The Collaborative International Dictionary of English v.0.48:

Complexity \Com*plex"i*ty\, n.; pl. Complexities. [Cf. F.
   complexit['e].]
   1. The state of being complex; intricacy; entanglement.
      [1913 Webster]

            The objects of society are of the greatest possible
            complexity.                           --Burke.
      [1913 Webster]

   2. That which is complex; intricacy; complication.
      [1913 Webster]

            Many-corridored complexities
            Of Arthur's palace.                   --Tennyson.
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