Parallel and serial processes in number-to-quantity conversion

Converting a multi-digit number to quantity requires processing not only the digits but also the number’s decimal structure, thus raising several issues. First, are all the digits processed in parallel, or serially from left to right? Second, given that the same digit, at different places, can represent different quantities (e.g., “2” can mean 2, 20, etc.), how is each digit assigned to its correct decimal role? We presented participants with two-digit numbers and asked them to point at the corresponding locations on a number line, while we recorded their pointing trajectory. Crucially, on some trials, the decade and unit digits did not appear simultaneously. When the decade digit was delayed, the decade effect on finger movement was delayed by the same amount. However, a lag in presenting the unit digit delayed the unit effect by 35 ms less than the lag duration, a pattern reminiscent of the psychological refractory period, indicating an idle time window of 35 ms in the units processing pathway. When a lag transiently caused a display of just one digit on screen, the unit effect increased and the decade effect decreased, suggesting errors in binding digits to decimal roles. We propose that a serial bottleneck is imposed by the creation of a syntactic frame for the multidigit number, a process launched by the leftmost digit. All other stages, including the binding of digits to decimal roles, quantification, and merging them into a whole-number quantity, appear to operate in parallel across digits, suggesting a remarkable degree of parallelism in expert readers.

Automatic place-value activation in magnitude-irrelevant parity judgement

Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed: However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question by using the parity congruency effect in two-digit numbers: It describes that responding to decade-digit parity congruent numbers (e.g., 35, 46; same parity of decades and units) is faster than to decade-digit parity incongruent numbers (e.g., 25; 36; different parities of decades and units). Here we investigate the (a-)symmetry of the parity congruency effect; i.e. whether it makes a difference whether participants are assessing the parity of the unit digit or the decade digit. We elaborate, how and why such an asymmetry is related to place-value processing, because the parity of the unit digit only interferes with the parity of the decade digit, while the parity of the decade digit interferes with both the parity of the unit digit and the integrated parity of the whole two-digit number. We observed a significantly larger parity congruency effect in the decade parity decision than in the unit parity decision. This suggests that automatic place-value processing also takes place in a typical parity judgment task, in which magnitude is irrelevant. Finally, because of the cross-lingual design of the study, we can show that these results and their implications were language-independent.

The Processing of Two-Digit Numbers Depends on Task Instructions

Recently, a lot of research has focused on resolving whether two-digit numbers are processed holistically or compositionally. This has led to inconsistent results. In the present study we investigated effects of task instructions. Subjects performed magnitude or parity judgments on targets preceded by masked primes containing parts of the target at a task-congruent (3#_37) or task-incongruent (#3_37) position. Priming effects were influenced by the instructions: In the magnitude task, the priming effects were primarily mediated by the congruency of the decade digit, whereas in the parity task they were elicited by the congruency of the unit digit, which is in line with a flexible compositional processing style. These and previous findings show that two-digit numbers can be processed in a very flexible way, depending on the task context.

The Involvement of the Inferior Parietal Cortex in the Numerical Stroop Effect and the Distance Effect in a Two-digit Number Comparison Task

The neural mechanism of number representation and processing is currently under extensive investigation. In this functional magnetic resonance imaging study, we designed a number comparison task to examine how people represent and compare two-digit numbers in the brain, and whether they process the decade and unit digits in parallel. We manipulated the decade-unit-digit congruency and numerical distance between the pairs of numbers. We observed both Stroop-like interference and the distance effect in the participants' performance. People responded more slowly to incongruent pairs of numbers and pairs of a smaller distance. The inferior parietal cortex showed common and distinct patterns of activation for both attentional selection and number comparison processes, and its activity was modulated by the Stroop-like interference effect and the distance effect. Taken together, these results support both parallel and holistic comparison of two-digit numbers in the brain.