TY - JOUR
AU - Casasanto,, Daniel
AB - Abstract How do humans compute approximate number? According to one influential theory, approximate number representations arise in the intraparietal sulcus and are amodal, meaning that they arise independent of any sensory modality. Alternatively, approximate number may be computed initially within sensory systems. Here we tested for sensitivity to approximate number in the visual system using steady state visual evoked potentials. We recorded electroencephalography from humans while they viewed dotclouds presented at 30 Hz, which alternated in numerosity (ranging from 10 to 20 dots) at 15 Hz. At this rate, each dotcloud backward masked the previous dotcloud, disrupting top-down feedback to visual cortex and preventing conscious awareness of the dotclouds’ numerosities. Spectral amplitude at 15 Hz measured over the occipital lobe (Oz) correlated positively with the numerical ratio of the stimuli, even when nonnumerical stimulus attributes were controlled, indicating that subjects’ visual systems were differentiating dotclouds on the basis of their numerical ratios. Crucially, subjects were unable to discriminate the numerosities of the dotclouds consciously, indicating the backward masking of the stimuli disrupted reentrant feedback to visual cortex. Approximate number appears to be computed within the visual system, independently of higher-order areas, such as the intraparietal sulcus. approximate number system, consciousness, occipital, SSVEP, vision Introduction Humans have a remarkable capacity for working with numbers. Symbolic mathematical ability is hard earned, requiring explicit instruction, and prolonged practice. Starting early in life, however, humans can rapidly assess approximate number with no training, an ability many researchers attribute to an “approximate number system” (ANS) (Dehaene et al. 1998). The intraparietal sulcus has been implicated as an important area supporting number processing, with many studies suggesting the intraparietal sulcus as the site where number representations arise. An alternative proposal suggests that the visual system may calculate number directly (e.g., Burr and Ross 2008). Experiments testing this proposal have localized number-sensitive signals to the occipital cortex but leave open the possibility that a higher-order cortical area like the intraparietal sulcus computes number and feeds this numerical information back to the visual system. In this study, we observe number-sensitive signals in the visual system under experimental conditions that disrupt reentrant feedback to the occipital cortex. Thus, we conclude that the visual system can compute number directly. The Intraparietal Sulcus as the Locus of Number Representations According to some researchers, the intraparietal sulcus is where number representations arise (Dehaene et al. 1999; Nieder 2016; Nieder and Miller 2004; Pinel et al. 2001; Zorzi et al. 2002). This suggestion is consistent with the observation that intraparietal sulcus responds to numerosities regardless of their sensory modality (Dehaene et al. 1998; Dehaene et al. 2003; Eger et al. 2003) and that adaptation to number has been found across sensory modalities (Arrighi et al. 2014). In light of this apparent modality independence, the intraparietal sulcus is believed to be “the first cortical hub to extract quantitative information” from stimuli (Nieder 2016, p. 369). The evidence that the intraparietal sulcus is involved in approximate number processing is strong and varied, including studies using positron emission tomography (e.g., Dehaene et al. 1996), functional magnetic resonance imaging (Naccache and Dehaene 2001; Piazza et al. 2007), transcranial magnetic stimulation (Andres et al. 2011; Cappelletti et al. 2007; Göbel et al. 2006), and clinical populations with brain lesions (Cipolotti et al. 1991; Dehaene and Cohen 1997). Yet, although it is clear that the intraparietal sulcus is involved in number processing, it is unclear whether this is the site (or the only site) where approximate number representations arise. Is Number Also Computed in the Visual System? In addition to amodal number representations in the intraparietal sulcus, could number processing also occur within sensory systems? On one proposal, number may be processed as “a primary visual property like color or motion” (Burr and Ross 2008, p. 1). Initial evidence for this proposal relied on behavioral adaptation effects (Burr and Ross 2008; Ross and Burr 2010). Subsequent neuroimaging studies have localized number-sensitive signals to the visual cortex using functional magnetic resonance imaging (fMRI) (DeWind et al. 2018, Castaldi et al. 2019, Cavdaroglu and Knops 2019) and electroencephalography (EEG) (e.g., Park et al. 2015; Fornaciai et al. 2017). One approach to testing for numerosity processing in the visual system is to evoke Steady State Visual Evoked Potentials (SSVEPs). SSVEPs are “exogenous ERPs...generated in response to a train of stimuli presented at a fixed rate” (Norcia et al. 2015, p. 1). Typically, stimuli in a train alternate between two values (e.g., a square patch switching between two levels of brightness), and the SSVEP emerges at the frequency of the alternation. The magnitude of the SSVEP signal increases as the magnitude of difference in the alternating values increases (the SSVEP would be stronger when the stimuli brightness alternated between 1000 and 3000 lux than alternating between 1000 and 1200 lux). SSVEP paradigms have been used for over half a century to probe the visual system (Regan 1989), and the occipital lobe has been identified as the primary source of the SSVEP signal using EEG, magnetoencephalography, positron emission tomography , and functional magnetic resonance imaging (e.g., Andersen et al. 2008; Di Russo et al. 2007; Fawcett et al. 2004; Hillyard et al. 1997; Müller et al. 1997; Sammer et al. 2005; c.f. Thorpe et al. 2007). The SSVEP paradigm can be adapted to test for a subject’s sensitivity to the numerosity of the stimulus by changing the numerical content within a stimulus stream at some fixed interval. If the subject is sensitive to the changes in numerosity, the changes will evoke an SSVEP at that frequency. Researchers have successfully used variants of this approach to record number-sensitive SSVEPs from adults (Guillaume et al. 2018; Park 2018), and children (Libertus et al. 2011; Park 2018). On the basis of SSVEP and fMRI studies showing number-sensitive signals in the occipital cortex (DeWind et al. 2018; Fornaciai et al. 2017; Park et al. 2015), researchers have claimed that the occipital cortex is calculating numerosity from visual input, suggesting that “visual quantities are perceptually discriminated automatically and rapidly (i.e., at a glance) within the occipital cortex.” (Guillaume et al. 2018, p. 180). These findings have been interpreted as “strong support for the hypothesis that number is rapidly and directly encoded early in the visual processing stream.” (DeWind et al. 2018, p. 76), and as confirmation that “number is encoded rapidly and directly very early in the visual processing stream” (Doricchi et al. 2019, p. 1). Can the claim that the visual system computes number be supported by observations of number-sensitive signals in the occipital cortex? Under a skeptical interpretation, number-related activity in the occipital cortex could result from number computations in classical number areas (e.g., intraparietal sulcus) which feed the resulting numerosity representation back down to occipital cortex. The visual system produces feedforward sweeps from the occipital cortex to higher-order cortical areas, followed by reentrant feedback to the occipital cortex (Dehaene et al. 2006; Lamme and Roelfsema 2000). It is possible to interpret studies showing number-sensitive signals in occipital cortex as evidence that number is computed there (DeWind et al. 2018; Doricchi et al. 2019). However, these studies are also consistent with the view that the intraparietal sulcus is where number representations originate (Dehaene et al. 1999; Nieder 2016). Number sensitive activity in occipital cortex could reflect feedback from the intraparietal sulcus, where number was computed, first. To distinguish these two possibilities and to clarify the first cortical locus of approximate number representation, in the present study we presented visual numerosity stimulation while disrupting reentrant feedback to the occipital cortex. The Present Study Here we report an SSVEP experiment testing whether occipital cortex responds to the numerosity of visual stimuli under conditions that disrupt feedback from higher-order cortical areas to the occipital cortex. We designed trains of stimuli to take advantage of a known property of SSVEPs: the magnitude of the evoked response increases with the magnitude of the difference between the alternating stimuli. Therefore, we varied the numerical ratio of the alternating dotclouds between trains of stimuli in order to probe subjects’ visual sensitivity to different numerosities. If the occipital cortex, per se, is sensitive to the numerical content of the dotclouds, then the strength of the SSVEP should increase as the dotcloud ratios increase. Observed SSVEPs should be weak for close ratios that are difficult for humans to discriminate reliably (e.g., 10:11 dots) and should increase asymptotically, plateauing at large ratios that are equally easy to discriminate (as is typically found for behavioral measures of approximate number discrimination; e.g., Libertus et al. 2012). To ensure that the observed SSVEPs index sensitivity to the numerosity of the stimuli, as opposed to sensitivity to other visual attributes, we constructed the stimuli according to a method developed by DeWind, Adams, Platt, and Brannon (DeWind et al. 2015). This method allows the numerical content of the stimuli to be partially orthogonalized with respect to the nonnumerical content, and for nonnumerical magnitudes to be controlled. Unlike previous tests of number processing in occipital cortex (including previous SSVEP tasks, e.g., Park 2018), here we used backward masking to disrupt reentrant feedback in order to test for number computations within occipital cortex, per se. Visual input is initially processed in a feedforward sweep from lower- to higher-order areas. Although visual areas respond selectively to complex stimuli during the feedforward sweep (e.g., faces; Oram and Perret 1992), feedforward processing is not sufficient for viewers to identify the stimuli consciously (Lamme 2006; Lamme and Roelfsema 2000). Conscious awareness appears to depend on subsequent reentrant feedback involving fronto-parietal areas feeding back- to lower-level visual areas (Dehaene et al. 2006; Di Lollo et al. 2000; Dux et al. 2010; Lamme 2003; Lamme and Roelfsema 2000). Backward-masking a target stimulus by rapidly presenting a new stimulus reduces or eliminates awareness of the first stimulus. The masking stimulus elicits a new cascade of feedforward activity, changing the state of the visual cortex as it processes the new stimulus. This feedforward activity disrupts the integration of reentrant feedback from higher-order areas that is necessary for conscious visual awareness (Fahrenfort et al. 2007). To achieve backward masking, we present dotcloud stimuli with 33 ms between stimulus onsets. Each dotcloud acts as a backward mask for the previous stimulus. If subjects are unable to report on the numerical contents of the stimulus, this would indicate that backward masking disrupted the reentrant processing that leads to conscious awareness of approximate number. If the occipital cortex is insensitive to stimulus numerosity under these conditions, this result would support the hypothesis that numerosity is first calculated in the intraparietal sulcus and fed back down to the occipital cortex. Alternatively, if a number-sensitive SSVEP is observed during unconscious processing of the backward-masked dotcloud stimuli, this result would support the hypothesis that approximate number representations can originate within the occipital cortex. Materials and Methods Participants Twenty-one adults from the University of Chicago community participated for cash compensation. Subjects had normal or corrected-to-normal vision. All subjects provided informed consent in writing. Dotcloud Stimuli Stimuli consisted of eleven sets of dotclouds. Each stimulus set contained 288 unique dotclouds. In a given set, half of the dotclouds had ten dots per cloud, and half had a single comparison number of dots. The eleven comparison quantities ranged from 10 to 20 dots. All dots within a given dotcloud were the same size. Dotclouds were constructed so that the number comparison increased across sets (i.e., 10:10, 10:11, 10:12, up to 10:20). Size (total surface area, individual dot surface area) and spacing (convex hull, sparsity) attributes were selected so that they varied across sets but did not systematically differ across the range of number comparisons. The stimuli were constructed so that the magnitude of variation within each attribute changed across trials. Importantly, the change in the magnitude of variation across trials differs between numerical and nonnumerical attributes (Figures 2 and 3), peaking in the middle of the range of dotcloud values for nonnumerical attributes but increasing linearly for number, thus allowing statistical separation of their effects. Design and Procedure Subjects completed two tasks across 2 h. The first task (“fast presentation of dotclouds”) involved passively viewing series of dotcloud stimuli flashing at 30 Hz presented with PsychoPy2 v1.84.0 (Peirce 2007) while EEG was recorded. Each dotcloud was on screen for 16.7 ms, with a 16.7 ms ISI between dotclouds. Each trial contained 9.6 s of dotcloud stimulation, after which subjects were asked to make a numerosity judgment: “Did all the dotclouds have the SAME quantity, or did some have a DIFFERENT quantity?” The subjects responded verbally, and the experiment recorded their answer with a keystroke (“s” or “d”). See Figure 1 for the trial structure. A block consisted of 11 trials. Each trial presented one of the 11 unique sets of dotcloud stimuli. Subjects completed as many blocks as possible in the first task for about 80 min. The completed number of blocks ranged from 15 to 24 blocks (165–264 trials). We then stopped recording EEG and they began the second task (“slow dotcloud presentation”). In the second task, subjects were presented dotclouds in pairs. After each pair of dotclouds was presented, subjects were asked to make a numerosity judgment: “Did both dotclouds have the SAME quantity, or did they have DIFFERENT quantities?” Subjects recorded their response with a keystroke (“s” or “d”). Dotclouds were randomly chosen as an adjacent pair from one of the eleven unique sets of stimuli used during fast dotcloud presentation. Dotcloud stimuli were presented serially to the subject. Each dotcloud remained on-screen for 200 ms, with a 100 ms interstimulus interval between presentation of the first and second dotcloud. A block consisted of 11 trials. Each trial presented one pair of dotclouds and contained a unique number comparison (e.g., 10:17). Subjects completed as many blocks as possible for about 10 min, and then the task was ended. During both tasks, the background was gray (#7F7F7F). All dots were orange (#FFA500). All on-screen text was white (#FFFFFF), as was a fixation cross that appeared 2000 ms before dotcloud stimulation began and remained on screen until the end of the trial. Subjects sat in a chair with their head approximately 24 inches away from the screen. At the start of all trials in the both tasks, the screen went gray and the fixation-cross appeared. After a 2 s delay, the dotcloud stimulation began. Figure 1 Open in new tabDownload slide Trial structure of the two tasks. (a) During fast dotcloud presentation, we recorded EEG while subjects watched dotclouds flashing on screen at 30 Hz. On each trial after 9.6 s of dotcloud stimulation, subjects judged whether all of the dotclouds had the same number of dots, or if some differed. (b) During slow dotcloud presentation, two dotclouds were presented and then subjects judged whether they differed in number. Each dotcloud was presented for 200 ms, with a 100 ms interstimulus interval. Figure 1 Open in new tabDownload slide Trial structure of the two tasks. (a) During fast dotcloud presentation, we recorded EEG while subjects watched dotclouds flashing on screen at 30 Hz. On each trial after 9.6 s of dotcloud stimulation, subjects judged whether all of the dotclouds had the same number of dots, or if some differed. (b) During slow dotcloud presentation, two dotclouds were presented and then subjects judged whether they differed in number. Each dotcloud was presented for 200 ms, with a 100 ms interstimulus interval. EEG Acquisition We collected EEG data using a whole-head 128-channel HydroCell Geodesic Sensor Net (Electrical Geodesics Inc., Eugene, OR), bandpass filtered from 0.1 to 100 Hz, and digitized at a rate of 250 Hz (Net Amps 200 TM, Electrical Geodesics, Inc.). Individual electrodes were adjusted until impedances were below 50 kΩ before recording. About every 10 min during breaks in-between blocks of stimuli, we checked for and corrected any electrode impedances that had risen above 50 kΩ. Using Netstation software, we exported recordings into a MATLAB-readable format (.raw). Subsequent analyses in MATLAB and R used the Fieldtrip toolbox (Oostenveld et al. 2011) and custom software. Analysis of SSVEPs Our analysis of the EEG signal recorded during fast presentation of dot clouds used the 15 Hz spectral amplitude of dotcloud stimuli attributes to predict the change in the strength of the observed 15 Hz SSVEP. We analyzed the 15 Hz frequency because the number of dots per dotcloud alternated at 15 Hz during the task. Dotcloud stimulation was being presented at 30 Hz. For a 15 Hz SSVEP to arise, the subject must be differentiating the dotclouds using some attribute of the stimulus that alternated at 15 Hz. We focused our SSVEP analyses on the Oz sensor. Oz is a typical choice for measuring SSVEPs because it is located centrally over occipital (visual) cortex. We calculated a signal-to-noise ratio (SNR) of the 15 Hz SSVEP to create a measure that was comparable across subjects and trials. We converted the recorded EEG signal on each 9.6 s trial (2400 samples) into the frequency domain with a Hanning window fast Fourier transform. We then divided the amplitude in the 15 Hz bin by the average amplitude in the 10 frequency bins adjacent on either side, yielding the SNR measure (following Rossion et al. 2012; Srinivasan et al. 1999). We excluded the two bins closest to 15 Hz in order to reduce roll-off contamination, calculating the noise as the average amplitude in the frequency bins 13.85 Hz to 14.79 Hz, and 15.20 Hz to 16.14 Hz. The frequency bins were spaced about 0.1 Hz apart. The SNR measure normalizes the signal, protecting against electrode recording idiosyncrasies (e.g., impedance drift) across subjects and blocks. We calculated the coefficient of variation for the raw 15 Hz signal and for the 15 Hz SNR within each trial type (e.g., 10:17). The mean coefficient of variation was five times greater for the raw signal than it was for the SNR (two-sided paired t(20) = 4.42, P = 0.001), indicating that the SNR was a more reliable measure of the SSVEP across subjects and trials. Analysis of Stimulus Attributes We performed a spectral analysis of the stimuli to extract the 15 Hz oscillations of seven dotcloud stimuli attributes within each stimulus set. Using a hanning-window Fourier transform, we calculated the 15 Hz amplitude for number, total surface area, individual dot size, sparsity, and convex hull (convex hull and field area are two closely related features that capture an aspect of dotcloud spacing. Convex hull is defined as the smallest enclosing polygon without concavity that encompasses all of the dots in a cloud. Field area is defined as the smallest circle that encompasses all of the dots in a cloud. In our stimuli, convex hull and field area were highly correlated (r = 0.96, P < 0.001). In the Results section, we report analyses that adopt convex hull as the measure, but we also analyzed the data using field area in place of convex hull. The reported effects of number remain robust no matter whether analyses include field area or convex hull). We included two amalgam measures in the spectral analysis, size and spacing, which, respectively, capture the size and spacing aspects of the dotcloud stimuli that are independent of numerosity (see DeWind et al. 2015 for details). Size is defined as log2(Size) = log2(Total Surface Area) + log2(Individual Dot Size), and spacing as log2(Spacing) = log2(Convex hull) + log2(Sparsity). We also calculated the 15 Hz amplitude of stimulus contrast energy (Kukkonen et al. 1993, Parish and Sperling 1991). Contrast energy is the sum of squared contrast values for all pixels in a stimulus. The occipital cortex, particularly early occipital cortex (Dumoulin et al. 2008), is sensitive to the contrast energy of a stimulus. We calculated contrast energy as ∑∑ C2(x,y), where the local contrast for an individual pixel C(x,y) is calculated as (L(x,y)-L0)/L0 with L(x,y) being the luminance of the pixel (taken as its greyscale value) and L0 being the mean luminance across all pixels in the stimulus. We created time-series data that simulated how the magnitude of a given stimulus attribute (e.g., total surface area) changed over time during the experiment in a given stimulus set. We created time points from 0 to 9.6 s with 3.3 ms spacing (300 Hz sampling). We then created values at each timepoint matching the magnitude of the attribute as displayed to the subject during the experiment. For timepoints coinciding with blank (gray) screens, we entered zero. For timepoints with a dotcloud stimulus on screen, we entered the magnitude of the attribute of interest (e.g., total number of orange pixels for total surface area). We used a Fourier transform to extract the spectral amplitude at 15 Hz for the seven spatial attributes of interest as well as contrast energy within each of the eleven stimulus sets. See Figures 2 and 3 for the 15 Hz spectral amplitude of the attributes plotted as a function of the number comparison in that stimulus set. When preparing the spectral amplitude values of each attribute for charting, we normalized the values for easier visualization. Each attribute had 11 amplitude values; one for each trial type. For each attribute, we normalized the 11 values to fall between zero and one, with the largest value set to one. This operation preserved the ratio between values for a given attribute across trials. Direct comparisons of amplitude between attributes are meaningless with or without normalization. However, normalizing the values to fall in the same range allows visual comparison of the way each attribute’s amplitude changes across trials. Figure 2 Open in new tabDownload slide Normalized spectral amplitude for dotcloud attributes number, size, and spacing, plotted as a function of the numerical ratio of dotclouds in each trial. The amplitude value shows how much an attribute changed at 15 Hz during fast dotcloud presentation. The change in amplitude for number across trials dissociates from the changes in amplitude of other dotcloud attributes. Figure 2 Open in new tabDownload slide Normalized spectral amplitude for dotcloud attributes number, size, and spacing, plotted as a function of the numerical ratio of dotclouds in each trial. The amplitude value shows how much an attribute changed at 15 Hz during fast dotcloud presentation. The change in amplitude for number across trials dissociates from the changes in amplitude of other dotcloud attributes. Figure 3 Open in new tabDownload slide Normalized spectral amplitude for stimulus contrast energy, plus the dotcloud spatial attributes number, individual dot size, total surface area, sparsity (labeled density), and convex hull, plotted as a function of the numerical ratio of dotclouds in each trial. The amplitude value shows how much an attribute changed at 15 Hz during fast dotcloud presentation. The change in amplitude for number across trials dissociates from the changes in amplitude of other dotcloud attributes. Contrast energy (green, unfilled boxes) and total surface area (blue, filled boxes) are almost perfectly correlated. Figure 3 Open in new tabDownload slide Normalized spectral amplitude for stimulus contrast energy, plus the dotcloud spatial attributes number, individual dot size, total surface area, sparsity (labeled density), and convex hull, plotted as a function of the numerical ratio of dotclouds in each trial. The amplitude value shows how much an attribute changed at 15 Hz during fast dotcloud presentation. The change in amplitude for number across trials dissociates from the changes in amplitude of other dotcloud attributes. Contrast energy (green, unfilled boxes) and total surface area (blue, filled boxes) are almost perfectly correlated. Regression Analyses To model the influence, the various stimuli attributes had on the strength of the SSVEP signal, we predicted changes in the SSVEP SNR across trials using the 15 Hz spectral amplitude of the stimulus attributes as regressors. Regression analyses were done using R v3.3.1 (R Core Team 2017) with the lme4 package v1.1–12 (Bates et al. 2015). We modeled subjects as a random effect, and the 15 Hz spectral amplitude of the stimulus attributes as fixed effects. When testing for an effect of interest we used a maximal approach (Barr et al. 2013). We included random by-subject slopes for that effect (e.g., by-subject slopes for number when testing for an effect of number) as well as by-subject intercepts. To test for statistical significance, we used likelihood ratio tests to compare the log likelihood of a full regression model to the log likelihood of a reduced model without the term of interest. This procedure yields degrees of freedom, a chi-square value, and a P-value. In the EEG data, each data point of observed SNR was labeled with subject, trial number, comparison (e.g. “10 versus 17”), and 15 Hz amplitude values for each of the eight stimulus attributes. All regression models used the entire dataset with no averaging or exclusions. In the behavioral datasets from our custom experiment scripts (two datasets, one each from the two tasks), we used the numerical ratio of the dotclouds to predict the same (0) or different (1) judgments with logistic regression. The numerical ratio was the comparison dotcloud number (from 10 to 20) divided by the standard dotcloud number (10), and ranged from 1.0 to 2.0 in 0.1 increments. Figures 4 and 5 present SNR calculated on a per-trial basis with scalar averaging; only the amplitudes of Fourier components were used in the calculations. Supplementary Figure S7 and Supplementary Figure S8 (see supplementary materials) present versions of the charts with SNR calculated using vector averaging, which considers phase information along with the amplitudes. Figure 4 Open in new tabDownload slide The signal to noise ratio of the 15 Hz SSVEP increases with greater differences in dotcloud numerosity. The dashed line indicates a SNR of 1. Error bars denote 95% confidence intervals. Figure 4 Open in new tabDownload slide The signal to noise ratio of the 15 Hz SSVEP increases with greater differences in dotcloud numerosity. The dashed line indicates a SNR of 1. Error bars denote 95% confidence intervals. Figure 5 Open in new tabDownload slide Grand averaged SSVEP signal shows greatest SNR over posterior midline sensors. Figure 5 Open in new tabDownload slide Grand averaged SSVEP signal shows greatest SNR over posterior midline sensors. Results Fast Dotcloud Presentation: Were Subjects Sensitive to Number per se? During fast dotcloud stimulation, changes in number predicted changes in the observed 15 Hz SNR (b = 0.44, χ2(1) = 15.29, P < 0.001; Fig. 4). Grand averaging of the 15 Hz SSVEP showed it was centered over posterior midline sensors (Fig. 5). Number predicted changes in SNR while controlling for size- and spacing-related attributes of the dotcloud stimuli: while controlling for total surface area and individual dot size (b = 0.43, χ2(1) = 14.29, P < 0.001), and while controlling for the amalgam measure size (b = 0.43, χ2(1) = 14.75, P < 0.001). Number also predicted SNR while controlling for the spacing-related attributes of convex hull and sparsity (b = 0.44, χ2(1) = 13.94, P < 0.001), and while controlling for the amalgam measure spacing (b = 0.48, χ2(1) = 17.17, P < 0.001). Finally, we controlled for size, spacing, and their interaction, finding that number continued to predict changes in the SNR (b = 1.00, χ2(1) = 15.41, P < 0.001). Contrast energy was almost perfectly correlated with the total surface area of the display (r = 0.996). Therefore, the results reported above that controlled for the total surface area of the dots suggest that the relationship between the SNR and number cannot be explained by the contrast energy of the stimuli. Furthermore, all of effects of number reported above remain significant when contrast energy was added to the models (all P values < 0.01). Fast Dotcloud Presentation: Were Subjects Conscious of the Changes in Number? The EEG data during fast dotcloud stimulation shows the subjects were responding to the numerical content of the dotclouds. However, we found that the subjects’ explicit numerosity judgments did not depend on the numerical ratio of the dotclouds (OR = 1.20, χ2(1) = 0.71, P = 0.400; Fig. 6). Despite roughly 90% of their trials containing dotclouds with different numbers of dots, subjects judged all the dotclouds to have the same number of dots about half the time. Although accuracy was poor, there could be a relationship between the EEG signal and judgment behavior. We tested whether subjects were more likely to judge dotclouds as differing in number on trials where they had a higher SNR but did not detect a relationship (OR = 1.019, χ2(1) = 1.61, P = 0.204). Figure 6 Open in new tabDownload slide In the task with fast dotcloud presentation, subjects were unable to accurately judge the numerical content of the dotcloud stimuli. When subjects were presented with dotclouds slowly, they were more likely to judge numerosity accurately as the numerical ratio between dotclouds increased. The dotted line shows chance levels of responding. Error bars denote 95% confidence intervals. Figure 6 Open in new tabDownload slide In the task with fast dotcloud presentation, subjects were unable to accurately judge the numerical content of the dotcloud stimuli. When subjects were presented with dotclouds slowly, they were more likely to judge numerosity accurately as the numerical ratio between dotclouds increased. The dotted line shows chance levels of responding. Error bars denote 95% confidence intervals. Could Subjects Judge the Numerical Content When Dotclouds Were Presented Slowly? When presented with the same dotcloud stimuli more slowly (200 ms per dotcloud, 100 ms interstimulus interval) in pairs, subjects showed a strong dependence on numerical ratio in their same-or-different judgments (OR = 363.072, χ 2(1) = 31.318, P < 0.001; Fig. 6). Discussion When subjects viewed dotclouds that alternated in numerosity at 15 Hz, this stimulation evoked a steady state 15 Hz signal (SSVEP) centered over posterior midline electrodes. The strength of the 15 Hz SSVEP depended on the numerical content of the stimuli even when the size and spacing of the dots were controlled, indicating that the SSVEP was generated in part by processing of numerical information, and not only the spatial attributes of the stimuli. Due to the rapid presentation of stimuli (33 ms between presentation onsets), each dotcloud was backward masked by the subsequent dotcloud. Accordingly, although the SSVEPs showed sensitivity to the numerosity of the dotclouds, subjects were unable to report the numerical content of the stimuli consciously, indicating that reentrant feedback related to the numerosity of the stimuli from higher-level cortices back to visual cortex was disrupted. These results suggest that approximate number representations arise within visual cortex, rapidly and unconsciously, independent of reentrant feedback from higher cortical regions typically associated with number processing. These findings are consistent with the proposal that numerosity is processed as a “primary visual property” of stimuli, “like color or motion” (Burr and Ross 2008, p. 1). Previous neuroimaging experiments have also shown number-sensitive activity in the visual system (Cavdaroglu and Knops 2019; Fornaciai and Park 2018; Park et al. 2015; Park 2018; DeWind et al. 2018). What has remained unclear, however, is whether this number-sensitive activity in the visual system arises from computations within the occipital cortex itself. Under an alternative account, number representations could arise first in the intraparietal sulcus, a cortical region long believed to be where number representations originate (Dehaene et al. 1999; Nieder 2016; Nieder and Miller 2004; Pinel et al. 2001; Zorzi et al. 2002), and the intraparietal sulcus could subsequently feed number representations back to the occipital cortex. If so, the number-sensitive activity in occipital cortex shown in previous experiments would not necessarily provide evidence that occipital cortex “computes” number (e.g., the way it computes color or motion), as opposed to “reflecting” number representations that originated elsewhere. The present results challenge this skeptical account, supporting the view that approximate number representations arise in the occipital cortex. If the occipital cortex, itself, computes numerosity, does this finding challenge the belief that number is represented in the intraparietal sulcus? Not necessarily. These findings do raise questions, however, about the role intraparietal sulcus plays in number processing. When researchers claim that the intraparietal sulcus computes number on the basis of visual stimuli (e.g., dotclouds), they may implicitly assume that the information fed forward from visual cortex does not include numerical content, but rather includes the visuo-spatial “ingredients” on the basis of which numerosity is computed. The present results suggest that instead (or in addition), visual cortex may send approximate number representations, per se, to the intraparietal sulcus. If so, rather than creating number representations de novo, the intraparietal sulcus may play other roles in numerical cognition, such as making number available for conscious processing (Dehaene et al. 2006) or guiding actions based on number representations (Fischer 2003, Andres et al. 2004, Lasne et al. 2019). Although the intraparietal sulcus has been identified as the site of amodal number representations (Naccache and Dehaene 2001), it may not contain modality independent number representations, at all (Bulthé et al. 2014; Cavdaroglu et al. 2015). Rather, the present data are consistent with the possibility that the intraparietal sulcus is important for comparing modality-specific number representations within and between sensory modalities (Cavdaroglu et al. 2015; Nieder 2012). Additional studies are needed to clarify the relative contributions of the occipital cortex and the intraparietal sulcus to number processing. The rapid SSVEP technique we used here is not well-suited to answer questions about the intraparietal sulcus, given that 1) SSVEPs have been localized primarily to occipital cortex (Andersen et al. 2008; Di Russo et al. 2007; Fawcett et al. 2004; Hillyard et al. 1997; Müller et al. 1997; Sammer et al. 2005), and 2) even if SSVEPs can be detected beyond occipital cortex, backward masking may disrupt the flow of information between the occipital cortex and the intraparietal sulcus in ways that could alter the way number is typically represented in the intraparietal sulcus (Lamme et al. 2002). In addition to backward masking, there is another way that rapid presentation of stimuli could disrupt typical intraparietal sulcus processing of stimulus numerosity. Visual features are subject to “temporal resolution” processing constraints; a stimulus can be presented so briefly that particular visual features are not processed and made available for conscious perception. Higher-order cortical areas tend to require more processing time (Holcombe 2009). Our results are agnostic about whether fast presentation of stimuli prevented accurate judgment of numerosity by disrupting reentrant feedback or by exceeding the temporal resolution of higher-order processing. Either kind of disruption would be sufficient to license the main inference we draw from the present data that the occipital cortex, per se, responds to the numerosity of the stimuli. The method we have used here may offer a way to unify the study of approximate number across disparate populations. Researchers have created a large variety of approximate number paradigms. Different tests have been developed for adults in different cultures, children, infants, and for different nonhuman species (e.g., cotton-top tamarins, Hauser et al., 2003; guppies, Agrillo et al. 2012). Using different tests for different populations complicates any direct comparisons. It may be difficult to make meaningful comparisons between, for example, female mosquitofish choosing a group to join while fleeing a sexually aggressive male (Agrillo et al. 2007), infants matching beeps to shapes (Izard et al. 2009), and adults choosing between yellow or blue dots (Libertus et al. 2012). Yet, because EEG has been measured in humans of all ages, from week-old infants (Norcia and Tyler 1985) to adults, and also in multiple vertebrate species from dogs (Kujala et al. 2013) to zebrafish (Hong et al. 2016), it may be possible to adapt the present paradigm for use across diverse samples. In pilot testing, we have found similar SSVEP results to those presented here when adult subjects were not instructed to attend to number and made no behavioral responses, suggesting that this task may be suitable for use with infants and nonhuman animals. 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TI - Unconscious Number Discrimination in the Human Visual System
JO - Cerebral Cortex
DO - 10.1093/cercor/bhaa155
DA - 2011-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/unconscious-number-discrimination-in-the-human-visual-system-aeOXlIPsHE
SP - 1
VL - Advance Article
IS - 
DP - DeepDyve
ER -