Who is Mr. Wither from That Hideous Strength and what is their importance?

Mr. Wither is the Deputy Director of the N.I.C.E., and he is, for all intents and purposes, the leader. He is a member of the inner circle within the N.I.C.E., and he communicates with the dark eldils regarding the plot against humanity. Wither has trained his mind to be able to carry out day-to-day tasks without his attention, and the rest of his mind wanders. Almost any conversation he has is one he is not paying attention to. He takes long walks around the N.I.C.E., and at one point Mark punches a ghost, or hallucination, of Wither, but it is unclear which it is.