Interesting discussion!

One thing not being brought to the fore is the **Innate** counting thing.

Counting is a learned thing! When counting is irrelevant in a "PRIMITIVE" culture, things about counting suddenly seem very different then in societies of "WEIRD" (Western Educated Industrialized Rich Democratic.....as termed by anthropologist Joe Henrich) people.

To illustrate I copy below an excerpt from the 12 february 2009 Nature Journal to illustrate:

From the article:

Darwin 200: Human nature: the remix

Dan Jones

There is evidence that humans have not just one innate number system, but two. The 'analogue estimation' system evaluates quantities in an approximate manner by relating them to imprecise notions such as 'amount of stuff' or 'extent of imaginary line'. The second system is more exact, but can initially, and innately, keep track of only three or four items11.

The exact number system can handle larger numbers, but this requires cultural learning and elaboration (the analogue system seems to function in much the same way across cultures). Some societies, such as the Pirahã; of the Amazon, have little need for large exact numbers (they do not trade or keep accounts), and use only 'one', 'two' and 'many'. The Pirahã also perform poorly at lining up groups of three or more objects (nine nuts, say, with nine batteries), or estimating when the last of 15 beans has been removed from a tin. Without the cultural demand for trading in large numbers, they have neither developed the concept nor invented the words12.

Cross-cultural studies also suggest that a basic grasp of geometric concepts, such as points, lines and parallelism, is a universal component of human cognition, or at least found in disparate cultures13. A similar story holds for how people relate numbers to space, but with an interesting twist. Western adults tend to order clusters of dots (grouped in 10, 100 and 1,000), along a linear scale, so that the distance between the group of 10 and 100 is much smaller than the gap between 100 and 1,000. Western infants, by contrast, group numbers on a logarithmic scale, with the gap between 100 and 1000 the same as that between 10 and 100. Cross-cultural studies among the indigenous Amazonian Mundurucú revealed that both children and adults order numbers logarithmically. Together with the results from Western infants, this suggests that the logarithmic system could be an innate and universal aspect of mathematical thinking, one that gets tweaked in Western populations through formal education in certain mathematical tools and techniques to produce a switch to the linear system14.