The butterfly effect describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state, e.g. a butterfly flapping its wings in Brazil can cause a hurricane in Texas.
Tuesday, June 4, 2019
#155 / Chaos Is A Friend
Quanta Magazine has published an article saluting Margaret Hamilton and Ellen Fetter, two women who played an important part in the discovery of chaos theory. The article, published on May 20, 2019, is titled, "The Hidden Heroines of Chaos."
I liked this article not only because of its appreciation for the role of these two women, whose seminal work was forgotten until recently; I liked the article because it provided a relatively understandable explanation of what "chaos theory" actually is. While the article is helpful in that way, it looks like James Gleick's 1987 book, Chaos: Making a New Science, is actually the most important go-to guide to chaos theory for the non-mathematician.
Wikipedia has this definition of one of the key concepts in chaos theory:
You can read a little bit more about this in the Quanta article. The "lesson" for us, I think, is pretty clear - and it is a helpful lesson. We are always trying to "predict" the future; chaos theory says we can only do that to a certain degree.
"Predictions" are always made by "observers." Measurements are taken, and then future results are extrapolated from the measurements we make now. Chaos theory seems to say that even the smallest deviation from a specified initial state can result in a wildly erroneous prediction about a future state. The weather looks just fine for that picnic we have planned in the park in Houston, but we forgot about that Brazilian butterfly!
There is another thing we need to remember when we think about the future, and try to convince ourselves that we can predict it. Human beings are not simply "observers." We are "actors," too, and our unexpected actions, completely unpredictable, can change the future rather dramatically, for good or ill.
Chaos theory helps remind us of that truth. Sometimes, we need such a friendly reminder!