The Butterfly Effect

更新：2023-11-22

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[00:01.48]Lesson 14
[00:03.37]The Butterfly Effect
[00:12.92]Why do small errors make it impossible to predict the weather system with a high degree of accuracy?
[00:23.11]Beyond two or three days, the world's best weather forecasts are speculative,
[00:29.38]and beyond six or seven they are worthless.
[00:33.23]The Butterfly Effect is the reason.
[00:36.14]For small pieces of weather --
[00:38.31]-- and to a global forecaster, small can mean thunderstorms and blizzards --
[00:44.49]any prediction deteriorates rapidly.
[00:47.67]Errors and uncertainties multiply, cascading upward through a chain of turbulent features,
[00:54.17]from dust devils and squalls up to continent-size eddies that only satellites can see.
[01:02.68]The modern weather models work with a grid of points of the order of sixty miles apart,
[01:08.82]and even so, some starting data has to be guessed,
[01:13.27]since ground stations and satellites cannot see everywhere.
[01:18.28]But suppose the earth could be covered with sensors spaced one foot apart,
[01:23.92]rising at one-foot intervals all the way to the top of the atmosphere.
[01:29.24]Suppose every sensor gives perfectly accurate readings of temperature,
[01:34.60]pressure, humidity, and any other quantity a meteorologist would want.
[01:41.09]Precisely at noon an infinitely powerful computer takes all the data and calculates what will happen at each point
[01:48.75]at 12.01, then 12.02, then 12.03...
[01:56.86]The computer will still be unable to predict whether Princeton, New Jersey, will have sun or rain on a day one month away.
[02:06.64]At noon the spaces between the sensors will hide fluctuations that the computer will not know about,
[02:13.59]tiny deviations from the average.
[02:16.66]By 12.01, those fluctuations will already have created small errors one foot away.
[02:24.03]Soon the errors will have multiplied to the ten-foot scale, and so on up to the size of the globe.