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Numbers are represented in egocentric space: Effects of numerical cues and spatial reference frames on hand laterality judgements
Neuroscience Letters 452 (2009) 176–180
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Numbers are represented in egocentric space: Effects of numerical cues and spatial reference frames on hand laterality judgements Massimiliano Conson a,∗ , Elisabetta Mazzarella a , Luigi Trojano a,b,∗ a b
Neuropsychology Laboratory, Department of Psychology, Second University of Naples, via Vivaldi 43, 81100 Caserta, Italy Maugeri Foundation, IRCCS, Scientific Institute of Telese Terme (BN), Italy
a r t i c l e
i n f o
Article history: Received 3 September 2008 Received in revised form 22 December 2008 Accepted 16 January 2009 Keywords: Visuospatial cognition Numerical cognition Egocentric representation Body representation
a b s t r a c t Convergent findings demonstrate that numbers can be represented according to a spatially oriented mental number line. However, it is not established whether a default organization of the mental number line exists (i.e., a left-to-right orientation) or whether its spatial arrangement is only the epiphenomenon of specific task requirements. To address this issue we performed two experiments in which subjects were required to judge laterality of hand stimuli preceded by small, medium or large numerical cues; hand stimuli were compatible with egocentric or allocentric perspectives. We found evidence of a left-toright number–hand association in processing stimuli compatible with an egocentric perspective, whereas the reverse mapping was found with hands compatible with an allocentric perspective. These findings demonstrate that the basic left-to-right arrangement of the mental number line is defined with respect to the body-centred egocentric reference frame. © 2009 Elsevier Ireland Ltd. All rights reserved.
Since Galton’s early intuition [12], growing evidence supported the existence of a close link between visuospatial and numerical cognition. The association between numbers and space has been conceptualized in the framework of the mental number line, according to which low numbers are related to the left side and high numbers to the right side of space. This left-to-right orientation of the representational continuum has been repeatedly verified by a stimulus–response compatibility effect known as the Spatial Numerical Association of Response Codes (SNARC): when subjects are required to evaluate whether a number is odd or even, their responses to larger numbers are faster on the right side of space, whereas responses to smaller numbers are faster on the left side [8,13]. However, in specific paradigms the SNARC effect may show different spatial arrangement. For instance, the left-to-right orientation of the mental number line is reversed when subjects are required to imagine numbers within an analog clock [1]. Moreover, a visuomotor finger–number compatibility task demonstrated faster right-hand responses to small numbers (and a large numbers/left-hand association); such a finding, while not congruent with a left-to-right oriented mental number line, could be explained in relation to different finger-counting strategies ([9], see
∗ Corresponding authors at: Neuropsychology Laboratory, Department of Psychology, Second University of Naples, via Vivaldi 43, 81100 Caserta, CE, Italy. Tel.: +39 0823 274784. E-mail addresses: [email protected] (M. Conson), [email protected] (L. Trojano). 0304-3940/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2009.01.043
also [20]). These data challenge the possibility that the left-to-right orientation of the mental number line reflects an invariant spatial arrangement of numerical magnitude, and suggest that assignment of spatial codes to numbers is only an epiphenomenon of specific task requirements. Alternatively, the assignment of a spatial code to a number could be based upon a default left-to-right orientation of the mental number line, although with some degree of task-dependent flexibility [7]. Recent studies on spatial representation of numbers have demonstrated that finger-counting habits may modulate the association of numbers with space, thus supporting the idea that numerical cognition develops from interactions of the body with its environment (i.e., embodied hypothesis) [23]. However, the left-to-right orientation of the mental number line has originally been ascribed to the development of reading skills [8], or to genuinely preverbal and space-related representation of numbers [22], favouring the hypothesis that numerical cognition is “disembodied” in nature. Brozzoli et al. [3] directly contrasted the two hypotheses by manipulating hand posture (palm-up or palm-down) in two experiments in which normal subjects had to detect tactile stimuli delivered to fingers of their right hand. Since visual presentation of small numbers facilitated perception of stimuli located on left-sided fingers (with large numbers facilitating detection of right-sided tactile stimuli), irrespective of hand posture, this SNARC-like effect was ascribed to space-based representation of numbers, independent from body-related representation [3]. However, these results could be compatible with an “embodied” hypothesis as well, if it is postulated that the left and the right of the
M. Conson et al. / Neuroscience Letters 452 (2009) 176–180
mental number line are coded according to a body-based egocentric space, where left and right are defined with respect to the midsagittal plane. A hint in this direction came from a recent study by Loetscher et al. [14] in which subjects had their head turned to the left or the right during a random number generation task; turning the head to the left biased the subjects’ production towards small numbers, whereas turning head to the right decreased the production of small numbers. These findings would support the idea of an intimate relationship between egocentrically defined frames of reference and number representation. In the present study, by means of a cueing paradigm, we aimed to verify whether left-to-right orientation of the mental number line reflects basic principles of egocentric spatial organization. Starting from the demonstration that low or high numbers can cue subjects’ attention towards the left or the right side of space [11], we asked subjects to perform a left/right decision on hand stimuli preceded by numerical cues, contrasting egocentric and allocentric hand representation. Indeed, hand stimuli are automatically coded with respect to self-body representation [6], but, consistently with biomechanical constraints [17], some hand postures may be referred to others’ body representation [5,16,21]. Ottoboni et al. [16] required subjects to respond to coloured stimuli embedded in centrally presented right or left hands, and found a correspondence between the hand and the side of the response (i.e., a regular Simon effect) for back views, and a reverse correspondence (reverse Simon effect) for palm views. To explain such findings, the authors suggested that the two postures (palms and backs) were automatically coded as observer’s own hands or as hands of somebody standing in front of the observer [16]. The relevance of the spatial reference frame in representing hand laterality has been further clarified: in a functional MRI study, Saxe et al. [21] reported that hand palms and backs activate an egocentric perspective or an allocentric one depending on finger orientation. Saxe et al. [21] also observed that this manipulation of hand stimuli (inducing egocentric or allocentric perspectives) determined the activation of segregate body representation areas, consistent with Chan et al.’s findings [5] on hand and body stimuli, processed in the two different spatial reference frames. Thus, hand stimuli may activate egocentric or allocentric perspectives on the basis of a combination of posture and finger orientation. In the present study we directly contrasted egocentric and allocentric frames of reference in processing hand stimuli primed by numerical cues. On the basis of the hypothesis of a body-based space representation of numbers, we can predict that the association between numbers and left/right-hand coding is defined with respect to an egocentric reference frame: a regular SNARClike effect (i.e., an association between low numbers and left hand) should be observed in judging hand stimuli consistent with a “one’s own body” egocentric perspective, and a reverse effect (i.e., an association between low numbers and right hand) should be observed in judging hand stimuli coded from a “the other’s body” allocentric perspective. The lack of any effect of egocentric or allocentric perspective on number–hand association would instead be consistent with the hypothesis of an abstract, disembodied space-based representation of numbers. Experiment 1: Subjects were presented with hand stimuli viewed from back in upright and upside down orientation, preceded by numerical cues. A left hand back in upright orientation (fingers up) is coded in an egocentric perspective, but the same image presented in upside down orientation (fingers downward) is coded with respect to an allocentric perspective, as when one looks at someone else’s hand [21]. Starting from the hypothesis of an association between numerical magnitude and egocentric space, an advantage is expected when judging a left hand back in upright position after a small numerical cue (and a right hand back after
177
a large number), and a reversed number–hand association when judging hands in upside down orientation. Twenty-eight normal subjects (16 females; mean age 24 years, S.D. 2.54) participated in the experiment. All subjects were righthanded as assessed by means of the Edinburgh Handedness Inventory [15] (mean score = 93.3) and were naïve with respect to the aims and the hypotheses of the study. Participants were sitting 60 cm from a computer screen with their head on a chin rest and their hands situated palm-down on thighs, out of sight. Subjects were instructed to refrain from moving their hands and fingers, and the experimenter (seated behind participants) checked that subjects complied with this instruction during the whole task. In each trial, a fixation point (800 ms) was followed by one of three numerical cues (2, 5, or 8), centrally presented for 600 or 1200 ms, and then by a line drawing of a hand. Left and right hand backs, portrayed with fingers up or fingers down, were centrally presented until subjects gave their response. Hand drawings were large approximately 9.5 cm along the widest axis, which corresponded to about 9.1◦ of horizontal visual angle. Subjects were required to decide whether they were presented with left or right hands and to press one of two keys on a foot pedal. Response key was counterbalanced between participants, with half responding congruently (to a right hand with their right foot) and the other half with the opposite (incongruent) mapping. Task instructions explicitly stated that numbers were not relevant to the task. After one practice block, 144 randomised trials were presented, 6 for each combination of hand laterality (left, right), hand orientation (fingers up, fingers down), numerical cue (2, 5, 8) and cue duration (600 and 1200 ms). The study was conducted in accordance with the ethical standards of the 1964 Declaration of Helsinki and written informed consent was obtained from all participants. A 2 × 2 × 3 × 2 × 2 mixed ANOVA was performed on correct RTs, with hand laterality (left, right), hand orientation (fingers up, fingers down), numerical cue (2, 5, 8) and cue duration (600, 1200) as within-subject factors, and stimulus–response mapping (congruent, incongruent) as between-subject factor. Results demonstrated significant main effects of hand orientation (fingers up: mean 1216.15, S.E.M. 49.3; fingers down: mean 2195.12, S.E.M. 128.1; F(1,26) = 144.710; p = .0001) and of stimulus–response mapping (congruent: mean 1409.36, S.E.M. 87.9; incongruent: mean 2002.11, S.E.M. 88.1; F(1,26) = 22.790; p = .0001). More relevantly, there was a significant laterality × orientation × cue interaction (F(2,52) = 21.293; p = .0001; see Fig. 1). All remaining main effects and interactions were not significant. Post hoc comparisons (paired t-tests) revealed that when identifying stimuli with fingers pointing up subjects were faster when the left hand was preceded by number 2 (2 vs. 8, t = −5.047, p = .0001; 2 vs. 5, t = −3.011, p = .006; 5 vs. 8, t = −1.014, p = .319), and the right hand was preceded by number 8 (8 vs. 2, t = 4.183, p = .0001; 8 vs. 5, t = 3.387, p = .002; 5 vs. 2, t = .831, p = .413); on the contrary, with fingers pointing down subjects were faster to identify the left hand when preceded by number 8 (8 vs. 2, t = 4.254, p = .0001; 8 vs. 5, t = 2.925, p = .007; 5 vs. 2, t = 1.456, p = .157), and the right hand when preceded by number 2 (2 vs. 8, t = −2.311, p = .029; 2 vs. 5, t = −1.972, p = .059; 5 vs. 8, t = −.879, p = .387). The overall error rate was 9.7%. The same 2 × 2 × 3 × 2 × 2 mixed ANOVA design as above performed on error rates showed significant main effects of hand orientation (fingers up: mean 5%, S.E.M. 1.2; fingers down: mean 14.7%, S.E.M. 1.3%; F(1,26) = 34.451; p = .0001) and of stimulus–response mapping (congruent: mean 4.2%, S.E.M. 1.3%; incongruent: mean 15.5%, S.E.M. 1.4; F(1,26) = 37.511; p = .0001). More relevant here, there was a significant laterality × orientation × cue interaction (F(2,52) = 21.293; p = .0001). All remaining main effects and interactions were not
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Fig. 1. Subjects’ performance on Experiment 1. Mean reaction times (upper row) and error rates (lower row) to hand stimuli are plotted by the three numerical cues, with respect to egocentric (left) and allocentric (right) perspectives.
significant. The pattern of error rates was entirely consistent with RTs data (see Fig. 1), but no post hoc comparison (paired t-tests) reached the significance level (p < .05). In synthesis, consistently with the “egocentric” hypothesis about the spatial reference frame of the mental number line, low numbers were compatible with “my” left hand and “your” right hand (both lying on the left side of “my” egocentric space), whereas high numbers were compatible with “my” right hand and “your” left hand (both lying on the right side of “my” egocentric space). Experiment 2: We then verified the generalization of these data to other hand stimuli. Palms too can be consistent with either an egocentric or an allocentric perspective, depending on their spatial orientation; palms are referred to one’s own body perspective when thumbs point upward and to the other’s body perspective when thumbs point downward [21]. Twenty-eight right-handed normal subjects (14 females; mean age 25 years, S.D. 2.52; mean score on the Edinburgh Handedness Inventory = 90.28) were required to judge laterality of palms presented with thumb up or down. The remaining experimental set-up was the same as above. The study was conducted in accordance with the ethical standards of the 1964 Declaration of Helsinki and written informed consent was obtained from all participants. Also in this case, all subjects were naïve with respect to the aims and the hypotheses of the experiment. A 2 × 2 × 3 × 2 × 2 mixed ANOVA with hand laterality (left, right), hand orientation (thumbs up, thumbs down), numerical cue (2, 5, 8) and cue duration (600, 1200) as within-subject factor and stimulus–response mapping (congruent, incongruent) as betweensubject factor was performed on correct RTs. Results demonstrated
significant main effects of hand orientation (thumbs up: mean 1568.78, S.E.M. 63.1; thumbs down: mean 1905.87, S.E.M. 101.3; F(1,26) = 26.796; p = .0001), and stimulus–response mapping (congruent: mean 1329.54, S.E.M. 87.9; incongruent: mean 2145.11, S.E.M. 89.1; F(1,26) = 26.796; p = .0001). Moreover, there was a significant laterality × orientation × cue interaction (F(2,52) = 11.601; p = .0001; see Fig. 2), without other significant main effects or interactions. Post hoc comparisons (paired t-tests) showed that when hand stimuli were presented with thumbs up (“my hands”, egocentric perspective) subjects were faster to identify left palm when preceded by number 2 (2 vs. 8, t = −2.873, p = .008; 2 vs. 5, t = −2.054, p = .050; 5 vs. 8, t = −.524, p = .604), and right palm when preceded by number 8 (8 vs. 2, t = 2.318, p = .028; 8 vs. 5, t = 2.043, p = .051; 5 vs. 2, t = .508, p = .615). On the contrary, with thumbs pointing downward (“your hands”, allocentric perspective) subjects were faster to identify right palm when preceded by number 2 (2 vs. 8, t = −2.986, p = .006; 2 vs. 5, t = −2.078, p = .046; 5 vs. 8, t = −1.625, p = .116), and left palm when preceded by number 8 (8 vs. 2, t = 2.594, p = .015; 8 vs. 5, t = 2.095, p = .040; 5 vs. 2, t = .724, p = .475). The overall error rate was 9.3%. The same 2 × 2 × 3 × 2 × 2 mixed ANOVA performed on RTs was also conducted on error rates. Results demonstrated a significant main effect of stimulus–response mapping (congruent: mean 3.2%, S.E.M. 1.4%; incongruent: mean 14.4%, S.E.M. 1.5%; F(1,26) = 32.568; p = .0001), and a marginally significant laterality × orientation × cue interaction (F(2,52) = 3.274; p = .046), without other significant main effects or interactions. Again, the pattern of error rates closely resembled that of RTs data (as shown in Fig. 2), but no post hoc comparison (paired t-tests) reached the significance level (p < .05).
M. Conson et al. / Neuroscience Letters 452 (2009) 176–180
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Fig. 2. Subjects’ performance on Experiment 2. Mean reaction times (upper row) and error rates (lower row) are plotted by the three numerical cues, with respect to egocentric (left) and allocentric (right) perspectives.
These findings thus closely replicated those from Experiment 1 in showing a significant inversion of number–hand association in egocentric and allocentric perspectives. Several findings suggested that the mental number line is more than a metaphor and refers to a visuospatial representation of numerical magnitude [7], but the organization of this spatial representation has not been clarified as yet [23]. In the present experiments we contrasted egocentric and allocentric reference frames in judging laterality of hand stimuli preceded by numerical cues and found that the spatial reference frame strongly modulated compatibility effects. Actually, number–hand association showed a regular direction (faster responses with the low number/left-hand and high number/right-hand associations) when hand stimuli were compatible with an egocentric perspective, whereas the direction was reversed (faster responses with the low number/right-hand and high number/left-hand associations) when subjects judged hands compatible with an allocentric perspective. Moreover, we also found shorter response latencies and lower error rates in egocentric vs. allocentric perspective. Studies on motor imagery have demonstrated that normal subjects solve hand laterality tasks by mentally simulating movements of their own body part, that is they tend to imagine their corresponding body part at the orientation of the to-be-judged visual stimulus [17]. Data showing that subjects’ performance is affected by specific biomechanical constraints and by the current state of subjects’ body during the task are consistent with this interpretation [6,17]. Thus, it would be possible to suggest that when participants were shown stimuli compatible with allocentric perspective in the present experiments, they mentally rotated their own hands until subjects’ body representation was compatible with stimuli before emitting a laterality judgement. Alternatively, it could be assumed that subjects employed an egocentric perspec-
tive transformation [24]. This process is involved in tasks where subjects are required to make left–right judgements on a schematic human figure after having imagined themselves to be in the bodyposition of the figure and to have its spatial perspective [2,24]. This task requires subjects to represent oneself outside boundaries of one’s body (third-person view) rather than constrained within them (first-person view). However, both interpretations (mental rotation and egocentric perspective transformation) are not compatible with the inversion of number–hand association observed in the present allocentric tasks. Our findings are more consistent with the idea that in egocentric trials hand stimuli are automatically processed as one’s own body parts, whereas in the allocentric trials the observers mentally represent hands as parts of a body facing them [5,21]. Processing hand stimuli according to allocentric reference frame produced a detrimental effect on subjects’ accuracy and response speed. The advantage of egocentric vs. allocentric trials has been also reported in a recent study employing spatial judgements on verbal stimuli [25]. This might be related to higher processing demands of the allocentric condition, that also seems to recruit more extensive brain regions than the egocentric perspective [25], but further research is warranted to elucidate this issue. The present results showed a significant main effect of stimulus– response mapping, i.e., subjects were faster and more accurate for spatially congruent responses (left foot response to left-hand and right foot response to right hand) than for incongruent responses, but this factor did not interact with hand orientation and cue. Recently, Schwarz and Müller [22] demonstrated that the SNARC effect is also evident with foot responses, a finding apparently at odd with the present lack of number-response side interaction. However, Schwarz and Müller [22] used a parity judgement task in which they only assessed spatial compatibility of numerical cues and foot response, whereas in the present experiments two kinds of
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association were at stake: a stimulus–response mapping between hand and foot, and a stimulus–stimulus association linking hand and numbers. The significant main effect of hand–foot compatibility follows usual stimulus–response mapping effects involved in action related processes, whereas the lack of first- or second-order interaction of response side with numerical cues would suggest that number–hand interaction occurred at a cognitive stage preceding response selection. Therefore, our results are consistent with evidence from studies demonstrating that the association between numbers and space also occurs in tasks without response selection ([11], see also [19]). The opposite direction of number–hand association as a function of egocentric or allocentric coding would support that left and right of the mental number line are uniquely defined with respect to an egocentric “one’s own body” representation, i.e., they are always anchored to the perspective of the observer. Moreover, the intimate relationships between egocentric frame and representation of numerical magnitude strongly suggest that the left-to-right orientation of the mental number line is rooted in spatial-specific cognitive mechanisms and is not only an epiphenomenon of task manipulations [7]. This interaction between numbers and egocentric body representation is in line with the general theoretical framework of the embodied nature of number representation [4,23]. Within this framework it is possible to reinterpret Brozzoli et al.’s [3] finding that cross-modal interaction between tactile stimulation and visual numerical cues is compatible with the left-to-right direction and independent from body posture. Actually, in Brozzoli et al.’s experimental set-up [3] the extrapersonal abstract representation of left and right overlapped with the egocentric perspective of experimental subjects. Consequently, their findings are completely consistent with the statement that the mental number line is represented in an egocentric perspective, where left and right are defined with respect to one’s own body midsagittal plane. The manipulation of the spatial reference frame in the present experiments allowed us to verify that this is precisely the case, and that the left and right of the mental number line are not to be considered as abstract, disembodied, spatial concepts, but rather are as “embodied” in egocentric representation of experimental subjects. The idea of the embodied nature of number magnitude representation has received growing consensus in literature, but it is worth mentioning that some authors ascribe the number/body association to the use of fingers as counting tools [4,9,18,20]. At the moment, the issue of finger-counting strategy is unresolved [23]. Data supporting the idea that subjects start to count on their right hand would predict an association between small numbers and right hand, and between high numbers and left hand [9,20]. A recent study in subjects who start counting from their left or from their right hand seems to suggest that the strength but not the direction of the SNARC effect may vary as a function of finger-counting strategy [10]. While it is not possible at the moment to reconcile contrasting data on this issue, our data are consistent with the embodiment hypothesis centred on egocentric space defined with respect to the body midsagittal plane. By demonstrating that the spatial reference frame may modulate the direction of numerical
magnitude representation, our data stress the importance of controlling the egocentric–allocentric access to body representation in studies exploring space–number interactions. Acknowledgement We are grateful to Lucia Abbamonte for her revision of the English text. References [1] D. Bächtold, M. Baumüller, P. Brugger, Stimulus–response compatibility in representational space, Neuropsychologia 36 (1998) 731–735. [2] O. Blanke, C. Mohr, C.M. Michel, A. Pascual-Leone, P. Brugger, M. Seeck, T. Landis, G. Thut, Linking out-of-body experience and self processing to mental ownbody imagery at the temporoparietal junction, J. Neurosci. 25 (2005) 550–557. [3] C. Brozzoli, M. Ishihara, S.M. Göbel, R. Salemme, Y. Rossetti, A. Farnè, Touch perception reveals the dominance of spatial over digital representation of numbers, Proc. Natl. Acad. Sci. U.S.A. 105 (2008) 5644–5648. [4] B. Butterworth, The Mathematical Brain, Macmillan, London, 1999. [5] A.W. Chan, M.V. Peelen, P.E. Downing, The effect of viewpoint on body representation in the extrastriate body area, Neuroreport 15 (2004) 2407–2410. [6] M. Conson, S. Sacco, M. Sarà, F. Pistoia, D. Grossi, L. Trojano, Selective motor imagery defect in patients with locked-in syndrome, Neuropsychologia 46 (2008) 2622–2628. [7] M.D. De Hevia, G. Vallar, L. Girelli, Visualizing numbers in the mind’s eye: the role of visuo-spatial processes in numerical abilities, Neurosci. Biobehav. Rev. 32 (2008) 1361–1372. [8] S. Dehaene, S. Bossini, P. Giraux, The mental representation of parity and number magnitude, J. Exp. Psychol. Gen. 122 (1993) 371–396. [9] S. Di Luca, A. Granà, C. Semenza, X. Seron, M. Pesenti, Finger-digit compatibility in Arabic numeral processing, Q. J. Exp. Psychol. 59 (2006) 1648–1663. [10] M.H. Fischer, Finger counting habits modulate spatial–numerical associations, Cortex 44 (2008) 386–392. [11] M.H. Fischer, A.D. Castel, M.D. Dodd, J. Pratt, Perceiving numbers causes spatial shifts of attention, Nat. Neurosci. 6 (2003) 555–556. [12] F. Galton, Visualised numerals, Nature 21 (1880) 252–256. [13] E.M. Hubbard, M. Piazza, P. Pinel, S. Dehaene, Interactions between number and space in parietal cortex, Nat. Rev. Neurosci. 6 (2005) 435–448. [14] T. Loetscher, U. Schwarz, M. Schubiger, P. Brugger, Head turns bias the brain’s internal random generator, Curr. Biol. 18 (2008) R60–62. [15] R.C. Oldfield, The assessment and analysis of handedness: the Edinburgh inventory, Neuropsychologia 9 (1971) 97–113. [16] G. Ottoboni, A. Tessari, R. Cubelli, C. Umiltà, Is handedness recognition automatic? A study using a Simon-like paradigm, J. Exp. Psychol. Hum. Percept. Perform. 31 (2005) 778–789. [17] L.M. Parsons, Temporal and kinematic properties of motor behavior reflected in mentally simulated action, J. Exp. Psychol. Hum. Percept. Perform. 20 (1994) 709–730. [18] E. Rusconi, V. Walsh, B. Butterworth, Dexterity with numbers: rTMS over left angular gyrus disrupts finger gnosis and number processing, Neuropsychologia 43 (2005) 1024–1609. [19] E.E. Salillas, R. El Yagoubi, C. Semenza, Sensory and cognitive processes of shifts of spatial attention induced by numbers: an ERP study, Cortex 44 (2008) 406–413. [20] M. Sato, L. Cattaneo, G. Rizzolatti, V. Gallese, Numbers within our hands: modulation of corticospinal excitability of hand muscles during numerical judgment, J. Cogn. Neurosci. 19 (2007) 684–693. [21] R. Saxe, N. Jamal, L. Powell, My body or yours? The effect of visual perspective on cortical body representations, Cereb. Cortex 16 (2006) 178–182. [22] W. Schwarz, D. Müller, Spatial associations in number-related tasks: a comparison of manual and pedal responses, Exp. Psychol. 53 (2006) 4–15. [23] G. Wood, M.H. Fischer, Numbers, space, and action—from finger counting to the mental number line and beyond, Cortex 44 (2008) 353–358. [24] J. Zacks, B. Rypma, J.D. Gabrieli, B. Tversky, G.H. Glover, Imagined transformations of bodies: an fMRI investigation, Neuropsychologia 37 (1999) 1029–1040. [25] T. Zaehle, K. Jordan, T. Wüstenberg, J. Baudewig, P. Dechent, F.W. Mast, The neural basis of the egocentric and allocentric spatial frame of reference, Brain Res. 16 (2007) 92–103.
Contents lists available at ScienceDirect
Neuroscience Letters journal homepage: www.elsevier.com/locate/neulet
Numbers are represented in egocentric space: Effects of numerical cues and spatial reference frames on hand laterality judgements Massimiliano Conson a,∗ , Elisabetta Mazzarella a , Luigi Trojano a,b,∗ a b
Neuropsychology Laboratory, Department of Psychology, Second University of Naples, via Vivaldi 43, 81100 Caserta, Italy Maugeri Foundation, IRCCS, Scientific Institute of Telese Terme (BN), Italy
a r t i c l e
i n f o
Article history: Received 3 September 2008 Received in revised form 22 December 2008 Accepted 16 January 2009 Keywords: Visuospatial cognition Numerical cognition Egocentric representation Body representation
a b s t r a c t Convergent findings demonstrate that numbers can be represented according to a spatially oriented mental number line. However, it is not established whether a default organization of the mental number line exists (i.e., a left-to-right orientation) or whether its spatial arrangement is only the epiphenomenon of specific task requirements. To address this issue we performed two experiments in which subjects were required to judge laterality of hand stimuli preceded by small, medium or large numerical cues; hand stimuli were compatible with egocentric or allocentric perspectives. We found evidence of a left-toright number–hand association in processing stimuli compatible with an egocentric perspective, whereas the reverse mapping was found with hands compatible with an allocentric perspective. These findings demonstrate that the basic left-to-right arrangement of the mental number line is defined with respect to the body-centred egocentric reference frame. © 2009 Elsevier Ireland Ltd. All rights reserved.
Since Galton’s early intuition [12], growing evidence supported the existence of a close link between visuospatial and numerical cognition. The association between numbers and space has been conceptualized in the framework of the mental number line, according to which low numbers are related to the left side and high numbers to the right side of space. This left-to-right orientation of the representational continuum has been repeatedly verified by a stimulus–response compatibility effect known as the Spatial Numerical Association of Response Codes (SNARC): when subjects are required to evaluate whether a number is odd or even, their responses to larger numbers are faster on the right side of space, whereas responses to smaller numbers are faster on the left side [8,13]. However, in specific paradigms the SNARC effect may show different spatial arrangement. For instance, the left-to-right orientation of the mental number line is reversed when subjects are required to imagine numbers within an analog clock [1]. Moreover, a visuomotor finger–number compatibility task demonstrated faster right-hand responses to small numbers (and a large numbers/left-hand association); such a finding, while not congruent with a left-to-right oriented mental number line, could be explained in relation to different finger-counting strategies ([9], see
∗ Corresponding authors at: Neuropsychology Laboratory, Department of Psychology, Second University of Naples, via Vivaldi 43, 81100 Caserta, CE, Italy. Tel.: +39 0823 274784. E-mail addresses: [email protected] (M. Conson), [email protected] (L. Trojano). 0304-3940/$ – see front matter © 2009 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2009.01.043
also [20]). These data challenge the possibility that the left-to-right orientation of the mental number line reflects an invariant spatial arrangement of numerical magnitude, and suggest that assignment of spatial codes to numbers is only an epiphenomenon of specific task requirements. Alternatively, the assignment of a spatial code to a number could be based upon a default left-to-right orientation of the mental number line, although with some degree of task-dependent flexibility [7]. Recent studies on spatial representation of numbers have demonstrated that finger-counting habits may modulate the association of numbers with space, thus supporting the idea that numerical cognition develops from interactions of the body with its environment (i.e., embodied hypothesis) [23]. However, the left-to-right orientation of the mental number line has originally been ascribed to the development of reading skills [8], or to genuinely preverbal and space-related representation of numbers [22], favouring the hypothesis that numerical cognition is “disembodied” in nature. Brozzoli et al. [3] directly contrasted the two hypotheses by manipulating hand posture (palm-up or palm-down) in two experiments in which normal subjects had to detect tactile stimuli delivered to fingers of their right hand. Since visual presentation of small numbers facilitated perception of stimuli located on left-sided fingers (with large numbers facilitating detection of right-sided tactile stimuli), irrespective of hand posture, this SNARC-like effect was ascribed to space-based representation of numbers, independent from body-related representation [3]. However, these results could be compatible with an “embodied” hypothesis as well, if it is postulated that the left and the right of the
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mental number line are coded according to a body-based egocentric space, where left and right are defined with respect to the midsagittal plane. A hint in this direction came from a recent study by Loetscher et al. [14] in which subjects had their head turned to the left or the right during a random number generation task; turning the head to the left biased the subjects’ production towards small numbers, whereas turning head to the right decreased the production of small numbers. These findings would support the idea of an intimate relationship between egocentrically defined frames of reference and number representation. In the present study, by means of a cueing paradigm, we aimed to verify whether left-to-right orientation of the mental number line reflects basic principles of egocentric spatial organization. Starting from the demonstration that low or high numbers can cue subjects’ attention towards the left or the right side of space [11], we asked subjects to perform a left/right decision on hand stimuli preceded by numerical cues, contrasting egocentric and allocentric hand representation. Indeed, hand stimuli are automatically coded with respect to self-body representation [6], but, consistently with biomechanical constraints [17], some hand postures may be referred to others’ body representation [5,16,21]. Ottoboni et al. [16] required subjects to respond to coloured stimuli embedded in centrally presented right or left hands, and found a correspondence between the hand and the side of the response (i.e., a regular Simon effect) for back views, and a reverse correspondence (reverse Simon effect) for palm views. To explain such findings, the authors suggested that the two postures (palms and backs) were automatically coded as observer’s own hands or as hands of somebody standing in front of the observer [16]. The relevance of the spatial reference frame in representing hand laterality has been further clarified: in a functional MRI study, Saxe et al. [21] reported that hand palms and backs activate an egocentric perspective or an allocentric one depending on finger orientation. Saxe et al. [21] also observed that this manipulation of hand stimuli (inducing egocentric or allocentric perspectives) determined the activation of segregate body representation areas, consistent with Chan et al.’s findings [5] on hand and body stimuli, processed in the two different spatial reference frames. Thus, hand stimuli may activate egocentric or allocentric perspectives on the basis of a combination of posture and finger orientation. In the present study we directly contrasted egocentric and allocentric frames of reference in processing hand stimuli primed by numerical cues. On the basis of the hypothesis of a body-based space representation of numbers, we can predict that the association between numbers and left/right-hand coding is defined with respect to an egocentric reference frame: a regular SNARClike effect (i.e., an association between low numbers and left hand) should be observed in judging hand stimuli consistent with a “one’s own body” egocentric perspective, and a reverse effect (i.e., an association between low numbers and right hand) should be observed in judging hand stimuli coded from a “the other’s body” allocentric perspective. The lack of any effect of egocentric or allocentric perspective on number–hand association would instead be consistent with the hypothesis of an abstract, disembodied space-based representation of numbers. Experiment 1: Subjects were presented with hand stimuli viewed from back in upright and upside down orientation, preceded by numerical cues. A left hand back in upright orientation (fingers up) is coded in an egocentric perspective, but the same image presented in upside down orientation (fingers downward) is coded with respect to an allocentric perspective, as when one looks at someone else’s hand [21]. Starting from the hypothesis of an association between numerical magnitude and egocentric space, an advantage is expected when judging a left hand back in upright position after a small numerical cue (and a right hand back after
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a large number), and a reversed number–hand association when judging hands in upside down orientation. Twenty-eight normal subjects (16 females; mean age 24 years, S.D. 2.54) participated in the experiment. All subjects were righthanded as assessed by means of the Edinburgh Handedness Inventory [15] (mean score = 93.3) and were naïve with respect to the aims and the hypotheses of the study. Participants were sitting 60 cm from a computer screen with their head on a chin rest and their hands situated palm-down on thighs, out of sight. Subjects were instructed to refrain from moving their hands and fingers, and the experimenter (seated behind participants) checked that subjects complied with this instruction during the whole task. In each trial, a fixation point (800 ms) was followed by one of three numerical cues (2, 5, or 8), centrally presented for 600 or 1200 ms, and then by a line drawing of a hand. Left and right hand backs, portrayed with fingers up or fingers down, were centrally presented until subjects gave their response. Hand drawings were large approximately 9.5 cm along the widest axis, which corresponded to about 9.1◦ of horizontal visual angle. Subjects were required to decide whether they were presented with left or right hands and to press one of two keys on a foot pedal. Response key was counterbalanced between participants, with half responding congruently (to a right hand with their right foot) and the other half with the opposite (incongruent) mapping. Task instructions explicitly stated that numbers were not relevant to the task. After one practice block, 144 randomised trials were presented, 6 for each combination of hand laterality (left, right), hand orientation (fingers up, fingers down), numerical cue (2, 5, 8) and cue duration (600 and 1200 ms). The study was conducted in accordance with the ethical standards of the 1964 Declaration of Helsinki and written informed consent was obtained from all participants. A 2 × 2 × 3 × 2 × 2 mixed ANOVA was performed on correct RTs, with hand laterality (left, right), hand orientation (fingers up, fingers down), numerical cue (2, 5, 8) and cue duration (600, 1200) as within-subject factors, and stimulus–response mapping (congruent, incongruent) as between-subject factor. Results demonstrated significant main effects of hand orientation (fingers up: mean 1216.15, S.E.M. 49.3; fingers down: mean 2195.12, S.E.M. 128.1; F(1,26) = 144.710; p = .0001) and of stimulus–response mapping (congruent: mean 1409.36, S.E.M. 87.9; incongruent: mean 2002.11, S.E.M. 88.1; F(1,26) = 22.790; p = .0001). More relevantly, there was a significant laterality × orientation × cue interaction (F(2,52) = 21.293; p = .0001; see Fig. 1). All remaining main effects and interactions were not significant. Post hoc comparisons (paired t-tests) revealed that when identifying stimuli with fingers pointing up subjects were faster when the left hand was preceded by number 2 (2 vs. 8, t = −5.047, p = .0001; 2 vs. 5, t = −3.011, p = .006; 5 vs. 8, t = −1.014, p = .319), and the right hand was preceded by number 8 (8 vs. 2, t = 4.183, p = .0001; 8 vs. 5, t = 3.387, p = .002; 5 vs. 2, t = .831, p = .413); on the contrary, with fingers pointing down subjects were faster to identify the left hand when preceded by number 8 (8 vs. 2, t = 4.254, p = .0001; 8 vs. 5, t = 2.925, p = .007; 5 vs. 2, t = 1.456, p = .157), and the right hand when preceded by number 2 (2 vs. 8, t = −2.311, p = .029; 2 vs. 5, t = −1.972, p = .059; 5 vs. 8, t = −.879, p = .387). The overall error rate was 9.7%. The same 2 × 2 × 3 × 2 × 2 mixed ANOVA design as above performed on error rates showed significant main effects of hand orientation (fingers up: mean 5%, S.E.M. 1.2; fingers down: mean 14.7%, S.E.M. 1.3%; F(1,26) = 34.451; p = .0001) and of stimulus–response mapping (congruent: mean 4.2%, S.E.M. 1.3%; incongruent: mean 15.5%, S.E.M. 1.4; F(1,26) = 37.511; p = .0001). More relevant here, there was a significant laterality × orientation × cue interaction (F(2,52) = 21.293; p = .0001). All remaining main effects and interactions were not
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Fig. 1. Subjects’ performance on Experiment 1. Mean reaction times (upper row) and error rates (lower row) to hand stimuli are plotted by the three numerical cues, with respect to egocentric (left) and allocentric (right) perspectives.
significant. The pattern of error rates was entirely consistent with RTs data (see Fig. 1), but no post hoc comparison (paired t-tests) reached the significance level (p < .05). In synthesis, consistently with the “egocentric” hypothesis about the spatial reference frame of the mental number line, low numbers were compatible with “my” left hand and “your” right hand (both lying on the left side of “my” egocentric space), whereas high numbers were compatible with “my” right hand and “your” left hand (both lying on the right side of “my” egocentric space). Experiment 2: We then verified the generalization of these data to other hand stimuli. Palms too can be consistent with either an egocentric or an allocentric perspective, depending on their spatial orientation; palms are referred to one’s own body perspective when thumbs point upward and to the other’s body perspective when thumbs point downward [21]. Twenty-eight right-handed normal subjects (14 females; mean age 25 years, S.D. 2.52; mean score on the Edinburgh Handedness Inventory = 90.28) were required to judge laterality of palms presented with thumb up or down. The remaining experimental set-up was the same as above. The study was conducted in accordance with the ethical standards of the 1964 Declaration of Helsinki and written informed consent was obtained from all participants. Also in this case, all subjects were naïve with respect to the aims and the hypotheses of the experiment. A 2 × 2 × 3 × 2 × 2 mixed ANOVA with hand laterality (left, right), hand orientation (thumbs up, thumbs down), numerical cue (2, 5, 8) and cue duration (600, 1200) as within-subject factor and stimulus–response mapping (congruent, incongruent) as betweensubject factor was performed on correct RTs. Results demonstrated
significant main effects of hand orientation (thumbs up: mean 1568.78, S.E.M. 63.1; thumbs down: mean 1905.87, S.E.M. 101.3; F(1,26) = 26.796; p = .0001), and stimulus–response mapping (congruent: mean 1329.54, S.E.M. 87.9; incongruent: mean 2145.11, S.E.M. 89.1; F(1,26) = 26.796; p = .0001). Moreover, there was a significant laterality × orientation × cue interaction (F(2,52) = 11.601; p = .0001; see Fig. 2), without other significant main effects or interactions. Post hoc comparisons (paired t-tests) showed that when hand stimuli were presented with thumbs up (“my hands”, egocentric perspective) subjects were faster to identify left palm when preceded by number 2 (2 vs. 8, t = −2.873, p = .008; 2 vs. 5, t = −2.054, p = .050; 5 vs. 8, t = −.524, p = .604), and right palm when preceded by number 8 (8 vs. 2, t = 2.318, p = .028; 8 vs. 5, t = 2.043, p = .051; 5 vs. 2, t = .508, p = .615). On the contrary, with thumbs pointing downward (“your hands”, allocentric perspective) subjects were faster to identify right palm when preceded by number 2 (2 vs. 8, t = −2.986, p = .006; 2 vs. 5, t = −2.078, p = .046; 5 vs. 8, t = −1.625, p = .116), and left palm when preceded by number 8 (8 vs. 2, t = 2.594, p = .015; 8 vs. 5, t = 2.095, p = .040; 5 vs. 2, t = .724, p = .475). The overall error rate was 9.3%. The same 2 × 2 × 3 × 2 × 2 mixed ANOVA performed on RTs was also conducted on error rates. Results demonstrated a significant main effect of stimulus–response mapping (congruent: mean 3.2%, S.E.M. 1.4%; incongruent: mean 14.4%, S.E.M. 1.5%; F(1,26) = 32.568; p = .0001), and a marginally significant laterality × orientation × cue interaction (F(2,52) = 3.274; p = .046), without other significant main effects or interactions. Again, the pattern of error rates closely resembled that of RTs data (as shown in Fig. 2), but no post hoc comparison (paired t-tests) reached the significance level (p < .05).
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Fig. 2. Subjects’ performance on Experiment 2. Mean reaction times (upper row) and error rates (lower row) are plotted by the three numerical cues, with respect to egocentric (left) and allocentric (right) perspectives.
These findings thus closely replicated those from Experiment 1 in showing a significant inversion of number–hand association in egocentric and allocentric perspectives. Several findings suggested that the mental number line is more than a metaphor and refers to a visuospatial representation of numerical magnitude [7], but the organization of this spatial representation has not been clarified as yet [23]. In the present experiments we contrasted egocentric and allocentric reference frames in judging laterality of hand stimuli preceded by numerical cues and found that the spatial reference frame strongly modulated compatibility effects. Actually, number–hand association showed a regular direction (faster responses with the low number/left-hand and high number/right-hand associations) when hand stimuli were compatible with an egocentric perspective, whereas the direction was reversed (faster responses with the low number/right-hand and high number/left-hand associations) when subjects judged hands compatible with an allocentric perspective. Moreover, we also found shorter response latencies and lower error rates in egocentric vs. allocentric perspective. Studies on motor imagery have demonstrated that normal subjects solve hand laterality tasks by mentally simulating movements of their own body part, that is they tend to imagine their corresponding body part at the orientation of the to-be-judged visual stimulus [17]. Data showing that subjects’ performance is affected by specific biomechanical constraints and by the current state of subjects’ body during the task are consistent with this interpretation [6,17]. Thus, it would be possible to suggest that when participants were shown stimuli compatible with allocentric perspective in the present experiments, they mentally rotated their own hands until subjects’ body representation was compatible with stimuli before emitting a laterality judgement. Alternatively, it could be assumed that subjects employed an egocentric perspec-
tive transformation [24]. This process is involved in tasks where subjects are required to make left–right judgements on a schematic human figure after having imagined themselves to be in the bodyposition of the figure and to have its spatial perspective [2,24]. This task requires subjects to represent oneself outside boundaries of one’s body (third-person view) rather than constrained within them (first-person view). However, both interpretations (mental rotation and egocentric perspective transformation) are not compatible with the inversion of number–hand association observed in the present allocentric tasks. Our findings are more consistent with the idea that in egocentric trials hand stimuli are automatically processed as one’s own body parts, whereas in the allocentric trials the observers mentally represent hands as parts of a body facing them [5,21]. Processing hand stimuli according to allocentric reference frame produced a detrimental effect on subjects’ accuracy and response speed. The advantage of egocentric vs. allocentric trials has been also reported in a recent study employing spatial judgements on verbal stimuli [25]. This might be related to higher processing demands of the allocentric condition, that also seems to recruit more extensive brain regions than the egocentric perspective [25], but further research is warranted to elucidate this issue. The present results showed a significant main effect of stimulus– response mapping, i.e., subjects were faster and more accurate for spatially congruent responses (left foot response to left-hand and right foot response to right hand) than for incongruent responses, but this factor did not interact with hand orientation and cue. Recently, Schwarz and Müller [22] demonstrated that the SNARC effect is also evident with foot responses, a finding apparently at odd with the present lack of number-response side interaction. However, Schwarz and Müller [22] used a parity judgement task in which they only assessed spatial compatibility of numerical cues and foot response, whereas in the present experiments two kinds of
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association were at stake: a stimulus–response mapping between hand and foot, and a stimulus–stimulus association linking hand and numbers. The significant main effect of hand–foot compatibility follows usual stimulus–response mapping effects involved in action related processes, whereas the lack of first- or second-order interaction of response side with numerical cues would suggest that number–hand interaction occurred at a cognitive stage preceding response selection. Therefore, our results are consistent with evidence from studies demonstrating that the association between numbers and space also occurs in tasks without response selection ([11], see also [19]). The opposite direction of number–hand association as a function of egocentric or allocentric coding would support that left and right of the mental number line are uniquely defined with respect to an egocentric “one’s own body” representation, i.e., they are always anchored to the perspective of the observer. Moreover, the intimate relationships between egocentric frame and representation of numerical magnitude strongly suggest that the left-to-right orientation of the mental number line is rooted in spatial-specific cognitive mechanisms and is not only an epiphenomenon of task manipulations [7]. This interaction between numbers and egocentric body representation is in line with the general theoretical framework of the embodied nature of number representation [4,23]. Within this framework it is possible to reinterpret Brozzoli et al.’s [3] finding that cross-modal interaction between tactile stimulation and visual numerical cues is compatible with the left-to-right direction and independent from body posture. Actually, in Brozzoli et al.’s experimental set-up [3] the extrapersonal abstract representation of left and right overlapped with the egocentric perspective of experimental subjects. Consequently, their findings are completely consistent with the statement that the mental number line is represented in an egocentric perspective, where left and right are defined with respect to one’s own body midsagittal plane. The manipulation of the spatial reference frame in the present experiments allowed us to verify that this is precisely the case, and that the left and right of the mental number line are not to be considered as abstract, disembodied, spatial concepts, but rather are as “embodied” in egocentric representation of experimental subjects. The idea of the embodied nature of number magnitude representation has received growing consensus in literature, but it is worth mentioning that some authors ascribe the number/body association to the use of fingers as counting tools [4,9,18,20]. At the moment, the issue of finger-counting strategy is unresolved [23]. Data supporting the idea that subjects start to count on their right hand would predict an association between small numbers and right hand, and between high numbers and left hand [9,20]. A recent study in subjects who start counting from their left or from their right hand seems to suggest that the strength but not the direction of the SNARC effect may vary as a function of finger-counting strategy [10]. While it is not possible at the moment to reconcile contrasting data on this issue, our data are consistent with the embodiment hypothesis centred on egocentric space defined with respect to the body midsagittal plane. By demonstrating that the spatial reference frame may modulate the direction of numerical
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