The Prisoner of Benda
"The Prisoner of Benda" | |
---|---|
Futurama episode | |
Episode no. | Season 7 Episode 10 |
Directed by | Stephen Sandoval |
Written by | Ken Keeler |
Production code | 6ACV10 |
Original air date | August 19, 2010 |
Episode features | |
Opening caption | What happens in Cygnus X-1 stays in Cygnus X-1 |
"The Prisoner of Benda" is the tenth episode in the
The episode was written by
. Series writer Eric Rogers considers this his favorite episode of the season.Plot
The episode begins with Emperor Nikolai of Robo-Hungary visiting. Bender voices a desire to steal his crown, but no one is willing to be his accomplice.
Meanwhile,
Bender — now in Amy's body — goes aboard Nikolai's yacht, planning to steal his crown. He knocks out Nikolai's first officer and cousin. After binding and gagging him, he realizes his timing is off and accidentally throws his watch through a metal detector. He is then 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 for a while. With Bender unable to find his real body, he tricks him into switching bodies with the robot Washbucket and inhabits Nikolai's body, planning to live the life of an Emperor. Washbucket, now in Amy's body, professes her love to
At the circus, the Professor is having a fine time as the world's most indifferent robot daredevil, when he meets the Grande Dame, the robot cannon Big Bertha. He politely asks if he could be shot from her, but she admits that she is so old, it would end her life. He asks if she would like a new, young body, but she turns him down briskly, telling him that her body may be old, but it is still hers to treasure, giving him pause for thought.
Meanwhile, insecure that
In the meantime, Zoidberg and Nikolai, in the respective bodies of Fry and Washbucket, become friends and attempt to assume the lives of Fry and Bender. Zoidberg is completely unused to normal living conditions however, and blows up Bender's apartment.
Back on the yacht, Nikolai's cousin and fiancee reveal to Bender that they have been having an affair, and are planning to kill him and blame the burglar. Even learning he is actually Bender does not change their minds. They chase him to the United Nations General Assembly. Watching from the Robot Circus, the Professor realizes what is going on, but the only way to get there in time would be by Big Bertha's cannon. He is hesitant because this would end her life, but as a loyal Robo-Hungarian she insists, and Bender is saved with the assistance of the Professor - and the circus' twenty loyal Robo-Hungarian robot clowns who travel in his chest compartment.
Finally, two Globetrotters, Ethan "Bubblegum" Tate and "Sweet" Clyde Dixon, mathematically prove that everyone's minds can be restored using two additional bodies. They proceed to do so, using themselves as the extras. Hermes reveals that Amy's temporary fast put her off her food long enough for him to shed some weight and Amy has been cured of her desire to binge-eat, while the Professor has gotten some of the thrills out of his system and learned that his old body is a memento of his life, not a punishment for his age. Realizing that common folk do not have such carefree lives as he had thought, Nikolai makes Clyde a Duke, and as he leaves, Bender realizes that the real crown is still in Nikolai's compartment. Having learned nothing, he begins plotting to re-steal the crown.
The theorem
In a 2010 interview,
In a 2012 interview, David X. Cohen said that this was probably the first time that a mathematical theorem was proven in a television script, and that it was probably Futurama's proudest mathematical moment.[6]
The episode is based on a body swap scenario in which no pair of bodies can swap minds more than once. The proof demonstrates that after any sequence of mind switches, each mind can be returned to its original body by using two additional individuals who have not yet swapped minds with anyone. 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 at least one of x, y.[3]
The proof
The proof appears on the blackboard in the episode. The proof reduces to treating individual cycles separately, since all permutations can also be represented as products of disjoint cycles.[3] So first let π be some k-cycle on [n]={1 ... n}. Without loss of generality, write:
Introduce the two new symbols x and y, and write:
Let (a b) be the
Note that these are distinct transpositions, each of which exchanges an element of [n] with one of x,y. By routine verification:
That is, σ reverts the original k-cycle to the identity and leaves x and y switched (without performing (x y)).
Next, let π be an arbitrary permutation on [n]. It consists of disjoint (nontrivial) cycles and each can be inverted as above in sequence after which x and y can be switched if necessary via (x y), as was desired.
Cultural references
The episode's title and the Robo-Hungarian emperor subplot are references to the 1894
Big Bertha, who shoots the Professor in Bender's body, was also the name of a German Howitzer during World War I.[11]
Broadcast and reception
"The Prisoner of Benda" originally aired on
The episode was unanimously acclaimed by critics, who largely praised the episode's complexity and writing.
References
- ^ Levine, Alaina G. "Profiles in Versatility". American Physics Society. Retrieved 2010-07-20.
- ^ Cohen, David (2010). Futurama volume 5 DVD commentary for the episode "The Prisoner of Benda" (DVD). 20th Century Fox.
- ^ Cut-the-Knot
- ^ The Guardian-James Grime profile
- ^ Grime, James [@jamesgrime] (May 2, 2012). "Video: I once made this video about Futurama and Keeler's Theorem" (Tweet). Retrieved February 15, 2022 – via Twitter.
- ^ "Futurama: Interview mit David X. Cohen, dem Co-Schöpfer der Serie". serienjunkies.de. May 27, 2012. p. 4. Retrieved June 3, 2012.
- ^ Fabien (August 20, 2010). "Futurama - The Prisoner of Benda". Critictoo. Archived from the original on 2010-08-21. Retrieved 2010-08-20.
- ^ a b c Handlen, Zack (August 19, 2010). "Futurama: "The Prisoner Of Benda"". The A.V. Club. Retrieved February 15, 2022.
- ^ a b c d Gandert, Sean (August 20, 2010). "Futurama Review: "The Prisoner of Benda" (6.10)". Paste. Retrieved February 15, 2022.
- ^ a b c Zalben, Alex (August 20, 2010). "Futurama - "The Prisoner of Benda" Recap". UGO Entertainment. Archived from the original on August 23, 2010. Retrieved 2010-08-20.
- ^ "Big Bertha | weapon".
- ^ a b Seidman, Robert (August 20, 2010). "More Thursday Cable: 'Project Runaway' Up; Futurama, Real Housewives of DC Fall + More". TVbythenumbers. Archived from the original on 2012-10-13. Retrieved 2010-08-20.
- ^ a b Barr, Merrill (August 19, 2010). "Review: Futurama — The Prisoner of Benda". Film School Rejects. Archived from the original on March 5, 2016. Retrieved February 15, 2022.
- ^ Gallagher, Danny (August 20, 2010). "'Futurama' - 'The Prisoner of Benda'". HuffPost TV. Archived from the original on June 12, 2012. Retrieved February 15, 2022.
- ^ a b Canning, Robert (August 20, 2010). "Futurama: "The Prisoner of Benda" Review". IGN. Retrieved February 15, 2022.
- ^ a b Wilkins, Alasdair (August 20, 2010). "Futurama's mind-switching mayhem gives us the most depraved sex scene ever". Gizmodo. Retrieved February 15, 2022.
- ^ "WGA Awards". Archived from the original on 2013-01-17. Retrieved 2011-02-06.
- ^ "CGEF Interview with Eric Rogers". Can't Get Enough Futurama. July 2010. Retrieved 2010-08-20.
- ^ "Futurama Preview: "The Prisoner of Benda"". IGN. August 18, 2010. Retrieved February 15, 2022.
External links
- Keeler's theorem and products of distinct transpositions
- "The Prisoner of Benda" at the Infosphere, the Futurama Wiki.
- "The Prisoner of Benda" at IMDb
- "A Prisoner of Benda" at MSN
- The Futurama Theorem at Math Goes Pop
- The Infosphere's take on the Futurama theorem