Citizendia
Your Ad Here

For other uses, see Butterfly effect (disambiguation).
Point attractors in 2D phase space.
Point attractors in 2D phase space. An attractor is a set to which a Dynamical system evolves after a long enough time In Mathematics and Physics, a phase space, introduced by Willard Gibbs in 1901 is a Space in which all possible states of a System

The butterfly effect is a phrase that encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Small variations of the initial condition of a dynamical system may produce large variations in the long term behavior of the system. In Mathematics, in the field of Differential equations an initial value problem is an Ordinary differential equation together with specified value called The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position So this is sometimes presented as esoteric behavior, but can be exhibited by very simple systems: for example, a ball placed at the crest of a hill might roll into any of several valleys depending on slight differences in initial position. BALL ( Biochemical Algorithms Library) is a C++ library containing common algorithms used in Biochemistry and Bioinformatics.

Contents

Theory

The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that may ultimately alter the path of a tornado or delay, accelerate or even prevent the occurrence of a tornado in a certain location. A butterfly is an Insect of the order Lepidoptera. Like all Lepidoptera butterflies are notable for their unusual life cycle with a Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five A tornado is a violent rotating column of air which is in contact with both the surface of the earth and a Cumulonimbus cloud or in rare cases the base of a Cumulus The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale alterations of events. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different. Of course the butterfly cannot literally cause a tornado. The kinetic energy in a tornado is enormously larger than the energy in the turbulence of a butterfly. The kinetic energy of a tornado is ultimately provided by the sun and the butterfly can only influence certain details of weather events in a chaotic manner.

Recurrence, the approximate return of a system towards its initial conditions, together with sensitive dependence on initial conditions are the two main ingredients for chaotic motion. In Mathematics, the Poincaré recurrence theorem states that certain systems will after a sufficiently long time return to a state very close to the initial state They have the practical consequence of making complex systems, such as the weather, difficult to predict past a certain time range (approximately a week in the case of weather). This article describes complex system as a type of system For other meanings see Complex systems. The weather is a set of all the phenomena occurring in a given Atmosphere at a given Time.

Origin of the concept and the term

The term "butterfly effect" itself is related to the work of Edward Lorenz, based in Chaos Theory and sensitive dependence on initial conditions, first described in the literature by Jacques Hadamard in 1890[1] and popularized by Pierre Duhem's 1906 book. Edward Norton Lorenz ( May 23, 1917) was an American Mathematician and meteorologist, and a pioneer of Chaos theory. In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Jacques Salomon Hadamard ( December 8, 1865 – October 17, 1963) was a French Mathematician best known for his proof of Pierre Maurice Marie Duhem ( 10 June 1861 – 14 September 1916) was a French physicist, mathematician and The idea that one butterfly could have a far-reaching ripple effect on subsequent events seems first to have appeared in a 1952 short story by Ray Bradbury about time travel (see Popular Media below), although Lorenz made popular the term. Ray Douglas Bradbury (born August 22 1920 is an American mainstream, Fantasy, horror, Science fiction and mystery In 1961, Lorenz was using a numerical computer model to rerun a weather prediction, when, as a shortcut on a number in the sequence, he entered the decimal . 506 instead of entering the full . 506127 the computer would hold. The result was a completely different weather scenario. [2] Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noting that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever. The New York Academy of Sciences is the third oldest scientific society in the United States Gulls (often informally Seagulls) are birds in the family Laridae " Later speeches and papers by Lorenz used the more poetic butterfly. A butterfly is an Insect of the order Lepidoptera. Like all Lepidoptera butterflies are notable for their unusual life cycle with a According to Lorenz, upon failing to provide a title for a talk he was to present at the 139th meeting of the American Association for the Advancement of Science in 1972, Philip Merilees concocted Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas as a title. The American Association for the Advancement of Science (or AAAS) is an organization that promotes cooperation between Scientists defends scientific freedom encourages |utc_offset = -2 to -4 |time_zone_DST = BRST |utc_offset_DST = -2 to -5 |cctld Texas ( is a state geographically located in the South Central United States and is also known as the Lone Star State.

Although a butterfly flapping its wings has remained constant in the expression of this concept, the location of the butterfly, the consequences, and the location of the consequences have varied widely. [3]

Illustration

The butterfly effect in the Lorenz attractor
time 0 ≤ t ≤ 30 (larger) z coordinate (larger)
Image:TwoLorenzOrbitsSmall.jpg Image:LorenzCoordinatesSmall.jpg
These figures show two segments of the three-dimensional evolution of two trajectories (one in blue, the other in yellow) for the same period of time in the Lorenz attractor starting at two initial points that differ only by 10-5 in the x-coordinate. The Lorenz attractor, named for Edward N Lorenz, is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its Butterfly Initially, the two trajectories seem coincident, as indicated by the small difference between the z coordinate of the blue and yellow trajectories, but for t > 23 the difference is as large as the value of the trajectory. The final position of the cones indicates that the two trajectories are no longer coincident at t=30.
A Java animation of the Lorenz attractor shows the continuous evolution.

Mathematical definition

A dynamical system with evolution map ft displays sensitive dependence on initial conditions if points arbitrarily close become separate with increasing t. The dynamical system concept is a mathematical Formalization for any fixed "rule" which describes the Time dependence of a point's position If M is the state space for the map ft, then ft displays sensitive dependence to initial conditions if there is a δ>0 such that for every point x∈M and any neighborhood N containing x there exist a point y from that neighborhood N and a time τ such that the distance

d(f^\tau(x), f^\tau(y)) > \delta \,.

The definition does not require that all points from a neighborhood separate from the base point x. In Topology and related areas of Mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a Topological space.

Appearances in popular culture

The concept of the butterfly effect is sometimes used in popular media dealing with the idea of time travel, usually inaccurately. This article details time travel itself For other uses see Time Traveler. Most time travel depictions simply fail to address butterfly effects. According to the actual theory, if history could be "changed" at all (so that one is not invoking something like the Novikov self-consistency principle which would ensure a fixed self-consistent timeline), the mere presence of the time travelers in the past would be enough to change short-term events (such as the weather) and would also have an unpredictable impact on the distant future. The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a Principle developed by Dr Therefore, no one who travels into the past could ever return to the same version of reality he or she had come from and could have therefore not been able to travel back in time in the first place, which would create a phenomenon known as time paradox. This article refers to the Time travel paradox In novels based on the television series Doctor Who, "Grandfather Paradox" is the semi-mythical

Movies

In arguably the earliest illustration of the butterfly effect in a story on film, an angel in It's a Wonderful Life (1946) shows George Bailey how rewriting history so that George was never born would detrimentally affect the lives of everyone in his hometown. It's a Wonderful Life is a 1946 American Film produced and directed by Frank Capra and based on the short story " The Greatest In a subtle butterfly effect, snow is falling in one version of reality but not the other. [4][5]

The 1998 British movie Sliding Doors runs two parallel stories of the same woman, Helen (Gwyneth Paltrow). Sliding Doors is a 1998 Film written and directed by former actor Peter Howitt. Gwyneth Kate Paltrow (born September 27 1972 is an Academy Award - Golden Globe - and double Screen Actors Guild Award -winning American In one universe, Helen manages to catch a London Underground train home on time, and in the other she misses it. This small event influenced her life dramatically.

The French film Le Battement d'ailes du papillon (2000), translated as Happenstance in the English release, makes direct references to the butterfly effect in title, dialogue, and theme. Happenstance is a 2000 French Comedy film starring Audrey Tautou and Faudel.

In many cases, minor and seemingly inconsequential actions in the past are extrapolated over time and can have radical effects on the present time of the main characters. In the movie The Butterfly Effect (2004), Evan Treborn (Ashton Kutcher), when reading from his adolescent journals, is able to essentially "redo" parts of his past. The Butterfly Effect is a 2004 American Fantasy / Drama movie starring Ashton Kutcher, Amy Smart Christopher Ashton Kutcher ( commonly known as Ashton Kutcher (born February 7 1978 is an American actor and former fashion model best known for playing Michael As he continues to do this, he realizes that even though his intentions are good, the actions he takes always have unintended consequences. Unintended consequences are outcomes that are not (or not limited to what the actor intended in a particular situation Despite its title, however, this movie does not seriously explore the implications of the butterfly effect; only the lives of the principal characters seem to change from one scenario to another. The greater world around them is mostly unaffected. Furthermore, the changes made in the past of the principal character are far from minor and in that sense the title of the film is a misnomer. An element of the butterfly effect in general terms is that differences in start conditions for different scenario outcomes are virtually undetectable, and consequences are not related to cause in a directly apparent way.

On the other hand, in the movie "Run Lola Run" (Lola rennt in German-1998), the butterfly effect is represented more clearly. Run Lola Run (original German title Lola rennt, translates as Lola Runs) is a 1998 Film by German There, minor and almost sub-conscious actions in everyday life can be seen to have gross and wide spread effects upon the future. For example, the fact that Lola bumps into someone instead of passing by may lead to a painful death after suffering paralysis. As such, seemingly inconsequential actions can be seen to have drastic long-term results. The second episode in the "Back to the Future" trilogy also vividly illustrates the cascading and broad effects of what seemed a minor change in the course of events: because the loathsome Biff Tannen accidentally gets his hands on a record book from 2015, he is able to grow rich and corrupt "Marty Mcfly"'s home town. Back to the Future is a 1985 science fiction Comedy film directed by Robert Zemeckis and produced by Steven Spielberg. Martin "Marty" McFly is a Fictional character and the main protagonist in the Back to the Future When McFly (Michael J. Fox) returns to 1985, he finds it utterly degraded from what had used to be. Michael J Fox (born Michael Andrew Fox; June 9 1961 is a Canadian / American

In the 2000 movie Frequency, a son, John Sullivan (James Caviezel), is presented with an opportunity to prevent the death of his father, Frank Sullivan (Dennis Quaid), through a miracle of nature in which they were both able to communicate across time 30 years using the same am radio, transmitting the signal via a freak occurrence of the Northern Lights. Frequency is a 2000 Film, which contains elements of the time travel, thriller and Alternate history Film genres James Patrick Caviezel Jr (kəˈviːzəl born September 26, 1968) is an American Film Actor, sometimes credited as Jim Caviezel Dennis William Quaid (born April 9, 1954) is an American Actor. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Amateur radio, often called ham radio, is both a Hobby and a service in which participants called "hams" use various types of Radio communications This one action, however, had several undesirable consequences, including the murder of his mother by a vicious killer known as the Nightingale who was supposed to have never been caught. In the original timeline, when the killer is lying unconscious in the hospital, he dies from a reaction of two medicines that were administered intravenously into his system. A timeline is a graphical representation of a Chronological sequence of events also referred to as a Chronology. Intravenous therapy or IV therapy is the giving of Liquid substances directly into a Vein. This was due to an oversight on his medical chart, in which the attending male nurse overlooked the fact that it stated that the patient had received a certain medication which could not be mixed with the other. In the alternate timeline, Frank visits his wife, a nurse, at the hospital immediately after surviving the fire in which he was supposed to die. She alters her routine slightly to see him, and of all things she then sees the wrong medication being administered to the killer. She prevents this from happening, and so the killer survives to murder not only her, but several more people; all nurses. Also, this film illustrates a theoretical side effect of the butterfly effect, where John is able to remember the original future time, as well as other alternate futures that were created each time his father changed something in the past. In Science fiction stories involving Time travel, an alternate future or alternative future is a possible Future which never comes to pass typically

In the 1990 movie "Havana" with Robert Redford and Lena Olin, Redford even makes a direct reference to: "And a butterfly can flutter its wings over a flower in China and cause a hurricane in the Caribbean. I believe it. They can even calculate the odds. It just isn't likely and it takes so long. " He's referring to the probability of the two of their characters ever getting together. Redford's character was a gambler in late 50's Cuba and Olin was spotted earlier in the movie looking at books on the Theory of Numbers and Probability in the apartment of Redford's character.

in 2008 dasavadaram, a movie built on the chaos theory which is the brainchild of kamalhasan who also plays 10 roles in it, all connected by the series of events to the Tsunami that attacked coasts of india and other countries which has their coast in indian ocean. The movie starts with a narration of what was happened. The lead artist kamalhasan, in his bio scientist role explains the butterfly theory with the visuals. The screenplay is built in such a way that it explain the pattern of nature which was considered as the god's job. Mr. kamalhasan connects the story of a man(kamal as priest) in 12th century who was killed by the king with all other of his 9 characters. check on the movie "dasavadaram" for furter details. The explanation provided in the movie Dasavatharam states that an incident in the 12th century of killing a priest and immersing the idol of Lord Ranganatha into the ocean resulted in the Tsunami in the film's climax which provides enough Sodium Chloride to destroy the effects of the bio-weapon virus.

Literature and print

In the 1952 short story by Ray Bradbury, "A Sound of Thunder", the killing of a butterfly during the time of dinosaurs causes the future to change in subtle but meaningful ways: e. Ray Douglas Bradbury (born August 22 1920 is an American mainstream, Fantasy, horror, Science fiction and mystery For the film adaptation see A Sound of Thunder (film, and for the Video game adaptation of the film see A Sound of Thunder (video game. g. , the spelling of English and the outcome of a political election. [6]

The butterfly effect was invoked by fictional chaotician Ian Malcolm in both the novel Jurassic Park and subsequent film adaptation. In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Jurassic Park is a Science fiction Novel that was written by Michael Crichton and published in 1990. He used it to explain the inherent instability of (among other things) an amusement park with dinosaurs as the attraction.

In Terry Pratchett's "Men at Arms," Zorgo the Retrophrenologist approves of hunting butterflies with crossbows, claiming that he "suppose(s) it stops them creating all these damn thunderstorms. Terence David John Pratchett, OBE (born 28 April 1948 is an English fantasy, Science fiction, and children's author. Men at Arms is the 15th Discworld Novel by Terry Pratchett first published in 1993 "

In the 1632 series series of time-travel science fiction by Eric Flint and David Weber et al. Eric Flint (born 1947 is an American Alternate history and Fantasy author, editor, and e-publisher. David Mark Weber is an American Science fiction and Fantasy author. , speculation about the butterfly effect that happens when the West Virginia town of Grantville is instantaneously dropped into 1632 Germany. The speculation is that the events which lead the genetic makeup of a human are so sensitive to chance that every human born in the world changed by the "Ring of Fire" event would be genetically different than they otherwise would have been within a very small period of time, depending on the distance from Germany, but in all cases within a year. Specifically, thousands of sperm vying for entry into an egg would be very sensitive to very small differences in position or timing that would assuredly result in a different sperm winning out, and a different person (a brother or sister, but no closer related than that) being born. The speculation centers especially on the birth of Baruch de Spinoza in Amsterdam a few months following the Ring event. Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21,

Interactive media

Television

In The Simpsons Halloween episode, "Time and Punishment", Homer repeatedly travels back to the time of dinosaurs with a time machine (à la Bradbury's A Sound of Thunder). " Treehouse of Horror V " is the sixth episode of The Simpsons ' sixth season and the fifth episode in the Treehouse For the film adaptation see A Sound of Thunder (film, and for the Video game adaptation of the film see A Sound of Thunder (video game. Each time there, Homer's actions (involving intentional and unintentional violence) drastically alter the current universe. Some of the changes include: A world dictator, a universe where his family is rich and classy and it rains donuts, and a seemingly normal universe, with the exception of everyone having long reptilian tongues.

In the Family Guy episode "Meet the Quagmires", Peter, with the help of Death, repeatedly travels back to the 80's to live up his teenage years and cancel a date with Lois. Family Guy is an animated American television sitcom created by Seth MacFarlane that airs on Fox and regularly on other "Meet the Quagmires" is the eighteenth and final episode of the fifth season of the FOX animated series Family Guy. In English Death is often given the name the " Grim Reaper " and shown as a skeletal figure carrying a large Scythe, and wearing a midnight black gown robe This leads to her marrying Quagmire and Peter marrying Molly Ringwald among other things, causing two drastic changes of the present (Chevy Chase is host of The Tonight Show, and Al Gore is president of the United States) and finally when things seem normal again it turns out Roger from American Dad! is living with them. Molly Kathleen Ringwald (born February 18, 1968) is an American Actress, Singer and Dancer. Cornelius Crane “Chevy” Chase (born October 8 1943 is an American Emmy Award-winning Comedian, Writer, and television and film The Tonight Show with Jay Leno as appropriate --> The Tonight Show is a long-running Albert Arnold Gore Jr (born March 31 1948 is an American environmental Activist, author Businessperson, former Politician, and former The United States of America —commonly referred to as the American Dad! is a satirical American animated series produced by Underdog Productions and Fuzzy Door Productions for 20th Century

In a 2004 television episode of comedy sitcom Scrubs called "My Butterfly", the episode is shown in two parts: The first in which a butterfly lands on a woman sitting in the hospital's waiting room, and the second where time is rewound and the butterfly instead lands on the man next to her. Scrubs is an Emmy and Peabody Award -winning American Comedy-drama that premiered on October 2 2001 on NBC. The following is a complete episode list for the television show Scrubs, which began being broadcast on October 2 2001 Both halves of the episode show the noticeably (albeit sensationally) different outcomes that stem directly from the original choice of landing locations of this butterfly[7].

In a first-season episode of the stop-motion animation show Robot Chicken titled "Operation: Rich in Spirit" there is a sketch where a young boy tries to explain the butterfly effect to a young girl. Robot Chicken is an Emmy -Award Winning American Stop motion animated television series created by Seth Green and Matthew Operation Rich in Spirit is the seventeenth episode of the first season of Robot Chicken. When the young girl squishes the butterfly, it causes earthquakes in Japan. A Japanese woman retaliates, stepping on a butterfly, which causes a volcano to erupt behind the children. The boy retaliates as well, ripping a butterfly in half, which causes Godzilla to terrorize Japan.

In a second season episode of CSI titled "Chaos Theory", the entire CSI team investigates a disappearance of a young woman at a local university. CSI Crime Scene Investigation is an American crime drama Television series that trails the investigations of a team of Las Vegas Chaos Theory is the second episode in the of the popular Television drama, which is set in Las Vegas, Nevada. Forensics leads them to possible suspects, and possible suspects all have probable motives, but nothing seems to pan out. This leads the team to discuss the "Chaos Theory": when combined, many seemingly innocuous events may have a deadly outcome, and closure is not always within reach.

The third season premiere of Heroes is entitled "The Butterfly Effect. Heroes is an American Science fiction television drama series created by Tim Kring, which premiered on NBC on September "

A Malcolm in the Middle episode shows Hal and Lois arguing about which one of them will take Malcolm and Reese to bowling and which one will stay at home with Dewey. Malcolm in the Middle was a seven-time Emmy Award -winning one-time Grammy -winning He had run off and married a good-natured Canadian woman This is a list of characters in the American television comedy series Malcolm in the Middle, which was originally televised from 2000-2006 on the Fox Network. This is a list of characters in the American television comedy series Malcolm in the Middle, which was originally televised from 2000-2006 on the Fox Network. This is a list of characters in the American television comedy series Malcolm in the Middle, which was originally televised from 2000-2006 on the Fox Network. This is a list of characters in the American television comedy series Malcolm in the Middle, which was originally televised from 2000-2006 on the Fox Network. Bowling is a Game / Sport in which players attempt to score points by rolling a Bowling ball along a flat surface either into objects called pins This is a list of characters in the American television comedy series Malcolm in the Middle, which was originally televised from 2000-2006 on the Fox Network. After that, the episode will show two timelines: one where Lois takes them and another one where Hal takes them. An event from the timeline where Lois goes to the bowling is shown as a flashback in a later episode, implying that timeline to be the one in canon. In history film television and other media a flashback (also called analepsis) is an interjected scene that takes the narrative back in time from the current

See also

Notes

  1. ^ Some Historical Notes: History of Chaos Theory
  2. ^ Mathis, Nancy: "Storm Warning: The Story of a Killer Tornado", page x. Causality (but not causation) denotes a necessary relationship between one event (called cause and another event (called effect) which is the direct consequence A chain reaction is a sequence of Reactions where a reactive product or by-product causes additional reactions to take place Determinism is the philosophical Proposition that every event including human cognition and behaviour decision and action is causally determined This article is about chain reactions. For the political theory, see Domino Theory. Dynamical systems theory is an area of Applied mathematics used to describe the behavior of complex Dynamical systems usually by employing Differential A fractal is generally "a rough or fragmented geometric shape that can be split into parts each of which is (at least approximately a reduced-size copy of the whole" A Rube Goldberg machine is a deliberately overengineered Apparatus that performs a very simple task in a very indirect and convoluted fashion Touchstone, 2007. ISBN 0-7432-8053-2
  3. ^ Butterfly Effects - Variations on a Meme
  4. ^ The American Dream and It's a Wonderful Life
  5. ^ Nitpickers.com : Movie Nitpick - It's a Wonderful Life - 1946 - Post and Review nitpicks on your favorite Movies
  6. ^ A Sound of Thunder. Amazon.com.
  7. ^ Scrubs: My Butterfly Recap. TV.com.

References

External links

Dictionary

butterfly effect

-noun

  1. The technical notion of sensitive dependence on initial conditions in chaos theory.
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic