Butterfly Effect Chaos Theory Explained


“Small causes may have larger effects.”

That is the summary of the butterfly effect within the chaos theory. It was a concept that was initially used for meteorological forecasting, but has become a component within the scientific community at-large as well.

The butterfly effect has a dependence on initial conditions and is highly sensitive. If there is a small change to even a single state, then the entire system can experience large differences. It is an idea that dates back to the year 1800 and the publication of The Vocation of Man. In this publication, philosopher Johann Fichte states that one cannot move a single grain of sand without affecting the whole.

That is an excellent summary of what the butterfly effect happens to be.

How Come the Butterfly Is So Often Misinterpreted?

Popular culture looks at the butterfly effect in one of two common ways.

1. That every event which occurs can be explained when the small reasons which caused the event can be located.
2. That if small influences could be located and altered before an event occurs, that event could be changed in some way.

This is exampled by the Ashton Kutcher movie The Butterfly Effect. In the movie, Kutcher’s character discovers an ability to go back through time consciously by reading journal entries or watching videos of past events. By making one small change in the past, large changes in the future occur.

Some changes are for the better, but others are quite negative.

The reason why popular culture looks at the butterfly effect in chaos theory in this manner is because we have a desire to comprehend what happens in the world. We want a clear explanation that makes sense. It is easier to cope with tragic events when we know that something specific happened to cause them.

It is the same reason why so many people attempt to limit the powers of a supernatural deity or create explanations for what happens after someone dies. Wouldn’t a supernatural deity be able to do whatever they wanted to do without limit since their powers are limitless? And do we know for certain that Uncle Joe is going to be giving Aunt Margaret a hug because they’re being reunited in heaven?

The fact is that people struggle with the concept of chaos, so they attempt to create a calm state in the middle of the storm.

What Does the Butterfly Effect Mean for Us Today?

Edward Lorenz is responsible for our modern interpretation of the butterfly effect. In 1961, he was computing forecast models based on a dozen mathematical equations. He had decided to run a sequence of data a second time. Instead of starting over from the beginning, he started in the middle. Once the data was entered, he discovered something unusual.

The second forecast didn’t match the first. It diverged dramatically, even though the data inputs were technically the same.

What happened? The computer Lorenz was using used six decimal points to calculate a long-term forecast. Lorenz had rounded up to the third decimal point to enter in the new figures, based on a print-out he had received.

Even though the differences were only fractional, the changes to the outcome were large and profound.

That means the data we consume every day can be very different over a long period of time than we anticipate. Even in terms of weather, we find the butterfly effect is still in play. When is the last time you saw a thermometer that said it was 75.242564 degrees outside? That temperature would be rounded down to 75 degrees. That is where the butterfly effect kicks in. If the temperature is higher than 75 and rounded down all the time, it could affect numerous items within a community.

Why Is It Called a Butterfly Effect?

In chaos theory, the results of mathematical equations can be unpredictable. The classic example of this is the double-rod pendulum. If one were to start the pendulum from a slightly different condition every time, then the observable result would be a trajectory that was completely different.

Yet even in unpredictability, there is still mathematical harmony. Whenever the chaos theory is instituted, the complete record of possible outcomes or trajectories tends to look like the wings of a butterfly.

A single path may look random and chaotic. When all possible paths are plotted, however, there is a certain symmetry to the movement. That is why there is a certain level of elegance to this theory, even though there is also chaos.

Geoff Boeing, in post-doctorate work at UC-Berkeley, describes chaos theory as a system. Imagine a butterfly flapping its wings in Brazil and that causing a tornado to occur in Texas. The reason why that may happen is because the equations that describe this theory are non-linear. It produces systems that are simple, results that can be completely unpredictable and divergent, yet provide a long-term outcome that falls within a certain range of predictability.

How does this happen? There is a basic equation that is used to produce a logistics map whenever chaos theory and the butterfly effect are being examined. It is this: xt+1 = rxt(1-xt).

Through this equation, the dynamics of the system are defined. X is the population, while T and R are the rate of growth. By adding parameters and recursive iterations, the level of unpredictability grows exponentially.

Yet in an infinite universe, there is a finite number of possibilities. If you shuffle a deck of cards long enough, you’ll find a pattern that repeats itself. The same is true in chaos theory and why the butterfly effect is so important to examine. By discovering where the small repetitions take place, it becomes possible to create better long-term predictions.

Why Is a Predictive Element So Important?

Imagine that you’re trying to create a new invention. Without chaos theory, you’re left with a trial-and-error method of research. Think Thomas Edison and the thousands of times he attempted to create a feasible light bulb. You can still achieve success, but it may take a very long time to reach the end of that journey.

Chaos theory can be used to build predictive models that can chart the trial-and-error process through data analysis. Instead of physically creating a prototype to test, the information can be examined to determine outcomes.

These predictive elements can be applied outside of mathematics and natural sciences as well. The butterfly effect can be used to predict consumer interactions with a new product. It can help people make better decisions regarding their career.

The butterfly effect in chaos theory doesn’t try to define simplicity. It instead shows that there is beauty to be found in what seems to be unpredictable. If given enough time, the chaos will repeat itself, patterns will be found, and that predictability allows us to understand the world in a better way.