Heck, I'll go so far as to suggest that unless one has done programming or mathematics work involving partial orderings, that one is unlikely to really understand just how non-linearizable the world is. (Though I imagine there may be other domains where one might encounter similar experiences.)

Programming and math are definitely the fields where most of my experience with partial orders comes from. Particularly domain theory and denotational semantics. Complete partial orders and all that. But the concepts also show up in economics textbooks. The whole concept of Pareto optimality is based on partial orders. As is demand theory in micro-economics. Indifference curves.

Theorists are not as ignorant or mathematically naive as you seem to imagine.