Carson is describing the structural necessity of the triangle — not as a poetic preference but as the condition of desire's visibility. Two points alone produce proximity or distance; they cannot produce longing. The third point is what makes the gap legible, makes the desirer feel the edge between what is held and what is not. Sappho's poem requires the man sitting across from the beloved precisely because his presence throws into relief what the speaker cannot have — and in that triangular current, desire becomes something you can feel the shape of rather than merely drown in.

This matters beyond lyric form. The soul in longing always manufactures the triangle, even unconsciously: the object, the obstacle, the one who seems to have the object. What you think is a simple wanting tends, on inspection, to have a third term operating in it — a rival, a memory, an idealized prior state against which the present is found wanting. Strip the triangle and you don't get satisfaction; you get numbness. Desire lives in the gap the third point opens. Carson's point is that the structure is not decoration; it is the only geometry in which eros can appear as eros, rather than collapsing into either possession or indifference.