William Dembski, No Free Lunch: Why Specified Complexity Cannot Be
Purchased Without Intelligence, Rowman & Littlefield, 2002.
A review by Jeffrey Shallit, Department of Computer Science,
University of Waterloo, Waterloo, Ontario, N2L 3G1.
Ever since its inception, the theory of evolution has come under attack
by creationists, who find its account of life's diversity threatening
to their religious beliefs. Modern creationists have had essentially
zero impact on science, but their political impact has been
significant, especially in the United States. There they have managed
to get evolution downplayed in biology curricula and disclaimers
inserted in biology textbooks.
Recently, a group of neo-creationists financed by the Discovery
Institute, a conservative Seattle think tank, has attempted another
approach to dismantle biological education: the so-called "Wedge
Strategy". This strategy is based on an allegedly scientific approach
called "intelligent design" (ID). Roughly speaking, advocates of ID
wish to infer intelligent causes from complex phenomena. Since life is
complex, ID proponents conclude it must have been designed by an
intelligence. Many intelligent design advocates openly admit that this
"intelligence" can be identified with the deity of Christianity
(Maynard, 2001). ID proponents have received much media attention,
although their scientific output, as measured by articles in
peer-reviewed scientific journals, is non-existent (Gilchrist, 1997;
Forrest, 2001).
But as the Wedge Strategy document (Anonymous, 1998) makes clear, the
real goal behind ID is not scientific, but political and religious. ID
proponents wish to "defeat scientific materialism" and replace
science with a new discipline that is "consonant with Christian and
theistic convictions".
Philosopher and mathematician William Dembski is one of the
intellectual leaders of the ID movement. In The Design Inference
(1998) he gave an account of his methodology from which one can
supposedly infer design, but did not seriously address evolution, which
can generate the appearance of design. Later, in Intelligent Design
(1999), he began an attack on the theory of evolution and evolutionary
algorithms that is continued in No Free Lunch, the book under review,
whose title I abbreviate henceforth as NFL.
Central to Dembski's argument is his concept of "specified complexity"
or "complex specified information" (CSI). CSI is not Shannon
information or Kolmogorov complexity, although both concepts are drawn
on in NFL. Roughly speaking, an event exhibits CSI if it matches a
pattern that is both improbable and describable with the background
knowledge of an intelligent agent. Dembski contends that the presence
of CSI is a reliable marker of intelligent design, and CSI cannot be
generated by algorithms, chance, or any combination of them. He
proposes a "Law of Conservation of Information", and argues that
evolutionary algorithms cannot generate CSI, thus casting doubt on
evolution's ability to account for the complexity in biological
organisms.
Has Dembski succeeded in making ID intellectually respectable? No.
Let me not pull any punches: Dembski's No Free Lunch is a poorly
written piece of propaganda and pseudomathematics.
What, precisely, is wrong with NFL? A detailed list of problems would
require dozens of pages, if not more: the recent critical review by
Richard Wein (2002) weighs in at 37,000 words. In this review I
restrict myself to six major themes: mathematical difficulties,
grandiose claims, equivocation, poor writing, misrepresentation, and
poor scholarship.
1. Mathematical difficulties.
For an event to contain CSI, it must be improbable. But improbable
with respect to which probability distribution? An event may appear
very improbable with respect to one distribution while being
significantly more probable with respect to another. Dembski wishes to
infer design in the absence of a causal history---hence, in the absence
of any historical basis for probability estimates---yet omits any
detailed discussion of how, after observing an event, we decide what
class of events it was drawn from.
Furthermore, Dembski appears to use two different methods of evaluating
the probability of an event. If a human being was involved in the
event's production, he typically estimates its probability relative to
a uniform probability hypothesis. For Dembski, a Shakespearean sonnet
exhibits CSI because it would be unlikely to be produced by choosing
several hundred letters uniformly at random from the alphabet. On the
other hand, if no human being was involved, Dembski nearly always bases
his probability calculations on the known causal history of the event
in question. This flexibility in the choice of a distribution allows
Dembski to conclude or reject design almost at whim.
Another significant error occurs on pages 152--154 of NFL, where
Dembski offers what appears to be a complete proof that deterministic
functions cannot generate CSI. This proof is a crucial step justifying
his "Law of the Conservation of Information" mentioned earlier.
First, he assumes that j is an event containing CSI, i is another
event, and f(i) = j for some function f. Next, he argues that "i
constitutes specified information at least as complex as j". (Here
the complexity of j is measured by -log_2 p, where p is the probability
that a random event would match a chosen pattern to which j conforms.)
Dembski's argument is full of the trappings of genuine mathematics:
domains, subsets, inverse maps, and homomorphisms of boolean algebras;
it looks convincing at first glance. There is no doubt that it really
is intended to be a proof, because on page 154 he states "Bottom
line: for functions to generate CSI they must employ preexisting
CSI."
But further down on that page we learn that the proof just presented
was, in fact, not a proof at all. Dembski's reasoning "did not take
seriously the possibility that functions might add information".
Strange --- a reader might suppose this was ruled out by the argument
just covered. But no! He apparently forgot that "the information in
f must now itself be taken into account". (Exercise: exactly where
in the argument on pages 152--154 does this omission occur?) To handle
this, Dembski introduces an operator U such that if f(i) = j then
U(i, f) = j and blithely states (p. 155) "Clearly, the information
inherent in (i,f) is no less than that in j." But it is not so
clear.
For one thing, it is not "information" that is at stake here, but
Dembski's CSI. It is certainly possible that both i and f could
fail to be specified in Dembski's technical sense, while at the same
time j is specified. For example, consider the case where
i is an encoded English message and f is an unknown and obscure
decryption function. If our background knowledge does not
include f, we may recognize j = f(i) as matching a pattern while
i and f do not.
For another, Dembski's notion of information is a statistical one; it
measures "information" through a rescaled form of probability. But
what is the probability distribution corresponding to f? We are not
told. It would certainly be possible at least in some cases, to
invent a probability distribution for f and reason about it, but
this crucial point is simply not addressed in sufficient detail.
Dembski also overlooks the possibility that additional information can
be accumulated simply by iterating f. If f is a length-increasing
mapping on strings, this makes measuring the information content of f
problematic, since choosing the correct associated probability
distribution becomes more obscure.
Dembski confuses things even further by stating "Note that in the case
of algorithms U is a universal Turing machine". Does this mean that
CSI could, in fact, be increased if f were noncomputable (in the theory
of computation sense)? How, indeed, would the CSI of a noncomputable f
even be defined? (Lest the reader think this is a fine technical
point, let me observe that Pour-El and Zhong (1997) have shown that the
unique solution of a certain wave equation with computable initial
conditions is uncomputable.) None of this is explored.
Omissions such as these cast serious doubt on Dembski's claims.
2. Grandiose claims.
Dembski has a high opinion of his own work. He states (p. xii--xiii)
that CSI "is increasingly coming to be regarded as a reliable empirical
marker of purpose, intelligence and design", although to my knowledge
Dembski's coined term "CSI" has not been adopted by any other
probabilist or information theorist. Nor have any papers about CSI
been published, either by Dembski or other researchers, in
peer-reviewed mathematics or statistics journals. Nevertheless, he
insists that specified complexity is the only way to detect design
(p. 116). He also claims his "Law of Conservation of Information" has
"profound implications for science" (p. 163).
On occasions Dembski elevates mathematical trivialities to the level of
profound insights. On page 166 he justifies a claim that "CSI is
holistic" (that is, it cannot be accumulated through an iterative
process) by calculating that the Shannon information of an English
sentence exceeds the sum of the information contained in its individual
words. But a careful examination of his argument shows the missing
information is precisely that contained in the space characters between
the words.
3. Equivocation.
The fallacy of equivocation is to use the same term to mean two
different things. For example, "Nothing is better than complete
happiness. A ham sandwich is certainly better than nothing.
Therefore, a ham sandwich is better than complete happiness." The
conclusion follows only because of the equivocation about the meaning
of "nothing".
The equivocation fallacy is an integral part of the argument in NFL.
For example, the word "specified" is a term of art for Dembski; it
means something very precise and particular, involving a complicated
interplay between functions, probability, rejection regions, and
background knowledge. One can certainly argue that the definition is
incoherent (as I do in Elsberry and Shallit (2002)), but that is not
the point I wish to make here. The point is that according to
Dembski's own rules as laid out in Section 2.5 of NFL, asserting that
something is specified requires a detailed argument involving a
probability calculation. It is not enough to simply assert it.
But that is just what Dembski does when it comes to analyzing
biological organisms. On page 289 he asserts, "At any rate, no
biologist I know questions whether the functional systems that arise in
biology are specified." Perhaps they don't. But the question is not,
Do biologists call such systems specified?, but Are they specified in
the precise technical sense demanded by Dembski? This is equivocation
at its finest (or worst).
Another example appears on page 213. There Dembski discusses the work
of Thomas Schneider (2000), who provided an experimental model showing
how Shannon information may increase in evolution. Dembski says, "As an
example of smuggling in complex specified information that is purported
to be generated for free, consider the work of Thomas Schneider."
Considering that Schneider, like everyone else who works in information
theory, has not made any reference to Dembski's CSI in his paper, this
claim of "smuggling" is unwarranted. Dembski's equivocation fallacy
comes from equating Shannon information --- a well-understood concept
that has been used for fifty years in literally thousands of scientific
papers --- with Dembski's own CSI, which has not.
There are many other examples of equivocation in NFL. The reader may
enjoy constructing a detailed list.
4. Poor writing.
Even a book with bad ideas and poor reasoning may be enjoyable if the
writing is good enough. (I have in mind almost anything by Wendell
Berry.) But NFL does not possess even this saving grace. The book
gives the impression of having been assembled haphazardly from
previously published essays.
Take the name choice in "complex specified information". As we
have seen, Dembski takes "information" to mean -log_2 p, where p
the probability of an event matching a chosen pattern. He calls the
information "complex" if p is small. Dembski's use of "complex" has
little to do with "complicated": for example, the record HHH ... H
representing flipping 500 heads in a row constitutes "complex
information" under his definition, even though the record of the event
is very simple. To add further to the confusion, to be "specified" for
Dembski means to conform to a pattern. He apparently modeled this
after another theory of information, the theory of Kolmogorov
complexity. But in the Kolmogorov theory, a string is called
"complex", or said to possess "high information", if no simple way to
specify it exists! Another term, such as Robin Collins' "specified
improbability", would have been less confusing.
Sometimes the poor writing takes the form of choosing strange
notation, as in the formal statement of the "Law of Conservation of
Information" on p. 160: I(A & B) = I(A) mod UCB .
Here "mod" does not mean what every computer scientist or number
theorist would expect: namely, "a mod b" as "the remainder upon
division of a by b". No, the reader has to wait until the next page to
find out that what Dembski really means is the inequality
I(A & B) <= I(A) + UCB
where UCB is 500. Then why not just say that, instead of bringing in
the confusing term "mod"?
Sometimes the form of the argument seems to be designed more to impress
and confound, rather than convey meaning, as in the discussion of
compact topological groups and Haar measures on page 105, or algebraic
groups on page 201. This material is inessential to the main argument
and could easily have been excised or summarized in a footnote.
Similarly, the concept of "invariant" is trivial enough that I can
explain it to my 7-year-old, but Dembski's discussion on page 274 is
extravagant in its use of mathematical notation.
Other times the impact of poor exposition is felt more deeply, as in
the definition of CSI itself. Is CSI a quantity expressible in bits as
implied on p. 160? Or does something either "exhibit" CSI or not
exhibit it, as implied on p. 163?
5. Misrepresentation.
I found several instances of misrepresentation in NFL. For example, on
p. 211, Dembski dismisses the work of artificial life researcher Tom
Ray as follows:
Thomas Ray's Tierra simulation gave a similar result,
showing how selection acting on replicators in a
computational environment also tended toward simplicity
rather than complexity --- unless parameters were set so
that selection could favor larger sized organisms
(complexity here corresponding to size).
I have to wonder how carefully Dembski has read Ray's work, because
this is not the conclusion I drew from reading Ray's papers. Curious, I
wrote an e-mail message to Ray asking if he felt Dembski's quote
was an accurate representation of his work. Ray (2002) replied as follows:
"No. I would say that in my work, there is no strong
prevailing trend towards either greater or lesser complexity.
Rather, some lineages increase in complexity, and others
decrease. Here, complexity does not correspond to size, but
rather, the intricacy of the algorithm."
A similar misrepresentation occurs in Dembski's selective quotation
of Keith Devlin's review of Dembski's earlier book, The Design
Inference. Dembski writes (NFL, p. 372) "Take for instance ...
mathematician Keith Devlin's appreciative remarks about my work in
his July/August 2000 article for The Sciences titled "Snake Eyes
in the Garden of Eden": `Dembski's theory has made an important
contribution to the theory of randomness --- if only by highlighting
how hard it can be to differentiate the fingerprints of design from
the whorls of chance'."
But, as anyone reading Devlin's review in its entirety will realize,
this line --- coming at the end of the review --- was an effort to
mitigate previous harsh comments. For example, in the very same review
Devlin observes that Dembski's work can be used to support two
different conclusions: human life arose by a combination of chance and
natural processes, and human life arose by design, and states: "But if
Dembski's new mathematics, which he developed to help poke holes in the
theory of evolution, can sustain two such contradictory conclusions,
then it does not resolve the debate at all." When I informed Devlin
that Dembski was quoting only one positive line of the review---as done
in NFL, in a paper (Dembski, 2000), and a Diane Rehm radio interview
(Dembski, 2001)---he labeled it misrepresentation and told me, "Anyone
who read the entire article would realize I was negative about
Dembski's thesis" (Devlin, 2002).
Yet another misrepresentation occurs in Dembski's discussion of
Dawkins' example of the power of selection, the famous Methinks it is
like a weasel example. Dawkins (1987) starts with a randomly chosen
string of 28 characters, and then breeds it by copying, together with a
certain probability of random error. He, or rather, his computer, next
evaluates a fitness function to find the string that most resembles the
target string "Methinks it is like a weasel". All the less-fit strings
die out, and the most-fit then goes on to breed again. After only a
small number of generations (64 in Dawkins' example) the target is
reached.
Dembski discusses this example on pages 181--183 of NFL, but he gets it
wrong. He insists that Dawkins' algorithm, instead of evaluating a
fitness function, behaves as follows: it "randomly alter[s] all the
letters and spaces in the current sequence that do not agree with the
target sequence" and "whenever an alteration happens to match a
corresponding letter in the target sequence, leave it and randomly
alter only those remaining letters that still differ from the target
sequence".
But Dawkins said nothing of the sort. To add insult to injury, Dembski
goes on in pp. 193--194 to propose an algorithm that he calls "slightly
different but more realistic". It turns out that this supposed new
algorithm is, in fact, much closer to Dawkins' original algorithm as
described in The Blind Watchmaker.
It is true that Dawkins did not provide many details about his
implementation. But researchers other than Dembski seem to have no
problem understanding Dawkins' algorithm. Discussions by both
Bach (1993) and Jacob (2001) make it clear they understand that,
in Dawkins' model, letters are not fixed once they match the target.
Even minor details are subject to careless misrepresentation. For
example, in Dembski's discussion of a certain sequence of bits
corresponding to prime numbers that appears in the movie Contact, he
says, (p. 9): "The SETI researcher who in the movie Contact
discovered this sequence put it this way: `This isn't noise, this has
structure.' "
Dembski gets it wrong three ways. The discoverer of the prime sequence
was Dr. Ellie Arroway (played by Jodie Foster). The character who
remarked about structure wasn't Arroway, but Kent Clark (played by
William Fichtner). The correct line in the movie is actually, "You
know the interlaced frames that we thought were noise? This has
structure. I'm hearing structure." And finally, this character wasn't
commenting about the prime sequence at all! His comment is about
another signal at a different frequency, which later proved to encode
blueprints for a machine.
These are just four of the misrepresentations in NFL. I could give
several more, but by now I hope the reader gets the point.
6. Poor scholarship.
For a book that purports to discuss fundamental questions about
information, complexity, and biology, there is remarkably little
discussion or awareness of previous work. Dembski does not cite any of
the following works, just to list a few:
- Kimura's paper where he shows how natural selection can
increase Shannon information (Kimura, 1961);
- Wicken's book on evolution and information (Wicken, 1987);
- The papers of Saunders and Ho (Saunders and Ho, 1976;
Saunders and Ho, 1981) that argue that complexity increases
during evolution;
- The paper of Nehaniv and Rhodes (1997) showing how, in a
finite automaton model, complexity can evolve in biological
systems.
The field of artificial life evidently poses a significant challenge to
Dembski's claims about the failure of evolutionary algorithms to
generate complexity. Indeed, artificial life researchers regularly
find their simulations of evolution producing the sorts of novelties
and increased complexity that Dembski claims are impossible. Yet NFL's
coverage of artificial life is limited to a few dismissive remarks, the
longest of which I have already quoted above. Indeed, the term
"artificial life" does not even appear in NFL's index. There is no
reference to, for example, the work of Adami, Ofria, and Collier (2000)
which suggests the possibility of increased complexity over time.
As a scholarly work, Dembski's NFL falls dramatically short.
I have covered six of the most significant problems with NFL. At
least some of these problems could have been avoided had Dembski been
more willing to test his claims through the peer-review process. But
intelligent design advocates have consistently failed to publish their
work in scientific journals (Gilchrist, 1997; Forrest, 2001). When
pressed, some say this is because academia is a "closed shop", run by
an "elite" that is biased against them.
This claim is undermined by the fact that many non-mainstream and
controversial views routinely get published in the scientific
literature. Just recently, controversial claims of table-top fusion
induced by the collapse of super-hot bubbles were published in a major
scientific journal (Taleyarkhan, West, Cho, Lahey, Nigmatulin, and
Block, 2002).
What intelligent design advocates fail to realize is that the
peer-review process could benefit them enormously, by identifying weak
arguments and incorrect claims before they are published. For example,
a thorough peer review might have revealed that a crucial calculation
on p. 297 of NFL is off by a factor of about 10^65.
The benefits of peer review are so obvious that I can only
conclude that some ID advocates are not really interested in the
advancement of science. Their goal is to replace science as it is
currently done with a form of religion, and that in turn may have
unintended consequences. In today's science it is not uncommon for
Christians, Jews, Muslims, and atheists to work together without
friction. But I doubt many Muslim, Jewish, or atheist scientists will
want to cooperate with a movement that insists, as Dembski does in
Intelligent Design, p. 210, that "Christ is indispensable to any
scientific theory, even if its practitioners don't have a clue about
him". One of science's most attractive aspects is the the way it
transcends religious and political differences. Let's keep it that
way.
Acknowledgements. In the preparation of this review I am pleased
to acknowledge extensive conversations with Wesley Elsberry and Richard
Wein. I also thank William Dembski for his generosity in sending me
a complimentary copy of No Free Lunch.
References
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About the author.
Jeffrey Shallit is a mathematician and computer scientist. He received
his Ph. D. from the University of California, Berkeley in 1983, and
has taught at the University of Chicago and Dartmouth College prior to
his present position at the University of Waterloo. With Eric Bach, he
is the author of Algorithmic Number Theory (MIT Press, 1996) and (with
Jean-Paul Allouche) Automatic Sequences (Cambridge University Press,
forthcoming).