Not just the butterfly, but also myriad other processes contributed to determining the time and place and size, most of them much more significantly. Let's compare this to something a little simpler: an avalanche of snow. Someone might say that a small noise 'caused' the avalanche, in the sense that if the small noise had not happened just then, then the snow would not have started to slip just then.
But of course, the main causes of an avalanche are first the build-up of snow over a long period, and then the particular properties of snow which enable it both to bind to itself and also slip past itself, and finally the influence of the gravitational field of the Earth and the shape of the mountain and so on.
And if one particular noise had not set it off, then something else would have done, very likely, soon after. This illustration does not capture the more interesting dynamics of a chaotic system, but it serves at least to show that the word 'cause' is being used in a rather misleading way when someone says an avalanche is caused merely by a cough, or when they say a hurricane is caused merely by a butterfly.
Such a statement fails to mention almost all the actual causes! I guess the point of the butterfly analogy is this. A chaotic system such as Earth's atmosphere has an exponential sensitivity to initial conditions.
This sensitivity is owing to the combination of gravity, heating from the sun, the rotation of the Earth, the physics of gas and water, etc. The location, timing, and strength of a hurricane are influenced mainly by these large-scale facts, but owing to the sensitivity, the details of the location are also influenced by smaller things such as the shape of the landscape, and even the particular shapes of waves on the ocean, and things like that.
Even after one has taken into account the effects of landscape and waves, one would still find that even smaller things have a non-negligible impact on the time and location, right down to tiny things like air currents disturbed by butterflies.
However, I do not know what are the limits on such effects: see the note added below. With thanks to Niels Nielsen, I will add that it is entirely possible that the local damping that is present in air is enough to make butterflies in fact irrelevant to weather systems. In order to model a portion of atmosphere, one might use some simple model such as the one introduced by Edward Lorenz. He was simply interested in exploring what sorts of things can happen; he was not attempting a thorough model.
In that model one finds deterministic chaos with all its interesting features, especially the exponential sensitivity to initial conditions. In such a model even the effect of a butterfly will be inexorably amplified up and up. However, a more realistic model will involve further features, including local damping. In such a model I think there can be damping of very small perturbations and exponential growth of somewhat larger ones.
Having said all that, I am not working directly in this area so I hope an expert who is will chip in to confirm this last statement. The butterfly and hurricane is just a metaphor.
It should not be interpreted as: A butterfly can trigger a hurricane. It's more like: the weather dynamics are so sensitive that you can not ignore any small perturbation, since that a small eddie somewhere can change the general behavior.
That is the butterfly is a perturbation to the convection rate or temperature change and the hurricane one of the possible solutions, that will change due to the flap of the butterfly. The problem is that the butterfly effect has been poorly explained and poorly represented in a lot of popular sources. The cause-effect relationship is reversed. The flapping of the wings does not cause a hurricane, but omitting the flapping of the wings causes the mistake in the prediction.
The Chaos theory deals only with error propagation in mathematical calculations. It only wants to give an estimate of the possible difference between the estimated outcome and the actual outcome taking into account the complexity of the calculations and eventual defects by imprecisions in the measuring instrument or missing data.
The answer by niels nielsen marked as correct is NOT correct. I'm surprised to see how difficult it is to get such a simple concept. I'll try and rewrite my answer with other words:. The air moved by the wings of a butterfly is one of the billions of data to take into account by the calculations. By itself it does not causes the hurricane, but it contributes together with all the other data to the cause of the hurricane. It can be said that its contribution is so small that it is negligible.
But the above blunt oversimplyfied statement is as much stupid as the oversimplified statement in Jurassic park style that created the misconception in the beginning.
All the Chaos theory says is that if your calculation if far too complex you cannot afford to miss even that tiny data that gives such a small contribution to the picture because that small error may increase exponentially. It is not true that the flap of a butterfly's wings can give rise to a hurricane thousands of kilometers away. To his surprise, that tiny alteration drastically transformed the whole pattern his program produced, over two months of simulated weather. The unexpected result led Lorenz to a powerful insight about the way nature works: small changes can have large consequences.
Yet his insight turned into the founding principle of chaos theory, which expanded rapidly during the s and s into fields as diverse as meteorology, geology, and biology. That the tiny change in his simulation mattered so much showed, by extension, that the imprecision inherent in any human measurement could become magnified into wildly incorrect forecasts. After Lorenz, we came to see that determinism might give you short-term predictability, but in the long run, things could be unpredictable.
After the war, he earned a doctorate in meteorology at MIT and largely stayed at the Institute until his death in That approach treated the atmosphere as one large system to be analyzed using the equations of fluid mechanics. Into the s, however, dynamic meteorology did not produce reliable forecasts. A less scientifically sophisticated alternative called synoptic forecasting, which analyzed the weather by studying atmospheric structures such as high- and low-pressure systems, produced better results.
Lorenz and others began experimenting with statistical forecasting, which relied on computers to develop forecasting models by processing observational data on such things as temperature, pressure, and wind.
By the late s, he was using a computer to run complex simulations of weather models that he used to evaluate statistical forecasting techniques. Some of his simulations, however, were too regular to be realistic; they yielded periodic patterns, or precisely repeating sequences.
Lorenz realized that sensitivity to initial conditions is what causes nonperiodic behavior; the more a system has the capacity to vary, the less likely it is to produce a repeating sequence. This sensitivity makes weather very difficult to forecast far in advance.
Confirming this intuition was a set of equations, using just three variables to represent the movement of a heated gas in a box, that Lorenz employed in his landmark paper. Lorenz realized that if such a simple system was so sensitive to initial conditions, he had discovered something fundamental. If a group of lions has a net gain of 10 members a year, that increase in population size can be plotted on a graph as a straight line. A group of mice that doubles annually, on the other hand, has a nonlinear growth pattern; on a graph, the population size will curve upward.
After a decade, the difference between a group that started with 22 mice and one that started with 20 mice will have ballooned to more than 2, Given that type of growth pattern, the real-life pressures on species—normal death rates, epidemics, limited resources—will often cause their population sizes to rise and fall chaotically.
While not all nonlinear systems are chaotic, all chaotic systems are nonlinear, as Lorenz observed. Yet chaos is not randomness. An estimation of the temperature that is off by just a fraction of a degree-Celsius leads to a cascade of errors later, making predictions that look out beyond a few days, but less than a few weeks, particularly challenging.
However, "the changes that make a difference are far bigger than a butterfly flapping its wings," Orrell said. People started applying chaos theory to a lot of systems and saying, 'Well, this property is sensitive to initial conditions, so we can't make accurate predictions.
In fact, according to Orrell, only in greatly simplified models of chaos like the strange attractor do microscopic changes have huge consequences, escalating and ultimately causing the attractor to diverge from the path it otherwise would have taken. More complex computer models like those used by meteorologists are much more robust.
As Orrell and a team of several other mathematicians demonstrated in , inputting butterfly-flapping-scale disturbances into these weather models don't cause the outcomes of the models to diverge.
If other factors in the weather system, such as warm Atlantic Ocean temperatures, high humidity and westerly winds with low wind shear, are joining forces to drive the formation of a hurricane , the flap of a wing, or lack thereof, won't stop them.
And the idea that a wing flap really could have an exponentially increasing effect doesn't make much physical sense, anyway, Orrell said. In short, butterflies can't muster up storms. If the butterfly effect isn't real, why, then, can't we humans accurately predict the weather more than a few days in advance?
It turns out that the answer to that question is controversial. Based on his research, Orrell believes errors in computer models themselves — for example, an oversimplification of the way atmospheric pressure and humidity interact — affect the outcome of weather systems much more drastically than do small perturbations.
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