Metonymy (in its broadest sense) and metaphor are the principal linguistic mechanisms of humor. The joke
has two acoustic metonymies and one mock-metaphor.
Metonymy and metaphor are not just important as rhetorical devices. The renowned literary critic and linguistics scholar Roman Jakobson made the point that they correspond to two fundamental, and fundamentally different, modes of processing symbolic information. The symbolic system most of us are most familiar with is a human language; these two poles (as Jakobson describes them) are so important that they show up in speech disorders: contiguity disorder is a type of aphasia in which metaphor takes over completely. A patient will say ``spyglass'' for ``microscope'' and ``fire'' for ``gaslight'' (these are Jakobson's examples); the context-driven grammar of the sentence disintegrates, leaving ``a heap of words.'' The polar pathology is similarity disorder, in which metonymy rules. These patients say ``fork'' for ``knife'', ``smoke'' for ``pipe'' and ``eat'' for ``toaster.'' The grammatical structure of the sentence is intact, especially from word to word; the subject is often omitted. In both disorders, communication is impossible.
Mathematics is also a symbolic system, devised by the same humans who developed natural languages. So it is not surprising that metonymy and metaphor should emerge as poles in the development of mathematics, both culturally and in any individual, and that awareness of this duality can be useful in learning and in teaching mathematics. This column will explore some mathematical examples of these two fundamental processes of human thought.
SUNY at Stony Brook