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)
It's just a demonstration of cause-and-effect.

Over time(years and years) even the smallest motions compound, and the eddies from butterfies wings will be the difference between a tornado and a clear day.