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When Spock advises Kirk that Khan's moves "indicate two dimensional thinking", Spock is commenting that Khan is using tactics learned from playing two-dimensional chess. As a Sikh, Khan was likely familiar with 2-D chess, which originated from his homeland. Kirk and Spock routinely played three-dimensional chess during Star Trek (1966). The key to 3-D chess, was using an "attack board" to come up from below or above your opponent. Hence, Kirk gives the helm command "all stop" and "Z-minus 10,000 meters". In the Cartesian coordinate system, the Z-axis measures above or below the horizontal plane. The next scene show the Enterprise moving in the Z-axis, not seen in other Star Trek films.

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