The Fallacies of Intelligent Design Theory
The coin tosses are independent of each other, so the total number of permutations is 25 = 32. The exponent, 5, is known as the entropy of the system of five coins. The entropy is the number of bits of data needed to describe the arrangement of the coins after each toss. That is, there is one bit that describes the 1st coin (H or T), one that describes the 2nd (H or T), and so on until the 5th coin has been tossed. In terms of communications transmitted, there are 5 bits altogether from each toss of 5 coins. The entropy of the communication channel, which is a measure of the disorder or uncertainty of the channel over which the information is transmitted, is 5. We gain information as we reduce the entropy. The entropy of the 5 coins arranged randomly is 5; when they are arranged in a specified way, it is 0. The information has increased by 5 bits. Thus, a nonrandom configuration displays less entropy and, therefore, more information than a random configuration.
Meaningful information is not measured in bits and cannot be at all treated using the methods and mathematical tools of information theory. Any random text carries much more information (in the sense of information theory) than any meaningful text of the same length.
Dembski's law of conservation of information states that the number of bits H cannot change in any natural process as a result of either chance or the operation of some physical law. For example, suppose we toss five fair coins in the air. The probability of any specific resulting sequence, say HTTHT, is (1/2)5. The Shannon uncertainty (Dembski information) contained in that sequence is H = -log (1/2)5.
No information is gained in this random process. Whatever the initial arrangement of the coins prior to their toss, it also contained five bits of information. However, what about a sequence such as HHHHH? Intuitively, it might seem that it contains more information than HTTHT, but it does not. In either case, Hafter = Hbefore = 5 and R = 0. However, if we pick two of the coins (Dembski would call it an act of design), R = 2 bits of information have been gained.
Suppose the sequence HHHHH is specified in advance. Then we have five bits of what Dembski calls specified information [words specified information in italics]. We could just as well have specified HTTHT, as long as we did so ahead of time or identified some other characteristic of the sequence that marked it as something other than a random occurrence. Now five heads in a row, or any specified sequence of five coins, can happen by chance. On average, about one of every 32 tosses of five coins will land with all five heads up. However, suppose we do the experiment with 500 coins instead of five and specify that all fall heads up. This would, on average, require 2500 = 10150 tosses of 500 coins each to obtain 500 heads by chance. Dembski rightly says this is, for all practical purposes, impossible, and defines 500 or more bits of information as complex. He argues that the observation of complex specified information in the universe is evidence for intelligent design. In particular, he holds that biological evolution cannot be the product of chance and natural law.
Dembski does not use the word complexity is its everyday sense nor in any pre-existing technical sense. Instead, he uses it in a misleading sense of his own: complexity is defined to mean improbability. He also uses the word information in the same sense. Further confusion is caused by Dembski's refusal to clarify the improbability to which he is referring. Sometimes he seems to mean the improbability of an event with respect to a specific natural hypothesis, and usually this is a hypothesis involving a uniform probability distribution, such as a hypothesis of purely random combination of components. At other times, he seems to mean that an event is complex if it is improbable with respect to all the natural hypotheses of which we can think. At still other times, he seems to mean that an event is complex if it is improbable with respect to all possible natural causes.
Dembski does not define precisely what he means by specificity. In the coin example above, the sequence is specified in advance. However, he cannot leave it at that because then his whole program to detect design after the fact would be defeated. So, as a dubious alternative, he allows specificity to be post-determined. An observed sequence might contain some message that is too unlikely to have occurred by chance. He uses an example from the film Contact, based on Carl Sagan's novel, in which an intelligent signal from outer space is detected containing the sequence of prime numbers up to 101. Dembski's incorrect claim is that complex specified sequences of information cannot happen naturally.
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The Information Theory Case Against Evolution: Pages 1, 2, (3), 4, 5, 6, 7
