I heard both many a time, but my vague memories suggest I used to hear *two-dimensional *more often and only in the last ten, fifteen years has *one-dimensional *fallen into vogue. Seems to me calling a character two-dimensional pretty much covers the notion that they have no depth and using *one-dimensional *is overkill - like saying, “he’s reeeeeeeeeeeeeeaaaaaallly two-dimensional!”
But lacking an OED to look into origins, I make the plea for help.
It’s clear what the internet prefers. Google “two-dimensional character” and get 272,000 hits. Google “one-dimensional character” and get 2,560,000 hits. But is one more proper than the other? And which came first?
I always thought they referred to two different types of bad character. A two dimensional character being one with little personality or history. And a one dimensional character being one that just has one exaggerated character trait. The male chauvinist pig who never does anything except go around being a male chauvinist pig; the slasher film killer who doesn’t do anything but kill people; the rabid feminist who doesn’t do anything but rant against men, etc.
I believe use of the term “one dimensional” is best used to describe the narrow focused mental quality of particular affected characters (e.g. seeing things only one way, from point A to B, with no capacity to consider tangential pathways of thought), whereas the term “two dimensional” is best used to describe the physical dimensions of a flat character (e.g. a cartoon, with height and width, but lacking depth).
While I see “one-dimensional” and “two-dimensional” as pejoratives being mostly synonymous, I think that which one is chosen to describe a (lack of) characterization is driven pretty much by what Der Trihs has to say here, and it’s a good bit of insight into people’s subliminal reasons for choices in terminology.