Entropy/Chaos and Butterfly theory
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Bwhaahahahahahahaha !!!! Good call..... Did you know butterflies die after a week ? Christian Secrets of a happy marriage #27: Never go to bed if you are mad at each other. It's more fun to stay up and fight.
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Bwhaahahahahahahaha !!!! Good call..... Did you know butterflies die after a week ? Christian Secrets of a happy marriage #27: Never go to bed if you are mad at each other. It's more fun to stay up and fight.
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yeah... and they lick their own feet. Many of them can't eat anything - they're just there to enjoy, reproduce, and fade to dust.
Now that's the way to live. David Wulff dwulff@battleaxesoftware.com
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Hmm, I didn't realize that there was a butterfly theory. I have always associated the butterfly effect with chaos theory. (Which is different from Entropy, but I come from a math background where chaos theory has a very specific meaning.) James Gleick wrote a good book on Chaos that is more for your non-science type person. http://www.amazon.com/exec/obidos/ASIN/0140092501/qid=997962072/sr=2-1/ref=aps\_sr\_b\_1\_1/002-2401946-7530437 Tim Smith Descartes Systems Sciences, Inc.
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Hmm, I didn't realize that there was a butterfly theory. I have always associated the butterfly effect with chaos theory. (Which is different from Entropy, but I come from a math background where chaos theory has a very specific meaning.) James Gleick wrote a good book on Chaos that is more for your non-science type person. http://www.amazon.com/exec/obidos/ASIN/0140092501/qid=997962072/sr=2-1/ref=aps\_sr\_b\_1\_1/002-2401946-7530437 Tim Smith Descartes Systems Sciences, Inc.
Another good book, more mathematical but still quite accessible, is Edward Lorenz's book The Essence of Chaos. (BTW, Lorenz, the father of chaos, writes in an appendix that he does not believe that a butterfly in Brazil causes thunderstorms in Texas. The connection between entropy and chaos is very complicated, subtle, and despite the fact that I have taught postgraduate courses on Nonlinear Dynamics and Chaos at university, I still don't understand it too well. Essentially, we believe that if you don't need to take quantum mechanics into account, the world behaves (at a small enough microscopic scale) as perfect Newtonian objects---billiard balls interacting via conservative forces. The problem here, as Poincaré pointed out in the 19th century, is that there is no "time's arrow" for any configuration of the system will eventually recur if you wait long enough no matter how nasty the system. This apparent contradiction between Hamiltonian dynamics and statistical mechanics is important enough to have been the subject of an article in Physics Today in August 1999 (Sorry, the article does not appear to be available online). There are also a whole host of connections and analogies between transitions to chaos and thermodynamic phase transitions which seem quite meaty but the essence of which still escape me. There's substance enough to spend a lifetime pondering the relations between thermodynamics and nonlinear dynamics. He was allying himself to science, for what was science but the absence of prejudice backed by the presence of money? --- Henry James, The Golden Bowl
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Another good book, more mathematical but still quite accessible, is Edward Lorenz's book The Essence of Chaos. (BTW, Lorenz, the father of chaos, writes in an appendix that he does not believe that a butterfly in Brazil causes thunderstorms in Texas. The connection between entropy and chaos is very complicated, subtle, and despite the fact that I have taught postgraduate courses on Nonlinear Dynamics and Chaos at university, I still don't understand it too well. Essentially, we believe that if you don't need to take quantum mechanics into account, the world behaves (at a small enough microscopic scale) as perfect Newtonian objects---billiard balls interacting via conservative forces. The problem here, as Poincaré pointed out in the 19th century, is that there is no "time's arrow" for any configuration of the system will eventually recur if you wait long enough no matter how nasty the system. This apparent contradiction between Hamiltonian dynamics and statistical mechanics is important enough to have been the subject of an article in Physics Today in August 1999 (Sorry, the article does not appear to be available online). There are also a whole host of connections and analogies between transitions to chaos and thermodynamic phase transitions which seem quite meaty but the essence of which still escape me. There's substance enough to spend a lifetime pondering the relations between thermodynamics and nonlinear dynamics. He was allying himself to science, for what was science but the absence of prejudice backed by the presence of money? --- Henry James, The Golden Bowl
As for the butterflies causing a storms, it seems that it's not as it causes it but more as it counts. The trick is that certain systems are living on the edge of chaos and even a smallest differences in their conditions can cause a tremendous differences in the long term. A weather system appears to be one of such systems. Having that, the smallest changes in the winds caused by butterlies will eventually result in storm someday, somewhere. But you can't point a single butterfly and blame it for particular storm - in fact every butterfly causes a storm, but we just can't tell when and where each one will occur. That uncertainity causes a long-term weather forecasts to be far less precise than we would want them to be.
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As for the butterflies causing a storms, it seems that it's not as it causes it but more as it counts. The trick is that certain systems are living on the edge of chaos and even a smallest differences in their conditions can cause a tremendous differences in the long term. A weather system appears to be one of such systems. Having that, the smallest changes in the winds caused by butterlies will eventually result in storm someday, somewhere. But you can't point a single butterfly and blame it for particular storm - in fact every butterfly causes a storm, but we just can't tell when and where each one will occur. That uncertainity causes a long-term weather forecasts to be far less precise than we would want them to be.
> ...But you can't point a single butterfly and blame it for > particular storm - in fact every butterfly causes a storm,... I'm pretty new to all this but isn't it just as likely that every butterfly might prevent a storm by tipping an unstable system the other way? Steve T.
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Seems like you are in the wrong forum. I think the questions about chaos will be best answered in the Visual Basic forum. And about the butterlies, you migh want to try in the C# forum, something that may or may not take off. Sorry guys, couldn't resist... ;)
lol! nice one... (2b || !2b)
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> ...But you can't point a single butterfly and blame it for > particular storm - in fact every butterfly causes a storm,... I'm pretty new to all this but isn't it just as likely that every butterfly might prevent a storm by tipping an unstable system the other way? Steve T.
No, that is why we call it "unstable" - it is much more likely to put it out of control than to put it back, something like a pencil standing on the sharp tip - very easy to disturb, but difficult to put in place. Weather is much the same - the winds "accumulate". They, well, blow. Less likely they will cancel themselfes and stop... Relating to butterfly - evey move of the wind will cause a huge change in the system if you only wait long enought. It may not be a large storm that will come, but there will always be a large storms caused by some starting conditions, be it a buttrlies. It's a "domino effect" - you put one brick and the whole thing gives...
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Now that's the way to live. David Wulff dwulff@battleaxesoftware.com
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> ...But you can't point a single butterfly and blame it for > particular storm - in fact every butterfly causes a storm,... I'm pretty new to all this but isn't it just as likely that every butterfly might prevent a storm by tipping an unstable system the other way? Steve T.
What Lorenz discovered during his computer simulations is that small changes can snowball and drastically change the results of non-linear systems over time. I find that some of the early weather graphs by Lorenz are most descriptive. Let us say this graph plotted the temperature. After a run of a large number of points, Lorenz needed to go back and re-run the program. When he ran it again using the output from the previous run, he found that over time the results diverged drastically. After research he discovered that in his output he printed 6 significant digits (lets say, I don't know the actual count). Well, internally, the computer was using 9 significant digits. The 3 missing digits caused these huge difference. That is a difference of less than 00.0001 percent. (I think we are talking after millions of computations) Thus, that spawned this notion that a butterfly (very insignificant) can change weather on a global scale. If I remember correctly, Lorenz rediscovered work by a man named Long. Tim Smith Descartes Systems Sciences, Inc.
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No, that is why we call it "unstable" - it is much more likely to put it out of control than to put it back, something like a pencil standing on the sharp tip - very easy to disturb, but difficult to put in place. Weather is much the same - the winds "accumulate". They, well, blow. Less likely they will cancel themselfes and stop... Relating to butterfly - evey move of the wind will cause a huge change in the system if you only wait long enought. It may not be a large storm that will come, but there will always be a large storms caused by some starting conditions, be it a buttrlies. It's a "domino effect" - you put one brick and the whole thing gives...
Okay - your balancing pencil analogy convinces me that a butterfly can't prevent a storm by flapping its wing - but it could still prevent a storm by NOT flapping a wing for a while. In fact if every flap of a butterfy's wing ultimately causes a storm (that otherwise would noy occur) then by simple predicate logic every time a butterfly comes to rest and stops flapping it must prevent a storm - in fact it must prevent as many storms as the number of wing-flaps that it rests for. I guess that's really more a matter of semantics ( does "not cause" == "prevent"? ) Based on absolutely nothing I feel that very, very few individual butterfly wing flaps ultimately result in storms that would not have happened anyway - and so by my own application of predicate logic very few butterfly's are entitled to feel smug about contributing to the well-being of some Florida coast resident in the distant future while taking a rest on a flower. :-O Steve T.
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What Lorenz discovered during his computer simulations is that small changes can snowball and drastically change the results of non-linear systems over time. I find that some of the early weather graphs by Lorenz are most descriptive. Let us say this graph plotted the temperature. After a run of a large number of points, Lorenz needed to go back and re-run the program. When he ran it again using the output from the previous run, he found that over time the results diverged drastically. After research he discovered that in his output he printed 6 significant digits (lets say, I don't know the actual count). Well, internally, the computer was using 9 significant digits. The 3 missing digits caused these huge difference. That is a difference of less than 00.0001 percent. (I think we are talking after millions of computations) Thus, that spawned this notion that a butterfly (very insignificant) can change weather on a global scale. If I remember correctly, Lorenz rediscovered work by a man named Long. Tim Smith Descartes Systems Sciences, Inc.
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Another good book, more mathematical but still quite accessible, is Edward Lorenz's book The Essence of Chaos. (BTW, Lorenz, the father of chaos, writes in an appendix that he does not believe that a butterfly in Brazil causes thunderstorms in Texas. The connection between entropy and chaos is very complicated, subtle, and despite the fact that I have taught postgraduate courses on Nonlinear Dynamics and Chaos at university, I still don't understand it too well. Essentially, we believe that if you don't need to take quantum mechanics into account, the world behaves (at a small enough microscopic scale) as perfect Newtonian objects---billiard balls interacting via conservative forces. The problem here, as Poincaré pointed out in the 19th century, is that there is no "time's arrow" for any configuration of the system will eventually recur if you wait long enough no matter how nasty the system. This apparent contradiction between Hamiltonian dynamics and statistical mechanics is important enough to have been the subject of an article in Physics Today in August 1999 (Sorry, the article does not appear to be available online). There are also a whole host of connections and analogies between transitions to chaos and thermodynamic phase transitions which seem quite meaty but the essence of which still escape me. There's substance enough to spend a lifetime pondering the relations between thermodynamics and nonlinear dynamics. He was allying himself to science, for what was science but the absence of prejudice backed by the presence of money? --- Henry James, The Golden Bowl