Status Symbol: The Trichologist
MILICH: What? You can't help me? BILL: You should see a trichologist. It's a hair specialist.
Bill suggests the type of doctor Milich needs but doesn’t offer him a doctor’s name. It “really isn’t my field” as Bill says, but we know that he recommended Ziegler an Osteopath earlier in the film.
VICTOR (to Bill): Hey! That osteopath you sent me to, the guy that worked on my arm? You ought to see my serve now. Guy's terrific.
Both doctors are specialists in a different medical field than Bill yet Ziegler gets a recommendation and Milich’s problem doesn’t give Bill a second thought. Milich is Bill’s societal server and therefore Bill doesn’t even think to recommend him a name.
Kubrick uses this motif of recommending specialists to denote a lower class individual making a gesture towards a higher class societal member to gain favor. Remember what Ziegler says about Nick in his final scene with Bill?
ZIEGLER: I recommended that little cocksucker to those people and he’s made me look like a complete asshole.