A Bit Confused

David Roche

Creationism and Information Theory

The argument of some creationists that modern information theory refutes Darwinian evolution is based on a confusion between two distinct information concepts. At the heart of the Darwinian thesis is not information, but complexity.

In recent years, the notion of "information" has crept into the arguments of creationists and other critics of evolution, particularly among proponents of Intelligent Design (ID) (see Edis, this issue). According to such arguments, information theory refutes Darwinian evolution. Carl Wieland (1997) sums up the argument nicely.

What mechanism could possibly have added all the extra information required to transform a one-celled creature progressively into pelicans, palm trees, and people? Natural selection alone can't do it-selection involves getting rid of information. A group of creatures might become more adapted to the cold, for example, by the elimination of those which don't carry enough of the genetic information to make thick fur. But that doesn't explain the origin of the information to make thick fur. [And] mutations ... are accidental mistakes as the genetic information ... is copied from one generation to the next. Naturally, such scrambling of information will tend to either be harmful, or at best neutral. ... Rather than adding information, they destroy information, or corrupt the way it can be expressed (not surprising, since they are random mistakes).

In other words, so goes the argument, the Darwinian process is inadequate for explaining the origins of biological (e.g., genetic) information. Natural selection cannot produce any new information; it merely shuffles or in some cases eliminates the information that was already there. And mutation cannot create new information either, because mutation is essentially a random process. So although variation occurs in nature and natural selection may operate on this variation, evolution leads to neutral or even degenerative change. It does nor provide the "progressive" component required to explain the origins of organisms with lots of information. Have you spotted the flaw in this argument? It's not as simple as you might think.

In one sense, proponents of this argument are right. Both natural selection and random mutations can be thought of as leading to a reduction in information. However--and herein lies the flaw--the type of information is different in each case. Information comes in different forms, so we need to be clear regarding what sort of information we are talking about.

One type of information we might call Shannon information. This is the type of information concept introduced by the Bell engineer Claude Shannon in 1948 when he laid the foundations of the modern science of information theory (Shannon and Weaver 1949). Shannon defined information in terms of reduction in uncertainty. So if I sent you the string of binary digits "010," I have specified one of eight possibilities. Assuming equiprobable digits, I have reduced your level of uncertainty by a factor of eight. Information is typically measured as the base-2 logarithm of the reduction in uncertainty, which in this case translates into three bits of information.

The Shannon information content of any system can be thought of as the reduction in uncertainty resulting from a complete specification of that system. In other words, you can think of Shannon information content in terms of the length of a concise and fully detailed description of the system. Such a definition therefore accounts for redundancy. A book consisting only of the letter "A" repeated 100,000 times is easy to describe. It has lots of redundancy and therefore little Shannon information. If we converted it into a computer file and ran it through a compression algorithm, we would end up with something much smaller than what we started with. A book of 100,000 completely random letters, in contrast, has no redundancy and therefore lots of Shannon information. There is no shorter description of a book of random letters than the book itself, so running it through a computer compression algorithm has little affect on its size. Shakespeare's play The Tempest also contains about 100,000 letters. Its Shannon information content is intermediate between the book of A's and the book of random letters. If we ran it through a computer-compression algorithm, we would end up with something somewhat smaller than what we starred with, but not drastically so. The Tempest contains more Shannon information than a book of 100,000 A's but less Shannon information than a book of 100,000 random letters. [1]

Another type of information concept is complexity. Physicist Murray Gell-Mann has helped in recent years to clarify this concept (Gell-Mann 1994; 1995). According to Gell-Mann, you can think of complexity as a measure of how difficult it would be to describe the regularities of something in complete detail. Mathematically, it is the difference between something's maximally compressed Shannon information content and its "incompressible" information content--the information content of those elements of the system that are truly random (Gell-Mann and Lloyd 1996). A book of 100,000 A's has little complexity. It does not have much incompressible information, while its compressible information is highly compressible. The regularities of the book can be completely described in one short sentence ("A book of 100,000 A's"). A book of random letters also has little complexity. It has lots of Shannon information, but virtually all of this information is incompressible because there are no regularities to compress. In c ontrast, The Tempest has lots of complexity. It has lots of regularities (e.g., words, rules of grammar, aspects of plot development etc.) and so virtually all of its information content is compressible. Yet once fully compressed, it is still quite large.

Shannon information and complexity are quite distinct concepts. As we have already seen, various systems can be interpreted as having lots of one without much of the other. A common mistake of those attempting to use information theory to debunk Darwinian evolution is to confuse the two concepts. Dembski's "complex specified information" is the most prominent example (Dembski 1998).

Once we understand the difference between these two types of information--Shannon information and complexity--it is easy to see what's wrong with the information argument against evolution. If we interpret biological systems in information terms, we can see that natural selection does tend to decrease the amount of information, but only Shannon information. Natural selection simply removes some members from a population, making it more homogenous and less diverse. The resulting population is easier to describe in detail and so has less Shannon information. Conversely, mutation makes the population less homogenous and so increases the amount of Shannon information.

Looking at the amount of complexity in the biological system, however, the situation is somewhat different. Mutation is a random process, and random processes do not, at least on their own, generate complexity. Natural selection, however, is nor a random process. It is an ordering process, creating structure from noise and increasing the degree of regularity in the biological system. Since complexity is simply the length of a concise description of all the regularities in such a system, natural selection, in conjunction with random mutation, can tend to increase complexity.

Whichever way we interpret the evolutionary critic, explaining the origin of biological information is straightforward. If by "information" the evolutionary critic means Shannon information, then there is very little to explain. The second law of thermodynamics will suffice. The world tends toward disorder, and this disorder is a physical embodiment of Shannon information. On the other hand, if we interpret "information" to mean complexity, then we are simply left with answering the familiar question of how the Darwinian process could give rise to such complex organs as the vertebrate eye; a question already thoroughly dealt with by many biologists (e.g., Dawkins 1986).

The great achievement of Darwinism is not that it explains the origins of information (in the Shannon sense), but that it explains the origins of complexity. And it does so in terms of a completely material process: random mutation followed by non-random selection. Via such a process, the simple can give rise to the complex; "from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved" (Darwin 1859).

David Roche is in the Unit for the History and Philosophy of Science, University of Sydney, Australia. E-mail: droche@unsw.edu.au.

Note

(1.) After writing this statement, I decided to test it empirically. I created three text files: one containing 100,000 As, another containing 100,000 pseudorandom letters, and a third containing Shakespeare's The Tempest. I then ran each through the compression program WinZip, and achieved compression ratios of 99.3%, 2.5% and 58.4% respectively.

References

Darwin, C. 1859. The Origin of Species by Means of Natural Selection. London: John Murray.

Dawkins, R. 1986. The Blind Watchmaker. London: Penguin.

Dembaki, W.A. 1999. The Design Inference: Eliminating Chance through Small Probabilities. New York: Cambridge University Press.

Gell Mann, M. 1994. The Quark and the Jaguar: Adventures in the Simple and the Complex. London: Abacus.

___. 1995. What is complexity? Complexity 1(1): 16-19.

Gell-Mann, M., and S. Lloyd. 1996. Information measures, effective complexity, and total information. Complexity 2(1): 44-52.

Shannon, C.E., and W. Weaver. 1949. The Mathematical Theory of Communication. Urbana: University of Illinois.

Wieland, C. 1997. Beetle bloopers: Even a defect can be an advantage sometimes. Creation Ex Nihilo 19(3): 30.

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