Written by Samruddhi Kashikar
It’s winter break and the cold weather has given you the perfect respite from work. This time, instead of snuggling up in your bed with a book and a steaming cup of coffee, you’ve planned an elaborate trip outside the country. The trip comes as a well deserved one after a whole year of very diligent and industrious work.
You’re the perfect tourist with a camera hanging around your neck, a map in your hand, and exploring the streets on foot to captivate the true essence of the country until you make one bad decision. The decision in its true form is seemingly harmless, all you decide to do is go to a busy and rustic, local marketplace before leaving for home.
“What could go wrong?”
And yet, two weeks later your doctor back home tells you that you have an unidentified, terminal disease. This eventually spreads from you to your family, your locality, and soon the entire country.
Now, the question arises how can such a trivial decision to go to a market, something that could just as easily be avoided, in one country turn into a colossal health hazard in another?
This phenomenon is known as the Butterfly Effect.
What is the Butterfly Effect?
To answer this question, let’s start with an even simpler question. Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? If you’re logically approaching this question, you know the answer has to be ‘Oh, hell no.’
The butterfly effect is a phenomenon where a small change in initial conditions can lead to vastly different results. In this case, the inconsequential flapping of a butterfly’s wings in Brazil can indeed make the weather go rampant in Texas.
Although it is impossible to accurately provide an explanation for this, the general way in which it can be thought about is that the flapping of the wings acts as a trigger that sets off a chain of events in a complex structure.
Say the butterfly flapped its wings in Brazil then this leads to a change, albeit a very minute one, in the fluid flow pattern of the wind. This small change increases exponentially by the time the currents reach Texas and what was supposed to be a gentle breeze could potentially turn into a raging tornado.
The same can be envisioned by assuming that there are two planets, the same in every way except for the fact that one of them has an extra butterfly. Now, the planet with the extra butterfly is more probable to be a home for the tornado than its counterpart.
The Discovery
It all began in 1961 when a meteorologist named Edward Lorenz was crunching some numbers on his computer to predict the weather. He decided to rerun the computer program halfway through the first trial and went to get coffee while the computer ran its simulation. What was expected was the same result as when the program ran for the first time, instead what he found was that the simulation had taken a completely different turn. It predicted weather that was nothing like the first time.
So, what went wrong?
Lorenz realized that the second time around he had fed the numbers to the computer by rounding off to three decimal places whereas the first time it was up to six decimal places. That small error of one over the thousandth decimal place had steadily grown over time and led to a diametrically opposite prediction for the same initial conditions.
This minor error which increased exponentially led to the discovery of deterministic chaos and the fundamental theory off of which the butterfly effect is based, called the Chaos Theory.
Chaos Theory
“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” — Albert Einstein
While our worldview is based on the more orthodox, and deterministic phenomena like gravity, electromagnetism, structural science, and so on, chaos theory deals with the more unpredictable things like weather, stock markets, etc.
Chaos theory has been developed from the recognition that apparently simple physical systems which obey deterministic laws may, nevertheless, behave unpredictably because of their dependence on initial conditions.
A science fiction short story called ‘A Sound of Thunder’ explains this dependence in a rather simple way. When the protagonist of the story ends up killing an irrelevant butterfly in the past, things take a turn for the worse, much into the future.
Although chaos theory essentially talks about unpredictability and uncertainty, the things that look indeterministic aren’t actually indeterministic at all, in that they must remain between the fixed boundary values and cannot exceed the set minimum and maximum values. However, the trajectory inside these fixed boundaries remains just as unpredictable. A great example of this is the double pendulum.
The double pendulum behaves like a single pendulum when released from a small initial angle and its trajectory can be predicted, whereas when released from a large initial angle it becomes extremely sensitive to initial conditions, hence producing chaotic behavior and the trajectory cannot be predicted. However, it cannot exceed the predetermined boundary conditions.
In this animation, the path that it takes can never be re-established. Considering, you release the pendulum from the same initial angle, with the same initial force every single time, it will still end up giving you vastly different trajectories. This happens because no matter how much ever you control the initial conditions you can never account for all the forces that are acting on it up to infinite decimal places. It might start off by taking the same path but in due course, it’ll start diverging wholly.
Significance in Everyday Life
We see chaos theory and the butterfly effect at work around us every day. The simplest form of chaos theory can be seen when you throw a ball. Regardless of how accurate and precise your angle or your skill is, small things like the direction and speed of the wind, specks of dirt on the ball, all play a very important role in determining where it finally lands.
Same is the case when you break the set of coins in a game of carrom. All the coins almost always land in different places even if you strike from the same position every time. This is due to the sensitive dependence on initial conditions.
NASA used this sensitive dependence to successfully steer a space probe towards a comet. It became the first-ever satellite to collect data from a comet. The ISEE-3 satellite was launched to monitor solar activity. This satellite was extremely sensitive to small changes and therefore was capable of reaching anywhere in the orbit with little to no effort. In spite of having very little fuel on board, it was able to reach its destination very easily by making use of chaos theory.
Not only macro systems like satellites but systems even within our own body can be explained with chaos theory. The neurons in our body have a chaotic trajectory. The firing of neurons starts as a simple deterministic pattern which later goes on to be extremely chaotic and unpredictable, all this for the generation of a simple thought.
Now, let’s go back to the very thing that led to the discovery of chaos theory, weather prediction. We can say confidently that the next lunar eclipse will occur on 30th November 2020, yet we cannot predict the weather on 30th November 2020 with the same accuracy. This is because the movement of the planets is based on Newtonian determinism whereas the weather pattern can change based on the flap of a butterfly’s wings. In fact, even the movement of the galaxies will form a chaotic system if you venture too much into the future.
If we were to account for the flapping of every butterfly’s wings on this planet, then maybe our prediction would be more accurate. Until then, though, we have to take the word of our local weatherman and be prepared for rain on a sunny day.
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