Illustration of the experimental paradigm and prediction of the 2 competing hypotheses. (A) After an adaptation phase, the subject participated in a same–different task while receiving TMS to the vertex, left IPS, or right IPS. During the baseline task, the # sign appeared, and TMS was not delivered. The adapted number was in digit form in Experiment 1 and verbal number form in Experiment 2. (B) According to the abstract representation hypothesis, numerical representation is subserved by format-independent neuronal populations; therefore, the effect of TMSA should be greater on processing of adapted quantity irrespective of format (e.g., 7, SEVEN), and this effect should decrease according to the distance of numbers of the mental number line (), thus, yielding a positive beta value between adaptation and numerical distance irrespective of the numerical notation. In contrast, the nonabstract representation hypothesis () posits that numerical information is implemented by format-dependent neuronal populations and, therefore, predicts that the TMSA effect will modulate specifically the quantity processing of the adapted format, thus, yielding a positive beta value between adaptation and numerical distance only to the numerical format that has been adapted. For example, if digits are adapted, then the TMSA effect should decrease according to the distance of the numbers of the mental number line, only for digits but not for verbal numbers). This effect should decrease according to the distance of numbers of the mental number line and should be absence for the nonadapted format.

A dissociation between digits and verbal numbers in the left and right IPS in Experiment 1. (A) Only stimulation of the left IPS yielded significant differences between the numerical formats and only digits significantly differed from zero. For the right IPS stimulation, the differences between the numerical formats were not significant, but the mean beta values for right IPS when digits were presented differed significantly from zero. Vertex stimulation did not yield any difference between the formats or difference from zero when the mean beta values of both numerical formats was compared with zero. (B) The beta values for the different formats for each subject after stimulation of the left IPS. Digits differed significantly from zero and from verbal numbers. Error bars depict 1 standard error of the mean.

Results from Experiment 2 completed a double dissociation between digits and verbal numbers in the left IPS by mirroring the TMSA result in Experiment 1 (). (A) Only the TMS to the left IPS yielded a significant difference between the beta values of digits and verbal numbers and a significant difference from zero for the verbal numbers. Stimulation of the right IPS and vertex did not yield a significant difference between the numerical formats or a significant difference from zero. (B) All participants showed a positive beta value between adaptation and numerical distance for verbal numbers after stimulation of the left IPS. In this experiment, verbal numbers differed significantly from zero and from digits. Error bars depict 1 standard error of the mean.