EXPLAINING SPECIFIED COMPLEXITY

William A. Dembski

Michael Polanyi Center
Baylor University
Waco, Texas 76798

In his recent book The Fifth Miracle, Paul Davies suggests that any laws
capable of explaining the origin of life must be radically different from
scientific laws known to date. The problem, as he sees it, with currently
known scientific laws, like the laws of chemistry and physics, is that they
are not up to explaining the key feature of life that needs to be
explained. That feature is specified complexity. Life is both complex and
specified. The basic intuition here is straightforward. A single letter of
the alphabet is specified without being complex (i.e., it conforms to an
independently given pattern but is simple). A long sequence of random
letters is complex without being specified (i.e., it requires a complicated
instruction-set to characterize but conforms to no independently given
pattern). A Shakespearean sonnet is both complex and specified.

Now, as Davies rightly notes, contingency can explain complexity but not
specification. For instance, the exact time sequence of radioactive
emissions from a chunk of uranium will be contingent, complex, but not
specified. On the other hand, as Davies also rightly notes, laws can
explain specification but not complexity. For instance, the formation of a
salt crystal follows well-defined laws, produces an independently known
repetitive pattern, and is therefore specified; but that pattern will also
be simple, not complex. The problem is to explain something like the
genetic code, which is both complex and specified. As Davies puts it:
"Living organisms are mysterious not for their complexity per se, but for
their tightly specified complexity" (p. 112).

How does the scientific community explain specified complexity? Usually via
an evolutionary algorithm. By an evolutionary algorithm I mean any
algorithm that generates contingency via some chance process and then sifts
the so-generated contingency via some law-like process. The Darwinian
mutation-selection mechanism, neural nets, and genetic algorithms all fall
within this broad definition of evolutionary algorithms. Now the problem
with invoking evolutionary algorithms to explain specified complexity at
the origin of life is absence of any identifiable evolutionary algorithm
that might account for it. Once life has started and self-replication has
begun, the Darwinian mechanism is usually invoked to explain the specified
complexity of living things.

But what is the relevant evolutionary algorithm that drives chemical
evolution? No convincing answer has been given to date. To be sure, one can
hope that an evolutionary algorithm that generates specified complexity at
the origin of life exists and remains to be discovered. Manfred Eigen, for
instance, writes, "Our task is to find an algorithm, a natural law that
leads to the origin of information," where by "information" I understand
him to mean specified complexity. But if some evolutionary algorithm can be
found to account for the origin of life, it would not be a radically new
law in Davies's sense. Rather, it would be a special case of a known
process.

I submit that the problem of explaining specified complexity is even worse
than Davies makes out in The Fifth Miracle. Not only have we yet to explain
specified complexity at the origin of life, but evolutionary algorithms
fail to explain it in the subsequent history of life as well. Given the
growing popularity of evolutionary algorithms, such a claim may seem
ill-conceived. But consider a well known example by Richard Dawkins (The
Blind Watchmaker, pp. 47-48) in which he purports to show how a cumulative
selection process acting on chance can generate specified complexity. He
starts with the following target sequence, a putative instance of specified
complexity:

METHINKS?IT?IS?LIKE?A?WEASEL

(he considers only capital Roman letters and spaces, here represented by
bullets-thus 27 possibilities at each location in a symbol string).

If we tried to attain this target sequence by pure chance (for example, by
randomly shaking out scrabble pieces), the probability of getting it on the
first try would be around 10 to the -40, and correspondingly it would take
on average about 10 to the 40 tries to stand a better than even chance of
getting it. Thus, if we depended on pure chance to attain this target
sequence, we would in all likelihood be unsuccessful. As a problem for pure
chance, attaining Dawkins's target sequence is an exercise in generating
specified complexity, and it becomes clear that pure chance simply is not
up to the task.

But consider next Dawkins's reframing of the problem. In place of pure
chance, he considers the following evolutionary algorithm: (i) Start out
with a randomly selected sequence of 28 capital Roman letters and spaces,
e.g.,

WDL?MNLT?DTJBKWIRZREZLMQCO?P

(note that the length of Dawkins's target sequence, METHINKS?IT?
IS?LIKE?A?WEASEL, comprises exactly 28 letters and spaces); (ii) randomly
alter all the letters and spaces in this initial randomly-generated
sequence; (iii) 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.

In very short order this algorithm converges to Dawkins's target sequence.
In The Blind Watchmaker, Dawkins (p. 48) provides the following computer
simulation of this algorithm:

        (1)     WDL?MNLT?DTJBKWIRZREZLMQCO?P

        (2)     WDLTMNLT?DTJBSWIRZREZLMQCO?P
...
        (10)    MDLDMNLS?ITJISWHRZREZ?MECS?P
...
        (20)    MELDINLS?IT?ISWPRKE?Z?WECSEL
...
        (30)    METHINGS?IT?ISWLIKE?B?WECSEL
...
        (40)    METHINKS?IT?IS?LIKE?I?WEASEL
...
        (43)    METHINKS?IT?IS?LIKE?A?WEASEL

Thus, Dawkins's simulation converges on the target sequence in 43 steps. In
place of 10 to the 40 tries on average for pure chance to generate the
target sequence, it now takes on average only 40 tries to generate it via
an evolutionary algorithm.

Although Dawkins uses this example to illustrate the power of evolutionary
algorithms, the example in fact illustrates the inability of evolutionary
algorithms to generate specified complexity. We can see this by posing the
following question: Given Dawkins's evolutionary algorithm, what besides
the target sequence can this algorithm attain? Think of it this way.
Dawkins's evolutionary algorithm is chugging along; what are the possible
terminal points of this algorithm? Clearly, the algorithm is always going
to converge on the target sequence (with probability 1 for that matter). An
evolutionary algorithm acts as a probability amplifier. Whereas it would
take pure chance on average 10 to the 40 tries to attain Dawkins's target
sequence, his evolutionary algorithm on average gets it for you in the
logarithm of that number, that is, on average in only 40 tries (and with
virtual certainty in a few hundred tries).

But a probability amplifier is also a complexity attenuator. For something
to be complex, there must be many live possibilities that could take its
place. Increasingly numerous live possibilities correspond to increasing
improbability of any one of these possibilities. To illustrate the
connection between complexity and probability, consider a combination lock.
The more possible combinations of the lock, the more complex the mechanism
and correspondingly the more improbable that the mechanism can be opened by
chance. Complexity and probability therefore vary inversely: the greater
the complexity, the smaller the probability.

It follows that Dawkins's evolutionary algorithm, by vastly increasing the
probability of getting the target sequence, vastly decreases the complexity
inherent in that sequence. As the sole possibility that Dawkins's
evolutionary algorithm can attain, the target sequence in fact has minimal
complexity (i.e., the probability is 1 and the complexity, as measured by
the usual information measure, is 0). In general, then, evolutionary
algorithms generate not true complexity but only the appearance of
complexity. And since they cannot generate complexity, they cannot generate
specified complexity either.

This conclusion may seem counterintuitive, especially given all the
marvelous properties that evolutionary algorithms do possess. But the
conclusion holds. What's more, it is consistent with the "no free lunch"
(NFL) theorems of David Wolpert and William Macready, which place
significant restrictions on the range of problems genetic algorithms can
solve.

The claim that evolutionary algorithms can only generate the appearance of
specified complexity is reminiscent of a claim by Richard Dawkins. On the
opening page of his The Blind Watchmaker he states, "Biology is the study
of complicated things that give the appearance of having been designed for
a purpose." Just as the Darwinian mechanism does not generate actual design
but only its appearance, so too the Darwinian mechanism does not generate
actual specified complexity but only its appearance.

But this raises the obvious question, whether there might not be a
fundamental connection between intelligence or design on the one hand and
specified complexity on the other. In fact there is. There's only one known
source for producing actual specified complexity, and that's intelligence.
In every case where we know the causal history responsible for an instance
of specified complexity, an intelligent agent was involved. Most human
artifacts, from Shakespearean sonnets to Dürer woodcuts to Cray
supercomputers, are specified and complex. For a signal from outer space to
convince astronomers that extraterrestrial life is real, it too will have
to be complex and specified, thus indicating that the extraterrestrial is
not only alive but also intelligent (hence the search for extraterrestrial
intelligence-SETI).

Thus, to claim that laws, even radically new ones, can produce specified
complexity is in my view to commit a category mistake. It is to attribute
to laws something they are intrinsically incapable of delivering-indeed,
all our evidence points to intelligence as the sole source for specified
complexity. Even so, in arguing that evolutionary algorithms cannot
generate specified complexity and in noting that specified complexity is
reliably correlated with intelligence, I have not refuted Darwinism or
denied the capacity of evolutionary algorithms to solve interesting
problems. In the case of Darwinism, what I have established is that the
Darwinian mechanism cannot generate actual specified complexity. What I
have not established is that living things exhibit actual specified
complexity. That is a separate question.

Does Davies's original problem of finding radically new laws to generate
specified complexity thus turn into the slightly modified problem of
finding find radically new laws that generate apparent-but not
actual-specified complexity in nature? If so, then the scientific community
faces a logically prior question, namely, whether nature exhibits actual
specified complexity. Only after we have confirmed that nature does not
exhibit actual specified complexity can it be safe to dispense with design
and focus all our attentions on natural laws and how they might explain the
appearance of specified complexity in nature.

Does nature exhibit actual specified complexity? This is the million dollar
question. Michael Behe's notion of irreducible complexity is purported to
be a case of actual specified complexity and to be exhibited in real
biochemical systems (cf. his book Darwin's Black Box). If such systems are,
as Behe claims, highly improbable and thus genuinely complex with respect
to the Darwinian mechanism of mutation and natural selection and if they
are specified in virtue of their highly specific function (Behe looks to
such systems as the bacterial flagellum), then a door is reopened for
design in science that has been closed for well over a century. Does nature
exhibit actual specified complexity? The jury is still out.


William A. Dembski

˙-˙-˙-˙-˙-˙-˙-˙-˙-˙-˙-˙
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