can anyone explain me the butterfly effect?
In: Physics
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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