Mathematics and the embodied mind

One of the things I need to consider is what is mathematics and where it comes from? One often hears the Platonist's kind of idea that mathematics exists 'out there' independant of human existence, that it is somehow fundamental to the universe, like the parts of a clock, allowing it to happen, that concepts such as the number pie have an existence beyond human thought. This idea of mathematics is similar to a belief, it is not proven, or testable. It also does not really answer the question of what it is.

An alternative view is that it is something that arises form within, something that is in part determined by our biology, and then later by our culture and mathematics as a cultural discourse. At the moment I am reading Lakoff and Nunez, "The Emodied Mind - What is Mathematics Really". It seems to me that the essential argument of the book is that mathematics is based on a series of increasing abstract conceptual methaphors that are originally grounded in the physical, and everyday experience of individuals. For example the natural 'hard wired' instincts of for example being able to conceive of a discrete object with an inside and an outside, the ability to put things into groups or piles, the ability to subitize (instantly recognise how many objects there are in a group - up to four in most people although I have heard of certain cases of autism where inidividuals are able to instantly identify larger numbers - I think Oliver Sachs talks of a group of twins where this is true.

At the moment I am just reading the chapter on arimthmetic, and the origins of addition, substraction, multiplication and division (I have often thought of all of these as just forms of addition - they can all certainly be expressed in terms of addition. Lakoff and Nunez go on later to talk of various metaphors such as the number line. There is no real number line - it is a metaphorical tool to think about number.

So in sum, as it appears to me, mathematics is a particular type and series of increasingly abstract and complex metaphor grounded on daily experience and the way the mind and body work. Of course I've yet to read more of this theory.

Additionally what makes this type of metaphorical symbolic thought different from other forms of thinking?

Why is this important in my research? Because I need to understand how we understand.