In this book, mathematician and philosopher William A. Dembski attempts to lay the mathematical and logical foundation for inferring the presence of intelligent design in biology. Note that “intelligent design” needn't imply divine or supernatural intervention—the “directed panspermia” theory of the origin of life proposed by co-discoverer of the structure of DNA and Nobel Prize winner Francis Crick is a theory of intelligent design which invokes no deity, and my perpetually unfinished work The Rube Goldberg Variations and the science fiction story upon which it is based involve searches for evidence of design in scientific data, not in scripture.
You certainly won't find any theology here. What you will find is logical and mathematical arguments which sometimes ascend (or descend, if you wish) into prose like (p. 153), “Thus, if P characterizes the probability of E0 occurring and f characterizes the physical process that led from E0 to E1, then P∘f −1 characterizes the probability of E1 occurring and P(E0) ≤ P∘f −1(E1) since f(E0) = E1 and thus E0 ⊂ f −1(E1).” OK, I did cherry-pick that sentence from a particularly technical section which the author advises readers to skip if they're willing to accept the less formal argument already presented. Technical arguments are well-supplemented by analogies and examples throughout the text.
Dembski argues that what he terms “complex specified information” is conclusive evidence for the presence of design. Complexity (the Shannon information measure) is insufficient—all possible outcomes of flipping a coin 100 times in a row are equally probable—but presented with a sequence of all heads, all tails, alternating heads and tails, or a pattern in which heads occurred only for prime numbered flips, the evidence for design (in this case, cheating or an unfair coin) would be considered overwhelming. Complex information is considered specified if it is compressible in the sense of Chaitin-Kolmogorov-Solomonoff algorithmic information theory, which measures the randomness of a bit string by the length of the shortest computer program which could produce it. The overwhelming majority of 100 bit strings cannot be expressed more compactly than simply by listing the bits; the examples given above, however, are all highly compressible. This is the kind of measure, albeit not rigorously computed, which SETI researchers would use to identify a signal as of intelligent origin, which courts apply in intellectual property cases to decide whether similarity is accidental or deliberate copying, and archaeologists use to determine whether an artefact is of natural or human origin. Only when one starts asking these kinds of questions about biology and the origin of life does controversy erupt!
Chapter 3 proposes a “Law of Conservation of Information” which, if you accept it, would appear to rule out the generation of additional complex specified information by the process of Darwinian evolution. This would mean that while evolution can and does account for the development of resistance to antibiotics in bacteria and pesticides in insects, modification of colouration and pattern due to changes in environment, and all the other well-confirmed cases of the Darwinian mechanism, that innovation of entirely novel and irreducibly complex (see chapter 5) mechanisms such as the bacterial flagellum require some external input of the complex specified information they embody. Well, maybe…but one should remember that conservation laws in science, unlike invariants in mathematics, are empirical observations which can be falsified by a single counter-example. Niels Bohr, for example, prior to its explanation due to the neutrino, theorised that the energy spectrum of nuclear beta decay could be due to a violation of conservation of energy, and his theory was taken seriously until ruled out by experiment.
Let's suppose, for the sake of argument, that Darwinian evolution does explain the emergence of all the complexity of the Earth's biosphere, starting with a single primordial replicating lifeform. Then one still must explain how that replicator came to be in the first place (since Darwinian evolution cannot work on non-replicating organisms), and where the information embodied in its molecular structure came from. The smallest present-day bacterial genomes belong to symbiotic or parasitic species, and are in the neighbourhood of 500,000 base pairs, or roughly 1 megabit of information. Even granting that the ancestral organism might have been much smaller and simpler, it is difficult to imagine a replicator capable of Darwinian evolution with an information content 1000 times smaller than these bacteria, Yet randomly assembling even 500 bits of precisely specified information seems to be beyond the capacity of the universe we inhabit. If you imagine every one of the approximately 1080 elementary particles in the universe trying combinations every Planck interval, 1045 times every second, it would still take about a billion times the present age of the universe to randomly discover a 500 bit pattern. Of course, there are doubtless many patterns which would work, but when you consider how conservative all the assumptions are which go into this estimate, and reflect upon the evidence that life seemed to appear on Earth just about as early as environmental conditions permitted it to exist, it's pretty clear that glib claims that evolution explains everything and there are just a few details to be sorted out are arm-waving at best and propaganda at worst, and that it's far too early to exclude any plausible theory which could explain the mystery of the origin of life. Although there are many points in this book with which you may take issue, and it does not claim in any way to provide answers, it is valuable in understanding just how difficult the problem is and how many holes exist in other, more accepted, explanations. A clear challenge posed to purely naturalistic explanations of the origin of terrestrial life is to suggest a prebiotic mechanism which can assemble adequate specified information (say, 500 bits as the absolute minimum) to serve as a primordial replicator from the materials available on the early Earth in the time between the final catastrophic bombardment and the first evidence for early life.