can anyone explain me the butterfly effect?
In: Physics
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!
It is basically the idea that a small cause somewhere can lead to a huge effect at a later time. Even the smallest decision can have huge consequences.
Every action has far-reaching and unpredictable consequences. The idea is that a butterfly flapping it’s wings on one side of the world can cause a hurricane on the other.
[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.
A butterfly is sitting on a leaf on a bush In California during the summer. The butterfly decides that it’s time to fly away from the bush, and flys off of the leaf. Flapping its wings to become airborne, the wind from its flapping blows off some dust off from the leaf, which then gets picked up by a smaller breeze that brings it up into the air and travels it further through the air. As the dust moves through the air, it picks up other gusts of air and makes it stronger as it travels and becomes one larger gust. After some time of this, the dust gusts becomes wind. That wind eventually gets strong enough that it actually (over simplified) pushes the clouds from the sky in California all the way over to Australia. By that time, the wind has gotten very strong, very strong and very fast. Effectively, when that wind gets strong enough, and that strong wind mixes with other rain clouds already I’m the sky, it becomes a hurricane.
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
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.
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.
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