The Butterfly Effect- The Power Of Small Changes

Updated: Oct 14, 2020

“You could not remove a single grain of sand from its place without thereby … changing something throughout all parts of the immeasurable whole.”

This quote was found in the book, “The Vocation of Man”, which was by Johann Gottlieb Fichte. This quote symbolizes a phenomenon that many of us might have heard before in our lives. It is called, “The Butterfly Effect”.

What this “Butterfly Effect” is, is basically (by definition in the chaos theory) the sensitive dependence on initial conditions in which a small change in one state of deterministic and nonlinear system can result in large difference in a later state.

What most of us are familiar with regarding this phenomenon is that “small changes will have a massive impact”, which is totally untrue.

The real understanding of this phenomenon is the fact that small changes in a state that has totally no randomness involved, which means that an output produced will always be the same from an initial condition and has an unproportionate ratio of input and output of the system, will lead to a large difference in a later state.

This means that the small changes will act as a catalyst in the initial conditions, which has the potential to snowball into a completely different direction when it reaches a much later state, which does not mean that the small changes has a direct effect on how big the subsequent impact will be.

This phenomenon was derived from the work of Edward Lorenz, a meteorologist. A simplified version of what happened was that Edward Lorenz was computing a weather prediction in 1961, which he stopped the computer and typed in a line of numbers before setting it running again and went for a coffee break.

After an hour or so, he returned to his desk and the computer has already simulated about two months’ worth of weather predictions. However, he found out that the results of the latter computations were completely different from the initial results before he went for his coffee break.

Determined to find out what went wrong, he decided to take matters into his own hands first before calling for a servicing on the computer as it would help speed up the process of figuring out the anomaly.

He realized that instead of the actual full precision of the numbers, he keyed in a rounded-off value of the values in the initial conditions. This led to cause the amplifying of the results as the computer went on processing, which made a massive difference between the actual results of the computation compared to what was actually produced.

Hence, he metaphorized this with the example of how the “minor perturbations like a butterfly flapping its wings”, could result in aiding the production of a catastrophe like “a tornado”.

This phenomenon is very relatable in our everyday lives. A careless mistake in an examination could end up being a grade difference in your results, which could cause you the opportunity to make it to your dream course, or a miscalculation in the projected earnings of your company could cause you to lose your job, or worse, the collapse of your company.