Spock's Brain
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Spock's Brain was an episode of Star Trek that both Izzy Sinclair and Destrii had seen. Destrii even went so far as to call it her "favourite". She cited "the bit where Sulu has to do the captain's log" as a particularly memorable moment and even quoted back a portion of the log, in unison with Izzy: "Captain Kirk's hunch that Spock's brain is on this planet appears to be correct!" (DWM: Ophidius)
Behind the scenes
The excerpt from the captain's log actually is a direct quote from the episode and it was entered by Sulu. Technically, however, it was a ship's log, rather than a captain's log.