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Cambridge Studies in Probability, Induction and Decision Theory

The Design Inference: Eliminating Chance through Small Probabilities

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A landmark of the intelligent design movement, The Design Inference revolutionized our understanding of how we detect intelligent causation. Originally published twenty-five years ago, it has now been revised and expanded into a second edition that greatly sharpens its exploration of design inferences. This new edition tackles questions about design left unanswered by David Hume and Charles Darwin, navigating the intricate nexus of chance, probability, and design, and thereby offering a novel lens for understanding the world. Using modern concepts of probability and information, it exposes the inadequacy of undirected causes in scientific inquiry. It lays out how we infer design via events that are both improbable and specified. Amid controversial applications to biology, it makes a compelling case for intelligent design, challenging the prevalent neo-Darwinian evolutionary narrative. Dembski and Ewert have written a groundbreaking work that doesn’t merely comment on contemporary scientific discourse but fundamentally transforms it.

583 pages, Paperback

First published January 1, 1998

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About the author

William A. Dembski

49 books117 followers
A mathematician and philosopher, Dr. William Dembski has taught at Northwestern University, the University of Notre Dame, and the University of Dallas. He has done postdoctoral work in mathematics at MIT, in physics at the University of Chicago, and in computer science at Princeton University. A graduate of the University of Illinois at Chicago where he earned a B.A. in psychology, an M.S. in statistics, and a Ph.D. in philosophy, he also received a doctorate in mathematics from the University of Chicago in 1988 and a master of divinity degree from Princeton Theological Seminary in 1996. He has held National Science Foundation graduate and postdoctoral fellowships. He is the recipient of a $100,000 Templeton research grant. In 2005 he received Texas A&M’s Trotter Prize.

Dr. Dembski has published articles in mathematics, engineering, philosophy, and theology journals and is the author/editor of over twenty books.

His most comprehensive treatment of intelligent design to date, co-authored with Jonathan Wells, is titled The Design of Life: Discovering Signs of Intelligence in Biological Systems.

As interest in intelligent design has grown in the wider culture, Dr. Dembski has assumed the role of public intellectual. In addition to lecturing around the world at colleges and universities, he is frequently interviewed on the radio and television. His work has been cited in numerous newspaper and magazine articles, including three front page stories in the New York Times as well as the August 15, 2005 Time magazine cover story on intelligent design. He has appeared on the BBC, NPR (Diane Rehm, etc.), PBS (Inside the Law with Jack Ford; Uncommon Knowledge with Peter Robinson), CSPAN2, CNN, Fox News, ABC Nightline, and The Daily Show with Jon Stewart.

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Displaying 1 - 12 of 12 reviews
Profile Image for Carmel Attard.
Author 3 books1 follower
January 26, 2022
'The Design Inference: Eliminating Chance through Small Probabilities' is not for everybody to read: it is preferable if one has a mathematical background particularly 'Set Theory' (with its mathematical symbols) and 'Probability Theory.' At times it is difficult to follow the book because of its mathematical formality, which the author does try to explain, but his explanations only become clearer to average reader at the end of the book. So certain parts might be somewhat frustrating to the ordinary reader: indeed, the author does recommend nontechnical readers’ “skipping the technical portions” (p. xiii) they might find difficult to understand. I suggest skimming over such parts particularly in chapters 3 and 4.
The book starts by pointing out that there are three ways things can happen: (1) naturally (following the laws of physics, chemistry & biology), (2) by chance, and (3) by design. If something happens all the time, for example, letting go of a ball always falls to the ground, the probability is high (=1): it’s following the laws of nature—in this case the law of gravity. If, blindfolded, someone picks a white ball from among 9 black balls, we can still attribute it to chance because it entails an intermediate probability of 0.1 = 1/10 (odds of 1 to 10). Again, throwing a double six from a pair of dice is not such a big deal since the odds are only 1 to 36 (probability of 1/36 = 0.0278); and picking the ace of spades from an ordinary (bridge/poker) pack of cards, could still be a matter of luck since the odds are still 1 to 52 (probability of 1/52 = 0.0192). But if, blindfolded, one picks a white ball from among a hundred (probability 0.01), a thousand (probability 0.001), or a million black balls (probability 10^-6), at some point one starts to suspect design. In other words, to conclude design we require a small probability of something happening (the smaller the better); but where is the cut-off point?
According to the author, “Probability is a relation between events and experimental arrangements:” the 'ideal likelihood' of something happening “relative to certain background information” (a 'chance hypothesis'—pp. 70, 73). Probability/likelihood is assigned a number (a fraction) between 0 and 1, which might not always be as easy as above to determine since it might entail a thorough knowledge of mathematics and statistics.
The author proceeds with, “Complexity theory measures the difficulty of a problem … complexity measures are measures of difficulty” (pp. 92–93). For example, suppose a safe has a combination lock marked with a hundred numbers (00 to 99) for which 5 turns in alternating directions are required to open the lock. Given only one opportunity, the probability of opening the lock is (1/100^5=) 10^-10, while a complexity measure might be 10^10, say. The complexity measure is therefore a number ranging from zero to infinity. The author then defines complexity as “-log2 of the probability,” and justifies it by stating, “The most convenient way for communication theorists to measure information is in bits [zeros & ones] (this accounts for the base 2 in the logarithm).” For instance, he adds, “the ASCII code … uses strings comprising eight 0s and 1s to represent the characters on a typewriter” (p. 117). This gives a one-to-one correspondence from (1 to 0) probability to (0 to ꚙ) complexity, respectively. (So, in the safe example, the complexity measure is about 33.22.)
Naturally, we would strongly suspect that if someone manages to flip a coin 100 times and obtain heads every time, it is by design; the coin is, most probably, not a fair coin (e.g. both sides are heads, say). Yet, if we flip a fair coin 100 times and record the sequence, although everyone agrees it is a random sequence, it will be practically impossible to repeat the same sequence. The odds of getting the same sequence again are 1 to 2^100 or about 1 to 1.3x10^30: the same as the odds of getting 100 heads in a row with a fair coin. (Lotteries are not won by the same numbers; if it happens, it rouses suspicion.) So what differentiates chance from design?
Imagine someone is one-hundred-odd yards away from a forest in the middle of winter (the trees have no leaves) and shoots an arrow at the trees. It misses the first two rows of trees and lands on the third row, say. One can safely say it was a random shot. Now, if one draws a bull’s-eye circle on the tree around where the arrow landed, we know it is a 'fabrication.' However, if one draws the bull’s-eye circle prior to the arrow shot, and the arrow lands in its center, we know we are dealing with a master archer. In the latter case, the bull’s-eye circle is a 'specification' as opposed to a fabrication. In other words, to differentiate design from chance, besides a small probability, we need a specification.
Still a specification (pattern) can be discovered after the fact; that is what detectives must do: find the circumstantial evidence, reconstruct the crime, and prove the perpetrator guilty beyond reasonable doubt. Moreover, the pattern is not always discernible (detachable) at first blush, as in the case of cryptography, say. Take, for example, the sequence: 0100011011000001010011100101110111, which seems random enough; but look at the same sequence separated by commas: 0,1,00,01,10,11,000,001,010,011,100,101,110,111; it is only the (one-digit, two-digit, and three-digit) binary numbers in sequence. But it’s not so easy to see at first blush.
Consequently, the author defines his 'Law of Small Probability' by stating, “specified events of small probability do not occur by chance” (p. 5). Naturally, this definition begs the question, how small is a small probability? Now, there are two kinds of small probability: (1) on a local scale and (2) on a cosmic scale. A scientific experiment, for instance, defines a 'rejection region' (prediction) within which occurrence the chance hypothesis is statistically excluded.
On the other hand, the 'null hypothesis' or mathematical expectation (the probability calculation) is too good to be true; and although ordinary statistics has no way of rejecting it as true, the design inference considers it fudged if satisfied exactly. For example, if a hundred-coin-flip sequence consists of heads followed by tails for fifty times, we know that it’s probably a fake sequence because it follows the expected theoretical result too closely.
Moreover if, for example, a robber tries to open a combination safe, it depends on how many opportunities he has: if he is allowed only one try, it’s one thing; if he has all night, it’s another. In the Canadian ‘Lotto649’ a player must choose six out of the first 49 natural numbers. The odds of winning this lottery are 1 to 13,983,816 (probability 7.15x10^-8), which is an extremely small probability; but if 14 million tickets are purchased, the odds of someone winning it are just about even. Indeed, there is a winner roughly every three draws.
The author, therefore, introduces the concept of 'probabilistic resources.' I think, this is the highlight of the book, his determining the 'cosmic' probabilistic resources as 10^150 (p. 209), which anchors his Law of Small Probability. He assumes “a noninflationary big-bang cosmology” (p. 214) and derives it from the product (multiplication) of the number of elementary particles in the universe (10^80), the number of seconds the universe has been (or will be) in existence (10^25 seconds—actually 20 billion years is closer to 10^18 seconds) and the number of physical states possible in one second (10^45), which is the inverse of the 'Planck time.' Physics contends that time cannot be finely split indefinitely: everything that occurs in the universe happens in what resembles movie slides of time, each 10^-45 of a second long (known as the Planck time). So long as the probability of any specified event is shown to be strictly less than half of 10^-150, we may safely infer design; however, there is still the remote possibility that we could be wrong: keep in mind that any probability, which is different from 0, is still only a probability.
The author also debunks 'inflationary theory' (pp. 214–17) and the 'anthropic principle' (pp. 60–62, 182, 185)—both of which imply a multi-universe (or 'multiverse')—and 'un-collapsed quantum probabilities' (p. 210n) as scientists’ futile attempts at increasing the probabilistic resources (i.e., scientists clutching at straws). For instance, he challenges the multiverse hypotheses as “universes that are by definition causally inaccessible to us” (p.62), and therefore “the status of possible universes other than our own remains a matter of controversy” (p. 182). If anything, he adds, they are irrelevant to what happens in our universe (p. 214). And regarding quantum probabilities, he states, “A specification is a determinate state. Measurement renders a quantum superposition determinate by producing a pure state, but once it does so we are no longer dealing with quantum superposition.” (p. 210n) He concludes, “This reversal of commonsense logic where we fixate on chance, and then madly rush to invent probabilistic resources necessary to preserve chance is the great pipedream of late twentieth-century cosmology and biology.” (p. 215)
Some of the higher mathematical (like geometric progressions) or statistical equations/formulae are simply given by the author with hardly any explanation or justification (e.g., pp. 67, 84, 176, 188, 203); not to mention that some mathematical symbols are too sketchily defined for the average reader. The critical reader, who is not very familiar with these fields, will naturally remain somewhat unconvinced by the final result. Footnotes showing a step-by-step calculation, derivation, or explanation would have helped convince such meticulous readers.
Finally, the author concedes that some rare disconnected coincidences do not imply design and should be left unexplained: we don’t have to invoke supernatural powers. But not every coincidence is sterile: he recommends testing 'interesting' events, exhibiting intelligence and/or mutual dependence, by running them rigorously through his filter thus eliminating doubt.
I think the book is somewhat disappointing in a couple of respects. First, the author refrains from implying intelligent agency once design is arrived at through his 'Generic Chance Elimination Argument'—although he does concede there is a close connection between the two (pp. xii, 8–9, 19, 36, 60, 62–66, 226–227); indeed, he points out, intelligent agency can also purposely mimic chance (p. 36). Intelligence, he adds, entails a learning ability and manifests itself in a deliberate choice of a course of action.
Second, even though the author refers to the origin-of-life through chance/design question several times (pp. iii, xii, 2, 55–62, 102–103, 182–183), he does not give his final opinion on the matter: he refrains from challenging mainstream origin-of-life evolutionary theory (Richard Dawkins) perhaps to keep his book as 'scientific' as possible. Indeed, the author exonerates Dawkins because the latter claims that Darwinian natural selection (or survival of the fittest) provides a gradual process to reach albeit a very small probability specification. For example, if one flips 100 coins in succession, and every time a coin shows heads is set aside, moving on to the next one, in no time, one can obtain 100 heads: needless to mention, this scenario is a far cry from trying to flip 100 heads in a row, with no tails in between. However, in his book 'The Blind Watchmaker,' Dawkins assumes a viable replicator arising by chance alone before natural selection takes over. But the odds against this happening are still astronomically high. Understandably, the author did not want to go that route; and, admittedly, it is somewhat beyond the scope of his book.
In conclusion, all in all, 'The Design Inference' is a great, ground-breaking book: especially for those who are keenly and honestly interested in the origin of life and our universe.
Profile Image for Ray.
196 reviews2 followers
January 18, 2008
Brilliant. This is a little more of a workout for nonspecialists compared to some of his other works. Dembski adapted this from his Ph.D. dissertation in math at Cambridge (after finishing a Ph.D. in philosophy and while simultaneously doing an MDiv at Princeton Seminary!).

Questions alot of assumptions and really stirs the pot. Get his other books as well!

Profile Image for Peter Kazmaier.
Author 5 books60 followers
January 29, 2016
Reading this book was a watershed experience for me. Dembski demonstrates that one can use statistics reliably to distinguish regularity, chance, and agency when it comes to asking the question: "Did this process happen by chance or not?" A significant part of the book is filled with statistical theorems used to support and develop the Design Inference methodology. Most of this is beyond my statistical acumen. Still Dembski does such excellent work explaining his concepts and conclusions with understandable examples that it very readable even for those who cannot get much beyond means, distributions and simple combinatorial statistics.

I know many readers will find Dembski's conclusions unsettling, but I found his argument thorough, lucid, and compelling.

Profile Image for Daniel.
71 reviews
March 20, 2015
Bill Dembski is my favorite thinker and by all means the person [who is only human] whose ideas have had the biggest impact in my thought. This book is the result of Dembski's second doctoral dissertation in philosophy of science (after a first one in probability). It lays the mathematical foundations for a design inference, ruling out the possibilities of chance and necessity. The exposition is in clear and formal mathematical and philosophical terms, but it can be understood by the educated layman. This is the first book in the superb trilogy of Dembski's thought, together with No Free Lunch and the more recent Being as Communion, and constitutes one of the pillars on which the modern intelligent design movement is built.
Profile Image for John.
439 reviews34 followers
January 14, 2012
A Fresh Take On Klingon Cosmology Courtesy of Dembski's Bizarre Usage of Probability Theory

Trying to read "The Design Inference: Eliminating Chance through Small Probabilities" is like trying to understand a Gilbert and Sullivan operetta or a James Joyce novel without having had any prior exposure to their works. One doesn't really need to have a first rate understanding of theoretical probability and statistics (which I don't since I am at best, a decent applied biostatistician), to realize that Dembski's argument holds little intellectual weight, in its preposterous claim that the likelihood of extremely rare events would point to the existence of an unseen "Intelligent Designer" (I wonder whether such events would be the result of random variation, which would not in itself point to an "Intelligent Designer", or rather, dare I say it - GOD - as the source of these events.). Or perhaps Dembski's rather ponderous text might be more appropriately, a suitable intellectual exercise demonstrating why Klingon cosmology does exist, replete with a Klingon heaven and hell (After all, since we see Klingons often on television, then they must truly exist.).

I had the unique opportunity of speaking to William Dembski a few years ago, after a debate on Intelligent Design held at the American Museum of Natural History, in which Dembski and fellow Intelligent Design advocate Michael Behe argued in favor, while opposing them were philosopher Robert Pennock, author of "Tower of Babel" (which contains a devestatingly brilliant critique of Intelligent Design) and my friend Ken Miller, author of "Finding Darwin's God (which has a superb critique of Behe's notion of irreducible complexity as proof of an unseen "Intelligent Designer"). Much to my amazement, Dembski could not answer well a trivial question I had regarding probability and statistics. So can I truly regard his book as a great leap forward in theoretical probability? Of course no, since "The Design Inference" is a philosophical text that should be of interest to those who enjoy hearing the "technobabble" of recent "Star Trek" television series, especially when such "technobabble" is translated into Klingon.

(Reposted from my 2006 Amazon review)
Profile Image for Mark Spencer.
28 reviews1 follower
August 12, 2024
Highly technical. Incredibly informative. Powerfully encouraging. A good read that I'm glad I took the time to work through.
10.5k reviews34 followers
August 18, 2024
DEMBSKI'S FIRST BOOK - WITH DESIGN AS A MEASURE OF INFORMATION

William Albert Dembski (born 1960) is a key figure in the "Intelligent Design" movement, who is a professor at the Southern Evangelical Seminary and a senior fellow of the Discovery Institute. He has written/edited many other books, such as Intelligent Design: The Bridge Between Science and Theology,' 'The Design Revolution: Answering the Toughest Questions About Intelligent Design,' 'Mere Creation; Science, Faith & Intelligent Design,' 'Uncommon Dissent: Intellectuals Who Find Darwinism Unconvincing,' 'Tough-Minded Christianity: Legacy of John Warwick Montgomery,' etc.

He wrote in the Preface to this 1998 book, "The crucial question ... is whether an arrangement of stones conforms to the right sort of pattern to eliminate chance. This monograph presents a full account of those patterns capable of successfully eliminating chance... Eliminating chance is closely connected with design and intelligent agency. To eliminate chance because a sufficiently improbable event conforms to the right sort of pattern is frequently the first step in identifying an intelligent agent. It makes sense, therefore, to define design as 'patterned improbability,' and the design inference as the logic by which 'patterned improbability' is detected and demonstrated. So defined, the design inference stops short of delivering a causal story for how an intelligent design acted. But by precluding chance and implicating intelligent agency, the design inference does the next best thing." (Pg. xi-xii)

He admits in his concluding chapter, "When the design inference infers design, its primary effect is to limit our explanatory options. Only secondarily does it help identify a cause. To identify a cause we need to investigate the particulars of the situation where design was inferred. Simply put, we need more details." (Pg. 227)

He adds, "I want to conclude this epilogue by stating what I take to be the main significance of the design inference for science. It is this: The design inference detects and measures INFORMATION." (Pg. 228)

This book---Dembski's first---is significantly more "technical" and detailed than his other books; but it will be of interest to those wanting more detail (mathematical formulae, etc.) than he provides in his more "popular" works.

Profile Image for Alan Fuller.
Author 6 books32 followers
January 29, 2024
This was not an easy book for me to read, but not because it was poorly written. It was because there were so many new terms, symbols, and ideas that I was unfamiliar with. I managed to muddle through it.

A language can compose an algorithm, which describes a pattern or specification. The more complex a specific pattern, the shorter the description. If there is an event that matches the pattern and has a very low probability, which means it falls in a rejection region, then a design inference can be drawn. The description used in the specification is in accordance with algorithmic information theory, which was developed back in the 1960’s.

SETI researchers, insurance fraud investigators, intellectual property lawyers, data falsification investigators, and cryptographers can all use design inference. The author targets Neo-Darwinian evolution.
Profile Image for Caleb.
107 reviews2 followers
May 19, 2024
Excellent read. Highly technical in places but the main idea of the book is accessible.
Profile Image for Taylor Belt.
55 reviews9 followers
August 3, 2025
This book was both extremely informative and interesting and I can't recommend it enough to anyone who would like to read it.
Profile Image for Frank Peters.
1,017 reviews58 followers
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June 15, 2016
This was not an easy or pleasant book to read. If I was to rate it honestly, I would give it a one. But this would be more of a reflection on me than on the book. Ultimately I do not have the mathematical skill to be able to understand the book fully. It didn’t help, that I have always had difficulty with both probability theory and any form of pure mathematics. However, I really like and respect what the author was seeking to accomplish, but unless you are a real mathematician (a PhD in Physics is not sufficient), I would recommend avoiding the book. I am certainly relieved that I am finished, and now plan to give the book away to someone who might understand it better than I did.
Profile Image for Jeffrey.
283 reviews20 followers
September 10, 2016
Dembski's peer-reviewed work on the design inference as it stands not attributed to any natural phenomena. An advanced work, but readable and enjoyable.
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