Author: Rebecca Buss
The BRB Bottomline: The Science of Surprises: Chaos Theory is an interdisciplinary subject that applies math and physics to the real world in order to describe unpredictable systems, such as earthquakes, market crashes, pandemics, and more.
Although there have been many movies where people travel to the future, it never seemed plausible in real life. Despite the fact that we can’t (yet) pull off what Marty McFly does in Back to the Future, by utilizing underlying patterns and deterministic laws, chaos theorists can somewhat anticipate what will happen next.
The Butterfly Effect
“The way a butterfly flaps its wings in Brazil could cause a tornado in Texas.” This is what MIT Professor Edward Lorenz qualifies as “The Butterfly Effect” and one of the main postulates of Chaos Theory. Lorenz was running a weather simulation and realized that rounding to three decimal places instead of six changed two months of simulated weather. He mainly accredited the large change to the extreme complexity of the system of weather and applied it to other elaborate systems. This is what chaos theory is all about: how minor changes to initial conditions can create major outcomes.
Make it Make Sense
Chaos Theory is a very difficult type of science since there is no certainty, no right answer, and it requires intricate explanations to be left with only a prediction. Nevertheless, it is a subject that many people study, and they continue to come up with the math and physics behind the theory. Some important steps in the journey of the discovery of chaos theory include Henri Poincaré’s phenomenon of sensitivity to initial conditions which, as stated above, was the birth of chaos theory. Other important steps include Andreï Nicolaïevitch Kolmogorov’s study of the statistics of dynamical systems and, of course, Lorenz’s Butterfly Effect: the official discovery of chaos theory. The actual mathematical concepts behind these systems are far too complicated for someone not versed in them, but they are still the foundation of how the calculations are made and the basis of what chaos theory is.
Chaotic Events
There are three main types of events present in Chaos Theory. The first is the Black Swan. These events are so extreme that they are considered basically impossible; they have a very low likelihood of happening, but have a significant impact. An example includes the September 11 attacks. Related to the Black Swan is the Grey Swan event, which refers similarly to something extreme and unpredictable. However, they are more frequent and, thus, in retrospect, could have been avoided, like the 2008 financial crisis. Lastly, there are Dragon King events; although still extreme, they are the most likely of the chaotic events: they are possible and can be predicted. Indeed, they follow a log-periodic pattern, meaning that there is a period of build-up to a breaking point and then a sharp drop. Examples include financial crashes, the dot com bubble, and the collapse of bitcoin.
Applications
Weather
One main application of chaos theory that almost everyone encounters in their daily lives is weather forecasting. While the weekly outlook is usually accurate, minor disturbances in air flow can drastically change what was originally predicted and are the reason why scientists are unable to predict the weather two years in the future. If they wanted to, scientists would need all of the specific initial conditions, meaning the exact position of all air molecules, and that is impossible.
The Pandemic
Another more recent application is the COVID-19 Pandemic. Since it is considered a Grey Swan Event, the world could not have predicted it would happen. However, once the pandemic was in full swing, around the time the lockdowns started, scientists created models using chaos theory. These models, using block-pulse, bernoulli polynomials, caputo derivatives, SEIR models, and more, could predict values such as the number of infections caused by COVID-19, how quickly it reaches its peak, and how quickly it dies.
Economics
Finally, chaos theory is widely used in the realm of finance. In fact, the widely known Efficient Market Hypothesis – the idea that the market reflects all available information – is proven wrong by the Fractal Market Hypothesis, a conjecture that there is still an element of uncertainty within the market. This uncertainty can be dissected using the Hurst exponent for the rate of chaos and the Lyapunov exponent to determine the rate of predictability. Simply put, chaos theory uses stock market variations and chaotic analyses of mathematical exponents to predict future behavior of markets, increasing the possibility of “beating the market” and making informed decisions as an investor.
Take-Home Points
- Chaos Theory combines mathematics and physics concepts to be able to predict what will happen next in complex systems.
- There is still always a hint of uncertainty – we can never be 100% sure what will happen next.
- Overall, chaos theory is a powerful subject that allows scientists to better understand the world and therefore concepts like weather forecasting, economics, and more.