February 26, 2025

Nafeesa Choudhury 

11th Grade

The Young Women's Leadership School of Queens 

Have you ever wondered about the power of small actions and how they can contribute to unforeseen outcomes that make you question and think about life from a deeper perspective? Relatively often, small actions are disregarded, not seen as that important, since they don’t seem to cause any significant changes. However, the butterfly effect would have to disagree with that statement. It is a part of a theory in mathematics called the chaos theory that emphasizes the power of small actions and how they can lead to huge outcomes. A well-known example of this theory is how the flapping of a butterfly’s wings can metaphorically cause a huge storm or a tornado. The idea introduced by Edward Lorenz, an American meteorologist, can help in explaining how our daily lives and even the world can be affected just by a tiny action! 

It all started when Edward Lorenz, a meteorology professor at MIT (Massachusetts Institute of Technology), was running tests on a computer model specifically designed to predict weather patterns. Lorenz had just changed a value by simply rounding it to 0.506 from 0.506127 in one of the simulations he had previously run over, and it drastically changed the results of the previous weather patterns. He later went on to publish a research article in 1963 called “Deterministic Nonperiodic Flow”, where he described and explained more about his findings. The article addressed how there are systems of equations designed to show the flow of fluid, which loses its energy over time, and “Phase space” represents the paths for the solutions to these systems of equations mentioned before. Phase space shows a system’s possible positions by graphing its variables such as speed or position, etc., and each point graphed shows the system’s situation at specific points in time, so if you were to look at the entire phase space, you could record the movement of the system over time. For solutions that have certain limits, small changes, in the beginning, can cause the outcomes to be different; therefore, the systems prove the significance of how small changes can lead to massive changes, or in other words, the chaos theory in mathematics. However, to prove that chaos doesn’t necessarily mean randomness, Lorenz used equations to show the motion of gas. When the results were graphed, it showed a pair of connected oval-like shapes that resembled the wings of a butterfly, that unique shape formed was called the “Lorenz attractor” to explain that even systems that are chaotic can follow patterns and behave with certain limits. 

As well as in 1972, at a conference for the American Association for the Advancement of Science, Lorenz included a larger audience to understand his idea of the “butterfly effect” by giving a talk with the title, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”,  a title given by meteorologist Philip Merilees,  where the slight change in the starting conditions of a system was represented by wings of the butterfly which can eventually lead to a considerable outcome, the tornado. The butterfly effect, which can also be shortly explained as "sensitive dependence on initial conditions," concludes the difficulty of predicting future outcomes. However, Lorenz’s ideas defy the scientific ideas introduced by Isaac Newton (laws of motion) and  Pierre-Simon Laplace (Laplace's Demon), where they believed by knowing the precise location and speed of the universe’s every particle, you could predict future outcomes, but the chaos theory and butterfly effect states how a certain initial small action can change the end result. 

But it sounds like a theory for science and math, could it actually be a factor in shaping our daily lives? Although it is a scientific and mathematical theory on outcomes and how small actions can influence them, it can have an impact on our daily lives more than we can ever imagine. It can affect our personal decisions, such as striking up a conversation with someone you have never met before or simply choosing a different route to go home or work. Perhaps that new person you got acquainted with changed your life in ways you never would’ve imagined, or how that different route saved so much of your time you got to work on time or went home earlier than it usually takes. The same thing applies to psychology or human behavior, an inevitable small change in environment or mood can impact your actions, the decisions you make in life, relationships, and so much more. Business is another excellent example as a tiny change in your marketing strategy or consumer behavior can lead to large outcomes, more or less profit or inflation in the economy, etc. It could be a sudden tweet that explodes into a heated argument or could inform people about an event they did not know was occurring. These examples prove how significant small actions can be. 

“Life is full of surprises”...The butterfly effect proves how tiny actions can spark such unpredictable outcomes. Whether it's human behavior, weather patterns, math equations, or business, our lives are quietly impacted by these small changes, of which we aren’t really aware most of the time. Through this theory, you should know never to underestimate the power of small actions, all it takes is a tiny action, and everything may change…