As our faithful chronicler reminds, on this day in 1967, the Enterprise had their second run-in with conman Harry Mudd (see previously, see also) after an android posing as a crew member hijacks the Enterprise, routing them to an unknown planet populated by androids, lorded over by Mudd I as apparent monarch, including a simulacrum of departed, nagging wife whom he can mute on command.
Mudd reveals that he arrived on this world by chance and is treated well but he is refused leave to depart until or unless he can provide the automatons more masters to study and serve, for which the crew is offered. Although tempting by various standards and accounts, Kirk implores senior staff not to be fooled by obsequiousness and remember their duty to their mission of exploration and one another.
Spock directs Kirk and Mudd to confuse the androids with contradictory and illogical statements, finally presenting a form of the liar’s paradox to the original hijacker, whom the science officer determined was not just a scout or emissary but the central locus of their collective mind. This feedback loop causes the main android to short-circuit, disabling the others. The androids are reprogrammed aligned with their original task of making the planet productive, Mudd paroled to the remain among the synthetic population, who no longer cater to his every wish. The episode was cowritten and directed by David Gerrold and Stephan Kandel, the collaborators who earlier produced “The Trouble with Tribbles” and is consistently ranked among the best storylines from Star Trek: TOS.