The central brain was a memory bank on the planetoid Memory Alpha that contained information about the entire history of the galaxy.
When the Zetarians went to Memory Alpha, they caused extreme damage to the central brain and burnt out the memory core. (TOS: "The Lights of Zetar")
Commander Will Decker also referred to a "central brain" complex when he scanned V'ger in the 2270s. (Star Trek: The Motion Picture)
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