I wish I understood better what you say about units. "It is the human mind that does the carving." Do you mean to say that words have nothing to offer except "convenience of thinking"?
Would you say that even great discoveries (relativity, uncertainty principle, ...) are convenient representations of what is given to us, not reflections of something essential?
Do you think the carving ceases at the borders of our thought? If so, what *is* taking place, out there, in here?