I remember reading that a butterfly on the otherside of the world can cause a hurricane on the opposite side, and it’s down to chaos theory, could someone explain what chaos theory is please? Thanks
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As a side note, a butterfly flapping it’s wings, which after a series of consequences, results in a hurricane, is a horrible example actually. That isn’t at all how hurricanes develop.
Is chaos theory and butterfly effect the same thing?
Compare a [simple pendulum](https://www.youtube.com/watch?v=02w9lSii_Hs) and a [double pendulum](https://www.youtube.com/watch?v=U39RMUzCjiU). For each of those, ask yourself this: Where is the tip of the pendulum going to be in five seconds’ time?
Simple pendulums are high school physics, they’re very _very_ predictable, their behaviour is very straightforward. Most importantly: If you make small adjustments to the initial height and speed of pendulum, that has a small effect on the position of the pendulum in five seconds’ time.
Double pendulums are incredibly unpredictable. Modeling their behaviour is fairly advanced physics, and any small tweak to the initial state can result in wildly different results five seconds down the line.
Chaos Theory is the study of these sorts of systems where the outcomes are highly sensitive to the initial state. Turns out that, even though those systems are pretty unpredictable on a moment-to-moment basis, you can often predict their large-scale overall behaviour with reasonable accuracy. The butterfly/hurricane thing is an exaggeration, but the point is that the weather is one of these chaotic systems that are incredibly sensitive to changes.
Paraphrasing Ian malcolm
Complexity theory is the idea that from far away complex systems look simple, and the closer you look the more complex they become. Seemingly simple and predictable systems are in fact inherently chaotic, and incredibly minute inputs lead to disproportionately enormous outcomes. The classic example that leads to the name “butterfly effect” is from modeling weather systems: a butterfly flaps its wings in London and it monsoons in Beijing, or whatever cities you want to insert. Predicting tomorrow’s weather is easy, but predicting next week’s weather? Next months? Next year’s? The complexity of the system makes predicting outcomes beyond the immidiately close to impossible.
In jurassic park Malcolm talks about cotton prices – we have accurate records of cotton prices going back long enough to provide a decent sample size for research. If you graph global cotton prices over the course of a decade, it looks generally the same as a graph of cotton prices over the course of a year, which looks generally the same as a graph of cotton prices over the course of a month, which looks generally the same as a graph of cotton prices over the course of a week, which looks generally the same as a graph of cotton prices over the course of a day, etc. All of this would lead you to believe cotton prices are a simple and easily predictable system. But in fact cotton prices are a product of a hugely complex system, wherein small changes in temperature, weather, shipping patterns, pest populations, etc. Can have enormous and unpredictable implications on the price of cotton at any given moment.
If you looked at a graph of your life – the entire lifetime from beginning to end would look generally like a decade, like a year, like a month, like a day. But can you predict accurately and specifically what’s going to happen to you a week from today? A month? A year? A month from now it will generally be colder than it is today, and a month from now I’ll generally be doing the same thing I am right now. But predicting specific outcomes in such inherently chaotic systems is incredibly difficult.
So many people don’t realise that the butterfly flaps its wings example is literal. That’s the chaos theory in action.
What it is actually about, is how large dynamic seemingly random chaotic systems can actually be predicted by initial conditions.
So a butterfly flaps its wings in texas – that moves the molecules in the air. All the air in the world is alllll connected, so it has a knock on effect that can eventually lead to a hurricane forming elsewhere.
I think the central insight of chaos theory is that we are very limited in making predictions of complicated systems (like the weather) because we never have perfect data or perfect models about the world and lots of little inputs that we can’t record contribute to outcomes over time.
I usually remember the difference between random and chaotic. Random means it’s impossible to predict, no matter how much information you have. Which atom of uranium is going to decay is random. Chaotic means there’s so much information you have. The stock market is chaotic, not random. So is the weather.
Side note: part of the reason for the stock market crash in 2009 was software trading based on chaos theory. But it was poorly done and didn’t account for the rare wide swings in certain stocks. It’s detailed in the book The Quants by Wall Street reporter Scott Patterson.
Are chaos theory and the butterfly effect the same thing? I always thought they were different .I can’t tell if most of y’all are confusing the two or I’m just wrong
The answers here are good, but I’ll try to simplify for ELI5.
Imagine a stream of water or a plume of smoke. The individual partials are chaotic and hard to predict. However, when the system as a whole is observed patterns can emerge. Even though systems like this are sensitive to small changes, the math allows us to have a lot of knowledge about it.
Fractals are another great example. The non linear equations generate seemingly random numbers, but with enough of those numbers graphed patterns surface.
And one more example. It’s difficult, maybe impossible to know exactly what an individual particle will do exiting from a jet engine. But, jet engine engineers understand what the jet wash behind the aircraft will do very well.
Said in a more understandable way I think. If you praise a child for their drawings when they are young, they will draw more and might become the second coming of Michelangelo. If you say ” Your drawing sucks” they will stop drawing and with one sentence you have created Literal Hitler and they become world famous for something else entirely. (Hitler genuinely wanted to become an artist but was rejected by the school)
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