What is the Butterfly Effect? Chaos Theory.

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A butterfly wing flap in Brazil, influences the atmosphere and thus can contribute to a tornado in Texas: This phenomenon is known as the butterfly effect. The term comes from Edward Lorenz, the pioneer of chaos theory.

Edward Norton Lorenz was born in West Hartford, Connecticut, on May 23, 1917. He explained in a book that he was interested in numbers early on. First he went to Dartmouth College, then in 1940 at Harvard University he completed his Masters in Mathematics. During World War II, he worked on weather forecasts for the U.S. Army Air Force. In 1946 he came to the Massachusetts Institute of Technology (MIT) and studied meteorology. There he received his doctorate and a professorship in 1962. He also discovered the butterfly effect while working at MIT.

A small mistake by Lorenz has a big impact

In 1961, Lorenz worked with a – by today’s standards – primitive computer on a simple weather forecast model. He used three variables for the simulation: temperature, air pressure and wind direction. He played through his model and got the first results. But when he calculated the model again, he made a minimal mistake: Instead of performing his calculations with the number 0.56127 as he did the first time, he accidentally omitted the last three digits and used 0.56. This minimal change led to a completely different result.

Small changes can make a big difference

Lorenz found that the smallest variations in a deterministic system – like in a weather model – can later lead to very large differences. This dependency on the initial conditions became known as the so-called butterfly effect. Since then, the metaphor has stood for the fact that relationships are so complex that the smallest deviations can have the greatest effect. His example: global weather, which is unpredictable in the long term. Accordingly, the weather is a so-called chaotic system. Lorenz realized that the phenomenon is based on a relatively simple system of equations. These equations create a pattern of infinite complexity and never lead to the same result. That was the beginning of the chaos theory.

The butterfly effect explained

So, what is actually behind the myth of a butterfly that triggers a tornado in Texas? In principle, an impact chain cannot be traced so often, so it is fiction. The core idea “small cause, big effect”, however, is based on a serious scientific foundation.

The popular expression “butterfly effect” actually describes the sensitivity to change in the initial conditions that occurs in the context of chaos theory. However, the term “chaos” is not intended to mean that correct coincidence (as in the case of radioactive decay) is involved. Because observable effects are based on strictly deterministic processes. The underlying deterministic rules can even be very simple.

The “butterfly” came to Lorenz’s mind when he saw a computer graphic of his calculations. It represents the results of a simple weather model using abstract points and lines. The graphic shows two “wings” that resemble butterfly wings, made up of points in a row. Each point corresponds to the solution of the system of differential equations, which consists of the three variables. The dots describe a chaotic movement on a loop line in three-dimensional space that never meets. Even if you make these calculations of the atmosphere again and again, they are never identical. But they will keep the same butterfly-like shape.

Cube experiment

A simple cube experiment is enough to illustrate this. Throwing a cube follows fixed physical rules:

  1. The throw itself
  2. Impact of the cube on the surface
  3. Rolling on the surface until it stops

Repeating the experiment will not always give the same result. The reason for this is that the player simply cannot repeat the initial conditions of the first throw exactly. Even a minimal change can lead to a completely different result.

In principle, all influencing factors can be precisely described for a cube. This is often not even possible, for example in weather forecast with mainframes. The input data is provided by a network of weather stations and satellite data. This results in a huge amount of data every day.

However, weather can only be rasterized (converted to a vector image) with a certain spatial resolution. Also, the many influencing factors influence each other in a very complex way. As a result, small errors in the measurement data, in conjunction with the rules on which the weather model is based, will grow very strongly in the course of the computer calculation. Thus, long-term weather forecast is not possible.

Kyoto prize in basic sciences

Until 1987, Lorenz was a professor at the Massachusetts Institute of Technology (MIT). In addition to numerous other scientific awards – for example, he received the Crafoord Prize from the Royal Swedish Academy of Sciences in Earth Sciences in 1983. Also, he was admitted to the Academy of Sciences of the former Soviet Union (USSR) in 1988. In 1991 he received the Kyoto Prize in the Basic Sciences division. At the award, his chaos theory was recognized as one of the most dramatic changes in humanity’s view of nature since Sir Isaac Newton. Edward Lorenz died on April 16, 2008 at the age of 90.

Chaos theory and research

Chaos research is a branch of physics and mathematics. It deals with order in dynamic systems. A dynamic system is understood to be the mathematical model of a process, the course of which depends crucially on the initial state and which cannot be predicted in the long term. The weather is such a non-linear, unpredictable process. Another example of chaotic systems is the traffic. It is impossible to know exactly when a traffic jam occurs again at certain points. Another example is the orbits of planets in our solar system and beyond: orbits of planets and moons can’t be endlessly calculated in advance either.

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