<p><a href="http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf"><em>Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?</em></a></p>

<p>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 <em>might</em> trigger a tornado in Texas does. </p>

<p>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, <a href="http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2"><em>Deterministic nonperiodic flow</em></a>, 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.</p>

<p>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.</p>

<p>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. </p>

CC BY-SA 3.0
2014-05-01T13:36:29.737Z
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.
gerrit
CC BY-SA 3.0
2014-05-08T15:24:24.440Z
This is a very good answer--succinct, informative, stays on topic. It really deserves to be number one and the accepted answer.
kwknowles
CC BY-SA 3.0
2014-04-30T17:30:08.463Z
2014-05-05T06:01:53.150Z
2014-05-05T06:01:53.150Z
David Hammen
<p>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.</p>

CC BY-SA 3.0
2014-04-19T17:22:10.147Z
2014-04-19T17:22:10.147Z
kwknowles
<p>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.</p>
<p>Here are a few excerpts of what they have found:</p>
<blockquote>
<p>New data from NASA's AIM spacecraft have revealed &quot;teleconnections&quot; 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.</p>
<p>For example, says Cora Randall, AIM science team member and Chair of the Dept. of Atmospheric and Oceanic Sciences at the University of Colorado, &quot;we have found that the winter air temperature in Indianapolis, Indiana, is well correlated with the frequency of noctilucent clouds over Antarctica.&quot;</p>
</blockquote>
<p>It demonstrates how apparently unrelated events can in fact be related to each other.</p>
<p><a href="http://science.nasa.gov/science-news/science-at-nasa/2014/16apr_teleconnections/" rel="nofollow noreferrer">Here is the full article to read.</a></p>

CC BY-SA 3.0
2014-05-05T03:51:51.407Z
2014-05-05T03:51:51.407Z
2020-06-18T08:25:19.090Z
L84
<p>It's just a demonstration of cause-and-effect.</p>

<p>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.</p>

CC BY-SA 3.0
2014-05-18T15:58:18.077Z
Even the smallest motion? How about Brownian motion?
Peter Jansson
CC BY-SA 3.0
2014-04-18T03:03:28.943Z
Solution: ELIMINATE ALL BUTTERFLIES!
Ben A. Noone
CC BY-SA 3.0
2014-04-18T03:07:20.423Z
kidding, I love butterflies.
Ben A. Noone
CC BY-SA 3.0
2014-04-18T03:25:47.043Z
[That didn't work out so well for Homer Simpson.](http://deadhomersociety.files.wordpress.com/2013/10/tohv-11.jpg)  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.
DrewP84
CC BY-SA 3.0
2014-04-18T03:03:18.257Z
2014-04-18T03:03:18.257Z
Ben A. Noone
<p>The butterfly is a colourful illustration of <a href="https://en.wikipedia.org/wiki/Chaos_theory" rel="noreferrer">Chaos Theory</a>, and the word butterfly came from the diagram of the state space (see below).</p>

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

<p>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 <em>do</em> know every bit.  Now, we repeat the calculation, but with one <em>tiny tiny</em> bit that is different; such as a butterfly flapping its wings.  As the nature of a chaotic system is such that a <em>very small</em> change in the initial value can cause a <em>very large</em> change in the final state, the difference between these two initial systems may be that one gets a tornado, and the other doesn't.</p>

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

<p>Many systems are chaotic:</p>

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

<p><img src="https://i.sstatic.net/wMghE.gif" alt="Double pendulum"> 
<br /><sup>(Figure from Wikipedia)</sup></p>

<ul>
<li>Or <a href="https://en.wikipedia.org/wiki/Run_Lola_Run" rel="noreferrer">try to help your boyfriend</a> 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 (<em>Note: this is not the plot of the linked movie, but my own morbid reinterpretation</em>).</li>
</ul>

<p>Tell me, did this butterfly cause World War III?</p>

<p>Not really.</p>

<p><img src="https://i.sstatic.net/NQiNn.png" alt="Lorenz attractors">
<br /><sup>(Figure from Wikipedia)</sup></p>

CC BY-SA 3.0
2014-04-19T23:35:06.460Z
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.
kwknowles
CC BY-SA 3.0
2014-04-21T13:02:27.197Z
@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.
gerrit
CC BY-SA 3.0
2014-04-21T17:17:13.063Z
@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](http://meta.earthscience.stackexchange.com/questions/34/level-of-the-questions-so-far)
kwknowles
CC BY-SA 3.0
2014-04-22T01:46:30.707Z
@kwknowles, the question states at the end "how can we know if it is true?" The answer is we can't, but we can work out that it may likely be true if the models of our weather are consistent with it.  The science is in the generation of models, but my question is more about applying such models to the butterfly case.
Kenshin
CC BY-SA 3.0
2014-04-22T18:53:58.777Z
@GeoDude Look at it this way. The but-for-a-butterfly-flap "theory" can be used to explain anything. Can a butterfly push me off a cliff? Yes. If you're teetering right on the edge and that's all it takes is just one puff of air, then whoops, over you go. Can a butterfly cause an airplane to crash? Yes. If it's right there on the nick of disaster and all it takes is one more puff of air, then BOOM, butterfly destroys jet liner. See how useless it is as a **scientific** theory? It doesn't help us understand how the world really works.
kwknowles
CC BY-SA 3.0
2014-04-22T18:58:53.790Z
@kwknowles It does help us, although I think your examples are not very good.  It's not a matter of being just on the edge; it's a matter of a system going through *an entirely different path* when a small change happens.  Can a butterfly cause a traffic accident?  Easily, if I'm cycling and it distracts me.  The point is that any change, no matter how small, can change the course of the universe... forever.
gerrit
CC BY-SA 3.0
2014-04-22T19:26:42.403Z
@gerrit That's not a very useful definition of "cause". If you make it that broad, you're saying _anything_ can cause _anything_. Like I said before... it's a beautiful meta-physical theory. It's just not Earth Science.
kwknowles
CC BY-SA 3.0
2014-04-22T19:30:48.167Z
@kwknowles I agree that the word *cause* is not the best one to use here.  The question used *result in*, but I'm open to other suggestions.  It's just semantics, really.  Regardless of the formulation, I think understanding the principles of chaos *does* further our understanding of how nature works.
gerrit
CC BY-SA 3.0
2014-05-05T03:45:03.983Z
I love your bus example of Chaos Theory! I heard a similar explanation of it where a butterfly flies past a woman after just landing on a flower. The pollen causes the woman to sneeze, a man says "God Bless You" (or appropriate phrase). The man and woman end up talking more...marriage...kid... The kid turns out to be [insert dictator name such as Hitler, Stalin, etc.] all originated with a butterfly with pollen on its wings causing a woman to sneeze. Chaos Theory is an interesting topic. =>
L84
CC BY-SA 3.0
2014-05-05T14:40:19.760Z
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?
kwknowles
CC BY-SA 3.0
2014-05-05T14:49:17.900Z
@kwknowles The *arbitrarily small* with regard to weather comes from the observation that even a numerical difference in a model initialisation (i.e. one bit difference) can result in an entirely different outcome in the long scale.  It is my understanding that indeed arbitrarily small changes in the initial value can result in arbitrarily large changes in the long term, in *any* chaotic system, including weather.  Is this a misrepresentation?
gerrit
CC BY-SA 3.0
2014-05-05T14:53:52.673Z
@gerrit I tried to edit that out (misrepresentation) but I took too long to realize my mistake, i.e. that I don't actually know myself. So, is there a reference wrt to weather (and not weather models)? That sensitivity you talk about in the models is cited as a flaw.
kwknowles
CC BY-SA 3.0
2014-05-05T15:02:44.333Z
@kwknowles It is my understanding that it follows directly from the observation that weather is a chaotic system (for which references are plentiful), and that *any* chaotic system shares this property.  I haven't heard before that this is a property in weather models and is considered a flaw compared to the actual weather.  The latter seems impossible to either verify or falsify.
gerrit
CC BY-SA 3.0
2014-05-05T18:58:16.653Z
@gerrit The problem with the _arbitrarily small differences in initial conditions leads to vastly different outcomes_ is that as the difference approaches zero you get a completely unpredictable system. Yet weather models are good for certain time scales--a day at least, right? To test this theory (and fix the models) scientists used Monte Carlo methods to randomly vary initial conditions. Instead of a uniform distribution of outcomes (every outcome is as likely as any other) they got a bell curve. The center of the curve is the prediction. This fits nicely with chaos theory strange attractors
kwknowles
CC BY-SA 3.0
2014-05-05T19:22:16.383Z
@gerrit You give a lower bound of 1 bit. That's not arbitrarily small. Edward Lorenz states that the lower bound would be the accuracy with which we can measure observables. Again, not arbitrarily small. It's not nit picking. It's the difference between science and philosophy. It's the difference between anything can cause anything and a theory that furthers weather prediction. Would you consider changing "arbitrarily small" to "very small"? You could also quantify the changes in outcomes: an error in measuring _X_ doubles every _N_ days (or hours), for example. __That__ would be science.
kwknowles
CC BY-SA 3.0
2014-05-06T14:16:43.203Z
@kwknowles I have changed *arbitrarily* to *very*.  I don't know enough about the topic to be quantitative (and I think it's not needed to answer this question).
gerrit
CC BY-SA 3.0
2014-05-07T17:05:29.417Z
@gerrit The quantitative terms are absolutely necessary to the answer. In fact, they are the only thing of worth you could have added to the answer. Otherwise, you could have simply stopped after the link to the Wikipedia article "The butterfly is a colourful illustration of _Chaos Theory_" Since the rest of the answer just restates what's there. What's the accepted Lyapunov exponent for the phenomenon? Does a butterfly flap meet that threshold? If you're not an expert, perhaps you shouldn't have posted an answer.
kwknowles
CC BY-SA 3.0
2014-05-07T17:11:56.567Z
@kwknowles I do not agree that the question as stated requires a quantitative answer.  It did not ask if the result could occur 1 day/3 days/1 month later, it asked if it could occur *at all*.  Expertise is relative; I believe my answer is useful, but I would certainly welcome a more thorough, mathematically expressed, quantitative answer.  The same comment for the question itself: I do not think being quantitative is a necessary condition for a post (question or answer) to be scientifically sound.
gerrit
CC BY-SA 3.0
2014-05-07T21:06:08.473Z
@gerrit I agree that quantitative answers are not required in the general case. I'm saying that quantitative information in this particular answer would have turned it from pop-sci/philosophy/repeat-of-already-available-info into an expert level question.
kwknowles
CC BY-SA 3.0
2014-09-11T14:20:20.117Z
This is a pretty interesting discussion, but I'm worried that it will get lost in the future when a moderator comes along and decides to cull the lengthy discussion. Maybe a better way to deal with the disagreements would be to ask more questions? I know I have a couple of good references for an answer to the how behaviour in models relates (or doesn't) to the real world, for instance.
naught101
CC BY-SA 3.0
2014-04-18T09:35:33.030Z
It would be accurate to say that the butterfly was a contributing factor though :P
naught101
CC BY-SA 3.0
2014-04-17T02:36:34.193Z
2014-05-06T14:15:47.040Z
2014-05-06T14:15:47.040Z
gerrit
<p>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?</p>

CC BY-SA 3.0
2014-04-21T02:30:31.493Z
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.
kwknowles
CC BY-SA 3.0
2014-04-21T02:34:39.140Z
@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.
Kenshin
CC BY-SA 3.0
2014-04-21T17:36:33.140Z
@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](http://en.wikipedia.org/wiki/Scientific_method). I'm only harping on this because we are defining the site right now. See [Level of the questions so far](http://meta.earthscience.stackexchange.com/questions/34/level-of-the-questions-so-far)
kwknowles
CC BY-SA 3.0
2014-04-21T23:38:20.777Z
@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.
Kenshin
CC BY-SA 3.0
2014-04-21T23:41:11.723Z
@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.
Kenshin
CC BY-SA 3.0
2014-04-22T19:08:50.263Z
@Geodude Regarding your comment that the question was reopened. Why address it to me? I didn't close your question or even vote it down. I guess you assumed because I put that "off topic" comment. It's not a criticism of you (or the question, even). That's a comment meant for everyone who answers or reads the answers. I don't know where else to put a comment like that.
kwknowles
CC BY-SA 3.0
2014-05-05T04:52:18.300Z
@kwknowles: While you're technically right, I think the question works well if taken as an iconic metaphor of small perturbations leading to large effects. That *is* testable: for example, you can set up repeatable physical fluid-dynamics experiments that have only extremely small initial differences, and show that eddies for in different places, at different times.
naught101
<meteorology><atmosphere><climate-models><chaos>
Is it true that a butterfly flapping its wings can result in a tornado in a distant location?
Kenshin
# Is it true that a butterfly flapping its wings can result in a tornado in a distant location?

(Asked by: username_0 on 2014-04-17)

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?

**Tags:** meteorology, atmosphere, climate-models, chaos

> **Comments:**
> **username_1**: 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.  
> **username_0**: @username_1, 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.  
> **username_1**: @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](http://en.wikipedia.org/wiki/Scientific_method). I'm only harping on this because we are defining the site right now. See [Level of the questions so far](http://meta.earthscience.stackexchange.com/questions/34/level-of-the-questions-so-far)  
> **username_0**: @username_1, 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.  
> **username_0**: @username_1, 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.  
> **username_1**: @Geodude Regarding your comment that the question was reopened. Why address it to me? I didn't close your question or even vote it down. I guess you assumed because I put that "off topic" comment. It's not a criticism of you (or the question, even). That's a comment meant for everyone who answers or reads the answers. I don't know where else to put a comment like that.  
> **username_2**: @username_1: While you're technically right, I think the question works well if taken as an iconic metaphor of small perturbations leading to large effects. That *is* testable: for example, you can set up repeatable physical fluid-dynamics experiments that have only extremely small initial differences, and show that eddies for in different places, at different times.  

---

## 5 answers

### Answer by username_4 on 2014-04-17. Score: 25 | Accepted 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.sstatic.net/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.sstatic.net/NQiNn.png)
  
(Figure from Wikipedia)

> **Comments:**
> **username_2**: It would be accurate to say that the butterfly was a contributing factor though :P  
> **username_1**: 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.  
> **username_4**: @username_1 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.  
> **username_1**: @username_4 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](http://meta.earthscience.stackexchange.com/questions/34/level-of-the-questions-so-far)  
> **username_0**: @username_1, the question states at the end "how can we know if it is true?" The answer is we can't, but we can work out that it may likely be true if the models of our weather are consistent with it.  The science is in the generation of models, but my question is more about applying such models to the butterfly case.  
> **username_1**: @GeoDude Look at it this way. The but-for-a-butterfly-flap "theory" can be used to explain anything. Can a butterfly push me off a cliff? Yes. If you're teetering right on the edge and that's all it takes is just one puff of air, then whoops, over you go. Can a butterfly cause an airplane to crash? Yes. If it's right there on the nick of disaster and all it takes is one more puff of air, then BOOM, butterfly destroys jet liner. See how useless it is as a **scientific** theory? It doesn't help us understand how the world really works.  
> **username_4**: @username_1 It does help us, although I think your examples are not very good.  It's not a matter of being just on the edge; it's a matter of a system going through *an entirely different path* when a small change happens.  Can a butterfly cause a traffic accident?  Easily, if I'm cycling and it distracts me.  The point is that any change, no matter how small, can change the course of the universe... forever.  
> **username_1**: @username_4 That's not a very useful definition of "cause". If you make it that broad, you're saying _anything_ can cause _anything_. Like I said before... it's a beautiful meta-physical theory. It's just not Earth Science.  
> **username_4**: @username_1 I agree that the word *cause* is not the best one to use here.  The question used *result in*, but I'm open to other suggestions.  It's just semantics, really.  Regardless of the formulation, I think understanding the principles of chaos *does* further our understanding of how nature works.  
> **username_5**: I love your bus example of Chaos Theory! I heard a similar explanation of it where a butterfly flies past a woman after just landing on a flower. The pollen causes the woman to sneeze, a man says "God Bless You" (or appropriate phrase). The man and woman end up talking more...marriage...kid... The kid turns out to be [insert dictator name such as Hitler, Stalin, etc.] all originated with a butterfly with pollen on its wings causing a woman to sneeze. Chaos Theory is an interesting topic. =>  
> **username_1**: 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?  
> **username_4**: @username_1 The *arbitrarily small* with regard to weather comes from the observation that even a numerical difference in a model initialisation (i.e. one bit difference) can result in an entirely different outcome in the long scale.  It is my understanding that indeed arbitrarily small changes in the initial value can result in arbitrarily large changes in the long term, in *any* chaotic system, including weather.  Is this a misrepresentation?  
> **username_1**: @username_4 I tried to edit that out (misrepresentation) but I took too long to realize my mistake, i.e. that I don't actually know myself. So, is there a reference wrt to weather (and not weather models)? That sensitivity you talk about in the models is cited as a flaw.  
> **username_4**: @username_1 It is my understanding that it follows directly from the observation that weather is a chaotic system (for which references are plentiful), and that *any* chaotic system shares this property.  I haven't heard before that this is a property in weather models and is considered a flaw compared to the actual weather.  The latter seems impossible to either verify or falsify.  
> **username_1**: @username_4 The problem with the _arbitrarily small differences in initial conditions leads to vastly different outcomes_ is that as the difference approaches zero you get a completely unpredictable system. Yet weather models are good for certain time scales--a day at least, right? To test this theory (and fix the models) scientists used Monte Carlo methods to randomly vary initial conditions. Instead of a uniform distribution of outcomes (every outcome is as likely as any other) they got a bell curve. The center of the curve is the prediction. This fits nicely with chaos theory strange attractors  
> **username_1**: @username_4 You give a lower bound of 1 bit. That's not arbitrarily small. Edward Lorenz states that the lower bound would be the accuracy with which we can measure observables. Again, not arbitrarily small. It's not nit picking. It's the difference between science and philosophy. It's the difference between anything can cause anything and a theory that furthers weather prediction. Would you consider changing "arbitrarily small" to "very small"? You could also quantify the changes in outcomes: an error in measuring _X_ doubles every _N_ days (or hours), for example. __That__ would be science.  
> **username_4**: @username_1 I have changed *arbitrarily* to *very*.  I don't know enough about the topic to be quantitative (and I think it's not needed to answer this question).  
> **username_1**: @username_4 The quantitative terms are absolutely necessary to the answer. In fact, they are the only thing of worth you could have added to the answer. Otherwise, you could have simply stopped after the link to the Wikipedia article "The butterfly is a colourful illustration of _Chaos Theory_" Since the rest of the answer just restates what's there. What's the accepted Lyapunov exponent for the phenomenon? Does a butterfly flap meet that threshold? If you're not an expert, perhaps you shouldn't have posted an answer.  
> **username_4**: @username_1 I do not agree that the question as stated requires a quantitative answer.  It did not ask if the result could occur 1 day/3 days/1 month later, it asked if it could occur *at all*.  Expertise is relative; I believe my answer is useful, but I would certainly welcome a more thorough, mathematically expressed, quantitative answer.  The same comment for the question itself: I do not think being quantitative is a necessary condition for a post (question or answer) to be scientifically sound.  
> **username_1**: @username_4 I agree that quantitative answers are not required in the general case. I'm saying that quantitative information in this particular answer would have turned it from pop-sci/philosophy/repeat-of-already-available-info into an expert level question.  
> **username_2**: This is a pretty interesting discussion, but I'm worried that it will get lost in the future when a moderator comes along and decides to cull the lengthy discussion. Maybe a better way to deal with the disagreements would be to ask more questions? I know I have a couple of good references for an answer to the how behaviour in models relates (or doesn't) to the real world, for instance.  

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### Answer by username_3 on 2014-04-30. Score: 14

[*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.

> **Comments:**
> **username_4**: 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.  
> **username_1**: This is a very good answer--succinct, informative, stays on topic. It really deserves to be number one and the accepted answer.  

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### Answer by username_1 on 2014-04-19. Score: 5

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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### Answer by username_5 on 2014-05-05. Score: 4

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/)


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### Answer by username_6 on 2014-04-18. Score: 1

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.

> **Comments:**
> **username_6**: Solution: ELIMINATE ALL BUTTERFLIES!  
> **username_6**: kidding, I love butterflies.  
> **username_8**: [That didn't work out so well for Homer Simpson.](http://deadhomersociety.files.wordpress.com/2013/10/tohv-11.jpg)  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.  
> **username_7**: Even the smallest motion? How about Brownian motion?  

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