>Now: it seems undisputable that the concept of counting numbers precedes >the concepts of rationals, integers, and so on both in individual >development and in social/mathematical history, but what about the >geometric figures? > >I think that a circle comes first (and I see it not as a disk although >that's what's usually presented to toddlers being prematurely tutored in >"shapes") both for an individual and society? Then what?
This is a fascinating question. I hope someone has authoritative information on it; I certainly don't! Anecdotally, I can mention that I've been in quite a few caves in Spain (Tito Bustillo, Altamira, ...) and France (Lascaux--well, the replica thereof--,...), with wall decorations from the Paleolithic era, and I've kept my eye out (and occasionally asked guides) for evidence of the beginings of mathematics. Groups of dots seem to be it, in that era, and those very rarely (and ambiguously); no circles, arcs, disks, no straight lines or broken lines or polygons. At least, I don't remember noting them; I'd like to be corrected.