Today I’m going to talk about “sensitive dependence on initial conditions”, which is one of the foundations of chaos theory.
Chaos theory. I find it a fascinating subject to talk about, so here goes. Some people (me included!) can be really confused by the mathematics that is involved. So I’m not even going to put up a single formula here. Some people can’t seem to fathom how “the flap of a butterfly’s wings in Brazil can set off a tornado in Texas.”
I’m just going to explain the concept to you. How can I best explain this something called “sensitive dependence on initial conditions”? Easy.
I want you to think of a single marble on top of a mountain peak like the Matterhorn. Imagine if we placed a marble way up there on the very highest point.
Now imagine, too, if an abnormal amount of snow had built up over the previous winter and there is now the possibility of a great big avalanche. And you all know how avalanches are caused, right?
Avalanches are initiated by too much snow that accumulates on the side of a mountain. Even the smallest rock moving can set it off. Even the force of the snow melting in the sun can change the distribution of weight of built up snow on a slope.
We all know that the marble might dislodge a slightly bigger rock on its way down, thus causing an avalanche. So we have a situation where a very small physical event like a marble falling down could potentially generate a much larger event like an avalanche at the bottom of the mountain. Well ‘okay’ you might say.
Now this is just where it becomes interesting. Because the slightest change in the way we placed that single marble down onto the summit might have caused it to fall one way or another. Or the slighest breeze in one direction or the other. Or some small feature on the surface of the rock on which it is placed. [Read more…]