9/20/2012

Order vs. Disorder - Groups of Blocks Order vs. Disorder - Groups of Blocks

By Rowdy Otto Riemer

I've mentioned before that to me, order simply means being a state our minds find interesting whereas disorder means being in a state that our minds do not find interesting. I think I've found a good way of explaining this.

Suppose you saw two groupings of blocks with several blocks in each group. Group A is stacked neatly forming a large cube. Most would consider this arrangement to be ordered. Group B is in a large pile. Most would consider this group to be disordered.

Over time, Earthquakes happen, the wind blows the blocks around, and various things bump into the groups of blocks altering their arrangements. After a while, the result is two jumbled piles of blocks that most would consider to be in disorder. Without someone restacking the blocks, Group A will never return to a cube-shaped stack, while Group B has always been a jumbled pile and can remain so indefinitely (well, until they are completely separated, destroyed, etc.).

How we look at the groups before and after the changes is due mostly to our categorical thinking. Before the change, Group A was very different from Group B. Group A is also very different before the change than afterwards. But we might think that Group B’s initial state is quite similar to the final states of both states. This is very much incorrect.

Just like Group A will never return to it’s initial state without someone rebuilding the stack (and even then, there will really be some variation), the arrangement of Group B was absolutely unique, and the blocks will almost certainly not return to their initial arrangement. And the final states of both groups have equally unique arrangements.

The arrangement of Group A’s initial state has special significance to us because we can make a simplistic concept in our heads of how the blocks are arranged. We only need to know that their orientation is identical (basically anyway) along with the dimensions of the block. We can remember that state because less information is needed to remember it.

However, Group B’s initial state is not uniform. Each block is oriented in a different way. To replicate the initial state of Group B, our brains would have to remember the position and orientation of each block. Our brains are simply not equipped for that. So we categorize the Group B as a disorganized random pile. Because the uniqueness of the arrangement of the blocks holds no significance to us, we see no significant difference between Group B’s initial state and the final states of both Groups A and B. We ignore that Group B is no more likely to return to it’s initial state through random interactions with its environment than Group A is.

We think of much of our world as chaotic. That is simply because the number of possible states of systems that our brain can make some sense of are greatly outnumbered by those that don’t. One might point out that the uniformity of Group A is a significant difference between Group A’s initial state and the other states. This is true, but the 4 states in this scenario are still not as different as we often seem to think. One might argue that it takes an intelligent being to create the initial state of Group B. In fact, wooden blocks would almost certainly never wind up in an arrangement like Group A’s initial state without an intelligent being putting them that way.

But that does not mean there are no natural processes that lead to the kind of geometric uniformity that our brains will find interesting and easy to understand. With wooden blocks, a neatly stacked cube formation has as little space between the blocks as possible (well, yeah, this can be nit picked, but it’s basically true). But there is no process that generally attracts the blocks together in a way that favors compact uniformity. However, you can find particles of similar kinds and shapes in nature that do have forces pulling them together in a manner that favors geometric uniformity.

Consider molecules of water as the water approaches freezing. In the liquid state, the molecules have enough kinetic energy to counteract the forces pulling them towards each other. As the temperature drops, so does this kinetic energy. Water molecules are polarized and have a given shape. As they come together, the polarization and shape force them into the geometric uniformity seen in ice.

No comments: