At the time of the story, 2075, the Moon (Luna) is used as a penal colony by Earth's government, with the inhabitants living in underground cities. Most inhabitants (called "Loonies") are criminals, political exiles, or descendants thereof. The total population is about three million, with men outnumbering women two to one, so that polyandry is the norm. Although Earth's Protector of the Lunar Colonies (called the "Warden") holds power, in practice there is little intervention in the loose Lunar society.
HOLMES IV ("High-Optional, Logical, Multi-Evaluating Supervisor, Mark IV") is the Lunar Authority's master computer, having almost total control of Luna's machinery on the grounds that a single computer is cheaper than (though not as safe as) multiple independent systems. The story is narrated by Manuel Garcia "Mannie" O'Kelly-Davis, a computer technician who discovers that HOLMES IV has achieved self-awareness and has developed a sense of humor. Mannie names it "Mike" after Mycroft Holmes, brother of Sherlock Holmes, and they become friends.