The Prisoner of Benda
Encyclopedia
"The Prisoner of Benda" is the 10th episode of the sixth season
Futurama (season 6)
Futurama sixth production season originally aired on Comedy Central from June 24, 2010 to September 8, 2011 and consisted of 26 episodes. The season marks the change of networks from Fox to Comedy Central.David X...

 of the animated sitcom, Futurama
Futurama
Futurama is an American animated science fiction sitcom created by Matt Groening and developed by Groening and David X. Cohen for the Fox Broadcasting Company. The series follows the adventures of a late 20th-century New York City pizza delivery boy, Philip J...

. It aired on Comedy Central
Comedy Central
Comedy Central is an American cable television and satellite television channel that carries comedy programming, both original and syndicated....

 on August 19, 2010. In the episode, Professor Farnsworth
Hubert J. Farnsworth
Professor Hubert J. Farnsworth, or simply The Professor, is a fictional character in the American animated television series Futurama. He is voiced by Billy West using a combination of impressions of Burgess Meredith and Frank Morgan. Farnsworth is the proprietor of the Planet Express delivery...

 and Amy
Amy Wong
Amy Wong, voiced by Lauren Tom, is a fictional character, one of the main characters from the Fox and Comedy Central television animated series Futurama. She works as an intern at Planet Express...

 build a machine that allows them to switch minds so that they may each pursue their lifelong dreams. However, they learn that the machine cannot be used twice on the same pairing of bodies. To try to return to their rightful bodies, they involve the rest of the crew in the mind switches, leaving each member free to pursue their own personal endeavors in a different crew member's body.

The episode was written by Ken Keeler
Ken Keeler
Kenneth "Ken" Keeler is an American television producer and writer. He has written for numerous television series, most notably The Simpsons and Futurama. According to an interview with David X. Cohen, he proved a theorem which appears in the Futurama episode "The Prisoner of Benda".-Career:After...

 and directed by Stephen Sandoval and was met with positive reviews from critics. The issue of how each crew member can be restored to their correct body given the limitation of the switching device is solved in the episode by what David X. Cohen
David X. Cohen
David Samuel Cohen , primarily known as David X. Cohen, is an American television writer. He has written for The Simpsons and he is the head writer and executive producer of Futurama.-Early life:...

 described in an interview as a mathematical theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...

 proved by Keeler, a Ph.D in Mathematics. The title and the story subplot is a reference to the 1894 adventure novel
Adventure novel
The adventure novel is a genre of novels that has adventure, an exciting undertaking involving risk and physical danger, as its main theme.-History:...

 The Prisoner of Zenda
The Prisoner of Zenda
The Prisoner of Zenda is an adventure novel by Anthony Hope, published in 1894. The king of the fictional country of Ruritania is drugged on the eve of his coronation and thus unable to attend his own coronation. Political forces are such that in order for the king to retain his crown his...

by English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...

 novelist Anthony Hope
Anthony Hope
Sir Anthony Hope Hawkins, better known as Anthony Hope , was an English novelist and playwright. Although he was a prolific writer, especially of adventure novels, he is remembered best for only two books: The Prisoner of Zenda and its sequel Rupert of Hentzau...

. Series writer Eric Rogers considers this his favorite episode of the season.

Plot

Professor Farnsworth
Hubert J. Farnsworth
Professor Hubert J. Farnsworth, or simply The Professor, is a fictional character in the American animated television series Futurama. He is voiced by Billy West using a combination of impressions of Burgess Meredith and Frank Morgan. Farnsworth is the proprietor of the Planet Express delivery...

 switches bodies with Amy
Amy Wong
Amy Wong, voiced by Lauren Tom, is a fictional character, one of the main characters from the Fox and Comedy Central television animated series Futurama. She works as an intern at Planet Express...

 using a new invention so that he can relive his youth. Likewise, Amy is reminiscent of her younger days of constantly eating and wishes to use the Professor's skinny body to gorge herself with food once again. Later, they find they cannot switch their bodies back with each other, because the device will not operate on the same pairing of bodies. The Professor thoughtlessly suggests they might be able to switch back to their original bodies with a third person. Bender switches bodies with the Professor (Amy's body) so he can perform a robbery without being identified. After realizing his mistake, the Professor, now in Bender's body, tires of trying to solve the problem. He decides to live a life of daring stunts and joins a robot circus.

Bender, now in Amy's body, goes aboard the yacht of Robo-Hungarian
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...

 emperor Nikolai, planning to steal his crown. He knocks out Nikolai's first officer and cousin. After binding and gagging him, he realises his timing is off and accidentally throws his watch through a metal detector, and is captured by the Emperor. When Bender states that he is really a robot who has switched bodies with a human, Nikolai reveals that he feels trapped by his wealth and wishes to live the life of a normal, "peasant" robot. Bender tricks him into switching bodies with a robot wash bucket and inhabits Nikolai's body, planning to live like an emperor. However, he discovers that Nikolai's fiancée and first officer are plotting to kill him, having been having an affair and planning to blame the burglar. They chase him to a meeting. Bender is saved with the assistance of the Professor, who is fired there in a cannon, and the circus' loyal Robo-Hungarian citizens.

Meanwhile, Leela switches bodies with Amy, thus inhabiting the Professor's body, when she comes to believe that Fry
Philip J. Fry
Philip J. Fry, known simply as Fry, is a fictional character, the main protagonist of the animated science fiction sitcom Futurama. He is voiced by Billy West using a version of his own voice as he sounded when he was 25.-Character overview:...

 only loves her for her beauty. In order to beat Leela at her own game, Fry switches bodies with Dr. Zoidberg in an attempt to repulse Leela. This leads them to one-up each other using various disgusting acts while on a date, which climaxes when the two have sex with each other in their equally grotesque bodies, and reconcile. During this time, Amy has overeaten in Leela's body, making it overweight. She switches bodies with Hermes
Hermes Conrad
Hermes Conrad is a fictional character in the Futurama animated series. He is voiced by Phil LaMarr.- Appearance and personality :Born in 2959, Hermes is a grade 36 bureaucrat from Jamaica. He manages the Planet Express delivery business with responsibilities that include paying bills, giving out...

, so she can continue eating while Hermes slims Leela's body back down. While eating, she witnesses Fry and Leela making out in the Professor and Dr. Zoidberg's bodies and loses her appetite for food. Concurrently, Zoidberg and Nikolai, in the respective bodies of Fry and the robot wash bucket, become friends and attempt to assume the lives of Fry and Bender, blowing up their apartment in the process. The bucket, now in Amy's body, professes its love to Scruffy the Janitor, but he turns it away. Finally, two Globetrotters
Harlem Globetrotters
The Harlem Globetrotters are an exhibition basketball team that combines athleticism, theater and comedy. The executive offices for the team are currently in downtown Phoenix, Arizona; the team is owned by Shamrock Holdings, which oversees the various investments of the Roy E. Disney family.Over...

, Ethan "Bubblegum" Tate and "Sweet" Clyde Dixon, mathematically prove that everyone's minds can be restored using two additional bodies and then successfully do so, with themselves as the extras.

Production

In an interview, David X. Cohen
David X. Cohen
David Samuel Cohen , primarily known as David X. Cohen, is an American television writer. He has written for The Simpsons and he is the head writer and executive producer of Futurama.-Early life:...

 revealed that the episode writer Ken Keeler
Ken Keeler
Kenneth "Ken" Keeler is an American television producer and writer. He has written for numerous television series, most notably The Simpsons and Futurama. According to an interview with David X. Cohen, he proved a theorem which appears in the Futurama episode "The Prisoner of Benda".-Career:After...

, a PhD mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, penned and proved a theorem based on group theory
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...

, and then used it to explain the plot twist in this episode. However, Keeler does not feel it carries enough importance to be designated a theorem, and prefers to call it a proof
Mathematical proof
In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments. That is, a proof must demonstrate that a statement is true in all cases, without a single...

. Cut-the-Knot
Cut-the-knot
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics. The site has won more than 20 awards from scientific and educational publications, including a Scientific American Web Award in 2003,...

, an educational math website created by Alexander Bogomolny, refers to this proof as the "Futurama Theorem."

The episode is based on an irreversible body swap
Body swap
A body swap is a storytelling device seen in a variety of fiction, most often in television shows and movies, in which two people exchange minds and end up in each other's bodies. Alternatively, their minds may stay where they are as their bodies adjust...

 scenario. The proof demonstrates that, no matter how many minds have been swapped, each can be returned to its original body by using only two additional individuals who have yet to swap minds with anyone, and without swapping between the same pair of bodies more than once.

A formal statement is as follows:
Let A be a finite set, and let x and y be distinct objects that do not belong to A. Any permutation of A can be reduced to the identity permutation by applying a sequence of distinct transpositions of A∪{x,y}, each of which includes just one of xy.

The proof

The proof appears on the blackboard in the episode. The proof reduces to treating individual cycle
Cycle (mathematics)
In mathematics, and in particular in group theory, a cycle is a permutation of the elements of some set X which maps the elements of some subset S to each other in a cyclic fashion, while fixing all other elements...

s separately, since all permutation
Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order...

s can also be represented as products of disjoint cycles. So first let be some -cycle on []={}. Without loss of generality, write:

Introduce the two new symbols and , and write:


Let be the transposition that interchanges and . For any } let be the permutation obtained as the (left to right) composition
Function composition
In mathematics, function composition is the application of one function to the results of another. For instance, the functions and can be composed by computing the output of g when it has an argument of f instead of x...

:


Note that these are distinct transpositions, each of which exchanges an element of [] with one of . By routine verification:


That is, reverts the original -cycle to the identity and leaves and switched (without performing ).

Next, let be an arbitrary permutation on []. It consists of disjoint (nontrivial) cycles and each can be inverted as above in sequence after which and can be switched if necessary via , as was desired.

Cultural references

The episode's title and the Robo-Hungarian emperor subplot are references to the 1894 adventure novel
Adventure novel
The adventure novel is a genre of novels that has adventure, an exciting undertaking involving risk and physical danger, as its main theme.-History:...

 The Prisoner of Zenda
The Prisoner of Zenda
The Prisoner of Zenda is an adventure novel by Anthony Hope, published in 1894. The king of the fictional country of Ruritania is drugged on the eve of his coronation and thus unable to attend his own coronation. Political forces are such that in order for the king to retain his crown his...

, in which a king is replaced by a commoner, by English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...

 novelist Anthony Hope
Anthony Hope
Sir Anthony Hope Hawkins, better known as Anthony Hope , was an English novelist and playwright. Although he was a prolific writer, especially of adventure novels, he is remembered best for only two books: The Prisoner of Zenda and its sequel Rupert of Hentzau...

. The episode also references the Turing test
Turing test
The Turing test is a test of a machine's ability to exhibit intelligent behaviour. In Turing's original illustrative example, a human judge engages in a natural language conversation with a human and a machine designed to generate performance indistinguishable from that of a human being. All...

, a philosophical test designed to assess whether a computer can demonstrate true intelligence; actor Nicolas Cage
Nicolas Cage
Nicolas Cage is an American actor, producer and director, having appeared in over 60 films including Raising Arizona , The Rock , Face/Off , Gone in 60 Seconds , Adaptation , National Treasure , Ghost Rider , Bad Lieutenant: Port of Call New Orleans , and...

; and the television character Fat Albert
Fat Albert and the Cosby Kids
Fat Albert and the Cosby Kids is an animated series created, produced, and hosted by comedian Bill Cosby, who also lent his voice to a number of characters, including Fat Albert himself. Filmation was the production company for the series. The show premiered in 1972 and ran until 1985...

.

Broadcast and reception

"The Prisoner of Benda" originally aired on Comedy Central
Comedy Central
Comedy Central is an American cable television and satellite television channel that carries comedy programming, both original and syndicated....

 on August 19, 2010. In its original American broadcast, "The Prisoner of Benda" received 1.774 million viewers, down nearly 150,000 from the previous week's episode, "A Clockwork Origin
A Clockwork Origin
"A Clockwork Origin" is the ninth episode of the sixth season of the animated sitcom, Futurama. It aired on Comedy Central on August 12, 2010. In the episode, Professor Farnsworth leaves Earth after being frustrated by anti-evolutionists' belief in "Creaturism", a form of Creationism...

". It received a 1.2 rating/2% share in the Nielsen ratings
Nielsen Ratings
Nielsen ratings are the audience measurement systems developed by Nielsen Media Research, in an effort to determine the audience size and composition of television programming in the United States...

 and a .8 rating/2% share in the 18–49 demographic, down two tenths of a point from the previous week.

The episode was unanimously well received by critics, who largely praised the episode's complexity and writing. Ken Keeler won a 2011 Writer's Guild Award for writing "The Prisoner of Benda." Zack Handlen of The A.V. Club
The A.V. Club
The A.V. Club is an entertainment newspaper and website published by The Onion. Its features include reviews of new films, music, television, books, games and DVDs, as well as interviews and other regular offerings examining both new and classic media and other elements of pop culture. Unlike its...

 gave the episode a positive review, rating it an A−. Handlen compared the episode favorably to the season 4 episode "The Farnsworth Parabox
The Farnsworth Parabox
"The Farnsworth Parabox" is the fifteenth episode of the fourth production season of Futurama. It first aired June 8, 2003, as the tenth episode in the fifth broadcast season. The episode was written by Bill Odenkirk and directed by Ron Hughart.- Plot :...

", writing, "Really, this is pure silly from beginning to end, using the show's internal logic to arrive in unpredictable places, and bringing to life a piece of fan fiction I doubt anyone has ever had the courage to write. It reminded me more than a little of 'The Farnsworth Parabox': a premise that uses the whole cast to just the right amount." Merrill Barr of Film School Rejects also gave the episode a positive review, praising the character development of Scruffy the Janitor in particular. With respect to the logic puzzle nature of the plot, Barr stated, "I have never understood less of what was going on in a single episode of Futurama. And I couldn't have loved it more." Sean Gandert of Paste
Paste (magazine)
Paste is a monthly music and entertainment digital magazine published in the United States by Wolfgang's Vault. Its tagline is "Signs of Life in Music, Film and Culture."-History:...

 rated the episode 9.1/10. He praised the intricate plot and writing, also comparing it to "The Farnsworth Parabox" and "Teenage Mutant Leela's Hurdles
Teenage Mutant Leela's Hurdles
"Teenage Mutant Leela's Hurdles" is the ninth episode of the fourth production season of Futurama. It first aired on March 30, 2003 as the seventh episode of the fifth broadcast season. The episode was directed by Bret Haaland and written by Jeff Westbrook.-Plot:Professor Farnsworth is chasing...

", writing, "...this sort of intertwined, Altman-esque plot offers up a level of complexity rarely offered by sitcoms, or any episodic television. 'The Prisoner of Benda' was a perfect example of how Futurama takes an extremely simple concept and executes it in a daring and unique way. It's not as showy as 'A Clockwork Origin' or 'The Late Philip J. Fry' from an animation standpoint, but with writing this tight we could be watching stick figures at 8 frames a second and it would still be worth seeing." Robert Canning of IGN
IGN
IGN is an entertainment website that focuses on video games, films, music and other media. IGN's main website comprises several specialty sites or "channels", each occupying a subdomain and covering a specific area of entertainment...

 gave the episode a 9.5/10, stating "'The Prisoner of Benda' was an absolutely stellar episode. The high-concept idea of switching minds/bodies was taking [sic] to extremes and delivered fantastic lines and great laughs throughout." In response to this episode UGO Entertainment critic Alex Zalben concluded that "this season of Futurama, despite a miss or two, has hit what might possibly be a series high for the past few episodes, and I can't wait to watch the rest. Kudos to Comedy Central for bringing back what is now officially the best animated show on TV." Alasdair Wilkins of io9
Io9
io9 is a blog launched in 2008 by Gawker Media. The blog focuses on the subjects of science fiction, futurism, and advancements in the fields of science and technology....

 also praised the episode's mathematical complexity, saying "This episode is maybe the most epically overstuffed Futurama episode ever, with only the intersecting ensemble piece "Three Hundred Big Boys
Three Hundred Big Boys
"Three Hundred Big Boys" is the sixteenth episode of season four of Futurama, which aired June 15, 2003.-Plot:Zapp Brannigan leads an attack on Tarantulon VI, claiming silken artworks. Earth President Richard Nixon gives the riches to the citizens of Earth as a $300 tax rebate. Leela plans to swim...

" even coming close. 'The Prisoner of Benda' easily could have stretched out to a 70-minute DVD movie, but I'm just as happy to see it as 22 minutes of finely concentrated crazy." In an interview, Futurama writer Eric Rogers stated that this was his favorite episode of the season.

External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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