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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?

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    $\begingroup$ This question is off-topic because it is not scientific. It can't be answered by scientific methods. No experiment can be constructed to test any of the answers' truth or falseness. Thought experiments aren't enough. Even the OP asks "How can we know this is possible?" It's a meta-physical question. $\endgroup$ – kwknowles Apr 21 '14 at 2:30
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    $\begingroup$ @kwknowles, I disagree with you about the scientific nature of the question. Many questions in physics are answered through simulations and they are not considered unscientific if you have a simulated model for some phenomenon. Whether we have such simulations or not I don't know but it is beside the point, the question can theoretically be answered via a scientific approach. $\endgroup$ – Kenshin Apr 21 '14 at 2:34
  • $\begingroup$ @Mew It's not a matter of how you test a theory. In order to use the scientific method a theory must be testable. In order to test the theory, data must be collected. Simulations are used in the scientific method, but they can't be used in place of real world data in order to test a theory. This isn't just my opinion, see Scientific method. I'm only harping on this because we are defining the site right now. See Level of the questions so far $\endgroup$ – kwknowles Apr 21 '14 at 17:36
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    $\begingroup$ @kwknowles, Suppose a medicine has been shown in clinical trials to benefit all humans it is tested on. I can approach a scientist and ask would the medicine benefit me. The scientist could say, that's untestable and unscientific - true. It is untestable because even if I take the medication and get better, there is no way to know I got better because of the medication. Does this mean all such questions fall out of the realm of science? NO. This is the nature of APPLIED SCIENCE. It is taking a model that we have developed through science, and applying that model to specific situations. $\endgroup$ – Kenshin Apr 21 '14 at 23:38
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    $\begingroup$ @kwknowles, now in this case, theoretically it is possible that we could develop a predictive model of weather, that is testable. After testing it many times, we could then plug in the initial conditions with and without butterflies flapping their wings and so on, and check the results. Now it doesn't matter weather this particular scenario is testable or not, if the underlying model is testable, then it is applied science. This is analogous to the medical situation, where the underlying model is that the medicine works, and then we apply it to an individual patient. $\endgroup$ – Kenshin Apr 21 '14 at 23:41
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The butterfly is a colourful illustration of 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
(Figure from Wikipedia)

  • Or try to help your boyfriend 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
(Figure from Wikipedia)

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  • $\begingroup$ It would be accurate to say that the butterfly was a contributing factor though :P $\endgroup$ – naught101 Apr 18 '14 at 9:35
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    $\begingroup$ I think I finally figured out what bugs me about this answer. It's interesting, even fun to think about, but it's not scientific. Science consists of testable hypotheses. A theory isn't true just because it makes sense. You have to be able to design an experiment, collect data, and test the truth or falseness of the claims. If you released butterflies into a number of storms you might see more than usual tornados (I doubt it), but you could never say any particular tornado was caused by a butterfly. The way this answer is constructed, butterflies could cause anything. $\endgroup$ – kwknowles Apr 19 '14 at 23:35
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    $\begingroup$ @kwknowles We cannot design a physical experiment to verify or falsify the hypothesis posed in the question, so we need to work by analogy and models. We do know that arbitrarily small changes in initial conditions can result in very large changes in a final situation. Wether or not this should be called a cause is a matter of definition. Ultimately, I think this question is more about semantics than about testable hypothesis. In the strict sense that you might prefer to see an answer, the question is unanswerable. $\endgroup$ – gerrit Apr 21 '14 at 13:02
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    $\begingroup$ @gerrit Analogy and models are only one part of the scientific method. The hypothesis must be testable. The question might be OK here if the answer pointed out that it's not really a scientific question. However, this answer is definitely off topic. It's just wool gathering. See Level of the questions so far $\endgroup$ – kwknowles Apr 21 '14 at 17:17
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    $\begingroup$ This answer somewhat misrepresents the connection between chaos theory and weather. No one has claimed that weather is sensitive to arbitrarily small differences in initial atmospheric conditions. The "size" of the difference has an associated time-scale of applicability. Small perturbations have short time-scales and therefore localized effects. Large perturbations have longer time-scales and therefore greater range of impact. This answer needs to cite references if it wants to claim otherwise. Specifically where does the arbitrarily small idea (wrt weather) come from? $\endgroup$ – kwknowles May 5 '14 at 14:40
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Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?

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, 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.

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  • $\begingroup$ I've heard that the term "butterfly effect" had been suggested to him based on what his state space diagram looked like to a layman, but I have no authoritative source for this anecdote. $\endgroup$ – gerrit May 1 '14 at 13:36
  • $\begingroup$ This is a very good answer--succinct, informative, stays on topic. It really deserves to be number one and the accepted answer. $\endgroup$ – kwknowles May 8 '14 at 15:24
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The causes of a single particular extreme weather event, like a tornado, may never be fully understood, especially if it is a chaotic system. The causes or contributing factors to the number of tornados expected for a particular atmospheric condition is much more fully understood and is certainly not chaotic. In that sense, butterflies do not cause tornados.

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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.

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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.

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    $\begingroup$ Solution: ELIMINATE ALL BUTTERFLIES! $\endgroup$ – Ben A. Noone Apr 18 '14 at 3:03
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    $\begingroup$ kidding, I love butterflies. $\endgroup$ – Ben A. Noone Apr 18 '14 at 3:07
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    $\begingroup$ That didn't work out so well for Homer Simpson. Homer traveled back in time and stepped on an insect by accident which in turn created compounding impacts that completely changed society when he returned to the present time. $\endgroup$ – DrewP84 Apr 18 '14 at 3:25
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    $\begingroup$ Even the smallest motion? How about Brownian motion? $\endgroup$ – Peter Jansson May 18 '14 at 15:58

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