Chaos v. Cosmos

July 3, 2007 by Dr. Mc.

Why is the universe not fractal? Ordinarily when one uses the word chaos, one means a condition of complete disorder. Chaos theory is very different. It has many implications, some valuable for medicine and other science, but the main idea is that when randomness occurs in the presence of some rules, patterns emerge. The simplest example I know is the Sierpinski Triangle. This can be constructed using a plain sheet of paper, pencil, and a die (singular of dice). Place three dots on the paper, which would form a triangle, if the dots were connected. Write two different numbers at each corner, using the numbers 1, 2, 3, 4, 5, & 6. It doesn’t matter which corner each number is at, so long as two different numbers are at each corner. Roll the die, and put the pencil point at whichever dot has the number rolled. Roll again and make a dot exactly half way to the dot of the next number rolled. From there, role again and make a dot exactly half way to the next, etc. As you can see, this is a combination of a few rules with randomness, and no matter what each roll of the die turns up, the overall layout of dots will form an exact and predictable pattern. Another interesting fact about chaos (randomness plus rules) is that the pattern is always fractal; that is, the pattern repeats itself infinitely at each level. Depending on how complex the original formula is, fractals can be quite complex and beautiful, but in all cases, there is at some level a repeating pattern.

What has this to do with the universe? The cosmos (the word means order) we know has rules which we call laws of physics. If one wants to believe that chance actually does occur in the universe, with no other ordering force (the alternative would have to be purposeful and directed), then the structure of the universe would have to be fractal; because rules plus randomness always yields fractal structure.

But this is not what we see. Yes, fractals can be used to predict some structures similar to nature, such as the branching of coral or broccoli, but there is no repeating pattern on the larger scale. Electrons have been pictured as traveling around protons (like planets), but this model is not adiquite. They are quantum in their positions, and two electrons seem to be able to occupy the same quantum level at the same time. Our planet moves around the sun, and the sun moves around the Milky Way, but the Milky Way has a pinwheel structure. Other galaxies may or may not have a pinwheel structure, and they are in turn clustered into groups that have no apparent pattern within the clusters. We now know that the clusters of galaxies form a greater pattern what appears to be either strings or like the shells of bubbles, with great voids in between. Is their a structure beyond that? We don’t know, but none of these levels is a repeat of any other level. If the structure of the universe cannot be predicted by chaos theory, then I am forced to conclude that there is something involved other than rules and randomness. There only remains purposive direction; or perhaps I should say Purposive Direction.

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