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Danny Elfman

Daniel Robert Elfman (born May 29, 1953) is an American film composer, singer, songwriter, and musician. He came to prominence as the lead singer and primary songwriter for the new wave band Oingo Boingo in the early 1980s. Since scoring his first studio film in 1985, Elfman has garnered international recognition for composing over 100 feature film scores, as well as compositions for television, stage productions, and the concert hall.

Elfman has frequently worked with directors Tim Burton, Sam Raimi, and Gus Van Sant, contributing music to nearly 20 Burton projects, including Pee-Wee's Big Adventure, Beetlejuice, Batman, Edward Scissorhands,  and Wednesday, as well as scoring Raimi's Darkman, A Simple Plan, Spider-Man, Spider-Man 2 and Doctor Strange in the Multiverse of Madness, and Van Sant's Academy Award-winning films Good Will Hunting and Milk. He wrote music for all of the Men in Black and Fifty Shades of Grey franchise films, the songs and score for Henry Selick's animated musical The Nightmare Before Christmas, and the themes for the popular television series Desperate Housewives and The Simpsons.

Among his honors are four Oscar nominations, three Emmy Awards, a Grammy, seven Saturn Awards for Best Music, the 2002 Richard Kirk Award, the 2015 Disney Legend Award, the Max Steiner Film Music Achievement Award in 2017, and the Society of Composers & Lyricists Lifetime Achievement Award in 2022.

Early life
Elfman was born on May 29, 1953, in Los Angeles, California, to a Jewish family of Russian descent. He is a son of Blossom Elfman (née Bernstein), a writer and teacher, and Milton Elfman, a teacher, and the brother of actor, musician, and journalist Richard Elfman. Elfman was raised in a racially mixed affluent community in Baldwin Hills, California, where he spent much of his time at the local movie theater discovering classic sci-fi, fantasy and horror films and first noticed the music of such film composers as Bernard Herrmann and Franz Waxman. Elfman has admitted to fabricating stories about his past out of boredom, including a false birthplace of Amarillo, Texas, and parents in the United States Air Force.

In his early school days, Elfman exhibited an aptitude for science with almost no interest in music, and was even rejected from elementary school orchestra "for having no propensity for music." This would change when he switched high schools in the late 1960s and fell in with a musical crowd, who introduced him to early jazz and the work of Stravinsky and his 20th-century contemporaries.

After finishing high school early with plans to travel the world, Elfman followed his brother Richard to France, where he performed violin with Jérôme Savary's Le Grand Magic Circus, an avant-garde musical theater group. He then embarked on a ten-month, self-guided tour through Africa, busking and collecting a range of West African percussion instruments until a series of illnesses forced him to return home. At this time, Richard was forming a new musical theater group in Los Angeles.

Oingo Boingo
After returning to Los Angeles from Africa in the early 1970s, Elfman was asked by his brother Richard to serve as musical director of his street theatre performance art troupe The Mystic Knights of the Oingo Boingo. Elfman was tasked with adapting and arranging 1920s and 1930s jazz and big band music by artists such as Cab Calloway, Duke Ellington, Django Reinhardt and Josephine Baker for the ensemble, which consisted of up to 15 performers playing upwards of 30 instruments. He also composed original pieces and helped build instruments unique for the group, including an aluminum gamelan, the 'Schlitz celeste' made from tuned beer cans, and a "junkyard orchestra" built from car parts and trash cans.

The Mystic Knights performed on the street and in theaters, and later in nightclubs throughout Los Angeles until Richard left in 1976 to pursue filmmaking. As a send-off to the group's original concept, Richard produced the film Forbidden Zone based on the Mystic Knights' stage performances. Elfman composed the songs and his first score for the film, and appeared as the character Satan, who performs a reworked version of Calloway's "Minnie the Moocher."

Before the release of Forbidden Zone, Elfman took over the Mystic Knights as lead singer-songwriter in 1976. In 1979, he pared the group down to eight players to record and tour as a ska-influenced new wave band. That summer, the group's name would change to Oingo Boingo. Their biggest success among eight studio albums penned by Elfman was 1985's Dead Man's Party, featuring the hit song "Weird Science" from the movie of the same name. The band also appeared performing their single "Dead Man's Party" in the 1986 movie Back to School, for which Elfman also composed the score. Elfman shifted the band to a more guitar-oriented rock sound in the late 1980s, which continued through their last album Boingo in 1994.

Citing permanent hearing damage from performing live and conflicts with his film-scoring career, Elfman retired Oingo Boingo in 1995 with a series of five sold-out final concerts at the Universal Amphitheatre ending on Halloween night. On October 31, 2015, Elfman and Oingo Boingo guitarist Steve Bartek performed the song "Dead Man's Party" with an orchestra as an encore to a live-to-film concert of The Nightmare Before Christmas score at the Hollywood Bowl. Elfman told the audience the performance was "20 years to the day" of Oingo Boingo's retirement.

Film scoring
As fans of Oingo Boingo, Tim Burton and Paul Reubens invited Elfman to write the score for their first feature film Pee-wee's Big Adventure in 1985. Elfman was initially apprehensive because of his lack of formal training and having never scored a studio feature, but after Burton accepted his initial demo of the title music, and with orchestration assistance from Oingo Boingo guitarist and arranger Steve Bartek, Elfman completed the score to great effect, paying homage to influential film composers Nino Rota and Bernard Herrmann. Elfman described the first time he heard his music played by a full orchestra as one of the most thrilling experiences of his life.

Following Pee Wee's Big Adventure, Elfman scored a string of comedies in the late 1980s, including Back to School starring Rodney Dangerfield, Burton's Beetlejuice and the Bill Murray film Scrooged. Non-comedy work included the all-synth score to Emilio Estevez's crime drama Wisdom and the big band, blues-infused music for Martin Brest's buddy cop action film Midnight Run.

In 1989, Elfman's influential, Grammy-winning score for Burton's Batman marked a major stylistic shift to dark, densely orchestrated music in the romantic idiom. This continued in his scores for Warren Beatty's Dick Tracy, Sam Raimi's Darkman and Clive Barker's Nightbreed, all released in 1990.

With Batman, Elfman firmly established a career-spanning relationship with Burton, scoring all but three of the director's major studio releases. Highlights include Edward Scissorhands (1990), Batman Returns (1992), Sleepy Hollow (1999), Big Fish (2003) and Alice in Wonderland (2010). In 1993, Elfman wrote the score and ten songs for the Burton-produced stop motion animated film The Nightmare Before Christmas, directed by Henry Selick, and also provided the singing voice for main character Jack Skellington, as well as the voices for secondary characters Barrel, the Clown with the Tear-Away Face and others. In 2005, he wrote the score and songs for Burton's Corpse Bride and provided the voice of the character of Bonejangles, and provided the score, songs and Oompa-Loompa vocals for Burton's Charlie and the Chocolate Factory that same year.

In addition to frequent collaborations with Burton, Raimi and Gus Van Sant, Elfman has worked with directors such as Brian De Palma, Peter Jackson, Joss Whedon, Errol Morris, Ang Lee, Richard Donner, Guillermo del Toro, David O. Russell, Taylor Hackford, Jon Amiel, Joe Johnston, and Barry Sonnenfeld. His scores for Sonnenfeld's Men in Black, Van Sant's Good Will Hunting and Milk, and Burton's Big Fish all received Academy Award nominations.

Since the mid-1990s, Elfman expanded his craft to a range of genres, including thrillers (Dolores Claiborne, A Simple Plan, The Kingdom, The Girl on the Train, The Woman in the Window), dramas (Sommersby, A Civil Action, Hitchcock), indies (Freeway, Silver Linings Playbook, Don't Worry, He Won't Get Far on Foot, White Noise), family (Flubber, Charlotte's Web, Frankenweenie, Goosebumps, Dolittle), documentary (Standard Operating Procedure, The Unknown Known), and horror (Red Dragon, The Wolfman), as well as entries in his well-established areas of horror comedy (The Frighteners, Mars Attacks!, Dark Shadows) and comic book-inspired action films (Hulk, Wanted, Hellboy II: The Golden Army).

Among his franchise work, Elfman composed the scores for four Men in Black films (1997–2019) and three Fifty Shades films (2015–2018). In 1996, he scored the first film in the Mission: Impossible series, adapting themes for the original television series by Lalo Schifrin as well as composing his own. Elfman scored Raimi's Spider-Man in 2002 and Spider-Man 2 in 2004, themes and selections from which were used for Raimi's Spider-Man 3, scored by Christopher Young. Elfman's Spider-Man theme was incorporated into the MCU film Spider-Man: No Way Home composed by Michael Giacchino.

Elfman entered the Marvel Cinematic Universe by providing additional music an 2015's Avengers: Age of Ultron, receiving composer credit with Brian Tyler. Elfman also scored MCU's Doctor Strange in the Multiverse of Madness in 2022, utilizing Giacchino's theme to the original Doctor Strange film, as well as themes from WandaVision and X-Men: The Animated Series, and music from Beethoven's Fifth Symphony and Bach's Toccata and Fugue.

For several high-profile sequel and reboot projects in the 2010s, Elfman incorporated established musical themes with his own original thematic material, including the DC Extended Universe's Justice League, The Grinch, Dumbo and Men in Black International.

Elfman was featured in the 2016 documentary Score, in which he appeared among over 50 film composers to discuss the craft of movie music and influential figures in the business.

Concert and stage music
Elfman's first piece of original concert music, Serenada Schizophrana, was commissioned by the American Composers Orchestra, who premiered the piece on February 23, 2005, at Carnegie Hall. Subsequent concert works include his first Violin Concerto "Eleven Eleven", co-commissioned by the Czech National Symphony Orchestra, Stanford Live at Stanford University, and the Royal Scottish National Orchestra, which premiered at Smetana Hall in Prague on June 21, 2017, with Sandy Cameron on violin and John Mauceri conducting the Czech National Symphony Orchestra; the Piano Quartet, co-commissioned by the Lied Center for Performing Arts University of Nebraska and the Berlin Philharmonic Piano Quartet, which premiered February 6, 2018, in Lincoln, Nebraska; and the Percussion Quartet, commissioned by Third Coast Percussion and premiered at the Philip Glass Days And Nights Festival in Big Sur on October 10, 2019.

2022 saw the first performances of three concert works. Elfman's Cello Concerto composed Gautier Capucon premiered by the Vienna Symphony in March, with subsequent performances by the Orchestre Philharmonique de Radio France in May and The San Francisco Symphony US premiere in November  Elfman's Percussion Concerto for Colin Currie premiered at London's Royal Festival Hall with London Philharmonic Orchestra, and was later performed at Soka University of America in California, with Pacific Symphony. His Wunderkammer, a commission from the National Youth Orchestra of Great Britain, toured the UK in summer 2022, culminating in a performance in London's Royal Albert Hall as part of the BBC Proms, with national radio and TV broadcasts.

In 2008, Elfman accepted his first commission for the stage, composing the music for Twyla Tharp's Rabbit and Rogue ballet, co-commissioned by American Ballet Theatre and Orange County Performing Arts Center and premiering on June 3, 2008, at the Metropolitan Opera House, Lincoln Center. Other works for stage include the music for Cirque Du Soleil's Iris in 2011, and incidental music for the Broadway production of Taylor Mac's Gary: A Sequel to Titus Andronicus in 2019. In October 2013, Elfman returned to the stage for the first time since his band Oingo Boingo disbanded to sing a handful of The Nightmare Before Christmas songs as part of the concert Danny Elfman's Music from the Films of Tim Burton, featuring suites of music from 15 Tim Burton films newly arranged by Elfman. The concert has since toured internationally and has played in Japan, Australia, Mexico and throughout Europe and the United States. Since 2015, Elfman has appeared regularly in a Hollywood Bowl Halloween concert featuring full orchestra performing the Nightmare Before Christmas score live to the film projection.

Elfman made his Coachella debut on April 16, 2022, with Danny Elfman: From Boingo to Batman to Big Mess to Beyond! The concert, postponed from Coachella 2020 due to the COVID-19 pandemic, featured Elfman's film and television music arranged for band, orchestra and choir, as well as songs from his solo album Big Mess and new arrangements of songs from his Oingo Boingo catalogue. Conducted by Steve Bartek, and featuring Elfman (vocals, guitar, percussion), Wes Borland (guitar), Stu Brooks (bass), Nili Brosh (guitar), and Josh Freese (drums), the concert was expanded for two shows Halloween weekend 2022 at the Hollywood Bowl.

Television and other projects
In addition to his music for film, Elfman also penned themes for the television series The Simpsons, Tales from the Crypt, The Flash and Desperate Housewives, which won Elfman his first Emmy. He also adapted his original themes for the animated versions of Batman and Beetlejuice. Occasional forays into serial television include episodes of Alfred Hitchcock Presents, Amazing Stories and Pee-wee's Playhouse, the miniseries When We Rise co-composed with Chris Bacon, and themes for the Netflix series Wednesday.

He has composed music for animated shorts, including Sally Cruikshank's Face Like A Frog and Tim Burton's "Stainboy" internet series.

Elfman provided background music for Luigi Serafini's solo exhibition il Teatro della Pittura at the Fondazione Mudima di Milano in Milan, Italy in 1998 and for the Tim Burton exhibition at MoMA in 2009.

In the 1990s, Elfman composed music for advertising campaigns for Nike, Nissan and Lincoln-Mercury, and in 2002 wrote the music for Honda's "Power of Dreams" advertising campaign, which was the first cinema commercial to be shot in the IMAX format.

In 2013 he composed the music and provided the English-language vocals for the Hong Kong Disneyland attraction Mystic Manor.

On October 31, 2019, the MasterClass online educational series released "Making Music out of Chaos," presenting 21 compositional and career lessons from Elfman's four decades of experience primarily in the film industry.

Elfman scored the 10-minute video "Joe Biden," which introduced Joe Biden's acceptance of the presidential candidacy nomination at the 2020 Democratic National Convention.

On November 16, 2021, Disney Branded Television announced that Elfman would compose score and songs of the upcoming Disney Television Animation and 20th Television Animation stop-motion animated comedy series Rhona Who Lives by the River created by Emily Kapnek, Elfman also serves as executive producer for the series.

Solo
In October 2020, Elfman released the single, "Happy," on Anti- Records and Epitaph Records. From January 2021 on the eleventh day of each month, he released five subsequent singles "Sorry", "Love in the Time of COVID", "Kick Me", "True", and a reworking the Oingo Boingo song "Insects" from the album Nothing to Fear. This culminated with the release of the double album Big Mess on June 11. Featuring 18 original songs this was Elfman's first solo studio album since 1984's So-Lo.

On August 11, 2021, Elfman released a remix of "True" with lead vocals shared between Elfman and Nine Inch Nails frontman Trent Reznor. A year later, Elfman released Bigger Messier, a compilation of 23 remixes of songs on the album Big Mess by artists including Reznor, Iggy Pop, Blixa Bargeld, Squarepusher, Boy Harsher and more.

Influences and style
Elfman has said his major influences are composers from Hollywood's Golden Age, such as Bernard Herrmann, Dimitri Tiomkin, Max Steiner, David Tamkin, Erich Wolfgang Korngold, and Carl Stalling; 20th century classical composers Sergei Prokofiev, Igor Stravinsky, Béla Bartók, Dmitri Shostakovich, and Carl Orff; and jazz, experimental and minimalist composers Kurt Weill, Duke Ellington, Harry Partch, Philip Glass, Lou Harrison, Terry Riley, and Steve Reich. Influences on specific scores include Erik Satie (Forbidden Zone), Nino Rota (Pee-wee's Big Adventure), George Gershwin (Dick Tracy), Pyotr Ilyich Tchaikovsky (Edward Scissorhands), and Jimi Hendrix (Dead Presidents). Though not considered direct influences per se, Elfman has discussed his respect and admiration for film composers Jerry Goldsmith, Ennio Morricone, Thomas Newman, Alexandre Desplat and John Williams, as well as classical composer John Adams.

Though many believe Richard Wagner informed his influential score to Batman, Elfman has said it was more likely from Wagner's influence on classic film composers such as Herrmann, Steiner, Waxman and Korngold, as he was unfamiliar with Wagner's work at the time.

Elfman counts Herrmann as his biggest influence, and has said hearing Herrmann's score to The Day the Earth Stood Still when he was a child was the first time he recognized film music as a cinematic art form and realized the powerful contribution a composer makes to the movies. Pastiche of Herrmann's music can be heard in Elfman's Pee-wee's Big Adventure, especially the cues "Stolen Bike" and "Clown Dream", which directly reference Herrmann's music from Psycho and The 7th Voyage of Sinbad respectively. His score to Batman makes more subtle nods to Herrmann's Journey to the Center of the Earth and Vertigo, and more integral homage can be heard in later scores for Mars Attacks! and Hitchcock, as well as the "Blue Strings" movement of his first concert work Serenada Schizophrana.

While Elfman is primarily known for writing large-scale orchestral works in the romantic, 20th century and Hollywood Golden Age film score traditions, his compositions have used a wide range of idioms, including rock and blues (Midnight Run, Hot to Trot), big band and jazz (Dick Tracy, Chicago), operetta (The Nightmare Before Christmas, Corpse Bride), funk and hip hop (Dead Presidents, Notorious), folk and indie rock (Taking Woodstock, Silver Linings Playbook), Americana (Article 99, Sommersby, Big Fish), minimalism (Good Will Hunting, Standard Operating Procedure, The Unknown Known), and atonal or experimental (Freeway, A Simple Plan, The Girl on the Train).

Given his appreciation and study of world music and his vast collection of instruments from non-Western cultures, Elfman will often use traditional instruments in his scores when there is an international setting, such as African percussion for Instinct, the oud for The Kingdom set in Saudi Arabia, and pan flute for Proof of Life set in South America.

When working on films with established musical identifiers, Elfman will often incorporate original themes in addition to his own thematic material. Examples include Lalo Schifrin's main theme and "The Plot" from the original Mission Impossible TV Series for Mission: Impossible; John Williams' theme for Superman, the Hans Zimmer/Junkie XL theme for Wonder Woman and his own original Batman theme for Justice League;  the "Welcome Christmas" song from the 1966 How the Grinch Stole Christmas! for The Grinch; and "Casey Junior," "Pink Elephants on Parade," and "When I See an Elephant Fly" from Disney's original 1941 animated film for Dumbo.

The songs for The Nightmare Before Christmas and Corpse Bride were influenced by Kurt Weill, Gilbert and Sullivan and early Rodgers and Hammerstein. At the request of Tim Burton, Charlie and the Chocolate Factory songs drew inspiration from Bollywood, the Mamas and the Papas, ABBA, and Earth, Wind & Fire individually.

Elfman's work in pop music and specifically as songwriter for Oingo Boingo was influenced by the Specials, Madness, the Selecter, Devo, Fun Boy Three, and XTC.

Film music
For his film scores, Elfman draws musical inspiration almost exclusively from viewing a cut of the film, and occasionally from visits to the set while the film is in production (he wrote and orchestrated his theme for Batman on an airplane to Los Angeles after visiting the set in London). While he prefers not to work from script, story or concept, exceptions include The Nightmare Before Christmas, for which ten songs needed to be written in advance of filmmaking, and Dumbo, for which he composed the main theme before filming began.

Once a rough cut of the film is ready, Elfman and the director have a spotting session to decide where to place music in the film, the emotional undercurrents of each scene, and overall tone. Elfman then spends a few weeks of free composition and experimentation to begin working out thematic material and to develop sounds and the harmonic palette.

When he has received approval on initial material from the filmmakers, Elfman begins to compose anywhere from 60 to 120 minutes of music cue-by-cue. He says two of the most important things to capture at this point are the tone of each scene and editorial rhythm. Next to thematic development, action set pieces tend to take Elfman the most time given the complexity of timing music to action.

Early in his career, he wrote out his scores using pencil, but has composed largely digitally since the mid-1990s.

Before recording the score, he demos each cue by mocking orchestral and choral parts on synthesizer to get approval from the director. Once approved, he provides a detailed, multi-line sketch of his composition to his lead orchestrator Steve Bartek, who ensures the sketches are appropriately broken down for sections of the orchestra (i.e. string, brass woodwind, some percussion), choir (SATB) and individual players.

Elfman also typically samples or records his own percussion and guitar playing to overlay with live orchestra. More than half of some scores feature Elfman's performance, including Dead Presidents, Mission: Impossible, Planet of the Apes, The Kingdom, The Girl on the Train and The Circle.

To produce the score, Elfman rents a recording studio and hires a conductor and orchestra/choir. He oversees the recording from the control booth so that he can troubleshoot with the film's director and recording engineers. The final recording is given to the film's sound department to mix with dialogue and sound effects for the film's complete soundtrack. Elfman will usually do a separate mix of select cues for an album presentation of the score, and has produced nearly 100 to date.

On the occasion that there are compressed deadlines or in the event he is not available to rescore or adapt his music if there are major edits to the film after the score's completion, Elfman will hire additional composers to work on small cues or sections of cues, adapting his existing material or themes. Examples include Jonathan Sheffer on Darkman, David Buckley on the Fifty Shades films, and Pinar Toprak on Justice League. Since the 1990s, Elfman has occasionally co-composed music or shared music writing credit (e.g.When We Rise, Spy Kids, Avengers: Age of Ultron, Men in Black International), or written themes that are then used or adapted by other composers, including Jonathan Sheffer (Pure Luck), Steve Bartek (Novacaine), John Debney (Heartbreakers), Deborah Lurie (9), and the Newton Brothers (Before I Wake).

During all his career, Elfman only once collaborated with another artist – meaning writing music together: it was with Siouxsie and the Banshees on the song "Face to Face" for Batman Returns in 1992. She created the foundation of the song, "and then I would take it and I would add stuff. And send it back to her". It was a long-distance collaboration as the studio needed the song very quickly. Elfman literally saw himself as a non-collaborator. "I'm not used to collaborating at all with anybody. I did one track with Siouxsie and the Banshees but that's it. I've always been in my own bubble, and that bubble has been very fertile".

Concert music
In the liner notes for the 2006 CD recording of his first concert work Serenada Schizophrana, Elfman wrote: "I began composing several dozen short improvisational compositions, maybe a minute each. Slowly, some of them began to develop themselves until finally I had six separate movements that, in some abstract, absurd way, felt connected."

To create the cadenzas for his violin concerto Eleven Eleven, Elfman collaborated with soloist Sandy Cameron, for whom the piece was written.

Vocals
Elfman often incorporates choral or vocal arrangements into his film scores, notably the use of women's and children's choirs (Scrooged, Nightbreed, Edward Scissorhands, Batman Returns, Sleepy Hollow, Alice in Wonderland, The Grinch), and solo voice or vocal effects (Beetlejuice, Mars Attacks!, Men in Black II, Flubber, Nacho Libre, Iris, Dark Shadows, The Girl on the Train). Evoking the "O Fortuna" from Carl Orff's Carmina Burana, he set made-up, Latin-sounding text for SATB choir in standout cue "Descent into Mystery" from Batman.

Elfman also adds his own vocals into compositions in much the same way he mixes his percussion and guitar performances into orchestral arrangements. Prominent use can be heard in the scores for To Die For (sung with director Gus Van Sant, credited to "Little Gus and the Suzettes"), Silver Linings Playbook, and his music for the Hong Kong Disneyland ride Mystic Manor. He provided the singing voice for characters in The Nightmare Before Christmas and Corpse Bride in addition to composing the scores and songs, and can be heard singing the "Day-O" call in the style of Harry Belafonte's "Banana Boat Song" in the first bars of the Beetlejuice main title.

For Tim Burton's Charlie and the Chocolate Factory, Elfman set Roald Dahl's text for the Oompa-Loompa characters as four stylistically distinct songs: the Bollywood-influenced "Augustus Gloop", the funk-infused "Violet Beauregarde", the psychedelic pop stylings of "Veruca Salt" and the baroque rock of "Mike Teavee". For all songs in the film, Elfman sang, manipulated and mixed several layers of his vocals to create the singing voices and harmonies of the Oompa Loompas, and incorporated his vocals into non-song score tracks that featured the characters, including "Loompa Land", "Chocolate River", "The Boat Arrives" and "The River Cruise".

Lyrics
Elfman typically writes the lyrics to songs he has composed for movies. He employs song structures from Tin Pan Alley and early musical theatre composers (32-bar form), and pop and rock of the 1950s and 1960s (verse-chorus). As his songs serve to advance the plot and develop characters, lyrics reflect storylines and imagery specific to the film and express the inner life of characters.

He wrote the lyrics and music for ten songs featured in the stop-motion musical The Nightmare Before Christmas. Drawing from Tim Burton's parody poem of A Visit from St. Nicholas and concept drawings, Elfman wrote each song in consultation with Burton before the film even had a script. These include the full-cast songs "This Is Halloween", "Town Meeting Song" and "Making Christmas"; four songs for the main character Jack Skellington, "Jack's Lament", "What's This?", "Jack's Obsession" and "Poor Jack", all sung by Elfman; and the other character songs "Kidnap the Sandy Claws", "Oogie Boogie's Song" and "Sally's Song". An eleventh song, "Finale/Reprise", reworks lyrics from the songs "This Is Halloween", "What's This?" and "Sally's Song" for the film's ending. Though uncredited, Burton contributed some lyrics to Nightmare, including the line "Perhaps it's the head that I found in the lake" in "Town Meeting Song".

Elfman composed five songs for Burton's Corpse Bride: "According to Plan", with lyrics co-written by screenwriter John August; "Remains of the Day" (which he sung as the character Bonejangles) and "Tears to Shed", both with additional lyrics by August; and "The Wedding Song", credited solely to Elfman. The song "Erased" was not used in the final film.

He wrote the lyrics to "Lullaby" from Charlotte's Web, the rock track "The Little Things" from Wanted which he also sang in English and Russian, and "Alice's Theme" from Alice in Wonderland. Elfman co-wrote the lyrics to "Twice the Love" from Big Fish and the "Wonka's Welcome Song" for Charlie and the Chocolate Factory with John August.

Elfman wrote the lyrics to all of Oingo Boingo's original songs 1979–1994 and has made residuals on the titular two-word opening phrase sung in his The Simpsons theme since the series first aired in 1989.

Personal life
As a teenager, Elfman dated his classmate Kim Gordon, who would later become one of the members of the rock band Sonic Youth. He has two daughters, Lola and Mali, from his marriage to Geri Eisenmenger. Mali is a film producer and actress. Elfman and Mali collaborated on her 2011 film Do Not Disturb.

On November 29, 2003, Elfman married actress Bridget Fonda. They have a son, Oliver. In 1998, Elfman scored A Simple Plan, starring Fonda. He is the uncle of actor Bodhi Elfman, who is married to actress Jenna Elfman.

Elfman has been an atheist since the age of 11 or 12. In an interview with the New York Post, he referred to himself as a "cynic-ologist".

Describing his politics during the 1980s, Elfman said, "I'm not a doomist. My attitude is always to be critical of what's around you, but not ever to forget how lucky we are. I've traveled around the world. I left thinking I was a revolutionary. I came back real right-wing patriotic. Since then, I've kind of mellowed in between." Several of his songs written for Oingo Boingo during this period satirized social politics, although Elfman stated his message was to "question, resist, challenge" and that his songs were not aligned to any one political agenda.

In 2008, Elfman expressed support for Barack Obama. For the 2020 Democratic National Convention, he scored the biographical video played ahead of Joe Biden's acceptance of the presidential nomination in the 2020 United States elections. In a series of posts on his Instagram page discussing the video, Elfman criticized Donald Trump, Richard Nixon, and the electoral college, and linked to several voter resources.

During his 18 years with Oingo Boingo, Elfman developed significant hearing damage as a result of the continuous exposure to the high noise levels involved in performing in a rock band. Afraid of worsening his condition, he decided to leave the band, saying that he would never return to that kind of performance. His impairment was so bad that he could not "even sit in a loud restaurant or bar anymore." However, he found performing in front of orchestras more tolerable, and returned several times to reprise his live performance of Jack Skellington.

Sexual harassment lawsuits
In July 2023, Rolling Stone reported that composer Nomi Abadi had accused Elfman of sexually harassing her between 2015 and 2017. According to the magazine's reporting, Abadi and Elfman signed a non-disclosure agreement in 2018, with Elfman agreeing to pay Abadi $830,000 in installments if she did not publicize her allegations against him. Abadi stipulated that part of the settlement would help establish a nonprofit foundation, the Female Composer Safety League. When Elfman defaulted on payments to the League, Abadi filed a breach of contract suit in Los Angeles Superior Court, leading to the matter becoming public.

After Rolling Stone revealed the existence of this agreement, Elfman denied the allegations, and said that he only agreed to the settlement because he feared that his "50-year career may be destroyed in one news cycle" if the claims had been published. Elfman stated Abadi had a "childhood crush" on him and intended to break up his marriage to pursue him romantically, but that he rejected her advances, leading to the allegations. Elfman's lawyer was quoted saying "accusations alone should not and do not equate to guilt, and Danny will defend himself and clear his name with the volume of evidence and the other party's own words — her words speak for themselves." The article also reports that Elfman provided two legal declarations, including one from a former friend of Abadi's, casting doubts on Abadi's claims.

In response, Abadi's attorney Jeff Anderson stated, "It is ironic that Mr. Elfman's current statements are directly contrary to the position he maintained in the underlying dispute and to the evidentiary record."

In October 2023, a Maryland woman, using the pseudonym Jane Doe XX, filed suit against Elfman for "sexual assault, gender violence, intentional infliction of emotional distress, sexual harassment and negligence." The woman alleged that between 1997 and 2002 Elfman groomed and sexually abused her in a similar fashion to Abadi's claims.

On July 10, 2024, Abadi sued Elfman for defamation concerning the statements he had made to Rolling Stone about the allegations in 2023.

In popular culture
Since The Simpsons' second annual Treehouse of Horror episode aired in 1991, launching "scary names" tradition in the opening and closing titles, Elfman has been alternately credited for the theme music as "Red Wolf Elfman", "Danny Skellingelfman", "Li'l Leakin Brain Elfman", "Boris Elfmonivich", "Danny Elfblood", "Danny 'Hell'fman", "The Bloody Elf", "Danny Elfbones", "Elfmunster" and "Daniel Beilzebelsman".

Elfman's composition "Clown Dream" from Pee-wee's Big Adventure is used in the video game Grand Theft Auto V and has often been used as the opening music for Primus concerts.

In the 2007 sixth season Star Wars parody "Blue Harvest", Family Guy lampooned Elfman's orchestral style. A scene shows Elfman replacing an incinerated John Williams to conduct a full orchestra playing the score, only to be decapitated by a lightsaber after conducting a few bars of oom-pah music.

Episode five of the 14th season of South Park in 2010 criticized Tim Burton for using the "same" music in all his films, referring to Elfman's scores.

In October 2016, Elfman produced a video clip for Funny or Die with original "horror" music composed to footage of Donald Trump pacing around Hillary Clinton at the second United States presidential election debates, 2016.

In 2019, selections from Elfman's Midnight Run score were used in the third season of Netflix's Stranger Things, including "Stairway Chase" in episodes 5 and 6, and "Wild Ride" and "Package Deal" in episode 6.

Christina Aguilera revealed that Elfman's music inspired her Las Vegas concert residency The Xperience.

American Film Institute
Elfman's scores for Batman and Edward Scissorhands were nominated for AFI's 100 Years of Film Scores.

Discography
Including commercial recordings of his film scores and the Oingo Boingo discography, Elfman has produced over 100 albums as of 2019.

title: Danny Elfman


text:
Dimension

[[File:Dimension levels.svg|thumb | 236px | The first four spatial dimensions, represented in a two-dimensional picture. 1. Two points can be connected to create a line segment.

2. Two parallel line segments can be connected to form a square.

3. Two parallel squares can be connected to form a cube.

4. Two parallel cubes can be connected to form a tesseract. ]]

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it –for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it –for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.

In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.

The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be Euclidean spaces or more general parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space.

In mathematics
In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object. For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc.

The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded. For example, a curve, such as a circle, is of dimension one, because the position of a point on a curve is determined by its signed distance along the curve to a fixed point on the curve. This is independent from the fact that a curve cannot be embedded in a Euclidean space of dimension lower than two, unless it is a line.

The dimension of Euclidean $n$-space $E^{n}$is $n$. When trying to generalize to other types of spaces, one is faced with the question "what makes $E^{n}$ $n$-dimensional?" One answer is that to cover a fixed ball in $E^{n}$ by small balls of radius $ε$, one needs on the order of $ε^{−n}$ such small balls. This observation leads to the definition of the Minkowski dimension and its more sophisticated variant, the Hausdorff dimension, but there are also other answers to that question. For example, the boundary of a ball in $E^{n}$ looks locally like $E^{n-1}$ and this leads to the notion of the inductive dimension. While these notions agree on $E^{n}$, they turn out to be different when one looks at more general spaces.

A tesseract is an example of a four-dimensional object. Whereas outside mathematics the use of the term "dimension" is as in: "A tesseract has four dimensions", mathematicians usually express this as: "The tesseract has dimension 4", or: "The dimension of the tesseract is 4" or: 4D.

Although the notion of higher dimensions goes back to René Descartes, substantial development of a higher-dimensional geometry only began in the 19th century, via the work of Arthur Cayley, William Rowan Hamilton, Ludwig Schläfli and Bernhard Riemann. Riemann's 1854 Habilitationsschrift, Schläfli's 1852 Theorie der vielfachen Kontinuität, and Hamilton's discovery of the quaternions and John T. Graves' discovery of the octonions in 1843 marked the beginning of higher-dimensional geometry.

The rest of this section examines some of the more important mathematical definitions of dimension.

Vector spaces
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.

For the non-free case, this generalizes to the notion of the length of a module.

Manifolds
The uniquely defined dimension of every connected topological manifold can be calculated. A connected topological manifold is locally homeomorphic to Euclidean $n$-space, in which the number $n$ is the manifold's dimension.

For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point.

In geometric topology, the theory of manifolds is characterized by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases $n > 4$ are simplified by having extra space in which to "work"; and the cases $n = 3$ and $4$ are in some senses the most difficult. This state of affairs was highly marked in the various cases of the Poincaré conjecture, in which four different proof methods are applied.

Complex dimension
The dimension of a manifold depends on the base field with respect to which Euclidean space is defined. While analysis usually assumes a manifold to be over the real numbers, it is sometimes useful in the study of complex manifolds and algebraic varieties to work over the complex numbers instead. A complex number (x + iy) has a real part x and an imaginary part y, in which x and y are both real numbers; hence, the complex dimension is half the real dimension.

Conversely, in algebraically unconstrained contexts, a single complex coordinate system may be applied to an object having two real dimensions. For example, an ordinary two-dimensional spherical surface, when given a complex metric, becomes a Riemann sphere of one complex dimension.

Varieties
The dimension of an algebraic variety may be defined in various equivalent ways. The most intuitive way is probably the dimension of the tangent space at any Regular point of an algebraic variety. Another intuitive way is to define the dimension as the number of hyperplanes that are needed in order to have an intersection with the variety that is reduced to a finite number of points (dimension zero). This definition is based on the fact that the intersection of a variety with a hyperplane reduces the dimension by one unless if the hyperplane contains the variety.

An algebraic set being a finite union of algebraic varieties, its dimension is the maximum of the dimensions of its components. It is equal to the maximal length of the chains $$V_0\subsetneq V_1\subsetneq \cdots \subsetneq V_d$$ of sub-varieties of the given algebraic set (the length of such a chain is the number of "$$\subsetneq$$").

Each variety can be considered as an algebraic stack, and its dimension as variety agrees with its dimension as stack. There are however many stacks which do not correspond to varieties, and some of these have negative dimension. Specifically, if V is a variety of dimension m and G is an algebraic group of dimension n acting on V, then the quotient stack [V/G] has dimension m − n.

Krull dimension
The Krull dimension of a commutative ring is the maximal length of chains of prime ideals in it, a chain of length n being a sequence $$\mathcal{P}_0\subsetneq \mathcal{P}_1\subsetneq \cdots \subsetneq\mathcal{P}_n $$ of prime ideals related by inclusion. It is strongly related to the dimension of an algebraic variety, because of the natural correspondence between sub-varieties and prime ideals of the ring of the polynomials on the variety.

For an algebra over a field, the dimension as vector space is finite if and only if its Krull dimension is 0.

Topological spaces
For any normal topological space $X$, the Lebesgue covering dimension of $X$ is defined to be the smallest integer n for which the following holds: any open cover has an open refinement (a second open cover in which each element is a subset of an element in the first cover) such that no point is included in more than $n + 1$ elements. In this case dim $X = n$. For $X$ a manifold, this coincides with the dimension mentioned above. If no such integer $n$ exists, then the dimension of $X$ is said to be infinite, and one writes dim $X = ∞$. Moreover, $X$ has dimension −1, i.e. dim $X = −1$ if and only if $X$ is empty. This definition of covering dimension can be extended from the class of normal spaces to all Tychonoff spaces merely by replacing the term "open" in the definition by the term "functionally open".

An inductive dimension may be defined inductively as follows. Consider a discrete set of points (such as a finite collection of points) to be 0-dimensional. By dragging a 0-dimensional object in some direction, one obtains a 1-dimensional object. By dragging a 1-dimensional object in a new direction, one obtains a 2-dimensional object. In general one obtains an ($n + 1$)-dimensional object by dragging an $n$-dimensional object in a new direction. The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that, in the case of metric spaces, ($n + 1$)-dimensional balls have $n$-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension -1.

Similarly, for the class of CW complexes, the dimension of an object is the largest $n$ for which the $n$-skeleton is nontrivial. Intuitively, this can be described as follows: if the original space can be continuously deformed into a collection of higher-dimensional triangles joined at their faces with a complicated surface, then the dimension of the object is the dimension of those triangles.

Hausdorff dimension
The Hausdorff dimension is useful for studying structurally complicated sets, especially fractals. The Hausdorff dimension is defined for all metric spaces and, unlike the dimensions considered above, can also have non-integer real values. The box dimension or Minkowski dimension is a variant of the same idea. In general, there exist more definitions of fractal dimensions that work for highly irregular sets and attain non-integer positive real values.

Hilbert spaces
Every Hilbert space admits an orthonormal basis, and any two such bases for a particular space have the same cardinality. This cardinality is called the dimension of the Hilbert space. This dimension is finite if and only if the space's Hamel dimension is finite, and in this case the two dimensions coincide.

Spatial dimensions
Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative distance. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See Space and Cartesian coordinate system.)

Time
A temporal dimension, or time dimension, is a dimension of time. Time is often referred to as the "fourth dimension" for this reason, but that is not to imply that it is a spatial dimension. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.

The equations used in physics to model reality do not treat time in the same way that humans commonly perceive it. The equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).

The best-known treatment of time as a dimension is Poincaré and Einstein's special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space. Time is different from other spatial dimensions as time operates in all spatial dimensions. Time operates in the first, second and third as well as theoretical spatial dimensions such as a fourth spatial dimension. Time is not however present in a single point of absolute infinite singularity as defined as a geometric point, as an infinitely small point can have no change and therefore no time. Just as when an object moves through positions in space, it also moves through positions in time. In this sense the force moving any object to change is time.

Additional dimensions
In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four fundamental forces by introducing extra dimensions/hyperspace. Most notably, superstring theory requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called M-theory which subsumes five previously distinct superstring theories. Supergravity theory also promotes 11D spacetime = 7D hyperspace + 4 common dimensions. To date, no direct experimental or observational evidence is available to support the existence of these extra dimensions. If hyperspace exists, it must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" at such tiny scales as to be effectively invisible to current experiments.

In 1921, Kaluza–Klein theory presented 5D including an extra dimension of space. At the level of quantum field theory, Kaluza–Klein theory unifies gravity with gauge interactions, based on the realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces electromagnetism. However at sufficiently high energies or short distances, this setup still suffers from the same pathologies that famously obstruct direct attempts to describe quantum gravity. Therefore, these models still require a UV completion, of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming a Calabi–Yau manifold. Thus Kaluza-Klein theory may be considered either as an incomplete description on its own, or as a subset of string theory model building.

In addition to small and curled up extra dimensions, there may be extra dimensions that instead are not apparent because the matter associated with our visible universe is localized on a (3 + 1)-dimensional subspace. Thus the extra dimensions need not be small and compact but may be large extra dimensions. D-branes are dynamical extended objects of various dimensionalities predicted by string theory that could play this role. They have the property that open string excitations, which are associated with gauge interactions, are confined to the brane by their endpoints, whereas the closed strings that mediate the gravitational interaction are free to propagate into the whole spacetime, or "the bulk". This could be related to why gravity is exponentially weaker than the other forces, as it effectively dilutes itself as it propagates into a higher-dimensional volume.

Some aspects of brane physics have been applied to cosmology. For example, brane gas cosmology attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can generically intersect. If initially there are many windings of strings around compact dimensions, space could only expand to macroscopic sizes once these windings are eliminated, which requires oppositely wound strings to find each other and annihilate. But strings can only find each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this kind of initial configuration.

Extra dimensions are said to be universal if all fields are equally free to propagate within them.

In computer graphics and spatial data
Several types of digital systems are based on the storage, analysis, and visualization of geometric shapes, including illustration software, Computer-aided design, and Geographic information systems. Different vector systems use a wide variety of data structures to represent shapes, but almost all are fundamentally based on a set of geometric primitives corresponding to the spatial dimensions:
 * Point (0-dimensional), a single coordinate in a Cartesian coordinate system.
 * Line or Polyline (1-dimensional), usually represented as an ordered list of points sampled from a continuous line, whereupon the software is expected to interpolate the intervening shape of the line as straight or curved line segments.
 * Polygon (2-dimensional), usually represented as a line that closes at its endpoints, representing the boundary of a two-dimensional region. The software is expected to use this boundary to partition 2-dimensional space into an interior and exterior.
 * Surface (3-dimensional), represented using a variety of strategies, such as a polyhedron consisting of connected polygon faces. The software is expected to use this surface to partition 3-dimensional space into an interior and exterior.

Frequently in these systems, especially GIS and Cartography, a representation of a real-world phenomena may have a different (usually lower) dimension than the phenomenon being represented. For example, a city (a two-dimensional region) may be represented as a point, or a road (a three-dimensional volume of material) may be represented as a line. This dimensional generalization correlates with tendencies in spatial cognition. For example, asking the distance between two cities presumes a conceptual model of the cities as points, while giving directions involving travel "up," "down," or "along" a road imply a one-dimensional conceptual model. This is frequently done for purposes of data efficiency, visual simplicity, or cognitive efficiency, and is acceptable if the distinction between the representation and the represented is understood, but can cause confusion if information users assume that the digital shape is a perfect representation of reality (i.e., believing that roads really are lines).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Dimension


text:
Dissolve

Dissolve may refer to:

 * Dissolution in chemistry, the process of dissolving a solute into a solvent to make a solution
 * Dissolve (filmmaking), in film and video editing, a transition between scenes
 * Dissolve (2019 film), a film by Kim Ki-duk
 * The Dissolve, a web magazine property of Pitchfork, covering movies
 * Dissolve (band), collaborative musical project between experimental guitarists Chris Heaphy and Roy Montgomery
 * "Dissolve", a song by Absofacto
 * ‘’Dissolve’’ a song by Joji from Smithereens

 * "Dissolve", a song by Daniel Johns from the album Talk
 * "Dissolve", a song by Hundred Reasons on the 2002 album Ideas Above Our Station

title: Dissolve


text:
Duodecimal

The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 1|units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "100" means twelve squared, "1000" means twelve cubed, and "0.1" means a twelfth.

Various symbols have been used to stand for ten and eleven in duodecimal notation; this page uses and, as in hexadecimal, which make a duodecimal count from zero to twelve read 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, , , 10. The Dozenal Societies of America and Great Britain (organisations promoting the use of duodecimal) use turned digits in their published material: $2$ (a turned 2) for ten and $3$ (a turned 3) for eleven.

The number twelve, a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range, and the smallest abundant number. All multiples of reciprocals of 3-smooth numbers ($a⁄2^{b}·3^{c}$ where $a,b,c$ are integers) have a terminating representation in duodecimal. In particular, $undefined 1/4$ (0.3), $undefined 1/3$ (0.4), $undefined 1/2$ (0.6), $undefined 2/3$ (0.8), and $undefined 3/4$ (0.9) all have a short terminating representation in duodecimal. There is also higher regularity observable in the duodecimal multiplication table. As a result, duodecimal has been described as the optimal number system.

In these respects, duodecimal is considered superior to decimal, which has only 2 and 5 as factors, and other proposed bases like octal or hexadecimal. Sexagesimal (base sixty) does even better in this respect (the reciprocals of all 5-smooth numbers terminate), but at the cost of unwieldy multiplication tables and a much larger number of symbols to memorize.

Origin

 * In this section, numerals are in decimal. For example, "10" means 9+1, and "12" means 9+3.

Georges Ifrah speculatively traced the origin of the duodecimal system to a system of finger counting based on the knuckle bones of the four larger fingers. Using the thumb as a pointer, it is possible to count to 12 by touching each finger bone, starting with the farthest bone on the fifth finger, and counting on. In this system, one hand counts repeatedly to 12, while the other displays the number of iterations, until five dozens, i.e. the 60, are full. This system is still in use in many regions of Asia.

Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Gure-Kahugu), Piti, and the Nimbia dialect of Gwandara; and the Chepang language of Nepal are known to use duodecimal numerals.

Germanic languages have special words for 11 and 12, such as eleven and twelve in English. They come from Proto-Germanic *ainlif and *twalif (meaning, respectively, one left and two left), suggesting a decimal rather than duodecimal origin. However, Old Norse used a hybrid decimal–duodecimal counting system, with its words for "one hundred and eighty" meaning 200 and "two hundred" meaning 240. In the British Isles, this style of counting survived well into the Middle Ages as the long hundred.

Historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, and the Babylonians had twelve hours in a day (although at some point, this was changed to 24). Traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches or 24 (12×2) Solar terms. There are 12 inches in an imperial foot, 12 troy ounces in a troy pound, 12 old British pence in a shilling, 24 (12×2) hours in a day; many other items are counted by the dozen, gross (144, square of 12), or great gross (1728, cube of 12). The Romans used a fraction system based on 12, including the uncia, which became both the English words ounce and inch. Pre-decimalisation, Ireland and the United Kingdom used a mixed duodecimal-vigesimal currency system (12 pence = 1 shilling, 20 shillings or 240 pence to the pound sterling or Irish pound), and Charlemagne established a monetary system that also had a mixed base of twelve and twenty, the remnants of which persist in many places.

Notations and pronunciations
In a positional numeral system of base n (twelve for duodecimal), each of the first n natural numbers is given a distinct numeral symbol, and then n is denoted "10", meaning 1 times n plus 0 units. For duodecimal, the standard numeral symbols for 0–9 are typically preserved for zero through nine, but there are numerous proposals for how to write the numerals representing "ten" and "eleven". More radical proposals do not use any Arabic numerals under the principle of "separate identity."

Pronunciation of duodecimal numbers also has no standard, but various systems have been proposed.

Transdecimal symbols
Several authors have proposed using letters of the alphabet for the transdecimal symbols. Latin letters such as $⟨ten, eleven⟩$ (as in hexadecimal) or $⟨\textturntwo, \textturnthree⟩$ (initials of Ten and Eleven) are convenient because they are widely accessible, and for instance can be typed on typewriters. However, when mixed with ordinary prose, they might be confused for letters. As an alternative, Greek letters such as $⟨A, B⟩$ could be used instead. Frank Emerson Andrews, an early American advocate for duodecimal, suggested and used in his 1935 book New Numbers $⟨T, E⟩$ (italic capital X from the Roman numeral for ten and a rounded italic capital E similar to open E), along with italic numerals 0–9.

Edna Kramer in her 1951 book The Main Stream of Mathematics used a $⟨τ, ε⟩$ (sextile or six-pointed asterisk, hash or octothorpe). The symbols were chosen because they were available on some typewriters; they are also on push-button telephones. This notation was used in publications of the Dozenal Society of America (DSA) from 1974 to 2008.

From 2008 to 2015, the DSA used $⟨X, Ɛ⟩$, the symbols devised by William Addison Dwiggins.

The Dozenal Society of Great Britain (DSGB) proposed symbols $⟨*, #⟩$. This notation, derived from Arabic digits by 180° rotation, was introduced by Isaac Pitman in 1857. In March 2013, a proposal was submitted to include the digit forms for ten and eleven propagated by the Dozenal Societies in the Unicode Standard. Of these, the British/Pitman forms were accepted for encoding as characters at code points and. They were included in Unicode 8.0 (2015).

After the Pitman digits were added to Unicode, the DSA took a vote and then began publishing PDF content using the Pitman digits instead, but continues to use the letters X and E on its webpage.

Base notation
There are also varying proposals of how to distinguish a duodecimal number from a decimal one. The most common method used in mainstream mathematics sources comparing various number bases uses a subscript "10" or "12", e.g. "5412 = 6410". To avoid ambiguity about the meaning of the subscript 10, the subscripts might be spelled out, "54twelve = 64ten". In 2015 the Dozenal Society of America adopted the more compact single-letter abbreviation "z" for "dozenal" and "d" for "decimal", "54z = 64d".

Other proposed methods include italicizing duodecimal numbers "54 = 64", adding a "Humphrey point" (a semicolon instead of a decimal point) to duodecimal numbers "54;6 = 64.5", prefixing duodecimal numbers by an asterisk "*54 = 64", or some combination of these. The Dozenal Society of Great Britain uses an asterisk prefix for duodecimal whole numbers, and a Humphrey point for other duodecimal numbers.

Pronunciation
The Dozenal Society of America suggested the pronunciation of ten and eleven as "dek" and "el". For the names of powers of twelve, there are two prominent systems.

Duodecimal numbers
In this system, the prefix e- is added for fractions.

As numbers get larger (or fractions smaller), the last two morphemes are successively replaced with tri-mo, quad-mo, penta-mo, and so on.

Multiple digits in this series are pronounced differently: 12 is "do two"; 30 is "three do"; 100 is "gro"; 9 is "el gro dek do nine"; 86 is "el gro eight do six"; 8,15 is "eight gro el do el, one gro five do dek"; ABA is "dek gro el do dek"; BBB is "el gro el do el"; 0.06 is "six egro"; and so on.

Systematic Dozenal Nomenclature (SDN)
This system uses "-qua" ending for the positive powers of 12 and "-cia" ending for the negative powers of 12, and an extension of the IUPAC systematic element names (with syllables dec and lev for the two extra digits needed for duodecimal) to express which power is meant.

After hex-, further prefixes continue sept-, oct-, enn-, dec-, lev-, unnil-, unun-.

Advocacy and "dozenalism"
William James Sidis used 12 as the base for his constructed language Vendergood in 1906, noting it being the smallest number with four factors and its prevalence in commerce.

The case for the duodecimal system was put forth at length in Frank Emerson Andrews' 1935 book New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics. Emerson noted that, due to the prevalence of factors of twelve in many traditional units of weight and measure, many of the computational advantages claimed for the metric system could be realized either by the adoption of ten-based weights and measure or by the adoption of the duodecimal number system.

Both the Dozenal Society of America and the Dozenal Society of Great Britain promote widespread adoption of the duodecimal system. They use the word "dozenal" instead of "duodecimal" to avoid the more overtly decimal terminology. However, the etymology of "dozenal" itself is also an expression based on decimal terminology since "dozen" is a direct derivation of the French word douzaine, which is a derivative of the French word for twelve, douze, descended from Latin duodecim.

Mathematician and mental calculator Alexander Craig Aitken was an outspoken advocate of duodecimal: "The duodecimal tables are easy to master, easier than the decimal ones; and in elementary teaching they would be so much more interesting, since young children would find more fascinating things to do with twelve rods or blocks than with ten. Anyone having these tables at command will do these calculations more than one-and-a-half times as fast in the duodecimal scale as in the decimal. This is my experience; I am certain that even more so it would be the experience of others."

- A. C. Aitken

"But the final quantitative advantage, in my own experience, is this: in varied and extensive calculations of an ordinary and not unduly complicated kind, carried out over many years, I come to the conclusion that the efficiency of the decimal system might be rated at about 65 or less, if we assign 100 to the duodecimal."

In media
In "Little Twelvetoes", American television series Schoolhouse Rock! portrayed an alien being with twelve fingers and twelve toes using duodecimal arithmetic, using "dek" and "el" as names for ten and eleven, and Andrews' script-X and script-E for the digit symbols.

Duodecimal systems of measurements
Systems of measurement proposed by dozenalists include:
 * Tom Pendlebury's TGM system
 * Takashi Suga's Universal Unit System
 * John Volan's Primel system

Comparison to other number systems

 * In this section, numerals are in decimal. For example, "10" means 9+1, and "12" means 6×2.

The Dozenal Society of America argues that if a base is too small, significantly longer expansions are needed for numbers; if a base is too large, one must memorise a large multiplication table to perform arithmetic. Thus, it presumes that "a number base will need to be between about 7 or 8 through about 16, possibly including 18 and 20".

The number 12 has six factors, which are 1, 2, 3, 4, 6, and 12, of which 2 and 3 are prime. It is the smallest number to have six factors, the largest number to have at least half of the numbers below it as divisors, and is only slightly larger than 10. (The numbers 18 and 20 also have six factors but are much larger.) Ten, in contrast, only has four factors, which are 1, 2, 5, and 10, of which 2 and 5 are prime. Six shares the prime factors 2 and 3 with twelve; however, like ten, six only has four factors (1, 2, 3, and 6) instead of six. Its corresponding base, senary, is below the DSA's stated threshold.

8|Eight and Sixteen only have 2 as a prime factor. Therefore, in octal and hexadecimal, the only terminating fractions are those whose denominator is a power of two.

Thirty is the smallest number that has three different prime factors (2, 3, and 5, the first three primes), and it has eight factors in total (1, 2, 3, 5, 6, 10, 15, and 30). Sexagesimal was actually used by the ancient Sumerians and Babylonians, among others; its base, sixty, adds the four convenient factors 4, 12, 20, and 60 to 30 but no new prime factors. The smallest number that has four different prime factors is 210; the pattern follows the primorials. However, these numbers are quite large to use as bases, and are far beyond the DSA's stated threshold.

In all base systems, there are similarities to the representation of multiples of numbers that are one less than or one more than the base.

''In the following multiplication table, numerals are written in duodecimal. For example, "10" means twelve, and "12" means fourteen.''

Conversion tables to and from decimal
To convert numbers between bases, one can use the general conversion algorithm (see the relevant section under positional notation). Alternatively, one can use digit-conversion tables. The ones provided below can be used to convert any duodecimal number between 0;1 and ,; to decimal, or any decimal number between 0.1 and 99,999.9 to duodecimal. To use them, the given number must first be decomposed into a sum of numbers with only one significant digit each. For example:

 * 12,345.6 = 10,000 + 2,000 + 300 + 40 + 5 + 0.6

This decomposition works the same no matter what base the number is expressed in. Just isolate each non-zero digit, padding them with as many zeros as necessary to preserve their respective place values. If the digits in the given number include zeroes (for example, 7,080.9), these are left out in the digit decomposition (7,080.9 = 7,000 + 80 + 0.9). Then, the digit conversion tables can be used to obtain the equivalent value in the target base for each digit. If the given number is in duodecimal and the target base is decimal, we get:

 * (duodecimal) 10,000 + 2,000 + 300 + 40 + 5 + 0;6 = (decimal) 20,736 + 3,456 + 432 + 48 + 5 + 0.5

Because the summands are already converted to decimal, the usual decimal arithmetic is used to perform the addition and recompose the number, arriving at the conversion result:

Duodecimal ---> Decimal 10,000   =   20,736    2,000    =    3,456       300    =      432       40    =       48        5    =        5  +     0;6  =  +     0.5 -   12,345;6  =   24,677.5

That is, (duodecimal) 12,345;6 equals (decimal) 24,677.5

If the given number is in decimal and the target base is duodecimal, the method is same. Using the digit conversion tables:

(decimal) 10,000 + 2,000 + 300 + 40 + 5 + 0.6 = (duodecimal) 5,954 + 1,18 + 210 + 34 + 5 + 0;$⟨Dozenal us 10.svg, Dozenal us 11.svg⟩$

To sum these partial products and recompose the number, the addition must be done with duodecimal rather than decimal arithmetic:

Decimal --> Duodecimal 10,000   =   5,954    2,000    =   1,18      300    =     210       40    =      34        5    =       5  +     0.6  =  +    0;$⟨$2$, $3$⟩$ ---   12,345.6  =   7,189;$\overline{7249}$

That is, (decimal) 12,345.6 equals (duodecimal) 7,189;$\overline{7249}$

Fractions
Duodecimal fractions for rational numbers with 3-smooth denominators terminate:
 * $\overline{7249}$ = 0;6
 * $\overline{7249}$ = 0;4
 * $\overline{3}$ = 0;3
 * $\overline{6}$ = 0;2
 * $\overline{3}$ = 0;16
 * $\overline{6}$ = 0;14
 * $\overline{3}$ = 0;1 (this is one twelfth, $\overline{6}$ is one tenth)
 * $\overline{3}$ = 0;09 (this is one sixteenth, $\overline{6}$ is one fourteenth)

while other rational numbers have recurring duodecimal fractions:
 * $\overline{2497}$ = 0;$\overline{2497}$
 * $\overline{7249}$ = 0;$\overline{4972}$
 * $\overline{7249}$ = 0;1$\overline{4972}$ (one tenth)
 * $\overline{9724}$ = 0;$\overline{9724}$ (one eleventh)
 * $1⁄2$ = 0;$1⁄3$ (one thirteenth)
 * $1⁄4$ = 0;0$1⁄6$ (one fourteenth)
 * $1⁄8$ = 0;0$1⁄9$ (one fifteenth)

As explained in recurring decimals, whenever an irreducible fraction is written in radix point notation in any base, the fraction can be expressed exactly (terminates) if and only if all the prime factors of its denominator are also prime factors of the base.

Because $$2\times5=10$$ in the decimal system, fractions whose denominators are made up solely of multiples of 2 and 5 terminate: $1⁄10$ = $1⁄undefined$, $1⁄14$ = $1⁄12$, and $1⁄5$ = $\overline{2497}$ can be expressed exactly as 0.125, 0.05, and 0.002 respectively. $1⁄7$ and $\overline{18635}$, however, recur (0.333... and 0.142857142857...).

Because $$2\times2\times3=12$$ in the duodecimal system, $1⁄undefined$ is exact; $\overline{2497}$ and $1⁄undefined$ recur because they include 5 as a factor; $\overline{1}$ is exact, and $1⁄11$ recurs, just as it does in decimal.

The number of denominators that give terminating fractions within a given number of digits, $n$, in a base $b$ is the number of factors (divisors) of $$b^n$$, the $n$th power of the base $b$ (although this includes the divisor 1, which does not produce fractions when used as the denominator). The number of factors of $$b^n$$ is given using its prime factorization.

For decimal, $$10^n=2^n\times 5^n$$. The number of divisors is found by adding one to each exponent of each prime and multiplying the resulting quantities together, so the number of factors of $$10^n$$ is $$(n+1)(n+1)=(n+1)^2$$.

For example, the number 8 is a factor of 103 (1000), so $\frac{1}{8}$ and other fractions with a denominator of 8 cannot require more than three fractional decimal digits to terminate. $\frac{5}{8}=0.625_{10}.$

For duodecimal, $$10^n=2^{2n}\times 3^n$$. This has $$(2n+1)(n+1)$$ divisors. The sample denominator of 8 is a factor of a gross $12^2=144$ in decimal), so eighths cannot need more than two duodecimal fractional places to terminate. $\frac{5}{8}=0.76_{12}.$

Because both ten and twelve have two unique prime factors, the number of divisors of $$b^n$$ for $b = 10 or 12$ grows quadratically with the exponent $n$ (in other words, of the order of $$n^2$$).

Recurring digits
The Dozenal Society of America argues that factors of 3 are more commonly encountered in real-life division problems than factors of 5. Thus, in practical applications, the nuisance of repeating decimals is encountered less often when duodecimal notation is used. Advocates of duodecimal systems argue that this is particularly true of financial calculations, in which the twelve months of the year often enter into calculations.

However, when recurring fractions do occur in duodecimal notation, they are less likely to have a very short period than in decimal notation, because 12 (twelve) is between two prime numbers, 11 (eleven) and 13 (thirteen), whereas ten is adjacent to the composite number 9. Nonetheless, having a shorter or longer period does not help the main inconvenience that one does not get a finite representation for such fractions in the given base (so rounding, which introduces inexactitude, is necessary to handle them in calculations), and overall one is more likely to have to deal with infinite recurring digits when fractions are expressed in decimal than in duodecimal, because one out of every three consecutive numbers contains the prime factor 3 in its factorization, whereas only one out of every five contains the prime factor 5. All other prime factors, except 2, are not shared by either ten or twelve, so they do not influence the relative likeliness of encountering recurring digits (any irreducible fraction that contains any of these other factors in its denominator will recur in either base).

Also, the prime factor 2 appears twice in the factorization of twelve, whereas only once in the factorization of ten; which means that most fractions whose denominators are powers of two will have a shorter, more convenient terminating representation in duodecimal than in decimal:

 * 1/(22) = 0.2510 = 0.312
 * 1/(23) = 0.12510 = 0.1612
 * 1/(24) = 0.062510 = 0.0912
 * 1/(25) = 0.0312510 = 0.04612

The duodecimal period length of 1/n are (in decimal)
 * 0, 0, 0, 0, 4, 0, 6, 0, 0, 4, 1, 0, 2, 6, 4, 0, 16, 0, 6, 4, 6, 1, 11, 0, 20, 2, 0, 6, 4, 4, 30, 0, 1, 16, 12, 0, 9, 6, 2, 4, 40, 6, 42, 1, 4, 11, 23, 0, 42, 20, 16, 2, 52, 0, 4, 6, 6, 4, 29, 4, 15, 30, 6, 0, 4, 1, 66, 16, 11, 12, 35, 0, ...

The duodecimal period length of 1/(nth prime) are (in decimal)
 * 0, 0, 4, 6, 1, 2, 16, 6, 11, 4, 30, 9, 40, 42, 23, 52, 29, 15, 66, 35, 36, 26, 41, 8, 16, 100, 102, 53, 54, 112, 126, 65, 136, 138, 148, 150, 3, 162, 83, 172, 89, 90, 95, 24, 196, 66, 14, 222, 113, 114, 8, 119, 120, 125, 256, 131, 268, 54, 138, 280, ...

Smallest prime with duodecimal period n are (in decimal)
 * 11, 13, 157, 5, 22621, 7, 659, 89, 37, 19141, 23, 20593, 477517, 211, 61, 17, 2693651, 1657, 29043636306420266077, 85403261, 8177824843189, 57154490053, 47, 193, 303551, 79, 306829, 673, 59, 31, 373, 153953, 886381, 2551, 71, 73, ...

Irrational numbers
The representations of irrational numbers in any positional number system (including decimal and duodecimal) neither terminate nor repeat. The following table gives the first digits for some important algebraic and transcendental numbers in both decimal and duodecimal.

title: Duodecimal


text:
David Hayes Agnew

David Hayes Agnew (November 24, 1818 – March 22, 1892) was an American surgeon.

Biography
Agnew was born on November 24, 1818, Nobleville, Pennsylvania (present-day Christiana). His parents were Robert Agnew and Agnes Noble. Agnew grew up as a Christian. He was surrounded by a family of doctors and had always known he was going to become a physician. As a young boy, he had a sharp sense of humor and was very intelligent.

He was educated at Jefferson College, and at Delaware College in Newark, Delaware. He graduated from the University of Pennsylvania School of Medicine on April 6, 1838. He returned to Nobleville to help his father in his clinic. He worked there for two years. His father was an asthmatic and moved to Maryland in 1840 because the climate was more suited to his condition. Agnew moved with him. On November 21, 1841, he married Margaret Irwin. In 1852, he bought and revived the Philadelphia School of Anatomy. He held responsibility for ten years until 1862. During the American Civil War he was consulting surgeon in the Mower Army Hospital, near Philadelphia, and acquired a considerable reputation for his operations in cases of gunshot wounds. On December 21, 1863, he became the Demonstrator of Anatomy and Assistant Lecturer on Clinical Surgery at The University of Pennsylvania. Later, he was requested to assist the Professor of Surgery in the Conduct of the surgical clinics. In the year 1865, he gave summer instruction courses. For the next seven years, he worked for the University as Demonstrator of Anatomy. A large portion of his success was due to his wife's energy, intelligence, and determination. She gave him an impetus to try harder and not be satisfied with his first try.

He was elected as a member of the American Philosophical Society in 1872.

Garfield case
On July 2, 1881, President James A. Garfield was shot by Charles J. Guiteau. He held the position of chief consulting surgeon. When a committee came to give him his money for helping, Agnew said, "Gentlemen, I present no bill for my attendance to President Garfield. I gave my services freely and gratuitously". He was never optimistic about the President's case and was not fooled by fallacious beliefs. This procedure helped create Agnew's reputation.

The Agnew Clinic
The Agnew Clinic is an 1889 painting by Thomas Eakins which depicts Agnew conducting a mastectomy operation before a gallery of students and doctors.

Accomplishments
David Agnew wrote The Principles and Practice of Surgery, covers an experience of fifty active years, and its value, preserving and presenting as it does the life-work of such a recognized authority, can hardly be overrated. It was a three-volume set that he published from 1878–1883. He also helped found the Irwin & Agnew Iron Foundry in 1846.

Death
Agnew caught a severe attack of epidemic influenza in 1890. He never fully recovered. Following this, he had an attack of broncho-vesicular catarrh. On March 9, 1892, he was put to bed for a series of medical problems. After a few days his condition began to improve, but suddenly, on March 12 it became much worse. On March 20, he fell into a comatose condition. Agnew stayed like this until he died at 3:20 p.m. on March 22, 1892. He is now buried in West Laurel Hill Cemetery.

title: David Hayes Agnew