Monday, September 19, 2005

A couple loose ends on complexity and order.

Just to tie up a couple of loose ends from back here, as long as you're with me so far, let's summarize, the relationship between complexity and "design" -- if there is one.

The less-educated creationists (read: morons) have an annoying tendency to link complexity with design or with some vague notion of a "pattern" that they claim requires a designer of some kind. In a word, crap.

Using the notions explained in that previous article, consider a simple binary sequence that begins (spaces are added just for the aesthetic value and clarity) "11 00 111 000 11111 00000 1111111 0000000 ..." What would be the most obvious continuation of that sequence?

Most people would recognize the series of prime numbers (2, 3, 5, 7 ...) and, based on our earlier definition of "complexity," we could say that this sequence had a fairly low complexity value since I could explain the sequence to you by stating simply, "Alternating groups of ones and zeroes, with each pair of those groups having the next prime number of elements" or something to that effect that makes it clear what the sequence is.

But even though this sequence has a low complexity, chances are it wouldn't occur naturally in nature. If you came across this sequence somewhere, you'd be fairly safe in assuming that it had a "designer" or author. In other words, even something with low complexity might have a "pattern" that suggests a designer of some kind.

On the other hand, if you consider a lengthy, totally random sequence of bits, this sequence might easily occur in nature without any designer, but it would (because of its randomness) have a very high complexity. In short, even something with high complexity does not necessarily need a designer.

Note how non-intuitive this might be to some people -- sequences of low complexity might strongly suggest a designer, while other things with high complexity might occur naturally without any help. This is totally confusing to those who seem to think that complexity necessarily requires a designer, or vice versa.

See how tricky things get when you're forced to actually understand what you're talking about? Coming next: Applying complexity to real objects, and why Weasel Boy is a dick. (OK, I'll admit that doesn't logically follow: Weasel Boy is a dick regardless of the complexity of objects. But you knew that already, didn't you?)

dAVE said...

So, one could think of the level of complexity or information content as, for example, how compressable an image is. That is, an image with lots of smooth, one color area (like a minimalist painting) would be a smaller file post-compression, than something with a lot of random, disorganized stuff, like pebbles.

So, in many cases the information content goes up as randomness goes up. I guess the problem is that like "theory" the layman's definition is confused by ID/Creationist types to further their agenda.

CC said...

The above is essentially correct -- the more complexity in a sequence, the less compressible it is.

And, not surprisingly, images with more complexity or more "randomness" don't compress as much.

(Note carefully that, when we talk about compression here, we mean completely lossless compression -- so that the original image can be reconstructed exactly.)