The influence of the place-value structure of the Arabic number ...

magnitude representation is notation specific (e.g., Cohen-Kadosh, Cohen-Kadosh, Kaas,
Henik, & Goebel, 2007) or rather independent from input notation and thus amodal (e.g.,
Piazza, Pinel, Le Bihan, & Dehaene, 2007). This controversy was addressed in a recent target
article by Cohen Kadosh and Walsh (2009). Therein, the authors argued for non-abstract
notation specific representations of number magnitude in humans. However, as becomes
evident from the commentaries by Cantlon, Cordes, Libertus, and Brannon (2009), Dehaene
(2009), Ganor-Stern (2009), Grabner (2009) and others there is also considerable evidence
suggesting an abstract notation invariant representation of number magnitude. Interestingly,
Kucian and Kaufmann (2009) addressed this issue by claiming that this diverging pattern of
empirical results may indicate that there are indeed notation dependent representations which
nevertheless overlap to a certain degree, thereby mimicking an abstract notation independent
representation of number magnitude. So, the question may not be either notation specific or
notation unspecific but to what extend are notation specific and unspecific representations
involved in human number processing capabilities? The latter notion was briefly mentioned
by Cohen Kadosh and Walsh (2009, p. 322) but not elaborated on further. However, the
hybrid model of number magnitude representation (Nuerk & Willmes, 2005) may offer a first
theoretical framework for guiding future research on this question.
LIMITATIONS / PERSPECTIVES
When evaluating the computational results of the current study a number of
presuppositions and limitations that have been taken when setting up the computational
models should be kept in mind. Most importantly, programming of the current models was
largely determined by the psychological implications of the theoretical models. This means
that the separate representations of tens and units in the strictly decomposed model as well as
the separate representations of tens, units, and overall magnitude have been kept apart by the
present model architecture until their respective activations are evaluated at the output stage.
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