Spock

In a parallel universe, Spock was a Vulcan crewmember of the USS Enterprise in the 23rd century.

On one occasion, the Eleventh Doctor recalled memories of his fourth incarnation meeting up with Spock and the command crew of the USS Enterprise to combat a Cyberman invasion of Aprilia III. (IDW: Assimilation²)

Other references
A fictional character named Spock appeared in the science fiction television series Star Trek in the Doctor's universe. When the Third Doctor told Sgt. John Benton that he had visited a parallel universe, Benton asked, "You mean like that Star Trek episode where Spock had a beard?" (PDA: The Face of the Enemy)

"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)

Spock was a character that Rose Tyler associated with a more "professional" approach to the use of technology. Whilst in London in 1941, she once bemoaned the Ninth Doctor's reliance on the sonic screwdriver and conversation as his primary investigative tools. She demanded that he "give [her] some Spock" in their search for a downed Chula ambulance. Later, in an effort to explain to Captain Jack Harkness who the Doctor was, she gave the Time Lord the alias "Mr Spock", because she suddenly realised she didn't even know his proper name. (DW: The Empty Child)

Donna Noble also seemed familiar with the character of Spock. She compared the Tenth Doctor's method of reading a person's thoughts to that of Spock's "mind meld". (NSA: The Nemonite Invasion)

Behind the scenes
The mentions of Mr. Spock in The Face of the Enemy, Ophidius, The Empty Child and The Neonite Invasion treat him as a fictional character (as do, implicitly, other references to Star Trek and Star Trek: The Next Generation in Doctor Who stories). Assimilation², of course, treats him as a "real" individual. Reconciling these diegetic levels is an exercise best left to the reader.

Leonard Nimoy, who played Spock, was seriously considered to direct the 1996 TV movie, as recounted in the book, The Nth Doctor.

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