← Everything Everywhere Daily: History, Science, Geography & More
Everything Everywhere Daily: History, Science, Geography & More
Chaos Theory and the Butterfly Effect
00:14:53
Loading summary
Transcript1 lines
- [00:00]
A
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. This episode is sponsored by Newspapers.com as a history buff, you know that while textbooks record the dates of our nation's conflicts, they often lose the voices of the individuals who this Memorial Day, as we honor those who made the ultimate sacrifice, Newspapers.com invites you to go beyond the monument and discover the personal stories of the people we remember. Think of it as a bridge to the past, giving you access to over a billion pages of primary source history. This is your chance to move past the generalities of war and find the specific local heartbeat of that era. Newspapers.com provides a vibrant, unfiltered view of the past, letting you see the nuance, the sacrifice, and the everyday lives that shape the world that we live in today. It's more than an archive, it's a way to ensure these stories are never forgotten. This Memorial Day, give a voice to the names in your family tree. Visit newspapers.com today and use promo code everything everywhere at checkout for 20% off your subscription. Newspapers.com honor the past by uncovering its stories. This episode is sponsored by Quince. I recently moved into a new, larger place and I faced the challenge of decorating it. I of course am turning to Quince to help get the job done. In addition to clothes, Quince offers stylish home furnishings that makes my place look great at affordable prices. And I've also recently picked up a second cashmere sweater that I've talked about before just because I like it so much. The great thing about Quince is that their prices are 50 to 60% lower than those of similar brands. How Quint's works directly with ethical factories and cuts out the middleman so you're paying for quality, not brand markup. Everything is designed to last and makes getting dressed and decorating your home easy. Refresh your everyday with luxury you'll actually use. Head to quints.com daily for free shipping on your order and 365 day returns now available in Canada too. That's Q U I-n c-e.com daily for free shipping and 365 day returns. Quince.com daily. Chaos theory is technically 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. The 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 the more tempting it became to think that the whole universe might be predictable, at least 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 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, the thought experiment is often conducted under the assumption of a near infinite computer instead of a demon. 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. And 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 works really well. However. Cracks started to appear in the late 19th century. The French mathematician Henri Poincaret was studying the three body problem, which asks how three massive objects, such as the Sun, Moon and Earth, move under each other's gravity. Newtonian mechanics worked beautifully for two bodies, but adding a third body made the problem vastly more complicated. Poincare 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 Poincare didn't know was that his discovery, or the 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 the 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 very if the atmosphere obeys physical laws and computer 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 wasn't a full weather model by normal 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 a part of the simulation. But instead of starting from the beginning, he took a shortcut. He entered numbers from the middle of an earlier printout and restarted the model from there. He expected the second run to duplicate the first run from that point forward. And at first it did. The two weather patterns looked nearly identical. But after a while they began to separate and then they diverged completely. The new simulation produced a completely different weather pattern from the original. Lorenz first suspected a computer problem. But the computer wasn't broken. The difference was in the numbers that 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 wouldn't matter in ordinary linear systems. It probably wouldn't have a tiny input error would produce a tiny output error. His accidental discovery, which could be replicated on the 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 can't make exact long term predictions possible if tiny uncertainties inevitably grow. Lorenz then stripped the problem down even 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 also didn't 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 Non Periodic Flow in the Journal of Atmospheric Sciences. The title itself captures the paradox. Deterministic means that the system follows exact rules. Non periodic meant that it didn't simply repeat. Lorenz's paper showed that a simple deterministic system could produce unstable, irregular, non repeating behavior. In 1971, Lorenz gave a presentation titled does the flap of a butterfly's wing in Brazil set off a tornado in Texas? This was the origin of the phrase that you might be familiar, the butterfly effect. And 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're subject to the same physical laws as everything else. One of the simplest chaotic systems, if that even is a thing, would be a double pendulum. A basic pendulum is very simple. It's a weight suspended from a pivot point that moves back and forth. It's so simple and its behavior is so predictable that it's 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. Seems very simple, and it kinda is. 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 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. And again, it isn't behaving randomly, it's 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 RAND generator. While it technically isn't 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 a three day forecast today is about as good as a one day forecast was several years ago. But we still can't predict the weather weeks ahead. One estimate I've seen is that if you put weather monitoring stations exactly 1 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 outsized 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 of people. Yet how could someone at an art school admissions office in Vienna possibly have known the impact of such a decision? Henry Tandey was a British soldier in World War I 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 a window open and it led to the discovery of penicillin. Archduke Franz Ferdinand's driver took a wrong turn in Sarajevo and just happened to stop near Gavrilo. Principal 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 talking about the butterfly effect. There are countless small events that occur every day in everyone's life that ultimately shape history, and it's impossible to know what the repercussions of every one will be. 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's far, far more complicated than anyone ever expected. The executive producer of Everything Everywhere Daily is Charles Daniel. The associate producers are Austin Otkin and Cameron Kiefer. My big thanks go to everyone who supports the show over on Patreon. Your support helps make this podcast possible, and I also want to remind everyone about the community groups on Facebook and Discord. That's where everything happens that's outside the podcast, and links to those are available in the show notes. As always, if you leave a review on any major podcast app or in the above community groups, you too can have it read on the show.