The+Butterfly+Effect

=** Introduction **= toc

A butterfly’s flapping its wings in Brazil Amazon forest can set off a cascade of atmospheric events that, weeks later, arouses the formation of a tornado in Texas. This statement may sound absurd, yet it is the notion of the chaotic theory “Butterfly Effect”.The Butterfly Effect refers that a small change in initial condition can lead to a huge long-term chain reaction in dynamical system. It was fist used for weather prediction, and now this term has become a metaphor used in and out of science. It is a chaotic phenomenon. There are always constants and variables in the development of things; there are always followable rules andstants in the process of development; there are also unpredictable “variables”. Summing it up, there are complexity in the development of things. The initial of the butterfly effect is chaos, generated from inaccuracy, so everything could happen. Following Lorenz’s discovering the “Butterfly Effect”, the study of chaos has always been what scientists, sociologists, and anthropologists interested in.

=** The Development of the Theory **=

Talking about the origin of the statement, the mathematician Edward N. Lorenz coded a computer model, called a strange attractor, that can simulate climate changes and present them with images. He ended up to find that the image is chaotic, and very much like an open-wings butterfly. So, he called the image vividly as "a butterfly flapping its wings". It's a line that alternately spirals around two adjacent ovals, mapping out the chaotic solution to a set of interrelated equations. Lorenz found that the shape of the attractor was extremely sensitive to initial conditions. Moving its starting point just a wing's scale in any direction caused the line to draw a completely different butterfly. And this is also where the statement derived from. Lorenz discovered that as the difference grows exponentially, in this case, a tiny difference can cause great consequences. Lorenz raised this issue in a later speech. He believed that in the atmospheric system, with various of errors and slight uncertainties, it is possible for the results to accumulate, and eventually get amplified to form huge atmospheric changes. So, it is impossible to make accurate long-term prediction on the weather. Thus, Lorentz thought that he had found a new phenomenon: the outcome of a thing sensitively depends on the initial condition of its. He then named this "the instability of the initial value", also known as "chaos", or "butterfly effect". In 1963, American meteorologist Edward N. Lorenz first analyzed this effect in a paper submitted to the New York Institute of Science. He remarked that if the theory is proved to be correct, a seagull’s flapping wings is more than able to change the weather forever. And in his later speeches and papers, he used butterflies instead of seagulls to be more poetic. The reason for his statement is that a butterfly’s flapping its wings could cause the air system around it to change. Furthermore, it could produce a weak air flow, and the weak air flow will cause the surrounding air or other systems to have corresponding changes. That would also trigger a series of chain reactions, and finally leads to big changes in other systems. He calls it Chaos. Of course, the "butterfly effect" is still mainly a metaphor of Chaos. But it also refers that a mild difference can cause a series of great reactions. = = =** Applications on Some of the Areas **=

** In Weather Forecasting System **
“The butterfly effect is most familiar in terms of weather; it can easily be demonstrated in standard weather prediction models, for example.” [1] And initially the “Butterfly Effect” had strong connections with weather forecasting. The climate scientists James Annan and William Connolley claimed that chaos plays an important role in the development of weather prediction methods; models are sensitive to the initial conditions. However, they also followed up with the statement: "Of course the existence of an unknown butterfly flapping its wings has no direct bearing on weather forecasts, since it will take far too long for such a small perturbation to grow to a significant size, and we have many more uncertainties to worry about. So the direct impact of this phenomenon on weather prediction is often somewhat overstated.

** In Economic System **
In 2003, a case of suspicious mad cow disease was found in the United State, and people linked this with the collapse of the US economy that had just recovered. And they described it as a hurricane to the market. The cow was like the “butterfly’s wings” in this case. It caused direct impacts on the 175 billion US dollar beef industry of the US, and it also took away nearly 1.4 million working opportunities. Furthermore, it also affected the industry of corn and soybean which are the main forage for the cattle. In a bigger picture, the case induced people’s anxious of beef and American’s local food.

** In Mathematical System **
The "cotangents sequence" is a typical example of the butterfly effect. By plugging a=1, a=1.00001, and a=1.0001, the outcome of the equation a[n+1] =cot(a[n]) appears to be random and chaotic. And the difference is extremely significant after the 10th term. = Counter Ideas =

** In Weather Forecasting System **
Each flap of a butterfly's wings exerts a pressure on the surrounding air molecules in order to thrust the insect upward. It is true that each flap will cause a tiny change in the air pressure around the butterfly, but this fluctuation is insignificant compared to the air's total pressure, which is about 100,000 times larger. It is agreed that changes in air pressure are one of the key factors involved in changing the weather, but in the case of the butterfly, the air molecules easily absorb the blow of a wing flap, so that a few inches away from a butterfly, the turbulence it causes will have died down. Paul Roebber, a mathematician and meteorologist at the University of Wisconsin-Milwaukee, argues that the butterfly-scale chaos does not affect the success of weather prediction; however, larger perturbations play a significant role. “The influences of butterflies are still small-scale influences from a weather perspective, such as individual clouds — those effects are much more likely to grow and be important," Roebber said. "So butterflies: OK. But individual clouds: those can very dramatically influence the forecast five to 10 days from now, and until we can resolve those, improvements in our models won't lead to much improvement in our forecasts." In weather forecasts, the error becomes very large very rapidly, and then begins to tail off; so most of the error in the weather forecasts is not related to Chaos Theory.

** In Economic System **
Lorenz's work gives us a fresh way to think about cause and effect, but does not offer easy answers. “But in the popular imagination, that one picturesque little butterfly has became a metaphor for the surprising way that long chains of events unfold.” [2] A website (SmartMoney.com) market analysis from 2007 cites Lorenz, then suggests that hypothetical problems at Sony could affect a string of shippers, retailers, and investors: "One butterfly, in this case a Japanese butterfly, sets off the entire chain." Even applied to society, rather than nature, such claims value skepticism.“That we imagine the butterfly effect would explain things in everyday life, however, reveals more than an overeager impulse to validate ideas through science. It speaks to our larger expectation that the world should be comprehensible - that everything happens for a reason, and that we can pinpoint all those reasons. However, small they may be.” [3] But nature itself defies this expectation. It is probability, not certain cause and effect, that now dictates how scientists understand many systems, from subatomic particles to storms. "People grasp that small things can make a big difference," Emanuel says. "But they make errors about the physical world. People want to attach a specific cause to events, and can't accept the randomness of the world."

** In Mathematical System **
Orrell, who has a doctorate in prediction of nonlinear systems from the University of Oxford, talked about the butterfly effect earlier in 2006. As his point of view, mathematically, the Lorenz’s attractor was a fairly important discovery. However, he added: “But then it kind of got taken over as a bit of an excuse.” [4] People then started to apply this chaos theory to a lot of different areas and systems and said that such property is sensitive to initial conditions, so we can't make accurate predictions. This is somehow a disguised replacement of concept. =** Conclusion **=

There are a lot of comments on this theory. Some are critical, and others support the theory. In general, it could sometimes be applied to daily life that a minor error can lead to great deterioration, so we should pay attention to details. However, bringing this theory to science and research level might be a little bit too farfetched.Classical science has emphasized stability and permanence.Lorenz's work does give us a new way to pondering the cause and effect, yet it is still not convincing enough. “Developments spanning the last decades show, on the contrary, that instability, sensitivity and unpredictability underlie large classes (if not most) of phenomena occurring on macroscopic time and space scales - the scales of our everyday experience.” [5] “Thus global warming may make big storms more likely “loading the die,” Emanuel says, “but we cannot say it definitively caused Hurricane Katrina.” Science is to what we look up to understand the universe. Ed. Lorenz’s work deserves applause, still it should not be followed utterly. =** Cites **=

[1] Wikipedia. //Butterfly Effect.// The Free Encyclopedia [Internet]; [cited 2017 July 7]. Available from https://en.wikipedia.org

[2] & [3] Dizikes, P. The Meaning of the Butterfly: Why Pop Culture Loves the 'Butterfly Effect,' and Gets It Totally Wrong [Internet]; [cited 2017 July 7]. Available from http://archive.boston.com/bostonglobe/ideas/articles/2008/06/08/the_meaning_of_the_butterfly/?page=full

[4] Walkover, N. (2011, December 13). //Can a Butterfly in Brazil Really Cause a Tornado in Texas?// [Internet]; [cited 2017 July 7]. Available from https://www.livescience.com

[5] Scholarpedia. //Butterfly Effect//. The Peer-reviewed Open-access Encyclopedia [Internet]; [cited 2017 July 7]. Available from http://www.scholarpedia.org/article/Butterfly_effect

=** References **=

1. Walkover, N. (2011, December 13). //Can a Butterfly in Brazil Really Cause a Tornado in Texas?// [Internet]; [cited 2017 July 7]. Available from https://www.livescience.com

2. Onion, A. (2012 January 23). //Science Behind the Butterfly Effect// [Internet]; [cited 2017 July 6]. Available from http://abcnews.go.com

3. Williams, N. (2010, March 8). //Butterfly effect// [Internet]; [cited 2017 July 7]. Available from http://www.sciencedirect.com.colorado.idm.oclc.org

4. Lorenz, E. N. (1993). //The Essence of Chaos//, University of Washington Press

5. Lorenz, E. N. (1963). //Deterministic Nonperiodic Flow//, Journal of the Atmospheric Sciences

6. Michigan State University. //The Texas Butterfly Effect.// ScienceDaily [Internet]; [cited 2017 July 6]. Available from www.sciencedaily.com/releases/2016/06/160609115133.htm

7. Cornell University. //Where to Start to Launch The 'Butterfly Effect'.// ScienceDaily [Internet]; [cited 2017 July 6]. Available from: www.sciencedaily.com/releases/2004/02/040216083419.htm

8. Georgia Institute of Technology. (2017, March 15). //From the Butterfly's Wing to the Tornado: Predicting turbulence.// ScienceDaily [Internet]; [cited 2017 July 6]. Available from www.sciencedaily.com/releases/2017/03/170315144552.htm

9. University of Washington. (2016, February 23). //For Weather Forecasting, Precise Observations Matter More Than Butterflies//. ScienceDaily [Internet]; [cited 2017 July 6]. Available from www.sciencedaily.com/releases/2016/02/160223102849.htm

10. McGill University. (2015, August 18). //Harnessing the Butterfly Effect.// ScienceDaily [Internet]; [cited 2017 July 6]. Available from www.sciencedaily.com/releases/2015/08/150818153816.htm

11. Calamia, J. //The Physics-Defying Flight of the Bumblebee// [Internet]; [cited 2017 July 7]. Available from https://www.livescience.com

12. Kruszelnicki, K. //No More Butterfly Effect,// ABC Science[Internet]; [cited 2017 July 8]. Available from http://www.abc.net.au/science/articles/2002/03/18/436385.htm

13. Scholarpedia. //Butterfly Effect//. The Peer-reviewed Open-access Encyclopedia [Internet]; [cited 2017 July 7]. Available from http://www.scholarpedia.org/article/Butterfly_effect