Treating language like physics equations doesn't strike me as a terriblely useful approach. Language and culture are so intertwined that I tend to view them as aspects of a singular whole.
Language is, in many ways, rather arbitrary.
Not in all aspects but in many. Somewhere in there, these sounds we all make take on meaning and come to represent something. That, to me, is the crucial point at which the truly interesting things happen. It's not that a treatment of language in the abstract doesn't provide useful information. Language exists within a context and that context, I think, is the culture.