A Common Representation for Semantic and Physical Properties A Cognitive-Anatomical Approach Roi Cohen Kadosh and Avishai Henik Department of Behavioral Sciences and Zlotowski Center for Neuroscience, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Abstract. This is the first report of a mutual interference between luminance and numerical value in magnitude judgments. Instead of manipulating the physical size of compared numbers, which is the traditional approach in size congruity studies, luminance levels were manipulated. The results yielded the classical congruity effect. Participants took more time to process numerically larger numbers when they were brighter than when they were darker, and more time to process a darker number when its numerical value was smaller than when it was larger. On the basis of neurophysiological studies of magnitude comparison and interference between semantic and physical information, it is proposed that the processing of semantic and physical magnitude information is carried out by a shared brain structure. It is suggested that this brain area, the left intraparietal sulcus, subserves various comparison processes by representing various quantities on an amodal magnitude scale. Keywords: magnitude, size congruity effect, intrapartial sulcus
Three decades have passed since Paivio (1975) reported the size congruity phenomenon. The basic paradigm is as follows:; two stimuli appear on a computer screen and for each of the stimuli one dimension is relevant while another is irrelevant and to be ignored. Congruent trials are characterized by similar values of the relevant and the irrelevant dimensions. Incongruent trials are characterized by different values of the relevant and the irrelevant dimensions. Neutral stimuli differ only in the relevant dimension. For example, in a size congruity experiment with numerical stimuli, the participants have to decide which digit is numerically larger (i.e., numerical value is relevant) while ignoring the physical size of the stimuli (i.e., physical size is irrelevant). Under these circumstances the pair 2 4 is a congruent trial because the numerically larger digit is also physically larger. In contrast, the pair 2 4 is incongruent because the numerically smaller digit is physically larger. Stimuli in the neutral trials vary only in the numerical dimension (e.g., 2 4). Facilitation is commonly observed for congruent trials, which are faster than neutral trials. Interference is observed with incongruent trials, which are commonly slower than neutral trials. Since Paivio (1975) reported the size congruity phenomenon, many ” 2006 Hogrefe & Huber Publishers
studies have been carried out, demonstrating this effect for numerical comparisons of Arabic numbers by adults (e.g., Besner & Coltheart, 1979; Henik & Tzelgov, 1982; Pansky & Algom, 1999; Schwarz & Heinze, 1998) and by children (Girelli, Lucangeli, & Butterworth, 2000; Rubinsten, Henik, Berger, & Shahar-Shalev, 2002), when comparing numerosity (Pansky & Algom, 2002), word numbers (Cohen Kadosh, Henik, & Rubinstein, 2005a; Foltz, Poltrok, & Potts, 1984), animals sizes (Rubinsten & Henik, 2002) and physical sizes of numbers (Henik & Tzelgov, 1982; Schwarz & Heinze, 1998; Tzelgov, Meyer, & Henik, 1992). All of these studies manipulated two dimensions: semantic value and physical size. The processing of the relevant dimension is indicated by the distance effect. The distance effect shows that the distance between two stimuli influences the comparison of the stimuli; the larger the distance between two stimuli, the easier the decision, the shorter the reaction time (RT). This effect is considered to be a general phenomenon that applies not only to the comparison of numbers but to other objects as well (Moyer & Landauer, 1967). The distance effect was observed not only for numbers, implying that we use an amodal magnitude to repExperimental Psychology 2006; Vol. 53(2):87Ð94 DOI: 10.1027/1618-3169.53.2.87
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resent number quantity (Moyer & Landauer, 1967), but also for other semantic properties such as animal size (Rubinsten & Henik, 2002), as well as for physical properties such as physical size or luminance (Cohen Kadosh et al., 2005b; Pinel, Piazza, Le Bihan, & Dehaene, 2004). Although both the distance effect and size congruity effect indicate processing of magnitude, it is important to emphasize the difference between them. The numerical distance effect indicates that digits are processed in a refined way (e.g., placing the digits on a mental number line). In contrast, the size congruity effect indicates only crude processing of the numerical dimension (e.g., such as small or large) when it is irrelevant (Tzelgov et al., 1992). Note that if the irrelevant dimension is only crudely processed, the distances of the relevant and the irrelevant dimension should not interact. However, the distance of the relevant as well as the irrelevant dimensions was found to modulate the size congruity effect; as the distance between stimuli on the relevant dimension increases size congruity decreases, whereas as the distance on the irrelevant dimension increases size congruity increases (Schwarz & Ischebeck, 2003). In some studies (Schwarz & Heinze, 1998; Schwarz & Ischebeck, 2003) the interaction between congruity and (ir)relevant distance has been explained by the processing speed of each dimension. According to this explanation, large distances are processed faster relative to small distances that are processed slower. The slower processing of the smaller relevant distances allows for the irrelevant information have more time to affect the comparison than when the relevant distance is larger.
The Origin of the Size Congruity Effect Does size congruity and its interactions with distance occur at a late stage (Otten, Sudevan, Logan, & Coles, 1996) or at an early stage (Schwarz & Heinze, 1998) of processing? According to the late stage account, the different quantities are processed in parallel until later stages, where response competition occurs and the overt response is produced. In line with this approach, the response selection stage accepts inputs from quite different mechanisms used for comparisons of different stimuli that are processed separately (hence, the “general behavior rule” hypothesis). In contrast, according to the early stage account, the interference between the two dimensions is due to convergence of the quantities from different dimensions onto an amodal single representation whose outputs are further processed at later stages (e.g., response activation). In line with this account, the reciprocal inExperimental Psychology 2006; Vol. 53(2):87Ð94
fluence of the two dimensions, which is also modulated by distance, suggests that a common mechanism is used to compare completely different aspects of stimuli, leading to the idea that the brain is equipped with a general comparison mechanism (hence, the “shared brain mechanism” hypothesis).
A Neural Substrate for the Shared Mechanism It is important to stress the difference between the general behavior rule and the shared mechanism hypotheses. The first hypothesis suggests that the two different comparisons occur independently until motor initiation, where the competition between the responses occurs. In contrast, the shared mechanism hypothesis suggests that processing involves a common brain area that integrates different types of information before the response stage (i.e., shared brain mechanism). Support for the shared brain mechanism hypothesis (i.e., early stage account) has come from several sources. First, it is well grounded that numbers are processed serially (Dehaene, 1996). The additive factor method (Sternberg, 1969) proposed that under serial processing, an interaction between two factors occurs if the processing of both factors is carried out by a common stage of processing. The interaction between the (ir)relevant distance and congruity might suggest that the processing of both dimensions (i.e., physical size and numerical value) is probably carried out in the comparison stage, the same level at which the computation of the distance effect takes place. Second, recent studies by Fias, Lammertyn, Reynvoet, Dupont, and Orban (2003) and Cohen Kadosh et al., (2005b), have shown that a joint area in the left intraparietal sulcus (LIPS) is responsive when a comparison of physical size, angles, luminance and numerical value (i.e., magnitude) is carried out. These works support a recent theory proposed by Walsh (2003), which stresses the close relation between number, space and time, and suggests the IPS as the common area for such general computation. Third, powerful evidence is also coming from studies that showed that the irrelevant and relevant dimensions interfere with one another if processing of these two dimensions involves a shared brain structure (Fias, Lauwereyns, & Lammertyn, 2001; Lammertyn, Fias & Lauwereyns, 2002; Posner, Sandson, Dhawan, & Shulman, 1990). For example, Fias and colleagues (Fias et al., 2001; Lammertyn et al., 2002) examined the SNARC effect (spatial numerical association of response codes), an effect that points to spatial representation of numbers on a mental number line, with small numbers on the left and large numbers on the right (e.g., Dehaene, ” 2006 Hogrefe & Huber Publishers
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Bossini, & Giraux, 1993). The SNARC effect was observed when people compared the orientation of digits, but not when they compared their colors. Processing of numbers and orientation is carried out by the shared brain structure, namely, the parietal lobes (e.g., Fias, Dupont, Reynvoet, & Orban, 2002, for orientation, and Pinel, Dehaene, Rivie’re, & Le Bihan, 2001, for numbers). In contrast, processing of color is carried out by more ventral areas, namely, area v4 (see Gegenfurtner, 2003, for a recent review) or area v8 (Hadjikhani, Liu, Dale, Cavanagh, & Tootell, 1998). Accordingly, the authors conclude that the interference between irrelevant and relevant dimensions is determined by the degree of neural overlap of structures dedicated to processing of specific mental operations (i.e., the neural overlap theory).
The Current Study Neuroimaging findings have suggested the existence of a shared brain mechanism that is involved in processing semantic as well as physical magnitude (e.g., physical size, luminance). These findings together with the neural overlap (shared brain mechanism) theory led us to hypothesize that physical properties, such as luminance, will affect numerical judgments and vice versa. Moreover, the pattern of results (e.g., interaction between distance and congruity) should be similar for different irrelevant dimensions such as size and luminance. In contrast, dissimilarity among effects of various dimensions would support the hypothesis that the size congruity effect is due to separate processing of different magnitudes not shared by any neural substrate before response initiation. Another reason for choosing luminance as a dimension is that it has a different response code from physical size or numbers so that processing should not overlap. The current study examined whether luminance affects processing of numerical information in the same way that size influences numerical processing. We used an experimental design similar to one used previously (Cohen Kadosh et al., 2005, Experiment 2) except that instead of stimuli with different physical sizes we created stimuli with different luminance levels.
Method Participants Eighteen students (M = 23.87 years old, SD = 2.47) from Achva College participated in the experiment for partial fulfillment of a course requirement. All partici” 2006 Hogrefe & Huber Publishers
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pants had normal or corrected-to-normal vision and no reading or mathematical deficits. Stimuli Each trial was composed of two digits such that one digit appeared on each side of the center of a white computer screen. The center-to-center distance between the two digits was 10 cm and the participants sat 55 cm from the screen. The stimuli subtended a vertical visual angle of 1.8∞ and a horizontal visual angle of 0.8∞Ð1.3∞. There were three types of pairs: congruent, neutral and incongruent. A congruent stimulus was defined as a pair of digits in which the darker digit was also numerically larger (e.g., 2 4). A neutral stimulus was defined as a pair of digits that differed only in the relevant dimension (e.g., 2 4 for numerical comparison and 2 2 for luminance comparison). An incongruent stimulus was defined as a pair of digits in which the darker digit was numerically smaller (e.g., 2 4). We employed 8 digits to create three numerical distances: 1 (the digits 1Ð2, 3Ð4, 6Ð7, 8Ð9), 2 (the digits 1Ð3, 2Ð4, 6Ð8, 7Ð9) and 5 (the digits 1Ð6, 2Ð7, 3Ð8, 4Ð9). Each digit was presented an equal number of times for each distance. For the luminance stimuli we also used 8 different stimuli that created a set similar to the set of numeric stimuli. That is, there were eight different stimuli that varied in luminance levels while keeping constant the levels of hue and saturation. The photometric values of the 8 luminance levels were 175, 108, 82.5, 58.4, 46.5, 35.8, 27.7 and 20.9 cd/m2 (Adobe Photoshop 6.0 was used to create the stimuli). Selection of the luminance levels was made in order to create a logarithmic-like function of intensity as reported earlier for the representation of numerical quantity (Dehaene, 1989). The eight luminance levels were used to create 3 different luminance distances. The pairs for luminance distance 1 were composed from the luminance levels (units are indicated in cd/m2) of 175Ð108, 82.5Ð58.4, 46.5Ð35.8, and 27.7Ð20.9. The pairs for luminance distance 2 were 175Ð82.5, 108Ð58.4, 46.5Ð27.7, and 35.8Ð20.9. The pairs for luminance distance 5 were 175Ð46.5, 108Ð35.8, 82.5Ð27.7, and 58.4Ð20.9. Stimuli were arranged in blocks of trials with each block composed of 432 different stimuli that were presented twice (a total of 864 trials in each block). Within the set of stimuli prepared for numerical or luminance comparisons, each digit and each luminance level appeared an equal number of times on the left and the right. Each block had 27 different conditions; 3 luminance distances ¥ 3 numerical distances ¥ 3 congruency conditions. Each condition was repreExperimental Psychology 2006; Vol. 53(2):87Ð94
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sented by 32 trials (i.e., 4 luminance combinations ¥ 4 digit combinations ¥ 2 sides for the larger/darker digit) in a given block. Every experimental block was preceded by a block of 24 practice trials. This block was similar to the experimental block with the following exception: we used digits and luminance distances that were different from those employed in the experimental blocks. For numerical distance of 3 units the practice digits were 1Ð4, 3Ð6, 4Ð7, and 6Ð 9, and for numerical distance of 4 units the digits were 2Ð6, 3Ð7, 4Ð8, and 5Ð9. In the case of the luminance distance, for a distance of 3 units the pairs of luminance levels were 175Ð58.4, 82.5Ð46.5, 58.4Ð 35.8, and 46.5Ð20.9, and for luminance distance of 4 units the pairs of luminance levels were 175Ð46.5, 108Ð35.8, 82.5Ð27.7, and 46.5Ð20.9. The stimuli in the practice block were randomly sampled so that in each block there were 2 luminance distances ¥ 2 numerical distances ¥ 3 congruency conditions, with each condition being presented on 2 sides of the computer screen. As noted above, the same congruent and incongruent trials were used in both the numeric and luminance judgment tasks, whereas the neutral stimuli were different. Neutral stimuli for luminance comparisons included the same digit in two different luminance levels. In order to keep the factorial design we created the neutral stimuli from digits that were used in the other two conditions (congruent and incongruent) for a given luminance distance. For example, because the pair 1Ð2 was used to produce congruent and incongruent stimuli for numerical distance of 1 unit, neutral pairs created by using these two digits (i.e., 1 1 and 2 2) were included in the analysis as neutral trials for distance 1. Similarly, because the pair 1Ð3 was used to produce congruent and incongruent stimuli for numerical distance of 2 units, neutral pairs created by using these two digits (i.e., 1 1 and 3 3) were included in the analysis as neutral trials for distance 2. Each digit from all four pairs of a given numerical distance was used to create two stimuli, once presented as the darker member on the right (e.g., 2 2) and once presented as the darker member on the left (e.g., 2 2). In this way the statistical analyses of congruent, incongruent and neutral conditions were based on the same digits. Neutral stimuli in the numerical comparisons included two digits that were different in numerical distance but that had the same luminance level. In order to keep the factorial design we created the neutral stimuli from digits and luminance levels that were used for the other two conditions (congruent and incongruent) of a given numerical distance. For example, the pair 1Ð3 was used to produce congruent and incongruent stimuli for numerical distance of 2 units. Hence, neutral pairs created by using these two digits (i.e., 1 3) were included in the analysis as neutral triExperimental Psychology 2006; Vol. 53(2):87Ð94
als, twice for brighter luminance level (e.g., 1 3) and twice for darker luminance level (e.g., 1 3). Procedure The participant’s task was to decide which of two stimuli in a given display was larger or darker, with “larger” applying to numerical value in the numerical block and with “darker” applying to luminance level in the luminance block. Each participant took part in two sessions, two weeks apart. Each session was composed of one block of either the numerical task or the luminance task. Participants were asked to respond as quickly as possible but to avoid errors, and to attend only to the numerical value in the numerical block or to the luminance level in the luminance block. The participants indicated their choices by pressing one of two keys (i.e., P or Q on the keyboard) corresponding to the side of the display with the selected member of the digit pair. Order of the two blocks was counterbalanced and each block lasted approximately 40 minutes with a break in the middle of the experiment (after the 432nd trial).
Design The variables manipulated were: relevant dimension (luminance, numerical), luminance distance (1, 2 or 5), numerical distance (1, 2 or 5) and congruity (incongruent, neutral or congruent). Thus, we had a 2 ¥ 3 ¥ 3 ¥ 3 factorial design.
Results For every participant in each condition mean RT was calculated for correct trials only. These means were subjected to a four-way analysis of variance (ANOVA) with relevant dimension, luminance distance, numerical distance and congruity as within-subject factors. All main effects except for relevant dimension were significant. Participants responded faster to a large luminance distance than to a small one (528 ms vs. 461 ms), F(2, 34) = 80.26, MSE = 4,648, p ⬍ .001. Participants also responded faster to a large numerical distance than to a small one (507 ms vs. 478 ms), F(2, 34) = 72.83, MSE = 906, p ⬍ .001. In addition, there was a significant effect of congruity (519 ms and 472 ms, for incongruent and congruent conditions, respectively), F(2, 34) = 98.21, MSE = 1,881, p ⬍ .001. Three two-way interactions were significant: relevant dimension and luminance distance, F(2, 34) = 92.82, MSE = 4,652, p ⬍ .001, relevant di” 2006 Hogrefe & Huber Publishers
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Incongruent
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mension and numerical distance, F(2, 34) = 130.69, MSE = 597, p ⬍ .001, relevant dimension and congruity, F(2, 34) = 4.19, MSE = 4,021, p ⬍ .05., The threeway interactions for Relevant Dimension ¥ Luminance Distance ¥ Congruity, F(4, 68) = 20.90, MSE = 1,026, p ⬍ .001, and for Relevant Dimension ¥ Numerical Distance ¥ Congruity were significant, F(4, 68) = 5.98, MSE = 864, p ⬍ .001. However, the four-way interaction for Relevant Dimension ¥ Luminance Distance ¥ Numerical Distance ¥ Congruity was insignificant, F(8, 136) = 1.08, MSE = 561, ns.
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To further our understanding regarding the sources of the two three-way interactions (i.e., Relevant Dimension ¥ Congruity ¥ Numerical/Luminance Distance) we conducted simple effects analyses for numerical and luminance comparisons separately.
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The simple interaction between congruity and luminance distance was significant, F(4, 68) = 20.65, MSE = 628, p ⬍ .001, and further analyses showed an increase in the congruity effect as the luminance distance increased, F(1, 17) = 56.57, MSE = 709, p ⬍ .001, from 36 ms for a distance of 1 unit (526 ms for incongruent and 490 ms for congruent), to 91 ms for a distance of 5 units (567 ms for incongruent and 476 ms for congruent). The simple interaction between congruity and numerical distance was also significant, F(4, 68) = 3.99, MSE = 674, p ⬍ .005. Further analyses showed a decrease in the congruity effect as the numerical distance increased, F(1, 17) = 9.85, MSE = 678, p ⬍ .005, from 68 ms for a distance of 1 unit (577 ms for incongruent and 509 ms for congruent), to 46 ms for a distance of 5 units (508 ms for incongruent and 462 ms for congruent). The two twoway interactions (Congruity ¥ Luminance and Congruity ¥ Numerical Distance) are depicted in Figure 1.
Luminance Comparison The simple interaction between congruity and luminance distance was significant, F(4, 68) = 7.98, MSE = 1,155, p ⬍ .001, and further analyses showed a decrease in the congruity effect as the luminance distance increased, F(1, 17) = 36.97, MSE = 667, p ⬍ .001, from 56 ms for a distance of 1 unit (583 ms for incongruent and 527 ms for congruent), to 13 ms for a distance of 5 units (412 ms for incongruent and 399 ms for congruent). The simple interaction between congruity and numerical distance was also significant, F(4, 68) = 3.79, MSE = 801, p ⬍ .01, further analyses showed an increase in the congruity effect as the numerical dis” 2006 Hogrefe & Huber Publishers
Figure 1. Reaction time in the numerical comparison, as a function of congruity and distance (luminance, numerical). Error bars depict one standard error of mean (S.E.M.). tance increased, F(1, 17) = 4.26, MSE = 675, p = .05, from 33 ms for a distance of 1 unit (491 ms for incongruent and 458 ms for congruent), to 47 ms for a distance of 5 units (503 ms for incongruent and 456 ms for congruent). Figure 2 depicts these two-way interactions.
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Figure 2. Reaction time in the luminance comparison, as a function of congruity and distance (luminance, numerical). Error bars depict one S.E.M. Experimental Psychology 2006; Vol. 53(2):87Ð94
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Error Rates Error rates were generally low (2.6 % for the luminance block, and 3.2 % for the numerical block). Due to lack of variance in several conditions, a correlation analysis was conducted between RTs and error rates. The results did not show any RT-accuracy trade-off, r(27) = 0.88, p ⬍ .001 for luminance block, and r(27) = 0.87, p ⬍ .001 for numerical block.
Discussion We start by summarizing the results: 1) The congruity effect was found regardless of the type of comparison. Namely, participants were faster when the numerical and luminance dimensions were congruent (i.e., the same digit of the pair was larger numerically and darker) than when they were incongruent (i.e., a given digit of the pair was larger numerically but lighter). In the numerical comparison the congruity effect had both interference and facilitatory components, whereas in the luminance comparison the congruity effect was interference (and not facilitatory) based. 2) There was a distance effect for both numerical and luminance comparisons, that is, responding was faster for large distances than small ones. 3) Numerical and luminance distances modulated the congruity effects in numerical as well as in luminance comparisons. Increase of irrelevant distance increased the effect whereas increase of relevant distance decreased the effect. Most important, the irrelevant luminance level affected numerical comparison and the irrelevant numerical level affected luminance comparison. The interference of luminance with numerical comparisons is similar to the interference of physical size with numerical comparisons in earlier reports (Cohen Kadosh et al., 2005; Schwarz & Ischebeck, 2003). This evidence, of reciprocal interference between semantic and physical information, is in accordance with previous studies. These studies found the size congruity effect with a variety of stimuli, such as Arabic numbers (Besner & Coltheart, 1979; Girelli et al., 2000; Henik & Tzelgov, 1982; Pansky & Algom, 1999; Rubinsten et al., 2002), word numbers (Cohen Kadosh et al., 2005; Foltz et al., 1984), numerosity (Pansky & Algom, 2002), animal size (Rubinsten & Henik, 2002), physical size (Henik & Tzelgov, 1982; Tzelgov et al., 1992). The appearance of mutual interference between physical and semantic information implies that the brain is either equipped with a general comparison mechanism or that there is a gene-
ral rule of operation that is involved in the procedure of quite different mechanisms. Two hypotheses were presented in the Introduction; the “shared brain mechanism” (i.e., early stage account) and “the general behavior rule” (i.e., late stage account). We prefer the “shared brain mechanism” hypothesis over the “general behavior rule” hypothesis, and suggest that this mechanism involves the LIPS where activation is observed during the comparison stage of numbers (Dehaene, 1996; Pinel et al., 2001). A number of reasons support this suggestion. First, since numerical and luminance dimensions have different response codes it is less likely that the pattern of results is due to dimensional overlap at a later level such as response selection.1 In addition, we found an interaction between congruity and the distance effect, albeit with different response codes. In accordance with the additive factor method (Sternberg, 1969), such effects reflect a computation at the same stage, specifically, the comparison stage, where the computation of the distance effect takes place (Dehaene, 1996).Third, it has been shown by Fias et al. (2001) and Lammertyn et al. (2002) that interference between relevant and irrelevant information stems from overlap in neural activity. Irrelevant and relevant information that are processed by a shared brain area (i.e., as in the case of orientation and representation of numbers) tend to interfere with one another, in contrast with irrelevant and relevant information that are processed by distinct brain areas (i.e., as in the case of colors and numbers). Fourth, Fias et al. (2003) revealed activation in a joint area in the LIPS when a comparison of physical size, angles, and numerical value (hence, magnitude) was carried out. These findings indicate that the processing of different magnitudes is accomplished by the same brain area, on an amodal representation, similar to what Schwarz and Heinze (1998) and Walsh (2003) have suggested. A fifth support for the “shared brain mechanism” hypothesis comes from a recent fMRI (functional magnetic resonance imaging) study (Cohen Kadosh et al., 2005b) that was conducted in order to find whether the mechanisms involved in numerical processing were designed specifically for the number domain. Three different comparisons where employed: numerical comparison, size comparison, and luminance comparison. All three comparisons revealed widely overlapping activated cortical regions. More importantly, a joint area in the LIPS showed modulation by numerical, size and luminance distances. Sixth, Pinel et al. (2004) in parallel with this study scanned normal participants with fMRI while they compared size, number, and luminance stimuli that were varied orthogonally (i.e., a size congruity paradigm). The results showed overlap activation for
1 Crucially, participants showed the size congruity effect regardless of order. For example, the irrelevant luminance dimension affected the numerical comparison when luminance was not associated previously with any stimuli-response instruction. Hence, it can be inferred that luminance and numbers were automatically encoded and were represented as a magnitude.
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number and size in the IPS (including the LIPS). However, Pinel et al. did not find a mutual interference of numerical and luminance information, but only interference of numerical values on processing of luminance. Possible explanations for such a null result might be: 1) Processing of luminance in that study was harder than processing of numbers (as indicated by error rates); accordingly, luminance did not have enough time to be processed so that it could interfere with numerical processing. 2) Masking of luminance by physical size that was manipulated in the same experimental design. Seventh, the present results show that not only luminance, physical size and numerical representations are shared by the IPS, but that the patterns of behavioral interference among them are similar. It has been pointed out that the size congruity effect under the numerical comparison might be due to the capture of attention by the more salient stimulus (e.g., the darker digit). This idea may be generalized to all size congruity studies that use physical size as one of the two stimulus dimensions. However, this suggestion is not as appealing for the numerical dimension; Why should 6 capture attention more than 4? In spite of this, numerical values do influence physical judgments. Hence, although the possible contribution of attentional capture to the size congruity effect deserves additional study, it is less parsimonious than the shared brain mechanism explanation. Hence, all in all the accumulative results from this study and earlier size congruity studies, combined with the current knowledge of brain structure and functions, enable us to draw conclusions regarding stages of processing.
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Conclusions The current study examined the mutual influence of numerical and luminance dimensions in light of the possible shared brain mechanism for magnitude processing. We found that both numerical and luminance dimensions affected each other and the pattern of the results was similar to that found with the classical size congruity paradigm. Currently, there is growing evidence, together with the current results, that supports the existence of a general mechanism for magnitude processing located in the IPS. However, it should be noted that these findings are confined to the brain area level rather than the neuronal level. Future studies with primates using single cell recording are essential for validating the suggested relationship between numerical values and other magnitude dimensions, and the possible existence of such magneurons (magnitude neurons similar to the numerons of Nieder (2005)). In addition, it will be valuable to find out whether other magnitude stimuli yield effects similar to the ones that are observed under numerical judgments such as the SNARC effect (Walsh, 2003) Acknowledgements The authors wish to thank the two anonymous reviewers for their very instructive comments, and Jan Lammertyn for valuable suggestions on an earlier version of the manuscript. This work was partly supported by a grant to Roi Cohen Kadosh from the Kreitman Foundation, and by a grant to Avishai Henik from the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.
Facilitation and Interference Components In this experiment, as in others (e.g., Cohen Kadosh et al., 2005a; Henik & Tzelgov, 1982) the size congruity effect of the physical comparison was interferencebased whereas the size congruity effect of the numerical comparisons was usually composed of both facilitatory and interference components. Still, this is not an indication for a qualitative difference; rather, it is a mark of a quantitative difference. The size congruity effect of a physical comparison that is composed of both facilitatory and interference components was detected in many other studies (e.g., Rubinsten & Henik, 2002; Rubinsten et al., 2002). The physical dimension that is composed of more basic features is (usually) processed faster than the numerical dimension. Hence, the numerical information cannot speed up processing relative to the neutral condition. In contrast, when physical stimuli that are more difficult to process are employed, the facilitatory component clearly appears (e.g., Rubinsten & Henik, 2002; Rubinsten et al., 2002). ” 2006 Hogrefe & Huber Publishers
References Besner, D., & Coltheart, M. (1979). Ideographic and alphabetic processing in skilled reading of English. Neuropsychologia, 17, 467Ð472. Cohen Kadosh, R., Henik, A., & Rubinsten, O. (2005a). Are Arabic and word numbers processed in different ways? Submitted for publication. Cohen Kadosh, R., Henik, A., Rubinsten, O., Mohr, H., Dori, H., Van de Ven, V., et al. (2005b). Are numbers special? The comparison systems of the human brain investigated by fMRI. Neuropychologia, 43, 1238Ð1248. Dehaene, S. (1989). The psychophysics of numerical comparison: A reexamination of apparently incompatible data. Perception & Psychophysics, 45, 557Ð566. Dehaene, S. (1996). The organization of brain activations in number comparison: Event-related potentials and the additive-factors method. Journal of Cognitive Neuroscience, 8, 47Ð68. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371Ð396. Experimental Psychology 2006; Vol. 53(2):87Ð94
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Roi Cohen Kadosh Department of Behavioral Sciences Ben-Gurion University of the Negev Beer-Sheva Israel Tel. +972-8-6 47 72 09 Fax: +972-8-6 47 20 72 E-mail:
[email protected]
” 2006 Hogrefe & Huber Publishers
