Book Notes - Chaos: Making a New Science

Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability.

This book explores the small effects that we usually ignore in experiments to make things easy. Like a leaf falling on some planet in a different galaxy won’t have any impact on Earth.

Few scientists started noticing how few systems are not predictable (ideally everything should be predictable as per Newtonian physics, we just need to put all the variable in equation).

One of them was Lorenz, he noticed it while predicting the weather patterns in 1961. Computers were a little different back then, built with vacuum tubes instead of sophisticated chips, and GUI was not retina screens but a printer. You punch some initial conditions and then wait for the computer to run for a few hours and give output in the form of a printout.

Lorenz wanted to examine one particular sequence of weather, so instead of running the system from the start, he added initial conditions as the output of the last run’s printout. Computers were quite noisy back then, so he went out to get coffee and returned in an hour.

On returning he observed totally different output. The new run was not duplicating the older runs and weather conditions diverged so fast that within a few months, the whole resemblance in prediction disappeared.

Lorenz thought there was some issue with the vacuum tube but couldn't find any on inspection. So why does the same system give two different behaviors if everything is same? The issue was a negligible information loss, to save space the printout used only numbers till three precision points, so it printed .506 instead of .506127

This small change was inconsequential as per science, but it changed the whole trajectory of weather. This small change was like - a butterfly skipped flapping its wings only once in New York and resulted in tornado in India. Thus Butterfly Effect term was coined.

There was pattern, with disturbances. An orderly disorder.

Solving the greatest problem of Mankind

Back in 50's scientists were obsessed with weather prediction problem. Country that will be able to predict weather will automatically go leaps ahead. They will be able to seed clouds via airplane to make them rain at will, famine, droughts will be things of past.

Among them was John Von Neumann, who wanted to solve this problem via highly complex calculators (now knows as computers). He surrounded himself with meteorologists and gave breathtaking talks about his plans to the general physics community.

With the computer up and running, Von Neumann imagined that scientists would calculate the equations of fluid motion for the next few days. Then a central committee of meteorologists would send up airplanes to lay down smoke screens or seed clouds to push the weather into the desired mode. But Von Neumann had overlooked the possibility of chaos, with instability at every point.

The modern weather models work with a grid of points on the order of sixty miles apart, and even so, some starting data has to be guessed, since ground stations and satellites cannot see everywhere. But suppose the earth could be covered with sensors spaced one foot apart, rising at one-foot intervals all the way to the top of the atmosphere. Suppose every sensor gives perfectly accurate readings of temperature, pressure, humidity, and any other quantity a meteorologist would want. Precisely at noon an infinitely powerful computer takes all the data and calculates what will happen at each point at 12:01, then 12:02, then 12:03… The computer will still be unable to predict whether Princeton or New Jersey, will have sun or rain on a day one month away. At noon the spaces between the sensors will hide fluctuations that the computer will not know about, tiny deviations from the average. By 12:01, those fluctuations will already have created small errors one foot away. Soon the errors will have multiplied to the ten-foot scale, and so on up to the size of the globe.

If the weather ever did reach a state exactly like one it had reached before, every gust and cloud the same, then presumably it would repeat itself forever after and the problem of forecasting would become trivial.