The Dembski Anomaly

From EvoWiki

Abstract - According to William Dembski it is possible to detect "intelligent design"; but what is intelligent design then? This article attempts to track down, what it is that is so intelligent in design that it is impossible for natural processes to mimic design, though design can mimic natural processes.

1 Chance and Design
2 Specifications
3 "Itelligent Design"?
4 Related Articles
5 References

Chance and Design

In section 8, "Design Detection", of Specification, "Intelligent Design" proponent William Dembski quotes the 18^th century mathematician Abraham de Moivre. Part of the quoted passage is as follows:

Let us suppose that two Packs of Piquet-Cards being sent for, it should be perceived that there is, from Top to Bottom, the same Disposition of the Cards in both packs; let us likewise suppose that, some doubt arising about this Disposition of the Cards, it should be questioned whether it ought to be attributed to Chance, or to the Maker’s Design

That is, are the cards in the two packs arranged by the maker of the cards to suit some constant pattern, or is it by chance that the same order is to be found in both packs?

There are 52! different possible orderings of a pack of cards, so assuming each possible ordering to have the same probability, there is a probability of 1/52! for any particular ordering, a very small number; according to de Moivre small enough to warrant a design inference rather than a chance inference.

Specifications

For Dembski the issue at hand is that same competition between design and chance. And to arbitrate this competition he employs the concept of specification, a pattern that an event with a low probability to occur must exhibit in order to warrant a design inference, which for Dembski is the same as attributing the occurrence of the event to an intelligence. The simpler the pattern and the lower the probability of the event, the better.

In de Moivre’s example the pattern is given by the order of cards in a pack of cards, which itself might be a complex pattern. This is what Dembski calls a prespecification. In contradistinction hereto, "real" specifications are given à posteriori, and therefore to warrant a design inference must be simple patterns.

This may sound counterintuitive, which Dembski also acknowledges; but he still defends the proposition that a low probability event that exhibits a simple pattern warrants a design inference. The argumentation is a kind of pigeon hole principle. In de Moivre’s example we have 52! pigeons and only one pigeon hole. Let’s say we have a shuffled pack of cards, and we have no prior pattern to check the deck against; that’s 52! pigeons and 52! pigeon holes. However, we discover that the pack has all the cards suite by suite and in ascending order within each suite. Shouldn’t we start to be suspicious then, even though exactly this order wasn’t singled out as special from the outset? According to Dembski we should; this particular order has exactly the same (low) probability as any other order, but still we should say that exactly this order must have been arranged by an intelligence, whereas most other orders would have passed as a chance incidence.

In section 4, "Specifications via Compressibility", Dembski discusses exactly this, just with strings of binary digits instead. Let’s assume we want to compress all binary strings of length exactly N into the strings of length at most d with d < N. This is not possible; there are 2^N strings of length exactly N, but only 2^d+1-1 strings of length at most d, so even with d = N-1, there will be one uncompressible string. And if d is much smaller than N, the situation gets worse. But, wait a second, we can make 2^N compression algorithms, one for each of the 2^N strings of length N, can’t we? Dembski doesn’t directly discuss this, but it is actually what is the main rationale behind his reasoning - that this approach doesn’t solve the compression problem.

Dembski gives this example of a string:

(R)	11000011010110001101111111010001100011011001110111
	00011001000010111101110110011111010010100101011110.

It records the results of 100 tosses of a coin with heads represented by ‘1’ and tails represented by ‘0’. I will refer to this sequence in the following as the "Dembski sequence".

>We could make a compression algorithm that returned, say, the empty string as the compressed version of the Dembski sequence. The corresponding decompression algorithm would, given the empty string as input, return the Dembski sequence as output. This decompression algorithm might simply contain the Dembski sequence as a constant within its code.

But let’s move the goalposts slightly and say that we want self-unpacking compressed versions of strings; that means that the decompression algorithm itself is part of the compressed version of the string. The pigeon hole principle then states that there are irreducibly complex (in the sense of algorithmically irreducible) strings; strings that cannot be compressed into a shorter self-unpacking, compressed string.

There are simply strings that have no particular pattern to them, and that cannot be represented by a string shorter than themselves. Is the Dembski sequence such a string? Using some extra symbols we could represent it in this way:

(R’)	‘1’2\|4\|2\|1\|1\|1\|2\|3\|2\|1\|7\|1\|1\|1\|3\|2\|3\|2\|1\|2\|2\|3\|1\|3\|
	3\|2\|2\|1\|4\|1\|1\|4\|1\|3\|1\|2\|2\|5\|1\|1\|2\|1\|1\|1\|2\|1\|1\|1\|1\|4\|1.

The decompression algorithm will read this as: start with x = ‘1’, output 2 x, let x = ‘0’, output 4 x, let x = ‘1’, output 2 x, and so on.

Converted to binary this may however not require less digits than the 100 in the original, so maybe the Dembski sequence is indeed uncompressible given any machine (or program) that doesn’t already have a copy of the sequence.

"Itelligent Design"?

A TalkOrigins critique by Richard Wein, Not a Free Lunch But a Box of Chocolates, of Dembski's book No Free Lunch, spawned a minor interchange between Dembski and Wein. The last (at the present) article in this interchange is The Fantasy Life of Richard Wein: A Response to a Response, in which Dembski mentions the case of a Bell Labs physicist, who during a period of two and a half years had produced an extraordinary body of work, including several articles in two prestigious scientific journals. In these articles the physicist had published "graphs that were nearly identical even though they appeared in different scientific papers and represented data from different devices. In some graphs, even the tiny squiggles that should arise from purely random fluctuations matched exactly." (quote from the New York Times May 23^rd 2004). Bell Labs appointed an independent panel to determine whether the physicist had improperly manipulated his research data.

According to Dembski:

The theoretical issues raised in this case of putative data falsification are precisely those that my work on the design inference seeks to address. The match between the two graphs in [the physicist’s] articles constitutes an independently given pattern or specification (more precisely, the first published graph provides a specification for the second). Moreover, the random fluctuations in the graphs are highly improbable and thus "complex" in the sense I define it. The randomness here is well-understood. As a consequence, no unknown mechanism is being sought for how the graphs from independent experiments on independent devices could have exhibited the same pattern of random fluctuations. At issue is the question of data manipulation and design, and we get there by a pure process of elimination.

In other words, we have a case of design, when two instances of the same low probability event occur. How is this different from de Moivre’s two packs of cards? In my humble opinion, not really much. The physicist had published his results in two scientific journals with probably quite some overlap of readers, so it was only a question of someone comparing different articles from the same author. That is, the difference between a prespecification and a specification is more a question of the detecting agents ability to detect similarities, in this case to detect that two "different" graphs are one and the same.

Let’s return to the Section 4 of Dembski’s Specification article. I have already mentioned the Dembski sequence, named "(R)" (for "Random") by Dembski. It’s the only sequence that arose from actual coin tosses, and the next sequence is made up for the occasion:

(N)	11111111111111111111111111111111111111111111111111
	11111111111111111111111111111111111111111111111111.

This (N)onrandom sequence does exhibit an easily identifiable pattern, which Dembski formulates as: "repeat ‘1’ a hundred times." In my notation above it would become ‘1’100.

Dembski gives an additional couple of simple (and designed) sequences, and at p. 14 he gives the first 100 bits of the Champernowne sequence:

(Y R)	01000110110000010100111001011101110000000100100011
	01000101011001111000100110101011110011011110111100.

which he calls pseudo-random.

The full Champernowne sequence is built from the binary representations of the natural numbers in ascending order beginning with ‘0’ and ‘1’, then adding the 2-digit numbers, then the 3-digit numbers, and so on.

Note that if we here consider a generation to be all the numbers of the same length, then generation n+1 can be constructed from generation n by first running through all members s of that generation and adding ‘0’+s, where ‘+’ denotes concatenation, to the end of the output, and after that repeating the same with ‘0’ replaced by ‘1’. That is, we can write an algorithm that uses only two constant symbols, a copy operation, and simple concatenation of a symbol and a copied string.

Both the Dembski sequence and the Champernowne sequence are statistically random. With equal probability (50%) for each of the two digits, there is 50% chance that a digit will be followed by the same digit, 25% chance that it will be followed by two of the same digit, and in general a chance of 2^-n that it will be followed by n of the same digit. That is, there is a probability of 2^-n for a patch of at least n+1 of the same digit.

If we look at patches with an exact length instead, then things are slightly more complicated. For a patch of length n, there are 100-(n-1) possible starting positions; for instance, a patch of length 4 can start at positions 1 to 97. A patch at position 1 must has no predecessor, so it only needs to followed by the opposite digit of that of the patch, which there is a 50% chance for. A patch at the other end has no successor, so it only needs to follow the opposite digit of that of the patch, again we have a 50% chance. For all other positions the patch needs to follow the opposite digit and to be followed by the opposite digit, all in all 25%. The average number of patches of exactly length n is therefore (2*0.5 + (100-(n-1)-2)*0.25)/2^n-1, n = 1, 2, 3, …. In table form we have:

n	Min. length	Exact length	Dembski	Champer.
1	100	25.5	23	25
2	49.5	12.625	14	13
3	24.5	6.25	7	7
4	12.125	3.09375	4	4
5	6	1.53125	1	1
6	2.96875	0.7578125	0	0
7+	1.46875	1.46875	1	1

The Dembski sequence and the Champernowne sequence are both close to the expected, and actually with the Champernowne sequence beating the Dembski sequence slightly.

We have two sequences that are both statistically random, but only one of them is algorithmically random (at least, we have yet to find any pattern in the Dembski sequence). However, whereas the Champernowne sequence is statistically random, this is not an inherent property of the binary numbers. This is easily seen; with 100 bits we can list all the binary numbers from the two 1-digit ones to the sixteen 4-digit ones, and have two bits to spare. However, this can at most give us patches of maximum length four, and only two of those, ‘0000’ and ‘1111’. So, what’s the trick? It’s an effect of listing these numbers in a sequence. We will have ‘111’ followed by ‘0000’ followed by ‘0001’, the last two giving a patch of seven ‘0’s. In return we will have ‘1101’ followed by ‘1110’ followed by ‘1111’ giving two patches of four ‘1’s.

It’s not by design that the Champernowne sequence is statistically random, it’s a side-effect of an arrangement that had other reasons. Even a designed sequence can have non-designed properties.

In the TalkOrigins article Plagiarized Errors and Molecular Genetics, Edward E. Max writes:

One way to distinguish between copying and independent creation is suggested by analogy to the following two cases from the legal literature. In 1941 the author of a chemistry textbook brought suit charging that portions of his textbook had been plagiarized by the author of a competing textbook (Colonial Book Co, Inc. v. Amsco School Publications, Inc., 41 F. Supp.156 (S.D.N.Y. 1941), aff'd 142 F.2d 362 (2nd Cir. 1944)). In 1946 the publisher of a trade directory for the construction industry made similar charges against a competing directory publisher (Sub-Contractors Register, Inc. v McGovern's Contractors & Builders Manual, Inc. 69 F.Supp. 507, 509 (S.D.N.Y. 1946)). In both cases, mere similarity between the contents of the alleged copies and the originals was not considered compelling evidence of copying. After all, both chemistry textbooks were describing the same body of chemical knowledge (the books were designed to "function similarly") and both directories listed members of the same industry, so substantial resemblance would be expected even if no copying had occurred. However, in both cases errors present in the "originals" appeared in the alleged copies. The courts judged that it was inconceivable that the same errors could have been made independently by each plaintiff and defendant, and ruled in both cases that copying had occurred. The principle that duplicated errors imply copying is now well established in copyright law. (In recognition of this fact, directory publishers routinely include false entries in their directories to trap potential plagiarizers.)

The point here is that copying (= plagiarism) is detected by the presence of the same errors in the originals and in the alleged copies. While an original book is an example of design, there is no specification for it - only the copy can have a specification, namely the original. The two cases mentioned by Max here are very similar to the case mentioned by Dembski with the Bell Labs physicist, who plagiarized himself.

Max writes in his conclusion:

In "the case of the shared functionless sequences," an unbiased jury would surely conclude that copying from a shared ancestor was the most likely explanation, consistent with the evolutionary interpretation. This conclusion would follow the logic of actual copyright law in which shared errors are accepted as evidence of copying.

Usually we would associate intelligent design with creativeness, not with mechanical copy-operations, but Dembski turns it the other way around: acts of intelligence are detected due to their following of simple rules! Max uses these examples to by analogy claim that the occurrence of the same genetic errors within different species is due to a copy-operation, that is, common descent, not design. Why would an intelligent designer make the same errors several times?

This is, what I call the Dembski anomaly, that Dembski wants us to see design, where there is lack of design, only mechanical copy-operations.

In another article, Irreducible Complexity Revisited, Dembski writes p. 37 that:

The Darwinian mechanism works by accretion and modification: it adds novel parts to already functioning systems as well as modifies existing parts in them. In this way, new systems with enhanced or novel functions are formed.

Well, maybe it does, but to the rest of us that only means that the Darwinian mechanism appears slightly more intelligent than does what counts as intelligence for William Dembski.