Specified complexity, the subject of a new series I’m beginning today, is the legitimate offspring of the mathematical theory of information. You wouldn’t know that, however, from reading what’s said about it on the Internet. Take the opening sentence of the Wikipedia article on specified complexity: “Specified complexity is a creationist argument introduced by William Dembski, used by advocates to promote the pseudoscience of intelligent design.” It’s hard to imagine any other single sentence better crafted to discredit specified complexity. What further need is there to understand or engage this concept if that’s what it is?

In fact, specified complexity is a bona fide information measure. Yes, specified complexity is applicable to intelligent design, but its definition and properties make sense independently of its applications. In this series I want to define what specified complexity is, establish that it belongs squarely to standard information theory, review some intuitively clear applications of it, and show why it is an important concept even apart from its applications to intelligent design. 

Not My Invention

First, despite my widely acknowledged association with the term specified complexity, let’s be clear that I didn’t invent it. Critics of intelligent design treat specified complexity as a con man pretending to be a real scientist. Thus they liken it to debunked scientific concepts such as phlogiston or pseudosciences such as phrenology. 

But if you think of specified complexity as a job seeker with a resumé, the people put down as references (to vouch for the concept) are actually quite impressive. Indeed, some very respectable scientists were, for a time, happy to associate their names and reputations with the concept. Given its pedigree, there is no way to justify treating specified complexity as a bastard child of real science.

Biologist Leslie Orgel, a colleague of Francis Crick, introduced the term in 1973 in a book on the origin of life. Crick himself had toyed with a less developed version of the concept as far back as 1958 — see his paper “On Protein Synthesis” where he writes, “By information I mean the specification of the amino acid sequence of the protein.” In the years immediately following specified complexity’s coinage by Orgel, the underlying idea was widely accepted even if incompletely understood. 

With the term specified complexity, Orgel was trying to understand three distinct types of order:

Repetitive Order: BOATBOATBOATBOATBOATBOATBOATBOATBOATBOAT. Example in nature: A salt crystal.

Random Order: SBIPDYAQBUKHQFLYRTXHBIWGJNSCPVMZDLEGKYAC. Example in nature: Mixture of random polymers.

Complex Specified Order: THISSEQUENCEOFLETTERSISACARRIEROFMEANING. Example in nature: A DNA sequence coding for a protein.

In these examples, each sequence comprises 40 capital Roman letters. In the first, the word BOAT is repeated 10 times. Because BOAT is a known word, it may be regarded as specified in our language. Yet because the word BOAT is short and keeps being repeated, the entire sequence may also be regarded as simple. This, then, is an example of specified simplicity, which is therefore distinct from specified complexity. 

Note that we might have used the more random looking QOZK in place of BOAT and then generated the 40-letter sequence QOZKQOZKQOZKQOZKQOZKQOZKQOZKQOZKQOZKQOZK. In that case, QOZK might be regarded as unspecified, and yet because of the repetition, the entire sequence would still be regarded as simple. Accordingly, this sequence would be an example of unspecified simplicity, which is therefore also distinct from specified complexity. 

The example of random order, on the other hand, is neither specified nor simple. It is unspecified because there is no straightforward way to describe that sequence other than simply listing it in its entirety. Its generation, for instance, cannot be understood in terms of any easy formula. Compared to a four-letter word like BOAT, it is also relatively long, and therefore complex. It is an example of unspecified complexity, which is therefore distinct from specified complexity.

And finally, there’s the last example in which a sequence of 40 capital Roman letters spells a meaningful English sentence. It is specified in virtue of its use of English words arranged in grammatically correct syntax to make a meaningful statement. And yet there is no simple way to generate or account for it. It is an example of specified complexity. 

The Basic Intuition

I’m playing fast and loose with the terms specified and complexity in these examples, having yet to carefully define them. But these examples make clear the basic intuition underlying the concept. Moreover, these are exactly the sorts of examples Orgel had in mind when he introduced the concept. And indeed, for about thirty years after Orgel introduced the concept, specified complexity garnered wide respect in the scientific community. 

As an example of the respect shown to specified complexity in the first three decades after Orgel introduced the term, consider well-known physicist and science writer Paul Davies, who in his 1999 book on the origin of life (The Fifth Miracle) wrote: “Living organisms are mysterious not for their complexity per se, but for their tightly specified complexity.” Unwilling as they might be to attribute specified complexity to intelligence, scientists during that period at least understood that the emergence of specified complexity posed a challenge that needed to be explained.

So what happened to change the fortunes of specified complexity in the mainstream scientific community? The intelligent design movement happened. Design theorists Charles Thaxton, Walter Bradley, and Roger Olsen got the ball rolling in the 1980s in their book The Mystery of Life’s Origin, noting that specified complexity raised a significant problem for the origin of life. They went further by suggesting that intelligence should be regarded as a viable explanation in accounting for it. 

Separately, in the first edition of my book The Design Inference (Cambridge, 1998), I argued that specification and small probability combined to produce a reliable criterion for inferring intelligent agency. Although the term specified complexity did not occur in that book, it was there implicitly. The “specified” of “specified complexity” was there in the form of specification. And the small probability corresponded precisely to increased complexity as an information-theoretic notion. More on this shortly.

Cards on the Table

But the gamechanger in revising specified complexity’s scientific fortunes occurred in 2002. That year I published the sequel to The Design Inference. Reviewed in Nature and titled No Free Lunch, it was subtitled Why Specified Complexity Cannot Be Purchased Without Intelligence. All cards were now on the table. Scientists who rejected intelligent design and yet had previously seen merit in specified complexity now withdrew their support of the concept. 

Before proceeding, I want to underscore that in formalizing specified complexity as a precise information-theoretic concept, I attempted to preserve Orgel’s original intent. Critics of intelligent design, such as mathematician Jason Rosenhouse, suggest that I misappropriated Orgel, but I didn’t. Orgel appealed to information theory in formulating specified complexity, but in doing so he made some mistakes. Later in this series, I’ll compare Orgel’s pre-theoretic version of specified complexity with the theoretic version described here. Readers can then see clearly what he was trying to do and how specified complexity, as developed here, improves on his work.

Next: “Intuitive Specified Complexity.”

Editor’s note: This article appeared originally at BillDembski.com.