The Unpredictable Weather
Ed Lorenz and the Butterfly Effect
Pull out your phone and look at the forecast on a weather app or website right now.
How much do you trust the weather forecast for tomorrow? How about 7 days from now?
When I was living in the Mountain West it seemed like the weather forecast was reasonably reliable for 1-2 days out, but pretty unreliable at the 7 day mark.
Since moving to Florida I have come to realize that the weather forecast here is close to worthless.
For example, yesterday we took the family on an outing where we carted on a trail with our mini horses. It was bright and sunny when we left. The forecast for the day was 75 degrees and sunny. We drove only about 20 minutes from home to the trailhead, and dark clouds suddenly started gathering. We checked our weather apps again, and now it was showing 80% chance of rain. It rained for about an hour as we started our adventure, then cleared back up and was sunny on our way back to the truck.
Why is weather so unpredictable?
At the height of the rise of reductionism in the early- and mid-1900s, scientists were confident that the weather, like other complex phenomena that had been conquered by Newtonian reductionism, was like a complex machine that could be broken down, studied, understood, and predicted—not just 7 days out, but, with enough data points and formulas, possibly predicted for months or even years into the future.
It was in this setting in the 1960s that Ed Lorenz was studying mathematical models of the weather.
As the story goes, Lorenz had incorporated several factors that influence the weather into his equations (like temperature, humidity, atmospheric pressure, wind velocity and direction, and so forth), and could produce a printout of the numerical values of all of the variables that represented the future behavior of the weather.
One day Lorenz wanted to rerun a section of his weather predictor, so he looked back at the printout at the point he wanted to start the rerun, manually input one of the numbers at that point, and let the model run again. At first, the modeled weather pattern matched the original run exactly, which is what he expected. But soon after, the second run diverged so much from the first that it looked nothing liek the original.
He double checked the data to make sure there weren’t any errors when he put the numbers back in for the second run, and there were none.
So what had happened? Why did the second run diverge from the first so drastically?
As it turned out, the computer stored slightly more precise data than printout showed. He had used the less-precise number from the printout when he manually input the value for the second run. The computer had stored the precise number for that particular variable (we’ll just say it was wind speed for sake of clarity) as 0.506127 miles per hour, but the printout had rounded it down to 0.506 miles per hour, which is the number he used for the rerun.
The difference is only 0.000127 miles per hour—less than a thousandth of a mile per hour; or about 8 inches per hour off. So small a difference, like the puff of a butterfly’s wings.
The difference was so tiny that it should really have had no impact whatsoever on the long term prediction of the weather.
But it did.
Almost immeasurably tiny differences in the precision of the current conditions led to completely different outcomes of the system in the long term.
This principle eventually came to be called the Butterfly Effect—a butterfly flapping its wings in Brazil can cause a tornado in Texas. The future weather is so extremely sensitive to the almost-infinitely precise current conditions that it is literally impossible to predict. That is what your intuition says about the 7 day forecast, and that is exactly what the math of Ed Lorenz showed.
In a very practical way, Lorenz discovered the same principle that Henri Poincaré had shown mathematically 70 years earlier: although reductionism is extremely effective at discovering the nature and behavior of the basic parts of a complex system, as soon as we start putting the parts back together, the behavior of the system becomes totally unpredictable—even if we have a near-perfect understanding of the parts.
In that case, maybe we are placing a little too much confidence in the power of reductionism to understand and predict the complex world around us. Maybe there is something about the whole that is truly more than the sum of its parts.
Is the world more like a very complex machine that, with enough study and time, can be understood well enough to predict and control? Or is there enough complexity and sensitivity to current conditions that it is mostly unpredictable, despite our detailed knowledge of its parts?
Those are the very questions we will dive into next.