The butterfly effect is a phrase which encapsulates the more technical notion of sensitive dependence on initial conditions in chaos theory. Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system. 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.
The phrase refers to the idea that a butterfly's wings might create tiny changes in the atmosphere that ultimately cause a tornado to appear (or prevent a tornado from appearing). The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.
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. 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).
-5 seem coincident at first but, after some time, the divergence is obvious]] --> Sensitive dependence on initial conditions was first described in the literature by Jacques Hadamard in 1890 and popularized by Pierre Duhem's 1906 book. 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 the term "butterfly effect" itself is related to the work of Edward Lorenz. 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. Lorenz published his findings in a 1963 paper for the New York Academy of Sciences noted that "One meteorologist remarked that if the theory were correct, one flap of a seagull's wings could change the course of weather forever." Later speeches and papers by Lorenz used the more poetic butterfly. 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.
"Butterfly" is a song written and produced by American singer Mariah Carey and Walter Afanasieff for Carey's seventh album, Butterfly (1997). It is a ballad combining elements of pop and gospel, but Carey had originally conceived it as a house record with David Morales titled "Fly Away (Butterfly Reprise)". After realizing how personal the lyrics were and how they could be applied to Butterfly, she wrote "Butterfly" with Afanasieff. On the song's lyrics, Carey comments "It was '97 and I was leaving my marriage [to Tommy Mottola] which encompassed my life. I was writing the song 'Butterfly' wishing that that's what he would say to me."
It was released as the album's second single in 1997 (see 1997 in music). It did not appear on the U.S. Billboard Hot 100 chart because it was not issued as a commercial single in the United States; Billboard magazine rules at the time stipulated that a commercial release was required for a song to enter the Hot 100. It was a moderate success on charts that airplay-only singles were allowed to enter, such as the Rhythmic Top 40, Adult Contemporary and Mainstream Top 40 charts, and it reached number sixteen on Billboard's Hot 100 Airplay chart. "Butterfly" was not a substantial hit outside the U.S.: it reached number twenty-two in the UK and number twenty-seven in Australia, failing to match the success of "Honey", the album's first single. In France and Germany the single did not reach the top forty.
"Butterfly" was nominated for the 1998 Grammy Award for Best Female Pop Vocal Performance, which it lost to Sarah McLachlan's "Building a Mystery".
"Butterfly" is a popular song written by Bernie Lowe and Kal Mann and published in 1957. The song is credited to Anthony September as songwriter in some sources. This was a pseudonym of Anthony Mammarella, producer of American Bandstand.
Both the original recording of the song by Charlie Gracie and a cover version by Andy Williams reached #1 on the Billboard charts in 1957.
"Butterfly" is a rapcore song by Crazy Town from their album The Gift of Game that was released in February 2001.
The entire song consists of samples from the Red Hot Chili Peppers' song "Pretty Little Ditty" with additional lyrics by Shifty Shellshock and Epic on top.
"Butterfly" is a dance-pop song written by Australian singer Kylie Minogue and Steve Anderson for Minogue's seventh album Light Years (2000). It was produced by DJ-producer Mark Picchiotti. The song was released as a promotional single in autumn of 2001 and was a dance club hit, peaking at number fourteen in the United States on the Billboard Hot Dance Music/Club Play chart.
The song was originally issued to clubs in spring 2000 in the UK as a test pressing to gauge DJ reaction to Minogue's new material. "Butterfly" had been in the running to be the fourth single from Light Years, but due to its strong club influences it was pulled in favour of the radio-friendly "Please Stay". However, Mark Pichotti remixed the track and issued it in the United States through his own Blue2 label (a division of Blueplate Records), where it became a hit on the Billboard Dance music charts.
"Butterfly" is one of Smile.dk's most popular songs and featured on their 1998 album "Smile"
This song was featured in Dancemania series and Dance Dance Revolution (DDR 1st Mix) (1998). This song was popular for its catchy lyrics, and the moves in the song known as the "Butterfly turn". Butterfly is one of the most popular and recognisable songs from DDR and hence is known in various parts of the world, including Japan.
"Butterfly" has been remixed several times. Here is the mixcography:
"Butterfly" is a pop song, written and recorded by the French singer-songwriter, Danyel Gerard (born Gerard Daniel Khertakian, 7 March 1939, Parisblank">http://www.bardotagogo.com/bagglog/?p=8 http://www.discogs.com/artist/Danyel+G%C3%A9rard?anv=Danyel+Gerard) in the late 1960s. It was firstly a hit in the French language.
In the early 1970s English language words were written, and Gerard recorded it again in the _United States. It was a very popular song internationally, selling over five million copies. Many other musicians recorded it, both in instrumental and vocal versions. In the U.S., that list included Eydie Gormé and Eddy Arnold.
The single reached Number 11 (and spent 12 weeks) in the UK Singles Chart in October 1971. Lack of further chart activity in the UK saw both singer and song branded as a one-hit wonder. It was a similar story in the U.S., where the Gerard's single peaked at #78 in the Billboard Hot 100.http://wm01.allmusic.com/cg/amg.dll?p=amg&searchlink=DANYEL|GERARD&sql=11:j9fexqy5ldfe~T5
Butterfly is the final song from Weezer's second album, Pinkerton. It remains the only completely acoustic song in Weezer's album catalog and makes a particularly poignant end to the frenetic and noisy Pinkerton album. The song is known for its simplicity and sincere vocals highlighted by the closing lyric I'm sorry.
The song is written from Pinkerton's point of view at the end of the opera Madame Butterfly. "I told you I would return when the robin makes its nest" is a direct reference to the opera.
In 2002 a full-band version of the song was often played live. At a July 11, 2002 show in Chicago after playing the full band version of the song Cuomo quipped "They said we couldn't do that at a rock show."
"Butterfly" is a 1998 Towa Tei single.
