The butterfly effect: the impact of deterministic chaos on our lives

The butterfly effect teaches us to ackowledge the chaotic nature of life, to be mindful of our starting conditions, to generate the best catalysts to achieve our goals, and to constantly adjust our forecast.

What do predicting the weather, studying cognitive processes, and starting a war have in common? They all require to take into account the butterfly effect, where a tiny change in initial conditions can have an outsized effect on the outcome.

As Terry Pratchett and Neil Gaiman wrote in Good Omens: “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.”

Many people are familiar with the concept of the butterfly effect through the 2004 American science fiction film, in which changing one’s past leads to unintended consequences. However, few know the exact origin of the expression, and how it can be useful to understand the phenomenon in daily life. The butterfly effect started in meteorology, but you can see it at play in many areas of life and work, such as psychology, economics, politics, and more.

Predicting the weather

People have tried to forecast the weather for millennia. In about 350 BCE, Aristotle wrote Meteorologica where he described weather patterns. Before him, the Babylonians were predicting the weather using astrology and cloud patterns. In the Bible, Jesus says: “When evening comes, you say, It will be fair weather, for the sky is red, and in the morning, Today it will be stormy, for the sky is red and overcast. You know how to interpret the appearance of the sky, but you cannot interpret the signs of the times.”

At the end of the 19th century, the only forecasts available were published on a daily basis, using information transmitted through the telegraph, and focusing mainly on warnings of storms around the principal ports. They were based on highly subjective empirical rules.

It’s not until the 1920s that we started using mathematical rules to predict the weather. At the time, the work was excruciating and the results limited: it took at least six weeks to manually produce by hand a six-hour forecast for the state of the atmosphere over only two points in central Europe.

The first mathematical models were linear, with a large number of parameters. Over the years, researchers were crafting increasingly detailed equations for atmospheric dynamics. But the results were wrong. It took 37 years since the first attempt in the 1920s for a researcher named Karl-Heinz Hinkelmann to finally manage to produce a reasonable forecast, using a nonlinear approach.

Since then, many more parameters have been added to Hinkelmann’s model: solar radiation effects, moisture effects, sea ice and more. The goal was to make the model more and more precise. However, despite our best efforts, we can’t seem to be able to see more than a couple of weeks into the future. What’s going on?

The discovery of deterministic chaos

Edward Lorenz (1917–2008) was a meteorologist and mathematician who is best known as the founder of chaos theory. As the story goes, in 1961, Lorenz was using a simple computer to simulate weather patterns by modeling 12 variables, representing factors such as wind speed and temperature.

He wanted to review a sequence again, and in order to save time he decided to start the simulation in the middle of its course. To do this, he entered data from a printout that corresponded to conditions at that specific point in the original computer simulation. To his surprise, the weather forecast calculated by the computer was completely different from the previous results. Why?

After a bit of digging, Lorenz found the culprit: the rounded decimal number which was printed out. The computer model worked with 6-digit precision, but the number on the printout was rounded off to a 3-digit number. The difference was very, very small.

“At one point I decided to repeat some of the computations in order to examine what was happening in greater detail. I stopped the computer, typed in a line of numbers that it had printed out a while earlier, and set it running again. I went down the hall for a cup of coffee and returned after about an hour, during which time the computer had simulated about two months of weather. The numbers being printed were nothing like the old ones. I immediately suspected a weak vacuum tube or some other computer trouble, which was not uncommon, but before calling for service I decided to see just where the mistake had occurred, knowing that this could speed up the servicing process. Instead of a sudden break, I found that the new values at first repeated the old ones, but soon afterward differed by one and then several units in the last decimal place, and then began to differ in the next to the last place and then in the place before that. In fact, the differences more or less steadily doubled in size every four days or so, until all resemblance with the original output disappeared somewhere in the second month. This was enough to tell me what had happened: the numbers that I had typed in were not the exact original numbers, but were the rounded-off values that had appeared in the original printout. The initial round-off errors were the culprits; they were steadily amplifying until they dominated the solution.” — Edward Lorenz in The Essence of Chaos.

This is when Lorenz discovered that a very small change in starting conditions can lead to vastly different outcomes. Now, for a fun fact… When Lorenz published his seminal paper about his discovery and started receiving feedback from fellow scientists, he commented: “One meteorologist remarked that if the theory were correct, one flap of a sea gull’s wings would be enough to alter the course of the weather forever.” Following suggestions from colleagues, in later papers and speeches, he used the more poetic butterfly instead of the sea gull.

The butterfly effect as we know it was born. It is now considered an underlying principle of chaos theory, describing how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. And it is why, despite incrementally adding new, more precise parameters, meteorologists cannot predict the weather beyond a couple of weeks. We can look back at the atmospheric conditions of the past, but we cannot foresee the future up to a certain point.

Lorenz Attractor - The Butterfly Effect

Entropy and the arrow of time

Time moves forward, right? Most people would never question what they consider to be a fact: if you break a glass, you can’t unbreak it. If you say something, you can’t unsay it. You grow older; not younger. Another way to look at this is to realise that things get increasingly messier as time goes. The universe tends to go from order to disorder; from quiet to noise; from nothingness to somethingness. This is what scientists call the arrow of time, and it has a lot to do with the butterfly effect and the chaos theory.

As physicist and mathematician Arthur Eddington explained: “Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing which cannot be undone.”

Many science-fiction books are based on the premise of inverting the arrow of time; and a subset of these books use the butterfly effect to explain how small changes in the past can have a massive impact on the present. To this day, we haven’t managed to tame entropy and reverse the arrow of time. The butterfly effect suggests it may be impossible. But that shouldn’t prevent us from keeping on trying to find exceptions to the rule.

The butterfly effect in action

Even if you don’t care about predicting the weather, the butterfly effect is everywhere. Being aware of its powerful impact on outcomes can be crucial to humble predictions and realistic decision-making. Here are three examples of the butterfly effect in psychology, history, and business.

  • Dynamic systems in cognitive science. Bifurcation and non-linearity are central to the way the mind works. Tiny changes in neurotransmitters can have a massive impact on cognition. It’s often impossible to know what exactly tipped a cognitive system. “The dynamic approach to cognition emphasises the complex process of human development including mental, behavioural, neural and social systems interacting with each other over the life  course (…) Small changes in certain parameters can lead to enormous effect on their attitudes, actions, and behaviours which are before seen as coherent, stable, consistent, and predictable,” explain researchers of Yüzüncü Yıl University’s Department of Psychiatry.
  • The catalyst for World War II. There have been many books and movies speculating about how history would have been different if a young Adolf Hitler had been accepted in art school. He was rejected twice by the Academy of Fine Arts in Vienna, once in 1907 and again in 1908. Imagine a world where Hitler had been solely focused on painting quaint countryside landscapes with trees and lake houses. A seemingly small decision from a school committee resulted in events that shaped the world.
  • Chaos in business. “We all seem to be looking for the Holy Grail, the nexus point in a complex system. This is where a small change in the marketing mix will yield a large improvement in marketing dynamics,” writes Rajagopal in The Butterfly Effect in Competitive Markets. Many business models wrongly apply linear thinking to complex problems. A typical example is the rational customer who always maximises economic utility. We now know it’s not the case. Consumer decisions may seem predictable at first, but they are chaotic and complex: consumers don’t actually behave like rational agents. Again, it may be hard to predict exactly which factor may tip their behaviour one-way or another; and even harder to predict their behaviour over long periods of time.

While we can be mindful of our starting conditions and try to generate the best catalysts to achieve our goals, understanding the butterfly effect is about embracing the chaotic nature of life. Our current data can only bring us so far in predicting the future; small changes can have a massive impact on the outcome. In order to succeed, we need to constantly adjust our forecast. Only then we can thrive in the midst of complexity.

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