Abacus (#118; Topic I)

Yesterday, an ex-colleague at the World Bank asked me to substitute for him at two events, both on "China Today", in West Virginia. With a Rotary Club being the sponsor, in my resume, I included a line stating that, at one time, when I was a partner in the Taipei office of an international CPA headquartered in Manila, I was a Rotarian, using Abacus as my name. Ah, abacus, the world's first calculator. An authentic version of this Chinese invention is a rectangular wooden frame, with a fixed divider about 1/4 from the top along the longer side, 17 columns (the number is invariably a prime number: 11, 13, 17, and 19 are commonest); for each column, two beads above the divider, resting at the top of the frame (each with a value of 5) and five below, resting at the bottom of the frame (each with a value of 1). Using an abacus is straight forward -- common sense plus simple directions. For example, in adding numbers 1 through 4 in sequence, one first pushes up a below-divider bead toward the divider, yielding 1; when adding 2 to it, two below-divider beads are pushed up -- the three below-divider beads together represents the new subtotal at this point (3). When adding 3 to this subtotal, pushing three more below-divider beads is no longer possible (only two are still available), one needs to invoke a simple direction: "plus 5 minus 2" ("plus 5" = pushing an above-divider down; "minus 2" = removing 2 below-divider beads) -- the resulting one above-divider bead (with a value of 5) + one below-divider bead = 6. Adding 4 to this subtotal needs another simple direction: "minus 6, increment 1 [to the column to the left]" -- columns are in the base-10 mode; a bead in a left column is 10 times more valuable than its immediate-right counterpart -- here, the bead to the left (with a value of 1 x 10) + no beads in the column to the immediate right (0) = 10. Last December, our son, returning from a vacation in Cambodia, brought back, as a gift to me, an artwork with 2 abacuses, each with 23 columns, with each column having only one above-divider bead and four below-divider beads. (The second above-divider bead and the fifth below-divider bead are for overflows, useful when doing multiplication or division. They are frequently omitted in abacuses made in Japan and other Asian countries.)
Posted 7:45 pm, Wednesday, April 5, 2006