I like water as an example of true Chaos. I remember waiting for some friends outside a restaurant a while back: sitting outside and watching a fountain gurgle away for 15 minutes. A lot of my life is taken up with waiting for others when I'm being social so one must learn to take value from those still moments. The fountain itself told me nothing, yet it acted as a focal point for my thoughts: is that what people mean when they say "we have so much to learn from..."? Often that's said about things I find it nebulous at best to learn from and I often feel it's because the speaker, lacking wisdom, hopes this platitude will suffice to cover, but perhaps they mean it helps us learn from ourselves.
Well anyways, the fountain proved a perfect demonstration of chaos. Every path the water took from its apex to its low point was constantly changing. Any individual part of the water (be it a molecule or a full drop) was entirely unpredictable: no meaningful guess could be made as to which path it would take down the rock face, nor once a path was chosen, which part of that path it flow in. To predict it would require more computational power than the world has today, and a greater knowledge of the exact properties of that fountain and the surrounding environment than we are even capable of gathering.
Yet for all that, the patterns were clear and certain types of predictions could be made, and with great confidence. The overall space in which the water had to flow (ignoring the small portion which evaporated) was actually quite limited. Within that certain paths were dominate, and though their size waxed and waned, and they moved slightly around, they too followed a prescribed course that could be easily described.
Which was the reality of the system? Was it deterministic, easily categorized and predictable, or was it beyond fathoming: outside the capacity of human intelligence to see before it happened? The answer, of course, depends on what you find interesting about the fountain. Are you a spec of water, constantly bounced to and fro by powers you have no control over? Or are you an outside observer, taking in the beauty of countless drops of water flowing by?
Yet even if you are that drop you can still know certain things, as long as your time-scale is big enough. You may not know if you will head left or right at the next junction, but after a hundred passes through this system you can certainly limit your possible futures. You know eventually you will take the leftward course and see the smaller but more frequent drops that come with that course. And should you head right you can count on the big falls before plunging into the ocean below and slowly circling down to the pump to return once more on your journey.
Certainly if this is allegorical (and on my blog it better be) then we are the drop of water, but what is our time scale? Do we have enough time in this life to see the patterns and curves, or to be assured of a future in any of them, or is our life span only a few turns in an endless cycle? In the fountain there are clear bounds placed by the rock walls of the structure: for us that is the forces of intelligence in our lives that have the strength to create lasting impact. Random events and chance encounters may move us back and forth, and in the right time change us from one route to another. They do not, however, have the power to limit our actions: they are not long term enough for that. The two constants in every life is the force of a person's own will and the will of God. Then we add in other we choose to surround ourselves with long enough to ensure their personal drive will be strong enough to shape our lives. Parents and friends, husbands and wives, Satan perhaps though we all hope not. It may be chance that forces us on a path bound by one person or another, but it is that influence that creates the characteristics of our course through life. Strange attractors those boundaries are called in science. Not a bad name.