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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. [1913 Webster]