Chaos Theory and the Butterfly Effect

Podcast Transcript

For centuries, scientists imagined the universe as a giant clock, where every motion could, in theory, be predicted.

Then mathematicians and meteorologists discovered something unsettling: even systems governed by simple rules could become impossible to forecast.

A tiny change at the beginning could grow into a completely different outcome, an idea now known as the Butterfly Effect.

It reshaped how we understand weather, orbits, biology, and even world history.

Learn more about Chaos Theory and the Butterfly Effect on this episode of Everything Everywhere Daily.

Chaos theory is a branch of mathematics, but I’m going to start this episode by talking about philosophy and theology. In particular, the concept of determinism.

Determinism is the philosophical idea that every event is fully caused by prior events according to the laws of nature. In a deterministic universe, the present state of things fixes what will happen next. Given the same starting conditions and the same laws, the same outcome must follow.

This idea gained prominence during the Enlightenment due to the success of Newtonian physics. Newton’s laws made it possible to predict the motion of planets, falling objects, projectiles, pendulums, and tides with extraordinary precision. The more physics succeeded, the more tempting it became to think that the whole universe might be predictable in principle.

One of the classic thought experiments in determinism was proposed by the French mathematician Pierre-Simon Laplace. He imagined an intelligence, often called Laplace’s demon, that knew the exact position and motion of every particle in the universe.

If such an intelligence also knew all the laws of nature, it could calculate the entire future and reconstruct the entire past. In this view, the universe is like an enormous clock. Every gear turns because another gear made it turn.

Today, this thought experiment is often conducted under the assumption of a near-infinite computer.

By suggesting that events follow from prior causes according to discoverable laws, it encouraged the search for regular patterns in nature, especially in physics, astronomy, chemistry, and later biology.

The success of Newtonian mechanics made the universe seem less like a realm of mystery or divine whim and more like an orderly system that could be measured, modeled, and predicted.

This wasn’t just a scientific position; it also became a theological one. Many people argued that God was akin to a watchmaker. He built the initial conditions at creation, and then let the world tick away.

For most simple things, such as the orbit of one body around another, the collision of billiard balls, or the working of a pendulum, determinism worked really well.

However, cracks started to appear.

In the late 19th century, the French mathematician Henri Poincaré. was studying the three-body problem, which asks how three massive objects, such as the Sun, Earth, and Moon, move under each other’s gravity.

Newtonian mechanics worked beautifully for two bodies, but adding a third body made the problem vastly more complicated. Poincaré discovered that even in a system governed by clear mathematical laws, the motion could become so complex that long-term prediction was effectively impossible.

The Three-Body problem is so notoriously difficult that it became the central plot point in a similarly named series of science fiction books about an advanced civilization that couldn’t solve the problem.

What Poincaré didn’t know was that his discovery, or lack thereof, was the start of a whole new field of study known as Chaos Theory.

Many other scientists encountered problems that proved extremely difficult to solve. What their problems all had in common was that even the slightest change in initial conditions would result in radically different outcomes.

The major development in the field occurred in 1961 by total accident.

Edward Lorenz was a meteorologist and mathematician at MIT. At the time, weather prediction was being transformed by computers. The goal was straightforward: if the atmosphere obeys physical laws and computers can calculate those laws fast enough, then perhaps long-term weather forecasting would eventually become reliable. Lorenz was testing that assumption.

He built a simplified computer model of the atmosphere. It was not a full weather model by modern standards. It used a small number of variables meant to represent features such as temperature, pressure, wind, and convection. The important point was that the model was deterministic. Given the same starting numbers, it should produce the same future pattern every time.

One day in 1961, Lorenz wanted to rerun part of a simulation. Instead of starting from the beginning, he took a shortcut. He entered numbers from the middle of an earlier printout and restarted the model there. He expected the second run to duplicate the first run from that point forward.

At first, it did. The two weather patterns looked nearly identical. But after a while, they began to separate. Then they diverged completely. The new simulation produced a completely different pattern from the original.

Lorenz first suspected a computer problem. But the computer was not broken. The difference was in the numbers he had typed in. The computer stored the numbers internally with more decimal places, but the printout showed rounded values.

A number such as 0.506127 had appeared on the printout as 0.506. Lorenz had assumed that this tiny difference would not matter. In ordinary linear systems, it probably would not. A tiny input error would produce a tiny output error.

His accidental discovery, which could be replicated on a computer, was that a deterministic system could be extremely sensitive to its initial conditions. The model was not random. It followed fixed equations. But because the equations were nonlinear, a tiny difference at the beginning could be amplified into a huge difference later.

MIT describes Lorenz as the first to recognize what we now call chaotic behavior in mathematical weather models, and notes that he realized small differences in systems like the atmosphere could produce large and unexpected effects.

This was a direct challenge to the older scientific expectation that better measurements and more powerful computers would eventually allow nearly unlimited prediction. Lorenz showed that the problem was deeper.

The limit was not just bad instruments or incomplete data. In some systems, there is a built-in predictability horizon. You can improve the forecast, but you cannot make an exact long-term prediction possible if tiny uncertainties inevitably grow.

Lorenz then stripped the problem down further. Instead of using a larger weather model, he studied a very simple system of three equations representing atmospheric convection, the motion that occurs when warm fluid rises and cool fluid sinks. This became the famous Lorenz system.

The three equations produced astonishing behavior. The system never settled into a stable point. It never repeated in a simple cycle. Yet it did not fly off into total disorder either. Its path remained confined within a particular shape. That shape became known as the Lorenz attractor, the famous butterfly-shaped figure associated with chaos theory.

In 1963, Lorenz published his landmark paper, “Deterministic Nonperiodic Flow,” in the Journal of the Atmospheric Sciences. The title itself captures the paradox. “Deterministic” meant the system followed exact rules. “Nonperiodic” meant it did not simply repeat. Lorenz’s paper showed that a simple deterministic system could produce unstable, irregular, nonrepeating behavior.

In 1971, Lorenz gave a presentation titled “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”

This was the origin of the phrase you might be familiar with, the Butterfly Effect.

The Butterfly Effect is really at the heart of Chaos Theory.

There are chaotic systems all around us. One key thing to understand is that chaotic systems are not random. They might appear random, but they are subject to the same physical laws as everything else.

One of the simplest chaotic systems, if that is even a thing, would be a double pendulum.

A basic pendulum is very simple. It is a weight suspended from a pivot point that moves back and forth. It is so simple and its behavior so predictable that it is used in physics courses and has even been used to keep time.

A double pendulum is a pendulum with another pendulum at the end of it. It seems very simple, but that simple addition of a pendulum to a pendulum makes it go from one of the most predictable devices to one of the most unpredictable chaotic devices.

There are some great videos online that demonstrate just how different the outcomes of a double pendulum can be with even the slightest changes in the initial conditions.

If the second pendulum has a starting position even one millionth of a degree different, it will behave totally differently in just a few swings of the main pendulum.

Again, it isn’t behaving randomly. It is behaving according to the laws of physics. It’s just that its behavior is so dependent on its initial conditions.

Oddly enough, the company Cloudflare uses a camera pointed at a wall of double pendulums in their London office as a random number generator. While it isn’t technically random, predicting the behavior of a wall of double pendulums is so complicated that it could never be calculated, especially in real time.

What Edward Lorenz figured out was that the weather is fundamentally chaotic. This is why there is a limit to our ability to predict the weather. Weather forecasting has improved, and three-day forecasts are about as good as one-day forecasts were years ago, but we still can’t predict the weather weeks ahead.

One estimate I’ve seen says that if you put weather monitoring stations exactly one meter apart across the entire surface of the Earth, going all the way up to space, and you had the computational ability to handle all that data, the best you could do is predict the weather going out 30 days.

Of course, perhaps the greatest example of the butterfly effect might be history. History is filled with examples of small events that had outside impacts.

Many people have speculated about what might have happened if Adolf Hitler had been accepted to art school. He might never have gone down the path that led to the deaths of millions. Yet, how could someone in an art school admissions office in Vienna have possibly known the impact of such a decision?

Henry Tandey was a British soldier in WWI and a recipient of the Victoria Cross. In the final days of the war, he encountered a German corporal near the front lines and spared his life. That corporal’s name was Adolf Hitler.

Alexander Fleming accidentally left open a window, which led to the discovery of penicillin.

Archduke Franz Ferdinand’s driver took a wrong turn in Sarajevo and happened to stop near Gavrilo Princip. Princip had missed his earlier opportunity to assassinate the archduke, but this accidental turn put the archduke directly in front of him, allowing him to fire the shots that helped trigger World War I.

East German bureaucrat Gunter Schabowski accidentally said the wrong thing on television, which caused East Berliners to rush the Berlin Wall, which caused it to fall, which ultimately ended the East German state, which started the collapse of communism.

My father served in Vietnam and would occasionally mention stories of bullets flying past his head. Maybe if one enemy soldier 60 years ago hadn’t set his gun down in the mud, you wouldn’t be listening to me right now talk about the Butterfly Effect.

There are countless small events that occur every day that ultimately shape history, and it is impossible to know the repercussions of every one.

The interesting thing is that Chaos Theory didn’t disprove Determinism. It doesn’t mean that cause and effect aren’t real. It just means that it is far, far more complicated than anyone ever expected.