T-Stone has written in defense of Dawkin’s idea that theists proposing Intelligent Design would need to have a God who was more complex than the universe is. Important to this discussion is the following point T-Stone raises:
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.
Unfortunately for T-Stone, if he paid attention to what he has written here he’d see that he’s soundly refuted Dawkins. After all, if maximal randomness is equivalent to maximal complexity, then it is easy for me to write a program that will generate completely random output. In other words, it is easy for me—a person who is not maximally complex—to produce a program with output that is maximally complex. Thus, if we want to play T-Stone’s game and use complexity in this sense, then Dawkin’s argument must be surrendered.
If I can make a program that is more complex than I am, then God can create a universe that is more complex than He is.
FWIW, I disagree with T-Stone’s version of information and complexity. And despite what his post would lead you to believe, the idea that “maximal randomness = maximal complexity” is not true for all information theories. And in fact, if I were to use T-Stone’s definition of complexity then I would ask him to explain not why there is so much complexity in the universe, but rather why there is so little complexity. If complexity = randomness, then it doesn’t take a rocket scientist to realize that there’s a lot of the universe that is not random, and therefore there is a lot of this universe that is not complex. Under his information theory, randomness is the default. We do not need to explain random data. We do need to explain structured and ordered data. Therefore, we do not need to explain complexity; we need to explain non-complexity.
T-Stone is just giving a sleight of hand here. It would be like a mathematician saying “a > b” and having T-Stone say, “The greater than sign is inverted with the less than sign, therefore ‘a > b’ means ‘a is less than b’.”
But as soon as he engages in his sleight of hand, we respond: “If the greater than sign is inverted with the less than sign, then ‘a > b’ is no longer true, rather ‘a < b’ is.”
Inverting the operator without inverting the operands does not refute the original expression.
