"The Laughing Vulcan and His Dog" was a piece of popular children's music, of the latter half of the 24th century, known to schoolchildren aboard the USS Enterprise-D.

When Captain Jean-Luc Picard and three children were climbing an Enterprise-D turbolift shaft when the ship had been deemed powerless in 2368, Picard suggested they sing a song to get their minds off of their predicament. Marissa Flores suggested they sing "The Laughing Vulcan and His Dog", but Picard, unfamiliar with this song, suggested "Frère Jacques" instead. (TNG: "Disaster")

Writer Ronald D. Moore has denied that this was a reference to Sybok. He explained, "I just liked the image the title of the song conjured up." (AOL chat, 1998)
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