Debunking the Butterfly Effect

[bascule]

Dr. Roger Pielke, head of the American Association of State Climatologists, debunks the Butterfly Effect:

 

http://climatesci.atmos.colostate.edu/?p=68

 

There is a popular notion that the “butterfly effect” describes a climate system that is exceptionally sensitive to very small perturbations. As just one example, a google search turned up the following description of it,

 

“In the arcane field of chaos theory, there is what scientists call “the butterfly effect,” the popular notion that when a butterfly flaps its wings in Asia the action may eventually alter the course of a tornado in Kansas.” (http://www.roanoke.com/editorials/commentary/wb/xp-32390).

 

Even the scientific community presents this perspective, e.g., see http://www.cmp.caltech.edu/~mcc/chaos_new/Lorenz.html, from which the following text is extracted,

 

“The ‘Butterfly Effect’, or more technically the “sensitive dependence on initial conditions”, is the essence of chaos……..The “Butterfly Effect” is often ascribed to Lorenz. In a paper in 1963 given to the New York Academy of Sciences he remarks: ‘One meteorologist remarked that if the theory were correct, one flap of a seagull’s wings would be enough to alter the course of the weather forever.’ By the time of his talk at the December 1972 meeting of the American Association for the Advancement of Science in Washington, D.C. the sea gull had evolved into the more poetic butterfly - the title of his talk was ‘Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?’ In the applet we also see a second incarnation of the Butterfly - the amazing geometric structure discovered by Lorenz in his numerical simulations of three very simple equations that now bear his name.”

 

The solution of the Lorenz equations from this informative website illustrates the “butterfly” looking field that results. Figure 6 from Tsonis and Elsner (1989) has a particularly clear illustration of the butterfly solution.

 

This second definition of the butterfly effect is the correct use of the term “butterfly effect.” However, the first usage of the “butterfly effect” in that “when a butterfly flaps its wings in Asia the action may eventually alter the course of a tornado in Kansas” is incorrect. The information from the butterfly is quickly lost on scales close to the size of the butterfly, as the atmosphere is a dissipative system such that only particularly significant powerful forcings, or small climate forcings near a climate transition (but certainly not as small as a butterfly’s flapping winds) can upscale (i.e., teleconnect) to the global scale. Indeed, if we accepted the first definition of the “butterfly effect”, everything that an individual human does on any scale (e.g., brushing your teeth) would be a climate forcing that would influence weather thousands of kilometers away. Of course, that is preposterous.

 

To communicate accurately in climate science, we need to make sure we properly present the significance of Lorenz’s seminal research. There certainly are thresholds (i.e., “tipping points”) that can result in sudden and large changes in climate regimes. This is a characteristic of chaotic nonlinear systems which we discuss for example, in

 

Pielke, R.A., 1998: Climate prediction as an initial value problem. Bull. Amer. Meteor. Soc., 79, 2743-2746.644.

 

Zeng, X., R.A. Pielke, and R. Eykholt, 1993: Chaos theory and its applications to the atmosphere. Bull. Amer. Meteor. Soc., 74, 631-644.

 

Pielke, R.A. and X. Zeng, 1994: Long-term variability of climate. J. Atmos. Sci., 51, 155-159.

 

Zeng., X. and R.A. Pielke, 1993: What does a low-dimensional weather attractor mean? Phys. Lett. A., 175, 299-304.

 

The consequences of this chaotic nonlinearity is the ocureence of the concept of critical thresholds which we discuss in Rial, J., R.A. Pielke Sr., M. Beniston, M. Claussen, J. Canadell, P. Cox, H. Held, N. de Noblet-Ducoudre, R. Prinn, J. Reynolds, and J.D. Salas, 2004: Nonlinearities, feedbacks and critical thresholds within the Earth’s climate system. Climatic Change, 65, 11-38.

 

The flap of a butterfly’s wings, however, while it seeks to capture the concept of the “sensitivity of the climate system to small perturbations of the initial conditions” overstates the true characteristic of the Earth’s climate system.

 

http://climatesci.atmos.colostate.edu/?p=70

 

In response to the variety of comments on the weblog of October 6, 2005 entitled “What is the Butterfly Effect”, I asked Associate Professor Richard Eykholt of the Department of Physics at Colorado State University to provide his perspective on the discussion. Professor Eykholt is an internationally respected expert on chaos and nonlinear dynamical systems. His website provides information on his excellent professional and academic credentials.

 

His response to my request (dated October 11, 2005) is reproduced, with his permission;

 

“Roger:

 

I think that you captured the key features and misconceptions pretty well. The butterfly effect refers to the exponential growth of any small perturbation. However, this exponential growth continues only so long as the disturbance remains very small compared to the size of the attractor. It then folds back onto the attractor. Unfortunately, most people miss this latter part and think that the small perturbation continues to grow until it is huge and has some large effect. The point of the effect is that it prevents us from making very detailed predictions at very small scales, but it does not have a significant effect at larger scales.

 

Richard Eykholt”

 

This summary should put to rest the misconception about the “butterfly effect.” In answer to the question presented in the original weblog on this subject, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?”, the answer is absolutely no.

[Kedas]

“Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas?”, the answer is absolutely no.

I don't think this is true but it's obvious that not all small changes lead to a big change.

(we don't have enough space for all those tornados)

 

Otherwise doesn't that mean that anything you do can't have a big impact on the future of the world since the 'main path' is defined by attractors.

With other words the end result and the path is predefined or if Einstein died in an accident at young age someone else would have replaced him.

[starbug1]

Is there even a "reliable" scientific model or equation that maps out "the Butterfly effect?" Has it ever been proven? To me it's just a flimsy and transient theory with a mysterious catch-phrase, "When a bufferfly flaps its wings in Asia, a series of tornadoes will result in Kansas." how cute. The reverse: it's me saying that I can go swimming in the Gulf, and 2 weeks later Japan is under water from a series of killer tsunamis.

 

What a ridiculous and irritating attribute to chaos theory. It's an arcane theory within another arcane theory.

 

But yes, hopefully, debunked. Imagine a world where this was reality, it would be damn windy all the time.

[insane_alien]

technically the "butterfly effect" is only an analogy for chaos theory. it doesn't mean that butterflys are the masters of the weather or anything like that.

[Kedas]

But yes' date=' hopefully, debunked. Imagine a world where this was reality, it would be damn windy all the time.[/quote']

 

It's not saying that a small change is the origin of this it is saying that a small change in the past could make a big difference in the future.

[Cap'n Refsmmat]

Achoo!

 

 

'Scuse me.... sorry for the rain.

[Nevermore]

Come now, Cap'n. We both know that a small change can cause a major event. If the wind had been even slightly different in the battle of long island, the US could very well not be a country today. And what about the finnicky nature of the earth? If the planet was ever so slightly positioned differently, the entire course of evolution would be different.

Now, I am in no way saying that it is always true, but a butterfly could alter a tornadoe on the other side of the earth.

For an example, watch this (edgy) animation:

http://www.flashplayer.com/animation/smokekills.html

 

Or this (better for little kids) one:

http://www.flashplayer.com/animation/safetyatwork.html

[starbug1]

It's not saying that a small change is the origin of this it is saying that a small change in the past could[/b'] make a big difference in the future.

 

Obviously. It was a pun. I read Jurassic Park.

 

it doesn't mean that butterflys are the masters of the weather or anything like that.

 

you never know.

[CanadaAotS]

I enjoyed that flash. lmao.

here's another along those lines:

http://www.albinoblacksheep.com/flash/end.php

[reverse]

]Uhhh..

is that what the butterfly effect is…

 

I thought it was a reference to the Bradbury short story “a sound of thunder”

In it, some time traveling T-Rex hunters totally change the future by stepping off the designated path and squashing a butterfly.

 

That is a very cool story… recommended reading.

 

I’m right into this concept that a small change can have a large effect.

So what type of reasoning do you guys use to decide the deviation caused by a small cause.

 

I know if I’m pointing a rifle for example,

just a single degree off target at the barrel - will mean a great error at the target..

and the error increases with respect to distance from the gun.

[starbug1]

I thought it was a reference to the Bradbury short story “a sound of thunder”

In it' date=' some time traveling T-Rex hunters totally change the future by stepping off the designated path and squashing a butterfly.[/quote']

 

There is a Simpsons epsiode that shows the effects of the Butterfly effect..controlled by Homer.

 

..a world where no donuts exist..only as rain. In the end Homer settles for a lizard-tongued family.

 

and of course the movie "the butterfly effect" with ashton kutcher.

[reverse]

Hey.... is there some new movie out based on "a sound of thunder"?

I did a google image search and all these film still and PS2 game covers came up.

 

First they sneak Zathura up on me ...now this.

[starbug1]

Yeah there is. You never heard about it or saw it in all but the big city theatres because it bombed at the box office. And from what I know, the director never made any great movies. I'm looking forward to seeing it nonetheless.

 

A Sound of Thunder

[MattC]

It seems like too much thought is being devoted to this matter. Clearly, it is highly unlikely (though what scientist would say that it is "impossible"?) that a butterfly will affect weather at all, but I have never, even as a child, taken the "butterfly effect" phrase literally. It seems clear to me that small things can have large impacts.

For instance, if someone with a flu coughs on me, and the number of virus bodies that enter my system is one short of the number that will lead to morbidity, some small change in air currents, as with a butterfly passing right between myself and the person with the flue, might affect the number of pathogens that I inhale. If I get sick because of the flapping of a butterfly's wings, that illness, and in a sense that butterfly, might cause much greater changes. What if my illness makes me not get a job I am applying for ... and what if my experience at that job would lead me to develop some technological advance that would affect the cleanliness of energy generation all over the world (at the least speeding things up; it's reasonable to assume that any given invention would tend to get invented even if the real inventors never came along, it just may take longer). That could have a significant impact on the climate.

The point is not that butterflys or birds or any individual small organisms might have power over large things, but that little things often have unexpected results.

[reverse]

how about considering this from a real life point of view.

 

Can you think of any small event or choice that you made that had a large knock on effect in your life.

 

like say ...your best friend is the person you happened to sit next to in class just because you got there a bit late because the cat decided to throw up on your clothes.

[JustStuit]

I met my best friend in 4th grade because we happened to sit together on a bus trip and we happened to be playing the same video game.

[Nevermore]

how about considering this from a real life point of view.

 

Can you think of any small event or choice that you made that had a large knock on effect in your life.

 

like say ...your best friend is the person you happened to sit next to in class just because you got there a bit late because the cat decided to throw up on your clothes.

I brought my cell phone to school, and it was stolen. In searching for it, the school made some interesting discoveries about the thief, and his brother was eventualy jailed by the FBI for drug dealing.

[starbug1]

how about considering this from a real life point of view.

 

Can you think of any small event or choice that you made that had a large knock on effect in your life.

 

like say ...your best friend is the person you happened to sit next to in class just because you got there a bit late because the cat decided to throw up on your clothes.

 

I met my best friend in 4th grade because we happened to sit together on a bus trip and we happened to be playing the same video game.

 

I have always been a firm believer in random action. I have always despised the "if it's your time' date=' it's your time" religious meme, the deja vu reality (to a much lesser extent), fate, destiny, and the trivial small "butterfly wings" of everyday life.

 

In the case of meeting someone who later becomes your best friend (because you sat next to him or you had the same video game), I think it's likely that you would have met sooner or later.

 

If I happen to drop a screw on a runway and I wonder if it will cause an airplane to blow out a tire, a plane is rotating and running over the screw. The tire blows and you assume it must have been solely because of the screw. This is the main fault of "the butterfly effect;" you can only assume in the brief action/reactions like the screw blowing the plane tire. There are reasons that this has no significance. For instance, where the screw punctured the tire there may have been a thin spot. This means, although we're not certain, that the screw sped up the inevitable. It could be that the plane travels no more than 100 feet and it blows unaided, thus having no connection to the screw whatsoever. Maybe 45 flights later, the tire finally blows. But these are necessarily short-lived and "confined" examples of the butterfly effect.

 

To be a real example, there must be a chain of events. Meeting a friend in class because you were late is not fate, and it is not an example of "the butterfly effect." To really notice the effects, a chain of events would have to occur.

 

In the "friend" example, it is just as likely that you showed up on time, but met him at lunch instead of in the classroom. Or instead of seeing each other playing a video games, you heard each other talking about it another day. Whether your friend made new ones during this time is possible too, but if you are today really great friends, then ruling by similar interests, that path would have automatically steered you, regardless of the other friends made.

 

Let's assume, now, that you got up on time for school and sat next to someone different in class. Meanwhile, your "friend" is going off and consorting with the wrong crowd, maybe even your enemies. This, in most cases, would mean that, although he might have been your friend for awhile, he is not your best friend today. The fact is that a friend who is also currently friends with your enemies will probably never be a "best" friend anyway. These sometime unexplainable occurances have a way of solving themselves, mostly because you have the power to choose and think ahead.

 

 

In the airplane example, it's out of your hands. But let's say, hypothetically, that this screw you dropped was, by a fluke, kicked up by the tire into the engine compartment and gets jammed where it won't affect the engine. then, while in flight, this screw jarrs lose and throws off a propellor, triggering an explosion which blows off the wing. As hysteria insues in the cabin, the plane goes down right into a nuclear power plant in the middle east, therby catalysing the deaths of millions. the arab country it landed in thinks it was under attack to obtain the most possible deaths with a single target. They fire their nukes back and the US, who, thinking they are being attacked without provokation, engage their missile. blah, blah. nuclear war and nuclear winter follow, and the world's species as we know it is in grave danger of extinction. It happens all because you dropped a damn screw at an airport that was going to take you on a spring break vacation to maui. Probable? not a chance.

 

Why don't we see this happening? Simply because it can't. There is no "butterfly effect." Stepping on a butterfly in prehistoric times will not cause the ceasation of the human species before it can originate; accidentally dropping a screw will not result in the end of the world; and meeting a friend a day late, no matter what the circumstances, will not result in the separation of the two forever.

 

What happens is the ability for events to correct themsevles. I'm not sure what the science is, but I know it was talked about in detail in Michael Crichton's book "Timeline." In the book, a group of people are transferred back in time via parallel universes. And despite what they think, no matter what they do there, history will not be altered. No outcome in the future can be affected by their presense, including their eventual existence.

 

Why does this happen? It's because a human life is insignificant. Think of every major scientific breakthrough. If Newton hadn't lived, someone else would have been there to forumlate the theory of gravity. In the case of Einstein, if his grandfather and grandmother never met his parents might not have met, and if they hadn't snogged one night in June, he might not have been born. It's a possibilty that we may never have come up with relativity, but you can't prove it. There is never enough information to prove the existance of this form of preprogrammed history, and there is never any proof that things might have been different because to put it short "what's done is done." There is no logic behind using deduction to map out all the variables in a series of events and take it back to something as small as dropping a screw. It can't be done.

 

Another example:

If your friend spends fifteen minutes looking for his car keys and you later find out he was killed in a car accident, you think if only he had remembered where he put his freaking keys, he might not be dead.

 

It doesn't work that way. What about the guy who ran into him, what if he hadn't run the red light because he was pissed off it took him fifteen minutes to get his burger king. And if the guy taking his order hadn't been late for work so he was backlogged with orders. And if his car would start, he wouldn't have been late for work. If he had gotten his starter fixed last week like he should have. If he hadn't been preoccupied with his mother who was in jail. If his mother hadn't sold weed. If she had better parents that were role models. And so on and so on.

 

There is absolutely no logic behind these events because they incorporate literally hundreds of events by literally millions of people. Everyone is always affecting each other in a convoluted web of events. There is no damn butterfly flapping its wings. Period.

 

I brought my cell phone to school, and it was stolen. In searching for it, the school made some interesting discoveries about the thief, and his brother was eventualy jailed by the FBI for drug dealing.

 

As well in this case, although it may look like an event you started, this man was going to jail anyway. same with the kids in my school. They had luckily (to my dissatisfaction) removed the pot from their lockers just before we had a random drug search by the drug dogs. the same people still do drugs, and they are no less precautios, and they will probably end up in jail right after they drop out of high school.

 

Can you think of any small event or choice that you made that had a large knock on effect in your life.

 

personal choices have the only true effect in your life because you know you made it happen. However, there is usually an exterior influence. We are all influenced by what we see and hear from others. so the event is your responsibility but the source is not, which is flooded in an unitelligible web of events.

[reverse]

Tell it to judge Judy.

 

By your reasoning …you could never blame any criminal for any action…

 

Judge Judy usually says something like “if it where not for your negligence none of this damage would have occurred”..

[starbug1]

HA! just giving the scenarios.

By your reasoning …you could never blame any criminal for any action…

 

It doesn't work that way.

 

Love the judge judy remark.

[reverse]

Ok…

 

How about tell it to Isaac Newton….

 

I don’t recall the rule of cause and effect that goes…

 

“For every reaction there are an infinitely incalculable amounts of action.”

 

Start screwing with this and you are opening the door to…to…creationism, for goodness sake!

[starbug1]

Ok…

 

How about tell it to Isaac Newton….

 

I don’t recall the rule of cause and effect that goes…

 

“For every reaction there are an infinitely incalculable amounts of action.”

 

I think yer a little mixed up. I'm not advocating 'infinitely incalculable amounts of action' date='" nor have I ever wanted to. I was furthering my explanation on how to [i']disprove[/i] and to show how preposterous the bufferfly effect is. Hence the general sarcasm and highly exaggerated story-line.

 

Start screwing with this and you are opening the door to…to…creationism, for goodness sake!

 

God no

[Severian]

It is fairly clear that not all systems are chaotic, but it is also fairly clear that some systems are. The determination of which is which is not very interesting.

[starbug1]

The determination of which is which is not very interesting.

 

 

Example?

[padren]

I've had a few thoughts on this subject lately, my general take is you can measure the volatility of a system, based on how many unlikely conditions need to be met in order for a small influence to have a large effect and to what degree of amplification.

 

I think its worth suspecting that our social system is very volatile, and if it wasn't for the very wide array of means by which the culture can adapt to change and compensate for any given change we'd have a lot of trouble getting by. (Of course we still have a lot more people quitting smoking than we have nuclear wars, so its not that volatile.)

 

A system like the oceans, would be very non-volatile, since basically every major effect (tsunamis etc) can be traced to other large causes, such as earthquakes, which have causes such as continental drift.

 

Systems like weather systems, while fairly complex and more volatile than the oceans (macroscopically) still don't appear to be so volatile that factors as small as butterflies are likely to have much effect.

 

So as far as volatility goes, social systems appear the most volatile (imo) and things like the oceans would be some of the least. Its not a measure of what is possible, but what is likely and how likely.

 

 

I think the butterfly effect pertaining to weather is more interesting because of the truth behind the fact we really don't know how to trace a weather system back very far - its volatile enough that it may as well have been a butterfly (no matter how unlikely) because we just can't track what will and will not turn into a storm to earlier than a couple of super-cells.