This was Patrick McGoohan's final guest appearance on a television series before his death on January 13, 2009 at the age of 80.
Patrick McGoohan played "Number Six" in a British TV Show called "The Prisoner" (1967.) "Number Six" is a former Government Agent captured like Homer Simpson and trapped on an Isolated Island. In "The Computer Wore Menace Shoes," he is "Number Six" as Homer plays "Number Five." Thus, this is a tip of the Bowler Hat to the British show "The Prisoner" some 33-years later.
The title is a play on Disney's 'The Computer Wore Tennis Shoes.'
After telling Homer that "they keep us here because we know too much," Number Six points to a person filling a cup from the water cooler and says "Number Twenty Seven there knows how to turn water into gasoline." She looks very similar to the character of the Woman played by Virginia Maskell in Arrival (1967).
Blackboard: "I will only provide a urine sample when asked"