can anyone explain me the butterfly effect?
In: Physics
The scientist and mathematician Edward Lorenz was studying long-range weather forecasting with a computer simulation. One day he ran a weather simulation that had a start value of 0.506127, but when he reran it he decided to just enter 0.506 because he assumed that the last three tiny digits wouldn’t make much difference.
He was very surprised to see that while the weather in the simulation started off similar, soon it diverged completely into different weather. He realized that weather has “sensitive dependence on initial conditions” — a tiny difference in weather at the start would result in huge changes down the line. As a poetic example, he later wrote that the flap of a butterfly’s wings in Brazil could later set off a tornado in Texas.
A further extrapolation is that the butterfly effect is often brought up simultaneously with sci-fi time travel mechanisms. For media that use a non-fixed timeline approach (think back to the future and not harry potter), some character tends to mention the butterfly effect as a way of warning people from messing with things because, as others have explained, even the most innocent, tiny changes can result in something catastrophically different in the future.
If you want to play with a chaotic system (and you have a calculator or a spreadsheet or something handy), a very simple example is the “full logistic map”. Pick a number between 0 and 1. Calculate `4 × number × (1 – number)`, where `number` is your number. Then plug the result back into the same formula and repeat the process a few times, recording the numbers you get to a few decimal places. Now try the same thing but starting with a very slightly different number, e.g. if your original number was 0.6, try something like 0.602. Your two lists of numbers should (of course) start off looking very similar, but the gap between the numbers on the two lists, starting in this case at 0.002, will grow rapidly until the lists look completely different.
The reason this is so important is because if a real-world system behaves like this, then it’s inherently difficult to predict its long-term behaviour, because in the real world we never know the *exact* initial state of a system, we only have an approximate measurement of it.
However, it’s important to be clear that while chaotic systems are pretty common, they certainly aren’t universal. The study of chaos originated in attempts to predict weather, where there certainly are some chaotic effects, but the butterfly-tornado quote is just a metaphor, not a literal description of how reality works. And obviously there are plenty of weather patterns that can be predicted long-term, e.g. we know that in most of the northern hemisphere, July 2050 will be hotter than January 2050.
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