The elimination of ambiguity and redundancy are unquestioned goals in the exact sciences, and yet, as this paper shows, there are inescapable lower bounds that constrain our wish to eliminate them. The author discusses contributions by Richard Hamming (inventor of the Hamming code) and Satosi Watanabe (originator of the Theorems of the Ugly Duckling). Utilizing certain of their results, the author leads readers to recognize the unavoidable, central roles in effective communication, of redundancy, and of ambiguity of meaning, reference, and (...) identification. (shrink)