Mental Model: The Butterfly Effect

It used to be thought that the events that changed the world were things like big bombs, maniac politicians, huge earthquakes, or vast population movements, but it has now been realized that this is a very old-fashioned view held by people totally out of touch with modern thought. The things that change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe

– From Terry Pratchett and Neil Gaiman’s Good Omens

In a complex system, such as the world we live in, a minuscule event can alter the course of our lives significantly. This phenomenon was demonstrated by Edward Lorentz (1917 – 2008), a mathematician and meteorologists at Massachusetts Institute of Technology and the creator of today’s Chaos Theory. Because of his love for studying the weather, Lorentz was bothered by the difficulty of weather prediction, with meteorologists only being able to predict conditions for short periods of time, usually a couple of days at most. With the advent of computers, he created a mathematical model using a set of differential equations that represented changes in temperature, pressure, etc. One day, in 1961, while re-examining a series of data from his model, Lorentz decided to save time and restart the study mid-point instead of restarting the entire run. Therefore, he entered the conditions near the middle of a previous run, and began his calculations. The result he found was surprising: a somewhat different prediction. While the data from the second run should have matched those from the first, they soon diverged, with the second losing all resemblance to the first. This led him to realize that long-term weather prediction was doomed to fail, since such models exhibit a “sensitive dependence on initial conditions.” In other words, he learned that weather prediction models are inaccurate since it is impossible to know the initial starting conditions, and a small change can alter the results significantly.

Subsequently, using the butterfly analogy, he explained in speeches and interviews that a butterfly can potentially create tiny weather changes which, while not creating a typhoon, could alter its trajectory. In such a way, its flapping wing can represent minuscule changes in atmospheric pressure, and these changes compound as the model progresses. Thus, since small, nearly imperceptible changes can have massive implications in complex systems, Lorenz concluded that it was impossible to attempt to predict the weather.

How the Butterfly Effect Affects Our Lives

For want of a nail the shoe was lost,
For want of a shoe the horse was lost,
For want of a horse the rider was lost,
For want of a rider the battle was lost,
For want of a battle the kingdom was lost,
And all for the want of a horseshoe nail.

– Benjamin Franklin

A horseshoe nail can be inconsequential, or it can result in the loss of a kingdom. As noted by Lorentz, a small error in the initial data magnifies over time.

Set in 2055, A Sound of Thunder by Ray Bradbury tells the story of a man named Eckels who travels back 65 million years to kill a dinosaur, a Tyrannosaurus Rex. Despite being warned not to deviate from his tour guide’s plan, Eckels panics at the sight of the creature, steps off their path, and leaves the guide to kill the T Rex. Enraged, the guide kills the dinosaur and orders Eckels to remove the bullets before they return to 2055. Upon arrival, they find that their world has changed, with the language being altered and a dictator now in charge. Eckels notices a crushed butterfly stuck to his boot and realizes that, by stepping off the path, he had killed the insect and inadvertently changed the future. As Bradbury writes;

Eckels felt himself fall into a chair. He fumbled crazily at the thick slime on his boots. He held up a clod of dirt, trembling, “No, it cannot be. Not a little thing like that. No!”

Embedded in the mud, glistening green and gold and black, was a butterfly, very beautiful and very dead.

“Not a little thing like that! Not a butterfly!” cried Eckels.

It fell to the floor, an exquisite thing, a small thing that could upset balances and knock down a line of small dominoes and then big dominoes and then gigantic dominoes, all down the years across Time. Eckels’ mind whirled. It couldn’t change things. Killing one butterfly couldn’t be that important! Could it?

As it turns out, such a small thing can be that important. One minuscule event can alter the outcome of an entire system, as Lorentz found with his weather models. In life, a change of friends, habits, or routines can have a significant long-term impact on our end-results.  As seen in Multiplicative Systems, a weakness in a process may end up negating all its gains. Lorentz’s Butterfly Effect illustrates how this actually occurs: A small negative event compounds over time, resulting in a completely different outcome that does not resemble what a person initially intended to achieve. Much like the butterfly that flaps its wings in the Amazon and cause a storm to ravage Europe, so can a flaw at any point in your life can end up destroying your whole future. On the other hand, a small improvement today can also result in massive benefits in the long-term.

Thus, from Lorentz’s butterfly analogy, it is clear that tiny changes in starting conditions can have a massive impact on the end-results of a particular system. Additionally, it shows that even though we think that we can predict the future besides having some degree of control over some processes, such as the weather and the economy, we cannot. These systems are chaotic and prone to change, and these small alterations can affect their outcomes significantly.

A Quote I am Thinking About:

“The greatest danger for most of us is not that our aim is too high and we miss it, but that it is too low and we reach it.”

– Michelangelo



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