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Symbolic magnitude modulates perceptual strength in binocular rivalry
Cognition 119 (2011) 468–475
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Cognition journal homepage: www.elsevier.com/locate/COGNIT
Brief article
Symbolic magnitude modulates perceptual strength in binocular rivalry Chris L.E. Paffen a,⇑, Sarah Plukaard a, Ryota Kanai b a Experimental Psychology, Department of Psychology, Faculty of Social Sciences & Helmholtz Institute, Utrecht University, Heidelberglaan 2, 3584 CS, The Netherlands b Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London WC1N 3AR, United Kingdom
a r t i c l e
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Article history: Received 9 April 2010 Revised 17 January 2011 Accepted 22 January 2011 Available online 12 February 2011 Keywords: Magnitude estimation Numerosity Visual perception Binocular rivalry
a b s t r a c t Basic aspects of magnitude (such as luminance contrast) are directly represented by sensory representations in early visual areas. However, it is unclear how symbolic magnitudes (such as Arabic numerals) are represented in the brain. Here we show that symbolic magnitude affects binocular rivalry: perceptual dominance of numbers and objects of known size increases with their magnitude. Importantly, variations in symbolic magnitude acted like variations in luminance contrast: we found that an increase in numerical magnitude of adding one lead to an equivalent increase in perceptual dominance as a contrast increment of 0.32%. Our results support the claim that magnitude is extracted automatically, since the increase in perceptual dominance came about in the absence of a magnitude-related task. Our findings show that symbolic, acculturated knowledge about magnitude interacts with visual perception and affects perception in a manner similar to lower-level aspects of magnitude such as luminance contrast. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Estimation of magnitude constitutes a fundamental aspect of human cognitive functioning. Motivated by this observation, it has been argued that the human brain contains a general substrate for processing magnitude information (Walsh, 2003) – a hypothesis termed ‘‘A Theory of Magnitude’’, or ATOM. In support of ATOM, behavioral studies have shown that task irrelevant magnitude information interferes with processing of task relevant magnitude information. A well-known example of such an interference is the size congruity effect: when participants compare physical size or numerical value of two items while ignoring the other dimension, the response is faster when the task irrelevant magnitude information is congruent (e.g., large both in numerical and physical size) than when it is incongruent (Henik & Tzelgov, 1982; Tzelgov, Meyer, & Henik, 1992). Moreover, neuroimaging and
⇑ Corresponding author. Tel.: +31 30 2533372; fax: +31 20 2534511. E-mail address: [email protected] (C.L.E. Paffen). 0010-0277/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cognition.2011.01.010
behavioral studies suggested that magnitudes are represented in cortical regions around the intraparietal sulcus (IPS) (Cohen Kadosh et al., 2005; Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003), although it is debated whether magnitude is represented in a single abstract code (Dehaene, Dehaene-Lambertz, & Cohen, 1998; Libertus, Woldorff, & Brannon, 2007; McCloskey, 1992), or whether different sources of magnitude are represented separately (Campbell, 1994; Cohen Kadosh & Walsh, 2009). At a basic level, aspects of visual quantities such as luminance contrast or saturation are directly represented as the firing rate of neurons in early visual areas (e.g. Dean, 1981). Such magnitude information therefore directly corresponds to the intensity of visual sensory representation and provides a substrate of how such quantity is represented in the brain. On the other hand, this is not trivial in the case of symbolic representations of numerosity (e.g. Arabic numerals), because the visual appearances of numerical symbols are not directly connected with the magnitudes they represent. In the present study, we examine whether perceptual strengths of symbolic magnitude behave in a similar man-
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ner as other basic visual magnitudes such as luminance contrast. To evaluate this possibility, we use binocular rivalry in which perception alternates between dichoptically presented images (Blake & Logothetis, 2002). Of relevance to the current study is that the signal strength of an image is reflected by the perceptual dominance of an image during binocular rivalry: increasing the signal strength of an image (e.g. increasing the contrast of the image) increases the time this image is perceived during rivalry (Levelt, 1968). We reasoned that if symbolic magnitude information affects perception in a manner similar to contrast, increasing magnitude information in an image should increase perceptual dominance of that image during binocular rivalry. To test this, we measured influences of magnitude information of numbers (Experiments 1–3) or objects (Experiment 4) against a common non-numerical symbol ‘‘#’’. This allowed us to keep magnitude information irrelevant to the task and avoid potential interferences of magnitude information at a decision stage, which have been argued to play a role in the size congruency effect (Cohen Kadosh, Lammertyn, & Izard, 2008). 2. Experiment 1 2.1. Method 2.1.1. Observers A total of 11 observers performed Experiments 1 (including two of the authors; cp & sp). The rest of the observers were naïve as to the purpose of the study. All observers had normal or corrected to normal visual acuity. 2.1.2. Apparatus and stimuli Stimuli were presented using an Apple dual 2 GHz PowerPC G5 and a linearized LaCie Electron blue IV 220 monitor, using MATLAB and the Psychtoolbox extensions. Dichoptic presentation was achieved using a mirror-stereoscope. Stimuli consisted of images of numbers 2, 4, 6 and 8 and # (Fig. 1) of the font Helvetica. The numbers and the hash were presented in opposite luminance polarity. The numbers were all black (0.1 cd m2), whereas the # was white (59.7 cd m2). In order to equate frequency content in the stimuli, we computed the average Fourier spectrum of all the images and imposed this back to each image. As a result each image had the identical power spectrum profile (see Fig. 1). The size of each image was 2.6 deg 2.6 deg. In order to aid binocular fusion, a white frame surrounded the rival images (this fusion frame was used in all the following experiments). The images were presented on a black background with a luminance of 0.1 cd m2. 2.1.3. Procedure Observers sat in front of the screen in a darkened room, while their head was kept steady by a chin and a forehead rest. Dichoptic presentation was achieved by a mirror-stereoscope. The length of the optical path was 57 cm. Observers initiated a trial by pressing the space bar. In all experiments a trial lasted for 30 s, during which an observer was required to keep fixating at a red fixation cross, presented in the center of the images and refrain from
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making eye-movements. The task of the observer was to continuously indicate whether the number (right arrow key) or the neutral (left arrow key) image was dominant in perception. We instructed the observers to indicate the dominant percept, even in the case of mixed or piecemeal percepts. A total of four combinations (2, 4, 6 or 8 versus #) were presented 16 times per observer. Trials were presented in random order and dichoptic presentation of number and # were counterbalanced between the eyes. 2.2. Results Fig. 2a shows a significant (Spearman’s rho = 0.28, p1 < 0.05)2 increase in the fraction of time the number image dominates in perception with increasing magnitude. In general, an increase in the fraction of time an image dominates in perception during rivalry can come about by an increase in the mean percept duration of that image, a decrease in the duration of the other image, or by a combination of both. Interestingly, when analyzing these mean percept durations, we find a significant decrease in mean dominance of the neutral image (Spearman’s rho = 0.27, p < 0.05) with increasing magnitude of number. The increase in mean dominance of the number image, however, is not significant (Spearman’s rho = 0.15, p < 0.15). 2.3. Discussion The results of Experiment 1 show that perceptual dominance of the number image increases with its magnitude. The fact that mean dominance duration of the number image does not increase with its magnitude, but that mean dominance of the neutral image does decrease, could be seen as puzzling. However, this finding is in correspondence with a well-known property of binocular rivalry referred to as Levelt’s 2nd proposition (Levelt, 1968), which states that an increase of the contrast of image A shortens the mean dominance duration of image B without affecting the dominance duration of image A. Thus, increasing magnitude of number appears to change dominance in a manner similar to raising the contrast of an image. That is, magnitude seems to be affecting perceptual dominance as if the actual physical contrast of the rival images was varied. Interestingly, the fact that numerosity predominantly shortened dominance durations of the number image is in line with Yu and Blake (1992) who found that meaningful images were suppressed for shorter amounts of time. On the other hand, these findings contrast with those of experiments in which global contexts modulate the dynamics of binocular rivalry: a visual context surrounding rival images has been shown to primarily lengthen the dominance period of a rival target congruent with the context, leaving its suppression phase unaffected (Sobel & Blake, 2002). Why some factors affect the suppres-
1 All p-values reported in this study are from one-tailed significance testing. 2 As the fraction dominance of the number and neutral image mirror each other (total dominance adds to 1), we only report statistics on the fraction dominance for the number image.
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Fig. 1. Stimuli used in the experiments. On each trial, one of four images was presented to one eye (row A: a number image in Experiments 1 and 3, row B: a rotated number for Experiment 2a, row C: a scrambled number for Experiment 2b, row D: a ball image for Experiment 4), while the ‘#’ image was presented to the other eye.
sion phase of rivalry and other the dominance phase remains a question open to future investigation. 3. Experiment 2 Although we equated the Fourier spectrum across the images in Experiment 1, it remains possible that the observed relationship between numerosity and perceptual dominance duration is entirely driven by differences in the images rather than magnitudes of numbers. In order to examine this possibility, we performed two control experiments. Experiment 2a tests whether low-level contour-properties are responsible for the increase in dominance by rotating all the images. In these rotated images, the local conflict between the images is identical to that in Experiment 1, while the magnitude information is degraded. If the local-contour information is responsible for the results in Experiment 1, we should observe a similar increase in dominance in Experiment 2a. In Experiment 2b we seek to entirely remove the magnitude information from the number images by scrambling them. Again, if some attribute other than magnitude is responsible for the increased dominance observed in Experiment 1, we should also observe this in Experiment 2b.
3.1.2. Stimuli Stimuli and Apparatus in Experiment 2a were identical to those of Experiment 1 except that all the images (number and neutral images) were rotated 90° counterclockwise. In order to get the images for Experiment 2b, we took the unfiltered number images of Experiment 1, took six blocks (83 83 pixels) of the area covered by the number and replaced them randomly (Fig. 1). Next, the four scrambled number images and the neutral one were filtered (equating the power spectrum) in the same way as in Experiment 1.
3.1.3. Procedure The procedure of Experiments 2a and b were the same as in Experiment 1, except for the task of the observer. In Experiment 2a, observers were asked to continuously indicate whether the rotated number (right arrow key) or the neutral (left arrow key) was dominant in perception (Experiment 2a). In Experiment 2b, observers were asked to continuously indicate whether the scrambled image (right arrow key) or the neutral (unscrambled; left arrow key) was dominant in perception (Experiment 2a).
3.2. Results 3.1. Method 3.1.1. Observers A total of 11 observers performed in Experiment 2a; seven observers in Experiment 2b. Six observers (including two authors) who performed in Experiment 1 also performed in Experiment 2a; four (including one author) also performed in Experiment 2b.
Fig. 2b shows perceptual dominance for rotated numbers. With the rotated numbers, no significant trend was observed (Spearman’s rho = 0.2, p = 0.08). Scrambling the number image abolished the relation between magnitude of number and perceptual dominance: no significant increase is observed in perceptual dominance with increasing magnitude (Spearman’s rho = 0.10, p = 0.31).
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Fig. 2. Results of all the experiments. Fig. 2A–C: Each graph depicts the fraction of time the number image or the neutral image (‘#’) was dominant in perception as a function of magnitude. Large circles and squares represent means for all observers for the number and neutral images respectively. Small circles and squares represent data for individual observers. The solid and dashed lines represent the regression of dominance on magnitude for the number and neutral images respectively. Perceptual dominance increases with magnitude of number (A). When the images are rotated, the significant increase in dominance is gone (B), as well as when the number images are scrambled (C). Fig. 2D and E: Perceptual dominance as a function of magnitude (D) and RMS contrast of the number image (E). In D, small squares, diamonds and circles represent dominance data for the number image of 7%, 13% and 24% RMScontrast respectively. In E, small circles, diamonds, squares and triangles represent dominance data for the number image of magnitude 2, 4, 6 and 8 respectively. Perceptual dominance increases with increasing magnitude of number (D) and contrast (E). Fig. 2F: Perceptual dominance as a function of estimated size of golf (circles), tennis (squares), soccer (diamonds) and basketball (triangles). The solid line represents the regression of dominance on estimated size of balls. Perceptual dominance increases with estimated size.
3.3. Discussion Experiment 2 shows that degrading magnitude information abolishes the relation between perceptual dominance and magnitude of number. Rotation of number
images degraded the correlation between the magnitudes of rotated numbers and perceived duration compared with the upright numbers used in Experiment 1. However, a weaker but non-significant correlation still remained with this manipulation (Spearman’s rho = 0.2). One possible rea-
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son for this trend is the fact that numbers and their magnitudes are still recognizable and their magnitude information can be extracted. This hypothesis is comparable to the well-known face inversion effect in which recognition of inverted faces is degraded (Yin, 1969). This degraded recognition is argued to be the result of a slight but significant decrease in activity in the fusiform face area, an area involved in processing of faces (e.g. Gauthier, Tarr, Anderson, Skudlarski, & Gore, 1999). Our result of Experiment 2a is comparable in the sense that processing of magnitude information was degraded, but not totally abolished. Consistent with this idea, when the numbers were made completely unrecognizable by scrambling while maintaining local conflicts, the correlation was completely abolished. These results together indicate that low-level image features such as contours are not the primary contributing factor for the observed relationship between numerical magnitudes and dominance duration in binocular rivalry. Instead, our results suggest that activation of neurons representing numbers is essential for the observed relationship between numerical magnitude and dominance duration in binocular rivalry. 4. Experiment 3 Now we return to the notion that numerical magnitude influences dominance during rivalry in the same way as a manipulation of contrast. In the following experiment, we gauge the influence of numerical magnitude in units of luminance contrast. To do so, we varied both the luminance contrast and the numerical magnitude of images simultaneously in the same experiment. This way, we can quantify how much contrast needs to increase to parallel an increase in numerical magnitude in its effect on perceptual dominance. 4.1. Method 4.1.1. Observers A total of eight observers performed in Experiment 3. Two of the observers (including one author) who performed in Experiment 1 also performed in this experiment. One observer was excluded from the analysis since he experienced almost no alternations at the lowest contrast level used. Thus, analysis was performed on the remaining seven observers. 4.1.2. Stimuli The stimuli used were identical to those of Experiment 1 in most aspects, except that the contrast of the number image was varied from trial to trial (RMS-contrast of 7%, 13% and 24%), while that of the neutral # image remained constant (RMS-contrast of 17%). 4.1.3. Procedure The procedure was identical to that of Experiment 1, except that a full-factorial design resulted in 96 trials (four repetitions of four levels of magnitude, three levels of contrast and two levels of eye to which the number image was presented). The order of conditions was randomized across trials.
4.2. Results The results are displayed in Fig. 2D and E. A repeated measures ANOVA revealed main effects of contrast (Fig. 2E; F(2, 36) = 24.3, p < 0.001) and numerical magnitude (Fig. 2E; F(3, 36) = 17.8, p < 0.001) but no interaction between them (F(6, 36) = 1.3, p > 0.05), supporting the idea that both contrast and numerical magnitude affected perceptual dominance independently. To explicitly test whether perceptual dominance increased for larger numerical values, we computed non-parametric (i.e. Spearman) correlations between magnitude of number and fraction dominance, after discounting the influence of contrast. The correlation between magnitude and dominance was significantly positive (Spearman’s rho = 0.20, t(81) = 1.81, p < 0.05), replicating our Experiment 1. The expected monotonic increase in dominance duration with increasing contrast was also clear. The correlation between contrast and dominance duration was highly significant (Spearman’s rho = 0.87, t(81) = 15.9, p < 0.001). Next, we computed how much contrast needed to be increased to achieve an equal amount of influence on perceptual dominance as when increasing the numerical magnitude. To do so, we constructed a simple multiple regression model where fraction dominance was modeled as a linear sum of contrast and numerical magnitude and a constant term. The estimated coefficients for the effects of contrast and numerical magnitude corresponded to an increase of fraction dominance by 1% increase in contrast and increase in numerical magnitude by 1, respectively. This analysis showed that a 1% increase in RMS contrast corresponded to a 1.7% increase in dominance fraction and an increase in numerical magnitude of 1 corresponded to a 0.6% increase in dominance fraction. The ratio between these two (0.32%) indicates how much contrast needed to be increased to achieve the effect of a unit increment of numerical magnitude. Thus, the difference between the smallest value (i.e., 2) and the largest value (i.e., 8) corresponded to an RMS contrast difference of 1.9%. 4.3. Discussion The results of Experiment 3 replicated those of Experiment 1: increasing magnitude increased perceptual dominance of the number image when engaged in binocular rivalry. In addition, the results show that it is possible to equate increases in magnitude as increases in effective contrast of the images: an increase in magnitude of adding one paralleled a 0.32% contrast increment by increasing perceptual dominance by 0.6%. This finding strengthens our notion that variations in magnitude affect perceptual dominance in a similar manner as luminance contrast. 5. Experiment 4 In Experiments 1 and 3 we showed that magnitude of symbolic representation of numbers affects binocular rivalry. Still, one might argue that the increase in perceptual dominance observed are due to variations in the shape of the number images used. It has been shown, for example,
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that the shape of numbers can account for numerical distance effects (Cohen, 2009). To avoid the potential problem of influences of shape information, we test whether magnitude information whose representation that is entirely dissociated from its physical property modulates dominance duration in binocular rivalry. In particular, we examined influences of the conceptual knowledge of object size (known size of various types of balls) on binocular rivalry. In order to quantify whether perceptual dominance correlates with known size, we also asked the observers to estimate the size of the images.
5.3. Discussion The positive correlation between known size of physical objects and perceptual dominance shows that yet another manifestation of symbolic magnitude modulates perceptual strength during binocular rivalry. Of importance here is the fact that the physical size of the images on the screen did not vary in this experiment. Thus, conceptual knowledge about physical size is able to modulate the dynamics of binocular rivalry.
6. General discussion 5.1. Method 5.1.1. Observers A total of 10 observers performed in Experiment 4. Seven of the observers (including two authors) who performed in Experiment 1 also performed in Experiment 4.
5.1.2. Stimuli For the rivalry Experiment, we used images of balls of increasing size: a golf ball, a tennis ball, a soccer ball and a basketball (Fig. 1). The four balls and the neutral image were filtered using the same procedure as in Experiment 1. Importantly, all images of the balls and the neutral image had the same size (the area covered by the ball was the same in all images). The size of the images was 2.6 deg 2.6 deg.
5.1.3. Procedure The procedure was the same as for Experiments 1–3. A total of four combinations (golf ball, tennis ball, soccer ball or basketball versus the neutral image) were presented 16 times per observer. Trials were presented in random order and dichoptic presentation of number and # were counterbalanced between the eyes. The task of the observer was to continuously indicate whether the ball (right arrow key) or the neutral (left arrow key) image was dominant in perception. Since it cannot be assumed that our observers know the exact size of the balls and their mentally represented size of the balls was more relevant to the experiment, they were asked to estimate the diameter of each ball by drawing two points indicating its width (diameter) on a piece of A3 paper. The distance between these two points was taken as the estimated size. Observers estimated the size by looking at each of the images used in the rivalry experiment. The size of the images was 3.5 by 3.5 cm.
5.2. Results The estimated sizes of the balls are in summarized in Table 1. Fig. 2f shows a positive correlation between estimated size of balls and perceptual dominance during binocular rivalry: perceptual dominance of the ball image increases with estimated size. The increase in perceptual dominance is significant (Spearman’s rho = 0.39, p < 0.01).
The results of our present study show that symbolically represented magnitude information can affect the dynamics of binocular rivalry. Our experiments suggest that the influence of numerical magnitude on perceptual strength occurs in a highly automatic fashion, since numerosity or size information was irrelevant to the report of percepts during binocular rivalry, excluding possible confounds of conflicts in response selection. Our results are of relevance to the current debate on the automaticity of quantity processing. It is debated whether quantity is extracted automatically (see Tzelgov & Ganor-Stern, 2005), or not (Cohen, 2009; Pansky & Algom, 2002), or artifacts of nonnumerical features (Pansky & Algom, 2002). Our results clearly demonstrate that variations in symbolic magnitude can affect perception when irrelevant to the task, thereby supporting the claim that magnitude information is extracted automatically. Furthermore, we showed that variations in numerical magnitude affect binocular rivalry similarly as luminance contrast does, as they obey a well-known relationship between image contrast and perceptual dominance called Levelt’s 2nd proposition. The contrast-like modulation of perceptual dominance by magnitude is further established by Experiment 3 in which we show that increasing numerical magnitude by adding one paralleled a contrast increase of 0.32%. These findings suggest that numerical magnitude interacts with visual perception by affecting effective contrast and thereby support the notion of the common magnitude system as proposed by ATOM (Walsh, 2003). That is, variations in symbolic magnitude affect processing in a manner similar to basic features as luminance contrast, a finding corroborating with the core argument of ATOM.
Table 1 Estimated sizes (diameter) of balls in cm for each observer. Golf ball
Tennis ball
Soccer ball
Basketball
Ah An Cp Em Es Sm Sn Sp Uv Vr
4.6 5.0 4.4 4.2 6.8 4.2 3.3 5.1 6.0 3.9
9.5 7.2 7.2 7.3 9.0 8.4 7.8 8.0 10.2 7.3
28.4 30.7 24.1 19.8 28.2 23.5 20.4 26.1 29.0 23.1
32.8 26.7 29.1 27.0 32.1 26.4 23.5 31.7 28.7 29.0
Mean (sd)
4.8 (1.0)
8.2 (1.1)
25.3 (3.7)
28.7 (2.9)
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Our findings are consistent with the notion of highly automatic interactions between numerical magnitude and luminance or contrast. Although it was believed that numerical magnitude interferes with processing of spatially defined magnitude (e.g. physical size), but not with non-spatial magnitude (e.g. luminance) (Pinel, Piazza, Le Bihan, & Dehaene, 2004), more recent studies suggested that non-spatial magnitude such as brightness (Cohen Kadosh, Cohen Kadosh, & Henik, 2008) and duration (Xuan, Zhang, He, & Chen, 2007) exhibit mutual interferences with numerosity. For example, digit-color synaesthetes exhibit a tendency to associate larger numbers with brighter colors (Cohen Kadosh, Henik, & Walsh, 2007), while their associated colors did not show any systematic relationship with hue or saturation. Even more so, when non-synaesthetic subjects make numerical or luminosity judgments, there is a mutual interference from the other task irrelevant magnitude information (Cohen Kadosh & Henik, 2006). Our results are also in line with a recent study suggesting that non-symbolic numerical magnitude constitutes a fundamental visual experience based on the finding of perceptual adaptation to numerosity represented by visual arrays (Burr & Ross, 2008a). However, it has been debated whether the adaptation effect is due to numerosity as such or due to low-level visual properties contained in the textured stimuli (Burr & Ross, 2008b; see Durgin, 2008). By contrast, we used symbolic representations of numerical and size magnitudes in the present study and therefore possible confounding factors such as physical size or density were dissociated from the magnitude information represented by the symbols. Although activity in higher level processing areas can correlate with perception during binocular rivalry (e.g. Tong, Nakayama, Vaughan, & Kanwisher, 1998), it is unlikely that magnitude information represented in an area such as the IPS directly responsible for percepts during binocular rivalry. As the alternations in binocular rivalry entails percepts of the fine details of the images (e.g., background texture), we hypothesize that the actual appearance of number or ball images during binocular rivalry is represented in a relatively early stage such as the primary visual cortex and the interaction of magnitude information with perception was due to modulation of activities in early visual areas via feedback from the magnitude estimation system. We can, however, only speculate about the level from which numerical magnitude interacts with representations of the dissimilar images competing during binocular rivalry. Higher-level feedback towards lower levels at which the images compete does however provide an explanation why the reported effect of magnitude on binocular rivalry is only modest (about 10% increase in dominance from ‘2’ to ‘8’; see Fig. 2A). This modest effect on the dynamics of rivalry has also been reported for other higher-level phenomena such as attention (e.g. Lack, 1978; Meng & Tong, 2004; Paffen, Alais, & Verstraten, 2006), emotion (e.g. Alpers & Pauli, 2006) and semantic content (e.g. Costello, Jiang, Baartman, McGlennen, & He, 2009; Jiang, Costello, & He, 2007). The fact that these high-level phenomena have a modest impact on the dynamics of rivalry has generally been taken to indicate
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Cognition journal homepage: www.elsevier.com/locate/COGNIT
Brief article
Symbolic magnitude modulates perceptual strength in binocular rivalry Chris L.E. Paffen a,⇑, Sarah Plukaard a, Ryota Kanai b a Experimental Psychology, Department of Psychology, Faculty of Social Sciences & Helmholtz Institute, Utrecht University, Heidelberglaan 2, 3584 CS, The Netherlands b Institute of Cognitive Neuroscience, University College London, 17 Queen Square, London WC1N 3AR, United Kingdom
a r t i c l e
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Article history: Received 9 April 2010 Revised 17 January 2011 Accepted 22 January 2011 Available online 12 February 2011 Keywords: Magnitude estimation Numerosity Visual perception Binocular rivalry
a b s t r a c t Basic aspects of magnitude (such as luminance contrast) are directly represented by sensory representations in early visual areas. However, it is unclear how symbolic magnitudes (such as Arabic numerals) are represented in the brain. Here we show that symbolic magnitude affects binocular rivalry: perceptual dominance of numbers and objects of known size increases with their magnitude. Importantly, variations in symbolic magnitude acted like variations in luminance contrast: we found that an increase in numerical magnitude of adding one lead to an equivalent increase in perceptual dominance as a contrast increment of 0.32%. Our results support the claim that magnitude is extracted automatically, since the increase in perceptual dominance came about in the absence of a magnitude-related task. Our findings show that symbolic, acculturated knowledge about magnitude interacts with visual perception and affects perception in a manner similar to lower-level aspects of magnitude such as luminance contrast. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Estimation of magnitude constitutes a fundamental aspect of human cognitive functioning. Motivated by this observation, it has been argued that the human brain contains a general substrate for processing magnitude information (Walsh, 2003) – a hypothesis termed ‘‘A Theory of Magnitude’’, or ATOM. In support of ATOM, behavioral studies have shown that task irrelevant magnitude information interferes with processing of task relevant magnitude information. A well-known example of such an interference is the size congruity effect: when participants compare physical size or numerical value of two items while ignoring the other dimension, the response is faster when the task irrelevant magnitude information is congruent (e.g., large both in numerical and physical size) than when it is incongruent (Henik & Tzelgov, 1982; Tzelgov, Meyer, & Henik, 1992). Moreover, neuroimaging and
⇑ Corresponding author. Tel.: +31 30 2533372; fax: +31 20 2534511. E-mail address: [email protected] (C.L.E. Paffen). 0010-0277/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cognition.2011.01.010
behavioral studies suggested that magnitudes are represented in cortical regions around the intraparietal sulcus (IPS) (Cohen Kadosh et al., 2005; Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003), although it is debated whether magnitude is represented in a single abstract code (Dehaene, Dehaene-Lambertz, & Cohen, 1998; Libertus, Woldorff, & Brannon, 2007; McCloskey, 1992), or whether different sources of magnitude are represented separately (Campbell, 1994; Cohen Kadosh & Walsh, 2009). At a basic level, aspects of visual quantities such as luminance contrast or saturation are directly represented as the firing rate of neurons in early visual areas (e.g. Dean, 1981). Such magnitude information therefore directly corresponds to the intensity of visual sensory representation and provides a substrate of how such quantity is represented in the brain. On the other hand, this is not trivial in the case of symbolic representations of numerosity (e.g. Arabic numerals), because the visual appearances of numerical symbols are not directly connected with the magnitudes they represent. In the present study, we examine whether perceptual strengths of symbolic magnitude behave in a similar man-
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ner as other basic visual magnitudes such as luminance contrast. To evaluate this possibility, we use binocular rivalry in which perception alternates between dichoptically presented images (Blake & Logothetis, 2002). Of relevance to the current study is that the signal strength of an image is reflected by the perceptual dominance of an image during binocular rivalry: increasing the signal strength of an image (e.g. increasing the contrast of the image) increases the time this image is perceived during rivalry (Levelt, 1968). We reasoned that if symbolic magnitude information affects perception in a manner similar to contrast, increasing magnitude information in an image should increase perceptual dominance of that image during binocular rivalry. To test this, we measured influences of magnitude information of numbers (Experiments 1–3) or objects (Experiment 4) against a common non-numerical symbol ‘‘#’’. This allowed us to keep magnitude information irrelevant to the task and avoid potential interferences of magnitude information at a decision stage, which have been argued to play a role in the size congruency effect (Cohen Kadosh, Lammertyn, & Izard, 2008). 2. Experiment 1 2.1. Method 2.1.1. Observers A total of 11 observers performed Experiments 1 (including two of the authors; cp & sp). The rest of the observers were naïve as to the purpose of the study. All observers had normal or corrected to normal visual acuity. 2.1.2. Apparatus and stimuli Stimuli were presented using an Apple dual 2 GHz PowerPC G5 and a linearized LaCie Electron blue IV 220 monitor, using MATLAB and the Psychtoolbox extensions. Dichoptic presentation was achieved using a mirror-stereoscope. Stimuli consisted of images of numbers 2, 4, 6 and 8 and # (Fig. 1) of the font Helvetica. The numbers and the hash were presented in opposite luminance polarity. The numbers were all black (0.1 cd m2), whereas the # was white (59.7 cd m2). In order to equate frequency content in the stimuli, we computed the average Fourier spectrum of all the images and imposed this back to each image. As a result each image had the identical power spectrum profile (see Fig. 1). The size of each image was 2.6 deg 2.6 deg. In order to aid binocular fusion, a white frame surrounded the rival images (this fusion frame was used in all the following experiments). The images were presented on a black background with a luminance of 0.1 cd m2. 2.1.3. Procedure Observers sat in front of the screen in a darkened room, while their head was kept steady by a chin and a forehead rest. Dichoptic presentation was achieved by a mirror-stereoscope. The length of the optical path was 57 cm. Observers initiated a trial by pressing the space bar. In all experiments a trial lasted for 30 s, during which an observer was required to keep fixating at a red fixation cross, presented in the center of the images and refrain from
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making eye-movements. The task of the observer was to continuously indicate whether the number (right arrow key) or the neutral (left arrow key) image was dominant in perception. We instructed the observers to indicate the dominant percept, even in the case of mixed or piecemeal percepts. A total of four combinations (2, 4, 6 or 8 versus #) were presented 16 times per observer. Trials were presented in random order and dichoptic presentation of number and # were counterbalanced between the eyes. 2.2. Results Fig. 2a shows a significant (Spearman’s rho = 0.28, p1 < 0.05)2 increase in the fraction of time the number image dominates in perception with increasing magnitude. In general, an increase in the fraction of time an image dominates in perception during rivalry can come about by an increase in the mean percept duration of that image, a decrease in the duration of the other image, or by a combination of both. Interestingly, when analyzing these mean percept durations, we find a significant decrease in mean dominance of the neutral image (Spearman’s rho = 0.27, p < 0.05) with increasing magnitude of number. The increase in mean dominance of the number image, however, is not significant (Spearman’s rho = 0.15, p < 0.15). 2.3. Discussion The results of Experiment 1 show that perceptual dominance of the number image increases with its magnitude. The fact that mean dominance duration of the number image does not increase with its magnitude, but that mean dominance of the neutral image does decrease, could be seen as puzzling. However, this finding is in correspondence with a well-known property of binocular rivalry referred to as Levelt’s 2nd proposition (Levelt, 1968), which states that an increase of the contrast of image A shortens the mean dominance duration of image B without affecting the dominance duration of image A. Thus, increasing magnitude of number appears to change dominance in a manner similar to raising the contrast of an image. That is, magnitude seems to be affecting perceptual dominance as if the actual physical contrast of the rival images was varied. Interestingly, the fact that numerosity predominantly shortened dominance durations of the number image is in line with Yu and Blake (1992) who found that meaningful images were suppressed for shorter amounts of time. On the other hand, these findings contrast with those of experiments in which global contexts modulate the dynamics of binocular rivalry: a visual context surrounding rival images has been shown to primarily lengthen the dominance period of a rival target congruent with the context, leaving its suppression phase unaffected (Sobel & Blake, 2002). Why some factors affect the suppres-
1 All p-values reported in this study are from one-tailed significance testing. 2 As the fraction dominance of the number and neutral image mirror each other (total dominance adds to 1), we only report statistics on the fraction dominance for the number image.
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Fig. 1. Stimuli used in the experiments. On each trial, one of four images was presented to one eye (row A: a number image in Experiments 1 and 3, row B: a rotated number for Experiment 2a, row C: a scrambled number for Experiment 2b, row D: a ball image for Experiment 4), while the ‘#’ image was presented to the other eye.
sion phase of rivalry and other the dominance phase remains a question open to future investigation. 3. Experiment 2 Although we equated the Fourier spectrum across the images in Experiment 1, it remains possible that the observed relationship between numerosity and perceptual dominance duration is entirely driven by differences in the images rather than magnitudes of numbers. In order to examine this possibility, we performed two control experiments. Experiment 2a tests whether low-level contour-properties are responsible for the increase in dominance by rotating all the images. In these rotated images, the local conflict between the images is identical to that in Experiment 1, while the magnitude information is degraded. If the local-contour information is responsible for the results in Experiment 1, we should observe a similar increase in dominance in Experiment 2a. In Experiment 2b we seek to entirely remove the magnitude information from the number images by scrambling them. Again, if some attribute other than magnitude is responsible for the increased dominance observed in Experiment 1, we should also observe this in Experiment 2b.
3.1.2. Stimuli Stimuli and Apparatus in Experiment 2a were identical to those of Experiment 1 except that all the images (number and neutral images) were rotated 90° counterclockwise. In order to get the images for Experiment 2b, we took the unfiltered number images of Experiment 1, took six blocks (83 83 pixels) of the area covered by the number and replaced them randomly (Fig. 1). Next, the four scrambled number images and the neutral one were filtered (equating the power spectrum) in the same way as in Experiment 1.
3.1.3. Procedure The procedure of Experiments 2a and b were the same as in Experiment 1, except for the task of the observer. In Experiment 2a, observers were asked to continuously indicate whether the rotated number (right arrow key) or the neutral (left arrow key) was dominant in perception (Experiment 2a). In Experiment 2b, observers were asked to continuously indicate whether the scrambled image (right arrow key) or the neutral (unscrambled; left arrow key) was dominant in perception (Experiment 2a).
3.2. Results 3.1. Method 3.1.1. Observers A total of 11 observers performed in Experiment 2a; seven observers in Experiment 2b. Six observers (including two authors) who performed in Experiment 1 also performed in Experiment 2a; four (including one author) also performed in Experiment 2b.
Fig. 2b shows perceptual dominance for rotated numbers. With the rotated numbers, no significant trend was observed (Spearman’s rho = 0.2, p = 0.08). Scrambling the number image abolished the relation between magnitude of number and perceptual dominance: no significant increase is observed in perceptual dominance with increasing magnitude (Spearman’s rho = 0.10, p = 0.31).
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Fig. 2. Results of all the experiments. Fig. 2A–C: Each graph depicts the fraction of time the number image or the neutral image (‘#’) was dominant in perception as a function of magnitude. Large circles and squares represent means for all observers for the number and neutral images respectively. Small circles and squares represent data for individual observers. The solid and dashed lines represent the regression of dominance on magnitude for the number and neutral images respectively. Perceptual dominance increases with magnitude of number (A). When the images are rotated, the significant increase in dominance is gone (B), as well as when the number images are scrambled (C). Fig. 2D and E: Perceptual dominance as a function of magnitude (D) and RMS contrast of the number image (E). In D, small squares, diamonds and circles represent dominance data for the number image of 7%, 13% and 24% RMScontrast respectively. In E, small circles, diamonds, squares and triangles represent dominance data for the number image of magnitude 2, 4, 6 and 8 respectively. Perceptual dominance increases with increasing magnitude of number (D) and contrast (E). Fig. 2F: Perceptual dominance as a function of estimated size of golf (circles), tennis (squares), soccer (diamonds) and basketball (triangles). The solid line represents the regression of dominance on estimated size of balls. Perceptual dominance increases with estimated size.
3.3. Discussion Experiment 2 shows that degrading magnitude information abolishes the relation between perceptual dominance and magnitude of number. Rotation of number
images degraded the correlation between the magnitudes of rotated numbers and perceived duration compared with the upright numbers used in Experiment 1. However, a weaker but non-significant correlation still remained with this manipulation (Spearman’s rho = 0.2). One possible rea-
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son for this trend is the fact that numbers and their magnitudes are still recognizable and their magnitude information can be extracted. This hypothesis is comparable to the well-known face inversion effect in which recognition of inverted faces is degraded (Yin, 1969). This degraded recognition is argued to be the result of a slight but significant decrease in activity in the fusiform face area, an area involved in processing of faces (e.g. Gauthier, Tarr, Anderson, Skudlarski, & Gore, 1999). Our result of Experiment 2a is comparable in the sense that processing of magnitude information was degraded, but not totally abolished. Consistent with this idea, when the numbers were made completely unrecognizable by scrambling while maintaining local conflicts, the correlation was completely abolished. These results together indicate that low-level image features such as contours are not the primary contributing factor for the observed relationship between numerical magnitudes and dominance duration in binocular rivalry. Instead, our results suggest that activation of neurons representing numbers is essential for the observed relationship between numerical magnitude and dominance duration in binocular rivalry. 4. Experiment 3 Now we return to the notion that numerical magnitude influences dominance during rivalry in the same way as a manipulation of contrast. In the following experiment, we gauge the influence of numerical magnitude in units of luminance contrast. To do so, we varied both the luminance contrast and the numerical magnitude of images simultaneously in the same experiment. This way, we can quantify how much contrast needs to increase to parallel an increase in numerical magnitude in its effect on perceptual dominance. 4.1. Method 4.1.1. Observers A total of eight observers performed in Experiment 3. Two of the observers (including one author) who performed in Experiment 1 also performed in this experiment. One observer was excluded from the analysis since he experienced almost no alternations at the lowest contrast level used. Thus, analysis was performed on the remaining seven observers. 4.1.2. Stimuli The stimuli used were identical to those of Experiment 1 in most aspects, except that the contrast of the number image was varied from trial to trial (RMS-contrast of 7%, 13% and 24%), while that of the neutral # image remained constant (RMS-contrast of 17%). 4.1.3. Procedure The procedure was identical to that of Experiment 1, except that a full-factorial design resulted in 96 trials (four repetitions of four levels of magnitude, three levels of contrast and two levels of eye to which the number image was presented). The order of conditions was randomized across trials.
4.2. Results The results are displayed in Fig. 2D and E. A repeated measures ANOVA revealed main effects of contrast (Fig. 2E; F(2, 36) = 24.3, p < 0.001) and numerical magnitude (Fig. 2E; F(3, 36) = 17.8, p < 0.001) but no interaction between them (F(6, 36) = 1.3, p > 0.05), supporting the idea that both contrast and numerical magnitude affected perceptual dominance independently. To explicitly test whether perceptual dominance increased for larger numerical values, we computed non-parametric (i.e. Spearman) correlations between magnitude of number and fraction dominance, after discounting the influence of contrast. The correlation between magnitude and dominance was significantly positive (Spearman’s rho = 0.20, t(81) = 1.81, p < 0.05), replicating our Experiment 1. The expected monotonic increase in dominance duration with increasing contrast was also clear. The correlation between contrast and dominance duration was highly significant (Spearman’s rho = 0.87, t(81) = 15.9, p < 0.001). Next, we computed how much contrast needed to be increased to achieve an equal amount of influence on perceptual dominance as when increasing the numerical magnitude. To do so, we constructed a simple multiple regression model where fraction dominance was modeled as a linear sum of contrast and numerical magnitude and a constant term. The estimated coefficients for the effects of contrast and numerical magnitude corresponded to an increase of fraction dominance by 1% increase in contrast and increase in numerical magnitude by 1, respectively. This analysis showed that a 1% increase in RMS contrast corresponded to a 1.7% increase in dominance fraction and an increase in numerical magnitude of 1 corresponded to a 0.6% increase in dominance fraction. The ratio between these two (0.32%) indicates how much contrast needed to be increased to achieve the effect of a unit increment of numerical magnitude. Thus, the difference between the smallest value (i.e., 2) and the largest value (i.e., 8) corresponded to an RMS contrast difference of 1.9%. 4.3. Discussion The results of Experiment 3 replicated those of Experiment 1: increasing magnitude increased perceptual dominance of the number image when engaged in binocular rivalry. In addition, the results show that it is possible to equate increases in magnitude as increases in effective contrast of the images: an increase in magnitude of adding one paralleled a 0.32% contrast increment by increasing perceptual dominance by 0.6%. This finding strengthens our notion that variations in magnitude affect perceptual dominance in a similar manner as luminance contrast. 5. Experiment 4 In Experiments 1 and 3 we showed that magnitude of symbolic representation of numbers affects binocular rivalry. Still, one might argue that the increase in perceptual dominance observed are due to variations in the shape of the number images used. It has been shown, for example,
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that the shape of numbers can account for numerical distance effects (Cohen, 2009). To avoid the potential problem of influences of shape information, we test whether magnitude information whose representation that is entirely dissociated from its physical property modulates dominance duration in binocular rivalry. In particular, we examined influences of the conceptual knowledge of object size (known size of various types of balls) on binocular rivalry. In order to quantify whether perceptual dominance correlates with known size, we also asked the observers to estimate the size of the images.
5.3. Discussion The positive correlation between known size of physical objects and perceptual dominance shows that yet another manifestation of symbolic magnitude modulates perceptual strength during binocular rivalry. Of importance here is the fact that the physical size of the images on the screen did not vary in this experiment. Thus, conceptual knowledge about physical size is able to modulate the dynamics of binocular rivalry.
6. General discussion 5.1. Method 5.1.1. Observers A total of 10 observers performed in Experiment 4. Seven of the observers (including two authors) who performed in Experiment 1 also performed in Experiment 4.
5.1.2. Stimuli For the rivalry Experiment, we used images of balls of increasing size: a golf ball, a tennis ball, a soccer ball and a basketball (Fig. 1). The four balls and the neutral image were filtered using the same procedure as in Experiment 1. Importantly, all images of the balls and the neutral image had the same size (the area covered by the ball was the same in all images). The size of the images was 2.6 deg 2.6 deg.
5.1.3. Procedure The procedure was the same as for Experiments 1–3. A total of four combinations (golf ball, tennis ball, soccer ball or basketball versus the neutral image) were presented 16 times per observer. Trials were presented in random order and dichoptic presentation of number and # were counterbalanced between the eyes. The task of the observer was to continuously indicate whether the ball (right arrow key) or the neutral (left arrow key) image was dominant in perception. Since it cannot be assumed that our observers know the exact size of the balls and their mentally represented size of the balls was more relevant to the experiment, they were asked to estimate the diameter of each ball by drawing two points indicating its width (diameter) on a piece of A3 paper. The distance between these two points was taken as the estimated size. Observers estimated the size by looking at each of the images used in the rivalry experiment. The size of the images was 3.5 by 3.5 cm.
5.2. Results The estimated sizes of the balls are in summarized in Table 1. Fig. 2f shows a positive correlation between estimated size of balls and perceptual dominance during binocular rivalry: perceptual dominance of the ball image increases with estimated size. The increase in perceptual dominance is significant (Spearman’s rho = 0.39, p < 0.01).
The results of our present study show that symbolically represented magnitude information can affect the dynamics of binocular rivalry. Our experiments suggest that the influence of numerical magnitude on perceptual strength occurs in a highly automatic fashion, since numerosity or size information was irrelevant to the report of percepts during binocular rivalry, excluding possible confounds of conflicts in response selection. Our results are of relevance to the current debate on the automaticity of quantity processing. It is debated whether quantity is extracted automatically (see Tzelgov & Ganor-Stern, 2005), or not (Cohen, 2009; Pansky & Algom, 2002), or artifacts of nonnumerical features (Pansky & Algom, 2002). Our results clearly demonstrate that variations in symbolic magnitude can affect perception when irrelevant to the task, thereby supporting the claim that magnitude information is extracted automatically. Furthermore, we showed that variations in numerical magnitude affect binocular rivalry similarly as luminance contrast does, as they obey a well-known relationship between image contrast and perceptual dominance called Levelt’s 2nd proposition. The contrast-like modulation of perceptual dominance by magnitude is further established by Experiment 3 in which we show that increasing numerical magnitude by adding one paralleled a contrast increase of 0.32%. These findings suggest that numerical magnitude interacts with visual perception by affecting effective contrast and thereby support the notion of the common magnitude system as proposed by ATOM (Walsh, 2003). That is, variations in symbolic magnitude affect processing in a manner similar to basic features as luminance contrast, a finding corroborating with the core argument of ATOM.
Table 1 Estimated sizes (diameter) of balls in cm for each observer. Golf ball
Tennis ball
Soccer ball
Basketball
Ah An Cp Em Es Sm Sn Sp Uv Vr
4.6 5.0 4.4 4.2 6.8 4.2 3.3 5.1 6.0 3.9
9.5 7.2 7.2 7.3 9.0 8.4 7.8 8.0 10.2 7.3
28.4 30.7 24.1 19.8 28.2 23.5 20.4 26.1 29.0 23.1
32.8 26.7 29.1 27.0 32.1 26.4 23.5 31.7 28.7 29.0
Mean (sd)
4.8 (1.0)
8.2 (1.1)
25.3 (3.7)
28.7 (2.9)
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Our findings are consistent with the notion of highly automatic interactions between numerical magnitude and luminance or contrast. Although it was believed that numerical magnitude interferes with processing of spatially defined magnitude (e.g. physical size), but not with non-spatial magnitude (e.g. luminance) (Pinel, Piazza, Le Bihan, & Dehaene, 2004), more recent studies suggested that non-spatial magnitude such as brightness (Cohen Kadosh, Cohen Kadosh, & Henik, 2008) and duration (Xuan, Zhang, He, & Chen, 2007) exhibit mutual interferences with numerosity. For example, digit-color synaesthetes exhibit a tendency to associate larger numbers with brighter colors (Cohen Kadosh, Henik, & Walsh, 2007), while their associated colors did not show any systematic relationship with hue or saturation. Even more so, when non-synaesthetic subjects make numerical or luminosity judgments, there is a mutual interference from the other task irrelevant magnitude information (Cohen Kadosh & Henik, 2006). Our results are also in line with a recent study suggesting that non-symbolic numerical magnitude constitutes a fundamental visual experience based on the finding of perceptual adaptation to numerosity represented by visual arrays (Burr & Ross, 2008a). However, it has been debated whether the adaptation effect is due to numerosity as such or due to low-level visual properties contained in the textured stimuli (Burr & Ross, 2008b; see Durgin, 2008). By contrast, we used symbolic representations of numerical and size magnitudes in the present study and therefore possible confounding factors such as physical size or density were dissociated from the magnitude information represented by the symbols. Although activity in higher level processing areas can correlate with perception during binocular rivalry (e.g. Tong, Nakayama, Vaughan, & Kanwisher, 1998), it is unlikely that magnitude information represented in an area such as the IPS directly responsible for percepts during binocular rivalry. As the alternations in binocular rivalry entails percepts of the fine details of the images (e.g., background texture), we hypothesize that the actual appearance of number or ball images during binocular rivalry is represented in a relatively early stage such as the primary visual cortex and the interaction of magnitude information with perception was due to modulation of activities in early visual areas via feedback from the magnitude estimation system. We can, however, only speculate about the level from which numerical magnitude interacts with representations of the dissimilar images competing during binocular rivalry. Higher-level feedback towards lower levels at which the images compete does however provide an explanation why the reported effect of magnitude on binocular rivalry is only modest (about 10% increase in dominance from ‘2’ to ‘8’; see Fig. 2A). This modest effect on the dynamics of rivalry has also been reported for other higher-level phenomena such as attention (e.g. Lack, 1978; Meng & Tong, 2004; Paffen, Alais, & Verstraten, 2006), emotion (e.g. Alpers & Pauli, 2006) and semantic content (e.g. Costello, Jiang, Baartman, McGlennen, & He, 2009; Jiang, Costello, & He, 2007). The fact that these high-level phenomena have a modest impact on the dynamics of rivalry has generally been taken to indicate
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