In a few recent discussions, I’ve gotten the old “a butterfly flaps its wings…” explanation. I think it’s another example of glib response replacing, say, concrete argumentation.
So the question is:
Can a butterfly’s wing flapping effect weather conditions locally or globally? I mean, the force would dissipate far too early to have any serious effect, right? And if I’m right, then who came up with this nonsense?
“As far as we know”, weather is completely unpredictable by any mathmatical means, nor is it possible to trace an hypothetical hurricane back to it’s roots; the hypothetical flapping of a butterflies wings. But in theory it is not totally impossible from a scientific standpoint, even though the idea has been touched upon by religious scholars and musicians alike for many millenia. The song Ripple by the Grateful Dead comes to mind every time I consider this theory.
What you must understand is that from a mathmatical standpoint it would presently be impossible to ever factor in the infinite number of elements that would contribute to such an equation, giving creedence to the idea that “everything affects everything”, my first major celestial conclusion developed while tripping on LSD. But what it would look like in a sofware model is a very complex fractal. One so complex that it would essentially be the mathmatical equation of all life and reasoning; basically, the most profound scientific find of all time. My theory is that the equation would be a simple “n”, the “n” of course standing for infinity, but could also stand for “nonsense.”
This is where the chaos theory comes in; The ultimate be all end all for the stout aethiest who finds it difficult to stop assigning a scientific theory to everything and putting their faith in a completely undefinable higher source…a God.
The idea behind chaos theory is that the effect could be global.
In practical terms, yes, the effect of the flap is dissipated right away. HOWEVER…
Complex systems like weather are controlled by many small factors that add up to one result (weather is an emergent system). Chaos theory would say that the factors that have some influence could be as small as the flapping of a butterfly’s wings (although this may be a bit of poetic license just to make a point).
Think of it this way. To predict the weather 5 minutes from now, you just need to look out the window. To predict the weather 1 day from now, you need to look at things like cloud type and temperature many miles upwind of your position. To predict weather 5 days from now, you need that information plus information from weather systems even further upwind, plus pressure systems across the continent, plus local lake effects, plus oceanic currents/tempatures, plus jet stream positions, plus…etc. etc. etc. The point is, the further out you want to predict, the more detailed information you need. At some point, even the smallest of factors has some input on the emergent system. Ever wonder why weather forecasts are limited to 5 days? Beyond that, there’s just too much involved to make any kind of accurate prediction.
So that little butterfly flaps its wings and moves/heats a small pocket of air. That pocket of air interacts with the countless other pockets of air which are connected 'round the world. The sum total of all those pockets of air result in what we call weather.
Odds are, no effect would result from the wing-flap, but chaos theory would say that some effect is possible.
That’s my impression anyway. I’m no expert on the subject.
I’ve never used Fluent, so I’m not sure what their limitations are, but a lot of the canned software makes simplifying assumptions that are incompatible with the kinds of non-linear equations used in issues like realistic weather modeling. However, it does bring up the main point of this class of equations.
Calculations display the “butterfly effect” if they are extremely sensitive to initial and/or boundary conditions. Whenever you run a simulation of some system of equations using Fluent or any other model, you have to specify an initial condition (the starting values) and boundary conditions (what happens at the edge of your simulated region). Some classes of equations are extremely sensitive to these values, so if you change the initial condition by a tiny amount, the end results differ widely. This is the butterfly effect: a small perturbation at some location will effect the entire system drastically. Non-linear dynamics is full of examples like this, and you can probably demonstrate this to yourself with a physical model like a multi-body pendulum without having to try to conceptualize world-wide weather.
Actually, the wing-flap always has an effect. In a chaotic system the slightest change in local initial conditions eventually percolates through the entire system, affecting its global state. You can’t really say that the wing flap caused the storm, though, anymore than anything else in the system did.
It’s really just a dramatic way of contrasting chaotic systems with non-chaotic systems. In non-chaotic systems small localized effects can be safely ignored because they will be swamped by the global behavior of the system. (For example, you don’t need to factor in the slight aerodynamic effect of each rivet in the skin of a rocket to calculate its trajectory.) In chaotic systems all local effects eventually become global.