Union of the Hideously and Improbably Deformed, an organization founded by the wife on an MP in the mid 20th century. Many members, including Joelle, wear face veils; they also carry membership cards. Marathe pretends to be a member in order to disguise his identity when he goes undercover as a Swiss resident of Ennet House. In the time before the novel is set Mario was approached to be a member, but Hal vehemently opposed this and Mario did not join.
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The timeline below shows where the term U.H.I.D. appears in Infinite Jest. The colored dots and icons indicate which themes are associated with that appearance.
Chapter 40
...first person to give Hal a copy of the O.E.D., and when a representative from U.H.I.D. approached Mario in the Y.D.P.F.A.H., Hal told him to get lost.
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Chapter 43
...speaking with Erdedy and Joelle van Dyne. There are a handful of veiled people from U.H.I.D. there that night. Joelle has just moved into Ennet House after a grisly overdose and...
(full context)
Chapter 54
...member of the Union of the Hideously and Improbably Deformed, and mentions the similarities between U.H.I.D. and AA. It is revealed that the person Joelle is talking to is Don Gately....
(full context)