Phosphene symbols may possibly be common to all mammals, since we share a similarly evolved visual cortex. But spoken language is without a doubt unique only to humans. No one knows why human brains got so big. Perhaps they grew to accommodate the demands of an evolving, and increasingly complex verbal language system. Having a syntax for language then allowed humans to develop rational brains that are both anticipatory and also reflective, or able to re-member and reassemble. Recognition may be an ability we share with mammals, but recall may be a uniquely human ability. Our rational brain structure, shaped by the demands of spoken language, perhaps made it possible for humans to not only associate sounds to meanings (spoken language) but also to organize and structure the language in our minds (syntax and memory). The demands of language could have been the impetus for human brain growth. Perhaps the evolved brain, suitable for sending and receiving spoken language, also primed humans in their early attempts at geometric graphical depiction, and quite soon after, written language. I think verbal language abilities in humans needed to be quite significantly evolved before attempts at graphical depiction was even cognitively possible.
So, if we want to decipher early geometric patterns, we might very well begin by applying a parsing method equivalent to natural language parsing. The rationale here is that the human mind evolved to accommodate spoken language, but that this also opened the door into the world of association and syntax for a different form of communication -- graphics. When parsing a natural language sentence, there is a start and an end, and an intermediary construction consisting of a subject and an object, possibly with an indication of a context of some kind. One attribute of natural language is its inherent ambiguity, not only in the words used, but also conveyed by sentence structure (ambiguous prepositional phrases) and also voice tonality and inflection. These additional 'channels' of information help to convey the meaning of the message.
It is possible I am simply restating what Chomsky has already proposed, so I must do a bit more research about his position.