Actually, there's one more
step we take to get from
roads-in-
Rome, to trivia.
The word "trivia" directly comes from the words describing the first group of the Seven Liberal Arts.
The Seven Liberal Arts can be arranged into two groups, the second group (known as the artes reales or physicae) is made up of arithmetic, geometry, astronomy, and music. The first group, though, is where "trivia" comes from.
Grammar, rhetoric, and dialectic (the sciences of language, oratory, and logic) make up the first group, which is called artes triviales or trivium. They get their name from the junction of three roads and we, in turn, get 'trivia' directly from the group.
Sound not quite as ironic now? :)