No. 90: Nov-Dec 1993
It was discouraging enough to learn that many natural systems, from simple pendulums to our weather, are basically chaotic; that is, tiny changes in the initial conditions upon which predictions are based can lead to highly unpredictable outcomes. Chaotic systems are usually qualitatively predictable but not quantitatively predictable. We have no choice but to live with this chaos; it seems that that's the way the cosmos is constructed! However, it now seems that the situation is even worse than chaotic! Some systems, perhaps most systems, are also indeterminate, meaning that we cannot predict their qualitative behavior either. A simple example is the water swirling down the bathtub drain. This is not only chaotic but it has two qualitative final states: clockwise and counterclockwise. Regardless of which hemisphere you are in, you can change the direction of swirl with negligible effort. Each of the two final states of motion is still quanti tatively unpredictable. Systems that are more complex will possess many different final states, all chaotic. Can nature really be fundamentally chaotic as well as qualitatively uncertain?
J.C. Sommerer and E. Ott have mathematically examined a relatively simple system consisting of a single particle moving in a force field, experiencing friction, and being periodically jolted. Besides settling into chaotic motion, this particle may also be forced away to infinity -- two radically different final states. The analysis revealed that for any set of initial conditions leading to the first type of behavior, there was an infinite number of slightly different initial conditions that would lead to the second type of behavior. In other words, systems that we have long thought to be deterministic, like the motions of the planets, may be not only chaotic but indeterminate.
Since Sommerer and Ott found their indeterminate system easily, we must face the possibility that the future behavior of just about everything is beyond our capability to predict, even with our best instruments and computers. Apparently the universe is built in such a way that exact science is impossible.
(Sommerer, John C., and Ott, Edward; "A Physical System with Qualitatively Uncertain Dynamics," Nature, 365:138, 1993. Also: Peterson, I.; "Finding Riddles of Physical Uncertainty," Science News, 144:180, 1993.) Comment. This discovery is even more profound than Heisenberg's Uncertainty Principle, which is merely quantitative in character and for practical purposes rules only the atomic world. From the above we see that the entire cosmos is uncertain quantitatively and qualitatively. A heck of a way to construct a universe!