DeviantPenguin wrote:bended-to-the-earth apologies for not being precise.
innate VS. acquired ability is herein understood in the cognitive psychology meaning
innate : common to all humanity, whatever their culture is (the diverse numeration systems all have the same symbolic operations, and moreover, they use the same brain areas)
That numeration system was invented.
The symbolic operations where invented.
Read up on ancient math -- the notation they had to deal with was painful!
Can you imagine trying to describe an exponential function, when all of your math was in "plain english" and you could only describe multiplication by talking about what happens when you make a rectangle, lay poles on it 1 unit apart from each other, then align the poles into one long line?
When you had no zero, no negative numbers, and the most advanced system of value was length?
When describing area and length as the same kind of numbers was alien to you?
When your numbers where described in words, and you had no bases? To say 200 you would say "a hundred and a hundred" -- you couldn't express 100+100=200, because the shortest way of saying 200 was the same as the shortest way of saying 100+100.
The current indo-arabic-european mathematical notation has won out only because it kicked the crap out of competarers. Even then, I strongly expect it is taught very differently in different areas: so much so that claiming that mathematics is cross-cultural because it uses the same symbols would be like saying that english and french are the same language, because they use the same alphabet.
Even within one nation: I use mathematical symbols in a completely different way than civil engeneers would, than physicist would, than cashiers would, than high school teachers would. While we share a basic pigeon (1+1=2), I require a massive amount of translation help to understand engeneering and physicist math. And while I can understand how to "spell" the same math sentences that a high school teacher would use, I would read them as having a very different "pronounciation" than the high school teacher, because I treat the symbols differently.
The cashier could be argued to only understand the language of math at a pigeon level. At the same time, his dialect is different: 99 plus 14% is clearly 1.13, and not 1.1286. To him, +14% has a bunch of implicit meanings associated with it -- I can understand those meanings, but they aren't my native mathematical language anymore.
'course, this doesn't matter much: note that IQ "logic" tests correlate horribly on before/after on people who have taken formal training in mathematics.