behe has not eliminated other actions of randomness besides the simple random joining of proteins. There are many alternative possibilities. A few examples follow.

(1) There could exist stable protein sequences quite similar to the clotting (or any other) sequence. Assume, for example, that there is such a stable sequence which differs from the one necessary to perform the clotting, by, say, 5% only. If the sequence in question is stable, it tends to hang around a long time. Perhaps it is biologically useful or perhaps it resulted, along a common chemical pathway, from something biologically useful. In such a case, we have to explain the emergence of a sequence differing only by 5% from an existing one, by random combinations, which is immensely easier. Those "sequences correct by 95%" could, in their turn, have earlier evolved in similar fashion from "sequences correct by 90%").

There is no need to assume that the whole edifice was created in a single step from the primordial soup.

(2) Perhaps the clotting (or any other useful) sequence can be decomposed into relatively few fragments ("bricks") which are also parts of other biologically useful sequences. Then the clotting sequence could have resulted from the random combination of bricks broken off sequences that already existed. Again, this is immensely easier probability-wise.

Suppose that we have 4 types of blocks. Consider a particular sequence which is 100 blocks long. Estimate the likelihood of its emergence by a random joining of blocks. There are 803469022129495137770981046171215126561215611592144769253376 of "100 blocks long" sequences of 4 different blocks. Of course, this number is extremely large, hence the probability of the spontaneous emergence of the particular sequence is exceedingly small, so, having accepted Behe's approach, we don't expect to see the right sequence to emerge any time soon. Now suppose that each group ("brick") of 10 blocks is a stable configuration. All of the 10 "bricks" we need can be "made" in parallel, each by joining 10 blocks at random, which is immensely easier because there are only 524800 ways to join 10 blocks in a sequence. Given the required 10 "bricks," there are approximately 1858 million ways to join 10 of them together, which is also a reasonably small number for nature. So, overall, the expected time for the first appearance of the required 100-block sequence is reasonably modest.

(3) There can be an adaptive search process. Consider a field of size 100x100 meters, which contains a single pit somewhere in it, while the overall surface of the field is slightly sloped toward the pit. We define the "pit" as an area of 1x1 meter. If we want to find the pit by randomly probing points in the field, we will not be surprised if it takes a long time. However, we can find it much faster by a certain, still random process. Put a drunken man at a random place in the field and allow him a "random walk." At each time unit (say, every second) the man takes a step in a random direction. However, downhill steps are on average a little bit longer than uphill steps. Eventually, the man will reach the pit. It might still take a long time, but the expectation of the time will be much less than the expectation of the time required using random probing at the field.

(In computer science there are a number of optimization methods that rely on this type of random process. There are even some directly modeled on evolutionary processes and using the same terminology. They are often quite successful at optimizing functions over search spaces much too complicated for traditional methods).

(4) It might be true that sequences which are very close to the clotting sequence are of no use for modern organisms, but maybe they were useful to earlier organisms. It could be that in early times there was some primitive organism with some primitive (but useful) protein sequence and that the organism and sequence evolved together into gradually more complex forms. Changes in either the organism or the sequence could help direct the evolution of the other, so there is no real surprise if the sequence is useful to the organism at each point of time.

Even if options (1)-(4) can be ruled out somehow, what about some mechanisms (5), (6), etc., that we didn't think of yet? To assume that everything in nature happens only according to known mechanisms would unduly limit the path to the scientific elucidation of the unknown.

In the following sections I shall concentrate on the main thrust of Behe's book, namely on his attempts to prove the so-called "intelligent design" based on his concept of "irreducible complexity."

4. Anti-Darwin crusade

The very title of Behe's book, Darwin's Black Box makes a reader expect an effort to debunk Darwin's theory of evolution. Of course, debunking Darwin is a common pastime of creationists. One of the arguments favored by creationists is that the view of the Darwinists is "just a theory." Of course, this is true. Every scientific theory is "just a theory." However, the opponents of evolution favor some other concepts despite their being "just theories" if they perceive these concepts as supporting their beliefs. For example, many creationists happily embrace the big bang theory, which seems to jibe well with the biblical story about creation. Of course, the big bang theory is also essentially "just a theory." It has no direct experimental confirmation and is based on a sophisticated interpretation of observational data. Nevertheless, the creationists tout this theory as a "scientific proof" of their religious beliefs. Darwin's theory of evolution is less fortunate in that it seems to contradict the biblical story and, therefore, its being "just a theory" is claimed by creationists to be its critical flaw.

It is interesting to note that Behe never admits to being a creationist. He suggests arguments in favor of "intelligent design" without ever mentioning who the supposed designer could be. However, this fig leaf covering something Behe seems reluctant to admit is quite transparent. No wonder open creationists have accorded Behe's book effusive accolades. There is no doubt whatsoever that Behe's real thesis is that the creation story is fully compatible with the biochemical evidence while the evolution theory is not.

On page 15 of his book Behe says that Darwin's theory explains the microevolution very well, but fails to explain macroevolution. In this paper, I shall not dispute that statement by Behe, since this paper is not about Darwin's theory. I shall instead address the particular arguments suggested by Behe in favor of "intelligent design" theory.

5. Intelligent design according to Behe

Of course, the concept of intelligent design being responsible for the existing universe's structure in general, and for the existing forms of living organisms in particular, was not invented by Behe. In various forms, this concept has been discussed many times before Behe. Behe's contribution to this discussion is in evoking the images of immensely complex biochemical systems and claiming that the complexity of those systems is "irreducible" and therefore points to "intelligent design."

There are many descriptions of those fascinating, exceedingly complex biochemical systems in Behe's book. Among those examples are the mechanism of blood clotting, the device used by bacteria for moving (the "cilium" mechanism), the structure of human eye, etc. All these systems look like real miracles and it is fun to read Behe's well written discussions of those immensely complex combinations of proteins, each performing a specific function.

The complexity of the biochemical systems had been demonstrated by Behe in a very convincing way.

To lead the way to his conclusion about intelligent design, Behe claims that the complexity in question is "irreducible." This term means that the removal even of a single protein from the convoluted chain of proteins interaction would render the entire chain non-operational. For example, removing even one protein from the process of blood clotting would make blood either not clot, causing the organism to hemorrhage, or totally coagulate, also leading to organism's demise.

From that statement Behe proceeds to claim that the alleged irreducible complexity could not be the result of an evolutionary process and therefore can only be attributed to "intelligent design."

Let us discuss all three steps in Behe's reasoning, namely a) complexity, b) irreducibility, and c) attribution to intelligent design.

6. Complexity as a façade for probability

Complexity is one of the two components of Behe's irreducible complexity concept. Regrettably, Behe himself does not offer any definition of what he means by complexity. Therefore, to analyze the actual meaning of his overall idea of irreducible complexity, we have to find clues in his descriptions of those biochemical systems he views as being complex.

As mentioned above, Behe's concept has been touted as a revolutionary breakthrough in the development of a convincing denial of Darwin's evolution theory. My intention in this paper is not to disprove the idea of an intelligent design in general, but only to test the arguments offered by Behe in favor of that concept. I am concerned in this paper only with the validity of Behe's arguments which have been acclaimed by the adherents of the creation as a crushing blow to the evolutionists' views.

When discussing the concept of complexity, we can turn to the writings of some supporters of Behe who invested considerable effort in solidifying Behe's assertions by plugging certain obvious holes in them, including his failure to define complexity.

In particular, it is interesting to look at a definition of complexity offered by Dembski. To explain why Dembski's explanation should be considered as a legitimate elaboration on Behe's discourse, let us review certain quotations. Behe wrote a foreword to Dembski's book Intelligent Design mentioned before. Behe wrote: "Although it is difficult to predict (frequently nonlinear) advance of science, the arrow of progress indicates that the more we know, the deeper design is seen to extend. I expect that in the decades ahead we will see the contingent aspect of nature steadily shrink. And through all of this work we will make our judgments about design and contingency on the theoretical foundation of Bill Dembski's work." It is a very favorable evaluation of Dembski's work by Behe. It provides us with the confidence that Behe fully accepts Dembski's treatment of complexity. Indeed, nowhere can we find a single instance of Behe's disagreement with any of Dembski's arguments.

It seems relevant to point out that Dembski's work has been acclaimed in similar superlative terms also by other adherents of intelligent design. For example, Rob Koons, an associate professor of philosophy at the University of Texas, writes (quoted from the cover of Dembski's book Intelligent Design): "William Dembski is the Isaac Newton of the information theory, and since this is the Age of Information, that makes Dembski one of the most important thinkers of our time."

Since in this paper I concentrate mainly on Behe's book, I will not discuss here Dembski's supposed contribution to information theory (which in my view entails serious faults). A detailed review of that matter is offered in a separate paper (see A consistent inconsistency). Also, a brief discussion of informational aspects of the "intelligent design theory" can be seen in my review of P. Johnson's books and articles, at A militant dilettante in judgement of science. What is relevant for the discussion in this paper is that Dembski enjoys a great deal of authority amongst the proponents of intelligent design, and therefore, when he writes about subjects related to Behe's work, his opinions can be viewed as authoritative expressions of that camp's position.

In Dembski's book The Design Inference we find the following definition of complexity (page 94): The complexity of a problem Q with respect to resources R, denoted φ (Q|R) and called "the complexity of Q given R" is the best available estimate of how difficult it is to solve Q under the assumption that R obtains.

In the same book Dembski provides a similar definition of "difficulty." According to Dembski, complexity is just "disguised probability." In his theory, complexity is reflected in the difficulty of solving a problem, and this, in turn, is tantamount to the small probability of finding a solution to the problem by chance. I intend to dispute that conclusion in some of the following sections. A detailed discussion of Dembski's theories of probability and complexity, including the above definition, is given at A consistent inconsistency, where serious deficiencies of the above definition are revealed. For our discussion of Behe's book it is sufficient to point out that complexity defined by Dembski is essentially a concept quite different from complexity in Behe's interpretation.

However critical we may be of Dembski's definition of complexity, we possess no other definition given by "design theorists," so we have to turn to the definition given by the "Newton of information theory" in our attempts to interpret the gist of complexity in Behe's theory.

When applying the above definition of complexity to Behe's biochemical systems we see that actually there are two different notions of complexity. Complexity as defined by Dembski is practically synonymous with a difficulty of solving a problem. On the other hand, in Behe's scheme, the complexity is in the structure of the biochemical system. It is determined by the number of components of the system and the number of links and interconnections between those components. The more components the system includes and the more interconnections between those components exist, the more complex is the system. The two concepts of complexity are essentially different. However, there is a link between the two definitions. It is probability. The harder it is to solve problem, the smaller, according to Dembski, the probability that it will be solved by some unguided random actions. The more complex a system is, insist Dembski and Behe, the smaller the probability that it could have emerged as a result of unguided random events. I submit that more often than not the relation between the complexity of a system (as implied by Behe) and the probability of its spontaneous emergence is opposite to the relation assumed by Dembski.

In the meantime, to illustrate Dembski's logic, take a look at his example of a problem whose solution through an unguided effort is highly improbable. It is an attempt to open a safe's lock in a single try without knowing the correct combination. Since there are many millions of possible combinations of dial's positions, to correctly guess the right combination on the first attempt is highly improbable, and this improbability, says Dembski, translates into the very high complexity of the problem. (Actually this example was first discussed by Richard Dawkins in his book The Blind Watchmaker, W.W. Norton & Co., 1986).

The biochemical systems described by Behe exemplify the other type of complexity. For example, the blood clotting mechanism is based on the interaction of many proteins, each performing a precisely defined function. The system includes many components interconnected by multiple links. It is very complex. The complexity implied by Behe is in the structure of biochemical systems, i.e. in the large number of components and the large number of interconnections among them. This complexity allegedly translates into the very small probability that such a system could have emerged spontaneously via random events. This is viewed by Behe and his supporters as an argument in favor of those system being the product of intelligent design.

To summarize the above discussion, the only aspect of Dembski's complexity that has a bearing on Behe's line of arguments is the suggestion that the complexity of a system translates into the very small probability of its emergence via unguided random events. All other aspects of complexity (of which there are many) are irrelevant for Behe's discourse. Later I will return to discussing complexity in general and of biochemical systems in particular, from a viewpoint, ignored by Behe. But now let us take a closer look at the very facet of complexity which is at the core of Behe's use of it, namely its probability aspect.

First, recall our discussion of Behe's calculation of probabilities. Can a very small probability serve as a decisive argument against the possible occurrence of an event? As Dembski himself admits, it cannot. Events whose probability is exceedingly small occur every day.

Imagine tossing a die with the letters A, B, C, D, E, and F on its six facets. Assume it has been tossed one hundred times. After each trial we write the letter facing up on a piece of paper. The combination of 100 letters obtained after 100 trials constitutes an event. There are six to the power of 100 possible events, i.e. of possible combinations of 100 letters comprising six letters listed above. This is an enormously large number, about 6.5 times ten to the power of 77. Only one particular set of letters out of that vast number of possible sets has occurred. Whatever combination has actually resulted from the test, it has an exceedingly small probability, close to one divided by more than ten to the power of 77. The denominator of that fraction is by 43 orders of magnitude larger than the number Behe calls (page 96) "horrendously large." This fraction is by 28 orders of magnitude smaller than the lowest limit of probability for a random event as suggested by Borel (ten to the power of minus 50). Nevertheless, the event in question, whose probability was so exceedingly small, actually occurred. Nobody would be surprised by the occurrence of that exceedingly improbable event, because some combination of 100 letters must have unavoidably happen, all of the possible combinations having an equally minuscule probability, hence when one of those exceedingly improbable events occurred, there was no reason for surprise.

Unfortunately, in many publications aimed at supporting the intelligent design theory, including Behe's book, very small calculated probabilities of events such as the spontaneous emergence of proteins, are offered as alleged proof that such events could not happen. An often repeated statement in such publications is that events whose probability is so exceedingly small, just do not happen. That statement is tantamount to the absurd assertion that nothing happened, i.e. that no set of letters resulted from 100 tests. The indisputable fact is that exceedingly improbable events happen all the time.

Behe's use of biological system's complexity to posit the improbability of their spontaneous emergence without intelligent effort is hardly convincing.

While Behe shares this misconception about the impossibility of events whose calculated probability is very small with many other proponents of intelligent design, another prominent advocate of the intelligent design, the mathematician Dembski is one of the few who realize the falsity of that assertion. Indeed, on page 3 of Dembski's The Design Inference, we read: "Sheer improbability by itself is not enough to eliminate chance." This is true and runs contrary to Behe's interpretation of low probabilities. On page 130 of Dembski's Intelligent Design we read a similar assertion, again contrary to Behe's understanding of probabilities: "complexity (or improbability) isn't enough to eliminate chance and establish design." These statements are especially telltale since they are written by a man highly regarded by proponents of intelligent design, including Behe, and who himself is one of the staunchest "design theorists."

Since, unlike Behe, Dembski understands that very small probabilities do not prove design or disprove chance, he suggests a more elaborate criterion, which, in his view, enables one to empirically discover design. Dembski's idea is expressed in the concept of what he calls Explanatory Filter. This term denotes a three-step scheme for choosing one of the three causes of events, which, according to Dembski, are regularity, chance and design. A detailed discussion of Dembski's theory is offered at A consistent inconsistency.

Let us briefly summarize Dembski's approach. Like many other proponents of intelligent design theory, Dembski maintains that a very low probability of an event (which he views as tantamount to its complexity) is a necessary condition to infer design. However, unlike many other adherents of intelligent design theory, Dembski realizes that an extremely small probability (high complexity) of an event, even if necessary, is not in itself a sufficient condition to infer design. He perceives the additional condition that will make up for the missing sufficiency in what he calls either "specification" or "pattern." Therefore, according to Dembski, if an event is a) highly improbable, and b)"specified," this points to design. (Note, that if we consider the entire three-step explanatory filter, it becomes clear the "specification" serves as a sufficient condition only if the condition of low probability is also present. If an event is specified but has a high probability, it does not lead to a design inference. Only the combination of low probability and specification provides a necessary and sufficient condition for a design inference).

I find some points in Dembski's argument highly disputable, including his assertion that his filter produces no false positives. In the review of Dembski's work at A consistent inconsistency examples are shown disproving Dembski's assertions. To see how Behe relates to Dembski's theory, let us review a quotation from Behe's foreword to Dembski's book Intelligent Design. Behe writes: "For example, if we turned a corner and saw a couple of Scrabble letters on a table that spelled AN, we would not, just on that basis, be able to decide if they were purposely arranged. Even though they spelled a word, the probability of getting a short word by chance is not prohibitive. On the other hand, the probability of seeing some particular long sequence of Scrabble letters, such as NDEIRUABFDMOJHRINKE, is quite small (around one in a billion billion billion). Nonetheless, if we saw that sequence lined up on a table, we would think little of it because it is not specified – it matches no recognizable pattern. But if we saw a sequence of letters that read, say, METHINKSITISLIKEAWEASEL, we would easily conclude that the letters were intentionally arranged that way. The sequence of letters is not only highly improbable, but also matches an intelligible English sentence. It is a product of intelligent design."

The above quotation is a concise representation of Dembski's idea stripped of its mathematical and sophisticating embellishments. Note, that this quotation shows that Behe has abandoned the assertion made in his own book that events of a very low probability just do not happen. Instead, he now adopts Dembski's more sophisticated approach asserting that design must be inferred only when there is a combination of a very small probability with a recognizable pattern. As it is argued in the review of Dembski's work referred to above, whereas Dembski correctly denies the evidentiary power of low probability alone, adding specification does not eliminate the probabilistic nature of design inference. In Dembski's discourse, design inference is made if an event has a very low probability and also displays a recognizable pattern. To be recognizable, the pattern, according to Dembski, must meet two additional conditions. One is the so-called "detachability," and the other, "delimitation." In its turn, detachabaility entails "conditional independence" of the background information and "tractability." All these concepts are critically discussed in detail in the review of Dembski's work at A consistent inconsistency.

In view of the above, how can Dembski's filter, so highly praised by Behe, help the latter in proving the "irreducible complexity?" The answer does not seem to be very encouraging for Behe and his supporters. There are no distinguishable "recognizable detachable patterns" in the biochemical systems so beautifully described by Behe. Looking at those immensely complex biochemical machines, we do not see detachable recognizable patterns as defined by Dembski, but rather pattern that are, according to his definition, not detachable (as we have no independent background knowledge enabling us to match the observed pattern to any sample known a priori). Actually, given the purely subjective character of "detachability," the question of Dembski's filter application to biochemical machines is moot.

After reviewing Dembski's concept of complexity it seems that the only input that concept provided to Behe's theory is that biochemical machines are highly improbable because they are very complex. We will see later that even this statement is highly questionable. However, even if it were true, it would provide no new insight into Behe's concept of irreducible complexity. Indeed, Dembski's definition of complexity contains no facet which could lead one to the elucidation of irreducibility of complexity. To try revealing what can make complexity irreducible, we have to look elsewhere. Therefore, before discussing irreducibility, we have to talk about complexity, from a viewpoint different from that chosen by Dembski.

7. Complexity from a layman's viewpoint

I will later return to complexity as a mathematical concept, limiting myself in this section to some general discussion of the intuitively understood meaning of complexity of a system.

In Behe's view, enormous complexity (combined with its alleged irreducibility) is a sign that the system in question must have been designed by some unnamed intelligent mind.

Is complexity indeed an attribute of an intelligent design? Human experience points in the opposite direction. The simpler the solution to a problem, the more intelligence and ingenuity it requires. The entire history of technological progress proves that the best designs are always also the simplest.

Let us look at a few examples.

Remember the electronic circuits which appeared at the beginning of the 20^th century. They were based on vacuum tubes. The simplest vacuum tube, a diode, had a number of fragile parts, soldered together in a vacuumed vessel. A triode, which was a necessary part of any amplifier, had several electrodes of complex shape soldered into a glass or metallic body with a bunch of contacts penetrating the walls of the vessel.

Remember the first computer, created in the forties under the guidance of J. Presper Eckert and John Mauchly. This wonderful achievement of the human mind from today's point of view seems to be a monster. It was a huge contraption containing 18,000 vacuum tubes and 3,000 switches. If we accepted Behe's concept, improvements in electronics and computer design should have proceeded via increased complexity of both vacuum tubes and circuitry. Indeed, for a while, the increased ability of electronic circuits to perform various tasks was achieved by increasing the complexity of both the tubes and the circuits. Vacuum tubes with four, then with five, six, seven, etc. electrodes, were designed. The number of tubes in a circuit increased. The more complex the tubes and the circuits became, the slower their performance improved, hitting a wall when the cost of the systems became prohibitive without a substantial improvement in performance, and was accompanied by a drop in reliability. Then, in the late forties, the transistor was invented. A transistor is an ultimately simple piece of a device, incomparably simpler than a vacuum tube. Its introduction led to the enormous simplification of electronic circuits and thus to the vastly increased ability to perform more complex tasks. While modern computers are much more complex than that built by Eckert and Mauchly, were they to perform only the same tasks as the computer of the forties, they could be immensely simpler. This simplification has enabled the enormous progress in computations, communications and automatics we enjoy today.

Remember another example, from a completely different field. In the 19^th century, various inventors tried to design a sewing machine. A number of patents were granted. All those machines were primitive, unreliable, and heavy, and inventors tried to solve the problem by adding more parts, each designed to get rid of some of the shortcomings of the machine but at the same time making it more complex.

In 1851, a man by the name of I. M. Singer came up with a novel idea. His invention incorporated two elements. One was the use of a simple shuttling hook and the other, of a simple needle of a special shape. These two elements immediately made all the complex devices used by Singer's predecessors unnecessary. His machine was much simpler that any before him, while also much more reliable and easier to use. It became the model for further improvements by A. B. Wilson, who introduced a swinging hook, thus further simplifying the design.

Would anybody say that Singer's and Wilson's predecessors were more intelligent than these two inventors because the predecessors' designs were more complex?

It has been agreed among experts in warfare that the Russian-made tank T-34, designed by Joseph Kotin, was the best tank of WW2. It was also the simplest in design.

The best submachine guns in their categories are considered to be the Russian piece designed by Kalashnikov (AK47) and the Israeli-made Uzi. Both are also the simplest in design among all the submachine guns ever produced. The Uzi has only seven parts, and is easily assembled and dissembled.

Many more such examples could be listed.

Now recall my statement that Dembski's definition of complexity requires qualification. I mentioned that Dembski's assertion, obviously supported by Behe, that complexity is equivalent to low probability is highly questionable. Let us now elaborate. Imagine that you have embarked on an excursion from Rome into the Italian countryside and have lost your way. Of course, everybody knows that all roads lead to Rome. Since you wish to be back in Rome as soon as possible, you would like to choose the shortest road . There are many different roads for you to choose from, but only one of them, let us denote it S, is the shortest (i.e. the simplest) while there are many other roads which all are more complex than S. However, you do not know which of the roads is your most desired S. Imagine that you decide to rely on chance, say, you assign a number to every possible road, write those numbers on pieces of paper and then randomly pull one of the numbers out of your hat. Of course, the probability that the randomly chosen road turns out to be S is much smaller than the probability that the randomly chosen road turns out to be one of the more convoluted ones, simply because there are so many convoluted roads but only one shortest road. Imagine now that you do not rely on chance but rather decide to approach the problem in an intelligent way. For example, you buy a map in the nearest village and determine the shortest road to Rome. In this case you have a very good chance of selecting the shortest of available roads.

Hence, if you learned that your friend who lost his way in the countryside, chose the shortest, i.e. the simplest road to Rome, you would have a good reason to assume that he made an intelligent decision, choosing the road by design rather than by chance. If, though, you learned that your friend chose some convoluted, complex way, it would rather indicate that he relied on chance.

Similarly, any task in either a mechanical or a biological system can be performed in many ways. There are always much more of complicated, convoluted ways of performing a task than of simple ways to do the same job. If a machine, be it mechanical or biochemical, is very complex, it points to its unintelligent origin. Nothing prevents a system of any degree of complexity from emerging as a result of unguided random events. If, though, a task is performed in a very simple way, there is a good chance a design is to blame. The simple reason for that is that there are many convoluted ways to do a job but only a few simple ways.

In view of the above, I submit that Dembski's assertion equalizing complexity with small probability can reasonably be turned upside down. The simpler the system that successfully performs a job, the smaller is the probability that it is a result of spontaneous random events. The more complex the system is, the less probable is its origin in an intelligent design. Of course, if the latter statement is accepted, it completely undermines the very core of Behe's concept.

Behe has convincingly showed that biochemical systems are extremely complex. That complexity, according to Behe, is one of two necessary facets pointing to intelligent design (the other is irreducibility). Why this complexity in itself should point to intelligent design, remains Behe's (and his supporters') secret.

Of course, Behe considers complexity together with irreducibility, and when combined, they, in his view, provide a strong argument in favor of intelligent design. In one of the next sections we will discuss the role of the alleged irreducibility of the systems described by Behe. We have not yet completed our separate discussion of complexity, but now we necessarily have to discuss it together with irreducibility.

8. What is the real meaning of irreducibility?

The discussion of Behe's concept of irreducible complexity must be twofold. On the one hand, we will have to discuss the following question: if the biochemical systems described by Behe, are, as he asserts, indeed irreducibly complex, does this indeed point to a deliberate design? On the other hand, we will have to address the question of whether or not these systems are not just complex, but indeed irreducibly complex.

Behe's book, while written for laymen, also purports to base his conclusions on an approach which is more or less scientific-like. He considers facts established by biochemical science and proceeds to make certain conclusions seemingly stemming from those facts. Therefore, in our discussion we may legitimately require from Behe adherence to some elementary rules of scientific discourse. Unfortunately, this aspect of Behe's approach leaves much to be desired.

Behe defines irreducible complexity as the tight interdependence of the system's constituent parts such that the removal of even one of its parts renders the system non-operational. However, he does not seem to offer criteria which would enable one to determine whether or not a system in question indeed meets that definition. His definition is made in an abstract way providing no clues how specifically to find out whether the removal of a part of the system will indeed make it dysfunctional. Moreover, he did not offer proofs that the systems he reviewed are indeed irreducibly complex in his sense.

There exists a quite rigorous and quite general definition of irreducible complexity, of which Behe was apparently unaware, and which actually defines something quite different from what Behe means by his term. This definition is given in the part of mathematical statistics called algorithmic theory of probability (ATP). That chapter of statistical science was developed in the 1960s. Its main creators were the American mathematician R. J. Solomonoff of Zator Co., the Russian mathematician A. N. Kolmogorov of the Russian Academy of Sciences and the American mathematician, G. J. Chaitin of the IBM research center. ATP is a sophisticated mathematical theory which makes use of elements of mathematical statistics, information theory, and computer science.

The definition of irreducible complexity developed in ATP, while being rigorously mathematical, is quite universal and applicable to any system, regardless of its particular nature. It is based on the concept of randomness, for which ATP provides a strict definition as well.

It seems easiest to explain the irreducible complexity according to ATP by using a mathematical example and a computer analogy, although this specific example and analogy in no way limit the applicability of the concept in question to any system, including the biochemical systems discussed by Behe. The following explanation will omit certain subtle points of the ATP theory, which are not necessary to understand its general idea.

Consider the following set of digits: 01 01 01 01 01….. and so on. It is obvious that this sequence is highly ordered. It is constructed by the repetition of zeroes and ones in pairs. The size of this sequence, depending on the number of repetitions, can be any number, for example, one billion bits. How can we program a computer to reproduce this sequence? It is obvious that there is no need to tell the computer all the numbers of which this sequence consists. It is sufficient to tell the computer the rule which determines the sequence. The program in question can be written in a very simple and short form, essentially boiling down to the following instruction: Print 0,1 n times , where n can be any number. The length of the program in question is much shorter than the length of the sequence itself. No matter how we increase the size of the sequence, the size of the program will always remain much shorter than the sequence itself.

Now imagine the following sequence: 0011011000101100111010011110100011.....etc. Such a sequence can be obtained, for example, by flipping a coin many times and writing 1 each time the result is heads, and 0 when it is tails.

Viewing this sequence, we cannot see any specific order in it. This set of numbers corresponds to our intuitive concept of a random sequence. (Actually, only an infinitely long sequence can be viewed a unequivocally random, but for our discussion this is not crucial.) How can we program a computer to reproduce this sequence? Since there is no evident rule determining which digit must follow any digits already known, there is no way to produce this sequence by using any program shorter than the sequence itself. To program a random sequence, we need to feed into the computer the entire sequence, which serves as its own program. Hence, the size of a program that produces a random sequence necessarily equals the size of the sequence itself. In other words, that disordered sequence, unlike an ordered sequence, cannot be reproduced by means of a shorter program (we can also discuss the problem in more general terms of algorithms instead of programs). Again, a random sequence cannot be encoded by a program of a reduced size, hence a random sequence is irreducible. Any ordered sequence, on the contrary, can be encoded (at least in principle) by a program (or an algorithm) which is shorter than the sequence itself. Therefore, an ordered sequence is reducible.

While the above discussion is a simplified presentation of some seminal concepts of ATP, it can, hopefully, help to comprehend the definition of irreducible complexity given in ATP. We will discuss this definition after a few preliminary remarks.

Every system, including the biochemical ones described by Behe, can be represented by a certain algorithm, or, if we prefer a computer-related parlance, it can be represented by a program which encodes the system. The code essentially boils down to a sequence of symbols which can be expressed in binary digits. If a system is not random, and hence obeys a certain rule, the encoding program in question (or algorithm) can be compressed, i.e. made shorter (in number of bits) than the size of the system itself, by using the rule in question.

Complexity of a system is defined in ATP as the minimum size of a program (or of an algorithm) that is capable of encoding the system. (Actually the minimal size can only be defined with a certain "fudge factor" involved, which, though, is not a crucial point for our discussion.) The more complex a system is, the larger the size of the minimal program that can encode that system. If the size of the minimal encoding program cannot be reduced below the size of the system itself, i.e. if the minimum size of the encoding program (or algorithm) approximately equals the size of the system itself, the complexity of such a system is defined as irreducible.

Note, that the definition of complexity in ATP is very different from the definition given by Dembski. The latter defined complexity in terms of the difficulty in solving a problem and identifies complexity as low probability. Dembski's definition provides no clue as to what can make complexity irreducible. The definition of complexity in ATP is a definition of the complexity of a system per se rather than of the difficulty in its reproduction. We will see later, that ATP complexity has a relationship to probability which is opposite to that of Dembski's complexity.

The basic definition relevant to our situation is then as follows: a system is irreducibly complex if the minimum size of a program that is capable of encoding the system approximately equals the size of the system itself. On the other hand, if a system is not random, there exists (at least in principle) a rule prescribing the structure of that system. Using that rule, an encoding program can be designed (at least in principle) which is much shorter than the system itself, as this system is represented by an ordered sequence of binary digits.

Hence, a very important consequence of the basic theorems of ATP is as follows: if a system is indeed irreducibly complex, it is necessarily random. (The proper term is quasi-random, because, strictly speaking, only infinitely large system can be unequivocally determined as random, but this subtle point is not crucial for this discussion.)

In other words, ATP has established that irreducible complexity is just a synonym for (quasi) randomness.

Whatever examples of biochemical systems Behe can come up with, he cannot eschew the indisputable mathematical fact: if a system is indeed irreducibly complex, it is necessarily random. Of course, any system that is the result of intelligent design (or even of an "unintelligent" design) is, by definition, not random. The unavoidable conclusion: if a system is indeed irreducibly complex, it cannot be the product of design!

We see that if Behe wished to stick to his term of irreducible complexity, his entire explanation, which suggests that biochemical systems are irreducibly complex and therefore must be products of a design, would make no sense.

In terms of ATP, however, biological systems are never irreducibly complex. Indeed, a tiny seed contains the entire information necessary to grow an oak. The complexity of an oak is reducible to the much smaller program encoded in a seed.

While Behe's term is a misnomer, and no biological system is irreducibly complex in terms of ATP, we can just say that Behe simply has not chosen his term well. Does his concept, mislabeled irreducible complexity, have nevertheless some meaning different from the term of ATP?

Reviewing Behe's multiple examples of biochemical machines, we can see that what he actually implies by his term, is the interdependence of all the components of a biochemical machine, such that the removal of any element of it renders it dysfunctional. We will have to discuss whether or not biochemical systems are indeed characterized by such a tight interdependence of all of their constituents, as suggested by Behe, and whether or not, if they indeed are, this indeed points to intelligent design.

9. Maximal simplicity plus functionality vs. irreducible complexity

Let us approach the problem of the connection between complexity and design utilizing an analogy to the famous watchmaker argument. In that argument, one is asked to answer the following question: if you found a watch, would you believe that it was a result of a spontaneous natural process or that it was designed by a watchmaker? Of course, the answer is unequivocal, and everyone agrees that a contraption which performs a well defined function must be the product of intelligent design. Let us analyze, what feature of that watch led to the conclusion that it was a product of design? Was it the watch's complexity?

To answer the last question, let us formulate the problem a little differently. Suppose you sit at a beach and pick various pebbles. Most of them have irregular shape, with a rough surface, with their color varying from spot to spot, and their density also varying over its volume. Suppose that you come across one particular piece which, unlike all other pebbles, is of a perfectly spherical shape, its color and density perfectly uniform all over its volume and its surface polished mirror-like. Obviously, the rational conclusion is that the perfectly spherical piece is an artifact, a result of an intelligent effort, including design, planning and a set of actions aimed at achieving the goal of producing that perfectly uniform ideal sphere. While we don't know the purpose of the designer of that spherical artifact, we have to admit that its spontaneous appearance is unlikely. Any other piece of pebble, with its irregular shape, is, more likely, a result of some spontaneous natural process. Now, the spherical piece is extremely simple and can be described by a very simple formula requiring only two numbers, the diameter and the constant density plus naming its color. The full description of that spherical artifact requires a simple program of a small size. Any other piece of pebble with its complex shape and a non-uniform distribution of density, color and surface roughness, cannot be described by a simple program, but rather by a much more complex one, containing many numbers.

This example again illustrates that complexity in itself is more likely to point to a spontaneous process of random events while simplicity (low complexity) more likely points to intelligent design. This is in full agreement with the definition of complexity given in ATP but contrary to the definition of complexity given by Dembski. Regarding the ideal sphere, its complexity in terms of ATP, that is its complexity as a system, is very small. However, the probability of its spontaneous emergence is also very small, which is opposite to the relation between Dembski's complexity and probability. In Dembski's terms, the simpler a system is, the larger its probability. A system which is simple in ATP's sense, but fully functional, is complex in Dembski's terms, since its probability is small. A system that is simple in ATP's sense and also fully functional more likely points to design than to chance. This conclusion is contrary to Behe's concept which attributes large complexity to design.

In fact, our conclusion about the likely origin of a watch was based not on its complexity, but rather on its functionality. The watch performs a definite task, and that gives rise to our conclusion. Nothing prohibits a very complex system from emerging as a result of random events. Functionality is what seems to point to intelligent design. In the case of an ideal sphere, we inferred design not because of the sphere's complexity, but because of its obvious artifactuality (the term introduced by D. Ratzsch, for example in his book Nature, Design and Science, State University of New York Press, 2001).

If we analyze the examples given by Behe, we have to conclude that his thesis was not about irreducible complexity but rather about the functionality of biochemical systems, or, more specifically, about a strict interdependence of the system's components, each of them being necessary for the system to properly function. In Behe's often discussed example of a mousetrap, the feature relevant to the discussion was not the trap's complexity or irreducibility. The indication of design was the trap's functionality, its ability to perform a certain task by means of a simple combination of parts.

It is easy to provide examples of systems which are even much simpler but nevertheless meet Behe's actual rather than proclaimed formula. One such example was given in a paper printed in the collection Mere Creation by the already mentioned mathematician Berlinski, who strongly supports the concept of intelligent design, but is obviously aware of weaknesses in Behe's position. Imagine a regular chair with four legs. Of course, it is a very simple system. Cutting off a leg renders the chair unusable. Hence, according to Behe's actual formulation, which he strangely seemed not to realize himself, that chair meets the requirement of what Behe unduly labeled "irreducible complexity."

Now, since complexity in itself more likely points to a spontaneous chain of random steps rather than to intelligent design, what are the features of a system which would point to intelligent design? It is a combination of simplicity with functionality. Hence, Behe's definition, first, should have been turned upside down (simplicity instead of complexity) and, second, complemented by one more necessary component - functionality.

If we discover that a system performs a certain task, it can (but not necessarily does) point to a design. The simpler the system in question, and the better it performs a certain task, the more likely is its origin in intelligent design. The more complex the system performing a certain task, the less likely is the suggestion of intelligent design. Hence, if Behe, and with him his followers, want to test whether a system was likely created via intelligent design, they must have in their possession criteria which would enable them to determine whether the complexity of the system performing a certain task is close to the minimally possible while preserving its functionality. Behe did not suggest nor did he apply such criteria to the biochemical systems he described. Therefore his assertion that those systems were "irreducibly complex" (which actually should be redefined as "most simple but functional") was not substantiated. The sheer complexity of the biochemical system is rather an argument against the probability of intelligent design, especially if it is not shown that their complexity is close to the minimum possible while preserving functionality.

As an example of an irreducibly complex system, Behe refers to a simple five-part mousetrap. A mousetrap can be constructed in various ways. What is missing in Behe's discourse, is proof that the particular design of a trap he described is indeed close to being as simple as possible. Moreover, it is easy to demonstrate that the five-part mousetrap described by Behe can easily be reduced to a four-part, three-part, two-part, and finally a one-part contraption still preserving the ability to catch mice. (A nice example of four- , three-, two- , and one-part contraptions each capable of catching mice, can be seen at John McDonald's website at A reducibly complex mousetrap). Alternatively, a mousetrap could be built in steps, starting from a one-part version, and adding more parts, improving the mousetrap's performance at each step. Behe should have thought more carefully about the example allegedly illustrating his thesis.

10. Two facets of intelligent design

Note that the concept of intelligent design is twofold. It comprises, first, the idea of design, and, second, the idea of that design being intelligent.

Just for the sake of illustration, imagine a situation which is intentionally simplified to the extreme, and not intended to be viewed as realistic. Hopefully readers will forgive the obvious frivolity of that example. Assume that on a certain planet X the civilization developed without developing chairs, so the inhabitants of that planet, if they wished to sit down, had to do so by sitting on the ground. Imagine further that an idea of a chair took hold and a competition was announced for inventing a comfortable chair. Now assume that among the submitted proposals were chairs with various numbers of legs. Of course, all of those chairs, once made, would be the results of design. However, not all of them would qualify to be viewed as designed intelligently. For example, chairs with only one or two legs attached at the corners of the seat would be impractical and therefore their design would be rather viewed as imbecilic. A chair with three legs would be the most intelligently designed since it would combine a reasonable level of comfort with the best stability, least dependent on the flatness of a floor. The design of a three-legged chair would deserve the definition of intelligent design. A four-legged chair would have the drawback of being less stable on an imperfectly flat floor. However, a four-legged chair may win as a little more comfortable. Hence, both the three-legged and four-legged designs could be reasonably viewed as intelligent. (Since this example is somehow on a facetious side, we ignore multiple possible variations of seats, such as chairs without legs, chairs hung from ceilings, sofas, etc.) Assume now that among the submitted designs were five, six, and seven-legged chairs. Now imagine that the inhabitants of X were not among the smartest people in the universe, so they chose to opt for seven-legged chairs (maybe in their religion number seven was also supposed to have a special meaning). Assume that a visitor from another planet, Y, where still no chairs had been in use, came to X and saw the seven-legged chairs. The visitor, who never saw any other type of chairs, might admire the seven-legged chairs as an amazing invention. Since he never saw four- or three-legged chairs, he might believe that all seven legs were necessary. If that visitor happened to be a disciple of Behe, and had never had a chance to try a four- or a three-legged chair, he could conclude that he saw in a seven-legged chair that famous irreducible complexity. This, in its turn, might lead him to the conclusion that a seven-legged chair was a result of intelligent design. He might never suspect that the design of that chair was in reality not very intelligent, but rather based on excessive complexity. (We will additionally discuss excessive complexity in a following section).

Similarly, many biochemical systems described by Behe could very well be excessively complex. If they are excessively complex, it can be ascribed either to an unintelligent design, or to a chain of random steps of evolution. I don't think anybody would entertain as reasonable the idea of an unintelligent design on a cosmic scale. Hence, unless there are proofs that the complexity of a system is not excessive, its complexity more likely points to randomness than to intelligent design.

At the beginning of this article we quoted David Berlinski, a mathematician who highly commended Behe's book (in rather general terms). It is of interest to look at another quote where Berlinski relates to specific points in Behe's book, using a mathematical approach. On page 406 of the collection Mere Creation Berlinski writes: "The definition of irreducible complexity makes strong empirical claims. It is foolish to deny this as well to suggest that these claims have been met. The argument having been forged in analogy, it remains possible that the analogy may collapse at just the crucial joint. The mammalian eye seems irreducibly complex; so, too, Eucariotic replication and countlessly many biochemical systems, but who knows?"

Indeed, who knows? This statement, rather devastating to Behe's theory, is especially impressive since it comes from a man who is regarded by the proponents of intelligent design as one of their most accomplished mathematicians and a staunch anti-Darwinist. Berlinski's statement reveals one of the weakest points of Behe's position – the absence of proof that the biochemical systems he describes indeed possess what he mislabeled irreducible complexity, but which actually is a tight interdependence of elements and an accompanying lack of compensatory mechanisms (see next sections).

Behe's discourse provides no proof that irreducible complexity (in his sense of the term) is indeed present in cells, it provides even less indications that the systems in question are irreplaceable, that is they cannot be replaced by another system, which would perform the same function, possibly in a more efficient way.

At least two features, if present in a system, speak against the hypothesis of intelligent design. One is excessive complexity, and the other, the absence of self-compensatory mechanisms.

11. Excessive complexity

We have established so far that if the irreducible complexity (either in ATP or in Behe’s sense) is indeed present, it rather points (for two different reasons) to the absence of design. However, this does not mean that if complexity is not irreducible, it must point to design. The complexity that is reducible (in Behe’s sense) can be justifiably viewed as excessive, and as such it also points to absence of design. Another term for it is redundant complexity (Niall Shanks and Karl H. Joplin, Redundant Complexity: A Critical Analysis of Intelligent Design in Biochemistry. Philosophy of Science, 66 (2) (June 1999): 268).

The proposition of the excessive complexity is not just a logical conclusion. There exists a direct experimental evidence pointing to the excessive complexity of some biochemical systems. Moreover, one such evidence relates precisely to that mechanism of blood clotting which Behe had chosen as an example of what he named irreducible complexity. In the 1990s, biochemists learned how to "knock out" individual genes from an animal's genome. In the paper by a group of researchers headed up by Bugge (Cell, v. 87, pages 709-719, 1996) the results of an ingenious experiment have been reported. These researchers succeeded in removing from a group of mice the gene which was instrumental in producing fibrinogen, a protein necessary for blood clotting. These mice lost the ability to clot blood and suffered from hemorrhage. In another group of mice, the researchers "knocked out" the gene responsible for production of plasminogen, the protein ensuring a timely cessation of blood clotting and hence preventing trombotic problems. As it could be expected, the mice without plasminogen had serious trombotic problems. However, when both groups of mice were crossed, the issuing generation, that had neither fibrinogen nor plasminogen, turned out to be normal for all intents and purposes. This experiment has shown that what Behe described as irreducible complexity of the blood clotting system, was actually excessive complexity, since the removal of two proteins (rather than of one only) from the system resulted in some alternative mechanism taking over.

As professor Russell Doolittle, who is a prominent microbiologist, an expert on blood clotting, wrote referring to Bugge et al (in Boston Review, v.22, No1, p.29, 1997) "Music and harmony can be achieved also with a smaller orchestra."

In a paper published in the collection "Science and Evidence for Design in the Universe" (Ignatius Publishers, 2000) Behe responded to Doolittle and argued that the experiment by Bugge at al did not actually prove what I call excessive complexity. Since I am not a biologist, I will not delve into the arguments offered by Doolittle or Behe. We see here a dispute between two microbiologists, so the problem for us, laymen, is whose view to trust. However, I could not fail to notice a peculiar feature of Behe's argumentation. In the mentioned paper he claimed that, after having considered Behe's rebuttal, Doolittle conceded being wrong in his interpretation of Bugge's results. To my inquiry, professor Doolittle categorically denied ( in a private message) having ever given a reason for Behe's claim. Contrary to Behe's claim, Doolittle strongly adheres to his original view. When I see a method of discussion in which to one's opponent is attributed something he never said, as seems to have been done by Behe in this case, I am inclined to doubt the rest of Behe's assertions as well.

Many more examples of excessive (or redundant) complexity of biological systems are known (see, for example the paper by Niall Shanks and Karl Joplin referred to earlier in this article).

This discourse shows that the enormous complexity of events in a cell, so amply demonstrated by Behe, very often can be referred to as excessive complexity. Therefore the conclusion that the complexity in question can only be attributed to intelligent design is unfounded. On the contrary, the complexity in question is quite often an excessive complexity, which points to its being a result of random events rather than that of deliberate design.

12. Absence of self-compensatory mechanisms

Excessive complexity is not the only argument against intelligent design. The strict interdependence of all elements of a biochemical system, even when it is not excessive, while not contradicting a possibility of design, clearly speaks against it being intelligent. Indeed, intelligently designed machines are expected to have built-in self-compensatory resources. If unforeseen circumstances render some elements of the machine dysfunctional, the self-compensatory mechanism automatically takes over the damaged function. If having bought a car we discovered that its designer failed to provide space and a holder for a spare tire, we hardly would praise the designer's intelligence. Without a spare tire, each time a tire blew, it would render the entire vehicle dysfunctional, precisely as the removal of or damage to a single protein allegedly renders the entire biochemical machine dysfunctional according to Behe's concept of "irreducible complexity". The very essence of Behe's mislabeled irreducible complexity implies the absence of self-compensatory mechanisms in biochemical machines. If the removal (or damage) of a single protein indeed makes the entire machine dysfunctional, as Behe asserts, it is a very serious fault of the alleged designer, whose intelligence immediately appears suspicious. Since, again, the hypothesis of a stupid designer acting on a cosmic scale is hardly satisfactory for any "design theorist," the constitution of biochemical machines, if they indeed are as described by Behe, is quite a strong argument against intelligent design.

(Biologists tell us, however, that biochemical systems do actually possess redundancy enabling them to compensate for the malfunction of certain parts of the protein machines. If that is true, then the systems so picturesquely described by Behe are hardly irreducibly complex.)

I can envision a counter-argument accusing me of not leaving room for intelligent design at all. Indeed, if, in my view, either the absence of self-compensatory mechanism or the irreducible complexity (in the ATM sense) both point to a random chain of events rather than to intelligent design, isn't this self-contradictory? My answer to such an argument is as follows: First, my task is not to suggest a criterion of intelligent design but rather to test the validity of Behe's arguments. In my view (see also A consistent inconsistency) the design inference is necessarily probabilistic. If we see a poem or a novel, we have no difficulty in attributing it to design because design is in this case overwhelmingly more likely than emergence of a long meaningful text as a result of random unguided events. Our inference in this case is based on our ken, as we have extensive experience with texts written by men and can easily recognize them. On the other hand, when we deal with a biological system, our probabilistic estimate cannot be based on our ken because we don't know in advance what the system in question must look like to be attributed to design. If a biological system is indeed "irreducibly complex," either in Behe's or in the ATP's sense, in both cases this is compatible with the assumption of its origin in a random process but (probabilistically) speaks against the design inference. If a biological system possesses redundancy which serves as a self-compensatory mechanism, this is equally compatible with both design inference and the absence of design, but in this case Behe's assertion of "irreducible complexity" is contrary to the facts. If a biological system had no built-in self-compensatory mechanisms (as Behe suggests) this is an argument against the intelligent design (although not necessarily against design as such).

Therefore Behe's entire concept hangs in the air. It does not provide a reasonable argument in the design vs. chance controversy.

I don't know arguments which would decisively disprove the suggestion of intelligent design. However, Behe's discourse, in my view, adds no valid argument in favor of intelligent design.

13. Conclusion

In this paper, I have omitted discussion of many secondary points and details in Behe's book, concentrating only on his main argument in favor of "intelligent design," the concept he calls by a misappropriated term of "irreducible complexity" of biochemical machines.

Behe maintains that the alleged irreducible complexity of the systems in biological cells could not emerge spontaneously and therefore must be attributed to intelligent design. Although Behe avoids naming the alleged designer, there is little doubt who this designer is supposed to be.

Without discussing the question of whether there was a divine designer or the biological systems are the result of a very long process of random interactions between molecules combined with a non-random natural selection, I have suggested in this paper that Behe's argumentation is flawed.

Let us briefly summarize the main points of our discussion.

1) The very term "irreducible complexity" has been misappropriated by Behe since, before Behe used it, it has been rigorously defined mathematically but denoted a different concept. If any system reviewed by Behe happened to indeed be irreducibly complex, according to the proper definition of that concept, it would mean that system is random, and, hence hardly the product of design.

2) An inseparable part of Behe's concept is the complexity of biochemical systems. That complexity itself, however, points not to an intelligent designer but rather to a chain of unguided random events. The probability of a spontaneous emergence of a complex system performing a certain function is much larger than the probability of the spontaneous emergence of a system which performs the same function in a simpler way. (The simpler the system capable of performing a certain function, the more complex the problem of creating such a system, and hence, the less probable its spontaneous emergence).

3) Biological systems are never irreducibly complex in the mathematical sense of the term. Their programs are intrinsically reducible to shorter sets of instructions contained in embryos, or seeds, or the combinations of spermatozoids and eggs, etc.

4) Since there is no proof that any of the systems described by Behe is indeed irreducibly complex (in Behe's terms), many of them may be excessively complex, which is an argument against intelligent design.

5). If any biochemical machine is indeed irreducibly complex (in Behe's terms) it means it lacks compensatory mechanisms and is highly vulnerable to any accidental damage to a single protein which would render the entire system dysfunctional. Such a structure of a biochemical machine, if it is indeed as described by Behe, points to a lack of intelligence of the alleged designer, and, hence, rather to the absence of a designer.

In view of the above, I submit that Behe's book and his theory of irreducible complexity add no valid arguments to the discussion of the "evolution vs intelligent design" controversy.

Behe's (and his supporters') rejection of Darwin's theory is limited to pointing to aspects of that theory which have not yet been sufficiently explained or understood. Every scientific theory is incomplete and fails to explain some facts. This does not negate the theory's positive features. Newton's mechanics fails to explain, for example, the behavior of elementary particles. This does not mean Newton's theory must be rejected. Indeed, this theory is extremely useful, for example, in planning the flights of spacecrafts where its precision is amazingly good. Darwin's theory (or Neo-Darwinism in its various forms) like any scientific theory, may be correct in some respects and weak in some other. We can't demand of any theory answers to all questions about the evolution, and even less about the origin of life. Moreover, the progress of science may indeed reveal that Darwin's theory contains more weaknesses than truths. This does not seem very likely, though, since the evolution theory certainly contains many empirically verified elements and to dismiss it, as some creationists actively try to do, would be a regrettable loss. Therefore, attempts to overthrow Darwin's theory, as Behe, Dembski, Johnson and their cohorts do with gusto, on the basis of often dubious and sometimes even obviously incorrect notions is not a fruitful way to search for truth.

14. Appendix (posted on May 18, 2002)

In his reply to John H. McDonald Behe insists that McDonald's counter-example with the reducible mousetrap is not good because when the trap is improved by adding new parts, each time this is done by intelligent design. While the statement itself is correct, it is meaningless in the context of the dispute. Using his argument, Behe displays either deliberate or inadvertent inconsistency. Indeed, when, in his foreword to Dembski's book Intelligent Design Behe discussed the difference between the phrase METHINKS IT IS A WIESEL and a string of gibberish of the same length, he maintained that the phrase from Hamlet was a product of intelligent design while the gibberish was due to chance. However, obviously the string of gibberish he provided was deliberately created by him to illustrate his point and was therefore a product of design not any less than the phrase from Hamlet. It was a product of design in precisely the same sense as less-than-five-parts mousetraps were deliberately designed by McDonald. In both cases the examples were deliberately designed to illustrate certain notions. Behe, though, inconsistently attributes McDonald's reduced mousetraps to design but his string of gibberish, to chance. To be consistent he should have viewed both cases in the same way. If McDonald's partial mousetraps are viewed as designed, then the string of gibberish must also be viewed as designed. If, though, the string of gibberish is viewed as chance-generated, then McDonald's mousetraps must be viewed in the same way. Indeed, although McDonald has indeed designed his mousetraps, it was done only to illustrate his thesis and did not imply that his model represented the biological reality. Neither did Behe's model of a five-part mousetrap. (It is sufficient to point out that mousetraps cannot replicate so, unlike biological systems, cannot be a result of evolution). The string of gibberish was designed by Behe to illustrate how a product of chance could look like. McDonald's series of mousetraps was designed in the same way, to illustrate how a system could have gradually developed from a simplest version through intermediate steps to the final five-part construction. What caused the development in question, conscious design or blind forces of evolution, was irrelevant for the purpose of McDonald's example. The latter, while not pretending to reflect the entire complexity of the actual process of evolution, nevertheless very well illustrates that Behe's mousetrap is not irreducibly complex in Behe's sense. Contrary to Behe's assertion, out of the five parts of the mousetrap, four can be removed one by one and the remaining contraption still can be made suitable for catching mice, i.e., preserving the functionality of the device although on a lower level of fitness. The trap also can be started as a one-part device and gradually improved by adding more parts enhancing its ability to catch mice at every step. This is a good illustration of the evolution process, which is necessarily simplified in order to exemplify just one of the features of the real biological evolution. While Behe's model is hopelessly inadequate since it contradict his main thesis of irreducible complexity, McDonald's model, although largely simplifying the evolutionary process, is quite adequate to illustrate some basic points of that process by showing how a good mousetrap can be built step-by-step, improving its fitness at each consecutive step. For this illustration, it is of no significance that in biological evolution the development of ever improving organs is not due to design but is governed by the powerful forces of natural selection while in McDonald's example he consciously changed the construction from step to step. What McDonald did consciously with his series of rather large steps of improving the mousetrap, is done in biological organisms very slowly but inexorably by the unconscious and undirected forces of natural selection. No casuistry of the type used by Behe can rebut the adequacy of McDonald's example.

15. Comment on May 26, 2002

Recently, John McDonald updated his example of a gradually developing mousetrap. His updated version offers an impressive rebuttal of Behe's unsuccessful attempt to dismiss the relevance of McDonald's original version of the series of mousetraps. In the new version, McDonald shows, instead of only four, rather large steps in the gradual development of Behe's five-part mousetrap, a series of much smaller steps, starting with a simple piece of a bent wire which could serve as a primitive and not very reliable mousetrap, but, which, as McDonald states, is still better than no mousetrap at all. In the process of improving the mousetrap, McDonald shows how some parts which are gradually added to improve the trap's performance, first are optional, but as other parts are added, the optional parts become necessary for the proper functioning of the device. This illustrates the evolutionary process in biology (while McDonald warns that his example is not a real picture of biological evolution but just an analogy for the sake of illustration). McDonald's new example is animated. It decisively lays to rest Behe's claim about the irreducible complexity of his mousetrap as a model of irreducible complexity of a cell. Of course, we can expect attempts on Behe's and his defender Dembski's part (see the paper A Free Lunch in a Mousetrap on this site) to stubbornly reject McDonald's spectacular example. There is little doubt, though, that such attempts will be as meaningless as the incoherent quasi-arguments that have been offered by Behe and Dembski as allegedly salvaging Behe's model until now.

Slightly different versions of this article have been printed in Russian in the journal Kontinent, No 107, 2001, published in Moscow, Russia, and in the journal Vremya Iskat, No 5, 2001, published in Russian in Jerusalem, Israel.

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