The characteristic of extrapolation in numerical inductive inference: An ERP study

Event-related brain potentials (ERPs) were recorded to study the characteristic of extrapolation in the number series completion task. Subjects were asked to judge whether the test number was following the number series according to the rule acquired from the prior three numbers presented. For Congruent Condition, the test number was the right answer which followed the prior three numbers with a rule (such as “+4”). For Incongruent Condition, the test number was unrelated to the prior three numbers. The difficulty effect was also examined by setting two levels of rule difficulty (easy rule vs. difficult rule). The electrophysiological results indicated that P2 and N2 amplitudes were larger in incongruent condition than in congruent condition. Moreover, N2 and P3 peak latencies were shorter in congruent condition than in incongruent condition. The negative component (N2) was considered as the reflection of the mismatch between the presented number and the inner answer. These findings also showed the direct effect of rule difficulty on P2 and P3 amplitudes. It suggested that the rule difficulty still affected the extrapolating process, possibly as the different quantity process and the more information load on internal operation needed for the difficult series.