Fractal Knowledge

What would a perfectly ordered world look like? I think that there is a tendency to think that it would be decomposable into nice, neat conceptual parts, amenable to our thought. But perhaps the opposite is true: perhaps the world which is rationally broken up for us is really arbitrary, while one which is perfectly ordered down to the very depths would forever defy our reasoning.

I bring up the analogy of a fractal. See here for an example. A property of the fractal is that it is infinitely self-similar (more precisely, quasi-self-similar): no matter how far you zoom in, no matter where along the boundary you look, you will find something which is in its own way similar to the whole. So the fractal is my paradigm of perfect order, down to an infinite precision and covering the entire figure.

Imagine living on the fractal. You are trying to make sense of the twists and turns which you encounter. You get a sense of order; it is indeed ordered. Parts do look like each other. But every time you think you have it down, you go a little bit further along the boundary, and something throws you off. You didn't get it quite right, so you have to go through your concepts and reanalyze the world. Since every part in its own way contains the whole (that is, it is in a way self-similar to the whole), you do gain some understanding of the entire fractal from each piece. But you also can't really get any part of the fractal unless you were to grasp the entire thing all at once.

So an infinite order would entire that we could understand something, and understand everything in understanding something, but no understanding would be unrevisable. No set of concepts, no affirmative propositions could be held for any length of investigation.

By contrast, what would a world be like which we could break down into nice, neat concepts? At first, such a world appears ordered. But then we turn to the concepts themselves. Why is green what it is? Just because. Why a straight line? Just because. This "just because" is the only answer givable to any such question, no matter what the basic concept or simple nature at hand is. In the end, we have to posit an Intelligent Kludger to put the mess of arbitrariness together, because there's nothing in the parts themselves to suggest order; only in the arrangements.