A Cognitive Typology for Numerical Notation

Abstract

The numerical notation associated with texts and other representational media used in ancient societies is an important means by which past cognitive processes may be reconstructed. No satisfactory typology exists, however, to help understand the relationship between numerical symbols and cognitive processes. As a result, theories concerning the development of numeration remain mired in a unilinear and ethnocentric framework in which our own (Hindu-Arabic or Western) numerals are seen as the ultimate stage of evolution. It is suggested herein that there are two separate dimensions that need to be considered when classifying and evaluating numerical notation systems, and that these dimensions are structured in highly constrained ways. A new typology is presented in which systems are classified into five major types on the basis of these dimensions. Using this typology, a multilinear model is presented for the patterned diachronic change in numerical notation systems, which refutes both unilinear evolutionary theories and radically relativistic propositions regarding how individuals in pre-modern societies represented numbers.

In touch with numbers: Embodied and situated effects in number magnitude comparison

“…In the two-dimensional Arabic number system (reflecting the dimensions place and value), the numerical value of a digit (0-9) depends on its spatial position within the digit string, with its value increasing by powers of 10 for each position from right to left (e.g., 51 = 5 × 10 1 + 1 × 10 0 vs. 15 = 1 × 10 1 + 5 × 10 0 ; Chrisomalis, 2004;Zhang & Norman, 1995). Considering two-digit Arabic numbers, the spatial position of the tens digit in relation to the unit digit is spatially shifted towards the left.…”

Two-digit number processing: holistic, decomposed or hybrid? A computational modelling approach

“…The position within a digit string defines the value of each digit on a power-of-ten dimension (cf. Chrisomalis, 2004;Zhang & Norman, 1995). However, the way in which these two dimensions of numbers are represented psychologically on the mental number line is subject to controversial debates.…”

Language influences on numerical development—Inversion effects on multi-digit number processing

“…The Arabic number system is the world's most widely-used number system (see Zhang and Norman, 1995; Chrisomalis, 2004; Widom and Schlimm, 2012, for taxonomies of number systems). It relies on a simple formal structure: Based on a set of ten symbols (i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) it is possible to assemble any possible number.…”