On knowing about nothing. The processing of zero in single and multi-digit multiplication

Background: Zero has a special role in calculation: indeed it is not obvious which representation may be invoked in multiplication or division by zero. In particular, zero as an operand, unlike any other operand, makes any quantity disappear. Aims: The study is intended to shed light on the mechanisms mediating the manipulation of zero. Methods & Procedures: Three neuropsychological patients, AF, FV, and FS, are described, whose specific pattern of preserved/ impaired performance with single-and multi-digit multiplication shows selective problems with the use of zero (Nx0 and 0xN). Outcome & Results: AF's performance in single-and multi-digit multiplication showed a clear dissociation between spared fact-based problems and impaired 0 rule-based problems. FV was totally unable, in multi-digit multiplication, to apply adequately the 0 rule that he could master in simple calculation. Finally, FS showed, within the rule-based problems, a clear-cut dissociation between a preserved performance on Nx0 problems and an impaired performance on 0xN problems, a difficulty that almost disappeared in multi-digit multiplications. Conclusions: Overall the reported dissociations indicate that a full grasp of the concept of zero may not be used in routine calculation, and that processing of zero rather appears to rely on a collection of independent, shallow representations.