From Clockwork to Chaos

Shamie Dasgupta

12th April, 2021
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It all started with a tiny computer glitch...

Sometime in 1961, Professor Edward Lorenz was entering values into a powerful computer software used for simulating weather patterns. The software required twelve variables each representing critical factors like temperature and wind speed. After finishing his task, professor Lorenz left his office to get coffee while the machine continued to run the values. When he finally returned, the result he saw on the screen changed his perspective of science.

While entering values, Lorenz had rounded off one value from .50217 to .506. However, that minute alteration drastically transformed the whole pattern of over two months of simulated weather. Somehow for a deterministic set of equations, a tiny change in the initial conditions resulted in a completely different outcome.

The concept that small changes can lead to drastic consequences, was later coined as the Butterfly Effect. The term was adopted after Lorenz used the metaphorical example of a butterfly to explain chaos. He demonstrated that under extreme sensitivity to initial conditions implied, even the flutter of a butterfly’s wings over one region could influence the weather of a completely different region. This profound phenomenon has found its widespread application as deterministic chaos.

Chaos theory is the science of predicting the behavior of unpredictable systems. It is a mathematical instrument that helps in shaping the ordered structures from a sea of chaos. It helps in breaking apart the complex workings of diverse unpredictable systems and then understanding their unique nature.

Lorenz’s groundbreaking work challenged some of the most quintessential theories of physics. His work pointed to the limitations of deterministic Newton’s laws. The laws published by Newton in 1687 proposed a Clockwork Universe - that is, he compared the universe to a mechanical clock, which always ticked along in the same way, in the same phase as an ideal machine. Like a mechanical clock, the universe was predictable and always dictated by the laws of physics. Similarly, Laplace had asserted in his book A Philosophical Essay on Probabilities, that “if everything about the universe was known in its current state, then the past and the future would not remain uncertain.” Newton and Laplace never thought that the universe could be unpredictable, However, after Lorenz's discovery, it came to light that determinism may give short-term predictability, but in the long-term, things can remain unpredictable. 

On the flip side, chaos is not randomness. Lorenz demonstrated it with the help of a set of equations representing the motion of the gas. After the values were plotted on a graph, the result showed a definite shape of two oval-like figures joined at the middle, and oddly it resembled a butterfly. Thus, his equations drew two contradicting conclusions: repulsion of the trajectories within the data, and attraction beyond it. Such dynamics were hence referred to as the ‘Lorenz attractor’.

The solar system is a chaotic system with a prediction that stretches about a hundred million years! Surprisingly, this was discovered way before Chaos Theory was first formulated. Mathematician Henri Poincaré showed that while Newton’s theory of gravity can interpret how two planetary bodies rotate under their mutual attraction, the addition of another planetary body to the system leads to the equations becoming unsolvable. Even applying probability to adjust the equations, some other factors simply can not be ignored.

Unless one uses a system that is not sensitive to initial conditions, knows every data point with hundred percent accuracy, and uses ideal measuring instruments, they cannot achieve results that are not chaotic. If one relies on the weather forecasts to prepare their schedule they can not blame the meteorologists if it suddenly starts raining because predicting the weather with complete accuracy is nigh impossible. Chaos theory shows that even with advanced technology, predictions can, in fact, never be perfect. 

Who knew the world could be as random as a coin toss?

References:

Bang, S. W. A. (2018, February 14). Chaos Theory, The Butterfly Effect, And The Computer Glitch That Started It All. Forbes. https://www.forbes.com/sites/startswithabang/2018/02/13/chaos-theory-the-butterfly-effect-and-the-computer-glitch-that-started-it-all/?sh=7bf94e7b69f6 

Dizikes, P. (2020, February 11). When the Butterfly Effect Took Flight. MIT Technology Review. https://www.technologyreview.com/2011/02/22/196987/when-the-butterfly-effect-took-flight/. 

Jonathan Borwein (Jon) Laureate Professor of Mathematics, & Michael Rose PhD Candidate. (2020, April 15). Explainer: what is Chaos Theory? The Conversation. https://theconversation.com/explainer-what-is-chaos-theory-10620#:~:text=In%201961%2C%20a%20meteorologist%20by,more%20accurately%20predict%20the%20weather.

About the Author

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Currently majoring in Statistics and an art aficionado.