Topical Guide 133
Mark Dorset
Mathematics: Finger-Counting, Dactylonomy
Memory, Faulty: Causes of, Results of
IN ONE MISERABLE WEEK, I did learn to answer questions about the times tables more quickly than Mr. Beaker could snap his fingers. … However, I didn’t really learn the times tables very well at all. I memorized them as I might have memorized lines for a performance, and it worked pretty well. … But as soon as I had put on my performance, the lines began to slip away from me. Later, when I needed to know one of the products that had, while my mind was occupied with something else, crept into the dark unknown, never to return, I would reconstruct it from one of the ones that remained or count it out on my fingers, at least in my mind.
Little Follies, “The Girl with the White Fur Muff”
Abstract
Studies like the one conducted by Domahs et al. (2010, in Cognition) corroborate that finger counting habits affect how numbers are processed, and legitimize the assumption that this effect is culturally modulated. The degree of cultural diversity in finger counting, however, has been grossly underestimated in the field at large, which, in turn, has restricted research questions and designs. In this paper, we demonstrate that fingers as a tool for counting are not only naturally available, but are also—and crucially so—culturally encoded. To substantiate this, we outline the variability in finger counting and illustrate each of its types with instances from the literature. We argue that the different types of finger counting all constitute distinct representational systems, and we use their properties—dimensionality, dimensional representation, base and sub-base values, extendibility and extent, sign count, and regularity—to devise a typology of such systems. This allows us to explore representational effects, that is, the cognitive implications these properties may have, for instance, for the efficiency of information encoding and representation, ease of learning and mastering the system, or memory retrieval and cognitive load. We then highlight the ambivalent consequences arising from structural inconsistencies between finger counting and other modes of number representation like verbal or notational systems, and we discuss how this informs questions on the evolution and development of counting systems. Based on these analyses, we suggest some directions for future research in the field of embodied cognition that would profit substantially from taking into account the cultural diversity in finger counting.Andrea Bender and Sieghard Beller, “Nature and culture of finger counting: Diversity and representational effects of an embodied cognitive tool,” in Cognition
Volume 124, Issue 2, August 2012, Pages 156-182
In Arabic, dactylonomy is known as “Number reckoning by finger folding” (=حساب العقود). The practice was well known in the Arabic-speaking world and was quite commonly used as evidenced by the numerous references to it in Classical Arabic literature. Poets could allude to a miser by saying that his hand made "ninety-three", i.e. a closed fist, the sign of avarice. When an old man was asked how old he was he could answer by showing a closed fist, meaning 93. The gesture for 50 was used by some poets (for example Ibn Al-Moutaz) to describe the beak of the goshawk.
See also: Memory, Faulty: Causes of, Results of TG 34
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