Representing Exact Number Visually Using Mental Abacus

Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation. Human adults, unlike other animals, have the capacity to per- form exact numerical computations. Although other creatures are sensitive to precise differences between small quantities and can represent the approximate magnitude of large sets, no nonhuman species can represent and manipulate large, exact numerosities (Feigenson, Dehaene, & Spelke, 2004). Multiple forms of evi- dence suggest that this human capacity is related to natural lan- guage (Barner, Chow, & Yang, 2009; Dehaene, Spelke, Pinel, Stanescu, & Tsivkin, 1999; Frank, Everett, Fedorenko, & Gibson, 2008; Gordon, 2004; Pica, Lemer, Izard, & Dehaene, 2004; Wynn, 1990). Language, however, may not be the sole cognitive system capable of symbolically representing exact number. Experienced users of an abacus—a physical calculation device—can learn to perform arithmetic computations mentally, as though visualizing a mental abacus (MA; Hatano, Myake, & Binks, 1977; Hatano & Osawa, 1983; Hishitani, 1990; Miller & Stigler, 1991; Stigler, 1984; Stigler, Chalip, & Miller, 1986). Previous work, reviewed below, has described the MA phenom- enon and has provided suggestive evidence that MA is represented nonlinguistically, in a visual format. However, this proposal re- mains tentative for two reasons. First, early studies that directly tested the role of language in MA were compelling but imperfect and used sometimes informal methods to test small and unusual populations of participants. Second, previous proposals fail to explain how MA could be represented in a visual format. The present study addressed these issues in a series of three experi- ments. We conducted detailed studies of MA processing to ask how it might be represented in visual working memory, given known limitations on the nonlinguistic processing of quantity information. In addition, we used a dual-task paradigm to test the role of language in MA computations. Taken together, our results support the view that MA relies on visual resources, and in particular the ability to represent multiple groupings of objects in parallel, to create visual representations of exact number that differ fundamentally from those constructed using natural language.