Will the movement of air caused by the flapping of a butterfly’s wings bring about a storm thousands of miles away?

Edward Lorenz, a meteorologist who became the father of the modern field of chaos theory, died April 16, 2008 of cancer in Massachusetts aged 90. While he was alive, Lorenz's research led him to develop what became known as the "butterfly effect," the idea that an infinitesimally small alteration; like the flapping of an insect's wings, can lead to potentially monumental consequences.

The butterfly effect is a phrase which encapsulates the more technical notion of sensitive dependence on initial conditions in his theory of chaos. Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system.

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that will ultimately cause a tornado to appear (or prevent a tornado from appearing). The flapping wings represents a small change in the initial condition of the weather system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the weather system might have been vastly different.

As a professor at the Massachusetts Institute of Technology (MIT), Lorenz was the first to identify chaotic behavior in the mathematical modeling of weather systems, in which small differences in a dynamic system, like the weather, "could trigger vast and often unsuspected results.

The original experiment that lead to Lorenz's groundbreaking theory was conducted in 1961, when he was using a numerical computer model to rerun a weather prediction. When, as a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127, the result was a completely different weather scenario.

I appreciate the concept that when you are playing with numbers, they can lead you into chaos. Let me give you an example. In 1955, I was working for an architect who designed bridges. When the design was finished, he asked me to calculate what this fee would be, based entirely on the weight of the bridge. I spent a week calculating the weight of the bridge by looking at the plans and calculating the weight of every steel member of the bridge, bolts included. Unfortunately, I accidentally struck an additional number on the large calculator when putting in his fee to begin with and didn’t catch the mistake. That small additional number boosted the figures. The more I punched in the numbers, the total cost of his fee exponentially increased ever so slowly until his fee appeared in the final tally in the billions of dollars instead of thousands of dollars. There was a week's work for naught over a small insignificent number accidentally punched in at the beginning of my task.

Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noting that if the theory were correct, one flap of a seagull's wings could change the course of weather forever. Later speeches and papers by Lorenz replaced the seagull with the more poetic butterfly.

To suggest that a butterfly flapping its wings in Brazil can cause a storm in Texas, seems a bit preposterous, to say the least. It would be no different than suggesting that if someone coughs in a particular direction, he will bring about a wind storm thousands of miles away. It’s also like saying that if you drop a small stone in the Pacific on the west coast of North America, it will cause an enormous tidal wave off the coast of Japan.

We know that a wind that suddenly blows across a surface of a large body of water that is calm will generate a ripple effect and if the wind suddenly stops, the ripples will die away until they become non existent. However, if the wind becomes constant, the ripples could later grow into enormous waves.

So, if there is no demonstrable direct link between a small action and a great shift, then why would we believe that anything one person does, such as coughing, will have an effect on the weather or the state of the sea thousands of miles away? As I see it, even if a million people standing on a shore were to cough in unison, I doubt that it would even cause a ripple in the water and it certainly wouldn’t cause a storm thousands of miles away.

In order for the theory that Lorenz promoted to be appreciated to some degree with respect to butterfly wings flapping in the air, the flapping would have to be constant and there would have to be many butterflies flapping their wings at the same time and in the same direction and yet, it still it wouldn’t cause a storm thousands of miles away.

I remember when I was kid hearing people saying that if everyone in North America were to stand on a chair and then jump to the ground at exactly the same moment; it would cause an earthquake on the other side of our planet. I suppose that if that many people jumped to the ground at the same time, the combined weight of millions of tons of human beings would hit the surface of North America all at one time but because the weight would be distributed all over North America, the effect would be lessened to such a degree that it really wouldn’t have an effect at all even in North America, let alone on the other side of the planet.

There are situations when numbers will play an important role in having an effect. For example, years ago, university students in one of the universities in the United States, decided to all flush their toilets in their living quarters at exactly the same time. The result was that the plumbing system couldn’t handle the demand. But when they flushed then individually, the plumbing system wasn’t affected at all.

Even if the flapping of the wings of a butterfly could cause a storm thousands of miles away, surely someone coughing in the direction of the butterfly would simply nullify the effect of the butterfly’s flapping wings.

I am afraid that Lorenz’s theory about the butterfly’s flapping wings is not really a good way to explain Lorenz’s theory of chaos.