Work is not information

Suppose you are searching for a DNA sequence that translates to a protein with certain properties. To simplify matters, let's say you know magically that the sequence is 300 bases in length. You might roll a fair four-faced die 300 times to guess a sequence, and then conduct an experiment to see if the guess is correct. Clearly, there is no knowledge of the specific problem manifest in the die-rolling procedure.

Now let's say you do 1000 repetitions of the die-rolling procedure, and conduct 1000 experiments to check the randomly generated DNA sequences. The probability of "hitting the target" with a "query" of nature increases. But does this mean that you exploited more knowledge about the problem than you did previously? Of course not. It means only that you did more work.

In their recently published article, Conservation of Information in Search: Measuring the Cost of Success, Bill Dembski and Bob Marks sometimes measure work and call it active information. They claim,

Active information captures numerically the problem-specific information that assists a search in reaching a target.

But in Section III.A they demonstrate otherwise:

Multiple queries clearly contain more information than a single query. Active information is therefore introduced from repeated queries.

Now wait just a gol-dern minute, Billy Bob! The first sentence says that a procedure doing more work yields more information about the solution to the problem than a procedure doing less work. The second says that the procedure doing more work has more more information about how to solve the specific problem than a procedure doing less work. The error here is not just equivocal use of the word information. The authors go on to calculate a gain in active information for repetition of an utterly uninformed procedure.

Dembski and Marks commit the same errors in Section III.F.1, where they show that increasing the number of offspring in an evolutionary search increases the probability of obtaining an offspring more fit than the parent. To make this probability gain into active information, they redefine the search as just one generation of the evolutionary search they originally considered.

The fact that you can gain information by doing work does not imply that work is itself information.

[1/2/2010: I contradicted myself in saying "repetition of an utterly uninformed procedure" after predicating that "you know magically that the sequence is 300 bases in length." In a forthcoming post, I will explain that what Dembski and Marks call the endogenous information of a search problem seems endogenous only if one ignores magical circumscription of the solution space.]