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In the number-to-position methodology, a number is presented on each trial and the observer places it on a straight line in a position that corresponds to its felt subjective magnitude. In the novel modification introduced in this study, the two-numbers-to-two-positions method, a pair of numbers rather than a single number is presented on each trial and the observer places them in appropriate positions on the same line. Responses in this method indicate not only the subjective magnitude of each single number but, simultaneously, provide a direct estimation of their subjective numerical distance. The results of four experiments provide strong evidence for a linear representation of numbers and, commensurately, for the linear representation of numerical distances. We attribute earlier results that indicate a logarithmic representation to the ordered nature of numbers and to the task used and not to a truly non-linear underlying representation.

Judgments of the physical size in which a numeral is presented are often affected by the task-irrelevant attribute of its numerical magnitude, the Size Congruity Effect (SCE). The SCE is typically interpreted as a marker of the automatic activation of numerical magnitude. However, a growing literature shows that the SCE is not robust, a possible indication that numerical information is not always activated in an automatic fashion. In the present study, we tested the SCE via grasping by way of resolving the automaticity debate. We found results that challenge the robustness of the SCE and, consequently, the validity of the automaticity assumption. The SCE was absent when participants grasped the physically larger object of a pair of 3D wooden numerals. An SCE was still recorded when the participants perceptually indicated the general location of the larger object, but not when they grasped that object. These results highlight the importance of the sensory domain when considering the generality of a perceptual effect.

A cornerstone of contemporary research in numerical cognition is the surprising link found between numbers and space. In particular, people react faster and more accurately to small numbers with a left-hand key and to large numbers with a right-hand key. Because this contingency is found in a variety of tasks, it has been taken to support the automatic activation of magnitude as well as the notion of a mental number line arranged from left to right. The present study challenges the presence of a link between left-right location, on the one hand, and small-large number, on the other hand. We show that a link exists between space and relative magnitude, a relationship that might or might not be unique to numbers.

People indicate the physical size or the parity status of small numbers faster by a left-hand key and those of larger numbers by a right-hand key. Because magnitude information is not required for successful performance in these tasks, the presence of a number-space association (the SNARC effect) has been taken to indicate the automatic activation of numerical magnitude in all tasks with numerals. In order to test this account, in a series of five experiments, we derived two consensual markers of automatic activation of irrelevant numerical magnitude, the size congruity effect (for judgments of physical size), and the Garner effect (for judgments of parity). Both markers were found independent of the SNARC effect. Consequently, we question the traditional explanation of the SNARC effect and offer an alternative account in terms of a highly overlearned stimulus-response loop.

The size congruity effect is the interesting result that comparisons of the sizes of the physical formats in which numerals appear are affected by the numerical magnitudes of the respective numerals. We demonstrated that separating the physical and the numerical attributes in space leaves the effect unchanged. We then applied the spatially separated version to two-digit numerals and showed the effect to be comparable to that obtained with single numerals. We showed further that the effect is sensitive to the relative salience of the numeric and physical dimensions, to the extent that when the latter is the more salient dimension, a reverse effect obtains by which physical size interferes with number comparison. The results can be explained by a relative speed of processing account, but they are also compatible with an attention account that does not appeal to the notion of automaticity.

It is commonly believed that humans are unable to ignore the meanings of numerical symbols, even when these meanings are irrelevant to the task at hand. In 5 experiments, the authors tested the notion of automatic activation of numerical magnitude by asking participants to compare, while timed, pairs of numerical arrays on either numerosity or numerical value. Garner and Stroop effects were used to gauge the degree of interactive processing. The results showed that both effects were sensitive to the discriminability of values along the constituent dimensions, to the number of stimulus values used, and to practice and motivation. Notably, Stroop and Garner effects were eliminated under several conditions. These findings are incompatible with claims of obligatory activation of meaning in numerical processing, and they cast doubt on theories positing automatic processing of semantic information for alphanumerical symbols.