What is chaos theory?
Chaos theory is the mathematical study behind dynamical systems – trying to explain observations of chaos, disorder and irregularities with hidden patterns and laws (whereupon these governing laws are incredibly sensitive to a change in the initial conditions).
Think of the butterfly effect as a prime example of chaos theory – according to chaos theory, the butterfly effect is due a small change of the initial conditions of a system (a butterfly flapping it’s wings) which results in a large overall change of a system (a hurricane appears in China a month later).
Because of the sensitivity of the initial conditions, long-term predictions of these systems is rendered impossible. Even in deterministic systems (a system with no randomness involved), long-term predictions are still rendered impossible (this is referred to as deterministic or simple chaos).
Figure 1 (shown below) - the butterfly effect.
The origin of chaos theory:
The first considerable leap in chaos theory was made by Edward Lorenz in 1960 – he is considered to be the “father of chaos theory”.
In 1961, Lorenz tried recreating a computer programme that he made back in 1960, the programme would predict a possible model for future weather occurrences. However, unlike the first time, he decided to start in the middle of the sequence and input simplified data (the data was rounded to three digits rather than the original six digit value back from 1960) and leave it to run. This lead the programme to evolve differently when compared to the original pattern. By inputting simplified data, Lorenz had changed the initial conditions of the system, and though this change was minute (only three decimal places), Lorenz was left with a pattern that didn’t even closely resemble the original. After Lorenz realised it’s impossible to accurately predict the weather, he went on to discover and refine what is now known as chaos theory.
He then proceeded to take the equations for convection and stripped them down to their simplest, most fundamental state, leaving him with three equations which showed that the system had nothing to do with convection but rather the dependence placed on the sensitive initial conditions. These equations actually managed to accurately model a water wheel, a system which gave rise to entirely random behaviour.
In the end, Lorenz could only publish his work in a meteorological journal considering he was a meteorologist, not a mathematician. Recognition was only given to his revolutionary discoveries after he had been discovered by someone else.
Applications of chaos theory:
Chaotic behaviours exist in many naturally occurring systems and has been used to explain and comprehend irregular observations such as lightning, blood vessels, stars and clouds. Chaos theory has also helped bring clarity to turbulence and fluid flow. Not only can chaotic behaviour be observed in naturally occurring systems, but also in artificial systems such as road traffic and the stick market.
Not only can chaotic behaviour be observed and explained by chaos theory, but chaos theory can also be applied to a multitude of different areas of study such as meteorology, anthropology, sociology, physics, environmental science, computer science and much more.
References:
Jmcinerney. “IMHO - PDF Document.” Presentica, 17 May 2020, www.presentica.com/doc/11379635/imho-pdf-document.
Wikipedia contributors. “Chaos Theory.” Wikipedia, 24 Mar. 2021, en.wikipedia.org/wiki/Chaos_theory#History.
Photo references:
Figure 1:
[OC] Lorenz Attractor. (2020, January 29). Reddit. https://www.reddit.com/r/dataisbeautiful/comments/evml5m/oc_lorenz_attractor/