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podcast transcript
For centuries, scientists have imagined the universe as a giant clock whose every movement could theoretically be predicted.
Then mathematicians and meteorologists noticed something disturbing. In other words, even systems managed with simple rules can become unpredictable.
Small changes at first can lead to completely different results – this is the butterfly effect.
It has transformed the way we understand weather, orbit, biology, and even world history.
Learn more about chaos theory and the butterfly effect in this episode of Everything Everywhere Daily.
Chaos theory is a branch of mathematics, but this episode starts with a story about philosophy and theology. Especially the concept of determinism.
Determinism is the philosophical idea that according to natural laws, all events are caused entirely by previous events. In a deterministic universe, the current state of things determines what happens next. Given the same starting conditions and the same laws, the same results should follow.
This idea rose to prominence during the Age of Enlightenment due to the success of Newtonian physics. Newton’s laws made it possible to predict with great accuracy the movements of planets, falling objects, projectiles, pendulums, tides, etc. The more successful physics became, the more tempting it became to think that the entire universe was in principle predictable.
One of the classic thought experiments in determinism was proposed by French mathematician Pierre-Simon Laplace. He imagined that an intelligence, often called Laplace’s Demon, knew the exact location 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. From this perspective, the universe is like a giant clock. All gears rotate because another gear causes them to rotate.
Nowadays, these thought experiments are often performed assuming a nearly infinite computer.
Proposing that events occur by prior causes according to discoverable laws helped to find regular patterns in nature, especially physics, astronomy, chemistry, and later biology.
The success of Newtonian mechanics made the universe look like an ordered system that could be measured, modeled, and predicted rather than a realm of mystery or divine whim.
This was not simply a scientific position. It also became theological. Many people have argued that God is similar to a watchmaker. He established the initial conditions in creation and then let the world go into motion.
For most simple things, such as the orbit of one object around another, the collision of billiard balls, and the operation of a pendulum, determinism worked really well.
But cracks began to appear.
Henri Poincaré, French mathematician in the late 19th century. I was studying the three-body problem, which asks how three massive objects – the Sun, Earth, and Moon – move according to each other’s gravitational pull.
Newtonian mechanics worked great for two bodies, but adding a third body made the problem much more complicated. Poincaré discovered that even in systems governed by clear mathematical laws, motions can become so complex that long-term predictions are virtually impossible.
The three-body problem is so difficult that it became the central plot of a similarly titled series of science fiction novels about an advanced civilization unable to solve the problem.
Poincaré did not know that his discovery, or lack thereof, was the beginning of an entirely new field of research known as chaos theory.
Many other scientists have faced problems that are very difficult to solve. What these problems had in common was that even a small change in the initial conditions led to fundamentally different results.
A major advancement in this field occurred with the 1961 Total Accident.
Edward Lorenz was a meteorologist and mathematician at MIT. At that time, weather forecasts were being changed by computers. The goal was simple. If the atmosphere obeys the laws of physics and computers can calculate these laws fast enough, perhaps long-term weather forecasts will eventually become reliable. Lorenz was testing that assumption.
He created a simplified computer model of the atmosphere. It was not an all-weather model by modern standards. A small number of variables are used to represent features such as temperature, pressure, wind, and convection. The important point was that the model was deterministic. Given the same starting number, you need to generate the same future pattern every time.
One day in 1961, Lorenz wanted to run part of the simulation again. Instead of starting from scratch, he took a shortcut. He entered the numbers in the middle of the previous printout and restarted the model from there. He expected the second run to duplicate the first from that point on.
It was like that at first. The two weather patterns looked almost identical. But after some time they began to separate. Then they completely split. The new simulation produced completely different patterns than the original.
Lorenz initially suspected a computer problem. But the computer wasn’t broken. The difference was in the numbers he entered. Computers internally stored numbers with more decimal places, but printouts showed rounded values.
Numbers like 0.506127 showed up as 0.506 in the printout. Lorenz thought this small difference would not matter. In a typical linear system this is probably not the case. Small input errors result in small output errors.
His accidental discovery, which could be replicated on a computer, was that deterministic systems can be extremely sensitive to initial conditions. The model was not random. It followed a fixed equation. But because the equations were nonlinear, small differences at first could amplify into large differences later.
MIT explains that Lorenz was the first to recognize what it now calls chaotic behavior in mathematical weather models, realizing that small differences in systems such as the atmosphere can have large and unexpected effects.
This was a direct challenge to the long-standing scientific expectation that better measurements and more powerful computers would eventually enable almost unlimited predictions. Lorenz showed that the problem goes deeper.
The limitations were not just poor tools or incomplete data. Some systems have built-in predictability bounds. Forecasts can be improved, but small uncertainties inevitably grow, making accurate long-term forecasts impossible.
Lorenz then took the problem further. Instead of using larger weather models, he studied a very simple system of three equations that represent atmospheric convection, the motion that occurs when warm fluids rise and cold fluids descend. This became the famous Lorentz system.
Three equations yielded surprising results. The system never settled into a stable point. It does not repeat itself in simple cycles. But it didn’t fly into complete chaos either. The path was confined within a specific shape. The shape became known as the Lorentz attractor, the famous butterfly shape associated with chaos theory.
In 1963, Lorenz published his landmark paper “Deterministic Aperiodic Flows”: Journal of Atmospheric Science. The title itself captures the paradox. “Deterministic” means that the system follows precise rules. “Aperiodic” simply means that it does not repeat. Lorenz’s paper showed that simple deterministic systems can produce unstable, irregular, and non-repeating behavior.
In 1971, Lorenz made an announcement titled: “Predictability: Does the flap of a butterfly’s wings in Brazil cause a tornado in Texas?”
This is the origin of the phrase you may be familiar with: the Butterfly Effect.
The butterfly effect is actually at the core of chaos theory.
There are chaotic systems around us. One important thing to understand is that chaotic systems are not random. It may seem random, but the same physical laws apply as everything else.
One of the simplest chaotic systems would be the double pendulum.
The basic pendulum is very simple. It is a weight suspended from a rotating shaft that moves back and forth. It is so simple and so predictable in its behavior that it is used in physics courses and has even been used to measure time.
A double pendulum is a pendulum that has another pendulum at its end. It may seem very simple, but just adding a pendulum to it takes it from one of the most predictable devices to one of the most unpredictable and confusing devices.
There is a great video online that shows how small changes to the initial conditions can change the results of a double pendulum.
If the second pendulum has a different starting position, even by a millionth of a degree, then just a few swings of the main pendulum will cause it to behave completely differently.
Again, it’s not like they’re acting randomly. It is acting according to the laws of physics. It’s just that its behavior is highly dependent on the initial conditions.
Oddly enough, the company Cloudflare uses a camera pointed at a double pendulum wall in its London office as a random number generator. Although not technically random, predicting the behavior of a double pendulum wall is too complex to calculate, especially in real time.
What Edward Lorenz discovered is that the weather is fundamentally chaotic. This is why our ability to predict the weather is limited. Weather forecasts have improved and three-day forecasts are now more or less the same as one-day forecasts from a few years ago, but the weather over the next few weeks is still unpredictable.
One estimate I’ve seen is that if you placed weather stations into space exactly one meter apart across the entire surface of the Earth, and had the computing power to process all the data, you would do your best to predict the weather for 30 days.
Of course, perhaps the greatest example of the butterfly effect is history. History is full of examples of small events that had external effects.
Many people have speculated what would have happened if Adolf Hitler had entered art school. He may never have taken the path that led to the deaths of millions of people. But how could someone in the admissions office of the art school in Vienna know the impact of such a decision?
Henry Tandey was a British soldier in World War I and recipient of the Victoria Cross. Late in the war, he met a German corporal near the front line and saved his life. The corporal’s name was Adolf Hitler.
Alexander Fleming accidentally left a window open, which led to the discovery of penicillin.
Archduke Franz Ferdinand’s driver took a wrong turn in Sarajevo and accidentally stopped near Gavrilo Princip. Princip had missed previous opportunities to assassinate the Archduke, but this fortuitous diversion placed the Archduke right in front of him, allowing Princip to fire the shot that helped spark World War I.
East German official Gunter Schabowski accidentally said the wrong thing on television, causing East Berliners to rush to the Berlin Wall, causing it to fall, ultimately destroying the East German state and beginning the collapse of communism.
My father served in Vietnam and would sometimes tell stories of bullets flying over his head. You probably wouldn’t be hearing me talk about the butterfly effect today if an enemy soldier hadn’t put his gun down in the mud 60 years ago.
Numerous small events occur every day that ultimately shape history, and it is impossible to know the impact of all of them.
What’s interesting is that chaos theory didn’t disprove determinism. That doesn’t mean cause and effect aren’t real. That means it’s a lot more complicated than anyone expected.
