Humans, unlike other animals, can perform exact numerical computations. Although other creatures are sensitive to precise differences between small quantities and can represent the approximate magnitude of large sets, no non-human species can represent and manipulate large, exact numerosities. In development, learning a linguistic counting system always precedes conceptual understanding of large numbers (Wynn, 1990; Le Corre, 2006), and indigenous groups who lack numerical vocabulary are unable to represent the exact magnitudes of large sets (Frank et al., 2008; Gordon, 2004; Pica et al., 2004). Such studies suggest that language may drive the creation of new representational resources in humans. Language, however, is not the sole cognitive system capable of symbolically representing exact number. Experienced users of an abacus—a physical calculation device— learn to perform arithmetic computations mentally, as though visualizing a “mental abacus” (MA) (Hatano, 1877; Hatano & Osawa, 1983; Hishitani, 1990; Stigler, 1984; Stigler et al., 1986; Miller & Stigler, 1991). MA thus provides an important case study of building complex representations using non-linguistic cognitive resources. The current study asks, given known limitations on the non-linguistic processing of quantity information, how the visual system could support the representation of large exact numerosities using MA. The abacus has been used in Asia since 1200 AD for rapid and precise calculation (Menninger, 1969). It represents number via the arrangement of beads into columns, where each column represents a place value that increases in value from right to left (Figure 1a). On a Japanese Soroban abacus, each column is divided into two levels separated by a horizontal beam. On the bottom are four “earthly” beads and on top is one “heavenly” bead, whose value is five times greater than the individual earthly beads below. Moving beads towards the dividing beam places the beads in “play,” thereby making them count towards the total number represented.