Edward Lorenz · Chaos
Why can't we know tomorrow's weather forever?
That time, that place
Lorenz was a meteorologist, and unusually for the time he was computing weather on a machine.
His model was very simple — a handful of equations imitating the motion of the atmosphere.
Why this question
One day he wanted to rerun an earlier calculation from the middle rather than start over.
He read a value off the printout and typed it in: 0.506. The number inside the machine had been 0.506127, but the printout carried only three decimal places.
A difference of less than one part in a thousand. It seemed of no consequence.
What was found
The results diverged completely.
At first the two runs tracked each other. Then they drifted apart, and by roughly two simulated months they described entirely unrelated weather.
What matters is that there is no randomness anywhere in these equations. The rules are fully determined; the same input always gives the same output. And prediction is still impossible.
Because the initial state cannot be known with infinite precision. However finely you measure, the residual difference grows without bound over time.
Having rules and being able to predict turned out to be two different things.
Know the rules and you can see as far ahead as you like
A difference in the fourth decimal producing an entirely different result two months on
The finding explains the limits of weather forecasting, and is why forecasts today present several scenarios at once