I passed along the discussion of x-squared in various languages to a Linguistics colleague, Prof Donna Jo Napoli, who was a math major as an undergraduate. She replied:
At 1:52 AM +0000 10/17/05, <email@example.com> wrote: > Many languages distinguish one from more than one (the english > singular vs. plural, for example) many languages distinguish > one (called the singular), two (called the dual), and more than > two (Old English did this, so did Ancient Greek) some languages > distinguish singular, dual, trial, and more than three (languages > of New Guinea, for example) and some languages even have singular, > dual, paucal (3, 4, or 5), and more than 5 (Polish does this in > some cases) > > So I wonder if the x-squared goes along with languages that have > (or once had) the dual. > > But i have no idea.
My own gut feeling is that her conjecture is probably wrong. I like the comment by someone on the list that having a special name for x^2 and x^3 makes sense in terms of the human history, because squaring and cubing were relevant to geometrical constructions in spaces that physically surround us. But then, as this person noted, the real question is: Why don't all languages (that have a mathematical component) have special names for these cases?
Steve Maurer Swarthmore College Swarthmore Pennyslvania, USA