What do a double pendulum, weather patterns, and a population of rabbits have in common? According to American mathematician and meteorologist Edward Lorenz, these peculiar topics might actually be pretty similar. Linked by the field of chaos theory, Lorenz proposed that the world isn’t as deterministic as we might think.

## What is Chaos Theory?

Recently, I have been working on an independent investigation into the behaviour of a Swinging Atwood Machine. This mechanism consists of a swinging pendulum (m) attached to a counterweight (M).

To my surprise, factors such as pendulum release angle, pendulum length, and pendulum to counterweight mass ratio all drastically affected the system’s motion. While conducting my experiment, I noticed that small changes in these initial conditions lead to very different results. Afterwards, I remembered a quote that I had once heard:

“Does the flap of a butterfly’s wings in Brazil set off a Tornado in Texas?”

–Edward Lorenz (1963)

At first thought, this question seems preposterous! How can something as insignificant as a butterfly influence natural disasters continents away? A metaphor born out of Lorenz’s efforts to algorithmically predict the weather, this question encapsulates the essence of chaos theory. By describing how small deviations can trigger momentous events given enough time, this metaphor has permeated popular culture. In fact, the infamous saying has made appearances in movies from Spielberg’s “Jurassic Park” to Pollack’s “Havana.” However, Lorenz’s original message is often lost in translation.

## Lorenz’s Theory

Lorenz’s famous metaphor stemmed from his work in modelling weather patterns. While trying to create a computer algorithm to model the weather, he rounded a six-decimal input to three-decimals. Lorenz noted that his apparatus was only accurate to three-decimals, so this edit should have no effect on the simulation. Nonetheless, this minuscule variation created an entirely different forecast! This simple demonstration of how a system’s utter dependence upon initial conditions paved the way for an entirely new branch of mathematics.

In 1963, Lorenz articulated his findings in a paper that would become one of the most cited scientific articles. In fact, it garnered over 6000 citations since its publication. Furthermore, his theory challenges one of the fundamental pillars of science: determinism. Although the power of science lies in our ability to model the world, there will always be a degree of unpredictability inherent to nature. Perhaps if we had an infinitely accurate method of making measurements, humanity would be able to erase uncertainty. However, due to imperfections in measurement and finite computing power, this is only wishful thinking for now.

Lorenz died in 2008, but the legacy he left behind is one of curiosity and wonder. Indeed, his work in chaos theory has rippled into a profound understanding of intricate systems. In fact, Lorenz’s epiphany touched nearly every branch of science, from ecology to fluid dynamics. From a MIT assistant professor in meteorology to the father of chaos theory, one might be tempted to call this an example of the butterfly effect in itself.

Written by: Flora Guo

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