In the book "The End of Science" chapter #8 "End of Chaoplexity" John Horgan writes..
"Definitions of complexity typically draw upon thermodynamics, information theory and computer science and involve concepts such as entropy, randomness and information -- which themselves have proved to be notoriously slippery terms."
Note that for John Horgan -- the science writer -- and apparently all others that he knows in science, there exists a scientific problem of complexity being "notoriously slippery."
"..all definitions of complexity have drawbacks. For example algorithmic information theory (Chaitin et al) holds that the complexity of a system can be represented by the shortest computer program describing it. But according to this criterion, a text created by a team of typing monkeys is more complex because it is more random and therefore less compressible -- than Finnegans Wake"
The solution of course is very simple. The "typing monkeys" are merely an anthropomorphisation of "randomness." "Randomness" is merely a uniform probability distribution over a set of possible outcomes. That is to say, if the probability of your slot machine's jackpot configuration (say, three lemons) is greater (or less) than the other configurations(say, two cherries and a banana) then its internal probability is distributed non-uniformly -- it is skewed/biased and it is subsequently non-random.
Horgan's "text" being "created by a team of typing monkeys" is but uniformly distributed, unspecified gibberish wherein the complexity here is an attribute of the complex (alphabet) system -- not an attribute of randomness! Randomness is by definition uniform and subsequently non-complex. "Finnegans Wake" on the other hand is specified, non-random and does not conform to a uniform distribution of letters.
Even if one were to remove all the redundancy from "Finnegans Wake," reducing it to a K-complex skeleton code, it still would not be the least bit random because any such "Finnegans Wake" is utterly specific and randomness is devoid of specifications. Any such Finnegans Wake code, non-randomly specifies Finnegans Wake -- IE it is a specific, non-random list of the specifications/instructions needed to produce the specific Finnegan's Wake text.
While the letter "A" is indeed specific, randomness is not. While letter and number systems are themselves complex and specified -- randomness is not.
Randomness is the absence of order, the absence of complexity, the absence of specifications and the absence of information. When expressed in a complex system, randomness appears as uniformly distributed noise or "gibberish." John Horgan bemoans the "end of science" -- not because science is ending and no more answers are possible -- but because he is talking to the wrong scientists -- scientists who worship randomness. For those who don't worship randomness, "complexity" is not the least bit "slippery."
Note added Jan 3/08. I thoroughly enjoyed reading "The End of Science." John Horgan is a very entertaining writer and I found the subjects he addresed therein to be extremely interesting. -WB