article: Perception of number and space are tightly intertwined. It has been proposed that this is due to ‘cortical recycling’, where numerosity processing takes over circuits originally processing space. Do such ‘recycled’ circuits retain their original functionality? Here, we investigate interactions between numerosity and motion direction, two functions that both localize to parietal cortex. We describe a new phenomenon in which visual motion direction adapts nonsymbolic numerosity perception, giving rise to a repulsive aftereffect: motion to the left adapts small numbers, leading to overestimation of numerosity, while motion to the right adapts large numbers, resulting in underestimation. The reference frame of this effect is spatiotopic. Together with the tuning properties of the effect this suggests that motion direction-numerosity cross-adaptation may occur in a homolog of area LIP. ‘Cortical recycling’ thus expands but does not obliterate the functions originally performed by the recycled circuit, allowing for shared computations across domains.
  Our perception of numerosity and space are tightly interrelated, as evidenced by the ‘mental number line’, where small numbers are mapped to the left and large numbers are mapped to the right (Dehaene et al. , 1993). This spatial arrangement of numbers is evident in preverbal infants (de Hevia and Spelke, 2010), non-human primates (Drucker and Brannon, 2014), and even birds (Rugani et al. , 2015), suggesting a deep evolutionary heritage of the mental number line, although there is evidence that it can be influenced by cultural practice (Shaki and Fischer, 2008). Number-space interactions are attributed to the fact that the neural bases of numerical and space processing both localize to parietal cortex (Hubbard et al. , 2005), as evidenced by the fact that parietal lesions disrupt both numerical and spatial processing (Zorzi et al. , 2002). It has been suggested that this co-localization is the result of ‘cortical recycling’ during evolution or normal development (Anderson, 2010; Dehaene and Cohen, 2007), i. e. , numerical cognition builds upon circuits that originally process space, because the computations that are used to gauge target coordinates or to transform reference frames can also be used for operations on numbers. But to what extent do such recycled circuits retain their original functionality? Does numerosity replace space, or does it augment it, allowing for shared computations across domains? We describe a new phenomenon in which visual motion direction, a spatial dimension ubiquitous in dorsal stream areas, adapts numerosity, giving rise to a repulsive aftereffect: motion to the left adapts small numbers, leading to overestimation of numerosity, while motion to the right adapts large numbers, resulting in underestimation. Thus, motion can literally move us up and down the mental number line. This indicates that numerosity coopts circuits encoding space. Furthermore, we show that the reference frame of this cross-adaptation effect is spatiotopic, not retinotopic, which, together with the tuning profile of the adaptation effect, indicates that motion direction-numerosity cross-adaptation may occur in a homolog of area LIP. Thus, recycled numerosity processing circuits indeed remain sensitive to purely spatial features. This shows that ‘cortical recycling’ augments but does not obliterate the spatial capacities of parietal circuits.
  A second characteristic of the neural circuitry in the IPS is that it serves to convert retinotopic coordinates prevalent in early visual areas into eye-, head-, and world-centered frames of reference. In particular, areas LIP and VIP both contain neurons with eye- and head-centered coordinates (Duhamel et al. , 1997; Mullette-Gillman et al. , 2005). However, the two areas can be distinguished based on their respective receptive field properties: while neurons in area LIP have spatially restricted receptive fields, each covering only a portion of the visual world, number-sensitive neurons in area VIP, the next stage of number processing, respond to stimuli distributed over the entire visual field (Nieder and Dehaene, 2009). We capitalized on these distinct properties of LIP and VIP and tested in Experiment 6 whether the cross-adaptation effect between motion direction and number occurs in a retinotopic (early visual areas) or spatiotopic (IPS) frame of reference, and whether it is spatially specific (LIP) or occurs over the entire visual field (VIP), thus allowing us to infer the cortical area in which motion and number processing interact. To this end, in Experiment 6 we replicated Experiment 1 but now also manipulated the location of the test/probe stimuli on the screen relative to subjects’ gaze (Figure 4): Subjects made two saccades between the adaptor and the test/probe stimuli. The second saccade would either bring their gaze back to the initial fixation location (Figure 4a and d), or to a new location 14 degrees visual angle (dva) away from the original center of gaze (Figure 4b and c). We then presented the test/probe stimuli either at the same location on the screen as the adaptor (Figure 4b), at the same location as the adapter relative to the subject’s current gaze (Figure 4c), or at a new location (Figure 4d). This allowed us to compare two frames of reference and the spatial specificity of the cross-adaptation effect. If the cross-adaptation effect was present only when subjects looked at a new location on the screen but the stimuli were presented at the same position relative to their current center of gaze (Figure 4c), it must take place in areas with a retinotopic frame of reference, i. e. , early visual areas; if cross-adaptation was evident only when subjects fixated at a new location but the stimuli were presented at the original location on the screen (Figure 4b), it must occur in an area with a spatiotopic frame of reference and with restricted receptive fields, such as LIP; and if it occurred when subjects looked at the original fixation spot but stimuli were presented at a location that neither matched retino- nor spatiotopic reference frames (Figure 4d), the area in which cross-adaptation takes place must support effects across the entire visual field, as would be predicted for VIP. Figure 5 shows that cross-adaptation between motion direction and number occurs even in the presence of two intervening saccades, replicating Experiment 1. More importantly, the results of Experiment 6 show that cross-adaptation takes place in a spatiotopic, not retinotopic frame of reference, but is restricted to the spatiotopic location of the stimulus and does not extend over the full field of view (motion direction × reference frame interaction, F (3,15) =4. 58, p=0. 018, η2=0. 478). Only the ‘same location’ and the ‘spatiotopic’ condition were significantly different from zero (both p=0. 015, Wilcoxon signed rank tests), while the ‘retinotopic’ and ‘full field’ condition were not (p=0. 71 and p=0. 84, respectively). Bayesian statistics (Benavoli et al. , 2014) confirmed that there was overwhelming evidence for an effect in the ‘same location’ and ‘spatiotopic’ (posterior probabilities >95%), but not in the retinotopic (posterior probability <44. 5%) or full field (posterior probability <29. 8%) conditions. Retinal eccentricity cannot explain our results, since it was matched in the ‘same location’ and the ‘retinotopic’ conditions (0 dva), and in the ‘spatiotopic’ and ‘full field’ conditions (14 dva), respectively, and thus orthogonal to the factor reference frame. Instead, spatiotopy allots the effect to a family of MAEs which are thought to tap into higher-order motion processing stages, such as the positional motion aftereffect (Turi and Burr, 2012), in contrast to the classical MAE, which occurs in a retinotopic frame of reference (Knapen et al. , 2009). This pattern of results is predicted by cross-adaptation occurring in a human LIP homolog. 10. 7554/eLife. 10806. 010Figure 4. Paradigm to test cross-adaptation in different reference frames. The design of Experiment 6 closely followed that of Experiment 1, but introduced two saccades (arrows) between the top-up adaptor and the test/probe stimuli. Initial stimulus and fixation locations are depicted in blue, final stimulus and fixation locations in red. (a) In the ‘same location’ condition, subjects made a 14 dva leftward or rightward saccade after the top-up adaptor had been presented, and then back to the original fixation dot. The location of the test/probe stimuli and adaptor was the same in space and on the retina, depicted here as blue (initial) and red (final) half-cycles. This condition served to replicate the cross-adaptation effect found in Experiment 1. (b) In the ‘spatiotopic’ condition, subjects made two consecutive leftward or rightward saccades (first 14 dva, second 28 dva), and test/probe stimuli were presented at the same screen position as the top-up adaptor but on a different retinal position. Here, a cross-adaptation effect would occur in an area that has spatiotopic but locally restricted receptive fields, such as LIP. (c) In the ‘retinotopic’ condition, subjects also made two consecutive leftward or rightward saccades (first 14 dva, second 28 dva) but test/probe stimuli were presented above and below the new fixation dot. Hence, stimuli occurred at the same retinal location (relative to the subjects’ gaze), but at different location in spatiotopic coordinates. Here, the cross-adaptation effect would occur in early, retinotopically organized visual areas. (d) In the ‘full field’ condition subjects first made rightward or leftward saccaded (14 dva), and then back to the original fixation dot (14 dva, as in the ‘same location’ condition). Test/probe stimuli were however presented at a new location opposite to the second saccade direction. Here, a cross-adaptation effect would only occur if the effect takes place in an area with very large receptive fields, such as VIP. DOI: http: //dx. doi. org/10. 7554/eLife. 10806. 01010. 7554/eLife. 10806. 011Figure 5. The reference frame of motion direction-numerosity cross-adaptation. A non-parametric rmANOVA showed that there was a significant interaction between reference frame and motion direction (F (3,15) =4. 58, p=0. 018, η2=0. 478). Only the ‘same location’ condition which replicated Experiment 1 with intervening saccades and the ‘spatiotopic’ condition with restricted receptive field sizes as predicted for area LIP showed a significant (both p<0. 05) cross-adaptation effect from motion-direction on numerosity (see text for statistics). Together with the tuning function of the effect, this indicates that the influence of motion direction on numerosity takes place at an intermediate, analog stage of number processing, and not in early visual areas with a retinotopic frame of reference or in area VIP with receptive fields covering the entire visual field. Data are represented as mean ± SEM. All data shown here are publicly available at Figshare (Schwiedrzik et al. , 2015). DOI: http: //dx. doi. org/10. 7554/eLife. 10806. 011
  Taken together, our results show on purely behavioral grounds that the neural circuits recycled to process number retain sensitivity to a visual feature intimately linked to our sense of space, namely motion direction. This indicates that ‘cortical recycling’ expands the original functionality of a circuit instead of replacing it, thus establishing a functional link across domains. The combination of properties we find in our study, namely the tuning function, receptive field size, and frame of reference of the motion direction-numerosity cross-adaptation effect matches the known properties of area LIP neurons at the first stage of number processing, which are broadly tuned to numerosity (Roitman et al. , 2007), have relatively small receptive fields (Ben Hamed et al. , 2001), and a spatiotopic frame of reference (Mullette-Gillman et al. , 2005). In contrast, neurons in area VIP, the next stage of number processing, are narrowly tuned and have large receptive fields (Nieder and Dehaene, 2009), and neurons in area MT, a preceding stage of motion processing, have a retinotopic frame of reference (Born and Bradley, 2005). Hence, a human LIP homolog in the IPS seems to be the most likely origin of the motion direction-numerosity cross-adaptation effect. Motion direction-numerosity cross-adaptation is consistent with studies showing that transcranial magnetic stimulation (TMS) over parietal cortex can disturb number comparisons and motion detection (Salillas et al. , 2009), as well as those showing that the number of items in a display can be overestimated when they move at high speed (Afraz et al. , 2004). However, our studies extend these findings in two critical ways: First, by showing that the very same circuits, and not only the same brain area targeted with TMS, process number and motion; and second, by showing that sensitivity of number processing extends to a spatial feature that is orthogonal to magnitude, namely motion direction (motion speed is a magnitude itself). The latter rules out that motion direction-numerosity cross-adaption is simply the consequence of the operation of a ‘generalized magnitude processing system’ (Walsh, 2003). Furthermore, as our results were not effector-dependent, they strongly suggest that number-space associations occur at the level of the representation, not sensorimotor mapping, which is another function of parietal cortex (Fogassi and Luppino, 2005) and has been invoked as an alternative explanation for number-space associations (Keus and Schwarz, 2005). Motion direction-numerosity cross-adaption can also not be easily explained by attention. Because moving stimuli can attract attention in their direction of motion (Mattingley et al. , 1994; Shi et al. , 2010), it is thinkable that attention was drawn down the number line during leftward motion adaptation, and up the number line during rightward motion adaptation. The consequence of this would however be the opposite pattern of results from what we found, namely underestimation after leftward motion (because attention is oriented down the number line) and overestimation after rightward motion (because attention is oriented up the number line). Experiment 4 also ruled out that attention was drawn to the left or to the right by illusory motion arising from a classical MAE (Figure 2—figure supplement 1 and Figure 2—figure supplement 2). Hence, attention is an unlikely explanation for motion direction-numerosity cross-adaptation. Our results are indicative of an opponent coding model such as the one proposed for the classical MAE (Mather and Harris, 1998), in which large and small numerosities compete (Figure 6). Here, adaptation causes broadly tuned neurons coding for large numbers to reduce their responsiveness, giving rise to an overshoot in the activity of neurons that code for small numbers, and vice versa, leading to under/overestimation. This is evident in the general rightward shift of PSEs reported in Experiment 1 and the leftward shift of PSEs reported in Experiment 2, and consistent with previously reported adaptation effects of static numerosity (Burr and Ross, 2008). Our model also captures the co-tuning of leftward motion and small numbers/rightward motion and large numbers: leftward motion increases the activity in the small number pool, resulting in increased overestimation after adaptation, while rightward motion increases the activity in the large number pool, resulting in increased underestimation after adaptation. This causes the differential shifts of PSEs with motion direction along the mental number line. 10. 7554/eLife. 10806. 012Figure 6. Hypothetical model of motion direction-numerosity cross-adaptation. We can explain the cross-adaptation effect using a two-pool opponent coding model similar to what is often invoked to explain the classical MAE and other aftereffects (Mather and Harris, 1998). Panel (a) exemplifies the effect of motion direction during adaptation with large numerosities (Experiment 1, Figure 2a), panel (b) exemplifies the effect of motion direction during adaptation with small numerosities (Experiment 2, Figure 2c). The two black lines reflect the activity level of two broadly tuned pools of neurons that respond maximally to small or large numbers, respectively. The tuning curves are overlapping such that any given stimulus produces activity in both pools. Adaptation to number causes each pool to reduce its firing rate proportionally to how well the stimulus activates the respective pool in the non-adapted state, e. g. , static or randomly moving dot clouds with large numbers of dots (as in Experiment 1, e. g. , in the lower cloud, or in Burr and Ross, 2008) lead to stronger adaptation in the pool for large numbers (blue). After adaptation, this pool’s response is reduced, shifting the point at which the two tuning curves intersect to the either to the right (a), i. e. , towards larger numbers, or to the left (b), i. e. , towards smaller numbers. This also shifts the point of subjective equality (PSE) in a comparison task (gray), leading to an underestimation (a) or overestimation (b) in how many dots are perceived. During adaptation with large numerosities, rightwards motion exaggerates underestimation (a) by activating the pool for large numbers more strongly, moving perception up the number line (green, inset), subsequently causing a stronger cross-adaptation effect (underestimation). In contrast, leftwards motion reduces the effect, moving perception down the number line (orange, inset), subsequently causing a cross-adaption effect in the opposite direction. During adaptation with small numerosities, leftwards motion exaggerates overestimation (b) by activating the pool for small numbers more strongly, moving perception down the number line (green, inset), subsequently causing a stronger overestimation effect. Rightwards motion reduces overestimation, moving perception up the number line (orange, inset). Monotonically increasing and decreasing tuning curves are consistent with numerosity tuning curves measured in monkey LIP (Roitman et al. , 2007) and with the fact that we could exert an effect on the perception dot numerosities far removed from the adaptor, e. g. , perception of 23–107 dots when adapting with 400 dots in Experiment 1, which would not be expected if each number was represented by narrow tuning curves as those found in monkey VIP (Nieder et al. , 2006). This was also supported by Experiment 5 which showed that there was no motion direction-numerosity cross-adaption when the number of dots in the adapter and the probe were matched (mean difference right vs. left −3. 69, p=0. 92, Wilcoxon signed rank test, one-sided; Bayesian posterior probability <0. 18%), as predicted for two-pool opponent coding models (Robbins et al. , 2007; Webster, 2011). DOI: http: //dx. doi. org/10. 7554/eLife. 10806. 012 Opponent coding further suggests that large adaptor – probe/test distances should lead to large repulsive aftereffects as they maximize the differential response ratio between the two pools, while models with multiple, narrowly tuned channels would predict the opposite (Robbins et al. , 2007; Webster, 2011). Specifically, if narrowly tuned neurons such as those found in area VIP (Nieder et al. , 2006) are adapted, the strongest effects of adaptation occur directly around the adaptor, while effects fall off as a function of adaptor-test/probe distance. This is characteristic of multichannel models. In contrast, in two-pool opponent coding with broadly tuned neurons such as those found in area LIP (Roitman et al. , 2007), adaptation at the probe location leads to no or only very small effects (assuming the probe stimulus serves as an explicit reference point), as adaptation influences the activity in both pools approximately equally, thus merely reinforcing the current level of overall adaptation. Indeed, we found that large adaptor – probe/test distances led to large repulsive aftereffects, while adapting and probing with the same number of dots did not lead to a significant motion direction-specific aftereffect. This further speaks for two-pool opponent coding and against multichannel models underlying numerosity adaptation. Together, this suggests that current theoretical models of number processing (e. g. , Dehaene and Changeux, 1993) should be expanded to include such an opponent process at the analog summation stage, which would be compatible with the broad neural tuning curves found in monkey area LIP (Roitman et al. , 2007). Finally, it has been shown that the approximate number sense predicts later mathematical achievement (Halberda et al. , 2008). If the link between motion and number can be further substantiated, it may open the venue to utilizing motion processing as a marker for number skill development (Sigmundsson et al. , 2010), and thus to identify children at risk for dyscalculia early in life.
  Fifty-five subjects participated in six experiments: In Experiment 1 we investigated motion direction-numerosity cross-adaptation with large numerosities in 11 subjects (4 female, mean age 22. 8 years, range 19–33 years, 9 right handed). In Experiment 2, we tested for motion direction-numerosity cross-adaptation with small numerosities in 11 subjects (4 female, mean age 27. 1 years, range 22–35 years, 9 right handed); one subject had to be excluded from data analyses because of an apparent failure to do the task. Experiment 3 addressed direct effects of motion direction on numerosity perception in the absence of adaptation in 10 subjects (5 female, mean age 32. 2 years, range 18–48 years, 9 right handed). Experiment 4 served as a control for classical MAEs in 11 subjects (6 female, mean age 33. 45 years, range 23–48 years, 10 right handed). Experiment 5 allowed us to contrast different coding schemes, i. e. , two-pool opponent process vs. multichannel models in 6 subjects (3 female, mean age 29. 8 years, range 22–39 years, 5 right handed). Experiment 6 was conducted to probe the reference frame of motion direction numerosity cross-adaptation in 6 subjects (2 female, mean age 23. 1 years, range 21–30 years, all right handed). All subjects had normal or corrected-to-normal vision, reported no history of neurological or psychiatric disease, and gave written informed consent before participation. All procedures were approved by The University Committee on Activities Involving Human Subjects at New York University. Subjects received monetary compensation for their participation. Stimulus presentation and response collection in all experiments were controlled using Presentation (v17. 2; Neurobehavioral Systems, Berkeley, CA, USA). Trials on which reaction times exceeded 2*median absolute deviation were excluded from the analyses. Psychometric functions were fitted in the Palamedes Toolbox (v1. 7. 0) (Prins and Kingdom, 2009) in Matlab (R2012b, The Mathworks, Natick, MA, USA), using a logistic function to obtain threshold and slope estimates per subject (fits using a cumulative Gaussian function yielded similar results). For Experiments 1,2, and 3 threshold and slope estimates, respectively, were compared using paired t-tests (two-sided) in SPSS (v22, IBM, Armonk, NY, USA). Effect sizes were computed as Hedges’ d (Hedges and Olkin, 1985), where values >0. 8 indicate a large effect and values <0. 5 indicate a small effect. For Experiment 4, we compared mean percentage ‘same’ responses using two-sided one-sample and paired t-tests; analyses of median percent ‘same’ responses using a percentile bootstrap procedure (Wilcox, 2010) yielded the same results. Given the sample sizes in Experiments 5 and 6, we resorted to non-parametric tests. Because we had a directional hypothesis (PSE right>left) in both experiments, planned comparisons were performed using one-sided exact Wilcoxon signed rank tests, but two-sided tests yielded identical patterns of results. In Experiment 6, threshold estimates were also entered into a non-parametric two factor repeated measures analysis of variance (rmANOVA) based on the aligned rank transform (Higgins and Tashtoush, 1994) using ARTool (v1. 5. 1) (Wobbrock et al. , 2011) to assess interaction effects. Effect size was computed as partial η2, where values >0. 14 indicate a large effect and values <0. 06 indicate a small effect. Spatial reference frames in Experiment 6 were determined by testing each experimental condition against 0. While it is standard in the literature to compare reference frames by contrasting conditions against 0 (Arrighi et al. , 2014; Knapen et al. , 2009; Turi and Burr, 2012), we note that such conclusions partially rest on non-significant results. We thus also performed Bayesian statistics, using an exact Wilcoxon signed rank test based on the prior ignorance Dirichlet process model (200000 samples, concentration parameter s=0. 53) (Benavoli et al. , 2014) to support our conclusions. All data are publicly available at Figshare (Schwiedrzik et al. , 2015).
summary: Our sense of number is thought to have emerged from the circuits of cortical neurons in the brain that originally represent space, a process known as' cortical recycling' . Accordingly, our perception of space and number are tightly intertwined: for example, people think about numbers on a mental number line, where smaller numbers are mapped to the left, and larger numbers are mapped to the right. Also, damage to a brain region called the parietal cortex disrupts both space and number processing. If number processing recycles the neurons that encode space, which form does this appropriation take? Recycling could preserve the original behavior of the neurons (processing space), thus enriching the neurons’ functional repertoire with a new capacity (processing number). Alternatively, the newly developed role could replace the original one, such that space and number cohabitate the same brain area but use separate neurons. To disentangle these hypotheses, Schwiedrzik et al. used a technique called' perceptual adaptation' . Here, continuously showing someone a particular feature eventually exhausts the neurons that respond to that feature. Neurons that respond to the opposite feature are however less exhausted and dominate perception. Consequently, people perceive the opposite of what they are adapted to. For example, after continuously seeing dots moving to the right, people perceive stationary dots as moving to the left. Similarly, after being exposed to large numbers of dots they underestimate how many dots they see. If the same neurons process numbers and space, then adapting to movement in a particular direction should influence number perception. During Schwiedrzik et al. ’s experiments, volunteers watched moving dots on a computer screen. After seeing dots move to the right, they underestimated the number of dots that then appeared on the screen. This is likely to be because larger numbers are mentally mapped to the right, and seeing rightward motion for a long time exhausted these neurons. This means that neurons that respond to smaller numbers (mentally mapped to the left) were more active when the new dots were presented, leading the volunteers to underestimate how many dots they saw. Adapting to leftward motion led to the opposite effect, with volunteers overestimating the number of dots. Thus, motion can literally move us up and down the number line. These results indicate that the same neurons encode both space and numbers. Cortical recycling does not erase the neurons’ original behavior: instead, neurons may carry out the same computations when processing numbers or space. This would allow the brain to add new functionality without sacrificing any of the computational resources for processing space.
keywords: neuroscience
title: Motion along the mental number line reveals shared representations for numerosity and space