>>720119630
Physics has had great success at describing certain kinds of behavior: planets in orbit, spacecraft going to the moon, pendulums and springs and rolling balls, that sort of thing. The regular movement of objects. These are described by what are called linear equations, and mathematicians can solve those equations easily. We've been doing it for hundreds of years.
But there is another kind of behavior, which physics handles badly. For example, anything to do with turbulence. Water coming out of a spout. Air moving over an airplane wing. Weather. Turbulent events are described by nonlinear equations. They're hard to solve-in fact, they're usually impossible to solve. So physics never understood this whole class of events. Until about 45 years ago. The theory that describes them is called chaos theory.
Chaos theory grew out of attempts to make computer models of weather in the 1960s. Weather is a complex system, namely the earth's atmosphere as it interacts with the land and the sun. The behavior of this system always defied understanding. So naturally we couldn't predict weather. But what the early researchers learned from computer models was that, even if you could understand it, you still couldn't predict it. Weather prediction is absolutely impossible. The reason is that the behavior of the system is sensitively dependent on initial conditions.
If I have a weather system that I start up with a certain temperature and a certain wind speed and a certain humidity - and if I then repeat it with almost the same temperature, wind, and humidity - the second system will not behave almost the same. It'll wander off and rapidly will become very different from the first. Thunderstorms instead of sunshine. That's nonlinear dynamics. They are sensitive to initial conditions: tiny differences become amplified.
The shorthand is the "butterfly effect." A butterfly flaps its wings in Beijing, and weather in New York is different.
