I would say that the physical processes that underlie our mental representations of concepts are fundamentally not serialized (part of why it is often so hard to put thoughts into words). They are non local in the sense that many different actors can operate on the data at the same time to create or modify some higher dimensional state and are not necessarily contingent on prior state in the way parsing is.

You can't really parse a paper by reading every paragraph at the same time. Even if you could do it physically, some ordering would have to be applied to interpret subsequent parts based on statements in earlier parts. Representations in the brain have no such inherent limitation on ordering.