Butterflies effect : The Chaos Theory

The Butterfly Effect: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle. Who knows what the long-term effects of teaching millions of kids about chaos and fractals will be?

In a technical sense, no. But it’s a good way of explaining how chaotic the current atmosphere is. The “butterfly effect” is a simple idea that explains how chaos theory works: Suppose that, in Brazil, a butterfly flaps its. As it flaps its wings, it shifts tiny amounts of air near it, causing a domino effect that eventually leads to tornadoes popping up in Texas. Problem is, in real life, the butterfly’s wings don’t move much air, and so any movements of air caused by a butterfly suddenly die down. The conditions that spawn changes in weather patterns are far more dramatic than a butterfly’s wings.

But it’s a great model to use: It explains why weather patterns are hard to predict. After all, it’s practically impossible to calculate every minute detail in the environment, which would be what we need to make a truly accurate forecast. It’s difficult to model all of those details, and so it’s hard to make a forecast that does not have a chance of being wrong. That’s why it’s difficult to give an accurate forecast for more than a few days (although I think we will provide better forecasting in the future).

It is a thought example born from another theory. Everything is an effect of a cause, and every cause is an effect of another cause. Meaning; our dynamic world is unfathomably complex. Change one cause, and in a long line of causes, the effect may be exponentially enormous. The logic is sound and scientifically correct. In a sense, we are all connected to previous causes and effects. Take the thought even further, and a butterfly in France may have a say in how a hurricane in Texas unfolds.

The butterfly effect is an idea born from Chaos Theory - which concerns dynamic systems and how their seemingly random and irregular qualities are in actuality governed by deterministic complex mechanics. Thusly, very sensitive to any change in initial conditions, like that flapping wings from a butterfly. Interestingly, the core of Chaos Theory says there is no chaos as it is commonly understood, only the appearance of chaos/randomness.

We had been hostel roommates while doing our masters. Before we knew it, we became the closest of friends. While we went our separate ways after masters, he moving to the US for his PhD and I moving to home in Mumbai for the same, we managed to keep in touch and I was one of the first to know about the big news (straight from his mouth, too). I remember feeling absolutely overwhelmed. I don’t think I’ve had a reaction like that to anything in a while. I was determined to attend the wedding. Even if it meant cancelling on conference trips. In my mind, I had already decided I wasn’t going to miss this for the world.

Now, I don’t remember his case, but when I’d been shortlisted for admission, I was required to list my preference for the ones I wanted to attend and I had put my ranking in the test about turned out to be too low to allow me admission to my first two preferences and I ended up moving to New Delhi. Had I not put Delhi as my #3 reference, I’d have gone to a different place, a different institute and I’d probably have never met him. Even if we did manage to have a chance encounter, we’d never have had the opportunity to bond with each other. I’d have never felt the warmth of his friendship.

I’d have never felt the rapture I did on coming to know he’s getting hitched. I’d have never attended the wedding. All because of a choice I made and put down on a sheet of paper. This is just one of the many, I suppose. Every choice we make end up shaping our lives in a unique manner. If we were to even slightly alter any one of those choices, we’d, in all possibility, end up with a completely different life with different social circles and friends. This happens all the time. In everyone’s life. There is a butterfly effect for everyone.

Welcome to the fascinating world of chaotic systems! The butterfly effect is when small changes in the initial conditions can lead to large changes in the end results. At first you might think that this is due to pure randomness - i.e. things happening without any underlying reason or formula. However, the really interesting thing is that even when the formulas are perfectly known, you can still see chaotic behaviour. Without Chaos

First let’s look at some non-chaotic behaviour. If I drop a ball, how long will it take to hit the ground? The answer is : t=2hg−−−√  where:

t = time (seconds)

h = height (metres)

g = acceleration due to gravity (metres per second per second) = 9.81 on the surface of the Earth.

So let’s say you drop a ball from a height of 10 metres. It will take 1.428 seconds to hit the ground. But let’s say you weren’t holding the ball quite right, and you actually dropped it from a height of 10.01 metres. What difference will it make? The ball will now take 1.429 seconds to drop. So a slight change in the initial conditions will only lead to a slight change in the end result. It’s non-chaotic. Close enough is good enough.