text:
Batgirl

Batgirl is the name of several fictional superheroines appearing in American comic books published by DC Comics, depicted as female counterparts and allies to the superhero Batman. The character Betty Kane was introduced into publication in 1961 by Bill Finger and Sheldon Moldoff as Bat-Girl, and was replaced in 1967 by Barbara Gordon, who became the most iconic Batgirl. The character debuted in Detective Comics #359 (January 1967) by writer Gardner Fox and artist Carmine Infantino, introduced as the niece/adoptive daughter of police commissioner James Gordon.

Batgirl operates in Gotham City, allying herself with Batman and the original Robin, Dick Grayson, along with other masked vigilantes. The character appeared regularly in Detective Comics, Batman Family, and several other books produced by DC until 1988. That year, Barbara Gordon appeared in Barbara Kesel's Batgirl Special #1, in which she retires from crime-fighting. She subsequently appeared in Alan Moore's graphic novel Batman: The Killing Joke where, in her civilian identity, she is shot by the Joker and left paraplegic. Although she is reimagined as the computer expert and information broker Oracle by editor Kim Yale and writer John Ostrander the following year, her paralysis sparked debate about the portrayal of women in comics, particularly violence depicted toward female characters.

In the 1999 storyline "No Man's Land", the character Helena Bertinelli, known as Huntress, briefly assumes the role of Batgirl until she is stripped of the identity by Batman for violating his stringent codes. Within the same storyline, the character Cassandra Cain is introduced. Cain is written as the daughter of assassins David Cain and Lady Shiva and takes the mantle of Batgirl under the guidance of Batman and Oracle. In 2000, she became the first Batgirl to star in an eponymous monthly comic book series, in addition to becoming one of the most prominent characters of Asian descent to appear in American comics. The series was canceled in 2006, at which point during the company-wide storyline "One Year Later", she is established as a villain and head of the League of Assassins. After receiving harsh feedback from readership, she is later restored to her original conception. However, the character Stephanie Brown, originally known as Spoiler and later Robin, succeeds her as Batgirl after Cassandra Cain abandons the role.

Stephanie Brown became the featured character of the Batgirl series from 2009 to 2011, prior to DC's The New 52 relaunch, which established Barbara Gordon recovering from her paralysis following a surgical procedure and starring as the title character of Batgirl once again. Barbara later returned to the Oracle role with Infinite Frontier in 2020, and currently operates as both Batgirl and Oracle, with Cassandra and Stephanie also serving as Batgirls. The Barbara Gordon version of Batgirl has been adapted into various media relating to the Batman franchise, including television, film, animation, video games, and other merchandise. Dan DiDio, co-publisher of DC Comics, expressed that Barbara is the best-known version of the character.

Detective Comics, Batman Family, and other appearances (1961–1988)
Following the accusations of a homoerotic subtext in the depiction of the relationship between Batman and Robin as described in Fredric Wertham's book Seduction of the Innocent (1954), a female character, Kathy Kane the Batwoman, appeared in 1956 as a love interest for Batman. In 1961, DC Comics introduced a second female character as a love interest for Robin. Betty Kane as "Bat-Girl" arrived as the niece of, and Robin-like sidekick to, Batwoman, first appearing in Batman #139 (April 1961). The creation of the Batman family, which included Batman and Batwoman depicted as parents, Robin and Bat-Girl depicted as their children, the extraterrestrial imp Bat-Mite and the "family pet" Ace the Bat-Hound, caused the Batman-related comic books to take "a wrong turn, switching from superheroes to situational comedy".

DC Comics abandoned these characters in 1964 when newly appointed Batman-editor Julius Schwartz judged them too silly and therefore inappropriate. Schwartz had asserted that these characters should be removed, considering the Batman related comic books had steadily declined in sales, and restored the Batman mythology to its original conception of heroic vigilantism. Bat-Girl, along with other characters in the Batman Family, were retconned out of existence following the 1985 limited series Crisis on Infinite Earths. However, even though Bat-Girl did not exist in the Post-Crisis continuity, a modified version of the character, Mary Elizabeth "Bette" Kane, introduced as the superhero Flamebird, continues to appear in DC Comics publications.

Schwartz stated that he had been asked to develop a new female character to attract a female viewership to the Batman television series of the 1960s. Executive producer William Dozier suggested that the new character would be the daughter of Gotham City's Police Commissioner James Gordon, and that she would adopt the identity of Batgirl. When Dozier and producer Howie Horowitz saw rough concept artwork of the new Batgirl by artist Carmine Infantino during a visit to DC offices, they optioned the character in a bid to help sell a third season to the ABC television network. Infantino reflected on the creation of Batgirl, stating "Bob Kane had had a Bat-Girl for about three stories in the ’50s but she had nothing to do with a bat. She was like a pesky girl version of Robin. I knew we could do a lot better, so Julie and I came up with the real Batgirl, who was so popular she almost got her own TV show." Yvonne Craig portrayed the character in the show's third season. Barbara Gordon and her alter ego Batgirl debuted in Detective Comics #359, "The Million Dollar Debut of Batgirl" (1967). In the debut story, while driving to a costume ball dressed as a female version of Batman, Barbara Gordon intervenes in a kidnapping attempt on Bruce Wayne by the supervillain Killer Moth, attracting Batman's attention and leading to a crimefighting career. Although Batman insists she give up crimefighting because of her gender, Batgirl disregards his objections.

In her civilian identity, Dr. Barbara Gordon is a career woman with a doctorate in library science, as well as being head of the Gotham City Public Library, "presumably one of the largest public libraries in the DC Comics version of reality." She was given a regular back-up slot in Detective Comics starting with issue #384 (February 1969), alternating issues with Robin until issue #404, after which she had the back-up slot to herself. Frank Robbins wrote nearly all of these back-ups, which were penciled first by Gil Kane and later by Don Heck. Barbara Gordon's Batgirl exceeded the earlier Bat-Girl and Batwoman characters in popularity, and readers requested for her to appear in other titles. Although some readers requested that Batwoman also continue to appear in publication, DC responded to the fan-based acclaim and criticism of the new character in an open letter in Detective Comics #417 (1971), stating: "I'd like to say a few words about the reaction some readers have to Batgirl. These are readers who remember Batwoman and the other Bat-girls from years back ... They were there because romance seemed to be needed in Batman's life. But thanks to the big change and a foresighted editor, these hapless females are gone for good. In their place stands a girl who is a capable crime-fighter, a far cry from Batwoman who constantly had to be rescued [by] Batman."

Batgirl continued to appear in DC Comics publications throughout the late 1960s and 1970s as a supporting character in Detective Comics, in addition to guest appearances in various titles such as Justice League of America, World's Finest Comics, The Brave and the Bold, Adventure Comics, and Superman. In the early-1970s, Batgirl reveals her secret identity to her father (who had already discovered it on his own) and serves as a member of the United States House of Representatives. She moves to Washington, D.C., intending to give up her career as Batgirl, and in June 1972 appeared in a story entitled "Batgirl's Last Case." Julius Schwartz brought her back a year later in Superman #268 (1973) in which she has a blind date with Clark Kent, establishing their friendship, and fights alongside Superman. Batgirl and Superman team up twice more, in Superman #279 and DC Comics Presents #19. Batgirl also guest-starred in other Superman related titles, such as #453 of Adventure Comics and in Superman Family #171, where she teams up with Supergirl.

The character is given a starring role in DC's Batman Family comic book which debuted in 1975. The original Robin, Dick Grayson, became her partner in the series, with the two frequently referred to as the "Dynamite Duo: Batgirl & Robin". Batgirl meets Batwoman in Batman Family #10, when the retired superhero briefly returns to crimefighting (before the Bronze Tiger murders Kane). The two fight Killer Moth and the Cavalier, and learn each other's secret identities. Batwoman retires once again at the conclusion of the story, leaving Batgirl to continue crimefighting. Although this series ended after three years of publication, Batgirl continued to appear in back-up stories published in Detective Comics through issue #519 (October 1982).

Crisis on Infinite Earths, a limited series published in 1985, was written to reduce the complex history of DC Comics to a single continuity. Although Batgirl is a featured character, her role is relatively small—she delivers Supergirl's eulogy in issue #7 of the 12-part series. The conclusion of Crisis on Infinite Earths changed DC Universe continuity in many ways. Following the reboot, Barbara Gordon is born to Roger and Thelma Gordon, and she is Jim Gordon's niece and adopted daughter in post - crisis continuity. Post-Crisis, Supergirl does not arrive on Earth until after Gordon has established herself as Oracle, and many of the adventures she shared with Batgirl are retroactively described as having been experienced by Power Girl. In Secret Origins (vol. 2) #20 (1987), Barbara Gordon's origin is rebooted by author Barbara Randal. Within the storyline, Gordon recounts the series of events that led to her career as Batgirl, including her first encounter with Batman as a child, studying martial arts under the tutelage of a sensei, memorizing maps and blueprints of the city, excelling in academics to skip grades, and pushing herself to become a star athlete.

Batgirl Special #1 and Batman: The Killing Joke (1988)
DC officially retired the hero in the one-shot comic Batgirl Special #1 (July 1988), written by Barbara Kesel. Later that year, she appears in Alan Moore's Batman: The Killing Joke. In this graphic novel, the Joker shoots and paralyzes Barbara Gordon in an attempt to drive her father insane, thereby proving to Batman that anyone can lose their minds after having "one bad day". She is deployed as a plot device to cement the Joker's vendetta against Commissioner Gordon and Batman. In 2006, during an interview with Wizard, Moore expressed regret over his treatment of the character, calling it "shallow and ill-conceived". He stated prior to writing the graphic novel, "I asked DC if they had any problem with me crippling Barbara Gordon—who was Batgirl at the time—and if I remember, I spoke to Len Wein, who was our editor on the project", and following a discussion with then-Executive Editorial Director Dick Giordano, "Len got back onto the phone and said, ‘Yeah, okay, cripple the bitch.'"

Although there has been speculation as to whether or not editors at DC specifically intended to have the character's paralysis become permanent, Brian Cronin, author of Was Superman A Spy?: And Other Comic Book Legends Revealed (2009) noted that DC had hired Barbara Kesel to write the Batgirl Special specifically to retire the character and set her in place for The Killing Joke. Gail Simone included the character's paralysis in a list of "major female characters that had been killed, mutilated, and depowered", dubbing the phenomenon "Women in Refrigerators" in reference to a 1994 Green Lantern story where the title character discovers his girlfriend's mutilated body in his refrigerator. Following the release of the graphic novel, comic book editor and writer Kim Yale discussed how distasteful she found the treatment of Barbara Gordon with her husband, fellow comic writer John Ostrander. Rather than allow the character to fall into obscurity, the two decided to revive her as a character living with a disability—the information broker called the Oracle.

"No Man's Land" (1999)
Eleven years after the editorial retirement of Barbara Gordon as Batgirl, a new version of the character was introduced in Batman: Shadow of the Bat #83 during the multi-title story arc "No Man's Land" (1999). In Batman: Legends of the Dark Knight #120 (1999), the new Batgirl is revealed to be Helena Bertinelli, an established DC comics superhero alternatively known as the Huntress. Bertinelli is eventually forced to abandon the mantle by Batgirl. No Man's Land also marks the introduction of Cassandra Cain in Batman #567 (1999). Depicted as a martial arts child prodigy, Cassandra Cain is written as a young woman of partly Asian descent who succeeds Helena Bertinelli as Batgirl, with the approval of both Batman and the Oracle.

Batgirl and other appearances (2000–2011)
The first Batgirl monthly comic was published in 2000, with Cassandra Cain as the title character. Raised by assassin David Cain, Cassandra Cain was not taught spoken language, but instead was taught to "read" physical movement. Subsequently, Cain's only form of communication was body language. The parts of the character's brain normally used for speech were trained so Cain could read other people's body language and predict, with uncanny accuracy, their next move. This also caused her brain to develop learning functions different from most, a form of dyslexia that hampers her abilities to read and write.

Despite Cain's disability, author Andersen Gabrych describes the character's unique form of language as the key factor in what makes Cain an excellent detective; the ability to walk into a room and "know" something is wrong based on body language. During "Silent Running", the first arc of the Batgirl comic book series, Cassandra Cain encounters a psychic who "reprograms" her brain, enabling her to comprehend verbal language, while simultaneously losing the ability to predict movements. This issue is resolved during the second arc of the series, "A Knight Alone", when Batgirl encounters the assassin Lady Shiva who agrees to teach her how to predict movement once again. Six years after its debut, DC Comics cancelled the Batgirl comic book series with issue #73 (2006), ending with Cain relinquishing her role as Batgirl.

When DC Comics continuity skipped forward one year after the events of the limited series Infinite Crisis, Cassandra Cain is revived as the leader of the League of Assassins, having abandoned her previous characterization as an altruist. The character's progression from hero to villain angered some of her fans and was accompanied by heavy criticism. Cain reprised her role as Batgirl in the "Titans East" (2007) storyline of Teen Titans, where it was discovered that she had been influenced by a mind-altering drug administered by supervillain Deathstroke the Terminator. Following the conclusion of the storyline, DC Comics has restored Cain's original characterization as a superhero and the character has been given a supporting role in the comic book series Batman and the Outsiders.

Following the events of Batman's disappearance, Cassandra, acting under her mentor's orders in the event of his death, handed over the Batgirl mantle to Stephanie Brown, the former Spoiler and the fourth Robin. After declining an offer from Tim Drake to reclaim the Batgirl mantle from Stephanie, Cassandra rejoined the Batman Family under the new identity of the Blackbat. She currently acts as the Hong Kong representative of Batman Inc.

Stephanie Brown does take the mantle of Batgirl after Cassandra Cain gives Brown her costume under Batman's orders. Eventually, Barbara Gordon approves of Brown as her newest successor — and she gives Brown her own Batgirl costume and becomes her mentor for a period. Brown is the fourth in-continuity Batgirl and the second Batgirl to star in her own ongoing Batgirl comic book series.

The New 52: Batgirl, Birds of Prey, and other appearances (2011–2016)
In September 2011, following the company-wide relaunch, Barbara Gordon stars in a new Batgirl series—one of The New 52 titles featuring the company's most iconic characters. The conclusion of the limited series Flashpoint (2011) establishes a new continuity within the DC Universe, with all characters regressing to an earlier age and stage in their careers, while remaining in a modern timeline. DC Senior VP of Sales, Bob Wayne, explained that with each of their titles reverting to issue #1, "our creative teams have the ability to take a more modern approach—not only with each character, but with how the characters interact with one another and the universe as a whole, and focus on the earlier part of the careers of each of our iconic characters." Barbara Gordon is biological daughter of James Gordon and Barbara Eileen Gordon in this continuity. Wayne also stated that "The Killing Joke still happened and she was Oracle. Now she will go through physical rehabilitation and become a more seasoned and nuanced character because she had these incredible and diverse experiences. Dan DiDio, Co-Publisher of DC Comics explained the decision by stating that "she'll always be the most recognizable [Batgirl]." Series writer Gail Simone stated: "For many years, I got to write the character as Oracle, and there is to this day, no character who means more to me. This is classic Barbara as she was originally conceived, with a few big surprises. It's a bit of a shock, to be sure, but we’re doing everything we can to be respectful to this character's amazing legacy, while presenting something thrilling that a generation of comics readers will be experiencing for the first time ...Barbara Gordon leaping, fighting, and swinging over Gotham. Now, when citizens of that city look up, they are going to see BATGIRL. And that is absolutely thrilling."

In the new, revised continuity, the events of The Killing Joke took place three years before the current storyline, and while it is established she was paraplegic during that time, Barbara Gordon is written as having regained her mobility after undergoing experimental surgery at a South African clinic. Although she resumes her work as Batgirl one year after her recovery, she continues to suffer from post-traumatic stress disorder, causing her to hesitate in battle when exposed to gunfire that could result in suffering new spinal damage. The character also exhibits survivor guilt due to the fact she has made a full recovery from her paralysis while others have not. Series writer Gail Simone stated that while the character is "one of the smartest and toughest women in comics ...One thing the book is truly about, is that the after-effects of something like PTSD (post-traumatic stress disorder) or other trauma-related syndromes, can strike even very smart, very intellectually tough people, even soldiers and cops", a subject that is generally overlooked in comic books. She also explained the method of the character's recovery is based upon real life experiences in that "some of the best real world work in the field of mobility rehabilitation is coming from South Africa. People have been talking about this as if it's some sort of mystical thing like returning from the dead, but there are treatments and surgeries that can restore mobility in some cases. Barbara's spine was not severed. That makes her a candidate."

Prior to its release, Batgirl #1 sold out at the distribution level with over 100,000 copies printed in its first run according to Diamond Comic Distributors. Along with Action Comics #1, Justice League #1, Batman #1, Batman and Robin #1, Batman: The Dark Knight #1, Detective Comics #1, Flash #1, Green Lantern #1, and Superman #1, retailers were required to order a second printing. Calvin Reid of Publishers Weekly states in a review of the first issue: "The artwork is okay though conventional, while Simone's script tries to tie up of the end of the previous Barbara Gordon/Oracle storyline and setup up the new Batgirl. Her formula: murderous villains, blood splattering violence and high flying superheroics mixed with single-white-female bonding ...plus a cliffhanger ending to the first issue that offers a nifty [segue] into the new world of Barbara Gordon and Batgirl." The New York Times critic George Gene Gustines wrote: "Unlike some of the other DC comics I read this week, Batgirl achieves a deft hat trick: a well-shaped reintroduction to a character, an elegant acknowledgement of fundamental history and the establishment of a new status quo. This is a must-buy series." Earning a B+ rating in a review from Entertainment Weekly, Ken Tucker writes that Simone "[takes] her Birds of Prey storytelling powers and focuses them on the newly revived Barbara Gordon as Batgirl. The result is a burst of exhilaration, as Barbara/Batgirl revels in her new freedom even as she encounters a so-far not-terribly-chilling villain called Mirror."

Since the series relaunch in September 2011, Batgirl has remained within the top 30 of the 300 best-selling monthly comic book publications sold in North America. Monthly estimated sales figures are as follows: Batgirl #1 with 81,489 copies (ranked 12th overall), Batgirl #2 with 75,227 (ranked 14th), Batgirl #3 with 62,974 (ranked 18th), Batgirl #4 with 53,975 (ranked 23rd), Batgirl #5 with 51,327 (ranked 26th), and Batgirl #6 with 47,836 (ranked 30th). The hardcover edition of volume 1, Batgirl: The Darkest Reflection, which collects issues #1–6, made The New York Times Best Seller list, alongside Animal Man: The Hunt, Batman & Robin: Born to Kill, Batman: Detective Comics, Wonder Woman: Blood, Batwoman: Hydrology, Green Lantern: Sinestro.

Additionally, Barbara Gordon makes an appearance in Birds of Prey #1, where the Black Canary offers her a spot on the new Birds of Prey roster. She declines the Canary's invitation, suggesting that Katana take her place instead. Series writer Duane Swierczynski has stated that Batgirl will join the team in issue #4. He commented that while she "is an essential part of this team", she is not the focus of the series, as she is hesitant to be associated with the other characters because of their status as outlaws.

In October 2014, the monthly Batgirl title underwent a soft reboot with the new creative team Brenden Fletcher (writer) Cameron Stewart (writer, layouts), Babs Tarr (artist) and Maris Wicks (colors). The first six-issue story explored Barbara Gordon's attempt to start a new life as a PhD student in the hip Gotham borough of Burnside. While seemingly light and engaging compared to Gail Simone's darker preceding run, the new arc ultimately dealt with Babs' inability to fully escape her earlier trauma and the villain was revealed as her own brain scans, an algorithm similar to the Pre-New 52 Oracle. While the reboot was highly praised for its fun, energy, innovative use of social media, and particularly for Tarr's art, issue #37 caused controversy with its depiction of a villain named Dagger Type, which some critics saw as a transphobic caricature. In response, the creative team issued a joint apology and revised the issue for the subsequent collected edition, Batgirl Vol. 1: The Batgirl of Burnside.

On March 13, 2015, DC Comics released 25 Joker-themed variant covers for its various monthly series for release that June, in celebration of the character's 75th anniversary. Among them was a cover to Batgirl #41 by artist Rafael Albuquerque that took its inspiration from The Killing Joke. The cover depicts the Joker standing next to a tearful Batgirl, who has a red smile painted across her mouth. The Joker has one hand holding a revolver draped over Batgirl's shoulder and is pointing to her cheek with the other hand, as if gesturing to shoot her.

The cover quickly drew criticism for highlighting a dark period in the character's history, especially when juxtaposed with the youthful, more optimistic direction of the series at the time. The hashtag #changethecover drew dozens of posts on Twitter and Tumblr asking DC to not release the variant. DC ultimately withdrew the cover from publication at the request of Albuquerque, who stated, "My intention was never to hurt or upset anyone through my art...For that reason, I have recommended to DC that the variant cover be pulled."

DC Rebirth: Batgirl and Batgirl and the Birds of Prey (2016–2020)
In March 2016, DC Comics announced it would be re-launching all of its monthly titles under the DC Rebirth event. The relaunch restores elements of the Pre-Flashpoint DC continuity while maintaining elements of The New 52 as well. Among the new titles and creative teams announced, volume 5 of Batgirl written by Hope Larson and volume 1 of Batgirl and the Birds of Prey written by Julie Benson and Shawna Benson were included. In the critically celebrated fifth volume of Batgirl, Barbara Gordon is a student attending Burnside College in the trendy Burnside neighborhood of Gotham City. The comic was praised for its fun, fresh approach to the character and for Batgirl's realistic new costume design.

Infinite Frontier: Batgirls (2021–present)
In 2021, DC's Infinite Frontier relaunch presented a new status quo, where Barbara has returned to the role of Oracle, suiting up as Batgirl only occasionally. For the most part, she supports Cassandra Cain and Stephanie Brown to operate as Batgirls, sharing the title.

Alternative versions
Various alterations of Barbara Gordon as Batgirl have appeared in storylines published in and out of mainstream continuity titles. Variants of the character within continuity often appear in stories which involve time travel, such as the crossover limited series Zero Hour: Crisis in Time, a follow-up story preceded by the 1985 limited series Crisis on Infinite Earths which altered mainstream continuity. Notable imprints of DC Comics such as Elseworlds and All Star DC Comics have also featured alternate versions of the character.

The Elseworlds imprint takes the company's iconic characters and places them in alternate timelines, places and events making heroes "as familiar as yesterday seem as fresh as tomorrow". As Batgirl, Barbara Gordon has made several appearances in Elseworlds comics since 1997. The character is given starring roles in the noir-style storyline Thrillkiller (1997), its sequel Thrillkiller '62 (1998), and the one-shot comic Elseworld's Finest: Supergirl & Batgirl (1998). In 2005, DC Comics launched its All Star imprint—an ongoing series of comics designed to pair the company's most iconic characters with the most acclaimed writers and artists in the industry. Similar to Elseworlds, All Star is not restricted to mainstream continuity and establishes a fresh perspective for the latest generation of readership. According to Dan DiDio, "[t]hese books are created to literally reach the widest audience possible, and not just the comic book audience, but anyone who has ever wanted to read or see anything about Superman or Batman."

An alternate Barbara Gordon was adapted into Frank Miller's All Star Batman and Robin the Boy Wonder (2005) as a teenage Batgirl. In addition, another variation of the character had been set to star in an eponymous All Star Batgirl title, written by Geoff Johns; however, the series was cancelled prior to publication.

Alternate versions of Batgirl aside from Barbara Gordon have also appeared in publications by DC Comics. In Batman Beyond Unlimited #18 (set in the continuity of the animated series Batman Beyond), the new Batgirl is a 15-year-old girl named Nissa. In Batgirl: Future's End #1 (Nov. 2014), set in an alternate future, a trio of Batgirls include Cassandra Cain, Stephanie Brown and newcomer Tiffany Fox—the daughter of Lucius Fox and the first African American character to be portrayed as Batgirl.

In the alternate history DC Comics Bombshells universe, there is no singular Batgirl. Instead, there exists a group of young female vigilantes known as "the Batgirls", whose ranks consist of a Batwoman fan named Harper Row, an African American mechanic named Kathy Duquesne, a young Caucasian girl named Nell Little, and a Singaporean-American dancer named Alysia Yeoh. In Digital Issue #42 (collected in Print Issue #14), Harley Quinn tells Pamela Isley about encountering "the Belle of the Bog", who appears to be a vampire version of Batgirl. DC Comics Bombshells Annual #1, published on 31 August 2016, reveals that Barbara Gourdon was a French fighter pilot during World War I. After she lost her boyfriend during the war, she traveled to Louisiana and did indeed become a vampire.

In 2021, Barbara Gordon is one of the main protagonists in Batman '89. While working in Gotham's police department, she dates Harvey Dent. She assumes the role of Batgirl in the second series, Echoes.

In 2022 Daphne Blake from Scooby-Doo became a temporary Batgirl in The Batman & Scooby-Doo Mysteries.

Characterization
Batgirl has officially been represented by four different characters – and two claimants – beginning with her introduction in 1961.

Betty Kane
During the Silver Age, a female character was introduced as a love interest for Robin. Betty Kane as "Bat-Girl" was depicted as the niece of, and Robin-like sidekick to, the original Batwoman. In 1964, however, editor Julius Schwartz asserted that Bat-Girl and other characters in the Bat-Family should be removed considering the decline in sales and restored the Batman mythology to its original conception of heroic vigilantism. During the Crisis on Infinite Earths storyline, Betty Kane was retconned out of existence. Mary Elizabeth "Bette" Kane is a reinvented version of the Betty Kane character during the Silver Age. As her original characterization was retconned out of existence during the Crisis on Infinite Earths storyline, a discrepancy arose where her Bat-Girl character had joined the West Coast version of the Teen Titans, but simply disappeared. The character was reintroduced as Bette Kane and the alias of Flamebird. Following Infinite Crisis, the character's past as Batgirl was hinted at as being a part of continuity. However, that reference included a revamped origin of the character and it may or may not have been the current Bette Kane.

Barbara Gordon
During the run of the Batman television series, DC editorial was approached about adding a female character back into the Batman family. Revising the character history and motivation, Julius Schwartz created Barbara Gordon. This character held the role of Batgirl from 1967 to 1988 when she was retired by DC editorial decision. The character's role was changed to a paraplegic source of information for all members of the Batman family and codenamed the "Oracle". She was later restored as Batgirl during The New 52 relaunch of the entire DC publication line in 2011. This was also the case with the DC Rebirth (2016). After the suicide of her psychopathic brother James Gordon Jr., Barbara ponders her role as Batgirl, becomes Oracle and continues to support the Batman family behind the computer screen, with the option to occasionally return to the role of Batgirl. Above all, she takes on the role of mentor for Cassandra Cain and Stephanie Brown, who now share the title of Batgirl.

Cassandra Cain
During the No Man's Land storyline, Cassandra Cain was given the role of Batgirl under the guidance of Batman and Oracle. Written as the daughter of assassins David Cain and Lady Shiva, she is trained from early childhood to read human body language instead of developing verbal and written communication skills as part of her father's conditioning to mold her into the world's deadliest assassin. However, after committing her first murder, she vows to never again use her martial-arts prowess to kill. In 2000, she became the first Batgirl to star in an eponymous monthly comic book series, as well as one of the most prominent characters of Asian descent to appear in American comics. The series was cancelled in 2006 and Cassandra Cain abandoned the role of Batgirl shortly thereafter. Years later, Cassandra rejoined the Batman family under the moniker the Blackbat. In The New 52, Cassandra reappeared in the comic series Batman and Robin Eternal with a slightly different history. Here she is also the murderer of Harper Row's mother, an ally of Batman. She called herself Orphan for a while and became part of the Batman family as well as the Outsiders. She later shares the name Batgirl with her friend Stephanie Brown.

Stephanie Brown
Stephanie Brown was formerly known as the Spoiler and then as the first in-continuity female Robin until her apparent death in 2006. Following her return to comics in 2009, she assumed the role of Batgirl. She maintained this position until 2011, the relaunch of the DC imprint under The New 52. The character reappeared in the DCU in Batman (vol. 3) #28, as the Spoiler. Stephanie reappears in the series Batman Eternal, where she again goes by Spoiler in an attempt to thwart her father's machinations. After DC Rebirth, she joined Batman's new team of vigilantes where she became the girlfriend of Tim Drake aka Red Robin before they break up. Eventually she shares the title Batgirl with her friend Cassandra Cain.

Helena Bertinelli
For a brief time during 1999's No Man's Land storyline, Helena Bertinelli assumed the mantle of Batgirl. After violating Batman's code against extreme violence, she was stripped of the mantle and returned to her alias of the Huntress.

Charlotte "Charlie" Gage-Radcliffe
After Cassandra Cain abandoned the role, a mystery character appeared as the new Batgirl in the Birds of Prey comic. Possessing superpowers, the teen claimed the empty mantle in an attempt to honor the character. However, Barbara Gordon quickly dissuaded the teen from continuing in the role. Charlie Gage-Radcliffe acquiesced, but modified her costume and changed her name to the Misfit.

Cultural impact
While Barbara Gordon and Cassandra Cain have both been the subject of academic analysis regarding the portrayal of women in comics, commentary on Barbara Gordon's Batgirl has focused on her character's connection to the women's liberation movement, doctoral degree and career as a librarian, while analysis of Cassandra Cain's Batgirl has focused on the character's double minority status as a woman and a person of color. Since her debut in DC Comics publication, and fueled by her adaptation into the Batman television series in 1967, Barbara Gordon's Batgirl has been listed among fictional characters that are regarded as cultural icons. Author Brian Cronin, in Was Superman A Spy?: And Other Comic Book Legends Revealed (2009) notes that following her 1967 debut, "Batgirl was soon popular enough to appear regularly over the next two decades and Yvonne Craig certainly made an impression on many viewers with her one season portraying young Ms. Gordon." In 2011, IGN ranked Barbara Gordon 17th in the Top 100 Comic Books Heroes. Cassandra Cain's Batgirl has become one of the most prominent Asian characters to appear in American comic books, and her understated sexuality is notable as being contrary to the common sexual objectification of female characters, especially those of Asian descent.

Feminist interpretations
In The Supergirls: Fashion, Feminism, Fantasy, and the History of Comic Book Heroines (2009), author Mike Madrid states that what set Barbara Gordon as Batgirl apart from other female characters was her motivation for crime-fighting. Unlike Batwoman who preceded her, "she wears his symbol on her chest, but she is not his girlfriend or faithful handmaiden." Because of the fact she does not pursue a romantic interest in Batman, "Batgirl is a female Batman can actually regard as a brilliant peer and a partner in the war on crime, the same way he would a male." Historian Peter Sanderson observed that Barbara Gordon's Batgirl reflected the Women's liberation movement of the 1960s.

During the 1980s, Barbara Kesel, after writing a complaint to DC Comics over the negative portrayal of female characters, was given the opportunity to write for Barbara Gordon in Detective Comics. Robin Anne Reid, in Women in Science Fiction and Fantasy: Overviews (2009) wrote that "Kesel's version of Batgirl established her as a character separate from Batman and Robin: a woman motivated to do what men do, but alone and in her own way. Her Secret Origins (1987) and Batgirl Special (1988) countered the victimized and objectified presentation of Barbara Gordon/Batgirl in Alan Moore's acclaimed The Killing Joke (1988)." She notes that Kesel's interpretation of the character emphasized her intelligence, technological skill, and ability to overcome fear.

Gail Simone included the character's paralysis in a list of "major female characters that had been killed, mutilated, and depowered", dubbing the phenomenon "Women in Refrigerators" in reference to a 1994 Green Lantern story where the title character discovers his girlfriend's mutilated body in his refrigerator. Simone highlighted the gender difference regarding the treatment of Batman and Batgirl regarding paralysis by stating that "[b]oth had their backs broken [Batman broke his in a dramatic Batcave confrontation with the villain Bane; Batgirl broke hers when she was ambushed in her home and shot in the spine by the Joker, never given a chance to fight]. Less than a year later, Batman was fine. Batgirl—now named Oracle—was in a wheelchair and remained so for many years."

In Superheroes and Superegos: Analyzing the Minds Behind the Masks (2010), author Sharon Packer wrote that "[a]nyone who feels that feminist critics overreacted to [Gordon's] accident is advised to consult the source material", calling the work "sadistic to the core".

Brian Cronin noted that "[many] readers felt the violence towards Barbara Gordon was too much, and even Moore, in retrospect, has expressed his displeasure with how the story turned out." Jeffrey A. Brown, author of Dangerous Curves: Action Heroines, Gender, Fetishism, and Popular Culture (2011) noted The Killing Joke as an example of the "inherent misogyny of the male-dominated comic book industry" in light of the "relatively unequal violence [female characters] are subjected to." While male characters may be critically injured or killed, they are more than likely to be returned to their original conception, while female characters are more likely to receive permanent damage. Reid states that although speculation behind the editorial decision to allow the paralysis of the character to become permanent included the idea she had become outdated, "if audiences had grown tired of Batgirl, it was not because she was a bad character but because she had been written badly."

Despite views that present the character's Batgirl persona as a symbol of female empowerment, a long-held criticism is that she was originally conceived as an uninspired variation of Batman "rather than standing alone as leader, such as Wonder Woman" who had no pre-existing male counterpart. In analyzing stereotypes in gender, Jackie Marsh noted that male superheroes (such as Batman) are depicted as hyper-masculine and anti-social, "while female superheroes are reduced to a childlike status by their names" such as the Batgirl character.

Representation for librarians
In The Image and Role of the Librarian (2002), Wendi Arant and Candace R. Benefiel argue that Batgirl's portrayal as a librarian is considered to be significant to the profession, in that it is represented as a valuable and honorable career. Even in light of the fact that the character abandons it to run for United States Congress, Barbara Gordon is seen as being given a "career switch that even most librarians would consider a step up." In the essay "Librarians, Professionalism and Image: Stereotype and Reality" (2007), Abigail Luthmann views the character less favorably, stating that "[t]he unassuming role of librarian is used as a low-visibility disguise for her crime-fighting alter-ego, and while her information-locating skills may have been useful to her extra-curricular activities no direct examples are given."

Representation for Asian Americans
The Cassandra Cain version of Batgirl, depicted as a biracial character (half White and half Chinese), is notable as one of the most prominent characters of Asian descent to appear in American comic books. Jeffrey A. Brown states that while her ethnicity is rarely mentioned in the comic books, Asian women have had a long history in comics of being portrayed as martial artists and are often exploited as sex objects. However, in the case of Batgirl, "Cassandra's racial identity is treated more implicitly than explicitly. Her costume design actually conceals her entire body so that while in her guise as Batgirl her ethnicity is completely unapparent." The fact that her sexuality is also understated represents a shift away from the typical portrayals of women, and Asian women in particular. The most controversial aspect of her character came about during the One Year Later event, when she is reintroduced as a villain. The abrupt shift in her character brought about negative criticism from readership. When questioned about the change in characterization, writer Adam Beechen stated: "They didn't present me with a rationale as to why Cassandra was going to change, or a motivating factor. That was left for me to come up with and them to approve. And we did that. But as far as to why the editors and writers and whoever else made the decision decided that was a good direction, I honestly couldn't answer."

In other media
Portrayed by Yvonne Craig, the character's first adaptation outside of comic books took place in the third season of Batman (1967), Barbara Gordon having been discussed months earlier by her father and Batman in the second-season episodes "Batman's Waterloo" and "The Duo Defy". Les Daniels, in Batman: The Complete History (2004), wrote that the goal of ABC was to "attract new audience members, especially idealistic young girls and less high-minded older men." According to Craig: "I used to think the reason they hired me was because they knew I could ride my own motorcycle ... I realized they hired me because I had a cartoon voice." A shared criticism of Batgirl and other female superheroes in television that came later (such as Wonder Woman and the Bionic Woman), is that she was not allowed to engage in hand-to-hand combat on screen. As such, "her fights were choreographed carefully to imitate the moves of a Broadway showgirl through the use of a straight kick to her opponent's face rather than the type of kick a martial artist would use." However, Craig has also stated: "I meet young women who say Batgirl was their role model ... They say it's because it was the first time they ever felt girls could do the same things guys could do, and sometimes better. I think that's lovely." During the early 1970s, Craig portrayed Batgirl once again in a public service announcement to advocate equal pay for women.

Since Batman, the character has had a long history of appearances in television and other media. As Batgirl, Barbara Gordon plays a supporting role in a string of animated series, voiced by Jane Webb in The Batman/Superman Hour (1968), Melendy Britt in The New Adventures of Batman (1977), Melissa Gilbert in Batman: The Animated Series (1992), Tara Strong in The New Batman Adventures (1997), Danielle Judovits in The Batman (2004), Mae Whitman in Batman: The Brave and the Bold (2008), and Briana Cuoco in Harley Quinn (2019). In 2012, Batgirl starred alongside Supergirl and Wonder Girl in Super Best Friends Forever, a series of shorts developed by Lauren Faust for the DC Nation block on Cartoon Network.

Barbara Gordon makes two cameo appearances in the first season of the animated series Young Justice, and is added as a recurring character in season two where she has adopted her Batgirl persona. Dina Meyer starred as Barbara Gordon in the television series Birds of Prey (2002). Although this series focused on her role as the Oracle, the series included flashbacks of the character's history as Batgirl.

In the film Batman & Robin, Alicia Silverstone played a variation of the character: Barbara Wilson, Alfred Pennyworth's niece. She appears in The Lego Batman Movie voiced by Rosario Dawson. The character is introduced as Barbara Gordon taking over from her father Jim Gordon to become the new Police Commissioner of Gotham. Towards the end of the film, she dons her cowl and teams up with Batman as Batgirl in addition to her role as Commissioner.

In The Dark Knight trilogy, James Gordon's wife is named Barbara Gordon, portrayed by Ilyssa Fradin in Batman Begins and Melinda McGraw in The Dark Knight. This is not a reference to Batgirl Barbara Gordon. It's been long established, most notably in the famous Batman: Year One, that the wife of James Gordon is named Barbara.

In addition to live-action television and animation, the character has appeared in a number of video games included in the Batman franchise. She appears in The Adventures of Batman & Robin and Batman: Rise of Sin Tzu voiced by Tara Strong. She also appears in Lego Batman for the PC, PlayStation 2, PlayStation 3, Xbox 360, Wii, DS, and PlayStation Portable. In Scribblenauts Unmasked: A DC Comics Adventure, The Barbara Gordon incarnation of Batgirl appears when Maxwell heads to Arkham Asylum to battle the Scarecrow. The other three Batgirls (Bette Kane, Stephanie Brown and Cassandra Cain) also appear as summonable characters. Barbara Gordon has been featured in all four main games of the critically acclaimed Batman: Arkham series, though she is only seen as Batgirl in the "A Matter of Family" DLC for the last game, Batman: Arkham Knight (2015), in which she is playable. Set before the events of the series' first installment, the DLC's plot revolves around Batgirl and Robin attempting to save the former's father, along with other police officers, from the Joker at an abandoned amusement park located on an oil rig. Barbara Gordon as Batgirl is one of the four main playable characters in the video game Gotham Knights (2022).

A child version of Barbara Gordon made an appearance in the television series Gotham. Actor Ben McKenzie teased about seeing Batgirl as a child in the series. Film director Nicolas Winding Refn revealed in an interview with Collider that he would like to direct a Batgirl movie.

Savannah Welch portrays Barbara Gordon in the third season of the 2018 live-action television series Titans.

In March 2017, it was announced that Joss Whedon would write, direct and produce a Batgirl film as part of the DC Extended Universe. The film would center on Barbara Gordon as Batgirl, with Gail Simone's The New 52 Batgirl comics used as "a starting point" for the film. In February 2018, it was announced that Whedon would be leaving the project as writer and director, citing that "[he] didn't really have a story". In April 2018, Warner Bros. announced that screenwriter Christina Hodson had been tapped to write the screenplay for Batgirl. After Whedon's exit, the studio said that it was actively looking for a female director. In May 2021, it was revealed that Adil El Arbi and Bilall Fallah had joined the project as co-directors. It was also revealed that the film is going to be an HBO Max Exclusive. In July 2021, actress and singer Leslie Grace was cast as Batgirl. The film was subsequently cancelled in August 2022.

Other collected editions

 * Batman: Bruce Wayne – Murderer? (Batgirl #24)
 * Batman: Bruce Wayne – Fugitive Vol. One (Batgirl #27 and 29)
 * Batman: Bruce Wayne – Fugitive Vol. Three (Batgirl #33)
 * Batman: War Games Act One – Outbreak (Batgirl #55)
 * Batman: War Games Act Two – Tides (Batgirl #56)
 * Batman: War Games Act Three – Endgame (Batgirl #57)

title: Batgirl


text:
Władysław III Spindleshanks

Władysław III Spindleshanks (Władysław Laskonogi; b. 1161/67 – 3 November 1231), of the Piast dynasty, was Duke of Greater Poland (during 1194–1202 over all the land and during 1202–1229 only over the southern part), High Duke of Poland and Duke of Kraków during 1202–1206 and 1228–1231, Duke of Kalisz during 1202–1206, ruler of Lubusz during 1206–1210 and 1218–1225, and ruler over Gniezno during 1216–1217.

He was the fifth son of Mieszko III the Old, Duke of Greater Poland and since 1173 High Duke of Poland, but the third-born from his second marriage with Eudoxia, daughter of Grand Prince Iziaslav II of Kiev.

The nickname "Spindleshanks" (Laskonogi) was given to Władysław in the Chronicle of Greater Poland. Jan Długosz assumed that this was in reference to Władysław's unusually long and thin legs.

Under the rule of Mieszko III the Old
The first appearance of Władysław in contemporary sources was around 1168 in reference to the congress of Jędrzejów where, as a small child, he was a witness in a donation to the local Cistercian monastery.

Between 1177 and 1179 Władysław, his parents and siblings were forced to leave Poland as a result of the rebellion of Casimir II the Just and Odon, Mieszko III's eldest son from his first marriage, who resented the clear favoritism showed by his father to the offspring of his second marriage. Władysław returned to his family only in 1181 and, despite being legally an adult, was not given his own district. Around 1186, Władysław married Lucia, daughter of Jaromar I, Prince of Rügen. The union, whose principal purpose was to increase the influence of Mieszko III in Western Pomerania, was childless.

After the death of Władysław's half-brother Odon on 20 April 1194, Władysław assumed the control of the Duchy in Southern Greater Poland (the Obra River), as guardian of his minor nephew Władysław Odonic (son of Odon, born ca. 1190).

On 13 September 1195, the death of his only surviving brother Bolesław in the bloody Battle of Mozgawa left Władysław as the sole heir of Mieszko III, and he began trying to restore the lands controlled by his father in the Duchy of Kraków and to assume the overlordship of Poland.

Duke of Kraków and Greater Poland
Mieszko III died on 13 March 1202. Władysław could succeed his father without barriers in Kraków, Greater and Lesser Poland, thanks to the support of the powerful voivode Mikołaj Gryfita. However, an opponent soon arose to the throne of Kraków: the eldest son of Casimir II the Just, Leszek I the White, but his candidacy collapsed because he based its rule on the count palatine Goworek, who was a stubborn enemy of the voivode Mikołaj.

Loss of the Kraków throne
Władysław's rule as Duke of Kraków and High Duke of Poland lasted for four years, until 1206, when, after the death of his principal supporter voivode Mikołaj Gryfita, Leszek I the White returned to the capital. The cause of the rebellion was a tough enforcement of rights against the powerful nobility and the alliance with the Pomeranians. Some historians placed the loss of Kraków by Władysław in an earlier period: a few months after the death of his father in 1202. In the absence of sources for this period, however, this fact is difficult to verify.

Plans to restore Polish suzerainty over Pomerania
Interest in the Pomeranian affairs, Władysław was involved in two events. The first was a solemn meeting with King Valdemar II of Denmark, during which attempted to resolve disputes and determine the zone of influence. The second event was a surprising agreement with the Duke of Wroclaw, Henry I the Bearded, under which Władysław surrendered the Duchy of Kalisz (part of the patrimony of his nephew Władysław Odonic) in exchange of Lubusz, whereby it was easier to pursue an active policy on the Baltic coast. But in 1209 Władysław lost Lubusz, taken by Conrad II of Landsberg, Margrave of Lusatia (his brother-in-law), who defeated the Duke in the Battle of Lubusz. Eventuality Henry I the Bearded, in the campaign between August 1210 and March 1211 could take Lubusz from the Germans, using the confusion after the death of Conrad II (6 May 1210) and the disputes about his heritage among the members of the House of Wettin.

Conflicts with Archbishop Henry Kietlicz and Władysław Odonic
The loss of Kalisz, putting into foreign hands, caused a deep dissatisfaction in Władysław Odonic, who considered this land as part of his patrimony. The young prince (at that time around 16 years) managed to gain the support of the Greater Poland nobles and foremost the Archbishop of Gniezno, Henry Kietlicz, who wanted the opportunity to obtain from Spindleshanks privileges for the local Church and thus limit the power of the ruling house.

However, despite the efforts of both Odonic and Archbishop Kietlicz, the rebellion was short-lived and unsuccessful. Both Kietlicz and Władysław Odonic had to flee to the court of Henry I the Bearded. The excommunication launched by Kietlicz against Spindleshanks was from little help to the insurgents, because of the support given to Mieszko III's son by Arnold II, Bishop of Poznań.

Somewhat surprising was the reaction to these events by Henry I the Bearded, who not only accepted the exiles, but also endowed Władysław Odonic with the Duchy of Kalisz, however, with the condition to return to him after he regained his inheritance. At the same time, the Archbishop Kietlicz went to Rome, where he had a personal meeting with Pope Innocent III. The protest made to the Holy See successfully blocked the attempt to appeal the curse made by Spindleshanks. The Pope also instructed the other Polish princes to help the Archbishop of Gniezno in returning to his diocese.

Congress of Głogów and reconciliation with Archbishop Kietlicz
Henry I the Bearded became a mediator between the warring parties, and on Christmas Day of 1208 he invited the two Greater Poland Dukes, the Archbishop of Gniezno and the Bishops of Wroclaw, Lubusz and Poznań to a meeting in Głogów. After long discussions, a settlement was finally reached between Spindleshanks and the Archbishop Kietlicz, who could return to Gniezno with all his goods restored, in exchange for lifting the anathema against the Duke. However, the conflict between uncle and nephew remained unsolved.

Congress of Borzykowa
In 1210 Spindleshanks supported the efforts of Mieszko I Tanglefoot, who wanted the restitution of the Testament of Bolesław III Wrymouth, under which the Silesian branch are the rightful overlords of Poland. At this point, Władysław was probably the immediate oldest member of the Piast dynasty after Mieszko I, and therefore, he certainly expect that after the imminent death of the venerable Duke of Racibórz he could receive the title of High Duke and the Duchy of Kraków. However, according to some historians, Henry I the Bearded was older than Spindleshanks. This was most probable, and was reflected in the bull issued by Pope Innocent III on 9 June 1210, where the Holy See demanded the restitution of all the hereditary rights of the Silesian branch according to Bolesław III's testament and also excommunicated Leszek I the White; this edict was made by the request of an anonymous Duke of Silesia, which could have only been Henry I the Bearded (because Mieszko I used the title of Duke of Raciborz-Opole). The situation became quite confused, as nobody was sure who held the real power.

In July 1210 Leszek I the White, Henry I the Bearded, Konrad I of Masovia and Władysław Odonic met with the local Bishops at the Synod of Borzykowa, with the purpose to solve the problematic and mysterious Papal Bull. Mieszko I Tanglefoot wasn't present at the meeting; with an army and thanks to the support of the Gryfici family, he could enter in Kraków and easily took Wawel. However, Archbishop Kietlicz didn't intend to accept the existing situation, and having received from the young princes and the local Church hierarchy words of support, began his efforts in Rome to withdraw the fateful Bull. These treatments were successful, and when in May 1211 Mieszko I Tanglefoot died, Leszek I the White was able to return to the throne of Kraków. The intentions of the older generation had failed.

Early rise of Archbishop Kietlicz and Władysław Odonic
In 1215 Władysław Spindleshanks' position was further weakened by the growth of the power of Archbishop Henry Kietlicz, who supported the provisions of IV Lateran Council, and the subsequent congress of the Junior princes in Wolbórz, where Leszek I the White, Konrad I of Mazovia, Władysław Odonic and Casimir I of Opole not only agreed to extend the economic and legal benefits for the Church, but also supported the claims of Odonic to obtain his rightful inheritance. Finally, in 1216, in order to avoid an armed confrontation, Spindleshanks gave Odonic the district who previously belonged to his father (the exact territory was a matter of dispute between historians: some believed that Odonic received Southern Greater Poland with the Obra River as frontier, and others consider that the young prince received the entire district of Poznań together with his castle). The agreement between uncle and nephew was confirmed by a Bull of Pope Honorius III issued on 9 February 1217. There has also been an official reconciliation with the Archbishop Kietlicz, who received the privilege from Spindleshanks to receive the revenues from the cistercian monastery of Łekno.

Fall of Archbishop Kietlicz and the Treaty with Leszek I the White
The terms of the reconciliation accorded in 1216 lasted less than a year. The proud and ambitious attitude of Archbishop Kietlicz effectively discouraged his supporters and stopped his meddling in Piast Dukes affairs. His importance suffered a further decline after the defeat of the policies of Pope Honorius III.

In 1217 an unexpected treaty was concluded between the previous antagonists Leszek I the White and Władysław Spindleshanks, under which if one or both rulers died without male issue, the other could inherit all his domains. This agreement clearly affected the interests of the Duke of Kalisz Władysław Odonic, Spindleshanks' nearest male relative.

Deposition of Władysław Odonic
In the same year the Duke of Greater Poland took advantage from the benevolent neutrality of Henry I the Bearded and finally decided to resolve the conflict with Odonic and took the district of his nephew, forcing him to flee the country. The formal alliance between Spindleshanks and Henry I the Bearded (similar to the previous agreement with Leszek I the White) took place at the end of 1217 or early 1218, during an assembly in Sądowel, through the mediation of the Bishops Paweł II of Poznań and Wawrzyniec of Lubusz. For unknown reasons, the content of the arrangements was beneficial only to the Duke of Greater Poland, who not only received the permission to retain Odonic's district (which included parts of Kalisz, who under the agreement of 1206, was returned to Silesia), but also obtain the district of Lubusz (captured in 1209 by the Margrave of Lusatia Conrad II but recovered by Henry I the Bearded one year later) during his lifetime. The agreement of Sądowel was ratified by a special papal bull issued on 9 May 1218, which further broke down the power of Archbishop Kietlicz.

The first test of the Triumvirate (Władysław III Spindleshanks, Henry I the Bearded and Leszek I the White) was the death in 1219 of Archbishop Henry Kietlicz and the common choice for the post of Archbishop, the chancellor Wincenty z Niałka, one of Spindleshanks' closest associates.

Return of Władysław Odonic
Despite the many benefits of Władysław Spindleshanks received in the congress of Sądowel he didn't participate in a national campaign against the pagan Prussians. The reason for this were the actions of his nephew Władysław Odonic, who, thanks to the hospitality and collaboration of Swantopolk II of Pomerania (probably Odonic's brother-in-law) began his struggle against the authority of his uncle. The situation worsened when, in October 1223, Odonic surprisingly attacked and managed to conquer the town of Ujście, and soon afterwards (in 1225) the adjacent district of Nakło.

Spindleshanks' situation became more complicated after the loss of Lubusz in 1225, captured by Louis IV, Landgrave of Thuringia, who took advantage from the constants fights of the Greater Poland Duke with his nephew and could conquer this important territory.

New phase in the War against Władysław Odonic. Defeat at Ujście
The decisive battle between uncle and nephew took place in 1227. Spindleshanks sent an army under the command of the voivode Dobrogost besieged Ujście, but he couldn't take the strong local fortress, and on 15 July, Odonic surprisingly attacked the voivode, who was completely defeated and killed. Thanks to this victory, Władysław Odonic was able to take control over almost all Greater Poland; however, Odonic's ally Swantopolk II unexpectedly broke the existing treaty, took Nakło and proclaimed himself Duke, ended his homage to Leszek I the White.

Congress of Gąsawa and murder of Leszek I the White
The alliance of his nephew with the Pomeranian ruler put Spindleshanks' rule in jeopardy, and he feared that he could lose the remain of his lands; so, he decided to make a pacific solution to his disputes with Odonic. On St. Martin's day (11 November) 1227 a solemn congress of Piast rulers, bishops and nobles in the small Kuyavian district of Gąsawa was convened, where this and others delicate issue were discussed in order to take further steps. In addition to the instigator of the reunion, Leszek I the White, were also present his brother Konrad I of Masovia, Henry I the Bearded, Wladyslaw Odonic (whose assistance is disputed by historians), the entire episcopate and numerous representatives of Polish magnate families. For unknown reasons, Władysław Spindleshanks didn't appear in Gąsawa, although is believed that both Archbishop Wincenty of Gniezno and Bishop Paweł II of Poznań watched his interests. Nobody expected the tragedy, which occurred on the morning of 24 November: during a short break between the deliberations in the town of Marcinkowo Górne, a group of Pomeranians attacked both Leszek I the White and Henry I the Bearded; Leszek I was killed and Henry I severely wounded, but did survive.

Contemporary sources and later historiography clearly recognize Swantopolk II as the crime's author. However, some historians believed that Władysław Odonic was an accomplice, passing all the plans and conversations to the Pomeranian ruler during the congress (according to the most recent work of Tomasz Jurek). Historians speculated that in 1227 the hostility between the Duke of Pomerania and Odonic suddenly appeared after Swantopolk II took Nakło. According to the proponents of the view that Odonic participated in the Gąsawa crime, believed that the capture of Nakło was only a distraction from the true intentions of Swantopolk II and Odonic. There are also other versions from these events, but because of shortage of resources and ambiguity there are several theories. Some historians believe that Władysław Spindleshanks was involved in Leszek I's death, because it was him, and not Swantopolk II, who obtain the greatest benefits from the crime. This is though very unlikely, as Władysław was later entrusted with the protection of Leszek's son, Bolesław, and the widow duchess Grzymisława wouldn't do such a thing as giving her son to her husband's murderer.

Recovery of the Kraków throne
After the crime of Gąsawa Władysław Spindleshanks turns directly to the offensive. At the beginning of next year and under unknown circumstances, the Duke of Greater Poland, with the help of Silesian troops, could defeat his nephew Odonic, who was taken prisoner. Spindleshanks then went to Lesser Poland, where he present his claim over the throne of Kraków under the basis of the agreement of mutual succession between him and Leszek I the White signed in 1217. Although the Duke of Kraków leave a one-year-old son, Bolesław V, it was clear that until he reached the proper age, the rule over Kraków had to be taken over by someone else. At the same time, Leszek I's brother Konrad I of Masovia appears in Lesser Poland and also put his claim over the Kraków throne.

The formal election of the new High Duke of Poland was made at a meeting in Wiślica on 5 May 1228, where most of the powerful nobles gathered around the Bishop of Kraków, Iwo Odrowąż, the voivode Marek z Brzeźnicy, Governor of Kraków and Pakosław the Old, voivode of Sandomierz. There was rejected the candidacy of Konrad I of Masovia in favor of Spindleshanks.

Congress of Cienia
The choice of Władysław Spindleshanks as High Duke wasn't unconditional choice, because during an assembly organized in Cienia Pierwsza he was compelled to sign two important documents. In the first, the Duke of Greater Poland ensured several privileges to the Church, and even expanded it. The second was about the infant son of Leszek I the White, Bolesław V: the new High Duke took over his guardianship and making him his general heir. At the same time he promised not introduce any new law without the consent of the nobility and clergy of Lesser Poland. In this way, for the first time, the royal power in Poland was made by election. Spindleshanks assumed the direct rule only over Kraków: the authority over Sandomierz was handed by Bolesław V's mother Grzymislawa, although formally, because at the end remained under the control of the High Duke.

Election of Henry I the Bearded as Governor of Krakow
Unfortunately, the political situation soon turned against Władysław Spindleshanks. His nephew Władysław Odonic, defeated and imprisoned by him, could escape to Płock and resume the war against him, which made the Duke of Greater Poland unable to prepare for the expected invasion against Konrad I of Masovia (who became now an ally of Odonic). Therefore, he decided with the approval of Kraków citizens (led by the powerful families of Odrowąż and Gryfici), to choose Silesian Duke Henry I the Bearded as ruler of the city, but only with the title of governor. Spindleshanks concession was given probably for the military support that Henry I give to him; in addition, the Silesian Duke obtain the promise of inheritance over Greater Poland, which was indeed a violation of the provisions contained in the Congress of Cienia, where Spindleshanks declared that Bolesław V was his heir.

War against Konrad I of Masovia and Władysław Odonic
Konrad I's military attack on Lesser Poland took place in the summer of 1228. The expedition, however, didn't bring success, because he was surprisingly attacked by Prince Henry, eldest son and heir of Henry I the Bearded, who successfully defeated the Masovian Duke in the Battles of Międzyborzem, Skałą and Wrocieryżem. Konrad didn't give up and one year later he again started military operations, this time with better results, especially after the capture and imprisonment of Henry I after a supposed meeting in Spytkowice; this event successfully paralyzed the opponents of his late brother Leszek the White and Konrad managed to control most of Lesser Poland, although he released Henry I from captivity thanks to the efforts of his wife Hedwig of Andechs. Immediately, he deprived his nephew Bolesław V from the Duchy of Sandomierz and invested his own son Bolesław with this land. Shortly thereafter, Konrad I and his ally Odonic began the direct war against Spindleshanks. Konrad I unsuccessfully besieged Kalisz, despite the help of Russian troops. Spindleshanks, too busy in his fight against Odonic in the north, couldn't came in time to aid the city; however, the powerful city walls were too much for the Silesian Duke, who was forced to withdraw.

Defeat and escape
Spindleshanks was soon defeated by his nephew under unknown circumstances, and forced to flee at the court of Duke Casimir I of Opole in Racibórz. The deposition of young Bolesław V by his uncle was the excuse for Henry I to attack the Masovian Duke. Spindleshanks also took advantage of this, and renewed his alliance with the Silesian Duke, with the formally transfer of all his rights over both Greater and Lesser Poland to Henry I.

Last attempt to recover Greater Poland
In the spring of 1231 Henry I made his last expedition with Spindleshanks against Władysław Odonic. Despite initial success, thanks to the help gave by Paweł, Bishop of Poznań, and Greater Poland noble families Nałęczów, Łabędziów and Niałków, ended in failure at the walls of Gniezno.

Mysterious death and succession
The expedition against his nephew Odonic was the last political activity of Spindleshanks. Following the information of medieval sources, although not properly confirmed by other sources of information, the demise of the former Duke of Greater Poland was under scandalous circumstances. According to the chronicles from the Cistercian French monk Alberic of Trois-Fontaines the almost seventy-years-old Spindleshanks was murdered in Środa Śląska by a German girl whom he tried to rape. According to some historians the story is not about Władysław Laskonogi, but his nephew Władysław Odonic.

Another source who confirm the unworthy conduct of Spindleshanks came from Jan Długosz, who wrote that in the last year of his life his subjects despised him because of his "fornication with prostitutes".

The date of death of Władysław III Spindleshanks was generally placed on 3 November 1231 (another proposed date, 18 August, was suggested only by Jan Długosz, wasn't confirmed, and is rejected by historians).

It is not known where he was buried. Some researchers, based on the information that the Duke died in exile, believes that Władysław III Spindleshanks was buried in Silesia, perhaps in Racibórz. Others, based on late chroniclers, assumes that he was buried in the Benedictine monastery in Lubiń.

At his death, Henry I the Bearded, by virtue of the inheritance treaty, became the main claimant over both Greater and Lesser Poland, but his rights over this areas where soon contested and he had to fight to conquer both.

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

title: Władysław III Spindleshanks


text:
Wikipedia:Articles for deletion/The Bells

Older AfD
From Cleanup: The Bells - source text (imported from Cleanup by SimonP)

* Wikipedia is not the Collected Works of Edgar Allan Poe. 00:43, 4 Jun 2004 (UTC)

---

Newer AfD
Listed for speedy deletion, but I think it should be handled here. - UtherSRG 02:00, 26 Jul 2004 (UTC)

 * Transcribe to WikiSource. - UtherSRG 02:00, 26 Jul 2004 (UTC)
 * Delete: Not sure about Wikisourcing it, as it contains errors and odd formatting. Geogre 03:14, 26 Jul 2004 (UTC)
 * Ok... so cleanup before transwiki. Wikisource? WikiBooks? - UtherSRG 11:42, 26 Jul 2004 (UTC)
 * Note this article has been through the vfd process before, and was awaiting transwiki to wikisource. Although looking at the last deletion debate you'd be hard pressed to say it reached any form of consensus. -- Graham  ☺ | Talk 12:59, 26 Jul 2004 (UTC)
 * For the record, I was the only one to vote last time around, and it wound up locked when I tried to relist it, so I shunted it to speedy. Even though that didn't work, at least now it's gotten noticed. DS 14:14, 28 Jul 2004 (UTC)

 * Delete and start from scratch. Gamaliel 15:59, 26 Jul 2004 (UTC)
 * I have got to say that would be no loss. It's not really central to the Poe canon, and it's not a tremendously studied poem. Geogre 03:06, 27 Jul 2004 (UTC)


text:
Jerónimo Lobo

Jerónimo Lobo (1595 – 29 January 1678) was a Portuguese Jesuit missionary. He took part in the unsuccessful efforts to convert Ethiopia from the native Ethiopian church to Roman Catholicism until the expulsion of the Jesuits in 1643. Afterwards he wrote an account of his time in Ethiopia, Itinerário, which is an important source for the history and culture of that country.

Life
He was born in Lisbon the third of at least five sons and six daughters to Francisco Lobo da Gama, the Governor of Portuguese Cape Verde, and Maria Brandão de Vasconcelos. He entered the Order of Jesus at the age of 14. In 1621 he was ordained a priest and was ordered as a missionary to India, and after surviving an attack on the fleet carrying him by English and Dutch ships off Portuguese Mozambique a year later, he arrived at Goa in December 1622.

With the intention of proceeding to Ethiopia, whose Nəgusä nägäst Susenyos I had been converted to Roman Catholicism by Pedro Páez, he left India in 1624. He struggled to overcome the difficulty that Ethiopia controlled none of the northern coastline, first disembarking at Pate and attempted to reach his destination along the Jubba River through country controlled by the Oromo, but was forced to return. Then in 1625 he set out again, accompanied by Afonso Mendes, the Catholic Patriarch of Ethiopia, and eight missionaries, landing at Beilul, a port on the coast of the Red Sea controlled by the king of Dankali, vassal to the Emperor of Ethiopia. After a month spent crossing the desert into the Ethiopian highlands, the party reached Fremona, where Lobo assumed the responsibilities of superintendent of the missions in Tigray.

His other activities included recovering the remains of Cristóvão da Gama, who had been captured and executed by Ahmad ibn Ibrihim al-Ghazi in 1542, at the request of his great nephew Francisco da Gama, Conde da Vidigueira and Governor-general of India. He also served as a missionary to the southwest of Lake Tana, where he visited the source of the Blue Nile in 1629.

The abdication of Emperor Susenyos (1632) deprived the Catholics of their protector; his successor, Fasilides, first confined them once again at Fremona, then in 1634 Lobo and his companions were exiled from Ethiopia, who were exposed to robbery, assaults and other indignities by the local population before reaching the Ottoman Naib at Massawa. He sent them to his superior at Suakin, where the Pasha forced the party to pay a ransom before they could proceed to India. Despite settling for a ransom of 4300 patacas (which he borrowed from local Banyan merchants), at the last moment the Pasha insisted on keeping Patriarch Mendes and three other senior priests for further money.

Once Lobo reached Diu, he left for Goa by canoe, arriving at the provincial capital on 8 December 1634. There he attempted to convince viceroy Miguel de Noronha, conde de Linhares to send an armament to the Red Sea to capture Suakin and Massawa, free the patriarch by force, and restore Catholicism to Ethiopia. Although the Viceroy was willing to make a punitive expedition against Suakin to free the Patriarch, he did not want to overextend Portuguese forces and garrison either port. Unwilling to settle for just freeing the patriarch, Lobo embarked for Portugal, and after he had been shipwrecked on the coast of Natal, then captured by pirates, he arrived at Lisbon. Neither at this city, however, nor at Madrid and Rome, was any approval given to Lobo's plan.

He accordingly returned to India in 1640, and was elected rector, and afterwards provincial, of the Jesuits at Goa. After some years he returned to his native city, where he died.

Writings
A number of Lobo's writings have survived. He entered into a correspondence with Henry Oldenburg of the Royal Society concerning the source of the Nile, which likely led to the publication in London of a little book entitled ''A Short Relation of the River Nile, of its source and current; of its overflowing the campagnia of Ægypt, until it runs into the Mediterranean and of other curiosities: written by an eye-witnesse, who lived many years in the chief kingdoms of the Abyssine Empire. Translated by Sir Peter Wyche''.

Gabriel Pereira reported in 1903 that he had found three short works in manuscript by Lobo in the library of the Duke of Palmela, and in 1966 Fr. Manuel Gonçalves da Costa discovered in the Ajuda library at Lisbon another short work of Lobo, Breve Notícia e Relação de Algumas Cousas Certas não vulgares, e dignas de se saberem, escritas e [sic] instância de Curiosos, which repeated the topics of A Short Relation.

His best known work is his memoirs of the years 1622-1640, which cover his voyage to India, his experiences in Ethiopia, and his journey back to Portugal; his Itinerário, however, was not published during his lifetime. Baltasar Teles made large use of Lobo's writing in his História geral da Ethiópia a Alta (Coimbra, 1660), often erroneously attributed to Lobo, but incorporated much from Manuel de Almeida's manuscript work. Lobo's own narrative was translated from a copy owned by the Count of Ericeira by the Abbé Joachim le Grand into French in 1728, under the title of Voyage historique d'Abissinie. An English abridgement of Le Grand's edition by Dr. Samuel Johnson was published in 1735 (reprinted 1789).

Fr. da Costa discovered another manuscript of Lobo's work in the Biblioteca Pública at Braga in 1947. This was not the same manuscript that le Grand translated; both were copies, with variations, of the original autograph left at the Casa de São Roque at the time of Lobo's death. The whole of this manuscript was translated by Donald M. Lockhart, and published with an introduction and notes by C.F. Beckingham by the Hakluyt Society in 1984.

title: Jerónimo Lobo


text:
Entropic uncertainty

In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations.

In 1957, Hirschman considered a function f and its Fourier transform g such that
 * $$g(y) \approx \int_{-\infty}^\infty \exp (-2\pi ixy) f(x)\, dx,\qquad f(x) \approx \int_{-\infty}^\infty \exp (2\pi ixy) g(y)\, dy ~,$$

where the  "≈" indicates convergence in $L$2, and normalized so that (by Plancherel's theorem),
 * $$ \int_{-\infty}^\infty |f(x)|^2\, dx = \int_{-\infty}^\infty |g(y)|^2 \,dy = 1~.$$

He showed that for any such functions the sum of the Shannon entropies is non-negative,
 * $$ H(|f|^2) + H(|g|^2) \equiv - \int_{-\infty}^\infty |f(x)|^2 \log |f(x)|^2\, dx - \int_{-\infty}^\infty |g(y)|^2 \log |g(y)|^2 \,dy \ge 0. $$

A tighter bound,

was conjectured by Hirschman and Everett, proven in 1975 by W. Beckner and in the same year interpreted as a generalized quantum mechanical uncertainty principle by Białynicki-Birula and Mycielski. The equality holds in the case of Gaussian distributions. Note, however, that the above entropic uncertainty function is distinctly different from the quantum Von Neumann entropy represented in phase space.

Sketch of proof
The proof of this tight inequality depends on the so-called (q, p)-norm of the Fourier transformation. (Establishing this norm is the most difficult part of the proof.)

From this norm, one is able to establish a lower bound on the sum of the (differential) Rényi entropies, $H_{α}(|f|²)+H_{β}(|g|²)$, where $1/α + 1/β = 2$, which generalize the Shannon entropies. For simplicity, we consider this inequality only in one dimension; the extension to multiple dimensions is straightforward and can be found in the literature cited.

Babenko–Beckner inequality
The (q, p)-norm of the Fourier transform is defined to be

 * $$\|\mathcal F\|_{q,p} = \sup_{f\in L^p(\mathbb R)} \frac{\|\mathcal Ff\|_q}{\|f\|_p},$$  where $$1 < p \le 2~,$$   and $$\frac 1 p + \frac 1 q = 1.$$

In 1961, Babenko found this norm for even integer values of q. Finally, in 1975, using Hermite functions as eigenfunctions of the Fourier transform, Beckner proved that the value of this norm (in one dimension) for all q ≥  2  is
 * $$\|\mathcal F\|_{q,p} = \sqrt{p^{1/p}/q^{1/q}}.$$

Thus we have the Babenko–Beckner inequality that
 * $$\|\mathcal Ff\|_q \le \left(p^{1/p}/q^{1/q}\right)^{1/2} \|f\|_p.$$

Rényi entropy bound
From this inequality, an expression of the uncertainty principle in terms of the Rényi entropy can be derived.

Letting $$g=\mathcal Ff$$, 2α=p,  and 2β=q,   so that  $1/α + 1/β = 2$  and   1/2<α<1<β,  we have
 * $$\left(\int_{\mathbb R} |g(y)|^{2\beta}\,dy\right)^{1/2\beta}

\le \frac{(2\alpha)^{1/4\alpha}}{(2\beta)^{1/4\beta}} \left(\int_{\mathbb R} |f(x)|^{2\alpha}\,dx\right)^{1/2\alpha}. $$ Squaring both sides and taking the logarithm, we get
 * $$\frac 1\beta \log\left(\int_{\mathbb R} |g(y)|^{2\beta}\,dy\right)

\le \frac 1 2 \log\frac{(2\alpha)^{1/\alpha}}{(2\beta)^{1/\beta}} + \frac 1\alpha \log \left(\int_{\mathbb R} |f(x)|^{2\alpha}\,dx\right). $$

Multiplying both sides by
 * $$\frac{\beta}{1-\beta}=-\frac{\alpha}{1-\alpha}$$

reverses the sense of the inequality,
 * $$\frac {1}{1-\beta} \log\left(\int_{\mathbb R} |g(y)|^{2\beta}\,dy\right)

\ge \frac\alpha{2(\alpha-1)}\log\frac{(2\alpha)^{1/\alpha}}{(2\beta)^{1/\beta}} - \frac{1}{1-\alpha} \log \left(\int_{\mathbb R} |f(x)|^{2\alpha}\,dx\right) ~. $$

Rearranging terms, finally yields an inequality in terms of the sum of the Rényi entropies,
 * $$\frac{1}{1-\alpha} \log \left(\int_{\mathbb R} |f(x)|^{2\alpha}\,dx\right)

+ \frac {1}{1-\beta} \log\left(\int_{\mathbb R} |g(y)|^{2\beta}\,dy\right) \ge \frac\alpha{2(\alpha-1)}\log\frac{(2\alpha)^{1/\alpha}}{(2\beta)^{1/\beta}}; $$
 * $$ H_\alpha(|f|^2) + H_\beta(|g|^2) \ge \frac 1 2 \left(\frac{\log\alpha}{\alpha-1}+\frac{\log\beta}{\beta-1}\right) - \log 2    ~.$$

Note that this inequality is symmetric with respect to $α$  and $β$:  One no longer need assume that $α<β$;  only that they are positive and not both one, and that  1/α + 1/β   = 2. To see this symmetry, simply exchange the rôles of i  and −i  in the Fourier transform.

Shannon entropy bound
Taking the limit of this last inequality as α, β → 1 yields the less general Shannon entropy inequality,
 * $$H(|f|^2) + H(|g|^2) \ge \log\frac e 2,\quad\textrm{where}\quad g(y) \approx \int_{\mathbb R} e^{-2\pi ixy}f(x)\,dx~,$$

valid for any base of logarithm, as long as we choose an appropriate unit of information, bit, nat, etc.

The constant will be different, though, for a different normalization of the Fourier transform, (such as is usually used in physics, with normalizations chosen so that ħ=1 ), i.e.,
 * $$H(|f|^2) + H(|g|^2) \ge \log(\pi e)\quad\textrm{for}\quad g(y) \approx \frac 1{\sqrt{2\pi}}\int_{\mathbb R} e^{-ixy}f(x)\,dx~.$$

In this case, the dilation of the Fourier transform absolute squared by a factor of 2$π$ simply adds log(2$π$) to its entropy.

Entropy versus variance bounds
The Gaussian or normal probability distribution plays an important role in the relationship between variance and entropy: it is a problem of the calculus of variations to show that this distribution maximizes entropy for a given variance, and at the same time minimizes the variance for a given entropy. In fact, for any probability density function $$\phi$$ on the real line, Shannon's entropy inequality specifies:
 * $$H(\phi) \le \log \sqrt {2\pi eV(\phi)},$$

where H is the Shannon entropy and V is the variance, an inequality that is saturated only in the case of a normal distribution.

Moreover, the Fourier transform of a Gaussian probability amplitude function is also Gaussian—and the absolute squares of both of these are Gaussian, too. This can then be used to derive the usual Robertson variance uncertainty inequality from the above entropic inequality, enabling the latter to be tighter than the former. That is (for ħ=1), exponentiating the Hirschman inequality and using Shannon's expression above,
 * $$1/2 \le \exp (H(|f|^2)+H(|g|^2))        /(2e\pi)    \le \sqrt {V(|f|^2)V(|g|^2)}~.$$

Hirschman explained that entropy—his version of entropy was the negative of Shannon's—is a "measure of the concentration of [a probability distribution] in a set of small measure." Thus a low or large negative Shannon entropy means that a considerable mass of the probability distribution is confined to a set of small measure.

Note that this set of small measure need not be contiguous; a probability distribution can have several concentrations of mass in intervals of small measure, and the entropy may still be low no matter how widely scattered those intervals are. This is not the case with the variance: variance measures the concentration of mass about the mean of the distribution, and a low variance means that a considerable mass of the probability distribution is concentrated in a contiguous interval of small measure.

To formalize this distinction, we say that two probability density functions $$\phi_1$$ and $$\phi_2$$ are equimeasurable if

 * $$\forall \delta > 0,\,\mu\{x\in\mathbb R|\phi_1(x)\ge\delta\} = \mu\{x\in\mathbb R|\phi_2(x)\ge\delta\},$$

where $μ$ is the Lebesgue measure. Any two equimeasurable probability density functions have the same Shannon entropy, and in fact the same Rényi entropy, of any order. The same is not true of variance, however. Any probability density function has a radially decreasing equimeasurable "rearrangement" whose variance is less (up to translation) than any other rearrangement of the function; and there exist rearrangements of arbitrarily high variance, (all having the same entropy.)

title: Entropic uncertainty


text: User talk:202.12.144.21

title: User talk:202.12.144.21