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.
Or at least secret decoder rings.
Two more bits of grist for the mill, see Sir Arthur Conan Doyle's The Adventure of the Dancing Men (Sherlock Holmes) and G.K. Chesterton's The Noticable Conduct of Professor Chadd:
Did language appear gradually by consensus and grow organically, or did it start with a few "gifted" individuals and spread either by imposition or imitation?
Cheers!