  Phonetic ambiguity and confusibility are bugbears for any form of bottom-up
or data-driven approach to language processing. The question of when an input
is ``close enough'' to a target word pervades the entire problem spaces of
speech recognition, synthesis, language acquisition, speech compression, and
language representation, but the variety of representations that have been
applied are demonstrably inadequate to at least some aspects of the problem.
This paper reviews this inadequacy by examining several touchstone models in
phonetic ambiguity and relating them to the problems they were designed to
solve. An good solution would be, among other things, efficient, accurate,
precise, and universally applicable to representation of words, ideally usable
as a ``phonetic distance'' metric for direct measurement of the ``distance''
between word or utterance pairs. None of the proposed models can provide a
complete solution to the problem; in general, there is no algorithmic theory of
phonetic distance. It is unclear whether this is a weakness of our
representational technology or a more fundamental difficulty with the problem
statement.
