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AJNR Am J Neuroradiol. 2003 Feb;24(2):193-200.

Quantity determination and the distance effect with letters, numbers, and shapes: a functional MR imaging study of number processing.

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Section of Neuroradiology, Department of Radiology, Yale University School of Medicine, 333 Cedar Street, New Haven, CT 06520-8042, USA.



The ability to quantify, or to determine magnitude, is an important part of number processing, and the extent to which language and other cognitive abilities are involved with number processing is an area of interest. We compared activation patterns, reaction times, and accuracy as subjects determined stimulus magnitude by ordering letters, numbers, and shapes. A second goal was to define the brain regions involved in the distance effect (the farther apart numbers are, the faster subjects are at judging which number is larger) and whether this effect depended on stimulus type.


Functional MR images were acquired in 19 healthy subjects. The order task required the subjects to judge whether three stimuli were in order according to their position in the alphabet (letters), position in the number line (numbers), or size (shapes). In the control (identify task), subjects judged whether one of the three stimuli was a particular letter, number, or shape. Each stimulus type was divided into near trials (quantity difference of three or less) and far trials (quantity difference of at least five) to assess the distance effect.


Subjects were less accurate and slower with letters than with numbers and shapes. A distance effect was present with shapes and numbers, as subjects ordered the near trials slower than far trials. No distance effect was detected with letters. The occipital lobes and intraparietal sulci were active with all three stimuli. Shapes required no additional areas, although analysis of the distance effect revealed that near shapes involved other brain regions, including the frontal lobes. Letters activated a large network comprising the frontal lobes, the anterior cingulate gyrus, and basal ganglia, but few additional areas were engaged by the distance effect. Numbers involved a smaller network including the inferior and middle frontal gyri. The left supramarginal gyrus and both inferior frontal gyri were active in the distance effect with numbers.


Numbers and letters, which are stimuli more associated with abstract symbolism compared with shapes, resulted in slower reaction times and an increased number of active brain regions. Shapes and numbers, but not letters, elicited a distance effect, indicating access to a mental continuum of quantity. The left supramarginal gyrus and both inferior frontal gyri were involved in the distance effect with numbers. The intraparietal sulci were important in determining stimulus magnitude for all stimuli.

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