Professor Ronald Rosenburg (MSU circa 1980) paced the front of the classroom.
I am going to teach you how to model systems that integrate mechanical, hydraulic and electrical systems. Some of you will try to model the US economy and other complex systems with these techniques. You will fail. You will fail because these techniques rely on predictable, linear responses from its components. Nearly all components that you select off-the-shelf are linear devices, at least they are if you selected components that are of the proper size.
There is nothing stable or linear-in-the-long-run in the real world. Some of you will still try to model the economy, either because you are not listening to me now or because you think your are smarter than me. Good luck with that.
The Butterfly Effect
In 1960, Edward Lorenz wanted to show a visitor a interesting weather phenomena that his computer had generated. To reproduce it, he reentered the state-space of the atmosphere that caused the phenomena.
He was not able to reproduce the phenomena.
Later investigation revealed that very, very minute changes in initial conditions caused vastly different, diverging results over time. It was as surprising as if I changed my aim by 25mm at 100 meters (1 MOA)....and I hit a spectator in the parking lot behind me.
Attempting to capture the degree of divergence, Lorenz coined the term Butterfly Effect. A butterfly taking off from a dandelion in China can trigger a typhoon in Baja California a month later. Obviously, the timing of every insect launching from every surface on the earth is not an input that can be modeled.
Ultimately, the Butterfly Effect topples the long term effectiveness of Central Planning. Even if the guys who are funding the effort are really, really smart people.
|Even very simple systems can generate complicated trajectories. This is a double pendulum. Now imagine the complexity that will result if one of the weights varies over time...the way people do or like nylon (a hygroscopic material that absorbs moisture from the atmosphere proportional to the humidity). Image from HERE|
Good luck with that.