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Randomness, Complexity, and All That
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John Wilkins links to this review of Steve Fuller's new book advocating Intelligent Design. My readership seems to be pretty strong at math, so I have some questions about the reviewer's critique of Fuller's handling of randomness. He says:

Merely out of mathematical whimsy, I want to consider Fuller’s very extensive discussion of “complexity” and “randomness.” This, as mathematicians and computer scientists are well aware, is a subject that has been thoroughly studied and analyzed for decades, generating a slew of deep results and fertile conjectures. Fuller, however, shows no awareness of the actual mathematical literature (even though much of it is accessible, at the basic level, to anyone with minimal mathematical skill). Instead, he seems content to take ID-theorist William Dembski as his guide. He attributes to Dembski a maxim to the effect that it is “impossible” to design a true random-number generator because it is ultimately possible to “infer” the algorithm that lies behind it (p. 61). But this grossly misunderstands a basic principle of complexity theory, the insight that in general it is not possible to devise an effective method for distinguishing a random from a non-random stream of data. Indeed, it is easily possible for virtually anyone to devise a simple way of generating such a data stream (making it highly “compressible” or non-random), which will, for all practical purposes, defeat any human attempt to say whether it is or isn’t random or how “compressible” it really is.

He then goes on to doodle his own little quick and dirty algorithm:

s^n = [(p^nth digit of the decimal expansion of sin(17/31) ) – 4] mod 10

where p^n is the nth prime number.

And then he says:

It is very easy for anyone knowing a bit of first-year calculus plus a bit of computer programming to write a program to generate this sequence using a couple of dozen lines of code, at most.

However, if I hand you, say, the first 3,000,000,000 terms of this sequence without giving you the generator as a program or purely in words, it will be impossible, for all practical purposes, for you to tell me whether this is a “random” sequence or a “compressible” one (it is, in fact, highly compressible), and still less possible for you to specify a generating algorithm.

Am I missing something here? Is it that easy to whip up an ironclad random-number generator? Correct me if I'm wrong, but you wouldn't even need the first 3 billion terms of such a sequence to determine that it was non-random, would you? If it were this easy to program a random-number generator, then why are random-number generator implementations so elaborate?

Also, as I posted on Wilkins' blog, the position that you can't create a truly random number generator in principle, seems valid to me, but also seems like a very weird argument for a creationist to be making. It seems like the logical consequence of such a position is that the universe is inherently deterministic. I wouldn't expect a theist to make such an argument.

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