Even though Dembski has picked a misleading name for his concept, it does not necessarily follow that the concept itself is of no value.  So let us consider the concept on its own merits.  The purpose of specified complexity, in Dembski's system, is as a marker of intelligent design.  He claims that, when an object exhibits specified complexity, we can reliably infer that it is the result of intelligent design.  He even claims that this is the only way of inferring intelligent design.  But inspection of his definition above reveals that this is nothing but an argument from ignorance, or god-of-the-gaps argument.  (Since Dembski is only arguing for an intelligent designer, and not God, perhaps it would be more appropriate to coin a new term "designer-of-the-gaps," but I will stick to the existing term.).  According to Dembski's definition, an object exhibits specified complexity, and is therefore the result of intelligent design, if we do not currently have a detailed explanation for its origin.  This is further supported by the following passage from No Free Lunch:

"But what happens once some causal mechanism is found that accounts for a given instance of specified complexity? Something that is specified and complex is highly improbable with respect to all causal mechanisms currently known. Consequently, for a causal mechanism to come along and explain something that previously was regarded as specified and complex means that the item in question is in fact no longer specified and complex with respect to the newly found causal mechanism." [NFL, p. 330]

Dembski's "specified complexity" is an unnecessary middleman, which acts as a smokescreen for a god-of-the-gaps argument.  Instead of presenting his argument as:

- all relevant chance hypotheses eliminated --> specified complexity --> design,

he could have presented it more straightforwardly as:

- all relevant chance hypotheses eliminated --> design.

The smokescreen is made denser by further equivocation over the meaning of specified complexity.  Dembski's formal definition of the term, as we have seen above, requires him to calculate a probability with respect to each relevant chance hypothesis.  Frequently, however, he drops this requirement and implies that it is sufficient to consider just once chance hypothesis.  This is the case with his so-called Explanatory Filter, which makes no mention of chance hypotheses, and in statements such as this one:

"Determining whether an irreducibly complex system exhibits specified complexity involves two things: showing that the system is specified and calculating its probability..." [NFL, p. 289]

In practice, almost every one of Dembski's examples considers only one chance hypothesis, and that chance hypothesis involves a uniform probability distribution, i.e. all possible outcomes have equal probability.  It is not surprising, then, that many of his readers--apparently including Young--have come to the conclusion that this is the only sort of probability distribution that need be considered.

Of course, the raison d'etre of Dembski's notion of specified complexity is to demonstrate the involvement of an intelligent designer in biological evolution.  So it will be instructive to take a brief look at his sole application of the method to biology.  The biological event he chooses is the origin of the flagellum of the bacterium E. coli.  In this case, Dembski considers only one chance hypothesis, and, as usual, it is based on a uniform probability distribution.  He takes the proteins which constitute the flagellum and considers all the possible ways of arranging these together.  He then argues that, under the hypothesis that all these configurations are equally likely, the probability is minuscule of obtaining anything that would function as a flagellum.  Now, regardless of whether the details of Dembski's probability calculation are correct, no one would dispute the conclusion. But it is irrelevant.  No one proposes that the flagellum arose by purely random arrangement of proteins (or of amino acids, another option that Dembski considers).  Evolutionary biologists propose that the flagellum evolved by a process involving natural selection, which is far from being purely random.  In short, this is just the old creationist "tornado in a junkyard" straw man, which likens evolution to the possibility of a Boeing 747 being constructed by a tornado randomly assembling its parts.

To be fair, Dembski's argument goes further.  He claims to give a "proscriptive generalization" based on "irreducible complexity" that rules out any possibility of the flagellum evolving by a Darwinian process of evolution.  This is apparently intended to justify treating the hypothesis of purely random assembly as the only relevant one.  Even if this proscriptive generalization were valid, the argument would clearly be a god-of-the-gaps argument: we've ruled out Darwinian evolution and purely random assembly; we can't think of any other possible explanations; therefore the flagellum exhibits "specified complexity" and must have been designed.  But since everyone already agreed that purely random assembly was not a viable explanation, that part of the argument is irrelevant, and the argument amounts to no more than the argument from irreducible complexity, an argument already made by Michael Behe[6].  The introduction of "specified complexity" to the argument serves no useful purpose at all.

Worse still, Dembski's argument from irreducible complexity is a failure.  Like Behe, Dembski fails to seriously consider the possibility that the flagellum may have evolved from a system with a different function.  Yet such co-option of existing systems is a fundamental part of evolutionary theory. Dembski considers only a straw man version of co-option, in which all the proteins in a system are individually co-opted from other functions.  (The same straw man is invoked by Bracht in his recent post to this forum.)  He does not consider the possibility that a major part of the system may have been co-opted from another function as a single unit.  When challenged on this point, his response is that it is unreasonable to expect him to establish a "universal negative"[5], i.e. to show that there is no viable evolutionary pathway to the flagellum.  But that is just what his proscriptive generalization was supposed to show.  Without it, the argument from irreducible complexity turns out to be another argument from ignorance.

So far I have concentrated on "complexity" and hardly mentioned "information."  In fact, little additional discussion is needed, since Dembski treats "information" as a synonym for "complexity," defining it by the formula -log₂p.  So Dembski's "information," like his "complexity," is just a rescaled measure of improbability.  As we saw above, however, Dembski likes to give the impression that he is using "information" in the widely-used technical sense invented by Claude Shannon and often known as "Shannon information."  Young appears to have been influenced by these suggestions, and assumed that this is really what Dembski's "information" means.  However, Dembski's usage is not the same as Shannon's.  Shannon, who was concerned with the efficiency and reliability of transmitting data through a communications channel, defined information in terms of the rate of transmission of data, considered over the ensemble of all possible messages which might be transmitted.  (Shannon information is discussed in more detail in the Appendix below. It is different from the "algorithmic information" mentioned above, though there are significant links between the two.)  Dembski, on the other hand, simply uses "information" as a synonym for improbability.  He also uses a term of his own invention, "complex specified information" or "CSI," as a synonym for "specified complexity."

Although I disagree with Young's interpretation of Dembski's argument, I do agree with his conclusion, namely that Dembski has made the subject unnecessarily complicated.  In short, I conclude that Dembski's use of the terms "specified complexity" and "information" is nothing but a smokescreen for a god-of-the-gaps argument.

If antievolutionists wish to argue that undirected evolution of a flagellum is implausible, they need to address the real arguments of evolutionary biologists and biochemists, and that means getting their hands dirty with the biochemical details.  (If they did so, there would be little for me to say in response, since I am no expert on biochemistry.)  Instead, they keep searching for magic bullets with which to slay the beast of evolution at a stroke.  Amongst the candidates so far have been thermodynamic entropy, irreducible complexity, specified complexity and information.  The latest would-be magic bullets are appeals to fitness landscapes, the No Free Lunch theorems and "TRIZ," as seen in recent work by Dembski and Bracht.  But those are subjects for another day.

I hope that this article will prove useful in clearing up some of the confusion surrounding "specified complexity" and "information."  A more detailed discussion of these issues can be found in my online critique[7] of Dembski's book No Free Lunch.

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APPENDIX - Shannon Information

[This appendix originally appeared as an endnote to my critique of No Free Lunch.  The mathematical notation may be easier to read in the original, which can be found at http://www.talkorigins.org/design/faqs/nfl/#shannon]

I have found in past discussions of Dembski's work that considerable confusion has been caused by his misuse of Shannon information theory.  Although not essential to my critique, I will attempt here to clear up some of this confusion.  My main source is The Mathematical Theory of Communication (Univ. of Illinois Press, 1949). This small book consists of two papers, one each by Claude Shannon and Warren Weaver.  An earlier (1948) but largely identical version of Shannon's paper is available online at http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html.  For a more gentle online introduction to information theory, see http://www.lecb.ncifcrf.gov/~toms/paper/primer/.

Shannon information theory is concerned with the transmission of messages through a communications channel.  The meaning of the messages is immaterial.  All that matters is the efficiency and accuracy with which messages are transmitted.  Messages are treated as if they were selected at random from an ensemble of possible messages.  This means that the same theory can also be used in relation to other types of probabilistic events, in which the occurrence of one outcome is observed out of a set of possible outcomes.

The rate of transmission of information is defined by Shannon as follows:

R = H(x) - H_y(x)

If we think in terms of transmitting a message, drawn randomly from a set of possible messages, from a transmitter to a receiver, then H(x) is the receiver's uncertainty about which message was (or will be) transmitted before receiving any message.  H_y(x) is the receiver's uncertainty about which message was transmitted after receiving a message.  R can also be thought of as the reduction in uncertainty as a result of receiving the message.  If the channel is free of noise--so the message received is always the same one that was sent--then H_y(x) = 0 and R = H(x).  The uncertainty H(x) (or simply H) is defined as follows:

H = - Σ_i=1...N p_i log₂p_i

where there are N possible messages and the probability of message i being transmitted is p_i.

It is important to bear in mind that R and H are rates, or averages (weighted by probability), based on the ensemble of all messages which could possibly be transmitted.  They are not values associated with the receipt of one particular message.  There is, however, another measure, defined as -log₂p_i, which is associated with receipt of a specific message.  It is sometimes known as surprisal, after M. Tribus [Thermostatics and Thermodynamics (D. van Nostrand Co., 1961)], as it indicates how surprised we should be at receiving that message.  The uncertainty H is then equal to the average surprisal, over all possible messages, weighted by probability.

There appears to be some disagreement about which measure is correctly known as the Shannon information.  Some writers, including Dembski, refer to the surprisal as the Shannon information associated with the receipt of one specific message.  The thinking seems to be that, if H is the rate of transmission of information averaged over all possible messages, then the surprisal must be the information associated with the receipt of one particular message.

However, this is not the usage of Shannon or Weaver, who refer to R as the information. Consequently, most information theorists refer to R as the Shannon information.  The expression -log₂p_i appears nowhere in the Shannon and Weaver papers.  For a noise-free channel, Shannon equates information with uncertainty:

"The quantity H has a number of interesting properties which further substantiate it as a reasonable measure of choice or information." [Shannon & Weaver, 1949, p. 51]

Weaver is more explicit, and makes it clear that information is a property of the ensemble of possible messages, not of one particular message:

"To be sure, this word information in communication theory relates not so much to what you do say, as to what you could say. That is, information is a measure of one's freedom of choice when one selects a message. If one is confronted with a very elementary situation where he has to choose one of two alternative messages, then it is arbitrarily said that the information, associated with this situation, is unity. Note that it is misleading (although often convenient) to say that one or the other message conveys unit information. The concept of information applies not to the individual messages (as the concept of meaning would), but rather to the situation as a whole, the unit information indicating that in this situation one has an amount of freedom of choice, in selecting a message, which it is convenient to regard as a standard or unit amount." [Shannon & Weaver, 1949, pp. 8-9]

Note that, when all the possible outcomes are equally probable (i.e. p_i is a constant p) the uncertainty reduces to - log₂p:

H = - Σ_i=1...N p_i log₂p_i
    = - N . p log₂p
    = - N . 1/N . log₂p
    = - log₂p

This must not be confused with the surprisal, although it has the same formula. For an ensemble of possible outcomes which are all equally probable, the surprisal of each outcome just happens to equal the uncertainty of the ensemble.

For the sake of an example, consider a 5-card hand dealt from a well-shuffled deck of 52 cards.  There are (52×51×50×49×48)/(5×4×3×2×1) = about 2 million possible outcomes.  Since all outcomes are equally probable p = 0.0000005, and the uncertainty (H) associated with the deal is -log₂(0.0000005) = 21 bits, using the special formula for equiprobable distributions just derived above.  Once we have seen the 5 cards there is no uncertainty about what was dealt, so H_y(x) = 0, and the Shannon information is given by R = 21 - 0 = 21 bits.

Now suppose that, as in Dembski's example (pp. 126-127), a royal flush (10-J-Q-K-A in one suit) is dealt.  There are 4 possible royal flushes (one in each suit), so the probability of a royal flush of any suit is 4 × 0.0000005 = 0.000002.  The surprisal of this event is therefore -log₂(0.000002) = 19 bits.

Like some other writers, Dembski refers to the surprisal (-log₂p_i) as Shannon information (p. 230n16).  This in itself is not particularly important.  What matters is not what he calls this measure but how he uses it.  The trouble is that he merely uses it as a disguised probability measure.  The function f(x) = -log₂x is a monotonic function, which means that greater surprisal always corresponds to greater improbability.  Every one of Dembski's statements about information could just as well (and with much greater clarity) be expressed as a statement about improbability.  He often uses the terms improbability, information and complexity interchangeably.  In the index of The Design Inference he even has an entry for "probability... information in disguise."  By disguising his probabilities as information, Dembski simply adds another layer of obfuscation to his arguments, without achieving anything of value.

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REFERENCES

6. Michael Behe, Darwin's Black Box, Simon & Schuster, 1998.

7. Richard Wein, "Not a Free Lunch But a Box of Chocolates: A critique of William Dembski's book No Free Lunch,” April 23, 2002, http://www.talkorigins.org/design/faqs/nfl/. This page includes links to Dembski's response to the critique, and to my rebuttal of that response.