A simple guide to chaos theory - BBC World Service

0:00 Imagine, the year is 1905. One day, the clock on the tower in Berne, Switzerland, is a little late. Two minutes late, to be more precise. For that reason, a man who lives near the tower does not wake up at the same time that he usually wakes up to go to work. Realising the mistake, he becomes a little nervous. It takes him a little longer to get dressed, drink some coffee and leave the house. He leaves five minutes later than usual. He is about to cross the street. Meanwhile, a banker gets into his new car without knowing that it has a problem with the brakes. Our man crosses the street and doesn't see the car. The man is run over and dies. This man is no less than Albert Einstein.

0:45 That year Einstein should have published four works that would become the basis of modern physics. Innovations like GPS, TV screens, the semiconductors that allowed us to create laptops, never happen. The computer, the laptop, the mobile you are watching this video on never come into existence. And this video... doesn't exist either. This sequence of events is an example of what is known as the butterfly effect, a manifestation of Chaos Theory. For many centuries, the world was explained through the laws of Isaac Newton and classical physics. According to these laws, if the current state of an object is known, its future behaviour can be predicted with relative ease.

1:31 Chaos Theory questions this deterministic vision: not everything is predictable anymore, nor does it work like clockwork. Since the 1800s, mathematicians have raised the idea that not all phenomena could be predicted by Newtonian laws. But a meteorologist named Edward Lorenz made chaos theory a visible phenomenon. It all started in 1961 when he was working on a mathematical model to forecast the weather. Lorenz entered data such as temperature, humidity, pressure, and wind direction into his computer. His computer would draw a graph modelling what the weather would be like, not always accurate, but very close to reality. One morning, Lorenz decided to verify some results.

2:16 He stopped the computer, to save time, entered the numbers himself, and went to grab a coffee. When he returned, the chart was incredibly different from the original. At the beginning it started out pretty similar, but in the middle it presented a completely different trajectory. Surprised, he checked the numbers. He found that the number he had entered was three tenths less than the number used by the computer. That difference, which altered the trajectory so much, is equivalent to a particle of dust on the Eiffel Tower, or one less feather in the weight of a duck. Lorenz deduced that this experiment was not a special case, that there were other systems in which tiny differences produced, over time, monumental changes,

3:02 making everything seem unpredictable... that the flapping of a butterfly in Brazil could, in theory, cause enough of a disturbance to spark a tornado in Texas. Even though we have a good idea of how the universe works, there are no measurements that allow us to determine the exact position and speed of every atom in the universe. And this "inaccuracy" in our calculations makes predictions difficult, one of the reasons why long-term prediction is impossible. But chaos is not the same as disorder. Although chaos makes predictions difficult, the universe is not random and effects still follow causes. And no matter how chaotic it may seem, a system always follows a trajectory towards a certain point.

3:49 For example, in the calculations Lorenz used for his model, the trajectory created a pattern that resembled the wings of a butterfly. Understanding these patterns of chaos has practical applications. In the stock market it reminds us that a slight fluctuation can cause a crisis in the market - and that is why we cannot speak of predictions but of probabilities. In the human body, it allows us to understand the chaotic behaviour of a heart with cardiac arrhythmia. Even in human behaviour, the butterfly effect can be used to analyse social phenomena. For example, how trolling on social networks can be triggered by a single negative comment. Our universe continues to obey the laws of cause and effect.

4:35 The sun will continue to rise every morning. The planes we build will keep flying. Ultimately, chaos theory introduces an element of uncertainty into our reading of the Universe. It reveals the limit of our knowledge.