Side comment: Subitizing (the not-counting thing; see http://en.wikipedia.org/wiki/Subitizing_and_counting ) has been rather extensively studied. I can't find good references, but it is apparently quite amenable to expertise. I have a friend who worked in inventory auditing (i.e. counting stuff in warehouses). He got into the 7-8 range. ISTR hearing of factory workings in my psych classes that got as high as 20 in their (hyper-specialized) domains.