Ordinary prose is linear, lending itself most naturally to describing the temporal evolution of a single thread or train of thought. Two words in the thread are neighbors only when one immediately precedes the other. When printed on a page, a word above another word in the following line is only coincidentally near it, and not a "neighbor" due to relatedness in content. In word-wrapping a sentence across a page, the positions of the line breaks are arbitrary, and do not contribute to the meaning of the sentence.
Expanding to two dimensions leads to the image of an array of words, in which words can be neighbors in some second dimension, other than the linear sequence of words. For example, in rhyming poetry, the last word of one line is a "neighbor" to a line with which it rhymes, and/or a "neighbor" to the last words of the preceding and the next line. The line breaks in printed poetry are not at all arbitrary, and contain part of the meaning of the poem.
Expanding further, to three dimensions, allows hypertext, i.e. any word can have a hyperlink to any other word, producing a mesh of vertices and connections that needs at least three dimensions of space in which to construct a physical representation.