Is the linkage between number and space congenital?

Mapping of numbers onto space plays a fundamental role for many aspects of mathematics, including geometry, Cartesian coordinates and mapping real and complex numbers onto lines or planes.   Children’s conceptions of how numbers map onto space shifts radically during the early school years.  Kindergarten children can represent numbers in space in a non-random manner, but their representation is compressed, seemingly logarithmic (placing, for example, the number 10 near the midpoint of a 1–100 scale). A logarithmic scale is based on orders of magnitude, rather than a standard linear scale, so each mark on the scale is the previous mark multiplied by a value.  The Richter magnitude scale is an example of a logarithmic scale.  The compressive non-linearity becomes progressively more linear over the first 3 or 4 years of schooling.

Strong support for this idea comes from a recent study of the Mundurucu, an Amazonian indigenous group with a limited number lexicon and little or no formal training:  both adults and children of this tribe map numbers and numerical quantities onto space in a logarithmic fashion.  This points to both genetic and cultural roots to numerical mapping: the ability to represent numbers in space appears to be innate, but formal mathematical training is required to refine the representation from logarithmic to linear. 

Interestingly, dyscalculic children from developed societies also show a more logarithmic representation of the numberline than controls.

Does attention affect the ability to map numbers onto a numberline in a linear fashion?  Attention has been shown to play an important role in number perception. Attentional-training (through videogame playing) increases the subitizing range (subitizing is the ability to grasp small numerosities without counting).

In this research:

Anobile, G., Cicchini, G. M., & Burr, D. C. (2012). Linear mapping of numbers onto space requires attention. Cognition, 122(3), 454-459.‏  http://win.pisavisionlab.org/PDF_Publications_PisaVisionlab/Giovanni_Anobile_Publications/2012_Linear_mapping_of_numbers_onto_space.pdf

there were only four participants:  the author and three students.  The participants watched  clusters of dots that were displayed  on a computer screen for a very short time period (not allowing them to count the dots when their quantity was large). Their task was to place the dot cluster on a numberline by clicking the mouse.    There were three possible numberlines, marked at each end with a single dot to the left and 10, 30 or 100 dots to the right.  The number of dots in a cluster was between 2 to 86 (of course, the 86 cluster appeared only with a 0-100 numberline).  In some of the trials the participants concurrently performed another task that demanded attention (pressing the mouse when a certain visual pattern appeared – a dual task).

When there was no dual task, the participants placed the dot clusters on the numberline linearly.  But in the dual task condition, participants placed the dot clusters on the numberline logarithmically.    Apparently,   the native system of number representation is logarithmic, even in typical adults with normal mathematical ability, and  the linearization of this representation requires attention.