godless dave
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And that's where the term "butterfly effect" came from. At least one of the early chaos theorists had read the story.
Butterfly Effect...
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And that's where the term "butterfly effect" came from. At least one of the early chaos theorists had read the story.
Skeptical Greg
Agave Wine Connoisseur
Are you sure about that ?
the_smasher
Scholar
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The Simpsons had a Treehouse of Horror segment based on the story.
http://en.wikipedia.org/wiki/Treehouse_of_Horror_V#Time_and_Punishment
Sherman Bay
Master Poster
Another way of looking at the Butterfly Effect is to take a phenomenon that is highly unstable and try to predict what happens when a tiny amount of force is applied from a random direction.
For example, try to balance a pencil on the point. It can be done, but the slightest air movement or vibration of the table can cause a magnification of the force and a violent result compared to the force applied.
Next, imagine a contraption where the position of the falling pencil determines what action happens next, and the process is repeated. The slightest change in the first force results in a drastic change in the final outcome due to repetitions, each with a random factor.
For example, try to balance a pencil on the point. It can be done, but the slightest air movement or vibration of the table can cause a magnification of the force and a violent result compared to the force applied.
Next, imagine a contraption where the position of the falling pencil determines what action happens next, and the process is repeated. The slightest change in the first force results in a drastic change in the final outcome due to repetitions, each with a random factor.
JoeTheJuggler
Penultimate Amazing
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Of course Pratchett has his own take on it--the Quantum Weather Butterfly.
From the Wiki article:
Of course with an infinite edge to the wing, it's easy to see why the flapping of the wings of this critter could cause hurricanes on the other side of the world (er. . .Disc, that is).
Skeptical Greg
Agave Wine Connoisseur
Just throw hand fulls of paint at a canvas..
I'll tell you one thing Chaos Theory doesn't predict. It doesn't say that if you create a theme park based on dinosaurs, the dinosaurs will go crazy and kill all the people. But, that's what the annoying mathematician in Jurassic Park kept saying. (While reading the book, I kept hoping for him to be the next victim.)
And, just because the dinosaurs did get loose and started killing people is no indication that he was right!
-- Roger
And, just because the dinosaurs did get loose and started killing people is no indication that he was right!
-- Roger
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The decision to activate a neural pathway over a different one, which could come down to a minute physical event in the brain, could mean the difference between deciding to build a great pyramid, or just choking the chicken and falling asleep.
In the 'straw that breaks the camel's back' scenario, the straw can be further divided, down to the smallest sub-atomic particle. All large actions can be traced backwards, in a way that makes it look like all the action is in the tiny effect.
In the 'straw that breaks the camel's back' scenario, the straw can be further divided, down to the smallest sub-atomic particle. All large actions can be traced backwards, in a way that makes it look like all the action is in the tiny effect.
Unlike a Bull
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When I took differential equations there was an article in my book about chaos theory which had nothing to do with diff. eq., but broke up the monotony of class pretty well.
The article was something like this:
Imagine you have a machine, similar looking to a compass, with a needle and degrees marked. Every second the machine doubles the angle between the needle and the zero degree mark.
You set the needle to whatever angle you want, and let the machine run for 30 seconds (30 angle doublings). It wouldn't be too incredibly difficult to predict where the needle would be at the end of the trial.
Now, suppose that after you set the angle, but before you turn the machine on, that ******* meddling butterfly comes along with it's flapping wings creating turbulence and mucking everything up. Suppose it perturbs the needle by one billionth of a turn (360/1,000,000,000 degrees). Now we set the machine in motion. In the first turn the one billionth of a turn error becomes doubled, then quadrupled, etc, so that after 30 seconds the error is 2^30/1,000,000,000 or 1,073,741,824/1,000,000,000 which is greater than one turn. We would have no way of predicting where the needle would be.
The article was something like this:
Imagine you have a machine, similar looking to a compass, with a needle and degrees marked. Every second the machine doubles the angle between the needle and the zero degree mark.
You set the needle to whatever angle you want, and let the machine run for 30 seconds (30 angle doublings). It wouldn't be too incredibly difficult to predict where the needle would be at the end of the trial.
Now, suppose that after you set the angle, but before you turn the machine on, that ******* meddling butterfly comes along with it's flapping wings creating turbulence and mucking everything up. Suppose it perturbs the needle by one billionth of a turn (360/1,000,000,000 degrees). Now we set the machine in motion. In the first turn the one billionth of a turn error becomes doubled, then quadrupled, etc, so that after 30 seconds the error is 2^30/1,000,000,000 or 1,073,741,824/1,000,000,000 which is greater than one turn. We would have no way of predicting where the needle would be.