Accidental Roundup of Numbers Led to Chaos Theory
An accidental observation of a meticulous meteorologist, Edward Lorenz, has catalysed and spawned the birth of chaos theory.
The chain effects of 0.0001
In 1961, Lorenz typed in some data into a computer program that could simulate weather patterns using 12 variables, including temperature and wind speed.
To save time, he copied and pasted computer printout of weather data, then started the simulation halfway of its original course.
He left for coffee while the computer program continued to run.
One hour later, the computer program had output two month’s worth of simulated weather data. Much to Lorenz’s chagrin, the weather predictions bore no resemblance to the previous calculation. Lorenz painstakingly examined his deterministic equations with close scrutiny, but nothing seemed to be wrong.
Soon he realized the 6-digit numbers he entered (0.506127) were rounded off to 3 decimal places (0.506) on the computer printout.
Furthermore, the minuscule difference of 0.0001, equivalent to one part per 10,000, doubled in size every 4 days. By the second month, the simulated data no longer resembled the original figures.
There would be a thunderstorm in Kansas on a particular day in one forecast, while clear blue sky in another forecast. A tiny difference in the degree of accuracy had generated dramatically different weather forecasts.
The rival between Lorenz and Laplace
Lorenz’s discovery completely overthrew the scientific consensus at the time off the window. The contemporary consensus rested upon Sir Issac Newton’s 1687 Principia and Pierre-Simon Laplace’s 1814 postulate that nature was a clockwork universe.
If an omniscient, omnipotent intellect knows of all the precise locations and momentums of every atom in the universe, Laplace believed that by applying the deterministic physical laws of nature, this intellect could predict the past and future of the universe.
Before Lorenz’s time, nature was prevalently thought of as a perfectly predictable system because of the laws of classical mechanics.
Lorenz’s theory in 1963 refuted and replaced Newton’s and Laplace’s longstanding worldview that had survived for more than a century.
Lorenz’s 1963 paper “Deterministic Nonperiodic Flow” laid the monumental foundation for chaos theory. In the groundbreaking paper, he said:
“In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent.” — Edward Lorenz
Rain or shine
COVID-19 nationwide lockdown and international travel bans have brought blue skies and pristine air back to China. According to China’s ministry of environment, the level of particulate matter PM2.5 fell by 18% between January and April 2020. NASA and ESA reported that nitrogen dioxide emissions in Chinese cities such as Wuhan dropped by 30%, compared with last year’s data.
This reminds us that what we do on a daily basis — driving cars, burning fossil fuels, using electricity, emitting carbon dioxide — can affect the weather to a great extent.
The mercurial weather is uber dynamic and hyper-sensitive to initial conditions in the atmosphere. However imperceptible and impalpable, any noise, signal, and slight abberrations are non-trivial to weather systems. If neglected, such tiny changes can give rise to large deviations with overwhelmingly massive consequences.
Nature is a nonlinear, nonperiodic system of chaos. Small perturbations in air pressure, humidity, wind speed and temperature can disproportionately tilt tomorrow’s weather in favor of a rainy day or a sunny day.
At the current state of our technology, seven-day weather forecasts are still accurate, while forecasts two weeks ahead are less so.
The corollary: we cannot predict too far into the future, any more than the chaotic weather one year from today.