# Does the butterfly effect apply in reality?

The problem seems to be treating the butterfly effect as if Lorenz was proposing a law of nature, when in fact it was only meant to raise certain questions, not necessarily answer them.

As I see it the butterfly effect is in essence similar to or in fact the same as cumulative error in a dynamic system. The thing is that in complex systems such as weather, cumulative error is not happening in only one place at one time, rather, an ongoing continuous process at an infinite number of places in the system.

This then becomes the straw that broke the camel's back problem, in that the cause of any specific event was not caused by an individual straw, but the effect of all the straws together, and so any effect of a butterfly can never be fully the cause of any effect later in time.

DaveC426913
Gold Member
As I see it the butterfly effect is in essence similar to or in fact the same as cumulative error in a dynamic system. The thing is that in complex systems such as weather, cumulative error is not happening in only one place at one time, rather, an ongoing continuous process at an infinite number of places in the system.

This then becomes the straw that broke the camel's back problem, in that the cause of any specific event was not caused by an individual straw, but the effect of all the straws together, and so any effect of a butterfly can never be fully the cause of any effect later in time.
It's more than cumulative error. A car with poorly-tuned steering will drift off course. That's cumulative.

On a bridge with no railings, a car that deviates from the bridge will fall in the drink. That's wide divergence from a course. That's what we're talking about.

I cannot prove whether a butterfly flapping it's wing has ever or will ever cause a major difference in weather. I'm pretty sure no one can. What I can prove however is that a slight change in initial conditions can cause a huge difference in outcome.

On October 31, 1998 I made a decision between an orange soda and a Mountain Dew. I chose the mountain Dew. As a result of the caffeine in that beverage I wasn't as sleepy as I would have been, so when I was invited to a Halloween party I decided to go. At that party I met the woman who later became my wife. The whole course of my life was irreversibly altered by the choice between orange soda and mountain dew.

This does not mean that every choice of beverage has drastic consequences or that drinking Mountain Dew will lead you to true love. It does mean that there are so many unknown variables in the world that the final outcome of any particular decision is unknowable.

It is entirely possible that the flapping of a butterflies wing could lead to a hurricane.

Certainly. A butterfly's wings cannot result in all the atmosphere leaving the planet. But it can result in a tornado.
I beg to differ.
Suppose that tornado kills the person who would otherwise have invented a super-weapon which would have protected us from the invading aliens who come to steal out atmosphere.

It's a stretch for sure but of the billions of butterfly wing-flaps how many cause a tornado. I would submit that for a given cause there is an inverse relationship between the magnitude of a given outcome and the probability of that outcome so that no outcome is impossible, but some are highly improbable.

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Pythagorean
Gold Member
DH:

are there any other well known systems in nature that have such discontinuities?

Also, I'm curious if there's any insight into quantum chaos from this indeterminate system?

Lastly, what do you think of this paper?
http://www.nature.com/nature/journal/v412/n6848/full/412712a0.html

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Claude Bile
Science Advisor
"Butterfly effect" is a poetic expression. One should not get too carried away with the poetic aspect of the expression to the detriment of the scientific content it is intended to convey. I can't help but think that people debating whether butterflies actually cause tornados (or some other variety of weather phenomenon) are missing the point somewhat.

Some points raised in this thread bear repeating. The "butterfly effect" was coined to describe the hyper-sensitivity of some categories of physical models with input parameters. Note that it is the models that were demonstrated to possess this behaviour, not the physical systems themselves, and this is what made the discovery remarkable. Hyper-sensitivity to initial conditions is a fundamental property of the model itself and is NOT due to random imperfections and unpredictable elements that the real-world throws up, i.e. even when parameters are known/computed to infinite precision, the hyper-sensitivity to initial conditions persists.

The remarkable thing in my eyes is that these principles extend to a massive variety of systems, from chaotic lasers, to weather, to the motion of planets through the solar system. That is why limiting discussion to butterflies and hurricanes is somewhat limiting in my view.

Claude.

It's a stretch for sure but of the billions of butterfly wing-flaps how many cause a tornado. I would submit that for a given cause there is an inverse relationship between the magnitude of a given outcome and the probability of that outcome so that no outcome is impossible, but some are highly improbable.
All the butterfly flaps cause a tornado, they even cause many tornado's.
If you would compare 2 worlds with the butterfly flap as the only difference and you look
at the weather after a few months, The weather will be completely different. Any place that had a tornado in the first world is very likely to not have one in the second (because tornado's are rare), so the single flap causes every weather phenomenon after few months. (The butterfly may need some more time to case an El Nino)
Larger inputs do not have a larger probability to cause something, they can just cause
something sooner.

This certainly is the case for weather models wich go completely out of sync after about two weeks for the smallest variation in their input. I don't see why this kind of amplification wouldn't work at smaller scales.
phenomena like turbulence and draining bath-tub vortices (wether caused by the coriolis force or not) can amplify very small causes to larger cooridinated movement of air or water)

The trouble with a fast moving thread, as this one was for a while, is that you can go away to formulate some ideas of something you want to say, and come back to find that it has moved on a long way – quite apart from the basic problem of trying to track everything that has been said. However, the moderator intervention that has taken place leaves me feeling that I cannot exactly be going to derail the thread, though I’m not sure if what I have to say is of any consequence to the discussion.

While I do understand that the original post was very specifically about the butterfly effect, which is clearly a point about weather systems, and DH has given us the precise provenance of that term, as others have pointed out, the term does refer to chaos theory, and according to the account that I read, the origins of chaos theory were not in modelling weather systems, but in population modelling. Weather system modelling is just one of the other fields to which chaos theory has subsequently been applied. Political voting patterns is another – apparently Al Gore invested a great deal of effort in the study of chaos theory.

In any case, the main point that I wanted to make, for those prepared to doubt chaos theory, is that, whereas with so many important theories in physics which we have no choice but to take on trust – its not so easy to build a particle accelerator in your attic – chaos theory is something you can try out for yourself with nothing more difficult to access than a computer spread sheet. Chaos theory is, essentially, just a mathematical formula, and not a particularly complicated one, though it is an iterative one, which simply means that one of the parameters is the previous iteration’s result. In the case of populations, each iteration is of course a new generation, and one of the parameters is the current population (or more accurately, the current population as a proportion of the population capacity of the environment). The origins, as I understand it, were two populations scientists with widely different views of population modelling. One was observing populations that, from a small start, would grow steadily, until they found an equilibrium that, provided external circumstances didn’t change, could be maintained pretty much indefinitely. The other was observing populations that would oscillate wildly, following repeated exponential explosions with near total collapses. The breakthrough came when these two models were shown to both be special cases of a more fundamental model, and they key change was the addition of the iterative element in the formula.

As a control engineer, the connection with the control algorithm known as ‘PID’ is quite obvious, and any control engineer of any experience knows well enough how tiny injudicious changes to the tuning parameters can turn a previously stable control system into a violently oscillating one. So for me, it is not so much of a stretch to conceive that the flap of a butterfly’s wing could be an earlier event in a sequence of which a tornado is a later event.

are there any other well known systems in nature that have such discontinuities?
Two real world examples, one natural, one man made.

1) Go to Switzerland in March, walk into the sowfields near the mountain sides. Start shouting and sooner or later you will trigger an avalance.

Does the ratio of the energy in your shout to the energy of the avalance compare with the ratio of the energy of a butterfly flap to the energy of a tornado?

2) Obtain a length of detcord and wire it to 40 kilos of Semtex. Supply an electrical signal from a battery.
Do this in a safe place not near Guantano Bay.

Does the ratio of the electrical energy to your det cord to the energy of the explosion compare with the ratio of the energy of a butterfly flap to the energy of a tornado?

Pythagorean
Gold Member
Two real world examples, one natural, one man made.

1) Go to Switzerland in March, walk into the sowfields near the mountain sides. Start shouting and sooner or later you will trigger an avalance.

Does the ratio of the energy in your shout to the energy of the avalance compare with the ratio of the energy of a butterfly flap to the energy of a tornado?

2) Obtain a length of detcord and wire it to 40 kilos of Semtex. Supply an electrical signal from a battery.
Do this in a safe place not near Guantano Bay.

Does the ratio of the electrical energy to your det cord to the energy of the explosion compare with the ratio of the energy of a butterfly flap to the energy of a tornado?
You seem to be talking about the butterfly effect in general. If so, that is not what I refer to. I was talking about DH's non-deterministic system.

D H
Staff Emeritus
Science Advisor
All the butterfly flaps cause a tornado, they even cause many tornado's.
This is wrong. First off, you are conflating sensitivity and causation. Secondly, you are stating this as as if it were fact. The fact is, we do not yet know the answer to the question raised by Lorentz way back in 1972. Meteorologists do not yet have the tools to even begin answering that question.

Regarding the imbroglio over Lorentz' question, Claude put it very nicely (emphasis mine),

"Butterfly effect" is a poetic expression. One should not get too carried away with the poetic aspect of the expression to the detriment of the scientific content it is intended to convey. I can't help but think that people debating whether butterflies actually cause tornados (or some other variety of weather phenomenon) are missing the point somewhat.
Once again, very nicely put. A lot of the moderation in this thread resulted from people taking Lorentz question far too seriously and being far too adamant in expressing their opinions.

While I do understand that the original post was very specifically about the butterfly effect, which is clearly a point about weather systems, and DH has given us the precise provenance of that term, as others have pointed out, the term does refer to chaos theory, and according to the account that I read, the origins of chaos theory were not in modelling weather systems, but in population modelling.
Robert May did most of his work in the early 1970s and published his seminal paper on the logistic map in 1976. Lorentz, however, preceded May by more than a decade. Modern chaos theory pretty much started with Lorentz.

If you dig deeper, you will find that neither Lorentz nor Mays can truly be called the "father of chaos theory". KAM theory and ergodicity theory were developed well before either Lorentz found that weather is chaotic and Mays found that populations can be.

D H
Staff Emeritus
Science Advisor
We're getting off-topic here, but it is my fault.

are there any other well known systems in nature that have such discontinuities?
Well, there's Painlevé conjecture, which has since been answered in the positive. Painlevé proved that the only singularities in the three body problem involve collisions. He raised the question whether non-collision singularities can arise in the n-body problem, with n>3. In response to this question, Von Zeipel quickly proved that singularities in the (Newtonian) n-body problem will arise only in the case of collisions or in the case of objects going off to infinity in finite time.

And yep, there are configurations of the Newtonian n-body problem that result in objects going off to infinity in finite time. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.146.2656&rep=rep1&type=pdf

Robert May did most of his work in the early 1970s and published his seminal paper on the logistic map in 1976. Lorentz, however, preceded May by more than a decade. Modern chaos theory pretty much started with Lorentz.

I confess that I had forgotten, but when I returned to my source I found that the author of the essay I had read is indeed Robert May. The populations scientists with the differing opinions of what drove population change he referred to were Charles Birch and John Nicholson. May does actually give quite a detailed account of the development of the science of ecology, under which population studies falls, and contained within his essay is the following statement:

‘Modern chaos theory actually began with a set of equations relating to weather forecasting, published in 1963… The equations were the work of the great meteorologist Edward Lorenz at the Massachusetts Institute of Technology.’​

Clearly that was something that didn’t lodge itself in my memory on first reading!

May also describes how he developed his ideas in conjunction with Jim Yorke, who had himself done work on the logistics map with Tien-Yien Li.

I think a few things have to be kept in mind when dealing with the butterfly effect in real world situations such as complex atmospheric phenomena:

In all complex dynamic systems such as the weather, any particular event will have a nearly infinite number of independent forces in play, each if you tracked back as far back as you wanted, could probably be tied to a small event such as a butterfly flapping it's wings, an acorn falling from a tree or a rock rolling down a hill, so a tornado occuring would be connected to an infinite number of butterfly effects, and it would be impossible to determine which particular butterfly effect caused the tornado. In fact I would state that the effects of all of them had to be in play for the tornado to spawn, and that no individual butterfly effect is in fact the ultimate cause of the tornado.

The guy who met his wife at a Halloween party could equally state that the reason he met her was caused by the fact that the store wasn't out of the soda that he ultimately claims casued him to meet her, that if the store had been out of the soda, he wouldn't have been presented with the choice and might possibly not have met his wife. Would he have gone to the Halloween party anyhow regardless of the soda he chose?

In a weather prediction model like Lorentz was using, variables would have been tied to things such as atmospheric pressure, wind speed, water vapor content, etc., and these variables would apply to large areas and volumes of atmosphere, not cubic centimeter resolution values, so there really isn't any representation in his model for the impact of antyhing anywhere near as small as a real life butterfly flapping his wings. That a value in his model with a difference of .00000001 may spawn a tornado but that value would be many orders of magnitude larger than the impact of a butterfly. So I would have to believe that Lorentz was never implying in reality that a butterfly would in fact have an impact in the weather.

I think the proof of the impact of the butterfly effect is limited to simple physics and mathematical models and computer models where infiinitely many things are not at play.

So I would have to believe that Lorentz was never implying in reality that a butterfly would in fact have an impact in the weather.
That's exactly my take on this. Just my opinion...