Tweedledum and Tweedledee were characters from Alice Through the Looking Glass by Lewis Carroll. They were brothers discovered by Alice as she traveled through Wonderland.

In 2268, under the control of the Platonians' psychokinetic abilities, James T. Kirk and Spock sang a nonsense verse that referenced language and characters from the book:

I'm Tweedledee, he's Tweedledum.
We're spacemen marching to and from.
We slythe among the mimsy troves,
And tire among the borogoves. (TOS: "Plato's Stepchildren")
A nonsense verse referencing this pair of characters was to have been recited by Spock, while similarly under psychokinetic control (albeit by Charlie Evans instead of the Platonians), in TOS: "Charlie X". NBC even cleared the copyright of the verse, to allow for its usage in the episode. As written in the final draft script of "Charlie X", the verse would have been:
Tweedledum and Tweedledee
Agreed to have a battle:
For Tweedledum said Tweedledee
Had spoiled his nice new rattle.
In the final edit of "Charlie X", however, this verse was evidently replaced with one from "The Tyger".

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