If you said 1/1000, you’ve given the answer provided more often by second graders than by undergraduates. And you’re also right.

Evidence from functional neuroimaging and developmental psychology indicate that the human brain possesses an abstract system for magnitude comparison, perhaps relying on the intraparietal sulcus of the posterior parietal cortex. One “feature” of this system is that it follow’s Weber’s Law – larger quantities are less discriminable from one another than smaller quantities. Thus, in this part of the brain numerical representations are not linear but logarithmic.

This system seems to be what drives the numerical processing of very young children. For example, first graders will routinely locate “50″ as closer to 100 on a number line than older children, and this shift is well described by a shift from logarithmic to linear representations of quantity during the elementary school years.

In general, this bias is detrimental – as anyone who has tried to teach basic arithmetic to a first-grader can attest. However, it leads to an advantage in one carefully crafted situation: the comparison of fractional values with identical numerators, for which the distance between the resulting values is actually a power function of the denominator.

Opfer & Devries demonstrated this by asking 24 second graders and another 24 undergraduates questions to place a hatch mark indicating the location of $1/60 minutes on a number line spanning $1/1 minute to $1/1440 minutes. Astonishingly, second graders were more accurate than undergraduates on this task, perhaps owing to their use of a logarithmic magnitude system. That is, children may perceive 60 as being closer to 1440 than 1, which leads to a bias in placing the hatch mark closer to the correct location when dealing with fractional values.

Children also outperformed adults on a version in which the denominator was specified in more familiar units of duration, such as $1/hour or $1/day. This is a more interesting effect that isn’t discussed much in the paper – one idea is that children’s perception of time is logarithmic as well, such that children perceive one hour as relatively more similar to one full day than adults. (As discussed previously…)