The song "Daisy Bell" sung by Bender during the first montage for his love of the ship is a reference to 2001: A Space Odyssey.
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While the two machines play a cat-and-mouse game, Leela continues to attempt to shut down the brain by popping the tops of its carbonated logic unit similarly to Dave shutting HAL 9000 down in 2001: A Space Odyssey (also winning free admission to Six Flags), which makes the ship even less rational.
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The episode parodies 2001: A Space Odyssey.
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