text:
Adam Strange

Adam Strange is a superhero appearing in American comic books published by DC Comics. Created by editor Julius Schwartz and designed by Murphy Anderson, he first appeared in Showcase #17 (November 1958).

Adam Strange made his live action debut in the television series Krypton, portrayed by Shaun Sipos.

Creation
In 1957, DC Comics editorial director Irwin Donenfeld held a meeting with editors Jack Schiff and Julius Schwartz in his office, asking them each to create a new science fiction hero, one from the present and one from the future. Given first pick Schiff chose to create one from the future, Space Ranger. Schwartz was happy with the pick feeling that readers would more readily identify with a hero from the present. He conceived the idea of an Earth man repeatedly traveling to a planet in the Alpha Centauri star system by using a "Zeta-beam" altered by space radiation. Since Adam Strange was the first Earthman on another planet, he named his character Adam after the Biblical first man. When asked about the inspiration behind the character, Gardner Fox stated "I suppose you could say that John Carter was in my subconscious, you had to think of some interesting way to transfer him to from earth up to the planet Rann before you even got started in on a plot, but it was fun to do."

Publication history
Adam Strange debuted in issues #17–19 of the tryout series Showcase, published November 1958-March 1959. The first artwork of the character was a cover for Showcase #17 by Murphy Anderson. Schwartz rejected the drawing and commissioned a new one by Gil Kane, though Anderson's costume design was retained. Schwartz then assigned the scribing of the stories to Gardner Fox and the penciling to Mike Sekowsky. Schwartz and Fox devised the plots for the stories in Schwartz's office and Fox would write the scripts at home. A science major, Schwartz specialized in giving Fox scientific pointers that gave the Adam Strange tales a plausibility that made them stand out from most science fiction comic books of the time.

Sales on the three-issue Showcase tryout were enough to justify giving Adam Strange a slot in Mystery in Space, which ran in issues #53–100 and 102. Though Schwartz and Fox continued their work on the character, Schwartz gave the penciler assignment to Carmine Infantino instead of Sekowsky. Most issues were inked by Murphy Anderson (although Bernard Sachs, Joe Giella and Sid Greene did a few issues each). After his adventures in Mystery in Space were cancelled, Adam Strange continued to have guest appearances in several DC Comics titles. Perhaps the most notable is an adventure written by Gardner Fox and illustrated by Murphy Anderson for Hawkman #18 (1967). In it, Hawkman fails to find his planet, Thanagar, and his search leads him to Rann, where he shares a adventure with Adam Strange. In the Justice League of America comic book, the Flash mentioned Adam Strange as a possible new member for the Justice League. When a letter to the editor pointed out the group had not met Adam Strange and could not have heard of him, as all his heroics took place on Rann, Schwartz and Fox wrote a story showing how the Justice League came to Rann and how Adam Strange saved them from Kanjar Ro. The story was published in Mystery in Space #75 and won the Alley Award for the "Best Book-Length Story" of 1962.

As of #92, Jack Schiff replaced Schwartz as editor of Mystery in Space and Lee Elias became the artist for Adam Strange. Following the discontinuation of the Adam Strange stories reprints were presented in Strange Adventures #217 through 244 (except for #222, which instead has a new story with Strange, written by Denny O'Neil, while #226 has a new Strange text story by Fox, with illustrations by Anderson).

Adam Strange had stories written by Dave Wood, Jerry Siegel and Dennis O'Neil, art by Lee Elias and inks by John Giunta.

Through the 1970s the character was a regular presence in the DC Universe despite having no series of his own. In September 1980 Adam Strange began as a back-up feature in Green Lantern (this lasted from #132 to #147). Later in the 1980s Alan Moore wrote a retcon of Adam Strange's reason for his visits to Rann. In this retcon the population of the planet, the majority of whom view the Terran with contempt, is sterile, and Adam Strange is there to be a breeding stud. In a 1990 limited series, The Man of Two Worlds, Adam learns of the population's opinion of him and Alanna dies giving birth to their daughter Aleea. In 1997, Grant Morrison revived the Justice League of America in the JLA series. During this period, Mark Waid featured Adam Strange when he filled in for Morrison. In JLA #20 (July 1998) Alanna is revealed to be alive and is briefly reunited with her husband and daughter before Adam is transported back to Earth.

Adam appeared in stories set in the Silver Age: Legends of the DC Universe 80-Page Giant #1 (1998); Silver Age: Showcase #1 (2000); DC Universe: Legacies #5 (2010); and DC Retroactive: Justice League - The '70s (2011).

In 2013, Jeff Lemire said he intended to introduce a New 52 incarnation of Adam Strange at some point in Justice League Canada, a series scheduled to launch in Spring 2014. Lemire's series was instead titled Justice League United, featuring Alanna as well as Adam.

The series Strange Adventures vol. 5, written by Tom King and illustrated by Mitch Gerads and Evan Shaner was launched in 2020, focusing on the character of Adam Strange.

Fictional character biography
Strange is an archeologist suddenly teleported from Peru, Earth, to the planet Rann through a "Zeta-Beam". Upon his arrival, he is attacked by one of the planet's predators and rescued by a dark-haired woman called Alanna. She takes him to her father Sardath, who explains that the Zeta-Beam was transmitted to Earth in the hopes that whatever form of intelligent life lived there would trace it back to Rann, and he also theorizes that in the 4.3 years it took the Zeta-Beam to reach Earth, it was exposed to radiation and transformed into a transportation beam. Called on to protect the planet from extraterrestrial threats using Rann's technology, Strange grew to care for the planet and its inhabitants, especially Alanna. Eventually, the effects of the beam's transportation wore off, automatically returning Strange to Earth at the exact point of departure—but not before Sardath had given him a schedule of beam firings, allowing him to periodically return to the planet. Using mathematical calculations, he was able to determine the exact time and the precise locations at which the Zeta-Beams would arrive. He travels the world and intercepts them, to defend Rann and be with Alanna.

Years later, during an exile in space, Swamp Thing arrives on Rann, where he meets Adam Strange. In this story it is revealed that centuries ago the planet's population suffered nuclear wars and left them not only with the loss of a large part of their ecosystem, but also with a genetic problem that made the majority of the population sterile, Alanna being one of the last born on the planet. Throughout history, Swamp Thing manages to create an ecological system in desert areas of the planet. Also, Alanna tells Adam that she was finally able to get pregnant.

Over time, Sardath perfected a beam he would call the "Mega Zeta-Beam" which would allow Adam to permanently transport himself to Rann. In those days, Adam learns that he did not really come to Rann by accident since the Zeta Ray was sent by Sardath to bring him with the intention that he would form a couple with Alanna and have children with her so that he could begin to change the genetics of the population. While Adam was destined to save the planet, it was not in the way he believed. He also learns that despite having been his primary protector for years, the people of Rann generally despised him for being an alien. Eventually, Alanna gives birth to a girl named Aleea, but apparently dies in the process.

Grayven, Darkseid's illegitimate son, tries to destroy Ranagar City and take the Zeta-Beam, Adam Strange is aided by the Darkstars and Green Lantern Kyle Rayner.

Hyathis attempted to overthrow the government of Rann by using her telepathy to turn an alien race called the Zaredians against the Darkstars. The Zaredian attack created a diversion which allowed Hyathis to kidnap Aleea. Her plans were upset by the arrival of Superboy and the Ravers.

Years later, Adam is on Rann raising his daughter Aleea and helping to restore the planet, when he learns that Alanna did not actually die but that Sardath secretly placed her in suspended animation and handed her over to the En'Taran Slavemasters, who were able to revive her, but that both were currently their prisoners and that, to free her, she had to deliver the planet Rann. Adam convinces the conquerors that he must kidnap the Justice League to rebuild the planet more quickly, and thus, together with the group, he not only rebuilds Rann but manages to defeat the En'tarang and free Alanna. Unfortunately in the process, Adam loses all traces of the Mega Zeta Ray in his body, and this causes his unwanted return to Earth. Strange returned to Rann and reunited with his family shortly after.

Planet Heist
Planet Heist, a 2004 eight-issue limited series, written by Andy Diggle, penciled by Pasqual Ferry and colored by Dave McCaig, replaced Adam Strange's costume with a spacesuit that allows for interstellar travel. Adam was prepared to relocate to Rann permanently when he was informed that the planet was destroyed and that he was blamed for its destruction. In fact, Sardath transported Rann to another dimension to save the planet from the cosmic being Starbreaker. Adam, with the help of the Omega Men and the Darkstars, among others, saved Rann and defeated the evil being.

Rann-Thanagar War
When Rann was moved from Alpha Centauri to Polaris, its orbit was believed to have pushed the planet Thanagar (which belongs to the Polaris stellar system) closer to its sun, destroying much of the surface (it was later discovered that the actions of Superboy-Prime moved Thanagar). Many Thanagarians were relocated to Rann, but enmity between the two races resulted in a war, depicted in Rann-Thanagar War. Strange, working with Hawkman, Hawkwoman, Kyle Rayner and Kilowog, tried to end the conflict, a six-issue precursor to DC's 2005 to 2006 limited series and DC crossover event, Infinite Crisis. Strange was eventually able to end the war when he discovered evidence of Superboy-Prime's role in Thanagar's relocation.

52
Adam was stranded on a paradise-like planet with Animal Man and Starfire. As a result of a teleportation accident involving the Zeta-Beam he lost both of his eyes, but in spite of his injuries he tried to fix a damaged spaceship so that the trio might return home. After being attacked by Devilance the Pursuer they eventually escaped, having realized that the entire planet was a trap.

This ragtag team made a stand against the villainess Lady Styx, whose undead legions were ravaging planets across the galaxy. With Styx presumably defeated and Animal Man seemingly killed, Strange and Starfire continued their journey back to Earth and Rann, still pursued by angry Lady Styx followers. With Starfire wounded in one such battle, and their ship breaking apart and malfunctioning, Adam was saved by Mogo and a rookie Green Lantern. Brought to Rann, Strange was equipped with new eyes cloned by Aleea and genetically engineered to grant him vision of the entire electromagnetic spectrum. He was briefly questioned by the Green Lantern Corps about the secret of 52 but, when an emergency arose during the interrogation, the Lanterns offered to respond in Strange's stead so he could return to his wife.

Countdown to Adventure
Adam Strange joined Animal Man and Starfire in the series Countdown to Adventure written by Adam Beechen in August 2007.

In issue #1, Adam finds himself replaced as Rann's protector by Champ Hazard, a former actor from Earth. However, Hazard has no regard for any life and is responsible for ending his battles in a horrifically bloody way. It appears Champ was infected by a madness plague created by Lady Styx before leaving Earth, and has infected one third of the people on Rann, causing them to riot and say "Believe in Her". Adam and his family escape to Earth, where he enlists the aid of Animal Man and Starfire, eventually discovering a way to cure the plague and restore the infectees to normal.

Rann-Thanagar Holy War
Adam Strange, along with many of the DC space heroes including Hawkman, Starfire, The Weird, and the Prince Gavyn Starman, battles Synnar the Demiurge. Adam Strange's actions in this story result in the depopulation of Prince Gavyn's Throneworld at the hands of Lady Styx. Later, to defeat Synnar and Lady Styx, Rann's atmosphere was explosively discharged into outer space with Rann's entire population Zeta-beamed to Throneworld. Strange also discovers in this story that he is a member of the so-called Aberrant Six.

Strange Adventures
With Throneworld renamed New Rann, Adam Strange once more teams up with the DC space heroes to investigate why some of the galaxy's stars are disappearing. It is discovered from the future spirit of Synnar that he is destined to be one of 'The Aberrant Six', a group critical to preventing the Synnar of today (trapped in The Weird's body) from destroying the universe. Ultimately the Aberrant Six did not form and the future Synnar was forced to leave, but not before Captain Comet's mercenary friend Eye was killed by Synnar's supreme god-enemy to prevent the forming of the Six. Comet was entrusted with Eye's robot companion Orb until she returns, told by Synnar that when that happens he will "continue his negotiations – all has changed, but remains as it was". Adam Strange realizes that one day Synnar will return and force him to join his Aberrant Six.

R.E.B.E.L.S.
Adam Strange then found himself joining up with Vril Dox as part of his R.E.B.E.L.S. Adam Strange helped to save the Vega system and several galaxies by defeating Starro the Conqueror. It was also around this time that Adam Strange visited New Krypton to protest the accord that their Council reached with the Thanagarians. Explaining that the Rannians have recently been on the losing end in a war with the Thanagarians, Adam questions the judgment of the Council in reaching this accord. Whilst there he aided Superman who was investigating a murder.

The plight of Rann's people was soon resolved by Vril Dox, seeking to restore his reputation after Starro the Conqueror stole L.E.G.I.O.N. from him and used it to enslave its client worlds. Dox Zeta-beamed Rann into the Vega system, in the orbit previously held by the now destroyed planet Tamaran, and proceeded to terraform Rann and make it suitable to sustain life again.

The restoration of the planet Rann was not Dox's only reason for relocating it into the Vega system. First, by putting Rann into Tamaran's orbit, it restored the gravitational balance to the Vega system, which had been thrown off by Tamaran's destruction. Secondly, in exchange for restoring their planet, the people of Rann agreed to let Dox rebuild L.E.G.I.O.N. headquarters on Rann.

Tamaranian refugees, led by Blackfire, attacked Rann believing that since the planet was in Tamaran's orbit they had claim to it. The violence was ended when Vril Dox, who was off-world at the start of the conflict, arrived with Thanagarian warships and stopped the fighting without bloodshed on either side. As it turned out, Dox was off-world negotiating an official end to the Rann-Thanagar War, using Rann's new-found distance from Thanagar and change in leadership on both sides as leverage.

Dox then went on to mediate the tension between the Rannians and the Tamaranians by proposing that the Tamaranians live on Rann's uninhabited southern continent.

Adam Strange, as well as protector of Rann, would also become a senior commander of L.E.G.I.O.N. ensuring peace with the Green Lantern Corps. He also helped create an alliance between Rannians, Tamaranians and L.E.G.I.O.N. after defeating Starro the Conqueror, ensuring security for Rann, the Vega System and the galaxy.

The New 52
In The New 52, a 2011 reboot of the DC Comics universe, Adam Strange was reintroduced to mainstream continuity as a Canadian archaeologist who has a relationship with Alanna (now Alanna Lewis, a former student of his). He and other heroes are teleported to his home planet Rann to stop the villain Byth Rok. He and Alanna then became founding members of the Justice League United. An accident with the Zeta Beam allowed Adam to merge with its time-space energy signature, allowing him to project his consciousness throughout all known reality. By the end of the series, Adam would lose his newfound abilities and return to normal.

During Vandal Savage's scheme to gain more power from the comet that made him immortal, the JLU assisted a weaker Superman's efforts to thwart his plans. However, the heroes were captured and their powers used as fuel to bring the comet closer to Earth to give Savage's descendants their own abilities. They were saved by Superman, who was now empowered by Kryptonite, and the heroes held back Savage's forces long enough for Superman to finally defeat the immortal, after which the hero dies.

DC Rebirth
Strange was next featured in The Death of Hawkman series, once again caught in the middle of the Rann/Thangar conflict. Suspicious that Thangar initiated the first attack, Adam began an investigation into the events with the aid of his friend Hawkman. The two soon discover that Despero was behind the conflict, aiming to collect the planets Nth Metal supply. They fought Despero, but the villain proved to be too strong to handle. In an act of desperation, Hawkman ordered Adam to active a machine that will magnetize all of the planets Nth Metal, killing Hawkman and Despero. A reluctant Adam agreed, but the machine unexpectedly sent him hurtling into another dimension. The dimension was revealed to be the home of Jonny Quest as part of the Future Quest series.

He soon found his way back to the DC Universe, where he divides his attention between his home world and his adopted world. He also became a reserve member of the Justice League.

Skills and equipment
Adam Strange lacks any real superhuman attributes, choosing to rely more on quick thinking and ingenuity. Before coming to Rann, Strange was an accomplished explorer and archaeologist who specialized in gathering and studying lost artifacts found in the remains of ancient civilizations. Applying these qualities to his new life on Rann, he would venture out with his new family into the wilds of their homeworld to study and rediscover its ancient history. Eventually his experiences accumulated on his adventures through the study and understanding of both Rannian culture and its vast technologies as well as its vested history, enabled Adam to pick up a host of vaunted combat techniques and scientific knowledge, giving him the edge needed to physically match and defeat immeasurably more imposing opponents over the many years. He has battled and bested adversaries both native and extraterrestrial in nature, such as Thanagarians, Durlans, Qwardians, En'Tarans, and Meta-Humans. This along with his many decades of thriving in the harsh environments of Rann, Earth and other galactic territories has made Adam an accomplished survivalist, having spent just as long traversing the rural areas as treacherous as the Amazon rainforest back on Earth.

Strange has a tactical intellect on par with - or exceeding - the likes of Bruce Wayne and Lex Luthor, and complements this with the learning that he has gained in his many years of study on Rann. He is able to reverse engineer functional technological wonders even from the damaged remains of an alien ship with ease. He is also an accomplished mathematician, who can expertly deduce the exact time and place when and where Sardath's Zeta Beam will hit on his home planet of Earth. Mark Waid showcases his intellect in his run on JLA. After Rann is conquered by a telepathic race called En'Tarans, Strange defeats them by secretly converting the planet into a giant Zeta Beam gun, powered by the latent Mega Zeta Radiation in his body. With the aid of the JLA, Strange successfully transports the En'Taran fleet to another part of the galaxy. In the aftermath of the Infinite Crisis event, Adam Strange loses his eyes in a freak Zeta Beam accident. Sardath is able to clone a new set of eyes from his granddaughter, Aleea Strange, and transplant them into Adam. These new eyes enable Adam to see the entire electromagnetic spectrum.

Technology
As the protector of Rann, Adam is well connected with Sardeth and his science council. Adam uses a colorful variety of technologies both as a hero and spacefarer. The resources pertaining to Rann's wonders of science available to him are numerous. He has studied, disassembled and rebuilt much of his own equipment; consisting mainly of high-tech munitions, armor, gadgets & utensils or cutting edge genetics engineering. Strange is also well versed in their mechanical function as well as practical use in his heroic endeavors.

Space suit
Strange is an adept aerial combatant, often making use of a fireproof, thermal insulated and environmentally adapted suit with which to traverse the terrains of foreign worlds or in the cold depths of space. With further upgrades, Strange’s costume boasts a built-in Zeta Beamer with which to warp lightyears across the universe in an instant.

The helmet is equipped with a life support system that protects Adam from harmful atmospheric conditions, while the suit itself pulls up a head-up display system with which to control his equipment via thought & voice command. Technology of which is slaved to his handheld blaster, sporting real-time threat assessment and targeting priority reticules to better combat adversaries.

The jetpack is a twin-engine propulsion system attached to a harness adorning his back capable of aerial aviation for an undisclosed amount of time. Strange is also versed in other kinds of rocket propulsion equipment like a booster system with hidden back up blasters, with his equipment Strange can also make escape velocity to break planetary orbit.

Alien arsenal
Adam Strange's primary weapon of choice is a Rannian laser pistol among other assorted weapons and munitions picked up from across the galaxy. He is a crack marksman with just about any ranged weapon on hand at the time, the gun comes with a targeting system conductor when worked in tandem with his costume and has a stun setting for non-lethal application.

Other munitions in his arsenal include Holo-Blasters, which are Hard-Light Energy arms that Strange can use to conjure any number of ordinance or enhanced protective shielding with while in a firefight. The effectiveness of these armaments makes them potent enough in dispatching Smite, one of Starro's lieutenants boasting physical capabilities rivalling Superman or Lobo. When properly calibrated by outside forces, these energy weapons can also channel the light of a Power Ring or a facsimile of its corresponding emotion that can dispatch a small enclave of Black Lanterns.

Zeta Beamer apparatus
One of Strange's as well as the planet of Rann's greatest resource is the Zeta Beam technology developed by Sardeth. Initially designed as a means of communications with intelligent life from across the universe, it was accidentally discovered to be an instantaneous means of intergalactic transport that rode along a cosmic radiation called Zeta Rays. The effects of the ray were always short lived, and their dissipation meant Adam would return to where he first intercepted the ray. This would be a running staple for years until later Zeta designs made its effects permanent, albeit at the cost debilitating mental sickness for its user. Eventual innovations in Rannian transport technology would produce a more streamlined device called the Zeta Beamer module, an A.I. commanded mobile drone in the form of a floating sphere that could be used to track Zeta Rays across galaxies and even into alternate universes. Like the Mega Zeta Beam, transport was also permanent, without the danger of Zeta Ray sickness. Further modifications integrated the transport device into Adam's space suit.

Just Imagine...
In Just Imagine... created by Stan Lee, Adam Strange is the superpowered teenage son of the villainous Reverend Dominic Darrk and Morgan/Morgan Le Fey, who stole his Sapphire of Ranagar in a bid to take his father's power. He indirectly leads to the formation of the Justice League as well as controlling a trio of villains under Reverend Darrk, called the "Doom Patrol". Adam realizes his energy powers are not a match for his father, so he feigns allegiance thus allowing Darrk to kill his own son.

Space Ranger
Adam Strange has a descendant, also named Adam Strange, in the future of the Space Ranger, as seen in Mystery in Space #94 (September 1964).

Elseworlds

 * The Silver Age Adam Strange is one of the "ghosts" in the empty "Planet Krypton" restaurant in The Kingdom: Planet Krypton #1.
 * Adam Strange made a brief appearance in Elseworlds' JLA: Another Nail when all time periods meld together. In the original series JLA: The Nail, he is found dead in Earth orbit by Hal Jordan after the Zeta Beam taking him to Rann was blocked by a force field surrounding Earth.
 * In Darwyn Cooke's DC: The New Frontier, Adam Strange is confined in Arkham Asylum because of his belief he has travelled to another world. This was done so the government can keep an eye on him. When the Centre appears off the coast of Florida, Dr. Leslie Thompkins returns his jet pack and energy weapon to him. It is Adam's idea to use Ray Palmer's shrinking device to destroy the threat, having read an article about his work while confined.
 * The 2009 weekly comics broadsheet Wednesday Comics featured an interpretation of Adam Strange by artist and writer Paul Pope that drew much more directly from the John Carter stories which inspired the character, casting the planet Rann as a much more fantasy-like world, and Alanna as a scantily clad warrior princess.

Future Quest
Adam Strange had a crossover with Jonny Quest in Adam Strange / Future Quest Annual #1 in March 2017.

Television

 * Adam Strange appears in Batman: The Brave and the Bold, voiced by Michael T. Weiss.
 * Adam Strange appears in Young Justice, voiced by Michael Trucco. This version is a scientist at S.T.A.R. Labs and a member of the Erdel Initiative who maintains the Justice League's Zeta-Beam technology.
 * Adam Strange appears in Krypton, portrayed by Shaun Sipos. This version is a college dropout and failed archeologist from Detroit who stole a piece of Rannian teleportation technology he calls a "Zeta-Beam" to become a superhero. Following a time disruption that erased Superman from existence, Strange uses the device to travel to Krypton 200 years in the past to warn Superman's grandfather Seg-El. Both fans and critics have noted similarities between the series' version of Strange and fellow DC character Booster Gold, with many outlets considering the former an amalgamation of the two.    Additionally, after the episode "House of Zod" aired, which features a scene where Strange flirts with a male soldier,  Sipos went on to explain on his Twitter account, "Krypton defies gender, race and sexual orientation". In an interview during San Diego Comic-Con 2018, he talked further about the decision to make Strange bisexual or sexually fluid, stating that he is "moving between any and all [sexual labels]. There don't need to be lines here".
 * A new series titled Strange Adventures was in development at HBO Max. It was said to be "a one-hour drama and superhero anthology series that will feature characters from across the DC canon", but not confirmed to feature Adam Strange himself. In August 2022, the series was scrapped.

Film

 * Adam Strange makes a non-speaking cameo appearance in Justice League: The New Frontier.
 * Adam Strange appears in films set in the Tomorrowverse:
 * Strange first appears in DC Showcase: Adam Strange, voiced by Charlie Weber. This version was teleported to the Eden mining colony during a Thanagarian attack, during which Alanna was killed. He attempts to return using a Zeta beam to search for his daughter Aleea, who may have survived, but years pass without it arriving, causing him to become alcoholic and depressed. Eventually, the beam returns, enabling him to continue his quest.
 * Strange appears in Green Lantern: Beware My Power, voiced by Brian Bloom.

Video games

 * Adam Strange appears in DC Universe Online.
 * Adam Strange appears as a character summon in Scribblenauts Unmasked: A DC Comics Adventure.
 * Adam Strange appears as a playable character in Lego DC Super-Villains, voiced by JP Karliak.

Miscellaneous

 * Adam Strange appears in Justice League Adventures.
 * Adam Strange appears in Justice League Unlimited #4.
 * Adam Strange appears in Young Justice #22.
 * Dr. Adam Strange appears in Smallville Season 11 as a S.T.A.R. Labs scientist and colleague of Dr. Emil Hamilton whose Zeta-Beam technology goes on to contribute towards the Watchtower's construction.
 * Adam Strange makes cameo appearances in DC Super Hero Girls.

Awards and reception
The character and series of the same name have received several awards over the years, including the 1967 and 1968 Alley Awards for Strip Most Desired for Revival. IGN ranked Adam Strange as the 97th greatest comic book hero of all time stating that:"If by fluke we were given the chance to ride a Zeta Beam into space, meet a sexy alien princess on the planet Rann, and fight extraterrestrial threats with high-tech weaponry, I wouldn’t want to go back to mundane Earth-life either. That makes us completely sympathetic to Adam Strange’s plight."

title: Adam Strange


text:
Life thru a Lens

Life thru a Lens is the debut solo studio album by English singer-songwriter Robbie Williams. It was Williams' first solo album following his departure from Take That. Released on 29 September 1997 through Chrysalis Records, it is influenced by Britpop, a departure from the poppier tone of the music Take That employed. The album's working name was The Show-Off Must Go On.

The album's first three singles, "Old Before I Die", "Lazy Days" and "South of the Border" (the only single to miss the top 10), were all moderate successes, but it was the fourth single "Angels" which catapulted Williams to international fame as a solo artist. Peaking at number 4, it has sold over 1 million copies in the UK and is his biggest-selling single to date. Fifth and final single "Let Me Entertain You" reached number three, becoming the album's third top-5 hit. "Freedom," Williams' first solo single, a cover of George Michael's 1990 hit, is not featured on the album.

Life thru a Lens debuted at number 11 on the UK Albums Chart and initially remained in the lower regions, but, upon the chart success of "Angels", it began steadily climbing and finally reached number one in April 1998, five months after its release. Though never selling more than 60,000 copies in a single week, the album has sold over 2,094,000 copies as of November 2013, making it Williams' fourth-best-selling studio album and fifth-best-seller overall.

The album cover art, a photograph of Williams at the centre of a crowd of photographers, was created by Andy Earl.

Recording and music
After trying hard to find his own sound during a period of personal upheaval, Williams began recordings for the album at London's Maison Rouge studios in March 1997, shortly after his introduction to Guy Chambers. The title track, "Life thru a Lens" was written about his then-girlfriend Jacqueline Hamilton-Smith who was a socialite. It is often mistakenly attributed to Tara Palmer-Tompkinson, but they did not date until 2006. "Ego a Go Go" was written about Gary Barlow, "South of the Border" discusses Kate Moss, and "Baby Girl Window" was inspired by Samantha Beckinsale and her late father, actor Richard Beckinsale. "One of God's Better People" and "Angels" were inspired by Williams' mother, Jan. Hidden track "Hello, Sir" is a poem that takes a dig at one of Williams' former teachers. Williams reprised part of the poem on the 1 Giant Leap song "My Culture".

The sound of the album is influenced by Britpop, especially bands such as Oasis, a direction his former Take That bandmate Mark Owen had also chosen to pursue on his debut album Green Man (1996). John Bush of AllMusic said that Life thru a Lens "continually betrays overt influences from Oasis and other Britpop stars, but triumphs nevertheless due to gorgeous production, Williams' irresistible personality, and the overall flavor of outrageous, utterly enjoyable pop music."

Critical reception
Writing for Melody Maker in October 1997, Robin Bresnark gave Life thru a Lens a negative review; "There's nothing here... sure, Robbie Williams is as fascinating a hapless goon as we're ever likely to come across. But this album feels more like a press release than an album – and that's not what I call music." However, John Bush of AllMusic was very positive in his four and a half stars out of five review, calling the album "excellent" and "one of the best U.K. debuts of the '90s".

Q ranked the album at number 43 in their 2004 list of "The 50 (+50) Best British Albums Ever" and in their unordered 2005 list of the "Ultimate Music Collection". Record Collector included the album in their unordered 2000 list of "10 Classic Albums from 21 Genres for the 21st Century", whilst Robert Dimery included the album in the book 1001 Albums You Must Hear Before You Die.

Commercial performance
Life thru a Lens was released in October 1997, not long after Williams's stint in rehab. It was launched with his first live solo gig at the Élysée Montmartre in Paris. At first, the album was slow to take off, debuting at number 11 on the UK Albums Chart, and falling to 104 not long after release, having sold a little over 30,000 copies. It reached the number one position after spending 27 weeks on the chart, as a consequence of the huge success of the "Angels" single, boosting the album's sales to 300,000. The album spent a total of 218 weeks on the chart and two weeks at number one, becoming the 58th best selling album of all time in the UK with sales of 2.4 million copies. Despite its success in Williams' homeland, the album failed to make a bigger impact in the international market. However, in Argentina, it reached the top ten in early 1998. Life thru a Lens has sold more than 4 million copies worldwide and has been certified as 8× Platinum in the UK.

Singles

 * "Old Before I Die", a track co-written by Williams, Eric Bazilian, and Desmond Child, was released as the album's lead single in April 1997, peaking at #2 on the UK Singles Chart. The song failed to make an impact in other international charts.
 * "Lazy Days" was released as the album's second single in the summer of 1997, amidst Williams' battle with addiction. He was allowed to check out from rehab to shoot the video for the song. The single charted at number-eight in the United Kingdom but, because promotion was nonexistent, struggled to reach the top forty of any other European chart.
 * "South of the Border" was released as the album's third single in September 1997. It failed to make a significant impact on the UK Singles Chart, peaking at #14, and as such, many saw this as the end of Williams' solo career.
 * "Angels", a song penned by Williams and Guy Chambers, was released as the album's fourth single. The decision to release the song came after Williams met the record company to discuss concerns about his future. The single was released in December 1997, soon becoming Williams' best selling-single in the United Kingdom, being certified 2× Platinum by the BPI. The song became a hit around Europe and Latin America and sold almost two million copies worldwide, rocketing sales of his album.
 * "Let Me Entertain You" was released as the album's fifth and final single in March 1998. It peaked at #3 on the UK Singles Chart, becoming one of Williams' signature songs and being the opening song for most of Williams' concerts throughout his career.

Track listing
Notes

Personnel

 * Robbie Williams – vocals, backing vocals
 * Guy Chambers – keyboards, guitar, backing vocals
 * Chris Sharrock – drums, snare
 * Andy Duncan – percussion
 * Martin Slattery – keyboards
 * Mark Feltham – harmonica
 * Gary Nuttall – guitar, backing vocals
 * Steve Power – keyboards, programming
 * Geoff Dugmore – drums, percussion
 * Steve Bush – programming
 * Derek Watkins – trumpet
 * Fil Eisler – guitar, bass guitar, tom-tom
 * Mark Smith – bass guitar, programming
 * Oscar O'Loughlin – guitar
 * Mark Smith – guitar, programming
 * Steve Sidwell – trumpet
 * Chester Kamen – guitar
 * Steve “Smiley” Barnard – drums, backing vocals
 * Dave Catlin-Birch – bass guitar, backing vocals
 * Kerry Hopwood – programming
 * André Barreau – guitar, backing vocals
 * Beverley Skeete – backing vocals
 * Carroll Thompson – backing vocals
 * Andy Caine – backing vocals
 * Claudia Fontaine – backing vocals
 * Nicole Patterson – backing vocals

Weekly charts

 * Finland's peak was at midprice-chart.

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

title: Life thru a Lens


text:
Patricia Crowther (Wiccan)

Patricia Crowther (born 14 October 1927) who also goes by the craft name Thelema, is a British occultist considered influential in the early promotion of the Wiccan religion and she is the mother of the witch or wiccan runes.

Early life
Crowther was born in Sheffield in 1927, then as Patricia Dawson. She was initiated into Witchcraft by fellow well-known Wiccan Gerald Gardner. Her handfasting to husband Arnold Crowther (1909–1974) took place in 1960.

Career
Along with Doreen Valiente, Lois Bourne, and Eleanor Bone, Crowther is considered to be one of the "early mothers" of modern Wicca. Patricia and her then-husband, Arnold Crowther, founded the Sheffield Coven in 1961, of which they were High Priestess and High Priest. Crowther has promoted Witchcraft through a number of book publications, contributions to occult magazines and journals, and through a number of interviews with local and national newspapers. She has also appeared several times on television.

In 1971, both Patricia and her then-husband Arnold wrote and presented A Spell of Witchcraft, a radio programme produced and broadcast by BBC Radio Sheffield in six 20-minute parts. The radio programme, the first of its kind in relation to modern Witchcraft as a religion, explored the history and folklore of Witchcraft and presented elements of a local coven's activities and practices within the community.

Books

 * 1965 - The Witches Speak (with Arnold Crowther)(Athol Publications)
 * 1973 - Witchcraft in Yorkshire (Dalesman) ISBN 0-85206-178-1
 * 1974 - Witch Blood (The Diary of a Witch High Priestess) (House of Collectibles) ISBN 0-87637-161-6
 * 1981 - Lid off the Cauldron: A handbook for witches (Muller) ISBN 0-584-10421-9
 * 1992 - The Zodiac Experience (Samuel Weiser Inc) ISBN 0-87728-739-2
 * 1992 - The Secrets of Ancient Witchcraft With the Witches' Tarot (Carol Publishing) ISBN 0-8065-1056-0
 * 1992 - Witches Were for Hanging (Excalibur Press of London) ISBN 1-85634-049-X
 * 1998 - One Witch's World (Robert Hale) ISBN 0-7090-6222-2 (published in America under the title High Priestess. Apart from the title, they are the same book) (Phoenix Publishing) ISBN 0-919345-87-5
 * 2001 - High Priestess: The Life & Times of Patricia Crowther (Phoenix Publishing Inc.) ISBN 978-0919345874
 * 2002 - From Stagecraft to Witchcraft: The Early years of a High Priestess(Capall Bann) ISBN 1-86163-163-4
 * 2009 - Covensense (Robert Hale) ISBN 9780709087205

title: Patricia Crowther (Wiccan)


text:
Cottonwood

Cottonwood or cotton wood may refer to:

Plants

 * Celtis conferta subsp. amblyphylla, a tree in the hemp and hackberry family
 * Hibiscus tiliaceus, a flowering shrub or tree in the mallow family
 * In the genus Populus, a number of difficult-to-distinguish trees:
 * Populus angustifolia (narrowleaf cottonwood), in the Great Basin
 * Populus balsamifera (balsam cottonwood), in Canada and parts of northern United States
 * Populus heterophylla (swamp cottonwood), in the eastern United States
 * Populus trichocarpa (black cottonwood), in the Pacific Northwest of North America
 * Populus x jackii (balm-of-Gilead)
 * Populus × acuminata, lanceleaf cottonwood,
 * Populus sect. Aigeiros, a section of three species
 * Populus deltoides (eastern cottonwood), in eastern, central, and southwestern United States, and parts of Canada and Mexico
 * Populus fremontii (Fremont cottonwood), in the southwestern United States and Mexico
 * Populus nigra (black poplar), in Europe, Asia, and Africa

Places

 * Cottonwoods, Manitoba, an unincorporated community in Manitoba, Canada

United States

 * Cottonwood, Alabama, a town
 * Cottonwood, Arizona, a city
 * Cottonwood, California, a census-designated place in Shasta County
 * Cottonwood, Yolo County, California, a ghost town
 * Cottonwood, Colorado, a neighborhood in the town of Parker
 * Cottonwood, Georgia, an unincorporated community in the City of Fayetteville, Georgia
 * Cottonwood, Idaho, a city
 * Cottonwood Falls, Kansas, a city
 * Cottonwood, Minnesota, a city
 * Cottonwood, Coal County, Oklahoma, an unincorporated community
 * Cottonwood, Sequoyah County, Oklahoma, an unincorporated community
 * Cottonwood, South Dakota, a town
 * Cottonwood, Callahan County, Texas, an unincorporated community
 * Cottonwood, Kaufman County, Texas, a city
 * Cottonwood West, Utah, an unincorporated area in Salt Lake County that has since become part of the cities of Holladay and Murray
 * Cottonwood Heights, Utah, a city south of Cottonwood West
 * Alamo, Texas, a city in Texas, US, the name of which means "Cottonwood tree" in Spanish/Mexican

People

 * Eli Cottonwood, ring name of professional wrestler Kipp Christianson formerly from WWE's NXT
 * Joe Cottonwood (born 1947), American author of fiction and poetry

Other uses

 * Cottonwood Limestone, a geologic member of limestone in Nebraska, Kansas, and Oklahoma
 * Cottonwood (EP), a 2019 EP by NLE Choppa

title: Cottonwood


text:
Talk:NAACP Legal Defense and Educational Fund

Origamiteⓣⓒ 03:27, 12 December 2014 (UTC)

Untitled
Most, but not all, of the information I am adding to this page comes from http://www.naacpldf.org. I have tried to stay within fair use, and have written the LDF asking for explicit permission to use this material. Since the sections of the site I am using are specifically intended for the press, I would presume that use of this material is actively welcome. -- Jmabel 19:27, Sep 28, 2004 (UTC)
 * I contacted Kay Shaw (kshaw@NAACPLDF.ORG) about this. She wrote back, (September 29, 2004 07:38 am): "I have forwarded your request to management for review. I included a strong recommendation that they approve use of the text... Also, we would like to include a credit that is something to the effect: Portions of this page is used with the permission of the NAACP Legal Defense and Educational Fund, Inc. and a copyright symbol." I haven't received anything more formal, but I think we can consider that clear lack of objection. I'm going to paraphrase Kay's wording slightly, because the grammar is wrong ("portions...is") and add it to the article. -- Jmabel | Talk 18:05, Oct 15, 2004 (UTC)

The article states that LDF Director-Counsel Jack Greenberg "ended 'all deliberate speed' in desegregation." Greenberg was involved in numerous cases such as Brown v. Board of Education which mandated that desegregation be effected with "all deliberate speed." While Greenberg was unhappy with the phrasing of the court's decision in Brown, neither he nor anybody else has eliminated the concept of "all deliberate speed" at least not so far as I am aware.

```` — Preceding unsigned comment added by Wicked Pedagogue (talk • contribs) 10:48, 4 March 2016 (UTC)

Cases litigated by NAACP/LDF
Maybe a category should be created: Cases litigated by NAACP, that is provided on the specific articles that deal with the cases. They have been so important in gaining civil rights. There is such a category for those litigated by the ACLU.--Parkwells (talk) 00:33, 29 March 2008 (UTC)

External links modified (February 2018)
Hello fellow Wikipedians,

I have just modified 2 external links on NAACP Legal Defense and Educational Fund. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20090515203226/http://www.tourolaw.edu/about/distinguished_visitors/public_interest_lawyer_in_residence/1997-elaine%20jones.asp to http://www.tourolaw.edu/about/distinguished_visitors/public_interest_lawyer_in_residence/1997-elaine%20jones.asp
 * Added archive https://web.archive.org/web/20100728034242/http://www.law.columbia.edu/fac/Theodore_Shaw to http://www.law.columbia.edu/fac/Theodore_Shaw

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 15:02, 10 February 2018 (UTC)

balance
One would never know from the chronological list that they ever had any failures. Nor is there any discussion about internal differences about strategy.  DGG ( talk ) 18:49, 6 December 2021 (UTC)

Acs Harassing the minority
What more can parents do when the system keep failing us!! We keep being told Acs are here to protect and guide and help us young people today I can say those are lies. I come here today because Acs has took my life and they also been harassing me and my children. I’m single mom of eight kids I’m 28 year old I do every and anything I can do for my kids Acs has never try to help me!! Most Acs did was kept trying paint me as this horrible mother and take my kids November 19 2021 Acs came into my bx new year project and without proper investigation they removed my children please I need help I have no one help me or advocating for my children or me!! Any one can help please my email is marioncrawford1993@gmail.com 68.194.225.35 (talk) 20:56, 14 March 2022 (UTC)

 * Can we delete this please? It is not relevant to this article at all. Scotty1141 (talk) 03:15, 24 March 2022 (UTC)

Reference #19 is not correct
The reference regarding Gardendale is not correct, the article speaks to Texas voter ID laws instead. Scotty1141 (talk) 03:28, 24 March 2022 (UTC)


text:
John Frame (theologian)

John McElphatrick Frame (born April 8, 1939) is a retired American Christian philosopher and Calvinist theologian especially noted for his work in epistemology and presuppositional apologetics, systematic theology, and ethics. He is one of the foremost interpreters and critics of the thought of Cornelius Van Til.

Biography
Frame was born in Pittsburgh, Pennsylvania and became a Christian at the age of 13 through the ministry of Beverly Heights Presbyterian Church, a congregation of the United Presbyterian Church of North America in Pittsburgh. He graduated from Princeton University, where he was involved in the Princeton Evangelical Fellowship (PEF) and Westerly Road Church. The PEF and Westerly Road had a profound impact on forming Frame's faith and theology. He says of their impact:

I owe much to PEF ... Fullerton and PEF cared deeply about people, spending hours in mutual prayer, exhortation, counseling, gospel witness. I never experienced that depth of fellowship in any Reformed church or institution ... So I am not much impressed by people who want to set up an adversary relation between "Reformed" and "evangelical." Today, Reformed writers often disparage evangelical ministries as circuses, as clubs that will do anything at all to gain members, who pander to the basest lusts of modern culture. That was not true of PEF, or of Westerly Road Church ... PEF would never have imagined the effect their ministry had on me: they turned me into a Reformed ecumenist!

Frame received degrees from Princeton University (A.B.), Westminster Theological Seminary (BD), Yale University (AM, and M.Phil. and began work on a doctoral dissertation). He received an honorary doctorate of divinity in 2003 from Belhaven College. He has served on the faculty of Westminster Theological Seminary, and was a founding faculty member of their California campus;, Frame is an emeritus faculty member at Reformed Theological Seminary in Orlando, Florida. He is an ordained minister in the Presbyterian Church in America.

Relations to other scholars: polemics and critical reviews
Frame is known for his critical view of historical modes of theology, including his criticism of such scholars as David F. Wells, Donald Bloesch, Mark Noll, George Marsden, D.G. Hart, Richard Muller, and Michael Horton. Particularly notable amongst Frame's critical analyses is "Machen's Warrior Children", originally published in Alister E. McGrath and Evangelical Theology: a Dynamic Engagement (Paternoster Press, 2003). More recently, Frame reviewed Horton's book Christless Christianity with a similar analysis. In 1998, he debated then librarian D.G. Hart in a student-organized discussion of the regulative principle of worship.

Multiperspectival epistemology
Frame has elaborated a Christian epistemology in his 1987 work The Doctrine of the Knowledge of God. In this work, he develops what he calls triperspectivalism or multiperspectivalism which says that in every act of knowing, the knower is in constant contact with three things (or "perspectives") – the knowing subject himself, the object of knowledge, and the standard or criteria by which knowledge is attained. He argues that each perspective is interrelated to the others in such a fashion that, in knowing one of these, one actually knows the other two, also. His student and collaborator Vern Poythress has further developed this idea with respect to science and theology. Reformed theologian Meredith Kline wrote a critique of this view, explaining that Poythress and Frame had used multiperspectivalism in ways that had led to what he considered incorrect conclusions in regards to the relation of Kline's position and Greg L. Bahnsen's on covenant theology (more specifically theonomy).

Presuppositions
As a former student of Van Til, Frame is supporter of the presuppositionalist school of Christian apologetics. He defines a presupposition as follows:

"A presupposition is a belief that takes precedence over another and therefore serves as a criterion for another. An ultimate presupposition is a belief over which no other takes precedence. For a Christian, the content of Scripture must serve as his ultimate presupposition. ... This doctrine is merely the outworking of the lordship of God in the area of human thought. It merely applies the doctrine of scriptural infallibility to the realm of knowing."

Rationalism and irrationalism in non-Christian thought
Frame, developing the thought of his mentor Cornelius Van Til, has asserted in both his Apologetics to the Glory of God and his Cornelius Van Til: An Analysis of His Thought, that all non-Christian thought can be categorized as the ebb and flow of rationalism and irrationalism.

Rationalism
In this context Frame defines rationalism as any attempt to establish the finite human mind as the ultimate standard of truth and falsity. This establishing of the autonomous intellect occurs within the context of rejecting God's revelation of himself in both nature and the Bible; a rationalist, in this sense, states that the human mind is able to fully and exhaustively explain reality.

Yet, when Frame speaks of "exhaustive explanations" he does not mean these systems seek omniscience; rather, he means that the history of non-Christian thought (though, admittedly, his focus is Western philosophy) is the history of various attempts to construct systems that account for everything (a distinctive metaphysic, epistemology and value theory).

According to Frame, examples of attempts to explain reality are found in Plato and Aristotle's form/matter dualism; the debate between the nominalists and the realists over the status of universals and particulars, and the "all is ... [fire, water, atoms,etc]" of the pre-Socratics. More examples would include Descartes' mind/body dualism, Spinoza's God or nature, and Leibniz's monadology, Plotinus' "The One" and his teaching on emanation, the British empiricists' attempts to limit knowledge and possibility to that which can be empirically verified, Kant's worlds of the noumena and the phenomena, and Hegel's dialectic.

Awards and recognition
Belhaven College awarded Frame an honorary Doctor of Divinity in 2003.

Personal life
Frame married Mary Grace Cummings in 1984, and has two sons and three stepchildren. As of 2024, he lives in Orlando, Florida.

Selected works

 * Introduction to Presuppositional Apologetics Part 1 & 2
 * Van Til: The Theologian, 1976 ISBN 0-916034-02-X
 * Medical Ethics, 1988 ISBN 0-87552-261-0
 * Perspectives on the Word of God: An Introduction to Christian Ethics, 1990 ISBN 0-8010-3557-0
 * Evangelical Reunion, 1991 ISBN 0-8010-3560-0
 * Apologetics to the Glory of God, 1994 ISBN 0-87552-243-2
 * Cornelius Van Til: An Analysis of his Thought, 1995 ISBN 0-87552-245-9
 * Worship in Spirit and Truth, 1996 ISBN 0-87552-242-4
 * Contemporary Worship Music: A Biblical Defense, 1997 ISBN 0-87552-212-2
 * No Other God: A Response to Open Theism, 2001 ISBN 0-87552-185-1
 * Salvation Belongs To The Lord: An Introduction To Systematic Theology, 2006 ISBN 1-59638-018-7
 * Systematic Theology: An Introduction to Christian Belief, 2013 ISBN 1-59638-217-1
 * A History of Western Philosophy and Theology, 2015 ISBN 978-1-62995-084-6
 * Theology of My Life: A Theological and Apologetic Memoir, 2017 ISBN 978-1-5326-1378-4

Theology of Lordship series

 * The Doctrine of the Knowledge of God, 1987 ISBN 0-87552-262-9
 * The Doctrine of God, 2002 ISBN 0-87552-263-7
 * The Doctrine of the Christian Life, 2008 ISBN 978-0-87552-796-3
 * The Doctrine of the Word of God, 2010 ISBN 978-0-87552-264-7

title: John Frame (theologian)


text:
The Seeds of Love

The Seeds of Love is the third studio album by British pop rock band Tears for Fears, released on 25 September 1989 by Fontana Records. It retained the band's epic sound while incorporating influences ranging from jazz and soul to Beatlesque pop. Its lengthy production and scrapped recording sessions cost over £1 million. The album spawned the title hit single "Sowing the Seeds of Love," as well as "Woman in Chains," and "Advice for the Young at Heart", both of which reached the top 40 in several countries.

The Seeds of Love was an international success, entering the UK Albums Chart at number one, and top ten in other countries including the U.S. It has been certified Gold or Platinum in several territories including the United Kingdom, the United States, France, Germany, Canada, and the Netherlands. Despite its success, personal tensions during recording led to band members Curt Smith and Roland Orzabal splitting up at the conclusion of their 1990 world tour, with Orzabal remaining as the band's sole official member until the two reunited in the early 2000s.

In October 2020, the remastered reissue of The Seeds of Love was released in several formats including a super deluxe edition, with B-sides, remixes, and a 5.1 surround sound mix.

Production
The first song composed for The Seeds of Love was "Badman's Song" (originally titled "The Bad Man Song"), written during the band's 1985 world tour after Roland Orzabal overheard two members of the tour personnel maligning him in a hotel room one night. The song was co-written by Orzabal with keyboardist Nicky Holland, who was touring with the band throughout 1985. Holland would go on to play an integral part in the writing and recording of The Seeds of Love, much as keyboardist Ian Stanley had on the band's previous album Songs from the Big Chair.

Recording sessions for the album began in late 1986 with producers Clive Langer and Alan Winstanley, but Orzabal and Curt Smith were unhappy with the results and so the recordings were scrapped in early 1987. Chris Hughes (who had produced both the previous Tears for Fears albums) was then brought back into the fold, but again conflicts arose over the direction of the new material. Orzabal in particular had grown weary of composing and playing music using machines and sequencers, as the majority of Tears for Fears' music had been up to that point, and was striving for something more organic and a different way of working.

""As a band, we came from the programmed pop era of the early '80s and we had inherited a sense of structure that permeated almost all our music. The way we were working was becoming too sterile. We wanted to do something more colourful, something that sounded big and warm. You cannot get that from machines. You only get that with real musicians and real players.""

- Curt Smith

The song "Sowing the Seeds of Love" was written in June 1987, the same week as the UK general election in which Margaret Thatcher and the Conservative Party won a third consecutive term in office (reflected in the lyric "Politician granny with your high ideals, have you no idea how the majority feels?"). Hughes and longtime TFF keyboardist Ian Stanley both left the project later in 1987 citing "creative differences", though their contributions to the track remained on the final album. After two failed attempts to make the album, the band opted to produce it themselves, assisted by engineer Dave Bascombe. Also in 1987, Orzabal and Smith flew over to the US to track down a hotel lounge pianist/vocalist named Oleta Adams, whom they had seen playing in Kansas City during their 1985 American tour. Hoping she could add to the organic feel by bringing a soulful warmth to their music, they invited Adams to work with them on their new album. Adams would ultimately perform on three tracks ("Woman in Chains", "Badman's Song" and "Standing on the Corner of the Third World"), and a solo recording contract was also offered to her by the band's record company Fontana.

Recording recommenced in early 1988 and lasted until the summer of 1989. Featuring an assortment of respected session players including drummers Manu Katché and Simon Phillips, bassist Pino Palladino, and a guest appearance by Phil Collins on drums, much of the album was recorded as jam sessions featuring different performances of the music and then edited down later. Some of the tracks, particularly "Badman's Song", were recorded several times in a variety of musical styles including, according to Holland, versions of the song that were reminiscent of Barry White, Little Feat and Steely Dan before settling on the jazz/gospel version that is on the finished album. Co-producer Dave Bascombe commented that the final version of the song was almost nothing like the original demo because it had gone through so many changes. The track "Swords and Knives" was originally written for the 1986 film Sid and Nancy (about the relationship between Sid Vicious and Nancy Spungen), but was rejected by the filmmakers for not being "punk" enough.

Due to the starry cast of session players and lengthy production process, including the scrapped earlier recordings, the album reportedly cost £1 million to make (by comparison, Songs from the Big Chair cost approximately £70,000 ). The final mix of the album was completed at London's Mayfair Studios in July 1989. Frustrations during the making of the album had also given rise to tensions between Orzabal and Smith, Orzabal having become something of an intricate perfectionist and Smith preoccupied with living a jet set lifestyle rather than focusing on the album (Smith's first marriage had also ended in divorce during the making of the album). At one point, Orzabal considered calling the album Famous Last Words (the title of the album's final track), commenting "it may well turn out to be our last album." Indeed, the duo did not make any further recordings together for over a decade.

Release
Now assigned to the newly reactivated Phonogram subsidiary label Fontana, the first single from the album, "Sowing the Seeds of Love", was released in August 1989. It became a worldwide hit, peaking at no.5 in the UK, no.2 in the US, and no.1 in Canada. The album was released in September 1989, entering the UK Albums Chart at no.1 and would be certified Platinum by the BPI within three weeks. In the US, it peaked at no.8 and was also certified Platinum. This album reached the top ten in numerous other countries around the world.

Two other singles from the album, "Woman in Chains" (recorded as a duet with Adams) and "Advice for the Young at Heart" (the only track featuring Smith on lead vocals) reached the Top 40 in UK and internationally. "Famous Last Words" was released as fourth single in mid-1990 by the record company without the band's involvement, though this only peaked at no.83 in the UK. A video compilation, Sowing the Seeds, featuring the promo videos for the first three singles from the album was also released in 1990.

The band embarked on a world tour to promote the album in 1990, featuring Adams both as a support act and as a player with the band (her solo album, Circle of One, produced by Orzabal and Dave Bascombe was also released during this time). The band's concert at the Santa Barbara County Bowl in May 1990 was filmed and released on home video, titled Going to California.

A 64-page companion book to the album, entitled Tears for Fears – The Seeds of Love, was also released in 1990 by Virgin Books and offers insight into the writing and recording process behind the album as well as the sheet music for each song and rare promotional photographs from the period.

The album was remastered and reissued in 1999 with four bonus tracks which were originally B-sides to the album's first three singles. It does not include the B-side "My Life in the Suicide Ranks" which was an additional B-side to "Woman in Chains" and could at the time only be found on the band's 1996 rarities compilation Saturnine Martial & Lunatic. The Seeds of Love was rereleased again in 2020 in five different formats including a 5-disc super deluxe edition boxed set featuring bonus material such as single versions, B-sides (this time including "My Life in the Suicide Ranks"), demos, outtakes, and a 5.1 surround-sound mix, again made by Steven Wilson, who also was responsible for the surround mix for Songs from the Big Chair. Other editions released at the same time include a 2-CD deluxe edition, a single CD edition, a vinyl album, and a vinyl picture disc album. The deluxe edition peaked at no.13 on the UK Albums Chart in October 2020.

Reception
Lloyd Bradley praised The Seeds of Love in Q, summarising the album as "such a radical departure from Tears for Fears' robust, anthemic pop songs of the early '80s as to make them seem irrelevant." In Rolling Stone, Michael Azerrad wrote, "If with the title track Tears for Fears beg comparison to the Beatles, it's in the unspoken assertion that popular music can also be outstanding music. That's something this remarkable record proves over and over again." Greg Kot of the Chicago Tribune described the album as "astonishing", with a "wide open, soulful spaciousness that belies the heavy production expenses". Los Angeles Times critic Chris Willman enjoyed the first three songs but lamented the "uncharacteristically frenzied rock 'n' roll climaxes" and "underdeveloped and overwrought" lyrics among the later tracks, describing the album as overall "just so-so". Simon Williams, writing for NME, perceived The Seeds of Love as a self-consciously "'adult' and 'mature'" effort and found that Tears for Fears had "tumbled from joyful pop simplicity to cliche-ridden complexity."

In a retrospective review for AllMusic, Stanton Swihart observed the album's "polished, atmospheric soul", labelling it "the apotheosis of Orzabal and Smith's evolution". A review of the 1999 reissue by AllMusic's Bruce Eder pointed towards "the best vocals in Tears for Fears' history" and "their most ambitious production". Appraising the 2020 reissue for Record Collector, John Earls alluded to Orzabal's "obsessive determination to achieve Steely Dan levels of technical perfection", while crediting his "melodic gifts" with preventing the album from "becoming too overblown". On the other hand, Ira Robbins of Trouser Press had praise for the title track and Adams's soulful vocals, but described the bulk of the album as "absurdly overintellectualized" and "almost impenetrable".

30th anniversary reissue
Following the reissue campaigns of The Hurting (2013) and Songs from the Big Chair (2014), in October 2020, the remastered super deluxe edition of The Seeds of Love was released in several formats, including B-sides, remixes, 22 previously unreleased recordings, and a 5.1 surround sound mix.

Paul Sinclair, founder and head editor of the website Super Deluxe Edition, co-compiled the track listing and interviewed band members, producers and collaborators for the extensive sleeve notes of the edition.

Track listing
Note
 * A remix of "Johnny Panic and the Bible of Dreams" was also released as a separate single in the UK in 1991 and reached number 70 on the UK Singles Chart and number one on the UK Dance Chart.

Personnel
Tears for Fears
 * Roland Orzabal – lead vocals (1–3, 5–8), backing vocals, guitars, keyboards, Fairlight programming
 * Curt Smith – bass guitar, backing vocals, co-lead vocals (3), lead vocals (4)
 * Ian Stanley – keyboards and Hammond organ (1, 3, 10)

Additional personnel

 * Oleta Adams – keyboards, vocals (1, 2), acoustic piano (2, 5), backing vocals (5, 12)
 * Nicky Holland – keyboards, backing vocals (2, 4, 7), acoustic piano (4, 6, 8), Kurzweil strings (8)
 * Simon Clark – keyboards, synthesizers (2, 5), Hammond organ (2, 4, 5, 7)
 * Neil Taylor – guitar arpeggio (1), rhythm guitar (7)
 * Robbie McIntosh – lead guitar (2, 7), slide guitar (2)
 * Randy Jacobs – guitar
 * Pino Palladino – bass (2, 5)
 * Phil Collins – drums (1 from 3:32)
 * Manu Katché – drums (1 until 3:32, 2, 5)
 * Chris Hughes – drums and production (3, 10)
 * Simon Phillips – drums (7 from 5:04)
 * Luís Jardim – percussion
 * Carole Steele – percussion (2, 5)
 * Richard Niles – orchestral arrangements (3)
 * Jon Hassell – trumpet (5, 8)
 * Peter Hope-Evans – harmonica (5)
 * Kate St John – saxophone (6), oboe (6)
 * Tessa Niles – backing vocals (2, 5, 7), female vocal (6)
 * Carol Kenyon – backing vocals (2, 5, 7)
 * Maggie Ryder – backing vocals (4)
 * Dolette McDonald – backing vocals (7)
 * Andy Caine – backing vocals (7)

Production

 * Producers – Tears for Fears and David Bascombe
 * Engineer – David Bascombe
 * Additional engineer – Steve Chase
 * Assistant engineers – Heidi Canova and Lee Curle
 * Mixing – Bob Clearmountain (tracks 1 and part of 7), David Bascombe (tracks 2–6, part of 7, and 8).
 * Mastering – Bob Ludwig
 * Art direction and photography – David Scheinmann
 * Oleta Adams' photo – Jeff Katz
 * Design – Stylorouge

title: The Seeds of Love


text: File:Bloodbath-Resurrection.jpg

title: File:Bloodbath-Resurrection.jpg


text:
Talk:Narrator (Windows)

Untitled
from VfD:

A non-notable piece of software from Microsoft. We can't list everything that comes with Windows XP here, and I doubt that that many people actually use this one. — El Chico!  Talk 19:32, 28 Sep 2004 (UTC)
 * Merge and Redirect I can't decide whether to merge with Screen reader or Windows XP. It doesn't deserve it's own article, but we should include some mention. -- Netoholic @ 21:05, 2004 Sep 28 (UTC)
 * To be honest, there's not much to merge. I think we could just drop the two existing sentences in both articles and we'd be fine.  As for the redirect, you should do it to Screen reader, because Narrator also came with Windows 2000, not just XP. —  El Chico!  Talk 21:18, 28 Sep 2004 (UTC)
 * No need to delete, as usual. Simply redirect. Mark Richards 22:27, 28 Sep 2004 (UTC)
 * Should be a footnote in XP that points to screen reader, redirect this to XP. --Improv 12:25, 29 Sep 2004 (UTC)
 * No, redirect to Screen reader, because it was not an XP-only feature (It was also 2000). — El Chico!  Talk 14:08, 29 Sep 2004 (UTC)
 * Changed mind on this new information -- Delete. --Improv 19:04, 1 Oct 2004 (UTC)

end moved discussion

I am using this page
I have to do a project on how computers talk (in sound). Technical and practically and policy wise we can and should list every windows component and have an article on them. one of the policies (or was it a guild line) say wikipedia is both a general encyclopaedia and a specialist encyclopaedia, so wikipedia can be an encyclopaedia of windows componants Oxinabox1 08:36, 5 February 2007 (UTC)

neutral?
I think this article could be brgging about microsoft's "accessibility". -RadSkat3 17:43, 12 May 2006 (UTC)

 * Tollge 2403:6200:8862:2EF5:E6D1:9DF6:D735:E6C9 (talk) 06:48, 10 June 2024 (UTC)

the program is annoying, but you can make him say funny things. it thinks Wikipedia is pronounced Wik i pedia 71.224.19.29

Mystified by the "it can also pronounce 'tequila'" comment on MS Anna. My Windows XP SP2 Narrator says "tequila" perfectly. 86.136.112.115 02:27, 21 February 2007 (UTC)

 * Mine pronounces it fine as well. As far as I can tell, Cumbiagermen added that piece of information, so perhaps they can clear things up. David H. Flint 03:26, 21 February 2007 (UTC)
 * My guess is that older systems did not pronounce "tequila" correctly. I did not test these systems but I have heard it pronounce that word as "tech-quil-lah". I assumed that the bug occurred up to SP2 and was fixed in Windows Vista, but I was mistaken. --Cumbiagermen 06:12, 21 February 2007 (UTC)
 * trollge incident 2403:6200:8862:2EF5:E6D1:9DF6:D735:E6C9 (talk) 06:48, 10 June 2024 (UTC)

Screen Reader?
Article mentions Narrator and Apple's VoiceOver as screen readers. This is not technically true. Narrator and VoiceOver respond to events that occur (new window, selection, cursor movement, mouse movement, etc.), but are not designed to allow navigation of the screen for reviewing. Full-fledged screen readers allow for this, in addition to announcing events. Charles Oppermann 20:53, 3 January 2007 (UTC)

glitch
The mentioned glitch is specific to the Microsoft Sam voice within SAPI, not to Narrator only IMHO. --Abdull 21:39, 17 April 2007 (UTC)

Question regarding Narrator
how do you shut off Microsoft Narrator from starting up everytime you turn on your computer? —Preceding unsigned comment added by 142.177.185.13 (talk) 04:09, 11 February 2008 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 04:36, 3 June 2022 (UTC)
 * Narratorwin11.png

Lg dawg
Y'all 158.62.62.100 (talk) 17:27, 7 January 2023 (UTC)

title: Talk:Narrator (Windows)


text:
LDF

LDF may refer to:

 * Leaders For Democracy Fellows Program
 * NAACP Legal Defense and Educational Fund
 * Lesotho Defence Force
 * Liberian Development Foundation
 * Liechtenstein disclosure facility
 * Lietuvos Darbo Federacija, the Lithuanian Labour Federation
 * Liga Dominicana de Fútbol
 * Local Defence Force, former Irish Army Reserve
 * Log Database File extension, for Microsoft SQL Server
 * Low-density fibreboard or particle board
 * London dispersion force, type of intermolecular force
 * Loss development factor in insurance pricing
 * LuraDocument Format, a LuraTech proprietary document format
 * Legado Del Fantasma, a professional wrestling group

Politics

 * Left Democratic Front, Kerala
 * Left Democratic Front (Maharashtra), India

title: LDF


text:
Killing vector field

In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object.

Definition
Specifically, a vector field $$X$$ is a Killing field if the Lie derivative with respect to $$X$$ of the metric $$g$$ vanishes:

 * $$\mathcal{L}_{X} g = 0 \,.$$

In terms of the Levi-Civita connection, this is

 * $$g\left(\nabla_Y X, Z\right) + g\left(Y, \nabla_Z X\right) = 0 \,$$

for all vectors $$Y$$ and $$Z$$. In local coordinates, this amounts to the Killing equation

 * $$\nabla_\mu X_\nu + \nabla_{\nu} X_\mu = 0 \,.$$

This condition is expressed in covariant form. Therefore, it is sufficient to establish it in a preferred coordinate system in order to have it hold in all coordinate systems.

Killing field on the circle
The vector field on a circle that points counterclockwise and has the same length at each point is a Killing vector field, since moving each point on the circle along this vector field simply rotates the circle.

Killing fields on the hyperbolic plane
A toy example for a Killing vector field is on the upper half-plane $$M = \mathbb{R}^2_{y > 0}$$ equipped with the Poincaré metric $$g = y^{-2}\left(dx^2 + dy^2\right)$$. The pair $$(M, g)$$ is typically called the hyperbolic plane and has Killing vector field $$\partial_x$$ (using standard coordinates). This should be intuitively clear since the covariant derivative $$\nabla_{\partial_x}g$$ transports the metric along an integral curve generated by the vector field (whose image is parallel to the x-axis).

Furthermore, the metric is independent of $$x$$ from which we can immediately conclude that $$\partial_x$$ is a Killing field using one of the results below in this article.

The isometry group of the upper half-plane model (or rather, the component connected to the identity) is $$\text{SL}(2, \mathbb{R})$$ (see Poincaré half-plane model), and the other two Killing fields may be derived from considering the action of the generators of $$\text{SL}(2, \mathbb{R})$$ on the upper half-plane. The other two generating Killing fields are dilatation $$D = x\partial_x + y\partial_y$$ and the special conformal transformation $$K = (x^2 - y^2)\partial_x + 2xy \partial_y$$.

Killing fields on a 2-sphere

The Killing fields of the two-sphere $$S^2$$, or more generally the $$n$$-sphere $$S^n$$ should be obvious from ordinary intuition: spheres, having rotational symmetry, should possess Killing fields which generate rotations about any axis. That is, we expect $$S^2$$ to have symmetry under the action of the 3D rotation group SO(3). That is, by using the a priori knowledge that spheres can be embedded in Euclidean space, it is immediately possible to guess the form of the Killing fields. This is not possible in general, and so this example is of very limited educational value.

The conventional chart for the 2-sphere embedded in $$\mathbb{R}^3$$ in Cartesian coordinates $$(x,y,z)$$ is given by
 * $$x = \sin\theta\cos\phi,\qquad y = \sin\theta\sin\phi,\qquad z = \cos\theta$$

so that $$\theta$$ parametrises the height, and $$\phi$$ parametrises rotation about the $$z$$-axis.

The pullback of the standard Cartesian metric $$ds^2 = dx^2 + dy^2 + dz^2$$ gives the standard metric on the sphere,
 * $$ds^2 = d\theta^2 + \sin^2\theta d\phi^2$$.

Intuitively, a rotation about any axis should be an isometry. In this chart, the vector field which generates rotations about the $$z$$-axis:
 * $$\frac{\partial}{\partial\phi}.$$

In these coordinates, the metric components are all independent of $$\phi$$, which shows that $$\partial_\phi$$ is a Killing field.

The vector field
 * $$\frac{\partial}{\partial\theta}$$

is not a Killing field; the coordinate $$\theta$$ explicitly appears in the metric. The flow generated by $$\partial_\theta$$ goes from north to south; points at the north pole spread apart, those at the south come together. Any transformation that moves points closer or farther apart cannot be an isometry; therefore, the generator of such motion cannot be a Killing field.

The generator $$\partial_\phi$$ is recognized as a rotation about the $$z$$-axis

 * $$Z = x\partial_y - y\partial_x = \sin^2\theta \,\partial_\phi$$

A second generator, for rotations about the $$x$$-axis, is

 * $$X = z\partial_y - y\partial_z$$

The third generator, for rotations about the $$y$$-axis, is

 * $$Y = z\partial_x - x\partial_z$$

The algebra given by linear combinations of these three generators closes, and obeys the relations
 * $$[X,Y] = Z \quad [Y,Z] = X \quad [Z,X] = Y.$$

This is the Lie algebra $$\mathfrak{so}(3)$$.

Expressing $$X$$ and $$Y$$ in terms of spherical coordinates gives

 * $$X = \sin^2\theta \,(\sin\phi\partial_\theta + \cot\theta\cos\phi\partial_\phi)$$

and
 * $$Y = \sin^2 \theta \,(\cos\phi\partial_\theta - \cot\theta\sin\phi\partial_\phi)$$

That these three vector fields are actually Killing fields can be determined in two different ways. One is by explicit computation: just plug in explicit expressions for $$\mathcal{L}_Xg$$ and chug to show that $$\mathcal{L}_Xg=\mathcal{L}_Yg=\mathcal{L}_Zg=0.$$ This is a worth-while exercise. Alternately, one can recognize $$X, Y$$ and $$Z$$ are the generators of isometries in Euclidean space, and since the metric on the sphere is inherited from metric in Eucliden space, the isometries are inherited as well. These three Killing fields form a complete set of generators for the algebra. They are not unique: any linear combination of these three fields is still a Killing field.

There are several subtle points to note about this example.

 * The three fields are not globally non-zero; indeed, the field $$Z$$ vanishes at the north and south poles; likewise, $$X$$ and $$Y$$ vanish at antipodes on the equator. One way to understand this is as a consequence of the "hairy ball theorem". This property, of bald spots, is a general property of symmetric spaces in the Cartan decomposition. At each point on the manifold, the algebra of the Killing fields splits naturally into two parts, one part which is tangent to the manifold, and another part which is vanishing (at the point where the decomposition is being made).
 * The three fields $$X, Y$$ and $$Z$$ are not of unit length. One can normalize by dividing by the common factor of $$\sin^2\theta$$ appearing in all three expressions. However, in that case, the fields are no longer smooth: for example, $$\partial_\phi = X/\sin^2\theta$$ is singular (non-differentiable) at the north and south poles.
 * The three fields are not point-wise orthogonal; indeed, they cannot be, as, at any given point, the tangent-plane is two-dimensional, while there are three vectors. Given any point on the sphere, there is some non-trivial linear combination of $$X, Y$$ and $$Z$$ that vanishes: these three vectors are an over-complete basis for the two-dimensional tangent plane at that point.
 * The a priori knowledge that spheres can be embedded into Euclidean space, and thus inherit a metric from this embedding, leads to a confusing intuition about the correct number of Killing fields that one might expect. Without such an embedding, intuition might suggest that the number of linearly independent generators would be no greater than the dimension of the tangent bundle. After all, fixing any point on a manifold, one can only move in those directions that are tangent. The dimension of the tangent bundle for the 2-sphere is two, and yet three Killing fields are found. Again, this "surprise" is a generic property of symmetric spaces.

Killing fields in Minkowski space
The Killing fields of Minkowski space are the 3 space translations, time translation, three generators of rotations (the little group) and the three generators of boosts. These are

 * Time and space translations
 * $$ \partial_t ~, \qquad \partial_x ~, \qquad \partial_y ~, \qquad \partial_z ~;$$
 * Vector fields generating three rotations, often called the J generators,
 * $$-y \partial_x + x \partial_y ~, \qquad -z \partial_y + y \partial_z ~, \qquad -x \partial_z + z \partial_x  ~;$$
 * Vector fields generating three boosts, the K generators,
 * $$x \partial_t + t \partial_x~, \qquad y \partial_t + t \partial_y ~, \qquad z \partial_t + t \partial_z.$$

The boosts and rotations generate the Lorentz group. Together with space-time translations, this forms the Lie algebra for the Poincaré group.

Killing fields in flat space
Here we derive the Killing fields for general flat space. From Killing's equation and the Ricci identity for a covector $$K_a$$,
 * $$\nabla_a\nabla_b K_c - \nabla_b\nabla_a K_c = R^d{}_{cab}K_d$$

(using abstract index notation) where $$R^a{}_{bcd}$$ is the Riemann curvature tensor, the following identity may be proven for a Killing field $$X^a$$:
 * $$\nabla_a\nabla_b X_c = R^d{}_{acb}X_d.$$

When the base manifold $$M$$ is flat space, that is, Euclidean space or pseudo-Euclidean space (as for Minkowski space), we can choose global flat coordinates such that in these coordinates, the Levi-Civita connection and hence Riemann curvature vanishes everywhere, giving
 * $$\partial_\mu\partial_\nu X_\rho = 0.$$

Integrating and imposing the Killing equation allows us to write the general solution to $$X_\rho$$ as
 * $$X^\rho = \omega^{\rho\sigma} x_\sigma + c^\rho$$

where $$\omega^{\mu\nu} = -\omega^{\nu\mu}$$ is antisymmetric. By taking appropriate values of $$\omega^{\mu\nu}$$ and $$c^\rho$$, we get a basis for the generalised Poincaré algebra of isometries of flat space:
 * $$M_{\mu\nu} = x_\mu\partial_\nu - x_\nu\partial_\mu$$
 * $$P_\rho = \partial_\rho.$$

These generate pseudo-rotations (rotations and boosts) and translations respectively. Intuitively these preserve the (pseudo)-metric at each point.

For (pseudo-)Euclidean space of total dimension, in total there are $$n(n+1)/2$$ generators, making flat space maximally symmetric. This number is generic for maximally symmetric spaces. Maximally symmetric spaces can be considered as sub-manifolds of flat space, arising as surfaces of constant proper distance
 * $$\{\mathbf{x}\in\mathbb{R}^{p,q}:\eta(\mathbf{x},\mathbf{x})=\pm \frac{1}{\kappa^2}\}$$

which have O(p, q) symmetry. If the submanifold has dimension $$n$$, this group of symmetries has the expected dimension (as a Lie group).

Heuristically, we can derive the dimension of the Killing field algebra. Treating Killing's equation $$\nabla_a X_b + \nabla_b X_a = 0$$ together with the identity $$\nabla_a\nabla_b X_c = R^c{}_{bad}X_c.$$ as a system of second order differential equations for $$X_a$$, we can determine the value of $$X_a$$ at any point given initial data at a point $$p$$. The initial data specifies $$X_a(p)$$ and $$\nabla_a X_b(p)$$, but Killing's equation imposes that the covariant derivative is antisymmetric. In total this is $$n^2 - n(n-1)/2 = n(n+1)/2$$ independent values of initial data.

For concrete examples, see below for examples of flat space (Minkowski space) and maximally symmetric spaces (sphere, hyperbolic space).

Killing fields in general relativity
Killing fields are used to discuss isometries in general relativity (in which the geometry of spacetime as distorted by gravitational fields is viewed as a 4-dimensional pseudo-Riemannian manifold). In a static configuration, in which nothing changes with time, the time vector will be a Killing vector, and thus the Killing field will point in the direction of forward motion in time. For example, the Schwarzschild metric has four Killing fields: the metric is independent of $$t$$, hence $$\partial_t$$ is a time-like Killing field. The other three are the three generators of rotations discussed above. The Kerr metric for a rotating black hole has only two Killing fields: the time-like field, and a field generating rotations about the axis of rotation of the black hole.

de Sitter space and anti-de Sitter space are maximally symmetric spaces, with the $$n$$-dimensional versions of each possessing $$\frac{n(n+1)}{2}$$ Killing fields.

Killing field of a constant coordinate
If the metric coefficients $$g_{\mu \nu} \,$$ in some coordinate basis $$dx^{a} \,$$ are independent of one of the coordinates $$x^{\kappa} \,$$, then $$K^{\mu} = \delta^{\mu}_{\kappa} \,$$ is a Killing vector, where $$\delta^{\mu}_{\kappa} \,$$ is the Kronecker delta.

To prove this, let us assume $$g_{\mu \nu},_0 = 0 \,$$. Then $$K^\mu = \delta^\mu_0 \,$$ and $$K_{\mu} = g_{\mu \nu} K^\nu = g_{\mu \nu} \delta^\nu_0 = g_{\mu 0} \,$$

Now let us look at the Killing condition
 * $$K_{\mu;\nu} + K_{\nu;\mu} = K_{\mu,\nu} + K_{\nu,\mu} - 2\Gamma^\rho_{\mu\nu}K_\rho = g_{\mu 0,\nu} + g_{\nu 0,\mu} - g^{\rho\sigma}(g_{\sigma\mu,\nu} + g_{\sigma\nu,\mu} - g_{\mu\nu,\sigma})g_{\rho 0} \,$$

and from $$g_{\rho 0}g^{\rho \sigma} = \delta_0^\sigma \,$$. The Killing condition becomes
 * $$g_{\mu 0,\nu} + g_{\nu 0,\mu} - (g_{0\mu,\nu} + g_{0\nu,\mu} - g_{\mu\nu,0}) = 0 \,$$

that is $$g_{\mu\nu,0} = 0$$, which is true.

 * The physical meaning is, for example, that, if none of the metric coefficients is a function of time, the manifold must automatically have a time-like Killing vector.
 * In layman's terms, if an object doesn't transform or "evolve" in time (when time passes), time passing won't change the measures of the object. Formulated like this, the result sounds like a tautology, but one has to understand that the example is very much contrived: Killing fields apply also to much more complex and interesting cases.

Conversely, if the metric $$\mathbf{g}$$ admits a Killing field $$X^a$$, then one can construct coordinates for which $$\partial_0 g_{\mu\nu} = 0$$. These coordinates are constructed by taking a hypersurface $$\Sigma$$ such that $$X^a$$ is nowhere tangent to $$\Sigma$$. Take coordinates $$x^i$$ on $$\Sigma$$, then define local coordinates $$(t,x^i)$$ where $$t$$ denotes the parameter along the integral curve of $$X^a$$ based at $$(x^i)$$ on $$\Sigma$$. In these coordinates, the Lie derivative reduces to the coordinate derivative, that is,
 * $$\mathcal{L}_Xg_{\mu\nu} = \partial_0 g_{\mu\nu}$$

and by the definition of the Killing field the left-hand side vanishes.

Properties
A Killing field is determined uniquely by a vector at some point and its gradient (i.e. all covariant derivatives of the field at the point).

The Lie bracket of two Killing fields is still a Killing field. The Killing fields on a manifold M thus form a Lie subalgebra of vector fields on M. This is the Lie algebra of the isometry group of the manifold if M is complete. A Riemannian manifold with a transitive group of isometries is a homogeneous space.

For compact manifolds
 * Negative Ricci curvature implies there are no nontrivial (nonzero) Killing fields.
 * Nonpositive Ricci curvature implies that any Killing field is parallel. i.e. covariant derivative along any vector field is identically zero.
 * If the sectional curvature is positive and the dimension of M is even, a Killing field must have a zero.

The covariant divergence of every Killing vector field vanishes.

If $$X$$ is a Killing vector field and $$Y$$ is a harmonic vector field, then $$g(X, Y)$$ is a harmonic function.

If $$X$$ is a Killing vector field and $$\omega$$ is a harmonic p-form, then $$\mathcal{L}_{X} \omega = 0 \,.$$

Geodesics
Each Killing vector corresponds to a quantity which is conserved along geodesics. This conserved quantity is the metric product between the Killing vector and the geodesic tangent vector. Along an affinely parametrized geodesic with tangent vector $$U^a$$ then given the Killing vector $$X_b$$, the quantity $$U^bX_b$$ is conserved:
 * $$U^a\nabla_a(U^bX_b)=0$$

This aids in analytically studying motions in a spacetime with symmetries.

Stress-energy tensor
Given a conserved, symmetric tensor $$T^{ab}$$, that is, one satisfying $$T^{ab} = T^{ba}$$ and $$\nabla_a T^{ab}=0$$, which are properties typical of a stress-energy tensor, and a Killing vector $$X_b$$, we can construct the conserved quantity $$J^a := T^{ab}X_b$$ satisfying
 * $$\nabla_a J^a = 0.$$

Cartan decomposition
As noted above, the Lie bracket of two Killing fields is still a Killing field. The Killing fields on a manifold $$M$$ thus form a Lie subalgebra $$\mathfrak{g}$$ of all vector fields on $$M.$$ Selecting a point $$p \in M~,$$ the algebra $$\mathfrak{g}$$ can be decomposed into two parts:
 * $$\mathfrak{h} = \{ X\in\mathfrak{g} : X(p) = 0 \}$$

and
 * $$\mathfrak{m} = \{ X\in\mathfrak{g} : \nabla X(p) = 0 \}$$

where $$\nabla$$ is the covariant derivative. These two parts intersect trivially but do not in general split $$\mathfrak{g}$$. For instance, if $$M$$ is a Riemannian homogeneous space, we have $$\mathfrak{g} = \mathfrak{h} \oplus \mathfrak{m}$$ if and only if $$M$$ is a Riemannian symmetric space.

Intuitively, the isometries of $$M$$ locally define a submanifold $$N$$ of the total space, and the Killing fields show how to "slide along" that submanifold. They span the tangent space of that submanifold. The tangent space $$T_pN$$ should have the same dimension as the isometries acting effectively at that point. That is, one expects $$T_pN \cong \mathfrak{m}~.$$ Yet, in general, the number of Killing fields is larger than the dimension of that tangent space. How can this be? The answer is that the "extra" Killing fields are redundant. Taken all together, the fields provide an over-complete basis for the tangent space at any particular selected point; linear combinations can be made to vanish at that particular point. This was seen in the example of the Killing fields on a 2-sphere: there are 3 Killing fields; at any given point, two span the tangent space at that point, and the third one is a linear combination of the other two. Picking any two defines $$\mathfrak{m};$$ the remaining degenerate linear combinations define an orthogonal space $$\mathfrak{h}.$$

Cartan involution
The Cartan involution is defined as the mirroring or reversal of the direction of a geodesic. Its differential flips the direction of the tangents to a geodesic. It is a linear operator of norm one; it has two invariant subspaces, of eigenvalue +1 and −1. These two subspaces correspond to $$\mathfrak{p}$$ and $$\mathfrak{m},$$ respectively.

This can be made more precise. Fixing a point $$p \in M$$ consider a geodesic $$\gamma: \mathbb{R} \to M$$ passing through $$p$$, with $$\gamma(0) = p~.$$ The involution $$\sigma_p$$ is defined as

 * $$\sigma_p(\gamma(\lambda)) = \gamma(-\lambda)$$

This map is an involution, in that $$\sigma_p^2 = 1~.$$ When restricted to geodesics along the Killing fields, it is also clearly an isometry. It is uniquely defined.

Let $$G$$ be the group of isometries generated by the Killing fields. The function $$s_p: G \to G$$ defined by
 * $$s_p(g) = \sigma_p \circ g \circ \sigma_p = \sigma_p \circ g \circ \sigma_p^{-1}$$

is a homomorphism of $$G$$. Its infinitesimal $$\theta_p: \mathfrak{g} \to \mathfrak{g}$$ is
 * $$\theta_p(X) = \left. \frac{d}{d\lambda} s_p\left(e^{\lambda X}\right) \right|_{\lambda=0}$$

The Cartan involution is a Lie algebra homomorphism, in that
 * $$\theta_p[X, Y] = \left[\theta_p X, \theta_p Y\right]$$

for all $$X, Y \in \mathfrak{g}~.$$ The subspace $$\mathfrak{m}$$ has odd parity under the Cartan involution, while $$\mathfrak{h}$$ has even parity. That is, denoting the Cartan involution at point $$p \in M$$ as $$\theta_p$$ one has
 * $$\left.\theta_p\right|_{\mathfrak{m}} = -Id$$

and
 * $$\left.\theta_p\right|_{\mathfrak{h}} = +Id$$

where $$Id$$ is the identity map. From this, it follows that the subspace $$\mathfrak{h}$$ is a Lie subalgebra of $$\mathfrak{g}$$, in that $$[\mathfrak{h}, \mathfrak{h}] \subset \mathfrak{h} ~.$$ As these are even and odd parity subspaces, the Lie brackets split, so that $$[\mathfrak{h}, \mathfrak{m}] \subset \mathfrak{m}$$ and $$[\mathfrak{m}, \mathfrak{m}] \subset \mathfrak{h} ~.$$

The above decomposition holds at all points $$p \in M$$ for a symmetric space $$M$$; proofs can be found in Jost. They also hold in more general settings, but not necessarily at all points of the manifold.

For the special case of a symmetric space, one explicitly has that $$T_pM \cong \mathfrak{m};$$ that is, the Killing fields span the entire tangent space of a symmetric space. Equivalently, the curvature tensor is covariantly constant on locally symmetric spaces, and so these are locally parallelizable; this is the Cartan–Ambrose–Hicks theorem.

Generalizations

 * Killing vector fields can be generalized to conformal Killing vector fields defined by $$\mathcal{L}_{X} g = \lambda g\,$$ for some scalar $$\lambda.$$ The derivatives of one parameter families of conformal maps are conformal Killing fields.
 * Killing tensor fields are symmetric tensor fields T such that the trace-free part of the symmetrization of $$\nabla T \,$$ vanishes. Examples of manifolds with Killing tensors include the rotating black hole and the FRW cosmology.
 * Killing vector fields can also be defined on any manifold M (possibly without a metric) if we take any Lie group G acting on it instead of the group of isometries. In this broader sense, a Killing vector field is the pushforward of a right invariant vector field on G by the group action. If the group action is effective, then the space of the Killing vector fields is isomorphic to the Lie algebra $$\mathfrak{g}$$ of G.

title: Killing vector field


text:
User:Fkuehne

I'm a student of Human Medicine living in Germany. In parts of my spare-time, I'm working for the VideoLAN open-source project on the Mac OS X and Win32 ports of VLC media player.

If you want to contact me, feel free to do so through my talk-page in the German Wikipedia, since I don't use the English one that often. You can find it here.

de:Benutzer:Fkuehne

title: User:Fkuehne