Question: I have heard that extreme storm events can be caused simply by a butterfly flapping its wings somewhere in a distant location. Is it true that such a small disturbance in the air in one location can result in such a large catastrophic event in another separate location? If so how can we know this is possible, and how is this even possible?

Answer: 
The butterfly is a colourful illustration of [Chaos Theory](https://en.wikipedia.org/wiki/Chaos_theory), and the word butterfly came from the diagram of the state space (see below).

A system that is *chaotic* is extremely sensitive on its initial value. In principle, if you know *exactly* how the state of the universe is now, you could calculate how it develops (but due to other reasons, it is *theoretically impossible* to know the state exactly — but that's not the main point here). The issue with a chaotic system is that a *very* small change in the initial state can cause a *completely different* outcome in the system (given enough time).

So, suppose that we take the entire atmosphere and calculate the weather happening for the next 20 days; suppose for the moment that we actually *do* know every bit. Now, we repeat the calculation, but with one *tiny tiny* bit that is different; such as a butterfly flapping its wings. As the nature of a chaotic system is such that a *very small* change in the initial value can cause a *very large* change in the final state, the difference between these two initial systems may be that one gets a tornado, and the other doesn't.

Is this to say that the butterfly flapping its wings results in a tornado? **No, not really**. It's just a matter of saying, but not really accurate.

Many systems are chaotic:

* Try to drop a leave from a tree; it will never fall the same way twice.
* Hang a pendulum below another pendulum and track its motion:

![Double pendulum](https://i.stack.imgur.com/wMghE.gif)

(Figure from Wikipedia)

* Or [try to help your boyfriend](https://en.wikipedia.org/wiki/Run_Lola_Run) in what must be one of the loveliest illustrations of Chaos Theory ever. Suppose you are running to catch the bus. You keep sight of a butterfly, which delays you by a split second. This split second causes you to miss the bus, which later crashes into a ravine, killing everyone on board. Later in life, you go on to be a major political dictator starting World War III (*Note: this is not the plot of the linked movie, but my own morbid reinterpretation*).

Tell me, did this butterfly cause World War III?

Not really.

![Lorenz attractors](https://i.stack.imgur.com/NQiNn.png)

(Figure from Wikipedia)
While it is not about butterflies, scientist have found weather in the United States and Noctilucent Clouds in Antarctica to be linked across thousands of miles.

Here are a few excerpts of what they have found:

> 
> New data from NASA's AIM spacecraft have revealed "teleconnections" in Earth's atmosphere that stretch all the way from the North Pole to the South Pole and back again, linking weather and climate more closely than simple geography would suggest.
> 
> 
> For example, says Cora Randall, AIM science team member and Chair of the Dept. of Atmospheric and Oceanic Sciences at the University of Colorado, "we have found that the winter air temperature in Indianapolis, Indiana, is well correlated with the frequency of noctilucent clouds over Antarctica."
> 
> 
> 

It demonstrates how apparently unrelated events can in fact be related to each other.

[Here is the full article to read.](http://science.nasa.gov/science-news/science-at-nasa/2014/16apr_teleconnections/)