The Butterfly Effect

THE BUTTERFLY EFFECT

The butterfly effect is an idea that tiny causes such as a butterfly flapping its wings in Brazil can cause a tornado in Texas. A single act of a butterfly flapping its wings will surely not lead to a storm, but such minor changes in a setup's initial conditions can completely alter the outcome.

This idea stems from a scientific paper written more than fifty years ago, in the 1960s, in a little office in MIT where an American meteorologist Edward Lorenz had created a weather simulator on his computer.

The simulation used countless equations and variables. Through the simulation, Lorenz performed various experiments; his breakthrough came when he wanted to redo a run, but to reduce his effort, he entered the numbers halfway through, hoping to receive the same results.

The new simulation followed the old simulation for a short while but then completely diverged, resulting in a different weather pattern.

Edward's first thought was that the computer had malfunctioned, but the real reason for such a vast difference was that the machines had rounded it to three decimal places while the computer calculated it to six places.

So, a difference of less than one part in a thousand created completely different weather. Lorenz's system displayed sensitive dependence on initial conditions, which has become the hallmark of chaos.

However, this does not mean that these systems are random. If we can input the same conditions, we will get the same results, but the issue is that even the smallest difference in the initial conditions will be amplified to a vastly different final state.

This system is both deterministic and unpredictable because, in actuality, one can never know the exact initial conditions up to infinite decimal places making this a sort of paradox.

Even Lorenz's original model seemed random until they graphed it, and it formed the shape of a butterfly (hence, the name).

This also shows why it is so difficult to predict the weather more than a week in advance.

These chaotic systems have been turning up everywhere. Even our solar system, which we consider the model of all orders, shows chaotic behaviour. This means that some planets would have collided or been thrown out of the system within the next ten to fifteen million years.

The further we try to predict chaotic systems, the harder it becomes, and in some cases, predictions are no better than guesswork.

Chaos puts limits on what we can know about the future. Before chaos theory, it was believed that if we change it a little initially, then there would be little change in the end, but these systems do not behave that way, and we needed new math to understand why.

This theory was ground-breaking as it threw off classical physics. Newton's third law states that every action has an equal and opposite reaction, but now we know this is not always true.

Newton believed that if we understood a few basic rules of the universe, then we can understand the universe too, but even a tiny change in something as huge as the universe will have a drastic change in the end.

We went from grasping a good chunk of our universe to who knows where.

The butterfly effect intrigues people so much because even the tiny, seemingly insignificant decisions we take every day can greatly impact our lives.

In that sense, humanity is also a lot like a chaotic system, and our small acts will someday change the world.