You really think counting is "built in" and isn't a fairly recent invention? How about reading and writing?
I think primitive man was, if anything, far more sensitive to the rhythms of nature than we are. After all, he's smack-dab IN IT in a way we moderns virtually never are. Where there is a sense of periodicity, can counting be far behind? Why would you consider the "invention" of counting as "a fairly recent innovation?" I see it as an ability that naturally emerges from a man's self-understanding of his own experiences.
Reading and writing are seemingly comparatively late developments, if I had to guess, 6th to 5th century B.C. Writing seems to be an invention; but it is based on articulating human experiences, so it is rooted in the natural. That is, it is not a totally "free" invention. And writing implies reading.