1271:"Why do meteorologists have such a hard time in foreseeing the weather with a reasonable degree of precision? Why do showers and storms seem to occur at random, so that many people find it absolutely natural to pray for rain or good weather while they would praying for an eclipse utterly ridiculous? We see that great perturbations generally occur in regions where the atmosphere is unstable. Meteorologists are well aware of the instability of the equilibrium and that somewhere there will be a hurricane, but where? They cannot tell, because a tenth of a degree more or less at any point will determine a hurricane here instead of there, and there will be devastations in areas that would have been spared. If one had known this tenth of a degree one could have foreseen the event, but observations were neither sufficiently frequent nor sufficiently precise, and for this reason everything seems to be due to the intervention of hazard. "
1268:“A very small unknown cause determines a considerable effect which we cannot understand. We therefore say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. but even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”
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causing a drop to fall off that would otherwise stick to it), and all these effects cascading _MIGHT_ just be the difference in a storm emerging or no storm emerging. Even though the butterfly wing is small and it's effect seems ignorable, in our reality the effect is almost infinitely complex and therefore unpredictable. But I think it's also important to notice that the wing moving is just part of the same reality in which a storm or no storm will emerge. The connection (or lack thereof) is more a matter of human interpretation or synchronicity.--
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highly simplified, and in particular do not adequately account for viscous effects. One can debate the strength of these damping effects, but they have to be mentioned, and clearly it is not safe to conclude from Lorenz's results with a toy model that the atmospheric system is highly sensitive to initial condition (I agree with JFB80 that this is where the hand-waving has traditionally come in). I have tried again to reword this sentence, but
Wolfram's objection is reasonable and should be noted.
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it to the other side of the earth? How long until one of those atoms is likely to be found in a randomly chosen cubic meter on the other side of the earth? Or to pose a similar question in a more cute form, when a baby is born on one side of the world and starts breathing, how long until a randomly chosen person on the other side of the world inhales an atom that the baby has previously exhaled?
92:. The error grow exponentially, but it still remains inside the same attractor. And in fact the concept of butterfly effect came from Lorentz who discovered attractors where this was possible. Before him there were no "strange attractors", and attractors were either cycles or pointed attractors. And the error would not grow exponentially.
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Which leads one to wonder, what is the speed of atmosphere transport/mix/diffusion (since that may be a limiting factor in substantial influence between one place and another)? Taking for example a random cubic meter of air on one side of the world, how long until one atom (out of about 10^20?) makes
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Wolfram is making a basic error, which shouldn't be in the article. I'm not clear why exactly you think this point is so fundamental. Viscous effects aren't in the Lorenz equations because they are irrelevant. Their addition in the real atmosphere makes no difference. I've run real GCMs, with viscous
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I've clumsily tried to clean up that paragraph. I'm trying to convey the sense that one set of initial conditions leads to one set of events, and another set of initial conditions (which differs only by the flap of a butterfly's wings) leads to another very different set of events; and that it's not
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You're thinking about it classically. Lorenz's simulation had changes of less 0.0001 degree of temperature causing the pattern of weather over the entire system to change. The effects of a butterfly flapping are damped out, but in the process it changes the local system some, which cascade over into
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Absolutely. Separating (or even deleting) the popular media references would be a great improvement, because the text is completely unbalanced, with around a dozen paragraphs on popular media, mostly focusing on time travel, versus about three on the core content. This detracts from the article as
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The
Butterfly Effect as described doesn't occur in the real world because air is a real gas possessing, among other things, viscosity. Viscosity causes disturbances to decay and disappear with time. The vorticity generated by the flapping of a butterfly's wings is damped out by viscosity and cannot
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Knowledge is not bound by limits of space that limit published encyclopedia articles. Rather than waste time on edit wars over "proper weight", the
Project is more rapidly advanced by collaborative editing with a spirit of generosity and openness to seeing as much material presented as possible. If
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I support
Sucnidea. You dont answer the point about the approximate nature of the Lorenz equations. Are they not based on a crude truncation of a Fourier series? If you do that sort of thing of course you will have sensitivity to initial conditions. Concerning viscosity, if you neglect it then you
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Exactly! Even though momentum will carry the movement forward, it is so infinitively smaller than the other natural forces which works all the time. The very reason to why the our planet keeps itself in a order so complex as this is because there are natural systems which maintains order. Also a
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The new section does not disparage classical physics or indicate that the butterfly effect is not applicable or important in classical physics. If editors believe classical physics is deserving of more attention than it is currently receiving, they are welcome to improve the article by increasing
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The section on semiclassical and quantum physics is a small proportion of the overall article, and better supported with reliable sources than the article as a whole. It is also clear that there is very little debate about the validity of the sources being used to support the relationship between
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An insignificant effect in your example might be a particular fish swimming in one direction for a moment rather than another. Conceivably through a long chain of events that could cause the fish population as a whole to increase or decrease one way or another. If such a chain (not a specific one,
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I may be wrong and don't really know where to find an answer to this question. The butterfly effect is listed in the dictionary as "a chaotic effect created by something seemingly insignificant, the phenomenon whereby a small change in one part of a complex system can have a large effect somewhere
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I agree 100%. I was baffled when I saw that example. A much better example would be the Plinko game from The Price Is Right: if you drop the Plinko chip from a specific and exact spot 5 times, it could end up in a different compartment every time (because the starting location varied by about the
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Wolfram is raising a basic point here which needs to be acknowledged in this page. As it currently reads, the page seems to imply that sensitivity to initial conditions in the Lorenz system is evidence for similar sensitivity in the atmosphere. But as
Wolfram points out, the Lorenz equations are
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on slight differences in initial position." .... This explanation only works if the initial conditions of the ball is the entire world. But there are also the valleys and the laws of nature, so the formulation "fully depending" is false. The butterfly does not cause the storm; the butterfly plus
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The basic error in this page is that sensitivity in the Lorenz equations appears to imply similar sensitivity in the atmospheric system. Wolfram's point stands. The grounds are that (a) viscosity is not properly accounted for, and (b) viscosity will have a damping influence. So you can't assume
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Indeed. My understanding is that the flap of a butterflies wings could well (and often does) cause a hurricane, but it can and does also, with equal probability prevent a hurricane. So more butterflies, or more airplanes doesn't mean we should expect more hurricanes in future, just at different
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No no no! The butterfly effect is not that a clap of butterfly wings _will always cause_ a storm. It's just that the very small thing (movement of wing) will cause some other things (air will move), which will cause a bunch of other things (more air will move, a flower leaf might move a little,
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Agreed. There are enough movie or TV plotlines that center on the BFly Effect (or some version of it) that it might almost constitute a separate genre, similar to the "Zombie" movie category. Plenty of examples listed in the Wiki article now, but there are many others, including
Twilight Zone
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sensitivity to initial conditions in the atmosphere unless these viscosity terms are fully taken into account, and are shown to be negligible. I have reworded the sentence to correct a typo but have omitted the phrase 'without grounds' since he does explain his reasoning in his book (cited).
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Riddle me this: if
Knowledge articles cannot be used as sources to support content, how can the absence of support in a Knowledge article be used to justify removal of content, especially when inclusion of that material is supported with citations of sources that meet Knowledge standards for
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The explanation is wrong. Sensitive dependence from initial condition does NOT refer to the fact that small changes in the starting condition will lead you to different attractors. But that with
Chaotic systems the system is globally stable but locally unpredictable. In other words, a slight
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This article doesn't seem to really explain the nature of the
Butterfly effect as it is understood in nonlinear dynamics. It looks as if the colloquial misconception is just being reproduced. The Butterfly effect refers to how perturbations which are small relative to the attractor grow
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It's an inappropriate illustration of the chaos idea. A hurricane has a huge vorticity which cannot be created by any number of butterflies because wing flapping does not create such vorticity. Atmospheric vorticity is created thermodynamically by the sun's rays - isn't that so Prof.
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you feel one POV is being represented by too many citations, the solution is to do your research to see if there are other peer reviewed sources representing your preferred POV that have not been included. Seek to bring balance to the article by adding material, not deleting it.
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The example in the intro of a ball at the crest of a hill does not exhibit sensitive dependence on initial conditions in the sense that the term is usually used in the dynamical systems literature. The example should be removed and replaced by an example of a chaotic system.
1030:, this paragraph has a flesh-kincaid grade level is 16.5. Shouldn't this be written at a more understandable level? I was trying to reference this article as a definition of the butterfly effect, but I think it's written at too high a grade level and should be simplified.
1069:, where the attractor is in figure-8 pattern (not quite the Lorenz attractor illustrated), which coincidentally describes a "butterfly effect". If someone is in a position to check the reference, perhaps it is worth a mention. That's Stabilité structurelle et morphogenèse,
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I agree, the actual bulk of this article needs citations if I am to be convinced that choas theory is really about small changes becoming uncontrollable. My understanding has been that it is small ERRORS that make things impossible to predict after an amount of time.
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a butterfly causing the tornado. This is an important point because there are many see also links linke domino effect / cascade / etc which could lead people to make the popular mistake that the flapping wing air is "amplified" through the system into a tornado.
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It's a metaphor, you dodo brain. It's hyperbole and a few other choice things as well. It's certainly not meant to be taken as a concrete statement of fact. Just because chaos theory has latched onto it as a convenient example doesn't mean it is scientific fact.
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I’ve addressed the issues raised above by adding a section on the butterfly effect in semiclassical and quantum physics, and by including quotes demonstrating that the citations are actually discussing the butterfly effect rather than merely including buzz
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And assuming that most natural air transport mechanisms are less than 100 mph average, it seems like the current existence of air travel may be perhaps modifying the answers to the above questions (despite being such a small fraction of the atmosphere)?
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Gleick does say that the shape of the Lorenz attractor resembles a butterfly's wings, but he does not suggest any connection with the term "butterfly effect". Lorenz's original example used a seagull, not a butterfly, so any connection seems unlikely.
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inherent to the butterfly effect arises from the vast potentiality in the whole system observed, i.e. the immense amount of possible intermediary states between start state and end state. Hence, from the perspective of potentiality, the systems are
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I don't believe this. Not necessarily that he didn't say it, but that its true. Viscosity simply doesn't remove these perturbations. Oh course, if
Wolfram has a careful mathematical proof then I'll revise my opinion, but I bet its just hand-waving
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It is generally considered bad form to remove sourced material whose relevance is established through citations without justifying such removal on the talk page. "I don't like it" is not justification. "I don't think it is relevant" is not
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specific places and times. Possibly even more or less generally if climate, as distinct from weather, is chaotic, but we wouldn't be able to say whether to expect each flap to cause more hurricanes, less, or not change the frequency of them.
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The introduction implies the butterfly is exclusive to nonlinear dynamics, then the example is given of a ball placed on top of a hill. I'm thinking of the "hill" z=C-x^2-y^2, which gives a linear dynamical system. 22:55, 7 May 2008 (UTC)
966:, May 16, 1903: "Lord Kelvin has been credited with the statement that the fluttering of a butterfly's wing sets up vibrations that shake the universe." Unfortunately I have not been able to find the source of Serviss' paraphrased quote.
436:'s theorem that in a perfect fluid vorticity can neither be created or destroyed? (by butterflies also) In a real fluid it is generated thermodynamically. The butterfly could alter the flow pattern but vorticity remains constant.
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notes that, while sensitivity to initial conditions is certainly a feature of some mathematical equations, perturbations of the sort produced by the flapping of a butterfly's wings will tend to dissipate due to the effect of
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It is not irrelevant because conservation of vorticity (or circulation) was sufficiently accurate to be used in an early computer method of numerical Weather Forecasting used for predicting hurricanes(by von Neumann etc. See
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If a butterfly flapping it's wings could influence weather patterns then with all the planes flying (propellor and jet propulsion) we would constantly live in a hurricane unlike any before. Sounds like GLOBAL WARMING to me.
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It would add to the article if it explained when the expression "Butterfly effect" was first used. Bradbury created the metaphor, Lorenz used it... but who first referred to critical dependence as the 'butterfly effect'?
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Basically, it looks to me like the page is simply putting forth the Jurassic Park explanation which is incorrect; a butterfly can beat it's wings in Peking all it likes and the weather in New York won't be any different.
1659:"For example, a ball placed at the crest of a hill may roll into any surrounding valley depending on, among other things, slight differences in its initial position."...this is a very poor example. JohnInLongmont
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At root this article is about the nature of the physical universe, all matter and energy interactions etc. But in the popular mind it tends to be associated with global weather, and the atmosphere in particular.
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As it is, this article is meaningless to non-experts in chaos theory. Example, "The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos
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opinions (as an expert in computational mathematics, rather than as a physicist) should be in the article unless implausible and contradicted by reliable sources. I say this even though he's often wrong. —
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But you dont give a proof, you just make an assertion. Are you not hand-waving too? What was stated was a point which needs proper consideration. Can you quote any work done to establish your statement?
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exponentially before being damped out by the overall behavior of the system. It's this kind of response which makes it impossible to make long-term predictions based upon the local behavior of a system.
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showed how the conservation law must be modified in real fluids, the modification depending on thermodynamic factors (solar radiation)as I said. This is a difficult subject and it needs careful thought.
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which nobody has spotted, which leads to a notion that the laws of nature are breached. I mean, dice or the shuffling of poker cards are much more commonplace examples of exactly the same phenomenon.
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affect the weather anywhere else on the planet. The disturbance caused by a jet plane's passage is damped out and the air mass through which it just flew returns to its original quiescent state. --
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According to this discussion you cannot neglect viscosity (see comment from JFB80), and if you have a reliable source which contradicts Wolfram then you can add that (see comment from EastTN).
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have a perfect fluid in which circulation is conserved by Kelvin's theorem and there is no way in which it can be generated by any number of butterflies. Certainly not for a tornado in Brazil.
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Neutrality requires that the article should fairly represent all significant viewpoints that have been published by a reliable source, and should do so in proportion to the prominence of each.
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Hello all, I am not a usual participant in editing Knowledge, but I thought I'd help citing the claim that Poincaré did in fact foresee the relation which Lorenz proved in the 60s.
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its coverage, as long as they support the added coverage with reliable sources. Should there be more complete coverage of the butterfly effect in classical physics? Absolutely.
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else". Is this like a one or two degree temperature drop causing fish population to decrease? I suppose temp. drop is a significant effect, so what would be considered insig.?
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The threshold question would seem to be "can we find a reliable source that says 'Wolfram is making a basic error'?" If so, it's easy - the text can say "The physicist
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I find that the butterfly effect is distinct from randomness; but by using dice or cards, you are implying that it relies on the existence of a non deterministic system.
670:, that doesn't mean that the author believes there is a connection. One would have to read the articles to determine whether the authors just put in popular buzz-words.
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The article states that using a butterfly as an example of the effect first appeared in Bradbury's short story. However, I've found an earlier use of it from 1903.
1328:{{Cite book |last=Wolfram|first=Stephen |title=A New Kind of Science |page=998 |location= |publisher=Wolfram Media |year=2002 |isbn=978-1579550080 }}</ref: -->
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Yeah, great idea. Lets fill the article with stuff we know is crap. That'll really help our readers, eh? Follow All Rules and remember: this is a bureaucracy
1205:, we need to understand what randomness truly is. And nobody does understand that. Randomness is, in fact, one of the toughest phenomena of all to model; cf.
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but in general) were likely to happen, then we would say the fish population would be chaotic and it would be impossible to predict how it would develop.
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You're not reading what I'm writing. And I don't think you understand what you're talking about. Simply repeating that viscosity-is-damping goes nowhere
988:, published the same year as Bradbury's story (1952), described a catastrophe initiated by the destruction of a wasp's nest. I am pleased to hear of the
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Wrong again. "I don't think it is relevant" is one of the best justifications for removal. In fact, in this case, it clearly isn't relevant. —
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everything around it (movement + state) plus the laws of nature does. The butterfly does not cause the storm - the effect only applies to
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I hate to interrupt your type up, but I'm very confused on this subject and you sound like you know what's going on.cold you help me
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effects included, and you get exactly what you expect from Lorentz: even the tiniest perturbations amplify. As they obviously must
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the larger system until it changes the whole system. Even classically, you can't damp out something without changing yourself.--
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You're often wrong, also.... Even if what he says is wrong, it's still an expert opinion, and could be mentioned as such. —
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1157:) 02:08, 22 July 2012 (UTC) At worst, the entire fascination with the unseeming "butterfly effect" relies on rampant
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Yup, I'm gonna split these. Whole section needs nuked from orbit, but there's less drama involved in splitting it.
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1209:. In reply to your question: Nothing in the butterfly effect, dice or cards are displays of perfect randomness.
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My understanding from this discussion is that we should keep the Wolfram remark, so I have put it back in.
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very simple, in fact they are quite the opposite. The essence of this argument could be important to add.
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effecting local conditions, but also non-local conditions that are then amplified through
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episodes (e.g., "Back There") and Star Trek episodes like "City on the Edge of Forever."
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I disagree, I think it's a fine example, especially for the layman. - Benjamin Franklin
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On second thought, that's actually more of an example of chaos....But it still works.--
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be in the lead, no matter how well-referenced it is (and I haven't checked yet). —
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Why the edit war removing sourced material? (butterfly effect in quantum mechanics)
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Memory is a bit dim after 38 years, but I'm fairly sure the term was alluded to in
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a whole. This is a significant topic and deserves proper encyclopedic treatment.
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is being overlooked here. Hypothetically, the butterfly flapping its wings is not
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reason to suspect that this is no mere rock we are sitting on.... --
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Henri Poincaré Prediction on Metereology's relation w/ Chaos Theory
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by George Woodward Warder quotes Prof. Garrett P. Serviss in the
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weight over classical physics, and the comment in the lead about
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Even if a number of authors use the butterfly effect in their
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graph being shaped like a butterfly's wings (see diagram).
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Lorentz Attractor graph is shaped like a Butterfly's Wings
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Air isn't a perfect fluid, so that theorem is irrelevant
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the butterfly effect and semiclassical/quantum physics.
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your's thankfully (
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Non-local effects of the Butterfly flapping its wings
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text based on original research, we're talking about
1233:I object to this formulation. To use the concepts
418:Wrong; you're using "creation" in the wrong sense
760:still seems inappropriate, but now plausible. —
1832:How many types of quantum butterfly are there?
1700:The name of the effect is also derived from the
1028:http://www.editcentral.com/gwt1/EditCentral.html
752:New section tagged as giving quantum physics an
655:effects. That doesn't suggest relevance to the
1026:The opening paragraph needs work. According to
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121:Any support for making this a separate article?
1640:'s most important aspect. - Benjamin Franklin
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1632:in a chain of cause-and-effect events.
1022:Opening Paragraph at high reading level
543:width of a hair--or less--each time).--
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1274:Poincaré Science et méthode 1903
959:The Universe a Vast Electric Organism
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900:Butterfly Effect in the Real World
117:Butterfly Effect and Popular Media
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952:Origin of the Butterfly Imagery
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1823:18:51, 17 July 2014 (UTC)
1783:'s most important aspect.
1548:20:49, 7 March 2014 (UTC)
1534:22:16, 4 March 2014 (UTC)
1519:16:36, 4 March 2014 (UTC)
1219:19:10, 23 July 2012 (UTC)
1189:02:55, 22 July 2012 (UTC)
1171:02:16, 22 July 2012 (UTC)
1100:09:30, 3 April 2011 (UTC)
947:15:22, 9 March 2010 (UTC)
537:04:15, 3 March 2009 (UTC)
304:16:30, 17 June 2009 (UTC)
186:15:21, 21 July 2008 (UTC)
1795:12:53, 17 May 2014 (UTC)
1736:13:12, 18 May 2014 (UTC)
1720:11:43, 17 May 2014 (UTC)
1690:11:44, 17 May 2014 (UTC)
1675:16:10, 15 May 2014 (UTC)
1650:11:51, 17 May 2014 (UTC)
1278:I really hope I helped!
1015:) 15:47, October 7, 2010
931:23:42, 9 July 2010 (UTC)
651:may produce macroscopic
643:. Unless I misread it,
568:18:54, 2 June 2009 (UTC)
553:18:51, 2 June 2009 (UTC)
498:19:06, 14 May 2011 (UTC)
474:18:20, 13 May 2011 (UTC)
460:16:44, 13 May 2011 (UTC)
446:16:29, 13 May 2011 (UTC)
428:19:10, 12 May 2011 (UTC)
414:18:18, 12 May 2011 (UTC)
398:) 15:47, October 7, 2010
371:13:12, 23 May 2010 (UTC)
341:13:12, 23 May 2010 (UTC)
168:04:16, 29 May 2008 (UTC)
861:WP:Scientific standards
1706:<ref)Gleick, James
1141:in initial conditions
843:
789:
1694:
1067:butterfly catastrophe
842:
788:
666:for works related to
237:Explanation Incorrect
42:of past discussions.
18:Talk:Butterfly effect
1785:- Benjamin Franklin
1761:non-local conditions
1571:William M. Connolley
1552:Grumble. Wolfram's
1526:William M. Connolley
1431:William M. Connolley
1388:William M. Connolley
1336:William M. Connolley
1201:In order to discuss
466:William M. Connolley
420:William M. Connolley
1777:Interconnectedness
1634:Interconnectedness
1086:Catastrophe_theory
432:Have you heard of
210:Intro inconsistent
194:is this true?....(
83:The image is wrong
1850:
1838:comment added by
1702:Lorentz attractor
1665:comment added by
1293:comment added by
1116:comment added by
1073:, Interéditions,
1036:comment added by
1017:
1003:comment added by
964:New York American
649:quantum mechanics
626:Further reasons.
527:comment added by
400:
386:comment added by
315:comment added by
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98:comment added by
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48:current talk page
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1769:cause-and-effect
1757:local conditions
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1620:The question of
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1147:fully depending
1134:fully depending
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1834:— Preceding
1831:
1811:
1807:
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1787:75.74.157.29
1781:chaos theory
1760:
1756:
1752:
1749:non-locality
1746:
1745:
1712:75.74.157.29
1708:Chaos Theory
1707:
1699:
1698:
1682:75.74.157.29
1679:
1661:— Preceding
1658:
1655:poor example
1642:75.74.157.29
1638:chaos theory
1625:
1622:non-locality
1619:
1585:Arthur Rubin
1559:Arthur Rubin
1553:
1508:
1483:
1479:
1332:
1317:
1312:
1289:— Preceding
1285:
1276:
1273:
1270:
1267:
1264:
1248:Narssarssuaq
1243:
1232:
1211:Narssarssuaq
1163:Narssarssuaq
1159:reductionism
1151:Narssarssuaq
1146:
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1118:90.208.122.8
1112:— Preceding
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730:Arthur Rubin
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692:reliability?
677:Arthur Rubin
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89:
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1779:is perhaps
1759:, but also
1636:is perhaps
1207:random seed
1084:); more in
1038:24.45.84.38
1032:—Preceding
999:—Preceding
990:Lord Kelvin
982:Rene Daumal
968:Lyle zapato
523:—Preceding
382:—Preceding
311:—Preceding
296:86.12.7.205
274:—Preceding
248:—Preceding
154:—Preceding
36:This is an
1755:effecting
1747:Regarding
1203:randomness
1181:Embrittled
1092:Memethuzla
996:'s dance.
923:Prosfilaes
581:bob bobato
483:) Further
1773:causality
1728:Gandalf61
1484:excluding
1480:inserting
1325:viscosity
1313:S added:
1071:René Thom
1056:René Thom
223:Jessy2000
196:Jessy2000
123:100TWdoug
72:Archive 3
66:Archive 2
60:Archive 1
1836:unsigned
1828:Question
1771:events (
1765:feedback
1663:unsigned
1630:feedback
1540:Sucnidea
1511:Sucnidea
1409:Sucnidea
1369:Sucnidea
1291:unsigned
1114:unsigned
1034:unsigned
1013:contribs
1001:unsigned
994:Nataraja
806:WP:UNDUE
754:WP:UNDUE
579:theory."
525:unsigned
485:Bjerknes
450:*plonk*
396:contribs
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250:unsigned
156:unsigned
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1309:Wolfram
1139:changes
653:chaotic
630:WP:LEDE
404:Lorenz?
363:sorsoup
348:Burt777
333:sorsoup
39:archive
1588:(talk)
1562:(talk)
1554:expert
1488:EastTN
1237:, the
939:Nabo0o
859:(From
804:(From
765:(talk)
733:(talk)
702:words.
680:(talk)
664:titles
619:(talk)
1597:JFB80
1446:JFB80
1352:JFB80
1239:chaos
1075:Paris
490:JFB80
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406:JFB80
138:C d h
16:<
1844:talk
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1775:).
1244:not
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