Stages of nonsymbolic number processing in occipitoparietal cortex disentangled by fMRI adaptation.

The neurobiological mechanisms of nonsymbolic number processing in humans are still unclear. Computational modeling proposed three successive stages: first, the spatial location of objects is stored in an object location map; second, this information is transformed into a numerical summation code; third, this summation code is transformed to a number-selective code. Here, we used fMRI-adaptation to identify these three stages and their relative anatomical location. By presenting the same number of dots on the same locations in the visual field, we adapted neurons of human volunteers. Occasionally, deviants with the same number of dots at different locations or different numbers of dots at the same location were shown. By orthogonal number and location factors in the deviants, we were able to calculate three independent contrasts, each sensitive to one of the stages. We found an occipitoparietal gradient for nonsymbolic number processing: the activation of the object location map was found in the inferior occipital gyrus. The summation coding map exhibited a nonlinear pattern of activation, with first increasing and then decreasing activation, and most activity in the middle occipital gyrus. Finally, the number-selective code became more pronounced in the superior parietal lobe. In summary, we disentangled the three stages of nonsymbolic number processing predicted by computational modeling and demonstrated that they constitute a pathway along the occipitoparietal processing stream.

Number processing pathways in human parietal cortex.

Numerous studies have identified the intraparietal sulcus (IPS) as an area critically involved in numerical processing. IPS neurons in macaques are tuned to a preferred numerosity, hence neurally coding numerosity in a number-selective way. Neuroimaging studies in humans have demonstrated number-selective processing in the anterior parts of the IPS. Nevertheless, the processes that convert visual input into a number-selective neural code remain unknown. Computational studies have suggested that a neural coding stage that is sensitive, but not selective to number, precedes number-selective coding when processing nonsymbolic quantities but not when processing symbolic quantities. In Experiment 1, we used functional magnetic resonance imaging to localize number-sensitive areas in the human brain by searching for areas exhibiting increasing activation with increasing number, carefully controlling for nonnumerical parameters. An area in posterior superior parietal cortex was identified as a substrate for the intermediate number-sensitive steps required for processing nonsymbolic quantities. In Experiment 2, the interpretation of Experiment 1 was confirmed with a connectivity analysis showing that a shared number-selective representation in IPS is reached through different pathways for symbolic versus nonsymbolic quantities. The preferred pathway for processing nonsymbolic quantities included the number-sensitive area in superior parietal cortex, whereas the pathway for processing symbolic quantities did not.

The SNARC effect does not imply a mental number line.

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate step in which numbers are categorized as either small or large between the number magnitude and the response representations. In a magnitude comparison task, we departed from the usual bimanual left/right response dimension and instead introduced the unimanual close/far dimension. A spatial-numerical association was observed: small numbers were associated with a close response, while large numbers were associated with a far response, regardless of the movement direction (left/right). We discuss why these results cannot be explained by assuming a direct mapping from the representation of numbers on a mental number line to response locations and discuss how the results can be explained by the alternative accounts.

The size congruity effect: is bigger always more?

When comparing digits of different physical sizes, numerical and physical size interact. For example, in a numerical comparison task, people are faster to compare two digits when their numerical size (the relevant dimension) and physical size (the irrelevant dimension) are congruent than when they are incongruent. Two main accounts have been put forward to explain this size congruity effect. According to the shared representation account, both numerical and physical size are mapped onto a shared analog magnitude representation. In contrast, the shared decisions account assumes that numerical size and physical size are initially processed separately, but interact at the decision level. We implement the shared decisions account in a computational model with a dual route framework and show that this model can simulate the modulation of the size congruity effect by numerical and physical distance. Using other tasks than comparison, we show that the model can simulate novel findings that cannot be explained by the shared representation account.

Distance in motion: response trajectories reveal the dynamics of number comparison.

Cognitive and neuroscientific evidence has challenged the widespread view that perception, cognition and action constitute independent, discrete stages. For example, in continuous response trajectories toward a target response location, evidence suggests that a decision on which target to reach for (i.e., the cognition stage) is not reached before the movement starts (i.e., the action stage). As a result, instead of a straight trajectory to the correct target response, movement trajectories may curve toward competing responses or away from inhibited responses. In the present study, we examined response trajectories during a number comparison task. Participants had to decide whether a target number was smaller or larger than 5. They had to respond by moving to a left or a right response location. Replicating previous results, response trajectories were more curved toward the incorrect response location when distance to 5 was small (e.g., target number 4) than when distance to 5 was large (e.g., target number 1). Importantly, we manipulated the response mapping, which allowed us to demonstrate that this response trajectory effect results from the relative amount of evidence for the available responses across time. In this way, the present study stresses the tight coupling of number representations (i.e., cognition) and response related processes (i.e., action) and shows that these stages are not separable in time.

Verbal-spatial and visuospatial coding of number-space interactions.

A tight correspondence has been postulated between the representations of number and space. The spatial numerical association of response codes (SNARC) effect, which reflects the observation that people respond faster with the left-hand side to small numbers and with the right-hand side to large numbers, is regarded as strong evidence for this correspondence. The dominant explanation of the SNARC effect is that it results from visuospatial coding of magnitude (e.g., the mental number line hypothesis). In a series of experiments, we demonstrated that this is only part of the story and that verbal-spatial coding influences processes and representations that have been believed to be purely visuospatial. Additionally, when both accounts were directly contrasted, verbal-spatial coding was observed in absence of visuospatial coding. Relations to other number-space interactions and implications for other tasks are discussed.