title: The Black Hole (1979 film)

text: A separate comic book adaptation of the film published by Whitman Comics in 1980 bypasses the whole issue of what happens inside the black hole by having the crew enter the black hole on one page and emerge apparently unharmed on the next page into a parallel universe where they encounter alternate versions of Reinhardt, BO.B., Maximilian and even Frank McCrae, Kate McCrae's father. Four issues were published. The first two issues adapted the film and the second two issues continued the story introducing a race of people called Virlights, whom they end up aiding against a rising tyrant. The rare fourth issue concludes with the promise of a fifth issue but the series was canceled before it was released. In Mexico, Editorial Novaro S.A. published the first four Whitman issues, including the fifth issue, but also released a sixth issue before the series ended. Other comic adaptations released in Europe have the crew emerging into another galaxy, thus confirming Reinhardt's theories. While wondering if they will ever return to Earth, they decide to explore this new universe.


title: The Black Hole (1979 film)

text: In the official Disney Read-Along recording and illustrated story book, the crew in the probe ship emerge safely on the other side of the black hole, while the "Cygnus" is "crushed like an eggshell." The story ends with Captain Holland saying, "We've been trained to find new worlds. Let's go find one for ourselves!" The children's book line, Little Golden Books, released a book entitled "The Black Hole: A Spaceship Adventure for Robots". The story involves V.I.N.CENT. and BO.B. exploring the "Cygnus", visiting its gardens, encountering the "humanoid robots", and escaping detection by Maximilian.


title: The Black Hole (1979 film)

text: The Mego Corporation produced 6 million action figures and models of the "USS Palomino" from the film, released in the fall of 1979. Nabisco issued a series of plastic pencil holders in the shape of the film's robot characters via specially marked boxes of breakfast cereal.


title: The Black Hole (1979 film)

text: In 1983, Disney put out a computer learning-game spinoff, "Space Probe: Math". This was a cassette containing two educational games designed for use with the Radio Shack TRS-80 Color Computer. The concept of the first game was that the "Palomino" had landed on an infected planet, Delta 5 Omega. All the crew were falling under "mind diffusion", basically a viral form of fatigue. The player (aged 7–14) had to solve multiplication or division problems to save the crew. In the second game, the player had to save a primitive world's crops, using (rectangular) area and perimeter problems.


title: The Black Hole (1979 film)

text: In March 1980, Disney began a partnership with Fotomat Corporation in a four-city market test to make 13 selected titles available for rental on videocassette, which was to be expanded nationwide by the end of the year. In September 1980, "The Black Hole" was made available for purchase or rental on videocassette. In 1982, Disney announced it had partnered with RCA to release nine of their films on the CED videodisc format, of which "The Black Hole" was re-released in the following year. The film was re-issued on VHS and LaserDisc as an installment of the "Making Your Dreams Come True" promotional campaign on November 6, 1985.


title: The Black Hole (1979 film)

text: On March 30, 1999, Anchor Bay Entertainment re-released the film on three separate VHS editions: Anniversary Edition, Collector's Edition, and Limited Edition as well as on DVD. The Limited Edition VHS was contained in a collectible tin box and accompanied with nine lobby cards, a 48-page booklet about the making of the film (featuring an interview with director Gary Nelson), and a script of an abandoned alternate ending. On August 3, 2004, and May 2, 2010, Disney re-released the film on DVD that was presented in its original widescreen aspect ratio. Its bonus features included the extended theatrical trailer and a making-of featurette about the film's visual effects.


title: The Black Hole (1979 film)

text: The film was released on Blu-ray for the first time on August 13, 2019, as a Disney Movie Club exclusive. None of the special features on previous home video releases were included.


title: The Black Hole (1979 film)

text: Roger Ebert of the "Chicago Sun-Times" gave the film two stars out of four upon its release, saying it "takes us all the way to the rim of space only to bog us down in a talky melodrama whipped up out of mad scientists and haunted houses." Janet Maslin, reviewing the film for "The New York Times," wrote that the film "is attractively unpretentious and at times quite snappy—among the more sensational stunts is a shot of a huge, molten meteor rolling towards a crew of tiny people, who appear to be right in its path. Its story, about a band of explorers and a wicked space tyrant who pretends to be nice, has a comic-book feeling. But as comic books go, this one is pretty much a page-turner." Gene Siskel of "The Chicago Tribune" found the film to be "dull" and claims "it takes much too long to get its less than grand finale, in which a space villain and some good guys face being swallowed by a collapsed star with enormous gravitational pull." While he praised the film's visual effects, he was critical of the film's cast, claiming they were "dead stars in their own right. If actors get paid to express emotions, then the cast in "The Black Hole" doesn't even deserve the minimum wage."


title: The Black Hole (1979 film)

text: Richard Schickel of "Time" magazine acknowledged that the "overpowering score, squads of menacing heavies, and, especially, two adorable robots—are straight "Star Wars" steals, and because, despite all this sincere flattery and a script and performances that are merely adequate, the fool thing works." He later praised the visual effects and miniature designs as an "amusing mixture of the plush and technological" concluding that it is "good to see the Disney craftsmen doing what they do best on such a grand and risky scale." Reviewing the film in "Ares Magazine", Vincent Misiano commented that "In the final analysis, "The Black Hole" is similar to its natural namesake. Nothing can escape from it either. Not a glimmer of imagination or inspiration. Perhaps if Pluto and Mickey hadn't been involved …" In "Imagine" magazine, Colin Greenland stated that "Even more awesome than the special effects is the stupidity of the script; and the cute robots will have you reaching for a tin-opener."


title: The Black Hole (1979 film)

text: Science fiction historian John Clute dismissed "The Black Hole" as "a silly concoction" where "the story disappears down the hole". Phil Hardy, writing in "The Aurum Film Encyclopedia", also gave the film a negative review, saying "The Black Hole" featured "the most heavy-handed dialogue imaginable" and added that the film's climax "has no dramatic power at all". Author John Kenneth Muir wrote an extensive review of the film that delved into some of the nuances and metaphysical ideas which marked "The Black Hole" as more adult-oriented fare than Disney had previously been involved with. In 2014, astrophysicist Neil deGrasse Tyson deemed the film to be the least scientifically accurate movie of all time. Criticizing the film, he noted, "They not only got none of the physics right about falling into a black hole, had they gotten it right it would have been a vastly more interesting movie."


title: The Black Hole (1979 film)

text: On the review aggregator website Rotten Tomatoes, the film has an approval rating of 40% based on 35 reviews with an average rating of 5.4/10. The site's consensus states: "While lavishly crafted and brimming with ambitious ideas, "The Black Hole" probes the depths of space with an unexciting story and hokey melodrama."


title: The Black Hole (1979 film)

text: Since the film's release, "The Black Hole" has become a cult classic among science fiction film fans.


title: The Black Hole (1979 film)

text: In November 2009, it was reported that Disney had plans to remake "The Black Hole". Director Joseph Kosinski, who also directed Disney's "" (2010) and producer Sean Bailey were attached to the production. By April 2013, Jon Spaihts, who wrote the script for the "Alien" prequel "Prometheus" (2012), had signed on as screenwriter.


title: The Black Hole (1979 film)

text: In 2016, it was announced that the remake was put on hold because Spaihts' script was considered "too dark for a Disney movie". Spaihts commented:"Black Hole" was an amazing experience. That was one of those movies I was stuck on until I cracked the beginning, and suddenly it just started to flow. I loved that script. It sits uneasily in Disney's world as a dark epic, and Disney is in a very colorful place. They already have multiple big space epics going, so I don’t know how or whether it'll find its way to light of day, but I sure wrote a heck of a movie and was thrilled to do it. It was very faithful to the original but clever in all the ways in that first film was silly, I hope.


title: The Black Hole (1979 film)

text: In June 2022, Kosinski revealed that the project was initially cancelled due to having numerous similarities to Christopher Nolan's "Interstellar" (2014). However, he expressed hope at reviving it in the future.


title: Purpose (Justin Bieber album)

text: Purpose is the fourth studio album by Canadian singer Justin Bieber. It was released through Def Jam Recordings and School Boy Records on November 13, 2015, as the follow-up to his 2012 album "Believe". The album features guest appearances from Big Sean, Travis Scott, Halsey, Skrillex, Diplo, and Ariana Grande. The deluxe version was released simultaneously on the same day. It features an extra guest appearance from Nas. Production was handled by Bieber himself, Skrillex and Diplo from Jack Ü, BloodPop, Benny Blanco, the Audibles, Soundz, Mike Dean, Ian Kirkpatrick, and Andre Harris, among others.


title: Purpose (Justin Bieber album)

text: In early 2015, Bieber collaborated with Skrillex and Diplo on the US top-ten single, "Where Are Ü Now", from their debut studio album as Jack Ü, "Skrillex and Diplo Present Jack Ü"; the song also appears on "Purpose". Bieber then found what would be the record's sonic direction and worked with Skrillex on a handful of the album's songs. "Purpose" was described as a mix of EDM and dance-pop, with influences of tropical house in some tracks and live instruments such as acoustic guitars in some others, with the help of his friend and frequent musical collaborator, Poo Bear.


title: Purpose (Justin Bieber album)

text: "Purpose" debuted at number one on the US "Billboard" 200, earning 649,000 album-equivalent units in its first week of release, giving Bieber the largest first-week sales of his career and his sixth number-one album in the United States. Elsewhere, it reached the top of the charts in another eleven countries. The album was supported by four singles: "What Do You Mean?", "Sorry", "Love Yourself", and "Company". The former three singles all reached number one on the Canadian Hot 100, US "Billboard" Hot 100 and the UK Singles Chart. The album was among the best-selling albums of both 2015 and 2016. "Purpose" is a pop, R&B, soul, and EDM album. The album was developed after the release of his compilation album, "Journals" (2013), which saw him move musically in a more R&B direction.


title: Purpose (Justin Bieber album)

text: "Purpose" was nominated for Album of the Year and Best Pop Vocal Album at the 2017 Grammy Awards. "Love Yourself" was nominated for Song of the Year and Best Pop Solo Performance. The album won the American Music Award for Favorite Pop/Rock Album. To promote the album, Bieber gave several televised interviews and performances, as well as releasing "dance videos" for all of the album's tracks in a project called "Purpose: The Movement". Furthermore, Bieber embarked on his Purpose World Tour in 2016, which was his first concert tour to perform in major stadiums worldwide. The album has since been certified 5× platinum by the Recording Industry Association of America (RIAA).


title: Purpose (Justin Bieber album)

text: While promoting his third studio album, "Believe" (2012), with the album's Believe Tour throughout 2012 and 2013, Bieber started recording songs on the tour and confirmed in January 2013 that he was writing for a new album. Five months later he confirmed a new album for 2013, with his manager announcing they were going to think outside the box and release a different type of album. In October 2013, Bieber started the "Music Mondays" project, a ten-week digital download campaign in which one new song was released every Monday night. After the completion of the project, in December 2013, Bieber released the ten songs from the campaign along with new tracks in a limited-edition collection called "Journals". Quickly afterwards in January 2014, record producer Douglas Romanow announced that Bieber was recording new music with him. In the same month, Jason "Poo Bear" Boyd, who previously worked on the majority of songs on "Journals", started recording heavily with the singer as well. The next month, the singer confirmed he was recording new music. In March 2014, he posted on his Instagram a preview of a song called "Life Is Worth Living", while in April, he promised on his Twitter about his new music and that it would be the "best" he had ever made, while working in the recording studio on the album.


title: Purpose (Justin Bieber album)

text: For over a few months in 2014, he continued to teased these snippets of new songs on his social media, – none of them were released, though some were later leaked online – as well as possible collaborators, such as Ariana Grande, T-Pain, Cody Simpson and others. With Simpson, he planned to release an acoustic collaboration album, but decided to cancel; instead they released a single called "Home to Mama" in November 2014. His label also organized writing camps with a handful of songwriters to write songs for the singer, however he didn't feel connected with the songs. In November 2014, it was reported that American DJs and producers Diplo and Skrillex were working with Bieber on the album. Eventually, he promised a new album for 2015, declaring that it was going to be "a great new chapter for me." In January 2015, his manager Scooter Braun shared on his Instagram a picture of Bieber with record producer Rick Rubin, while in March 2015, in an interview for "USA Today", Bieber announced he was working with Kanye West. During the interview, he also revealed that he had to redo the whole album since "it didn't match up to where I am now and where my head's at." According to himself, "What you are thinking about all the time is what you write, and now that I'm thinking about more positive things, it completely changes my music.


title: Purpose (Justin Bieber album)

text: In a July interview, he talked about working with Skrillex, saying: "Skrillex is a genius. He's super futuristic and I just love his sounds. I think being able to incorporate that sound with what I’m doing has been super cool because it's like new and fresh, and I feel like no one's done it before." Skrillex also commented about working with Bieber, explaining: "I heard some well-written songs that were really good that they wanted me to do production on and from there, we wrote some new songs. It was an opportunity to try some stuff that I had never done before and we ended up making something really unique." Bieber also commented about West, declaring: "I've been in the studio with him for the past month or so. I think that he just pushes you. He definitely wants it to be my way and my direction and he doesn't want to steal what I want...that's why artists love to go to him, because he pulls something out of you that other people don't." In August 2015, "Billboard" reported that Bieber was also working with Mason "MdL" Levy and Semi Precious Weapons' Justin Tranter. In October 2015, his manager teased a possible collaboration with American singer Halsey, while Bieber confirmed that British singer-songwriter Ed Sheeran wrote a song for the album.


title: Purpose (Justin Bieber album)

text: In August 2015, Jason Lipshut of "Billboard" reported that the album was "apparently [going to be] a mix of EDM-pop, soul following the downbeat acoustic-R&B of his 2013 project "Journals"." Lipshut also noted that "sources say that the new album will include multiple piano ballads in which Bieber reflects upon his personal missteps, as well as spoken-word outros where he directly addresses his fans." According to "SoulBounce", the album's sound is "reminiscent of Chris Brown’s pop side". In an interview during the Wango Tango festival, Bieber talked about the album's direction, saying: "Overall, I'm just happy with the place I'm at creatively. I feel like this is probably the best I've been. There's not really a direction. It's like, uplifting music that people can dance to...it's a little different, it's really uplifting and people are going to smile when they listen to it." When asked if the song "Where Are Ü Now", previously released as a single from Jack Ü (a duo between DJs and the album's collaborators Diplo and Skrillex) which features Bieber, would be indicative of the sound on the album, he responded that the album would have "'snippets of that type of stuff' (presumably EDM) but that that would be 'really musical [with] a lot of real instrumentation'." He also commented that he was "trying to have a consistent sound and I get kind of depressed cause I’m so... like, I want it to work so badly. You know I want people to love it, and inspire people and sometimes I feel like, is this good enough? Is this the direction I want to go?."


title: Purpose (Justin Bieber album)

text: "Purpose" blends dance beats, EDM vibes with stripped-down R&B ballads. The album also makes use of atmospheric instruments as well as hi-hats, bass and synths.


title: Purpose (Justin Bieber album)

text: The downtempo intro track "Mark My Words" was considered a prelude into the album's overall sound: a "mix of both up-beat and mellow tracks with striking production and songwriting," with Bieber using his falsetto. "I'll Show You" was considered a "chilled-out EDM ballad," having atmospheric synthesizers, fat bass, snapping trap percussion, and sheets of cascading synths. "What Do You Mean" and "Sorry" were both considered tropical house songs, with the former using "pan flute and piano" while having "hints of dark electropop" dance-pop and the latter having dancehall influences. The album also features the Euro disco, synth-pop and EDM track "Children", the funky disco pop "Been You" and "Get Used to It", the "airy, dubsteppy" and dark pop "The Feeling"—which "Complex" described as a "retread of the sad indie pop popularized by artists like Ellie Goulding and Tove Lo"—, as well as "Where Are Ü Now", which initially was a slow piano ballad named "The Most", which is available in its original format on some editions of the album, and was transformed in an EDM track that both Skrillex and Diplo "took a lot of his vocals and [...] added natural harmonies," as well as "taking Justin's vocals as he's singing 'I need you the most' and distorting it," which made people believe it was a "dolphin sound."


title: Purpose (Justin Bieber album)

text: In contrast to the dance-oriented songs present on the album, "Purpose" also features an acoustic pop song, "Love Yourself", which has minimal arrangement, using a guitar and a "brief flurry of trumpets" and folk influence, as well as the piano ballads "Life Is Worth Living" and the title track, "Purpose". Meanwhile, "Company" blends electropop and R&B, and it was compared to Bieber's previous release, "Journals" (2013). "No Pressure" is a "dreamy" and dark R&B track which features rapper Big Sean, who previously worked with Bieber on "Believe" "As Long As You Love Me" and "Journals" "Memphis", and has an "elastic guitar riff" and "shimmering, processed acoustic guitar." "No Sense" is a hip-hop tinged track, with bass-riddled synthesizers and influences of trap music, mostly due to Travis Scott's appearance. His rap was noted for being using auto-tune in excess, while Bieber's vocals were compared to those of Justin Timberlake. "We Are" and "Trust" also rely on hip-hop, with the first featuring a "heavy background looping" and the last "sharp production sounds and switches in flow," with a Drake-influence. "Hit the Ground", included on the Walmart and Japanese editions, features "organic shifts in tempo" and "Skrillex's imaginative drop," which was compared to "chip-tune bagpipes."


title: Purpose (Justin Bieber album)

text: While being asked about the themes on the album in an interview for "The Fader", Jason "Poo Bear" Boyd, one of the album's main songwriters, claimed: "It's about keeping in mind and in tune with what's going on with Justin. Just being honest. We really set up for this project to be inspirational. If we talked about a girl, it was something that just happened. Overall, we touch on his personal life like his relationship issues, but at the same time, it's a healthy balance of inspirational music. We're just thinking about making sure that it's not negative, but uplifting. Even the music that talks about his relationships, it's feel-good music. It's nothing that will make you depressed." In an interview for "USA Today", Bieber himself declared that the song on the album are "bout growing, being in touch with yourself. What can I say, it's life experiences, and knowing that you can and get back up and keep going. Hope and faith, that's what's gotten me through this too, my faith. What I believe in. You're around some people sometimes and it might taint what you believe. I think that's what happened with me, I lowered my beliefs." When asked about inspirations for the album and if his former girlfriend Selena Gomez inspired him, he admitted: "A lot of my inspiration comes from her. It was a long relationship and a relationship that created heartbreak and created happiness, and a lot of different emotions that I wanted to write about. So there's a lot of that on this album."


title: Purpose (Justin Bieber album)

text: "Purpose" was considered by "The Guardian"s Caroline Sullivan as an album with the songs serving as "a regretful look back and a fresh start." The album's themes were also seen as a "giant apology – to his ex, Selena Gomez, and to his public, for various well-documented misdemeanours." As described by "Complex" Sheldon Pearce, ""Purpose" is, at its core, a formal request for a pardon through music." The album's opening track, "Mark My Words", is a solemn plea, where he promises to "give you all I got," and "let his actions speak louder than his words." In "I'll Show You", an open letter to fans, offers "an autobiographical glimpse into the difficulty of growing up in the public eye." "What Do You Mean?" was described as "self-professed men's anthem for not being able to figure out the opposite sex," while "Sorry" asks "a sincere apology directed to what can be presumed is a former love" in attempt at a course correction. "Love Yourself" was noted for being a "deadpan kiss-off to a snobby ex," with some critics noting that the real meaning "hidden under the deceptive title 'Love Yourself' is "fuck yourself". "Company", the album's sixth track, "looks forward to getting to know someone attractive, but also sets some healthy boundaries for doing so," while "No Pressure" "invites an ex back into relationship, but insists, 'I don't wanna add to your pain at all', while Big Sean references Yoko Ono, "Street Fighter" and TV series "Empire". The eighth track "No Sense" "talks about sharing a bed with a woman", with Travis Scott rapping "lines about how he misses being 'boo'ed up'."


title: Purpose (Justin Bieber album)

text: The ninth track "The Feeling" "touches on questioning the overwhelming and emotional rush of falling in love," with Bieber and Halsey asking themselves: "Am I in love or am I in love with the feeling?." "Life Is Worth Living" finds Bieber "mull[ing] redemption and forgiveness [...] saying that you can crucify him but 'only God can judge me'." According to one of its songwriters, Jason Boyd, "[It's a] positive record that says life is worth living, we're supposed to live. We're supposed to be here. [...] People making mistakes, learning from them, and not letting that be it, but say, 'You know what? I'm not gonna do that again. Life is worth living, I'm not just gonna give up just because I fell. I'm gonna try harder because my life is worth it.' It just has such a positive meaning, I feel like it's gonna save a lot of lives." "Where Are Ü Now" "talks about caring and praying for an ex who didn't return the favor," "Children" has a social consciousness message and "advocates for making the world a better place for its youngest residents" and was unfavorably compared to Michael Jackson's tracks "Man In the Mirror and "Earth Song". The title track, "Purpose", "recounts a time that he was at the end of his rope, but God blessed him with purpose.", and is his second CCM song after "Pray". It ends with a "lengthy voiceover" thoughts about God. "Get Used To It" has "euphemisms about blooming flowers and exploding fireworks," "We Are" features Nas in lines about serendipity and doing yoga," "Trust" talks about "still believing in love", and "All In It" "reflects on trusting God to fill him up inside" and has a spoken outro where he declares that "God is perfect and he never disappoints, so I just get my recognition from Him and give Him my recognition." Justin revealed on "The Ellen DeGeneres Show" that there are three songs on the album about Gomez—"Mark My Words", "What Do You Mean?" and "Sorry".


title: Purpose (Justin Bieber album)

text: According to Bieber, he chose the album's title because he felt like he lost his purpose and felt that he finally got his purpose back. He continued: "'The word ['purpose'] is so important in life... My purpose is to inspire people and use my platform to help people'." As noted by MTV News' Patrick Hosken, in the album's cover, "Bieber is shirtless and assuming a very dignified stance, hands meeting in a prayer-like pose, head looking down at what lies at his torso: the word 'Purpose,' written in the same script we first saw [the] week when he unveiled the title." The cover also has a symbol, which "resembl[es] an asymmetrical cross with a small circle attached covering the entire background and painted on his torso." The deluxe edition uses the same cover, only the background & crosses are tinted in black. "Purpose" was initially banned in various Middle Eastern countries and Indonesia due to the cover art's heavy Christian references, most prominently Bieber's cross tattoo and his praying stance, which were deemed "too provocative". An alternate cover was issued for these countries, depicting Bieber atop of a cliff, looking out over a shore.


title: Purpose (Justin Bieber album)

text: In 2015, it was announced that Bieber was going to take his time to announce the album's release, since he was not going to rush an album just to rush an album. During a May 9 Wango Tango interview he revealed: "We're just wrapping it up now so it's in the final-touch stage...it's soon." In a September 2015 interview with Jimmy Fallon, the singer announced the album was going to be released on November 13, 2015. On October 2, 2015, Bieber revealed the album's title, "Purpose", on his Twitter account, while on October 9, 2015, he revealed through his Instagram account its cover art made by the street artist Retna. On October 16, 2015, "Purpose" was made available to pre-order. A remixed version of "What Do You Mean?" with additional vocals from Ariana Grande was made available to those who pre-ordered the album on iTunes. On October 28, 2015, Bieber announced the album track listing through a series of tweets that displayed each title graffitied on a wall in various countries.


title: Purpose (Justin Bieber album)

text: To promote the album, Bieber appeared on many magazines, such as "Billboard", "Complex", "Interview Magazine", "i-D", and "NME". Bieber debuted the track "What Do You Mean?" in a medley with "Where Are Ü Now" during the MTV Video Music Awards on August 30, 2015. This was followed by a number of other televised performances, where he also performed the song during "The X Factor Australia" "World Famous Rooftop", where he also sang 'Hold Tight', "All That Matters", "Boyfriend" and "As Long As You Love Me", "The Today Show", where he also performed "Where Are Ü Now", "Boyfriend" "As Long As You Love Me" and "Baby", "The Tonight Show Starring Jimmy Fallon", the 2015 "Think It Up" telecast, the 2015 MTV Europe Music Awards, NRJ Music Awards and BBC Radio 1's Teen Awards, where he also performed "Where Are Ü Now" and "Boyfriend". From November 9, 2015, to November 13, 2015, "The Ellen DeGeneres Show" hosted a #BieberWeek, where the singer gave interviews, participated of games, pranks, and performed "What Do You Mean?", "Sorry" and "Love Yourself". On November 17, 2015, he returned to the Tonight Show to perform "Sorry", while the next day he returned to "Today Show" and performed "What Do You Mean?", "Sorry", "Love Yourself", as well as new songs "Company", "The Feeling" with Halsey and "No Pressure" with Big Sean. Bieber also performed a medley of "What Do You Mean?", "Where Are Ü Now" and "Sorry" during the 2015 American Music Awards. Bieber also made a set during Capital FM's Jingle Bell Ball 2015.


title: Purpose (Justin Bieber album)

text: On November 14, 2015, Bieber released music videos for each track of the standard edition of the album on his Vevo account. The project was considered "a series of video vignettes to accompany the songs from the album" and "when they are played in sequence they form a 30-minute dance film." Mostly videos do not feature Bieber, however they feature several appearances from the album's guests, such as Big Sean, Halsey, Travis Scott, Skrillex and Diplo. The videos were choreographed by Bieber's longtime choreographer Parris Goebel.


title: Purpose (Justin Bieber album)

text: On November 11, 2015, Bieber announced that he will embark on the Purpose World Tour in support of the album. The tour started in Seattle, Washington on March 9, 2016, and concluded in London, United Kingdom on July 2, 2017.


title: Purpose (Justin Bieber album)

text: "What Do You Mean?" was released as the album's lead single on August 28, 2015. It was preceded by a social media campaign, which started on July 29, 2015, where Bieber "commissioned at least one celebrity per day to hold up a sign teasing the new track and counting down the days to its release." Upon release, the song became Bieber's first number one single on the "Billboard" Hot 100 chart in the United States, debuting at number one on the week listed on September 19, 2015, replacing The Weeknd's "Can't Feel My Face" for one week. It was also his first number-one single in Australia and the United Kingdom, where he also broke a streaming record, while also topping the charts of other eleven countries. The song's music video features "shirtless Bieber in bed with a young woman" and "getting kidnapped and punching around some masked men", as well as appearance from actor John Leguizamo.


title: Purpose (Justin Bieber album)

text: "Sorry" was announced as the album's second single on October 16, 2015. It was released on October 23, 2015. A day before, a music video for the song was released, showing a group of women dancing to the song. The song reached the top of the charts in the United States, remaining at the top for three weeks, as well as the Canadian and the UK charts. Moreover, the single has peaked within the top five in almost every other market, including number one in other six countries.


title: Purpose (Justin Bieber album)

text: "Love Yourself" was first premiered on Zane Lowe's Beats 1 radio show and released digitally on November 9, 2015, in advance of the album's release and later announced as the third official single on December 7, 2015. It entered several national charts after the release of "Purpose", and topped the charts in eight countries, including Australia, where it remained for seven weeks at the top, Ireland and New Zealand, spending eight weeks at number-one in Ireland and ten weeks at the summit of New Zealand the United Kingdom, where the song spent six weeks at the top, and the United States, becoming his third consecutive number-one single of the album.


title: Purpose (Justin Bieber album)

text: "Company" was announced as the album's fourth and final single on February 19, 2016. It was serviced to CHR/Pop stations on March 8, 2016, and was issued to Urban radio on March 29, 2016. The official music video was released on June 8, 2016.


title: Purpose (Justin Bieber album)

text: "I'll Show You" was released as the first promotional single on November 1, 2015, accompanied by a music video. It shows Bieber "running through a lush green landscape in Iceland, as well as "tumbling down hills," "skateboarding on top of an abandoned plane" and "[braving] ice water in just his [underwear]." It reached the top-ten in four countries, including Canada, and the top-twenty in six others, including Australia, the United States and the United Kingdom. The album also features Bieber's collaboration with Jack Ü, "Where Are Ü Now", originally released as a single from the latter's album, "Skrillex and Diplo Present Jack Ü". It became a top-ten single in more than ten countries, including the United States.


title: Purpose (Justin Bieber album)

text: Eight songs from the album charted in the top 40 of the UK Singles Chart the same week that the album was released. They were, in order of chart appearance, "Sorry", "Love Yourself", "What Do You Mean?", "I'll Show You", "Company", "Where Are Ü Now", "Mark My Words" and "The Feeling". Bieber set a record for having the most simultaneous top 40 entries from a living artist. In addition to this, every song from "Purpose" (standard edition and deluxe edition bonus tracks included) charted within the top 100, also within the same week.


title: Purpose (Justin Bieber album)

text: "Purpose" received generally positive reviews from music critics. At Metacritic, which assigns a normalized rating out of 100 to reviews from mainstream critics, the album received an average score of 63, based on 20 reviews. Kenneth Partridge of "Billboard" magazine gave the album four out of five stars, praising it for "[boasting] a consistent palette of lush, low-key electro-dance sounds", also commending the use of "sun-warped synths, chipmunk accent vocals, rattling trap hi-hats, and loads of bass." Leah Greenblatt of "Entertainment Weekly" also complimented "Purpose" for featuring "a skittering, metallic synthesis of dance music and modern R&B", arguing that this new musical direction "probably owes a lot to new-school collaborators Diplo and Skrillex, as well as the lesser-known production wizard Poo Bear." Similarly, Neil McCormick of "The Daily Telegraph" complimented the album for being "less of a mainstream crowd pleaser" but more of a "quirky, atmospheric electro R'n'B concoction with sci-fi sounds and offbeat vocal samples." He argued that this sound "[focuses] attention on the star's soft, supple and seductive singing" and concluded that "despite the presence of EDM star Skrillex amongst the production credits, surprising restraint is exercised throughout, with tracks rarely developing into full tilt techno anthems."


title: Purpose (Justin Bieber album)

text: "Spin" Andrew Unterberger praised the album, stating: "[B]y giving us the best album of his career, and subsequently re-ascending to Top 40's mountaintop, Bieber's answered his own question: In pop music, it's never too late to say you’re sorry." Bianca Gracie of "Idolator" agreed, claiming that the album "is no doubt Justin's best collective LP thus far and shows that he is finally confident in revealing his true artistry. And that is nothing to be sorry about, so keep your needy apologies to yourselves." Patrick Ryan of "USA Today" praised the "collaborative muscle and confidence" on the album, noting that they show "an artist who is completely unafraid to reinvent himself and create the very definition of a comeback album [...] With Purpose, he proves himself as one of today's most forward-thinking pop stars, and because of that, we're newly converted Beliebers." Al Horner of "NME" magazine gave the album three out of five stars commenting that "Purpose" "[is] certainly a start at reinvention" and that "plenty of good choices have been made here." In her review for "The Guardian", Caroline Sullivan noted that "the musical direction owes much to co-producer Skrillex, whose unexpectedly subtle electronic palette complements Bieber's affectedly breathy voice," arguing that "the voice soon palls, but the songs are often interesting." While analysing Bieber's "Purpose" and One Direction's "Made in the A.M.", Jon Caramanica of "The New York Times" argued that "even though Mr. Bieber is younger than all of the men of One Direction, he sounds exponentially more experienced, and exponentially more fatigued on "Purpose"," complimenting the album for showing that it proves that Bieber is "the best singer of the bunch, and the one with a clear vision for his sound, even if he's being largely denied it here." For "The National", the album "functions as a coming of age album in the worst way: learn how to emotionally abuse women, and then you’ll be a man," adding "Bieber's strategy is a Janus-faced one. He simultaneously apologises for and doubles down on his dislikeability – but cunningly, now manifests the latter in more socially acceptable ways."


title: Purpose (Justin Bieber album)

text: In his AllMusic review, Andy Kellman gave the album 3 out of 5 stars, and while calling it "a bumpy, oddly compelling restart," he observed that "'Purpose' should hook open-minded pop fans who previously paid him no mind, and it could even win back some of those who wrote Bieber off years ago." While providing a generally favorable comment on the album, Brad Nelson of "Pitchfork" found out that the album "doesn't particularly follow up on the advances suggested by his previous release, the 2013 R&B experiment 'Journals'," while also noting that "[t]he songs on Purpose have a similarly inanimate feeling; they seem to radiate more than they move." Annie Zaleski of "The A.V. Club" felt that the album "takes itself so seriously that too often it inadvertently suppresses exactly what made Bieber so appealing in the first place." Sam C. Mac of "Slant Magazine" was more mixed, opining that "[i]f Bieber wants to sell us on forgiveness and the self-improvement angle that lyrics like 'be a better me' seem to promote, maybe having the conviction to follow through on his intended musical reinvention would've been the best possible good faith gesture." For "Consequence of Sound" editor Janine Schaults, "Purpose reaches some of the highest highs and lowest lows in Bieber's career. Skrillex and Diplo successfully serve up twitchy beats ready to incite anything with a pulse, but the sentiment at the album's core leans toward insufferable. Even when Bieber hits mediocre, he reaches it by stumbling headfirst down a cliff."


title: Purpose (Justin Bieber album)

text: "Purpose" was featured on several year-end list of best albums. It was listed at number 15 on "Spin"<nowiki>'</nowiki>s "25 Best Pop Albums of 2015" list, with James Grebey stating: "The 21-year-old's malleable voice (which never lost its halo despite some sinning) has rarely sounded better, especially surrounded by warm tropical beats and thrillingly new-sounding production flourishes."


title: Purpose (Justin Bieber album)

text: In the United States, the competition between Bieber and One Direction began when the British boy band announced the release date of "Made in the A.M.", set to be their last album before their hiatus in March 2016. Many compared the "war" between the two pop forces to 50 Cent and Kanye West's 2007 battle for number one. However, Bieber's "Purpose" debuted at number one on the "Billboard" 200 chart for the week ending November 19, 2015, with 649,000 equivalent album units, including 522,000 traditional album sales. It marked Bieber's sixth number-one album and largest sales week. It also surpassed his previous high, logged with "Believe", which sold 374,000 units in 2012. Additionally, "Purpose"s debut marked the largest weekly unit total for an album since the "Billboard" 200 began tracking popularity based on overall equivalent units earned in 2014 and beat the debut week of Drake's "If You're Reading This It's Too Late" (which sold 535,000 equivalent units in 2015). Also, "Purpose"s 522,000 mark the largest sales week since Taylor Swift's "1989" debuted with 1.29 million (November 2, 2014) and the largest sales for a male artist album since Eminem's "The Marshall Mathers LP 2" sold 792,000 (November 3, 2013). "Purpose" also broke the global and US streaming record for an album in its first week of release with 205 million global streams and 77 million in the United States. In its second week, "Purpose" earned 290,000 units (down 55%). It sold 184,000 in traditional album sales (down 65%) and was beaten to the top by Adele's "25", which debuted at number one with a record-breaking 3.38 million. In December 2015, the album surpassed the 1 million mark in US sales, becoming Bieber's fifth million-selling album. Also, on this exact date, specifically December 5, 2015, every song on Purpose (even the deluxe version) had entered the Billboard Hot 100, except for "All In It". Eventually, the album was announced as the third best-selling album of 2015 in the US, with sales of 1,269,000 copies. As of December 2016, "Purpose" has sold 1.812 million copies in the nation.


title: Purpose (Justin Bieber album)

text: "Purpose" debuted at number 2 on the UK Albums Chart, selling 90,596 in its first week, marking the second highest first-week figures of 2015, at the time, behind One Direction's "Made in the A.M." (2015), which debuted at number one the same week with 93,189 chart sales. In its second and third week on sale it stayed at number three. "Purpose" was the fifth best-selling album of 2015 in the UK with combined sales of 645,000 copies. As of June 2016, the album has accumulated 1,200,000 combined sales in the UK.


title: Stealth startup

text: A stealth startup is a type of startup company that operates in stealth and silence to outsiders, avoiding public attention. This may be done to hide information from competitors (which may include non-disclosure agreements), or as part of a marketing strategy to manage public image and generate expectations and interest from potential clients. A Stealth Startup normally only operates in stealth mode for its first few years.


title: Stealth startup

text: The phenomenon is well known in the venture capital (VC) community. Since investors may have to disclose funding a stealth startup, their names are made public, but often only a general summary description is known about the company.


title: Mathematical proof

text: A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in "all" possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work.


title: Mathematical proof

text: Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement of natural language, are considered in proof theory. The distinction between formal and informal proofs has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics, oral traditions in the mainstream mathematical community or in other cultures. The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.


title: Mathematical proof

text: The word "proof" comes from the Latin "probare" (to test). Related modern words are English "probe", "probation", and "probability", Spanish "probar" (to smell or taste, or sometimes touch or test), Italian "provare" (to try), and German "probieren" (to try). The legal term "probity" means authority or credibility, the power of testimony to prove facts when given by persons of reputation or status.


title: Mathematical proof

text: Plausibility arguments using heuristic devices such as pictures and analogies preceded strict mathematical proof. It is likely that the idea of demonstrating a conclusion first arose in connection with geometry, which originated in practical problems of land measurement. The development of mathematical proof is primarily the product of ancient Greek mathematics, and one of its greatest achievements. Thales (624–546 BCE) and Hippocrates of Chios (c. 470–410 BCE) gave some of the first known proofs of theorems in geometry. Eudoxus (408–355 BCE) and Theaetetus (417–369 BCE) formulated theorems but did not prove them. Aristotle (384–322 BCE) said definitions should describe the concept being defined in terms of other concepts already known.


title: Mathematical proof

text: Mathematical proof was revolutionized by Euclid (300 BCE), who introduced the axiomatic method still in use today. It starts with undefined terms and axioms, propositions concerning the undefined terms which are assumed to be self-evidently true (from Greek "axios", something worthy). From this basis, the method proves theorems using deductive logic. Euclid's book, the "Elements", was read by anyone who was considered educated in the West until the middle of the 20th century. In addition to theorems of geometry, such as the Pythagorean theorem, the "Elements" also covers number theory, including a proof that the square root of two is irrational and a proof that there are infinitely many prime numbers.


title: Mathematical proof

text: Further advances also took place in medieval Islamic mathematics. While earlier Greek proofs were largely geometric demonstrations, the development of arithmetic and algebra by Islamic mathematicians allowed more general proofs with no dependence on geometric intuition. In the 10th century CE, the Iraqi mathematician Al-Hashimi worked with numbers as such, called "lines" but not necessarily considered as measurements of geometric objects, to prove algebraic propositions concerning multiplication, division, etc., including the existence of irrational numbers. An inductive proof for arithmetic sequences was introduced in the "Al-Fakhri" (1000) by Al-Karaji, who used it to prove the binomial theorem and properties of Pascal's triangle. Alhazen also developed the method of proof by contradiction, as the first attempt at proving the Euclidean parallel postulate.


title: Mathematical proof

text: Modern proof theory treats proofs as inductively defined data structures, not requiring an assumption that axioms are "true" in any sense. This allows parallel mathematical theories as formal models of a given intuitive concept, based on alternate sets of axioms, for example Axiomatic set theory and Non-Euclidean geometry.


title: Mathematical proof

text: As practiced, a proof is expressed in natural language and is a rigorous argument intended to convince the audience of the truth of a statement. The standard of rigor is not absolute and has varied throughout history. A proof can be presented differently depending on the intended audience. In order to gain acceptance, a proof has to meet communal standards of rigor; an argument considered vague or incomplete may be rejected.


title: Mathematical proof

text: The concept of proof is formalized in the field of mathematical logic. A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones. This definition makes the concept of proof amenable to study. Indeed, the field of proof theory studies formal proofs and their properties, the most famous and surprising being that almost all axiomatic systems can generate certain undecidable statements not provable within the system.


title: Mathematical proof

text: The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice. A classic question in philosophy asks whether mathematical proofs are analytic or synthetic. Kant, who introduced the analytic–synthetic distinction, believed mathematical proofs are synthetic, whereas Quine argued in his 1951 "Two Dogmas of Empiricism" that such a distinction is untenable.


title: Mathematical proof

text: Proofs may be admired for their mathematical beauty. The mathematician Paul Erdős was known for describing proofs which he found to be particularly elegant as coming from "The Book", a hypothetical tome containing the most beautiful method(s) of proving each theorem. The book "Proofs from THE BOOK", published in 2003, is devoted to presenting 32 proofs its editors find particularly pleasing.


title: Mathematical proof

text: In direct proof, the conclusion is established by logically combining the axioms, definitions, and earlier theorems. For example, direct proof can be used to prove that the sum of two even integers is always even:


title: Mathematical proof

text: This proof uses the definition of even integers, the integer properties of closure under addition and multiplication, and the distributive property.


title: Mathematical proof

text: Despite its name, mathematical induction is a method of deduction, not a form of inductive reasoning. In proof by mathematical induction, a single "base case" is proved, and an "induction rule" is proved that establishes that any arbitrary case implies the next case. Since in principle the induction rule can be applied repeatedly (starting from the proved base case), it follows that all (usually infinitely many) cases are provable. This avoids having to prove each case individually. A variant of mathematical induction is proof by infinite descent, which can be used, for example, to prove the irrationality of the square root of two.


title: Mathematical proof

text: A common application of proof by mathematical induction is to prove that a property known to hold for one number holds for all natural numbers:


title: Mathematical proof

text: Let } be the set of natural numbers, and let be a mathematical statement involving the natural number belonging to such that


title: Mathematical proof

text: For example, we can prove by induction that all positive integers of the form are odd. Let represent " is odd":


title: Mathematical proof

text: Proof by contraposition infers the statement "if "p" then "q"" by establishing the logically equivalent contrapositive statement: "if "not q" then "not p"".


title: Mathematical proof

text: For example, contraposition can be used to establish that, given an integer formula_1, if formula_2 is even, then formula_1 is even:


title: Mathematical proof

text: In proof by contradiction, also known by the Latin phrase "reductio ad absurdum" (by reduction to the absurd), it is shown that if some statement is assumed true, a logical contradiction occurs, hence the statement must be false. A famous example involves the proof that formula_10 is an irrational number:


title: Mathematical proof

text: To paraphrase: if one could write formula_10 as a fraction, this fraction could never be written in lowest terms, since 2 could always be factored from numerator and denominator.


title: Mathematical proof

text: Proof by construction, or proof by example, is the construction of a concrete example with a property to show that something having that property exists. Joseph Liouville, for instance, proved the existence of transcendental numbers by constructing an explicit example. It can also be used to construct a counterexample to disprove a proposition that all elements have a certain property.


title: Mathematical proof

text: In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because the majority of the cases were checked by a computer program, not by hand. The shortest known proof of the four color theorem still has over 600 cases.


title: Mathematical proof

text: A probabilistic proof is one in which an example is shown to exist, with certainty, by using methods of probability theory. Probabilistic proof, like proof by construction, is one of many ways to prove existence theorems.


title: Mathematical proof

text: In the probabilistic method, one seeks an object having a given property, starting with a large set of candidates. One assigns a certain probability for each candidate to be chosen, and then proves that there is a non-zero probability that a chosen candidate will have the desired property. This does not specify which candidates have the property, but the probability could not be positive without at least one.


title: Mathematical proof

text: A probabilistic proof is not to be confused with an argument that a theorem is 'probably' true, a 'plausibility argument'. The work on the Collatz conjecture shows how far plausibility is from genuine proof. While most mathematicians do not think that probabilistic evidence for the properties of a given object counts as a genuine mathematical proof, a few mathematicians and philosophers have argued that at least some types of probabilistic evidence (such as Rabin's probabilistic algorithm for testing primality) are as good as genuine mathematical proofs.


title: Mathematical proof

text: A combinatorial proof establishes the equivalence of different expressions by showing that they count the same object in different ways. Often a bijection between two sets is used to show that the expressions for their two sizes are equal. Alternatively, a double counting argument provides two different expressions for the size of a single set, again showing that the two expressions are equal.


title: Mathematical proof

text: A nonconstructive proof establishes that a mathematical object with a certain property exists—without explaining how such an object can be found. Often, this takes the form of a proof by contradiction in which the nonexistence of the object is proved to be impossible. In contrast, a constructive proof establishes that a particular object exists by providing a method of finding it. The following famous example of a nonconstructive proof shows that there exist two irrational numbers "a" and "b" such that formula_16 is a rational number. This proof uses that formula_10 is irrational (an easy proof is known since Euclid), but not that formula_18 is irrational (this true, but the proof is not elementary).


title: Mathematical proof

text: The expression "statistical proof" may be used technically or colloquially in areas of pure mathematics, such as involving cryptography, chaotic series, and probabilistic number theory or analytic number theory. It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics. See also the "Statistical proof using data" section below.


title: Mathematical proof

text: Until the twentieth century it was assumed that any proof could, in principle, be checked by a competent mathematician to confirm its validity. However, computers are now used both to prove theorems and to carry out calculations that are too long for any human or team of humans to check; the first proof of the four color theorem is an example of a computer-assisted proof. Some mathematicians are concerned that the possibility of an error in a computer program or a run-time error in its calculations calls the validity of such computer-assisted proofs into question. In practice, the chances of an error invalidating a computer-assisted proof can be reduced by incorporating redundancy and self-checks into calculations, and by developing multiple independent approaches and programs. Errors can never be completely ruled out in case of verification of a proof by humans either, especially if the proof contains natural language and requires deep mathematical insight to uncover the potential hidden assumptions and fallacies involved.


title: Mathematical proof

text: A statement that is neither provable nor disprovable from a set of axioms is called undecidable (from those axioms). One example is the parallel postulate, which is neither provable nor refutable from the remaining axioms of Euclidean geometry.


title: Mathematical proof

text: Mathematicians have shown there are many statements that are neither provable nor disprovable in Zermelo–Fraenkel set theory with the axiom of choice (ZFC), the standard system of set theory in mathematics (assuming that ZFC is consistent); see List of statements undecidable in ZFC.


title: Mathematical proof

text: Gödel's (first) incompleteness theorem shows that many axiom systems of mathematical interest will have undecidable statements.


title: Mathematical proof

text: While early mathematicians such as Eudoxus of Cnidus did not use proofs, from Euclid to the foundational mathematics developments of the late 19th and 20th centuries, proofs were an essential part of mathematics. With the increase in computing power in the 1960s, significant work began to be done investigating mathematical objects outside of the proof-theorem framework, in experimental mathematics. Early pioneers of these methods intended the work ultimately to be embedded in a classical proof-theorem framework, e.g. the early development of fractal geometry, which was ultimately so embedded.


title: Mathematical proof

text: Although not a formal proof, a visual demonstration of a mathematical theorem is sometimes called a "proof without words". The left-hand picture below is an example of a historic visual proof of the Pythagorean theorem in the case of the (3,4,5) triangle.


title: Mathematical proof

text: Some illusory visual proofs, such as the missing square puzzle, can be constructed in a way which appear to prove a supposed mathematical fact but only do so under the presence of tiny errors (for example, supposedly straight lines which actually bend slightly) which are unnoticeable until the entire picture is closely examined, with lengths and angles precisely measured or calculated.


title: Mathematical proof

text: An elementary proof is a proof which only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these results have been reproved using only elementary techniques.


title: Mathematical proof

text: A particular way of organising a proof using two parallel columns is often used as a mathematical exercise in elementary geometry classes in the United States. The proof is written as a series of lines in two columns. In each line, the left-hand column contains a proposition, while the right-hand column contains a brief explanation of how the corresponding proposition in the left-hand column is either an axiom, a hypothesis, or can be logically derived from previous propositions. The left-hand column is typically headed "Statements" and the right-hand column is typically headed "Reasons".


title: Mathematical proof

text: The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.


title: Mathematical proof

text: "Statistical proof" from data refers to the application of statistics, data analysis, or Bayesian analysis to infer propositions regarding the probability of data. While "using" mathematical proof to establish theorems in statistics, it is usually not a mathematical proof in that the "assumptions" from which probability statements are derived require empirical evidence from outside mathematics to verify. In physics, in addition to statistical methods, "statistical proof" can refer to the specialized "mathematical methods of physics" applied to analyze data in a particle physics experiment or observational study in physical cosmology. "Statistical proof" may also refer to raw data or a convincing diagram involving data, such as scatter plots, when the data or diagram is adequately convincing without further analysis.


title: Mathematical proof

text: Proofs using inductive logic, while considered mathematical in nature, seek to establish propositions with a degree of certainty, which acts in a similar manner to probability, and may be less than full certainty. Inductive logic should not be confused with mathematical induction.


title: Mathematical proof

text: Bayesian analysis uses Bayes' theorem to update a person's assessment of likelihoods of hypotheses when new evidence or information is acquired.


title: Mathematical proof

text: Psychologism views mathematical proofs as psychological or mental objects. Mathematician philosophers, such as Leibniz, Frege, and Carnap have variously criticized this view and attempted to develop a semantics for what they considered to be the language of thought, whereby standards of mathematical proof might be applied to empirical science.


title: Mathematical proof

text: Philosopher-mathematicians such as Spinoza have attempted to formulate philosophical arguments in an axiomatic manner, whereby mathematical proof standards could be applied to argumentation in general philosophy. Other mathematician-philosophers have tried to use standards of mathematical proof and reason, without empiricism, to arrive at statements outside of mathematics, but having the certainty of propositions deduced in a mathematical proof, such as Descartes' "cogito" argument.


title: Mathematical proof

text: Sometimes, the abbreviation ""Q.E.D."" is written to indicate the end of a proof. This abbreviation stands for ""quod erat demonstrandum"", which is Latin for ""that which was to be demonstrated"". A more common alternative is to use a square or a rectangle, such as □ or ∎, known as a "tombstone" or "halmos" after its eponym Paul Halmos. Often, "which was to be shown" is verbally stated when writing "QED", "□", or "∎" during an oral presentation. Unicode explicitly provides the "end of proof" character, U+220E (∎) .


title: Equations of motion

text: In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations describing the motion of the dynamics.


title: Equations of motion

text: There are two main descriptions of motion: dynamics and kinematics. Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term "dynamics" refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.


title: Equations of motion

text: However, kinematics is simpler. It concerns only variables derived from the positions of objects and time. In circumstances of constant acceleration, these simpler equations of motion are usually referred to as the SUVAT equations, arising from the definitions of kinematic quantities: displacement (), initial velocity (), final velocity (), acceleration (), and time ().


title: Equations of motion

text: A differential equation of motion, usually identified as some physical law and applying definitions of physical quantities, is used to set up an equation for the problem. Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a family of solutions. A particular solution can be obtained by setting the initial values, which fixes the values of the constants.


title: Equations of motion

text: To state this formally, in general an equation of motion is a function of the position of the object, its velocity (the first time derivative of , ), and its acceleration (the second derivative of , ), and time . Euclidean vectors in 3D are denoted throughout in bold. This is equivalent to saying an equation of motion in is a second-order ordinary differential equation (ODE) in ,


title: Equations of motion

text: where is time, and each overdot denotes one time derivative. The initial conditions are given by the "constant" values at ,


title: Equations of motion

text: The solution to the equation of motion, with specified initial values, describes the system for all times after . Other dynamical variables like the momentum of the object, or quantities derived from and like angular momentum, can be used in place of as the quantity to solve for from some equation of motion, although the position of the object at time is by far the most sought-after quantity.


title: Equations of motion

text: Sometimes, the equation will be linear and is more likely to be exactly solvable. In general, the equation will be non-linear, and cannot be solved exactly so a variety of approximations must be used. The solutions to nonlinear equations may show chaotic behavior depending on how "sensitive" the system is to the initial conditions.


title: Equations of motion

text: Kinematics, dynamics and the mathematical models of the universe developed incrementally over three millennia, thanks to many thinkers, only some of whose names we know. In antiquity, priests, astrologers and astronomers predicted solar and lunar eclipses, the solstices and the equinoxes of the Sun and the period of the Moon. But they had nothing other than a set of algorithms to guide them. Equations of motion were not written down for another thousand years.


title: Equations of motion

text: Medieval scholars in the thirteenth century — for example at the relatively new universities in Oxford and Paris — drew on ancient mathematicians (Euclid and Archimedes) and philosophers (Aristotle) to develop a new body of knowledge, now called physics.


title: Equations of motion

text: At Oxford, Merton College sheltered a group of scholars devoted to natural science, mainly physics, astronomy and mathematics, who were of similar stature to the intellectuals at the University of Paris. Thomas Bradwardine extended Aristotelian quantities such as distance and velocity, and assigned intensity and extension to them. Bradwardine suggested an exponential law involving force, resistance, distance, velocity and time. Nicholas Oresme further extended Bradwardine's arguments. The Merton school proved that the quantity of motion of a body undergoing a uniformly accelerated motion is equal to the quantity of a uniform motion at the speed achieved halfway through the accelerated motion.


title: Equations of motion

text: For writers on kinematics before Galileo, since small time intervals could not be measured, the affinity between time and motion was obscure. They used time as a function of distance, and in free fall, greater velocity as a result of greater elevation. Only Domingo de Soto, a Spanish theologian, in his commentary on Aristotle's "Physics" published in 1545, after defining "uniform difform" motion (which is uniformly accelerated motion) – the word velocity wasn't used – as proportional to time, declared correctly that this kind of motion was identifiable with freely falling bodies and projectiles, without his proving these propositions or suggesting a formula relating time, velocity and distance. De Soto's comments are remarkably correct regarding the definitions of acceleration (acceleration was a rate of change of motion (velocity) in time) and the observation that acceleration would be negative during ascent.


title: Equations of motion

text: Discourses such as these spread throughout Europe, shaping the work of Galileo Galilei and others, and helped in laying the foundation of kinematics. Galileo deduced the equation in his work geometrically, using the Merton rule, now known as a special case of one of the equations of kinematics.


title: Equations of motion

text: Galileo was the first to show that the path of a projectile is a parabola. Galileo had an understanding of centrifugal force and gave a correct definition of momentum. This emphasis of momentum as a fundamental quantity in dynamics is of prime importance. He measured momentum by the product of velocity and weight; mass is a later concept, developed by Huygens and Newton. In the swinging of a simple pendulum, Galileo says in "Discourses" that "every momentum acquired in the descent along an arc is equal to that which causes the same moving body to ascend through the same arc." His analysis on projectiles indicates that Galileo had grasped the first law and the second law of motion. He did not generalize and make them applicable to bodies not subject to the earth's gravitation. That step was Newton's contribution.


title: Equations of motion

text: The term "inertia" was used by Kepler who applied it to bodies at rest. (The first law of motion is now often called the law of inertia.)


title: Equations of motion

text: Galileo did not fully grasp the third law of motion, the law of the equality of action and reaction, though he corrected some errors of Aristotle. With Stevin and others Galileo also wrote on statics. He formulated the principle of the parallelogram of forces, but he did not fully recognize its scope.


title: Equations of motion

text: Galileo also was interested by the laws of the pendulum, his first observations of which were as a young man. In 1583, while he was praying in the cathedral at Pisa, his attention was arrested by the motion of the great lamp lighted and left swinging, referencing his own pulse for time keeping. To him the period appeared the same, even after the motion had greatly diminished, discovering the isochronism of the pendulum.


title: Equations of motion

text: More careful experiments carried out by him later, and described in his Discourses, revealed the period of oscillation varies with the square root of length but is independent of the mass the pendulum.


title: Equations of motion

text: Thus we arrive at René Descartes, Isaac Newton, Gottfried Leibniz, et al.; and the evolved forms of the equations of motion that begin to be recognized as the modern ones.


title: Equations of motion

text: Later the equations of motion also appeared in electrodynamics, when describing the motion of charged particles in electric and magnetic fields, the Lorentz force is the general equation which serves as the definition of what is meant by an electric field and magnetic field. With the advent of special relativity and general relativity, the theoretical modifications to spacetime meant the classical equations of motion were also modified to account for the finite speed of light, and curvature of spacetime. In all these cases the differential equations were in terms of a function describing the particle's trajectory in terms of space and time coordinates, as influenced by forces or energy transformations.


title: Equations of motion

text: However, the equations of quantum mechanics can also be considered "equations of motion", since they are differential equations of the wavefunction, which describes how a quantum state behaves analogously using the space and time coordinates of the particles. There are analogs of equations of motion in other areas of physics, for collections of physical phenomena that can be considered waves, fluids, or fields.


title: Equations of motion

text: From the instantaneous position , instantaneous meaning at an instant value of time , the instantaneous velocity and acceleration have the general, coordinate-independent definitions;


title: Equations of motion

text: Notice that velocity always points in the direction of motion, in other words for a curved path it is the tangent vector. Loosely speaking, first order derivatives are related to tangents of curves. Still for curved paths, the acceleration is directed towards the center of curvature of the path. Again, loosely speaking, second order derivatives are related to curvature.


title: Equations of motion

text: The rotational analogues are the "angular vector" (angle the particle rotates about some axis) , angular velocity , and angular acceleration :


title: Equations of motion

text: where is a unit vector in the direction of the axis of rotation, and is the angle the object turns through about the axis.


title: Equations of motion

text: The following relation holds for a point-like particle, orbiting about some axis with angular velocity :


title: Equations of motion

text: where is the position vector of the particle (radial from the rotation axis) and the tangential velocity of the particle. For a rotating continuum rigid body, these relations hold for each point in the rigid body.


title: Equations of motion

text: The differential equation of motion for a particle of constant or uniform acceleration in a straight line is simple: the acceleration is constant, so the second derivative of the position of the object is constant. The results of this case are summarized below.


title: Equations of motion

text: These equations apply to a particle moving linearly, in three dimensions in a straight line with constant acceleration. Since the position, velocity, and acceleration are collinear (parallel, and lie on the same line) – only the magnitudes of these vectors are necessary, and because the motion is along a straight line, the problem effectively reduces from three dimensions to one.


title: Equations of motion

text: Equations [1] and [2] are from integrating the definitions of velocity and acceleration, subject to the initial conditions and ;


title: Equations of motion

text: which breaks into the radial acceleration , centripetal acceleration , Coriolis acceleration , and angular acceleration .


title: Equations of motion

text: Special cases of motion described by these equations are summarized qualitatively in the table below. Two have already been discussed above, in the cases that either the radial components or the angular components are zero, and the non-zero component of motion describes uniform acceleration.


title: Equations of motion

text: In 3D space, the equations in spherical coordinates with corresponding unit vectors , and , the position, velocity, and acceleration generalize respectively to


title: Equations of motion

text: The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum of an object equals the force acting on it,


title: Equations of motion

text: The force in the equation is "not" the force the object exerts. Replacing momentum by mass times velocity, the law is also written more famously as


title: Equations of motion

text: Newton's second law applies to point-like particles, and to all points in a rigid body. They also apply to each point in a mass continuum, like deformable solids or fluids, but the motion of the system must be accounted for; see material derivative. In the case the mass is not constant, it is not sufficient to use the product rule for the time derivative on the mass and velocity, and Newton's second law requires some modification consistent with conservation of momentum; see variable-mass system.


title: Equations of motion

text: It may be simple to write down the equations of motion in vector form using Newton's laws of motion, but the components may vary in complicated ways with spatial coordinates and time, and solving them is not easy. Often there is an excess of variables to solve for the problem completely, so Newton's laws are not always the most efficient way to determine the motion of a system. In simple cases of rectangular geometry, Newton's laws work fine in Cartesian coordinates, but in other coordinate systems can become dramatically complex.


title: Equations of motion

text: The momentum form is preferable since this is readily generalized to more complex systems, such as special and general relativity (see four-momentum). It can also be used with the momentum conservation. However, Newton's laws are not more fundamental than momentum conservation, because Newton's laws are merely consistent with the fact that zero resultant force acting on an object implies constant momentum, while a resultant force implies the momentum is not constant. Momentum conservation is always true for an isolated system not subject to resultant forces.


title: Equations of motion

text: For a number of particles (see many body problem), the equation of motion for one particle influenced by other particles is


title: Equations of motion

text: where is the momentum of particle , is the force on particle by particle , and is the resultant external force due to any agent not part of system. Particle does not exert a force on itself.


title: Equations of motion

text: Euler's laws of motion are similar to Newton's laws, but they are applied specifically to the motion of rigid bodies. The Newton–Euler equations combine the forces and torques acting on a rigid body into a single equation.


title: Equations of motion

text: by equating the torque acting on the body to the rate of change of its angular momentum . Analogous to mass times acceleration, the moment of inertia tensor depends on the distribution of mass about the axis of rotation, and the angular acceleration is the rate of change of angular velocity,


title: Equations of motion

text: where is the angular momentum of particle , the torque on particle by particle , and is resultant external torque (due to any agent not part of system). Particle does not exert a torque on itself.


title: Equations of motion

text: For describing the motion of masses due to gravity, Newton's law of gravity can be combined with Newton's second law. For two examples, a ball of mass thrown in the air, in air currents (such as wind) described by a vector field of resistive forces ,


title: Equations of motion

text: where is the gravitational constant, the mass of the Earth, and is the acceleration of the projectile due to the air currents at position and time .


title: Equations of motion

text: The classical -body problem for particles each interacting with each other due to gravity is a set of nonlinear coupled second order ODEs,


title: Equations of motion

text: Using all three coordinates of 3D space is unnecessary if there are constraints on the system. If the system has degrees of freedom, then one can use a set of generalized coordinates , to define the configuration of the system. They can be in the form of arc lengths or angles. They are a considerable simplification to describe motion, since they take advantage of the intrinsic constraints that limit the system's motion, and the number of coordinates is reduced to a minimum. The time derivatives of the generalized coordinates are the "generalized velocities"


title: Equations of motion

text: where the "Lagrangian" is a function of the configuration and its time rate of change (and possibly time )


title: Equations of motion

text: Setting up the Lagrangian of the system, then substituting into the equations and evaluating the partial derivatives and simplifying, a set of coupled second order ODEs in the coordinates are obtained.


title: Equations of motion

text: in which is a shorthand notation for a vector of partial derivatives with respect to the indicated variables (see for example matrix calculus for this denominator notation), and possibly time ,


title: Equations of motion

text: Setting up the Hamiltonian of the system, then substituting into the equations and evaluating the partial derivatives and simplifying, a set of coupled first order ODEs in the coordinates and momenta are obtained.


title: Equations of motion

text: is "Hamilton's principal function", also called the "classical action" is a functional of . In this case, the momenta are given by


title: Equations of motion

text: Although the equation has a simple general form, for a given Hamiltonian it is actually a single first order "non-linear" PDE, in variables. The action allows identification of conserved quantities for mechanical systems, even when the mechanical problem itself cannot be solved fully, because any differentiable symmetry of the action of a physical system has a corresponding conservation law, a theorem due to Emmy Noether.


title: Equations of motion

text: All classical equations of motion can be derived from the variational principle known as Hamilton's principle of least action


title: Equations of motion

text: Combining with Newton's second law gives a first order differential equation of motion, in terms of position of the particle:


title: Equations of motion

text: The same equation can be obtained using the Lagrangian (and applying Lagrange's equations above) for a charged particle of mass and charge :


title: Equations of motion

text: where and are the electromagnetic scalar and vector potential fields. The Lagrangian indicates an additional detail: the canonical momentum in Lagrangian mechanics is given by:


title: Equations of motion

text: instead of just , implying the motion of a charged particle is fundamentally determined by the mass and charge of the particle. The Lagrangian expression was first used to derive the force equation.


title: Equations of motion

text: The above equations are valid in flat spacetime. In curved spacetime, things become mathematically more complicated since there is no straight line; this is generalized and replaced by a "geodesic" of the curved spacetime (the shortest length of curve between two points). For curved manifolds with a metric tensor , the metric provides the notion of arc length (see line element for details). The differential arc length is given by:


title: Equations of motion

text: and the geodesic equation is a second-order differential equation in the coordinates. The general solution is a family of geodesics:


title: Equations of motion

text: where is a Christoffel symbol of the second kind, which contains the metric (with respect to the coordinate system).


title: Equations of motion

text: Given the mass-energy distribution provided by the stress–energy tensor , the Einstein field equations are a set of non-linear second-order partial differential equations in the metric, and imply the curvature of spacetime is equivalent to a gravitational field (see equivalence principle). Mass falling in curved spacetime is equivalent to a mass falling in a gravitational field - because gravity is a fictitious force. The "relative acceleration" of one geodesic to another in curved spacetime is given by the "geodesic deviation equation":


title: Equations of motion

text: where is the separation vector between two geodesics, ("not" just ) is the covariant derivative, and is the Riemann curvature tensor, containing the Christoffel symbols. In other words, the geodesic deviation equation is the equation of motion for masses in curved spacetime, analogous to the Lorentz force equation for charges in an electromagnetic field.


title: Equations of motion

text: For flat spacetime, the metric is a constant tensor so the Christoffel symbols vanish, and the geodesic equation has the solutions of straight lines. This is also the limiting case when masses move according to Newton's law of gravity.


title: Equations of motion

text: In general relativity, rotational motion is described by the relativistic angular momentum tensor, including the spin tensor, which enter the equations of motion under covariant derivatives with respect to proper time. The Mathisson–Papapetrou–Dixon equations describe the motion of spinning objects moving in a gravitational field.


title: Equations of motion

text: Unlike the equations of motion for describing particle mechanics, which are systems of coupled ordinary differential equations, the analogous equations governing the dynamics of waves and fields are always partial differential equations, since the waves or fields are functions of space and time. For a particular solution, boundary conditions along with initial conditions need to be specified.


title: Equations of motion

text: Sometimes in the following contexts, the wave or field equations are also called "equations of motion".


title: Equations of motion

text: Equations that describe the spatial dependence and time evolution of fields are called "field equations". These include


title: Equations of motion

text: This terminology is not universal: for example although the Navier–Stokes equations govern the velocity field of a fluid, they are not usually called "field equations", since in this context they represent the momentum of the fluid and are called the "momentum equations" instead.


title: Equations of motion

text: Equations of wave motion are called "wave equations". The solutions to a wave equation give the time-evolution and spatial dependence of the amplitude. Boundary conditions determine if the solutions describe traveling waves or standing waves.


title: Equations of motion

text: From classical equations of motion and field equations; mechanical, gravitational wave, and electromagnetic wave equations can be derived. The general linear wave equation in 3D is:


title: Equations of motion

text: and is the phase velocity. Nonlinear equations model the dependence of phase velocity on amplitude, replacing by . There are other linear and nonlinear wave equations for very specific applications, see for example the Korteweg–de Vries equation.


title: Equations of motion

text: In quantum mechanics, in which particles also have wave-like properties according to wave–particle duality, the analogue of the classical equations of motion (Newton's law, Euler–Lagrange equation, Hamilton–Jacobi equation, etc.) is the Schrödinger equation in its most general form:


title: Equations of motion

text: where is the wavefunction of the system, is the quantum Hamiltonian operator, rather than a function as in classical mechanics, and is the Planck constant divided by 2. Setting up the Hamiltonian and inserting it into the equation results in a wave equation, the solution is the wavefunction as a function of space and time. The Schrödinger equation itself reduces to the Hamilton–Jacobi equation when one considers the correspondence principle, in the limit that becomes zero.


title: Equations of motion

text: Throughout all aspects of quantum theory, relativistic or non-relativistic, there are various formulations alternative to the Schrödinger equation that govern the time evolution and behavior of a quantum system, for instance:


title: Huddersfield

text: Huddersfield is a market town in the Kirklees district in West Yorkshire, England. It is the administrative centre and largest settlement in the Kirklees district. The town is in the foothills of the Pennines. The River Holme's confluence into the similar-sized Colne to the south of the town centre which then flows into the Calder in the north eastern outskirts of the town.


title: Huddersfield

text: The rivers around the town provided soft water required for textile treatment in large weaving sheds, this made it a prominent mill town with an economic boom in the early part of the Victorian era Industrial Revolution. The town centre has much neoclassical Victorian architecture, one example is which is a Grade I listed building – described by John Betjeman as "the most splendid station façade in England" –


title: Huddersfield

text: It hosts the University of Huddersfield and three colleges: Greenhead College, Kirklees College and Huddersfield New College. The town is the birthplace of rugby league with the local team, Huddersfield Giants, playing in the Super League. It also has a professional football team called Huddersfield Town, currently compete in the Championship, as well as two Rugby Union clubs Huddersfield R.U.F.C. and Huddersfield YM RUFC. Notable people from the town include twice British Prime Minister Harold Wilson (for Labour), film star James Mason born in the town and Jodie Whittaker, the 13th actor to play Doctor Who, was born in Skelmanthorpe.


title: Huddersfield

text: The town has been classed under Yorkshire, the West Riding of Yorkshire and West Yorkshire for statistics throughout its history. The town's population in 1961 was 130,652 with an increase to 162,949 at the 2011 census; it is in the West Yorkshire Built-up Area. The town is south-west of Leeds, west of Wakefield, north-west of Sheffield and north-east of Manchester.


title: Huddersfield

text: Local settlement dates back over 4,000 years. Castle Hill, a major landmark, was the site of an Iron Age hill fort. The remains of a Roman fort were unearthed in the mid 18th century at Slack near Outlane, west of the town.


title: Huddersfield

text: The earliest surviving record of the place name is in the Domesday Book of 1086, "Oderesfelt". It appears as "Hudresfeld" in a Yorkshire charter from 1121 to 1127, and as "Huderesfeld" in subsidy rolls in 1297. The name meaning has not complicated with the shifts of English, remaining 'Hud(d)er's field'.


title: Huddersfield

text: The modern name is pronounced without a word-initial /h/ in the local dialect, a trait ironically and independently shared by many Norman scribes' dialects of the Domesday Book era (see Old and modern French).


title: Huddersfield

text: The manor of Huddersfield was owned by long lease by the de Lacy becoming Lacey family until its 1322 takeback by the Crown. In 1599, William Ramsden bought it, and the Ramsden family continued to own the manor, which came to be known as the Ramsden Estate, until 1920. During their ownership they supported the development of the town.


title: Huddersfield

text: Closest wooded uplands in the inner part of the town's green belt, the town centre and the crest of the Pennines to the west: semi-panorama from Castle Hill. Three converted neoclassical mill sheds are in the foreground.


title: Huddersfield

text: Sir John Ramsden, 3rd Baronet built the Huddersfield Cloth Hall in 1766 and his son the fourth baronet was responsible for Sir John Ramsden's Canal in 1780. The Ramsdens endorsed the railway in the first wave of national railway building, in the 1840s.


title: Huddersfield

text: Huddersfield was a centre of civil unrest during this phase of the Industrial Revolution in which Europe saw frequent wars during and after which, as to those most acutely affecting Britain, cloth trade slumped which could be compounded by local crops failure, many local weavers faced starvation and losing their livelihood due to the new, mechanised weaving sheds.


title: Huddersfield

text: Luddites began destroying the great mills, sheds and machinery at such times; one of the most notorious attacks was on Cartwright – a Huddersfield mill-owner, who had a reputation for cruelty – and his Rawfolds Mill. Kirkpatrick Sale describes how an army platoon was stationed at Huddersfield to deal with these; at its peak, having about a thousand soldiers and ten thousand civilians. Luddites thus began to focus criminal damage on nearby towns and villages (less well-protected); their most damaging act was to destroy Foster's Mill at Horbury – a village about east. The government campaign that crushed the movement was provoked by a murder that took place in Huddersfield. William Horsfall, a mill-owner and a passionate prosecutor of Luddites, was killed in 1812. Although the movement faded out, Parliament began to increase welfare provision for those out of work, and introduce regulations to improve conditions in the mills.


title: Huddersfield

text: Two Prime Ministers spent part of their childhood in Huddersfield: Harold Wilson, born locally who attended Royds Hall School, and H. H. Asquith. Wilson is commemorated by a statue on the large front square (forecourt) to the town's station.


title: Huddersfield

text: In 1920, the Corporation bought the Ramsden Estate from that family, that had owned much of the town at least as to the reversion of long leases (a minor, overarching interest) since 1599, for £1.3 million. The town became "the town that bought itself". Most of the keynote central building freeholds belong to the local authority, as in a few towns in Britain such as Basingstoke.


title: Huddersfield

text: Huddersfield was incorporated as a municipal borough in the ancient West Riding of Yorkshire in 1868. The borough comprised the thus sidelined civil parishes of Almondbury, Dalton, Huddersfield, Lindley-cum-Quarmby and Lockwood, later dissolved. When the West Riding County Council was formed in 1889, Huddersfield became a county borough, exempt from its control.


title: Huddersfield

text: A more confined Huddersfield seat than the early 20th century scope has been represented by Labour since its creation in 1983 and is, by size of majority and length of tenure, a strongly-Labour leaning seat.


title: Huddersfield

text: Kirklees was the first part of the country to have a Green or other environmentalist party councillor – Nicholas Harvey – he was instrumental in protesting against the intended closure of the Settle and Carlisle Railway line. The council has councillors of Labour, Conservative Party and Liberal Democrat parties; these retained the deposit, reaching more than 5% of the vote in the last general election (for an MP who serves in the House of Commons).


title: Huddersfield

text: Huddersfield expanded in 1937, assimilating parts of the Golcar, Linthwaite, and South Crosland urban districts. The county borough was abolished in 1974 and its former area was combined with that of other districts to form the Metropolitan Borough of Kirklees in West Yorkshire.


title: Huddersfield

text: Council bids to gain support for city status were rejected by the people in a poll held by the "Huddersfield Daily Examiner"; the council did not apply for that status in the 2000 or 2002 competitions.


title: Huddersfield

text: Huddersfield had a strong Liberal tradition up to the 1950s reflected in several Liberal social clubs. The current Member of Parliament (MP) for the Huddersfield constituency is Barry Sheerman, a Labour Co-operative MP.


title: Huddersfield

text: Per the United Kingdom Census 2001 the population of the town's urban sub-area of the West Yorkshire Urban Area was 146,234, and that of the former extent of the county borough was 121,620. The wider "South Kirklees" had a population of 216,011.


title: Huddersfield

text: Huddersfield has the merger of the shallow valley floors of the River Colne and the Holme south of the town centre. This is in the eastern foothills of the Pennines which blend into the moorlands of the South Pennines west of the town.


title: Huddersfield

text: As with all of West Yorkshire a temperate oceanic climate exists, wetter than the low plains rain shadow proper towards East Yorkshire but drier than Cumbria. It is mild for the latitude – overnight frosts are quite frequent in winter yet daytime tends to exceed such temperatures due to onshore breezes from around Britain and as the Gulf Stream moderates temperatures. Summers are usually warm, punctuated by frequent rainy and hot spells. Winters are usually cool and damp, punctuated by frequent cold spells where snow is possible, especially on higher ground. According to the Köppen climate classification, Huddersfield is certified as "Cfb".


title: Huddersfield

text: After boundary changes in 2004, Huddersfield now covers eight of the twenty-three electoral wards for Kirklees Council. Neighbouring wards in the Colne Valley, Holme Valley, and Kirkburton are often considered to be part of Huddersfield though they are predominantly semi-rural. The very centre of town forms the Newsome ward of councillors. Eight wards make up Huddersfield proper; these with populations, extent and constituent suburbs (mid-year 2005 estimates) are:


title: Huddersfield

text: Huddersfield is within a green belt region that extends into the Kirklees borough and wider surrounding counties. It is in place to reduce urban sprawl, prevent the towns in the West Yorkshire Urban Area conurbation from further convergence, protect the identity of outlying communities, encourage brownfield reuse, and preserve nearby countryside. This is achieved by restricting inappropriate development within the designated areas, and imposing stricter conditions on permitted building.