Matt Mauzy, Chaos Theory

       “Chaos theory, in mechanics and mathematics, the study of apparently random or unpredictable behaviors in systems governed by deterministic laws.” (Britannica, 2018) I know what you are thinking, that sounds like my everyday life. One reason that the world is so unpredictable because it is just so complicated and there are just too many variables to keep track of. What if I told you, what you wear next Saturday could change the world as we know it. This is one of the ideas of Chaos Theory, one popular example and most well-known is called the ‘butterfly effect’ where a butterfly can flap its wings and change the weather halfway across the globe. Even with all the randomness around Chaos Theory states that there are underlying patterns, constant feedback loops, repetition, fractals and a sensitive dependence on initial conditions.

Lorenz System
“The Lorenz system (pictured above) is a system of ordinary differential equations first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.” (“Lorenz System”)

       Chaotic behavior can be seen in many natural systems around us, like weather and climate. Ever wonder why a weatherman tells you it will be sunny, yet it rains anyway? The reason is that weathermen give their predictions on statistics using computer models and observations. Even with the most advanced super computer, we would not be able to tell the weather 100% accurately. There are just too many variables that shape the weather around us. “While compared to decades ago, forecasts are so much better, they’re far from flawless.” (Halpern, 2018) Even with all the advances in technology we can use deterministic chaos to show that it will never give a perfectly accurate forecast all the time.

       Chaos Theory is a very interesting topic and one that I have wanted to write about for a while now. The most interesting thing is that these systems are predictable for a while and then something happens, and they appear to be random. There is an amount of time that the behavior of chaotic systems can be effectively predicted. This prediction is based on three things, which are how much uncertainty can be tolerated in the forecast, time scale on the dynamics of the system, and how accurately its current state can be measured. Then when these meaningful predictions cannot be made the certain systems appear random. So, with all this said, Chaos Theory shows that small changes can have a huge impact, such as a small change in the atmosphere can have a drastic change in the weather. So maybe we should watch how we act and react to those around us because small act of kindness can be multiplied when released into the world and we see this all the time. Thank you for taking the time to read this and I hope you got something from my ramblings.

References
The Editors of Encyclopedia Britannica (November 21, 2018) Chaos Theory. Retrieved from https://www.britannica.com/science/chaos-theory

Halpern, Paul (February 13th, 2018) Chaos Theory, The Butterfly Effect, and the Computer Glitch that Started it all. Retrieved from https://www.forbes.com/sites/startswithabang/2018/02/13/chaos-theory-the-butterfly-effect-and-the-computer-glitch-that-started-it-all/#32ffeb9969f6 “Lorenz System” Wikipedia: The Free Encyclopedia. Retrieved 18 December 2018 from https://en.wikipedia.org/wiki/Lorenz_system

Image Found Here:
https://en.wikipedia.org/wiki/Chaos_theory

Written on December 18, 2018