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The Knights of Eastern Calculus (or just "Knights" for short) are a secretive organization of hackers/crackers/otaku loyal to Eiri Masami-Deus, their name invoking the image of Pythagorian mystices/mathematicians. They seems to be based on the ancient Knights Templar and the more modern Knights of the Lambda Calculus (if they exist). No one knows if Knights is real, but it can be assumed that the Knights themselves know they are in Knights.
The Knights believe that the Truth is this: That the Wired is more "real" than physical reality, and that Eiri Masami is the God of the Wired. They are Deus's loyal followers, completely under his manipulation. They created "Lain in the Wired" to decieve those seeking the real Lain and bring them under Deus's influence also. They are also the ones behind the deaths related to the game PHANTOMa (created with technology from KIDs) and the capture of Iwakura Mika's soul.
A key point to remmember: without Knights (his worshipers), Eiri Masami has no existance as God. This is why when they are destroyed by the Men in Black he tries to convince Lain that he is the one God and that she is his creation. Lain refuses to believe this and this refusal to believe brings about Eiri's undoing.