# Are binary relations the same as "1-dimensional"?

Halford et al. (2010) claims discusses binary relations and that humans can process up to a quaternary relation. Are these equivalent to "0-dimensional," "1-dimensional" relational reasoning problems discussed elsewhere?

For example, a binary relation discussed in that paper, taller(Bob, Tom) involves comparing one dimension: height, so it could be a 1-dimensional problem, yet I can't find confirmation of the terminology.

A binary relation associates elements from two domains ('domain' and 'co domain') via a set of ordered pairs. You can represent it as a two dimensional array of boolean value where one writes True in row $$i$$ and column $$j$$ if and only if $$(i,j)$$ is in the relation.
By extension, a ternary relation or any finitary relation (of which a quartenary relation would be a particular case) associates elements from $$t$$ domains (where $$t=3$$ for a ternary relation) via a set of $$t$$-uples, and you can represent them as $$t$$-dimensional arrays of boolean values