Vox Day: The "Fractal Intelligence" Delusion

On a private email loop, I've been getting bits and pieces of Vox Day offered by way of theistic argumentation. In particular, theistic friends find Mssr. Beale's "take down" of Dawkin's complaint that "A God capable of calculating the Goldilocks values for the six numbers would have to be at least as improbable as the finely tuned combination of numbers itself”[1]. Now, I've only read just a few pages of the opening of The Irrational Atheist, and have now read through Chapter VIII, "Darwin's Judas" just as means of familiarizing myself with the arguments being advanced on the email loop, and I guess I've been out of the loop for a while with respect to the mensa-punk-apologist groove that's happening out there. There's a lot of the book I haven't read yet, but just from what I have, I can say... that is one target-rich environment for fisking.

Anyway, it's easy to poke fun of the smaller, tangential blunders Day makes - in response to Dawkins' complaint, for example, Day says:

"Third, does Dawkins seriously wish to argue that Martin Rees is more complex than the universe? We know Rees calculated the Goldilocks values, so if he can do so despite being less complex than the sum of everyone and everything else in the universe, then God surely can, too. "[2]

Day apparently thinks that "calculating", or maybe just reading a physics textbook describing these parameters' values, is what Dawkins is pointing to in his objection. Hah! Calculating, say, the weak nuclear force is no small feat, and one wonders if Day, even as confused as he is here, supposes that Rees calculates these values on his own, apart from the enterprise of science?

I think it's safe to say that Dawkins would laugh at this kind of response, the idea that calculating a set of parameters' values represents the kind of complexity Dawkins is referencing, and rightly so. It's the machinery (for lack of a better metaphysical term) that unifies and interrelates these parameters that implicates something fantastically sophisticated, complex. Like Day supposes that Rees has matched the complexity of an automobiles design(er) by figuring out the car's design parameters: gas mileage, horsepower, number of gears, number of tires, etc.

As Day works through the "Fractal Intelligence and the Complex Designer" section, though, the errors become more fundamental, and less silly. Day continues on page 153:

"There is no reason why a designer must necessarily be more complex than his design. The verity of the statement depends entirely on the definition of complexity. While Dawkins doesn’t specifically provide one, in explaining his “Ultimate Boeing 747 gambit,” he refers to the Argument from Improbability as being rooted in “the source of all the information in living matter.” Complexity, to Dawkins, is therefore equated with information." [3]

Day can be forgiven here for his frustration; Dawkins does not spell out a formal definition of organizational or algorithmic complexity in his book. But you don't have to be a super-genius to get familiar with the concepts as they are used in science and information theoretic application. I haven't read Day's section of "theistic bodycounts" from wars versus "atheistic bodycounts", but Day's supporters on my list regale me superlatives of Day's phenomenal research capabalities. If he's got such capabilities, he shot all his efforts in previous chapters; Day simply punts here and decides to equate complexity with information.

Oops. That's a really major blunder. Just in casual terms, complexity is a description of the "number of discrete and differentiated parts", and information is "reduction in uncertainty". Complexity and information are related on some level, and those terms do often occur together in computing and information theoretic contexts. But complexity is not information, any more than mass is acceleration.

Day then gets ready for his example, which he intends to use in refuting Dawkins thusly:

"But as any programmer knows, mass quantities of information can easily be produced from much smaller quantities of information. A fractal is perhaps the most obvious example of huge quantities of new information being produced from a very small amount of initial information. For example, thirty-two lines of C++ code suffice to produce a well-known fractal known as the Sierpinski Triangle."[4]

Now, a recursive algorithm can produce arbitrary large amounts of output; so long as it continues to recurse, code for rendering Sierpinski triangles is stuck in an infinite loop, with each iteration produce a new level of rendering. But, complexity is not information, and while code for Sierpinski triangles and Mandelbrot set fractals (the other example Day invokes here) can generate enormous, unlimited amounts of output, both Sierpinski triangles and fractals are classic examples of precisely the opposite of what Day understands: minimal complexity.

Day has the clues right there in front of him on the page. He's proud of the fact that in just 32 lines of C++ code, he can produce staggering amounts of output. But complexity in information terms is measured by the size of the smallest program required to precisely the output. That means that a 32 line program is, by the very definition of complexity, not complex at all, and is in fact a very elegant example of simplicity. The essence of a fractal is self-similarity. Recursion simply applies this features of itself to itself, on a different scale.

A 1,000 x 1,000 pixel grid of random pixels, on the other hand, isn't as pretty to look at as a rendering of the Mandelbrot set, but it is much more complex -- maximally complex, as it turns out (which is part of why it's not as appealing aesthetically as a fractal image!). It's counterintuitive to people who don't work with information theory and algorithmic complexity, but its a fact of the domain: randomness is the theoretical maximum for measured complexity. You can't get any more complex than purely random. In a random grid of pixels, we cannot guess anything about any pixels at all. In a rendering of Sierpinski triangles, or the Mandelbrot or Julia set, as soon as we see one level of rendering, prior to any recursion, we no everything about the rest of image, and can reproduce the fractal to any depth of detail without the original program.

What does all this mean? Well, at a high level, it means Day has no idea what he's talking about in this part of the book. Worse, in a book that's held up as a treatise against slipshod reasoning and sloppy argumentation, this section indicts the author rather than his subjects. Dawkins' argument may not stand on its own, and may prove unsound in some regard. But Day's refutation is an example that works in Dawkins' favor, if anything, and Day doesn't even know it.

Intrigued by the profoundly amateurish analysis in this section, I did a little googling, suspecting that Day's "expertise" comes on the cheap thanks to a DSL line and a web browser (and even that must be done in a lazy, half-ass fashion, as even nominal effort with Google will unearth simple, straightforward treatments of this subject that would have shown Day how confused he was). The reader can judge for themselves what the likelihood is of this connection, but consider: here’s a paragraph from the Wikipedia article on “Fractal”:

“Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes.”[5]

Note the similar phrasing used in the Wikipedia text, and Day’s quote above from page 155:

“considered to be infinitely complex”, and “not only considered to be complex, but infinitely complex”.[6]

Also notice Day’s use of “approximate fractals”, a term used in the Wikipedia text as well. That by itself may not be compelling, but considered with the list of examples provided --- clouds, mountain ranges, lightning bolts, coastlines and snowflakes -- all of which Day names in his list, except for coastlines (which Day may be identifying indirectly with his mention of ‘other natural examples’)... one cannot read the Wikipedia text beside Day’s discussion on page 155 without recognizing them as cognates. See for yourself:

Day, page 155:

“Nor do they require human intelligence or computers to produce them, as approximate fractals can be found in clouds, snowflakes, lightning, mountains, and other natural examples.”[7]

Wikipedia, “Fractal”:

“Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, and snow flakes.”[8]

Now, there’s nothing wrong per se with getting clued in by a Wikipedia page, or cribbing from its text in discussing fractals or other topics, but please note that there’s an important clue in these juxtaposed quotes. If Day is working from this Wikipedia article as his source here, it’s significant that he left out a key qualification - “(in informal terms)”. It’s parenthetical in the text, as it should be apparent to the informed reader, and is superfluous for readers familiar with formal concepts of complexity. But just in case, the text helpfully notifies the reader, and perhaps Day, if my conjecture is right, that fractals are “infinitely complex” only in a casual sense.

Day emphasize that Sierpinski triangles are not just complex, but "considered to be ... infinitely complex". He conveniently leaves out the key qualification that such characterizations obtain only in informal terms, why? Because it eviscerates his argument! In terms of actual, measured complexity, Sierpinski triangles aren't complex at all, they are 'complexity poor', as Day documents himself in his own arguments by noting that the output requires less than three dozen lines of code to produce.

All of this gets wrapped up with a new brand name that Day is proud to introduce to the reader: the argument from "Fractal Intelligence", as defeater for theoretical problems Dawkins identifies in a Complex Designer (if complex things require designers, then who designed God?). But because Day is thoroughly confused about the basics of complexity as a concept, he ends up writing comedy, rather than refutation. Unfortunately, because information theory and algorithmic complexity are outside the conceptual frameworks of most of his readers, Christians gobble this up, credulous, enthused by the prospects of Dawkings getting refuted. I have no idea how widespread Vox Day's books, articles or ideas are -- I'd not heard of him until he was brought up on my discussion loop a couple months ago -- but his gobbledygook is getting approving nods and applause in some Christian quarters, apparently, since I am seeing Chapter VIII of his book being seriously offered as a refutation of Dawkins objections on the complexity of God requiring his own Designer.

-Touchstone

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[1] Richard Dawkins, The God Delusion (Mariner Books), p. 143.
[2] Vox Day, The Irrational Atheist, p. 153.
[3] ibid., p. 153.
[4] ibid., p. 153
[5] http://en.wikipedia.org/wiki/Fractal
[6] Vox Day, The Irrational Atheist, p. 155.
[7] ibid., p. 155.
[8] http://en.wikipedia.org/wiki/Fractal