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The Chaos of it All

<span  style="font-size: 1.5rem;" >Imagine a demon who knows the precise location and exact momentum of every atom in the entire universe. Could that demon predict the future? Could it tell you what color shirt your great-great-grandson will wear on their forty-second birthday? After all, we live in a universe of causal physical laws, so it might seem that if the current state of the universe were sufficiently well understood, you’d be able to predict the future from the present.</span>

Philosophers have long argued about causal determinism – whether the happenings within the universe (and, therefore, obviously, your life) follow a predetermined causal course or whether there’s a role for chance and choice to alter the course of events. French scholar Pierre-Simon Laplace coined the all-knowing-future-predicting demon described above in the early 1800s.1 Laplace’s demon was part of an argument meant to show that free will cannot exist because if we understood the present well enough, we’d see that the future is already set.

There are many arguments for and against causal determinism (people have been arguing about it for centuries, after all). There’s one challenge to Laplace’s demon we’re going to focus on today that comes from chaos theory, or chaos math. This is a subfield of physics that studies systems that seem to be purely random, but can actually be described by a set of deterministic rules. You’ve probably seen Pink Floyd-esque videos moving through fractal landscapes. Here’s a good example.

What looks like infinite complexity is actually described2 by a very simple equation: ZN+1=ZN2+C. And the key point is that it is impossible to accurately predict the future from the present for chaotic systems such as this (or at least, impossible to predict very far into the future). This isn’t because there’s randomness in the system. There isn't. It’s because some systems can be entirely deterministic and yet intrinsically unpredictable! Even if Laplace’s demon knows all there is to know, he won’t be able to predict the future of chaotic systems.

Chaotic systems are often described as being “extremely sensitive to initial conditions.” What that means is that very small, almost imperceptible changes in the present can wind up having dramatic consequences in the future. You might have heard the term “butterfly effect,” or butterfly theory, to describe this idea. Let’s unpack.

Edward Lorenz was a mathematician interested in the climate.3 He was a pioneer in the 1960s in using computers to try and predict the weather. One day, he made a mistake – he accidentally typed in 0.506 instead of 0.506127. This was a tiny mistake, just a rounding error, and it shouldn’t have made any difference in the overall result. But it did make a difference. This tiny error led to a completely different weather pattern in the simulation. Lorenz dug into the numbers and saw how over time, a seemingly-minuscule change could propagate to an entirely different weather pattern. His climate model was extremely sensitive to initial conditions.

Lorenz put a poetic spin on the idea that tiny changes can result in huge weather shifts in a paper he presented at a scientific conference titled “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?.” In it, he describes his simplified climate model as a system of equations and the solution to those equations, termed the Lorenz attractor. An attractor is just a stable state into which a system tends to settle – an attractor state for a floating rock like Earth is to settle into an orbit around a more massive object like the sun. In an even more poetic turn, if you plot the Lorenz attractor in a certain way, it even looks like a butterfly. Some call it the butterfly attractor.

So, in light of what we’ve learned about the butterfly effect, why are weather forecasts wrong so often? They seem to do a fine job 2-3 days out, but not being able to trust what the forecast says is a common trope in our culture for a reason. Well, weather forecasting is not hard because of randomness in the atmosphere; the interaction of clouds and wind currents is causally deterministic. But that interaction is also chaotic – it’s sufficiently complex to be inherently unpredictable, no matter how much information you have at the time. So no, we’re unlikely to ever reach a point where NOAA satellites are sufficiently advanced to get an accurate weather prediction several months out. Technology is not the problem; the innate unpredictability of chaotic systems is!

Because the weather in the future is likely affected by small changes today, we could, in principle, make some small changes that would then have large effects on the weather in the future. Scientists at the RIKEN Center of Computational Science have shown that this is possible, at least in theory.4 Running computer simulations of weather patterns (much more complex than what Lorenz was using back in the ‘60s, but the same idea), the authors found that small changes made to the natural environment could keep the overall weather system from changing from one state to another. The problem, of course, in practice, is figuring out exactly what small changes today would have big effects in the future. Which butterfly needed to flap its wings in which country to have steered Hurricane Ian back out to the Atlantic?

1780–90, silk.

This 18th-century waistcoat created in France between 1780-90 shows beautiful embroidery of butterflies and insects engaging with fruit branches. Waistcoats were worn as a layer of protection and as ornamentation. Silk and shiny satins were utilized to reflect light and draw the eye to the intricate embroidery.

Image courtesy The Metropolitan Museum of Art.

Create your own ripple effect.

Your actions, even those that seem minor — the coffee beans you buy, the different jogging route you take, a smile you give to the person next to you on the street — could generate cascading effects that ripple throughout society.

Although the butterfly effect shows we can't predict how our actions will effect the future, choose to do something kind today with the hope that it will echo positively around the world.

Leave an encouraging note for a stranger to find.Let someone ahead of you in line.Share your gratitude for something with a friend or neighbor.

Tiny gestures like these might end up counting more than you think.


1 Bradly, Larry. “Laplace’s Demon.” Chaos and Fractals, 2010.
2Mandelbrot Magic.” Fractal Foundation.
3 Motter, Adilson & Campbell, David. “Chaos at fifty.” Physics Today, 66(5), 2013.
4 Miyoshi, Takomesha & Qiwen Sun. “Control Simulation Experiment with Lorenz’s Butterfly Attractor.” Nonlinear Processes in Geophysics, vol. 29 no. 1, 2022.

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