BUTTERFLY EFFECT BY NADIM CHOWDHURY
What is Butterfly Effect?
The "Butterfly Effect" is the propensity of a system to be sensitive to initial conditions. Such systems over time become unpredictable, this idea gave rise to the notion of a butterfly flapping it's wings in one area of the world, causing a tornado or some such weather event to occur in another remote area of the world. It is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. So this is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position
The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. Of course the butterfly cannot literally cause a tornado. The kinetic energy in a tornado is enormously larger than the energy in the turbulence of a butterfly. The kinetic energy of a tornado is ultimately provided by the sun and the butterfly can only influence certain details of weather events in a chaotic manner.
Who devised the idea?
1960, E Lorenz was doing weather prediction research at MIT. He managed to get funding to acquire a Royal McBee LGP-30 computer with 16 KB of memory that could do 60 multiplications per second. Lorenz set the new computer to solve a system of 12 differential equations that model a miniature atmosphere. To speed up the output, Lorenz altered the program to print only three significant digits of the solution trajectories, although the calculations themselves were carried out with a somewhat higher precision After seeing a particularly interesting run, he decided to repeat the calculation. As a shortcut on a number in the sequence, he entered the decimal .506 instead of entering the full .506127 the computer would hold and started the program. Lorenz went for a coffee break, and when he returned, he found that the results we completely different. At first he thought that some vacuum tubes in the computer were not working. Upon careful check, he realised that the discrepancies between the original and re-started calculations occurred gradually: First in the least significant decimal place and then eventually in the next, and so on
From the above mentioned event what Lorenz has discovered is that tiny differences in the starting conditions can have big effects on later on.
Why it is called Butterfly effect?
• Lorenz coined the phrase "butterfly effect" describing how a slight change in initial conditions can lead to drastically different outcomes. "The flap of a butterfly's wings in South America could be responsible for a tornado in Texas."
• He chose a butterfly because a three dimensional image of the trajectory mapped out by his equations looks like a butterfly.
Misconception
When the initial conditions change a bit, "does the flap of a butterfly's wings in Brazil set off a Tornado in Texas?"( Edward Lorenz Dec 1972, Talk given in Washington DC).There is a common misconception as with regards to the words "set off" (or cause in other formulations of the same idea). You cannot call uncle Eddie in Brazil and ask him to let his pet-butterflies flap their wings so that they cause a rain storm in Dhaka to soak your boy/girl-friend whom you are angry at. What is means is that you have to imagine two identical worlds. In one of the worlds you place a butterfly and let it flap its wings. In the other world you don't place the butterfly. Now you wait a while (a few months or more perhaps) and will see that the global weather patterns on your two worlds are completely different.
The butterfly effect refers to the exponential growth of any small perturbation. However, this exponential growth continues only so long as the disturbance remains very small compared to the size of the attractor. It then folds back onto the attractor. Unfortunately, most people miss this latter part and think that the small perturbation continues to grow until it is huge and has some large effect. The point of the effect is that it prevents us from making very detailed predictions at very small scales, but it does not have a significant effect at larger scales.
Butterfly Effect in popular culture
Even though the Butterfly Effect has not been widely known by the general public until recently because of the motion picture "The Butterfly Effect", and it didn't even have a name until Lorenz published his article in 1963, it was an idea that had been floating around for several decades. Many science fiction writers in the Golden Age of Science Fiction (1930's to 1950's) wrote time travel stories that utilized a plot device very similar to a Butterfly Effect. Those stories often portrayed people traveling back in time and causing some very minor, insignificant change in the past that in turn causes a massive alteration in the flow of history so that when those people returned to the present the world was nothing like it was when they left.
To state it simply the Butterfly Effect describes a cause and effect scenario where the cause is very small and the effect is very large. On a trivial note regarding Butterfly Effect science fiction involving time travel, Ray Bradbury (one of the great writers of the Golden Age of Science Fiction) in 1952 published a short story where time traveling hunters would go back in time to hunt dinosaurs. In the story one of the hunters kills a creature that is not supposed to die and a Butterfly Effect causes history to be changed when the time travelers return to the present. Ironically, the creature accidentally killed is a butterfly.
Some real life examples of this effect
1) Lorenz discovered how weather models, computer simulations, were sensitive to initial conditions. An extremely small change in one parameter often results in a model going in a very different direction from the previous run. This is why the IPCC does not use computer models to make predictions about climate change, and offers instead scenarios that illustrate possibilities
2) Some scientists believe the butterfly effect also exists in the atmosphere, although they can't prove it. Two climate blogs have been debating this: Real Climate and Climate Science.
3) Belgian mathematician hopes to use the butterfly effect and strange attractors to help build a complete model of climate and resources that will lead to a new approach to sustainable development. Jacques Nihoul of the department of Model Environment at the University of Liège, in Belgium, writing in the inaugural issue of the International Journal of Computing Science and Mathematics published by Inderscience, explains how a new approach to sustainable development and climate change could emerge from his research.
4) . The stock market: slight fluctuations in one market can affect many others.
5) Biology: A small change in a virus in monkeys in Africa creates a" thunderstorm" of an effect on the human population around the world with the appearance of the AIDs virus.
6) Evolution: small changes in the chemistry of the early Earth gives rise to life.
7) Psychology: Thought patterns and consciousness altered by small changes in brain chemistry or small changes in physical environmental stimuli.
When it comes into consideration
The butterfly effect occurs under two conditions:
1. The system is nonlinear.
2. Each state of the system is determined by the previous state. In other words, the output at each moment is repeatedly entered back into the system for another cycle through the mathematical functions that determine the system."
