The Butterfly Effect

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Does our past affect our present? Will the decisions we make today affect our tomorrow?

The answer to these questions might seem more philosophical than scientific, but it is one of the most widely applicable principles governing our everyday actions that gives some meaning to our collective existence. Many cultures believe that reality that unfolds every moment is nothing more than a  script being played out till the end of time. However, science has something very different to play in this regard.From tiny raindrops thrumming on cobblestones to mighty earthquakes shaking the foundations of soil, everything can be traced back to a starting event, and that is what chaos theory is all about – the never ending chain of cause and effect.

Without going much into the popular debate of fate versus choice, all of us reading this article have lived long enough to experience the inseparable nature of cause and effect, and how a set of initial conditions affect an outcome. We know that touching something hot creates a burning sensation or that the universe we know today perhaps owes its existence to the Big Bang. A very specialized branch of science known as Chaos Theory tries to answer this question in a scientific manner and asserts the existence of patterns in seemingly random and “chaotic” systems.

Long before, humanity was equipped to predict earthquakes and floods, these calamities were considered “acts of god”, things that were beyond our control. But with time, we’ve understood them and ascribed them to some initial events, which in turn must’ve depended on a preceding event. This relation between events and its causes is termed as “causality” and it is non-linear in nature i.e. it consists of feedback loops, repetitions, fractals which will be discussed in a later article in details. A very specific phenomenon of chaos theory that deals with causality is known as “Butterfly Effect”.

UNDERSTANDING CHAOS

“Chaos”, in this context, is a word used to describe the apparently randomness, with no discernible patterns between the sub-events. It is important to understand the relative nature of chaos before delving further into its theory. Chaos, is relative to the observer who is not equipped to predict the next sequence in what could possibly be, a hidden pattern. Also, overly complicated systems whose pattern is known can also be referred to as “chaotic” such as the number pi.

π = 3.1415926535…The decimal places are non-terminating and non-recurring and yet, we have formulas that is capable of determining its value. Thus, its randomness is debatable, much like every other random phenomena.

Consider the following animation:

Double-compound-pendulum
Double-pendulum

The double pendulum in the above image shows what”chaos” really means. The bottom half influences the lower half and the vice versa is also true. Both halves conform to the standard laws of mechanics, yet the pattern it traces is “chaotic” and highly sensitive to the initial position of the needle.

THE BUTTERFLY EFFECT

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The name “Butterfly Effect” had been coined by Edward Lorenz which he derived from the metaphorical example of a butterfly flapping its wings in Brazil that triggers a tornado in Texas several weeks later. In a theoretical model, Lorenz determined the exact details of the time of formation, path taken, the force of flapping necessary to produce such a result. Through this example, Lorentz demonstrated the sensitive dependency of outcomes on its initial conditions. However, in an attempt to replicate it, he had observed that rounding off the starting values even by very small quantities, produced a very different outcome i.e. small changes in initial conditions can cause large changes in outcome. The values had to be much more precise that what was practically possible.

PRACTICAL ERROR MARGIN

An important thing to note, in this context, is the dependency on the maximum allowed error margin  of initial values on the size of the system. Take the example, of the butterfly and tornado, we know that the system in question is large, in the sense, despite isolating them into a smaller sub-system, a practical tornado can further trigger a large chain of events. This system of tornado and butterfly is large.Besides, the same fluttering of wings can simultaneously cause another event. Thus,no event is truly isolated as it is part of the same universe.

Large practical events and its consequence can be visualized as an infinitely complicated branch of a tree that might affect the future of the system due to the absence of “finality” in any state.

In smaller isolated sub-systems, however, initials conditions can be subjected to larger error margins without altering the final outcome. This is due to the finite nature of final states. For e.g. let us consider the scenario of throwing a die. We are isolating the system, in the sense, the outcome of the die wont affect any outcome in the universe. The precise forces and direction required to score a six, lies within a certain ranges . This means that give or take a very small value k in the applied force, it would still turn out to be six.

Due to this implicit tolerance values, such outcomes can be replicated using specially calibrated apparatus leading to a six face in every throw. However, when it comes to the hand-throwing a die, the throw can still be thought of as random.

PRACTICAL RANDOMNESS – A CONSEQUENCE OF BUTTERFLY EFFECT

The butterfly effect helps us understand randomness and inter dependency of events. Randomness is defined as the quality or state of lacking a pattern. Events that cannot be per-determined is thought of as being “random”. This randomness is however, relative. As discussed earlier, the same natural calamities described during the medieval period as “acts of god” , can be predicted today, with the use of ordinary science. What was random earlier, isn’t so random at a current date. Thus, randomness is subjective and is only relative to the ability to determine the underlying pattern of everything.

The six outcomes of throwing a die is a function of the forces and direction of a throw. The average human brain cannot go through such precise calculations in every turn and thus the outcomes can be thought of as “random”. The same throw, if done through a special machine would be governed by a set of mathematical equation robbing the event of its “randomness”. Another example would be a “practical random number generator” would be taking the Milli-second stamp of a time signature at any given moment.Unless, specified, it is difficulty to determine the underlying pattern of such time-sensitive random generators. Thus, even a linear progressing time stamp generator can function as a random number generator.

WORKS OF FICTION

Several science fictions films is based on the butterfly effect, causality and concepts related to it.

butterfly-effect-the-the-butterfly-effect-movie-poster-1

In 2004, the film “The Butterfly Effect”  starring Ashton Kutcher and Amy Smart, accurately portrayed the phenomena through a well-made plot line and the ripple effect of our past on our present and the present on our future. Other films based on causality and time-travel are Deja Vu(2006), Looper(2012) and Predestination(2014), just to name a few.

To conclude, the implications of chaos theory in general and the butterfly effect in specific, extend way beyond science. It can be concluded that every outcome we face, can be traced back to some previous action, and that everything is a choice.

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