I stood in my basement staring at the crack in my foundation that I had sealed last summer, as torrential rains descended. The incoming brown liquid mocked my efforts at foundation repair. So, I braved the 90-degree weather and crawled under my deck, armed with my short-handled shovel and heavy-duty power drill. For several hours I labored through solid, concrete-like clay to dig a deep-enough hole to access the exterior of the foundation in order to seal the culprit.

Because I am an engineer, my mind turned to probabilities. What was the probability that this crack would have leaked again? What was the probability that it would have rained this much? What was the probability that the local weather forecaster was ever right?

Making sense of chaos

The forecasters have to predict the weather while trying to factor in temperature, humidity, precipitation, cloud cover, wind speed, wind direction, jet streams, cold fronts, warm fronts, and more. These seemingly random factors combine to cause weather (and my leaky basement).

Many years ago, one of my systems engineering professors discussed chaos theory, describing how systems, like the weather, are sensitive to and dependent on initial conditions, i.e., what happens first. He told us about the “butterfly effect,” in which a small change in the state of a system can result in differences in a later state.

For example, the flapping of the wings of a butterfly in China can affect the weather thousands of miles away in New York a few weeks later. Really? What’s the probability that a butterfly flapping its wings could influence weather thousands of miles away?