The world can be as simple or complex as you think it is

Physicists tell us that energy tends to become more random and disorderly. This increasing randomness is called entropy. The second law of thermodynamics deals specifically with energy. But because energy affects atoms and molecules, matter also tends to become disorderly, unless we expend energy to keep it organized.

Take my truck, for example.

Here is a “thought experiment” concerning entropy, complexity, randomness or whatever. Try to imagine a sequence of increasingly complex shapes. Start by thinking of the simplest geometric shape you can think of. That would be a point. Points are two-dimensional and have the same length and width. I think we could agree that they constitute something we could call “first-order complexity.”

Now, what could be more complex? A line. It also is two-dimensional, but has a midpoint and a beginning and end. Let’s call a line “second order complexity.” If we introduce a change in direction of the line it would increase complexity. A sharp change would be called an angle and a more gentle change would be called a curve. If we describe an angle as “third-order complexity,” the only variation left to us would be the degree of the angle, or the direction of the line.

If the line always angles in the same direction, it will eventually end up as a closed geometric shape: a triangle, square, rhomboid or something like that. Thinking like this, geometric figures become “fourth-order complexity.”

A curved line is more complex than an angle because it introduces the concepts of curvature, radius and diameter, as well as length, width and midpoint. A curved line becomes “fifth-order complexity.” As with geometric shapes, if we continue a curved line in one direction it will eventually form a closed circle. I’ll call a closed circle “sixth-order complexity.”

At this point we are almost out of two-dimensional complexities. But wait! What if we reversed the curvature in a regular manner? That would give us a wave. Waves have midpoints, beginnings, ends and radii, but also possess frequency and amplitude. Making waves is “seventh-order complexity.”

(Because I said so and because it’s my thought experiment.)

Now I think we really are stuck unless we go into the third dimension. Here we can either build closed, angular constructions such as cubes, or we can build three-dimensional balls that have a curved plane. They become “eighth-order complexity.”

Can a wave be made three dimensional? A three-dimensional wave would be called a coil, and coils are definitely more complex, so our “ninth-order complexity.”

But now, I am stuck. To make a coil more complex you would have to imagine a coil made into a coil. I can sort of envision that as “tenth-order complexity” in my mind. But when I take the next step and try to imagine a coil, in a coil, in a coil, my brain gets the hiccups! Is it possible to imagine a coil, in a coil, in a coil? Can you imagine a coil, in a coil, in a coil, in a coil?

I built a coil, in a coil, in a coil, once for a class. I wrapped a wire around a stick to make a coil. Then I pulled the coil off and wrapped it around the stick. Then I pulled that off and wrapped that around the stick again. But when we looked at it, it just looked like a big mess of wire. There was order there, but we couldn’t really see it.

So what is entropy?  Is there really any such thing as disorder? Perhaps what we call randomness and disorder in the universe is simply an order of magnitude that we do not have the ability to identify or imagine yet. Perhaps chaos is simply an order of complexity that we cannot perceive with our present technology, or imagine with our present minds.

Gary McCallister is professor of biology at Mesa State College.


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