It's All a Matter of Precision
by Paul Hibbert
When I first heard about the “butterfly effect” that was popularized in the 2004 movie I was somewhat dumbfounded that this wasn’t already common knowledge. What confounds me further is that it still hasn’t been recognized that the concept hasn’t been carried to its logical conclusion. Maybe I’m wrong. Maybe there is that recognition but I’ve not been privy to it. Maybe it goes by a name unknown to me. Maybe I’m just out to lunch. If so, please set me straight. There are many, many smarter people than me out there who make their living studying chaos theory.
As everybody knows, the butterfly effect is based on the fact that miniscule differences in initial conditions can lead to enormous differences in outcomes. The usual explanation is that of a butterfly flapping its wings in some remote location such as Asia can possibly result in a tornado in Kansas. Where I disagree with that position is that it doesn’t extend to the postulation that any change in an initial condition, no matter how small, will necessarily result in huge repercussions. The butterfly effect has the proviso that changes in the initial conditions may have a large effect but they may also die out. This is where I disagree. That the butterfly’s existence may just have been just a passing incident doesn’t tell the whole story. The butterfly’s flapping of its wings changed the movement of blades of grass or leaves. That changed the amount of light landing on adjacent leaves or dried the moist earth more, or less, than it would have without the presence of the butterfly. So, no matter how little immediate effect that has, the process proliferates, perhaps changing the path that an ant might have taken and being eaten or not eaten by a predator. The effect spreads, albeit with probabilities attached, but it doesn’t depend on living organisms. The same argument can be made by just using natural processes.
Consider the existence of a mountain on earth. Obviously it affects many things. Its gravitation pull will affect the orbit of passing satellites, and by extension, the moon. It will deflect winds blowing over it. Its weight changes the gross shape of the earth. Its albedo changes the amount of heat retained by the earth and the number of photons that may be reflected to different galaxies, and so on. But what is true for the mountain is also true for the smallest particle.
How can I prove this hypothesis? I can’t, but consider the following thought experiment. Imagine a large billiard table, an acre in extent with a number of pockets around the edge and populated by 10,000 billiard balls, randomly spaced. You strike a ball with your cue. Perhaps it strikes other balls or perhaps it just eventually stops. If you had struck the ball even by an infinitesimally different angle or force it would have struck other balls slightly differently, or it would be in a slightly different position. Now strike another random ball, and so on. Eventually a ball will go into a pocket (a significant event, like the tornado in Kansas) but this would likely not have happened if the initial condition had not been changed. All of the above is not new to anybody familiar with chaos theory, but what seems not to be appreciated is that the phenomenon of the slight difference in initial conditions doesn’t die out, but proliferates forever and everywhere because every new hit on a cue ball will find a greater and greater degree of disarray and new, other “events” will take place. Every new collision can be considered as a new starting condition. In fact, every micro millimeter of transit of a ball on its path as it tramples on the fabric of the felt is a new starting condition. So, there are a multitude of insignificant events (those events that don’t cause a ball to drop into a pocket) but those non-events will eventually and necessarily influence future significant events.
The philosophical point that I am trying to make is that, with our free will, we are continually changing the future by a virtually infinite amount by even our smallest decisions and actions.
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