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)
[*Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?*](http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf)

That was the title of Edward Lorenz's invited talk at the 139th meeting of the American Association of the Advancement of Science held in 1972. This is the origin of the term "butterfly effect". The catchy title suggests that the answer must be "Yes!" Why else ask that question? The bulk of the talk says the answer is "Nobody knows." "Nobody knows" doesn't jibe well with a sensationalistic, unscientific press. That a butterfly in Brazil *might* trigger a tornado in Texas does. 

Lorenz had discovered in 1961 that early 1960s weather simulations were incredibly sensitive to initial conditions. Did this mean the weather itself is incredibly sensitive to minute changes? That the answer to this question is also "yes" marked a very important discovery. Weather and climate are the quintessential chaotic systems. Lorenz's work marked the start of modern chaos theory. His seminal 1963 paper, [*Deterministic nonperiodic flow*](http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2), has been cited 13479 times, per Google scholar. (In comparison, his 1972 talk has "only" been cited 345 times.) The vast majority of those 13479 citations came after his 1972 AAAS talk. Sometimes it takes a catchy title to catch the attention of a scientist.

Taking Lorenz's talk literally, asking whether a flap of a butterfly's wings in Brazil truly can set off a tornado in Texas, misses the point of his talk and of his work. The key point is that weather is chaotic. The accuracy of a detailed weather forecast fourteen days from now is rather low because that two week interval is well beyond the relevant Lyapunov timescale for such detailed predictions.

What about that butterfly? It's wing flap is a very small perturbation. It's rather difficult to say that that flap caused anything of significance to happen because the relevant timescale for such infinitesimally small perturbations is very short.