Parity of Zero - Numerical Cognition

Numerical Cognition

Adults who do believe that zero is even can nevertheless feel unfamiliar or uncomfortable with the fact, enough to measurably slow them down in a reaction time experiment. For an experiment designed to investigate the task of parity determination, a numeral or a number word is flashed to the subject on a monitor, and a computer records the time it takes the subject to identify the number as odd or even by striking an appropriate button, such as a Morse key. Stanislas Dehaene, a pioneer in the field of numerical cognition, led a series of such experiments in the early 1990s. They showed that 0 was slower to process than other even numbers. Some variations of the experiment found delays as long as 60 milliseconds or about 10% of the average reaction time—a small difference but a significant one.

Dehaene's experiments were not designed specifically to investigate 0, but to compare competing models of how parity information is processed and extracted. The most specific extraction model, the mental calculation hypothesis, suggests that reactions to 0 should be fast: 0 is a small number, and it is easy to calculate 0 × 2 = 0. (Subjects are known to compute and name the result of multiplication by zero faster than multiplication of nonzero numbers, although they are slower to verify proposed results like 2 × 0 = 0.) The results of the experiments suggested that something quite different was happening: parity information was apparently being recalled from memory along with a cluster of related properties, such as being prime or a power of two. Both the sequence of powers of two and the sequence of positive evens 2, 4, 6, 8, ... are well-distinguished mental categories whose members are prototypically even. Zero belongs to neither list, hence the slower responses.

Repeated experiments have shown a delay at zero for subjects from a variety of national and linguistic backgrounds, representing both left to right and right to left writing systems; almost all right-handed; from 17–53 years of age; confronted with number names in numeral form, spelled out, and spelled in a mirror image. Dehaene's group did find one differentiating factor: mathematical expertise. In one of their experiments, students in the École Normale Supérieure were divided into two groups: those in literary studies and those studying mathematics, physics, or biology. The slowing at 0 was "essentially found in the group", and in fact, "before the experiment, some L subjects were unsure whether 0 was odd or even and had to be reminded of the mathematical definition".

This strong dependence on familiarity again undermines the mental calculation hypothesis. The effect also suggests that it is inappropriate to include zero in experiments where even and odd numbers are compared as a group. As one study puts it, "Most researchers seem to agree that zero is not a typical even number and should not be investigated as part of the mental number line."