can anyone explain me the butterfly effect?
In: Physics
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.
Interesting reading other people’s takes. I’m going to try and dumb it down even more, but if you’re interested, it belongs to the wider topic called chaos theory.
In short, it’s just saying that a ridiculously small change in input could give you drastically different results. The system is so sensitive that even a *butterfly flapping its wings can cause a rain storm*.
It’s like a drop of water on your knuckle. You’ll drop 2 drops in the “exact same” position and one will slide down the back of your hand and one might go to the left. It’s just due to a tiny change in where you dropped it (due to wind, or even your pulse moving your hand a tiny amount). To humans, it looks “random”.
The butterfly effect is minor differences in values of patameters in differential equation end up affecting the final result.
The reason this occurs is the way differential equations are solved, because a direct solution is rarely possible for them, they are solved iteratively until the values converge. But with enough iterations a difference of 0.(0)1 (e.g. 0.48763999 and 0.48764) in the intial parameters results in massive differences
When this is applied to weather prediction the difference is between a cyclone and not, because the the difference in the intial parameters is so small they were likened to a butterfly flapping it wings and thus the name
Most people here have the wrong idea of what the butterfly effect really is. Sure, small actions can have huge consequences, but that’s not the point.
What it really is about is that tiny changes in the initial conditions of a system can result completely different outcomes.
This particularly true with chaotic turbulence and weather. When doing the calculations, just rounding up a single decimal point can sometimes lead to predictions completely different from the more precise calculations. That’s why weather is very unpredictable from more than 3 days out.
So, no, a butterfly cannot cause a hurricane, but it can potentially result in the hurricane landing in one place instead of the other.
Think of a Roulette wheel. You can try duplicating the exact spin of the wheel and launch of the ball by hand but you’d never be able to achieve the same result.
This is because little changes propagate and become bigger and bigger differences in any complex system. The smallest degree difference, the slightest difference in timing, the slightest extra torque in the spin will guarantee a different result.
So you have predictable Newtonian physics where if you knew the location and momentum of every atom you could predict the result. However Heisenberg’s Uncertainty Principle says that we cannot determine both the position and momentum of a specific particle accurately – therefore it impossible for us to accurately predict the exact interactions of molecules.
And so Newtonian Physics when combined with Quantum Mechanics gives us Chaos Theory.
So a butterfly flaps it’s wings – the air molecules being moved interact and cause other air molecules to move that can chain effect other molecules and where the beginnings of a breeze were about to go in one direction now it goes in a slightly different direction. That breeze combines into other airflows and combines into effecting bigger and bigger movements of air. Now conditions might have been hovering on developing a hurricane out in ocean. A slightly different wind could now trigger the hurricane to occur where it may have dissipated before. The idea is if the butterfly hadn’t flapped it’s wings the seemly random events of the wind and weather would have turned out differently.
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.
The evolution of complex systems can be extremely sensitive to the initial conditions. A very small difference early on can mean that the system ends up in very different states later on.
Hence the presence of a butterfly flapping its wings *might* make significant differences to larger scale weather down the line.
[Basically think of a domino effect](https://youtu.be/y97rBdSYbkg?t=47).
It starts with a tiny domino, but that knocks over a bigger domino and a bigger domino and a bigger domino.
In the formulation it’s a butterfly flaps its wings, which moves the wind a bit, so it interacts with a different wind, which then pushes a warm front a fraction of a degree, which causes it too… and so on and so forth until what would have been a normal day is now a hurricane.
So why were people talking about it?
Well it was there to explain why predictions on very complicated systems (such as weather predictions) is hard.
Sure you can use radar to track clouds and warm fronts and stuff, but you can’t track every single butterfly, and a butterfly flapping its wings can screw up your predictions.
There’s an old song my parents used to sing to me that illustrates the butterfly effect pretty well:
For want of a nail, the shoe was lost
For want of a shoe, the horse was lost
For want of a horse, the rider was lost
For want of a rider, the message was lost
For want of a message, the battle was lost
For want of a battle, the war was lost
And all for the want of a horseshoe nail!
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