Moving along the mental number line: Interactions between whole-body motion and numerical cognition

Moving Along the Mental Number Line: Interactions BetweenWhole-Body Motion and Numerical Cognition

Matthias Hartmann, Luzia Grabherr, and Fred W. MastUniversity of Bern

Active head turns to the left and right have recently been shown to influence numerical cognition byshifting attention along the mental number line. In the present study, we found that passive whole-bodymotion influences numerical cognition. In a random-number generation task (Experiment 1), leftwardand downward displacement of participants facilitated small number generation, whereas rightward andupward displacement facilitated the generation of large numbers. Influences of leftward and rightwardmotion were also found for the processing of auditorily presented numbers in a magnitude-judgment task(Experiment 2). Additionally, we investigated the reverse effect of the number-space association(Experiment 3). Participants were displaced leftward or rightward and asked to detect motion directionas fast as possible while small or large numbers were auditorily presented. When motion detection wasdifficult, leftward motion was detected faster when hearing small number and rightward motion whenhearing large number. We provide new evidence that bottom-up vestibular activation is sufficient tointeract with the higher-order spatial representation underlying numerical cognition. The results showthat action planning or motor activity is not necessary to influence spatial attention. Moreover, our resultssuggest that self-motion perception and numerical cognition can mutually influence each other.

Keywords: numerical cognition, mental number line, body motion, self-motion perception, vestibularstimulation

Numbers are thought to be represented spatially along a hori-zontal, “mental” number line, ranging from small numbers on theleft to large numbers on the right. The small-left and large-right-association affects performance in spatial and numerical tasks,suggesting that the processing of numerical information is linkedwith the processing of spatial information (e.g., Casarotti, Michie-lin, Zorzi, & Umilta, 2007; Dehaene, Bossini, & Giraux, 1993;Fischer, 2001; Fischer, Castel, Dodd, & Pratt, 2003; Hubbard,Piazza, Pinel, & Dehaene, 2005). The most prominent example isthe effect of spatial-numerical association of response codes(SNARC): Relatively small numbers are responded to faster withleft-sided responses, while relatively large numbers are respondedto faster with right-sided responses (Dehaene et al., 1993). Themental number line has been used to investigate alterations inspatial attention after unilateral brain damage (Salillas, Grana,Juncadella, Rico, & Semenza, 2009; Vuilleumier, Ortigue, &Brugger, 2004; Zorzi, Priftis, Meneghello, Marenzi, & Umilta,

2006; Zorzi, Priftis, & Umilta, 2002). For example, Zorzi et al.(2002) asked patients suffering from neglect to bisect a givennumerical interval. The numerical midpoint was overestimated,that is, shifted toward the right side of the mental number line. Thisrightward shift is in line with results from line bisection taskswhere the indicated midpoint is also shifted to the right side.Similarly, numerical tasks have also been used to investigatealtered spatial attention induced by transcranial-magnetic stimula-tion (Göbel, Calabria, Farne, & Rossetti, 2006) or visuomotoradaptation (A. M. Loftus, Nicholls, Mattingley, & Bradshaw,2008; Rossetti, Jacquin-Courtois, Rode, Ota, Michel, & Boisson,2004). A commonality between these studies is that leftward orrightward shifts of attention influence numerical cognition.

When exploring the environment, the direction of body motionis likely to influence the focus of attention in space. A wealth ofstudies have investigated the influence of body motion on therepresentation of space (e.g., Amorim, Glasauer, Corpinot, &Berthoz, 1997; Klatzky, Loomis, Beall, Chance, & Golledge,1998; Presson & Montello, 1994; Simons & Wang, 1998; Wang &Spelke, 2000). However, the potential role of body motion indirecting spatial attention, and thus influencing higher order spatialcognition, is still poorly understood. Recently, the direction ofactive head turns has been found to influence numerical cognition(Loetscher, Schwarz, Schubiger, & Brugger, 2008). Participantswere asked to generate numbers as randomly as possible whilethey actively turned their head to the left and to the right side. Theauthors found that small numbers were generated more oftenduring leftward head turns as compared to rightward head turns,suggesting that active head turns direct attention to the correspond-ing side in mental number space. These results raise an important

Matthias Hartmann and Fred W. Mast, Department of Psychology andCenter for Cognition, Learning and Memory, University of Bern, Switzer-land; Luzia Grabherr, Department of Psychology, University of Bern,Switzerland.

The study was funded by the Swiss National Science Foundation(Pro�Doc Grant PDFMP1_127238). We thank Marco Hunziker for tech-nical assistance, Bob Grimes for programming, and Christophe Lopez andCaroline Falconer for helpful comments on an earlier version of themanuscript.

Correspondence concerning this article should be addressed to MatthiasHartmann, Department of Psychology, University of Bern, Muesmattstrasse45, CH-3000 Bern, Switzerland. E-mail: [email protected]

Journal of Experimental Psychology: © 2011 American Psychological AssociationHuman Perception and Performance2011, Vol. 00, No. 00, 000–000

0096-1523/11/$12.00 DOI: 10.1037/a0026706

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question: Is active body motion required to direct spatial attentionor does a passive displacement of the body suffice? An active headturn involves several processes including the prior intention tomove the head, the generation of motor commands and efferencecopies, and the processing of sensory feedback from receptors inthe neck and in the vestibular system. In contrast, a passivewhole-body motion primarily evokes sensory input from the ves-tibular system (Walsh, 1961) but does not involve an intention tomove nor any overt motor activity.

The vestibular system responds to linear and angular accelera-tion, and these cues are used to update body position across timeand space (Berthoz, Israel, Georges-Francois, Grasso, & Tsuzuku,1995). The involvement of vestibular processing in directing spa-tial attention has been highlighted in neurological patients (seeKarnath & Dieterich, 2005, for a review), but still relatively littleis known from investigations with healthy participants. This is notsurprising given that the processing of vestibular information, ingeneral, has been rather neglected in cognitive science. To ourknowledge, only one study has reported that vestibular informa-tion, induced by passive whole-body rotation, influences spatialattention allocation in healthy participants (Figliozzi, Guariglia,Silvetti, Siegler, & Doricchi, 2005). It is noteworthy, however, thatRorden, Karnath, and Driver (2001) did not find shifts of attentionwhen the vestibular system in healthy participants was stimulatedby means of caloric vestibular stimulation. A possible reason forthe different findings could be the use of distinct types of vestib-ular stimulation. To date, it is not yet clear whether vestibularinformation can influence attention in higher-order spatial repre-sentations such as the mental number line. The aim of this study isto explore whether vestibular information alone is sufficient toinfluence numerical cognition. Previous studies that investigatedthe influence of body motion on numerical cognition involvedmotor intention (Loetscher et al., 2008) and visuo-manual adapta-tion (Rossetti et al., 2004). In this study, we used a motionplatform allowing participants to be passively displaced.

In Experiment 1, we examined whether passive whole-bodymotion influences the generation of random numbers in a similarway as it was found for active head turns (Loetscher et al., 2008).Participants were passively displaced along all three main bodyaxes while generating random numbers from 1 to 30. We hypoth-esized that the direction of passive whole-body motion would shiftattention to the corresponding side in mental number space, whichin turn would influence the magnitude of generated numbers. Weexpected that smaller numbers would be generated more oftenduring leftward as compared to rightward passive whole-bodymotion. In addition to the left-small and right-large association,some studies have also found a down-small and up-large associ-ation (Cappelletti, Freeman, & Cipolotti, 2007; Gevers, Lammer-tyn, Notebaert, Verguts, & Fias, 2006; Ito & Hatta, 2004; Loet-scher, Bockisch, Nicholls, & Brugger, 2010; Sagiv, Simner,Collins, Butterworth, & Ward, 2006; Schwarz & Keus, 2004).These vertical magnitude associations may result from everydayexperiences with numbers. For example, climbing a staircase isaccompanied by increasing numbers of floors (and meters abovesea level), whereas the opposite is true for moving downward.We therefore hypothesized that participants would generate moresmall numbers during downward as compared to upward passivewhole-body motion. Regarding forward- and backward-magnitudeassociation, to the best of our knowledge, there is no empirical

evidence to which to refer. However, moving forward has beenassociated with thinking about the future, and moving backwardwith thinking about the past (Miles, Karpinska, Lumsden, & Mac-rae, 2010; Miles, Nind, & Macrae, 2010). We therefore hypothe-sized that moving forward could be associated with higher num-bers (progress, future associated with higher date on the timeline),whereas moving backward could be associated with smaller num-bers (regression, past associated with a smaller date on the time-line).

Producing numbers is only one aspect of numerical cognition.Two other major aspects are numerical comprehension, that is,converting the arabic or verbal numerical input into a semanticrepresentation, and calculation processes (McCloskey, Caramazza,& Basili, 1985). The random number generation task does notpermit drawing conclusions about the influence of passive whole-body motion on these processes. In Experiment 2, we used aforced-choice number task where a given number has to be rec-ognized and categorized as quickly as possible. In this task, theparticipant’s role changes from an active “producer” of numbermagnitudes to a “processor” of numbers with a binary choice. Thistask allows assessing whether the direction of passive whole-bodymotion actually influences the processing of a number that ispresented by an external source. Moreover, it can extend theknowledge from what is known about vestibular cross-modalattentional-facilitation effects. Vestibular cross-modal attentionalfacilitation has been demonstrated by Figliozzi et al. (2005). Theyinvestigated the processing of external visual and tactile stimulipresented to the left or right side of participants during passivewhole-body rotation. They found that stimuli presented on the sideof rotation were perceived to precede stimuli simultaneously pre-sented to the opposite side. They concluded that vestibular inputshifts attention toward the direction of rotation and, consequently,facilitates the detection of stimuli presented on the side of rotation.Is the influence of such a vestibular-induced attentional shiftlimited to the processing of stimuli that are presented in the left orright physical space? Or could it also influence the processing ofstimuli that are associated with left or right (such as small or largenumbers) even though they are simultaneously presented to bothears. The purpose of Experiment 2 was to determine whether theprocessing of externally presented numbers is facilitated duringwhole-body motion that is spatially congruent with the mentalrepresentation of the number. Participants were passively dis-placed leftward or rightward while performing a magnitude-judgment task. We hypothesized that a leftward passive whole-body motion would shift attention to the left side of the mentalnumber line, and consequently facilitates the processing and cat-egorization of small numbers. We also expected the correspondingeffect for rightward direction and the processing of large numbers.

An important, additional property of the number-space associ-ation is bidirectionality. Some studies found that perceiving num-bers can induce a shift of spatial attention toward the left and rightside, according to their magnitude. Fischer et al. (2003) askedparticipants to press a button as fast as possible when a dotappeared on the screen (either in the left or right half). Before thedot appeared, either a small or large number was centrally pre-sented. Although these numbers were irrelevant to the task, theyinfluenced participants’ responses: Dots on the left half of thescreen were detected faster when they were preceded by a smallnumber, and dots on the right half of the screen were detected

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faster when preceded by a large number. These results suggest thatthe perception of numbers automatically activates a spatial frameof reference, which in turn causes a shift in covert attention to theleft or right side. In accordance with this, a leftward bias has beenfound when participants were asked to indicate the midpoint of aline that consisted of small numbers, and rightward shift when theline consisted of large numbers (Calabria & Rossetti, 2005; Fi-scher, 2001). So far, evidence of the effect of numbers on spatialattention is limited to the visual space and eye movements (Fi-scher, Warlop, Hill, & Fias, 2004; Loetscher et al., 2010; Schwarz& Keus, 2004). It remains unclear whether numbers could influ-ence the perception of vestibular stimuli. This is the aim ofExperiment 3. It has been shown that the interpretation of self-motion information can be influenced by other sensory cues.Especially conflicting visual cues (e.g., Dichgans, Held, Young, &Brandt, 1972; Ishida, Fushiki, Nishida, & Watanabe, 2008;Mergner, Schweigart, Muller, Hlavacka, & Becker, 2000; Probst,Straube, & Bles, 1985; Zupan & Merfeld, 2003, 2008), but alsoauditory cues (see Valjamae, 2009, for a review) can bias self-motion perception. We investigated whether the perception ofself-motion direction could be influenced by hearing small andlarge numbers. We hypothesized that hearing a small numberwould facilitate the correct detection of a leftward motion (andvice versa for a large number).

To sum up, the present study investigates the role of passivewhole-body motion on directing attention and its impact on higherorder spatial representations. We are particularly interested inwhether the information elicited by passive whole-body motion issufficient to interact with numerical cognition. The results willprovide new insight into the role vestibular information can play inhigher-order cognitive processes in healthy participants.

Experiment 1

The purpose of Experiment 1 was to examine whether thedirection of passive whole-body motion could influence the mag-nitude of self-generated numbers. Participants were positioned ona motion platform and were asked to generate numbers at randomwhile the platform was moving leftward, rightward, downward,upward, forward, and backward and when the platform was sta-tionary. We expected an increase in the generation of smallernumbers during leftward as compared to rightward passive whole-body motion (Hypothesis 1), during downward as compared toupward whole-body motion (Hypothesis 2), and during backwardas compared with forward whole-body motion (Hypothesis 3).

Method

Participants. Twenty-four undergraduate students partici-pated in Experiment1 (21 female, 3 male, all right-handed). Themean age was 22.8, ranging from 19 to 35. They received coursecredit for their participation. The study was approved by the EthicsCommittee of the University of Bern, and participants gave in-formed consent.

Apparatus and motion stimuli. All motion stimuli used inthis study were translational motion stimuli (linear displacements).Translational motion stimuli were generated by means of a six-degrees-of–freedom, electric-motion platform (6DOF2000E,MOOG Inc., East Aurora, NY). We used single-cycle, sinusoidal

acceleration-motion profiles (Grabherr, Nicoucar, Mast, & Mer-feld, 2008) mimicking the characteristics of natural volitional headmovements. Each motion stimulus displaced the participant by0.3 m with a peak velocity of 0.3 m/s. This peak velocity is 10times above the highest individual threshold that we found in apretest with 13 participants (see also Benson, Spencer, & Stott,1986, for translational motion thresholds). The duration of eachmotion was 2000 ms. These specifications were the same for allthree motion conditions. Two separate computers with custom-made software were used for the control of the motion platformand the recording of participants’ responses (sampling rate of 1000Hz). We used Predictive Analytics SoftWare (PASW) Statistics 18(SPSS Inc., Chicago, IL) and Statistica 6 (StatSoft Inc., Tulsa, OK)for further data analysis.

Design and procedure. Participants were seated in a chairthat was mounted on the motion platform (see Figure 1). Seat beltswere fastened around participants’ shoulders, torso and hips. Theirheads were restrained with fixation straps. Participants were in-structed to name a number between one and 30 as randomly aspossible every two seconds (indicated by a beep). The experimentconsisted of four blocks: no motion (1), leftward and rightwardmotion (2), upward and downward motion (3), and forward andbackward motion (4). In Blocks 2–4, the two contrary motion

Figure 1. Picture of the six-degrees-of-freedom motion platform(6DOF2000E, MOOG Inc., East Aurora, NY). A blindfolded participant issecurely seated on the chair with the head fixed.

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stimuli alternated continuously (this is in analogy to the paradigmused by Loetscher et al., 2008). The order of the blocks and thestarting position (left vs. right, up vs. down, front vs. back) wascounterbalanced across participants. Forty responses were col-lected for each direction of passive whole-body motion and werewritten down by the experimenter during the task. To minimize theinfluence of distracting visual or auditory cues, participants wereblindfolded and exposed to white noise presented via in-ear head-phones. After the experiment, participants were asked whetherthey had a spatial representation of numbers during the task, andabout their strategy to generate random numbers. If they alsoparticipated in Experiment 2, these questions were asked afterExperiment 2.

Results and Discussion

The dependent variable was the mean magnitude of generatednumbers during each direction of whole-body motion. We com-puted a repeated-measures analysis of variance (ANOVA) with thefactor-motion direction (leftward, rightward, upward, downward,forward, backward, no motion), and three planned contrasts on themean magnitude of generated numbers (Hypothesis 1, leftward vs.rightward; Hypothesis 2, upward vs. downward; and Hypothesis 3,forward vs. backward). The main effect of motion direction washighly significant, F(6, 138) � 5.26, MSE � 1.08, p � .001, �p

2 �.186. Contrast analyses revealed significant differences betweenleftward and rightward motion, F(1, 23) � 13.09, MSE � 1.52,p � .001, �p

2 � .363, between downward and upward motion, F(1,23) � 6.08, MSE � 1.68, p � .022, �p

2 � .209, but not betweenforward and backward motion, F(1, 23) � 1.40, MSE � 1.12, p �.249, �p

2 � .057. As hypothesized, smaller numbers were generatedduring leftward as compared to rightward motion (M � 13.82,SD � 1.44 vs. M � 15.11, SD � 1.28), and during downward ascompared to upward motion (M � 13.79, SD � 1.19 vs. M �14.72, SD � 1.47, see Figure 2).

Figure 2 shows that all mean magnitudes of generated numberswere smaller than expected by chance (mean between 1 and 30 �15.5). This bias for small numbers is a general finding in randomnumber generation tasks (Banks & Hill, 1974; Dehaene, 1997).Two explanations for this bias have been established. First, peopleare more often confronted with small numbers than they are withlarge numbers in everyday life. Small numbers are therefore over-represented and come more often to mind during number genera-tion. Second, the small number bias has been interpreted as aconsequence of “pseudoneglect”, a phenomenon describing thepreference for the left over the right side of representational space(see Loetscher & Brugger, 2007, for a discussion of the smallnumber bias).

Subjective reports collected after the experiment revealed thatseven out of 24 participants relied on left-to-right oriented spatialrepresentation of numbers during the task. Four participants alsoreported a vertical mental representation of numbers, three of thema down-small and up-large orientation, and one a down-large andup-small orientation. None of the participants reported a spatialrepresentation of numbers from forward to backward. Moreover,all participants reported that they were focused on the task and didnot attend to the direction of whole-body motion. To test whetherthe influence of motion direction on number generation wascaused by those participants who have an explicit spatial repre-

sentation of numbers, we repeated the analysis without thoseparticipants. We still found a significantly lower mean magnitudeof numbers generated during leftward motion as compared torightward motion, and during downward as compared to upwardmotion.1

In accordance with Hypothesis 1 and Hypothesis 2, smallernumbers were generated during leftward as compared with right-ward passive whole-body motion, and during downward as com-pared with upward passive whole-body motion. This findingsuggests that the horizontal and vertical direction of passivewhole-body motion shifts attention along the mental number line,and therefore influenced the magnitude of self-generated numbers.Thus, sensory signals provoked by passive whole-body motion aresufficient to influence performance in a complex numerical task.However, number magnitudes were self-generated by the partici-pant, and therefore, the results from Experiment 1 leave open thequestion as to whether whole-body motion can influence numeri-cal comprehension. In Experiment 2 we aimed to establish whetherthe direction of passive whole-body motion can influence theprocessing of numbers when they are presented auditorily.

Experiment 2

Participants were positioned on the motion platform and wereasked to decide as fast as possible whether an auditorily presentednumber was smaller or larger than five during passive whole-bodymotion. We expected that small numbers would be evaluated fasterthan large numbers during leftward motion, and likewise, largenumbers would be evaluated faster than small numbers duringrightward motion.

Method

Participants. Twenty-four undergraduate students partici-pated in this study (four male, 20 female, all right-handed). Themean age was 22.9, ranging from 20 to 35. They received coursecredit for their participation.

Design and procedure. The main procedure and the motionstimuli were the same as those used in Experiment 1. Participantswere instructed to decide as fast as possible whether a number wassmaller or larger than five. Numbers (“two,” “three,” “four,” “six,”“seven,” and “eight”) were presented during either a leftward orrightward motion that lasted for 2000 ms. Numbers were auditorilypresented via headphones at peak velocity of the motion (1000 msafter motion onset). Responses were collected by means of tworesponse buttons that participants held in their left and right hands.Reaction time (RT) was measured from the onset of each numberstimulus. All number stimuli had the same duration of 500 ms. Thenext trial was triggered by the experimenter as soon as the re-sponse was given and the previous motion had stopped. A variableintertrial interval (1000–3000 ms) preceded the onset of the nextmotion stimulus. Leftward and rightward motion stimuli alter-nated. Numbers were presented in random order; the only limita-tion was that the same number not be presented more than twice

1 Mleftward � 13.91, SD � 1.56, Mrightward � 14.95, SD � 1.25; F(1,16) � 4.97, MSE � 1.85, p � .040, �p

2 � .237. Mdownward � 13.89, SD �1.20, Mupward � 14.75, SD � 1.50; F(1, 20) � 4.74, MSE � 1.62, p �.042, �p

2 � .191.

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consecutively. Each number was presented 10 times during left-ward and 10 times during rightward passive whole-body motion,resulting in 120 trials per session. Each participant performed twosessions. In one session, “smaller than five” had to be indicatedwith the left hand, and “larger than five” with the right hand. In theother session, the response mapping was reversed. The order ofresponse mapping was counterbalanced across participants.

Results and Discussion

The mean error rate (ER) over all conditions was very low(1.3%). Therefore, only RTs were further analyzed. Inaccuratetrials were excluded from the analysis of RTs. The remaining RTswere log transformed to normalize their distribution (Ratcliff,1993). Values more than 2.5 SDs below or above the meanindividual latency were excluded from the analysis (1.7%). To testwhether the overall RT for numbers smaller and larger than fivewas influenced by the direction of whole-body motion, we com-puted a repeated-measures ANOVA with eachvariable’s numbermagnitude (smaller than five vs. larger than five), motion direction(leftward vs. rightward), and response mapping (small indicated bythe left hand vs. small indicated by the right hand). Most importantto note was that number magnitude and motion direction inter-acted, F(1, 23) � 8.15, MSE � 0.001, p � .009, �p

2 � .262 (seeFigure 3). Mean RTs for small numbers were shorter duringleftward than they were during rightward whole-body motion (p �.01, Bonferroni post hoc test)2. There was also a significant maineffect of motion direction, F(1, 23) � 5.95, MSE � 0.001, p �.023, �p

2 � .205. RTs were generally shorter during leftwardwhole-body motion (M � 605, SD � 117) than they were duringrightward whole-body motion (M � 612, SD � 117). This findingwas unexpected and requires further investigation. Moreover, theresponse mapping significantly affected RTs, F(1, 23) � 6.09,MSE � 0.003, p � .021, �p

2 � .209. Consistent with previousfindings (e.g., Dehaene et al., 1993), RTs were shorter when“smaller than five” responses had to be indicated with the left hand

and when “larger than five” responses had to be indicated with theright hand, as compared to the reverse response mapping (M �597, SD � 122 vs. M � 620, SD � 112). However, there was nothree-way interaction between number magnitude, motion direc-tion, and response mapping, F(1, 23) � 1.36, MSE � � 0.000, p �.255, �p

2 � .056. This suggests that the effect of the direction ofwhole-body motion on the processing of small numbers was in-dependent of the hand with which the participant responded. Allother effects or interactions were not significant (all p’s � .15).

To analyze the effect of the direction of whole-body motion onRTs in more detail, we computed the individual mean RT for eachmotion direction and number. The means are illustrated in Figure4a. The curves show that RT was higher for the “inner” numbers“four” and “six”, as compared with the “outer” numbers. Thispattern of RTs can be explained by the “numerical-distance effect”which states that numbers represented close to a critical referencenumber are more difficult to discriminate than are numbers with alarger numerical distance (Dehaene, Dupoux, & Mehler, 1990;Gevers, Verguts, Reynvoet, Caessens, & Fias, 2006; Moyer &Landauer, 1967). This finding supports the claim that numbers arenot simply represented as category (left � small, right � large) butrather along a metric spatial dimension (Ishihara et al., 2006). Ofparticular interesting was that the hypothesized interaction be-tween motion direction and numbers seemed to be true only for theinner numbers but not for the outer numbers. To analyze the effectof motion direction for each number, we computed a regressionanalysis on dRT (dRT � RT during rightward motion–RT duringleftward motion; see Fias, 1996; Gevers, Verguts et al., 2006;Lorch & Myers, 1990, for a similar approach). Number-space

2 This analysis was also repeated without those participants who re-ported an explicit representation of a mental number line during theexperiment (n � 10). We still found a significant interaction betweennumber magnitude and motion direction, F(1, 13) � 5.68, MSE � 0.001,p � .033, �p

2 � .304.

Figure 2. Mean magnitude of numbers generated during different directions of whole-body motion. Asterisksindicate significant differences between two oppositional motion directions (� � p � .05, �� � p � .01). Errorbars show 95% within-subjects confidence intervals appropriate for evaluating the effect of motion directionwithin participants (G. R. Loftus & Masson, 1994; Masson & Loftus, 2003).

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compatibility effects are usually indicated by a negative-regressionslope of dRT as a function of numbers (e.g., Dehaene et al., 1993;Gevers, Verguts et al., 2006). However, a linear-regression linedoes not provide a good fit for our data, F(1, 142) � 1.12, p �.292, R2 � 0.8%, slope � �0.09. Instead, dRT can be well-fittedby a cubic function, F(3, 140) � 9.89, p � .001, R2 � 17.5% (seeFigure 4b). The cubic function shows the expected negative slopewithin the inner numbers (from “three” and “four” to “six” and“seven”) and takes into account that differences between leftwardand rightward motion are near zero for the outer numbers. Ourresults suggest that the processing of numbers is influenced by thedirection of whole-body motion only when the numerical judg-ment involves a certain level of difficulty, in this case a closespatial proximity between reference and test stimulus.

In Experiment 1, the random number generation task involvedexecutive functions such as cognitive flexibility and suppression ofhabitual responses, for example counting in an ascending order(Daniels, Witt, Wolff, Jansen, & Deuschl, 2003; Jahanshahi, Dirn-berger, Fuller, & Frith, 2000). In contrast, the numerical judgmenttask in Experiment 2 involved no free choice because the correctanswer was determined by the number stimulus. To correctlycategorize the number, the auditory input had to be converted intoa semantic representation and compared with a reference number.The results of Experiment 2 show that the influence of whole-bodymotion is not limited to the generation of numbers. The directionof whole-body motion influenced numerical comprehension,which is a more basic stage of numerical cognition. The results ofExperiment 1 and 2 have in common a general association betweenleftward body motion and “small,” and between rightward bodymotion and “large.”

Next, we wanted to investigate whether the association betweenbody motion and numbers is bidirectional. Indeed, previous re-

search found that the processing of small numbers leads to anautomatic shift of attention to the left side, and that of largenumbers to the right side. Perceiving numbers has been shown toinfluence attention in the visual field (Fischer et al., 2003) and ina bisection task involving active arm movements (Calabria &Rossetti, 2005; Fischer, 2001). Given the interactions betweennumber magnitude and the direction of passive whole-body motionfound in Experiment 1 and 2, it is by all means conceivable thatthere is also an effect in the reverse direction: Does the magnitudeof a perceived number influence the processing of passive self-motion information? This hypothesis was tested in Experiment 3.

Experiment 3

Participants were positioned on the motion platform and askedto decide as fast as possible whether they were moved leftward orrightward. In each trial, either a small (“one,” “two”) or a large(“eight,” “nine”) number was presented. We expected that themagnitude of the presented number would influence performance,either by biasing participants’ choice (more leftward responsesafter hearing a small number) or by influencing the time needed fora correct decision (faster detection of leftward motion after hearinga small number), or both.

Method

Participants. Thirty-six undergraduate students participatedin this study (eight male, all right-handed). The mean age was22.5, ranging from 20 to 28. They received course credit for theirparticipation. None of them had participated in Experiment 1 or 2.

Design and procedure. The main procedure was the same asin Experiments 1 and 2. In contrast to Experiments 1 and 2, themotion stimuli used in Experiment 3 differed in two aspects. First,we assumed that the numbers would influence the interpretation ofself-motion especially at the beginning of the motion (before thepeak velocity is reached). We therefore prolonged the phase priorto peak velocity by increasing the total time of the motion from2000 to 5000 ms. Second, we also lowered the peak velocity of themotion to make motion-direction detection more difficult. To giveconsideration to individual differences in motion-direction-detection sensitivity (Grabherr et al., 2008), peak velocity wasadjusted individually to each participant. For this reason, a sim-plified version of an adaptive threshold detection procedure wasrun prior to the main experiment. The procedure started with asuprathreshold motion (peak velocity � 0.08 m/s). After threecorrect responses, the velocity was lowered by 0.01 m/s. Thevelocity at which the participants made the first error was definedas low. Medium velocity was defined as low velocity plus 0.01m/s, and high velocity as low velocity plus 0.02 m/s. For the mainexperiment, motion intensity varied across these three individualvalues. Participants were instructed to decide as fast as possiblewhether they were moved leftward or rightward. When the motionhad stopped, a beep was presented for 500 ms. In order to reducethe variance in RTs, participants were encouraged to respondduring the acceleration phase (0–2500 ms) and at the latest whenthey heard the beep. Responses were collected by means of tworesponse buttons that participants held in their left and right hands.Numbers were auditorily presented via headphones. To investigatewhether an effect of numbers on motion-direction detection would

Figure 3. Mean reaction time (RT) for small and large numbers duringleftward and rightward whole-body motion. Asterisk marks a significantdifference between leftward and rightward motion (p � .01). Error barsshow 95% within-subjects confidence intervals appropriate for evaluatingthe effect of motion direction within participants (G. R. Loftus & Masson,1994; Masson & Loftus, 2003).

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be limited to a specific range of number-motion delay (see Fischeret al., 2003, e.g.), we chose three different number onsets: 500 msbefore motion onset, at motion onset, and 500 ms after motiononset. Leftward and rightward motions were randomly presented(within the displacement limitation of the MOOG device). Theduration of each number stimulus was 500 ms. Numbers werepresented in random order; the only limitation was that the samenumber not be presented more than twice consecutively. Small andlarge numbers were presented 36 times during leftward and 36times during rightward passive whole-body motion, resulting in144 trials. The different velocity levels and number onsets wereequally distributed across the 36 trials. After each motion, a rest of5000 ms was provided. A short break was given after completionof the first half of the trials. To control for possible response biasesinduced by the number, we again used two different responsemappings (leftward motion indicated by the left hand vs. leftwardmotion indicated by the right hand). The response mapping wascounterbalanced between participants.

Results and Discussion

Error rate. If the magnitude of the perceived number influ-enced the judgment of self-motion direction, ERs would be higherwhen small numbers are presented during rightward motion, andlikewise when large numbers are presented during leftward mo-tions. We would therefore expect an interaction between numbermagnitude and motion direction. To test this hypothesis, we cal-culated a repeated-measures ANOVA on the ERs with numbermagnitude (small, large), motion direction (leftward, rightward),strength of motion (low, medium, high), and number onset (500 msbefore motion onset, at motion onset, 500 ms after motion onset)as within-variables, and response mapping (leftward motion indi-cated by the left hand vs. leftward motion indicated by the right

hand) as a between-variable. The analysis of ERs revealed nosignificant interaction (two-way or higher-order) between numbermagnitude and motion direction (for all p � .148, �p

2 � .055). Thisshows that the magnitude of the perceived number did not influ-ence the leftward/rightward decision. There was only a main effectof strength of motion, F(2, 68) � 17.20, MSE � 11.28, p � .001,�p

2 � .336. Bonferroni post hoc tests show that the mean ER for thefast motion (M � 13.48%, SD � 2.18%) was significantly lowerthan for the medium motion (M � 17.48%, SD � 2.18%) or theslow motion (M � 20.15%, SD � 2.40%). All other main effectsor interactions were not significant (for all p � .09, �p

2 � .068).Reaction time. RTs were analyzed for correct decisions that

were given before the motion had stopped (�5000 ms). This wastrue for 80.77% of all trials. The latencies were log-transformed tonormalize their distribution. We hypothesized that the direction ofpassive whole-body motion would be detected faster when thenumber magnitude is congruent with the side of motion. To testthis hypothesis, we computed the same analysis for log RTs as wedid for the ERs and expected an interaction between numbermagnitude and motion direction. The analysis of RTs showed notwo-way interaction between number magnitude and motion di-rection, F(1, 34) � 3.81, MSE � 0.007, p � .059, �p

2 � .101.However, there was a highly significant three-way interactionbetween number magnitude, motion direction and strength ofmotion, F(2, 68) � 7.34, MSE � 0.006, p � .001, �p

2 � .178. Thissuggests that the number magnitude influenced RT for correctleftward or rightward decisions, depending on the strength ofmotion. We analyze this three-way interaction in more detailbelow. The overall-analysis of RT also revealed a main effect ofstrength of motion, F(2, 68) � 14.364, MSE � 0.004, p � .001,�p

2 � .297, and a main effect of number onset, F(2, 68) � 16.287,MSE � 0.008, p � .001, �p

2 � .324. Bonferroni post hoc tests

Figure 4. Left panel (a) shows mean reaction time (RT) for each number during leftward and rightwardwhole-body motion. Error bars show 95% within-subjects confidence intervals appropriate for evaluating theeffect of motion direction within participants (G. R. Loftus & Masson, 1994; Masson & Loftus, 2003). Rightpanel (b) shows individual differences between the reaction times (dRT) during rightward and leftward motion(rightward RT – leftward RT) for each number. The dotted line shows a model fit by means of a cubic function(R2 � 17.5%, p � .001).

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show significant differences between all three strengths of motion.Mean RT for the fast motion was 2020 ms (SD � 668 ms), for themedium motion, 2107 ms (SD � 693 ms), and for the slow motion,2174 ms (SD � 722 ms). RTs were also significantly higher whenthe number was presented 500 ms after motion onset (M � 2176ms, SD � 701), as compared with concurrent onset (M � 2093 ms,SD � 706), and 500 ms before motion onset (M � 2037 ms, SD �677 ms). These two variables also interacted, F(4, 136) � 4.73,MSE � 0.014, p � .001, �p

2 � .122. A Bonferroni post hoc testshowed that the different number onsets only influenced RT whenthe motion was strong or medium, but not when the motion wasslow. No other main effects or interactions turned out to besignificant (for all p � .103). Noteworthy is the congruent re-sponse mapping (leftward motion indicated with the left hand andrightward motion with the right hand) did not lead to fasterresponses as compared with the incongruent response mapping,F(1, 34) � 1.50, MSE � 1.326, p � .229, �p

2 � .042. This supportsthe assumption that spatial compatibility effects are only presentfor RTs faster than 500 ms (Umilta & Nicoletti, 1990).

To further analyze the three-way interaction between numbermagnitudes, direction of motion, and strength of motion, we com-puted three separate repeated-measures ANOVAs for eachstrength of motion. The interaction between number magnitudeand motion direction was only significant for the slowest motion,F(1, 35) � 16.85, MSE � 0.006, p � .001, �p

2 � .325, but not forthe medium motion, F(1, 35) � 2.40, MSE � 0.005, p � .131,�p

2 � .064, nor for the fast motion, F(1, 35) � 0.52, MSE � 0.009,p � .4753, �p

2 � .015. Bonferroni post hoc tests showed that RTto correctly detect a slow leftward motion was significantly shorterwhen participants perceived a small number as compared with alarge number, and likewise, the RT was significantly shorter todetect a slow rightward motion when they perceived a largenumber as compared with a small number (see Figure 5). Toensure that this interaction was not mediated by a motor-response

bias, we computed an additional ANOVA for the slowest motionwith each variable’s number magnitude and motion direction aswithin-, and response mapping as between-variables. The three-way interaction was not significant, F(1, 34) � 0.37, MSE �0.006, p � .546, �p

2 � .011. This shows that the effect of numbermagnitude on the processing of self-motion perception was inde-pendent of the hand with which the participant responded. There-fore, the results cannot be explained by a motor-response bias (i.e.,faster response with the left hand when hearing a small number orwith the right hand when hearing a large number). Processingnumbers of different magnitudes influenced the time needed tocorrectly judge the direction of slow self-motion; small numbersfacilitated the detection of a leftward motion and large numbers thedetection of a rightward motion.

General Discussion

The present study investigated the mutual influence betweenpassive whole-body motion and numerical processing. Essentially,we found that leftward whole-body motion facilitated the genera-tion and processing of small numbers while rightward motionfacilitated the generation and processing of large numbers. More-over, we found an effect in the reverse direction; the magnitude ofa number can influence the detection of self-motion direction.

In Experiment 1, we investigated whether passive whole-bodymotion along the transversal, frontal, and sagittal body planeswould influence the generation of random numbers in a similarway that was found for active head turns to the left and right side(Loetscher et al., 2008). We found that smaller numbers weregenerated during leftward as compared to rightward motion. Theseresults suggest that the direction of passive whole-body motionshifts attention along the mental number line. Our results implythat the effects reported by Loetscher et al. (2008) do not dependon the intention to move or on overt motor behavior. We show that

Figure 5. Mean reaction time (RT) for correct leftward- and rightward-motion direction detection for eachstrength of motion and number magnitude. Asterisks indicate a significant difference between the log RTs forsmall and large numbers for low-leftward and low-rightward motions (p � .05). Error bars show 95%within-subjects confidence intervals appropriate for evaluating the effect of number magnitudes within partic-ipants (G. R. Loftus & Masson, 1994; Masson & Loftus, 2003).

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bottom-up sensory signals evoked during passive whole-body mo-tions are sufficient to influence attention allocation in higher-orderspatial representations. Given that no visual or auditory cues wereprovided, we attribute these effects mainly to vestibular signals.Specifically, the results of Experiment 1 suggest that the process-ing of vestibular information from the otolith organs can influenceabstract thoughts that are not explicitly spatial, such as the mag-nitude of randomly generated numbers.

In addition to the small-leftward and large-rightward associa-tion, we found a small-downward and large-upward association.This finding supports Loetscher et al.’s assumption (2010) that theleft-to-right oriented mental number line might be an oversimpli-fication, and that a bottom-to-top orientation also exists. However,compared to the effect of horizontal whole-body motion on themagnitude of generated numbers, the effect of vertical whole-bodymotion was less strong. It is possible that vertical-magnitudeassociations are ambiguous. Up is generally associated with highermagnitudes, but this is not always the case. Numbers on a list, forexample in an Excel sheet, have an up-down orientation where“one” is on top and higher numbers follow. Likewise, the winnerof a competition stands highest on the podium and appears first ona top 10 list. Due to these ambiguous associations, it is possiblethat vertical passive whole-body motion had a less systematicinfluence on the magnitude of generated numbers. This lack of asystematic influence of motion direction on number magnitudemay also explain the absence of any effect for the forward-largeand backward-small associations.

In Experiment 2, we showed that the influence of whole-bodymotion is not limited to self-generation of numbers. In a speededforced-choice task, participants responded faster to small numberswhile moving leftward and faster to large numbers when movingrightward. This finding shows that the whole-body motion caninfluence the processing of externally presented numbers. Theresults of Experiment 2 are particularly interesting because thenumbers were, unlike the stimuli used by Figliozzi et al. (2005),not physically presented on the left or right side of the body.Numbers were synchronously presented to the left and right ear.Thus, vestibular information not only influences the processing ofstimuli that are presented in different locations in the physicalenvironment (Figliozzi et al., 2005), but also influences the pro-cessing of stimuli that have an implicit spatial association, such asnumbers.

Interactions between vestibular information and abstract repre-sentations such as numbers have, to our knowledge, not yet beenestablished in healthy participants. In patients suffering from ne-glect, vestibular stimulation has been shown to ameliorate neglectsymptoms in representational space (Geminiani & Bottini, 1992;Rode & Perenin, 1994). However, these results were interpreted asa result of a modulation in the endogenous representation ofegocentric space rather than the result of a shift in spatial attention(Geminiani & Bottini, 1992). Here, we argue that vestibular in-formation is an important source for the spatial allocation ofattentional resources in healthy participants and has the potential toinfluence higher-order cognition.

In Experiment 3, we investigated whether the number-spaceassociation also has a reverse effect. We were able to demonstratethat the processing of numbers can influence the detection ofwhole-body motion. Hearing a number whose position on themental number line was congruent with the direction of self-

motion facilitated the correct detection of motion direction. Theseresults are in line with the idea that perceiving numbers automat-ically shifts attention within the mental number space, which inturn produces a corresponding shift of attention in the externalworld (Fischer et al., 2003; Hubbard et al., 2005). This hypothesishas, to our knowledge, only been tested for the visual space. Herewe show that the effect of an attentional shift induced by theprocessing of numbers transfers to the processing of vestibularinformation. Previous research has shown that self-motion percep-tion can be biased by means of auditory-motion information (Val-jamae, 2009). The results from this study demonstrate that self-motion perception can also be influenced by abstract cues likenumbers that are (implicitly) associated with the left or rightdirection.

The effect of number magnitude on self-motion perception hadsome limitations. First, numbers did not influence RTs for motionstimuli that were clearly above the perceptual threshold. Numbersinfluenced motion detection when the motion was slow and itsdirection more difficult to detect. As in Experiment 2, the number-motion interaction only influenced performance when there was acertain level of difficulty in the task. Second, the shift in spatialattention toward the left or right side caused by the number did notreverse the perceived direction of self-motion. The accuracy ofparticipants’ judgments about the direction of passive whole-bodymotion was not influenced by the magnitude of the presentednumber. Motion-direction detection was influenced regardless ofwhether the number was presented before, at the same time, orafter the motion onset. In other studies, an effect of a directionalcue on a left- or right-sided target was found for specific delaysonly (e.g., Fischer et al., 2003). However, the use of differentparadigms can possibly account for this difference. Fischer et al.(2003) used a simple detection task where participants had to pressa button as soon as they saw the target. In our study, participantswere asked to indicate the direction of motion rather than the onset,increasing the variance in RTs. This could be a reason that, in thisstudy, the motion onset had no systematic influence on the inter-action between number magnitude and motion direction.

In our view, there are two possible mechanisms that underlie thenumber-motion interactions we found in this study. First, vestib-ular and numerical information converge at a certain stage ofneuronal processing. Neuroimaging studies highlight a coactiva-tion of areas in the parietal cortex, namely the intraparietal sulcus,during numerical and spatial processing (see Hubbard et al., 2005,for a review). Furthermore, activation of the intraparietal sulcushas been found during vestibular stimulation in humans (Lobel,Kleine, Bihan, Leroy-Willig, & Berthoz, 1998; Suzuki et al., 2001)and in monkeys (Bremmer, Klam, Duhamel, Ben Hamed, & Graf,2002). These findings suggest that common mechanisms can beinvolved in the processing of spatial, numerical, and vestibularinformation. Our results provide the first behavioral evidence of apossible link between these three processes. An alternative ap-proach to interpret our findings would be that vestibular informa-tion does not directly interact with numerical information. Rather,vestibular information activates a concept of “leftward” or “right-ward”. It would then be the activation of this concept that influ-ences the processing of numbers in a top-down manner. These twomechanisms are not mutually exclusive, and both might havecontributed to our results. However, in Experiment 1 and 2, par-ticipants reported that they were focused on the task and did not

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attend to the motion direction. They were not consciously aware inwhich direction they moved. This suggests that the latter mecha-nism would act in an implicit way and our results would stillhighlight the role of vestibular information in directing spatialattention. Moreover, when numerical processing is influenced bythe activation of the concepts “leftward” or “rightward,” thenvisual-motion cues would influence the processing of numbers.Salillas et al. (2009) presented moving dots (optokinetic stimula-tion) on a screen and asked participants to respond as fast aspossible to numbers that were either smaller or larger than five.They indeed found that neglect patients responded faster to smallnumbers during leftward motion. However, they did not find aninteraction between motion direction and number magnitude forthe control group. In their study, visual-motion information alonewas not sufficient to induce shifts in spatial attention in healthyparticipants.

The question concerning the stage in cognitive processing atwhich number-motion interactions can occur has been addressed inthe context of the SNARC effect. Some studies support an inter-action at an early level of processing, such as feature processingand stimulus identification (Fischer et al., 2003; Mapelli, Rusconi,& Umilta, 2003). Other studies have convincingly demonstrated aninteraction at a higher level of processing, namely at the response-related level (Gevers, Caessens, & Fias, 2005; Gevers, Verguts etal., 2006; Keus, Jenks, & Schwarz, 2005; Keus & Schwarz, 2005).For example, Keus et al., (2005) showed in an EEG study thatlateralized readiness potentials (LRP) for SNARC-incompatibletrials (e.g., smaller than five right) differed from SNARC-compatible trials within the time window of 248 to 331 ms afterstimulus onset. LRP indicates the preparation of a motor response,and the activity is therefore reflecting the response-preparationstage. Given the fact that number-motion interactions have shownsimilar properties as spatial-numerical interactions in general (e.g.,bidirectionality), it is possible that number-motion interactionsalso occur at a response-selection stage. However, this is notnecessarily the case. First, Figliozzi et al. (2005) showed thatvestibular information can modulate the processing of visual andsomatosensory information in the early stage of tactile perception.Second, in this study (Experiments 2 and 3), the interaction be-tween motion direction and number magnitude was independent ofthe response mapping. This supports the idea of Wood and Fischer(2008) in that the association between number and space is notlimited to the response-selection stage and not necessarily boundto action-related processes.

In the present study, we regarded vestibular information as themain source of information during passive whole-body motion(Merfeld, Priesol, Lee, & Lewis, 2010; Soyka, Robuffo Giordano,Beykirch, & Bulthoff, 2011; Walsh, 1961). However, we cannotrule out completely that the stimuli we applied evoked proprio-ceptive and visceroceptive cues that could possibly contribute, tosome extent, to the number-motion interaction. Future researchcould investigate the contribution of extravestibular information indirecting spatial attention, for example by testing patients withcomplete vestibular loss.

Conclusions

This study showed for the first time that the direction of passivewhole-body motion influences numerical cognition, and con-

versely, that numerical processing can influence self-motion per-ception. The findings highlight that bottom-up sensory signalsevoked during passive body motion are sufficient to interact witha higher-order cognitive representation in healthy participants. Ourresults emphasize the important role vestibular information canplay in the allocation of spatial attention. In light of these findings,vestibular contributions to spatial attention deserve a more prom-inent role in cognitive research, especially due to the fact thatinteracting with the environment most often involves body motion.Moreover, our findings confirm earlier studies showing that spatialrepresentations are involved when thinking of numbers (see Hub-bard et al., 2005, for a review), and point out the role of whole-body motion, which interacts with the spatial representation ofnumbers. This study extends the well-known small-left and large-right association by establishing small-leftward body motion andlarge-rightward body motion (and small-downward body motion,large-upward body motion) associations. We were able to demon-strate behavioral effects of these associations even when partici-pants were unaware of any spatial arrangement of numbers andwere inattentive to the direction of motion (Experiments 1 and 2).This suggests that these associations are automatic and that thedirection of passive whole-body motion is likely to influence, in asubtle way, the magnitude of numbers that come to mind or theprocessing of stimuli that are cognitively represented with spatialcharacteristics.

References

Amorim, M. A., Glasauer, S., Corpinot, K., & Berthoz, A. (1997). Updat-ing an object’s orientation and location during nonvisual navigation: Acomparison between two processing modes. Perception & Psychophys-ics, 59, 404–418. doi:10.3758/BF03211907

Banks, W. P., & Hill, D. K. (1974). Apparent magnitude of number scaledby random production. Journal of Experimental Psychology, 102, 353–376. doi:10.1037/h0035850

Benson, A. J., Spencer, M. B., & Stott, J. R. (1986). Thresholds for thedetection of the direction of whole-body, linear movement in the hori-zontal plane. Aviation, Space, and Environmental Medicine, 57, 1088–1096.

Berthoz, A., Israel, I., Georges-Francois, P., Grasso, R., & Tsuzuku, T.(1995). Spatial memory of body linear displacement: What is beingstored. Science, 269, 95–98. doi:10.1126/science.7604286

Bremmer, F., Klam, F., Duhamel, J. R., Ben Hamed, S., & Graf, W. (2002).Visual–vestibular interactive responses in the macaque ventral intrapa-rietal area (VIP). European Journal of Neuroscience, 16, 1569–1586.doi:10.1046/j.1460-9568.2002.02206.x

Calabria, M., & Rossetti, Y. (2005). Interference between number process-ing and line bisection: A methodology. Neuropsychologia, 43, 779–783.doi:10.1016/j.neuropsychologia.2004.06.027

Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2007). The middle houseor the middle floor: Bisecting horizontal and vertical mental numberlines in neglect. Neuropsychologia, 45, 2989 –3000. doi:10.1016/j.neuropsychologia.2007.05.014

Casarotti, M., Michielin, M., Zorzi, M., & Umilta, C. (2007). Temporalorder judgment reveals how number magnitude affects visuospatialattention. Cognition, 102, 101–117. doi:10.1016/j.cognition.2006.09.001

Daniels, C., Witt, K., Wolff, S., Jansen, O., & Deuschl, G. (2003). Ratedependency of the human cortical network subserving executive func-tions during generation of random number series—a functional magneticresonance imaging study. Neuroscience Letters, 345, 25–28. doi:10.1016/S0304-3940(03)00496-8

10 HARTMANN, GRABHERR, AND MAST

tapraid5/zfn-xhp/zfn-xhp/zfn00112/zfn2749d12z xppws S�1 12/7/11 3:41 Art: 2011-0371

Dehaene, S. (1997). The number sense: How the mind creates mathemat-ics. Oxford, England, United Kingdom: Oxford University Press.

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation ofparity and number magnitude. Journal of Experimental Psychology:General, 122, 371–396. doi:10.1037/0096-3445.122.3.371

Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparisondigital? Analogical and symbolic effects in two-digit number compari-son. Journal of Experimental Psychology: Human Perception and Per-formance, 16, 626–641. doi:10.1037/0096-1523.16.3.626

Dichgans, J., Held, R., Young, L. R., & Brandt, T. (1972). Moving visualscenes influence the apparent direction of gravity. Science, 178, 1217–1219. doi:10.1126/science.178.4066.1217

Fias, W. (1996). The importance of magnitude information in numericalprocessing: evidence from the SNARC effect. Mathematical Cognition,2, 95–110. doi:10.1080/135467996387552

Figliozzi, F., Guariglia, P., Silvetti, M., Siegler, I., & Doricchi, F. (2005).Effects of vestibular rotatory accelerations on covert attentional orient-ing in vision and touch. Journal of Cognitive Neuroscience, 17, 1638–1651. doi:10.1162/089892905774597272

Fischer, M. H. (2001). Number processing induces spatial performancebiases. Neurology, 57, 822–826.

Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceivingnumbers causes spatial shifts of attention. Nature Neuroscience, 6,555–556. doi:10.1038/nn1066

Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor biasinduced by number perception. Experimental Psychology, 51, 91–97.doi:10.1027/1618-3169.51.2.91

Geminiani, G., & Bottini, G. (1992). Mental representation and temporaryrecovery from unilateral neglect after vestibular stimulation. Journal ofNeurology, Neurosurgery & Psychiatry, 55, 332–333. doi:10.1136/jnnp.55.4.332-a

Gevers, W., Caessens, B., & Fias, W. (2005). Towards a common pro-cessing architecture underlying Simon and SNARC effects. EuropeanJournal of Cognitive Psychology, 17, 659 – 673. doi:10.1080/09541440540000112

Gevers, W., Lammertyn, J., Notebaert, W., Verguts, T., & Fias, W. (2006).Automatic response activation of implicit spatial information: Evidencefrom the SNARC effect. Acta Psychologica, 122, 221–233. doi:10.1016/j.actpsy.2005.11.004

Gevers, W., Verguts, T., Reynvoet, B., Caessens, B., & Fias, W. (2006).Numbers and space: A computational model of the SNARC effect.Journal of Experimental Psychology: Human Perception and Perfor-mance, 32, 32–44. doi:10.1037/0096-1523.32.1.32

Göbel, S. M., Calabria, M., Farne, A., & Rossetti, Y. (2006). Parietal rTMSdistorts the mental number line: Simulating ”spatial” neglect in healthysubjects. Neuropsychologia, 44, 860–868. doi:10.1016/j.neuropsycho-logia.2005.09.007

Grabherr, L., Nicoucar, K., Mast, F. W., & Merfeld, D. M. (2008).Vestibular thresholds for yaw rotation about an earth-vertical axis as afunction of frequency. Experimental Brain Research, 186, 677–681.doi:10.1007/s00221-008-1350-8

Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactionsbetween number and space in parietal cortex. Nature Reviews Neuro-science, 6, 435–448. doi:10.1038/nrn1684

Ishida, M., Fushiki, H., Nishida, H., & Watanabe, Y. (2008). Self-motionperception during conflicting visual-vestibular acceleration. Journal ofVestibular Research: Equilibrium & Orientation, 18:267–272.

Ishihara, M., Jacquin-Courtois, S., Flory, V., Salemme, R., Imanaka, K., &Rossetti, Y. (2006). Interaction between space and number representa-tions during motor preparation in manual aiming. Neuropsychologia, 44,1009–1016. doi:10.1016/j.neuropsychologia.2005.11.008

Ito, Y., & Hatta, T. (2004). Spatial structure of quantitative representationof numbers: Evidence from the SNARC effect. Memory & Cognition,32, 662–673. doi:10.3758/BF03195857

Jahanshahi, M., Dirnberger, G., Fuller, R., & Frith, C. D. (2000). The roleof the dorsolateral prefrontal cortex in random number generation: Astudy with positron emission tomography. Neuroimage, 12, 713–725.doi:10.1006/nimg.2000.0647

Karnath, H. O., & Dieterich, M. (2005). Spatial neglect—a vestibulardisorder? Brain: A Journal of Neurology, 129, 293–305. doi:10.1093/brain/awh698

Keus, I. M., Jenks, K. M., & Schwarz, W. (2005). Psychophysiologicalevidence that the SNARC effect has its functional locus in a response-selection stage. Cognitive Brain Research, 24, 48–56. doi:10.1016/j.cogbrainres.2004.12.005

Keus, I. M., & Schwarz, W. (2005). Searching for the functional locus ofthe SNARC effect: Evidence for a response-related origin. Memory &Cognition, 33 681–695. doi:10.3758/BF03195335

Klatzky, R. L., Loomis, J. M., Beall, A. C., Chance, S. S., & Golledge,R. G. (1998). Spatial updating of self-position and orientation duringreal, imagined, and virtual locomotion. Psychological Science, 9, 293–298. doi:10.1111/1467-9280.00058

Lobel, E., Kleine, J. F., Bihan, D. L., Leroy-Willig, A., & Berthoz, A.(1998). Functional MRI of galvanic vestibular stimulation. Journal ofNeurophysiology, 80, 2699–2709.

Loetscher, T., Bockisch, C. J., Nicholls, M. E., & Brugger, P. (2010). Eyeposition predicts what number you have in mind. Current Biology, 20,R264–265. doi:10.1016/j.cub.2010.01.015

Loetscher, T., & Brugger, P. (2007). Exploring number space by randomdigit generation. Experimental Brain Research, 180, 655–665. doi:10.1007/s00221-007-0889-0

Loetscher, T., Schwarz, U., Schubiger, M., & Brugger, P. (2008). Headturns bias the brain’s internal random generator. Current Biology, 18,R60–R62. doi:10.1016/j.cub.2007.11.015

Loftus, A. M., Nicholls, M. E. R., Mattingley, J. B., & Bradshaw, J. L.(2008). Left to right: Representational biases for numbers and the effectof visuomotor adaptation. Cognition, 107, 1048–1058. doi:10.1016/j.cognition.2007.09.007

Loftus, G. R., & Masson, M. E. J. (1994). Using confidence intervals inwithin-subject designs. Psychonomic Bulletin & Review, 476–490. doi:10.3758/BF03210951

Lorch, R. F., Jr., & Myers, J. L. (1990). Regression analyses of repeatedmeasures data in cognitive research. Journal of Experimental Psychol-ogy: Learning, Memory, and Cognition, 16, 149–157. doi:10.1037/0278-7393.16.1.149

Mapelli, D., Rusconi, E., & Umilta, C. (2003). The SNARC effect: Aninstance of the Simon effect? Cognition, 88, B1–10. doi:10.1016/S0010-0277(03)00042-8

Masson, M. E. J., & Loftus, G. R. (2003). Using confidence intervals forgraphically based data interpretation. Canadian Journal of ExperimentalPsychology/Revue Canadienne de Psychologie Experimentale, 57, 203–220. doi:10.1037/h0087426

McCloskey, M., Caramazza, A., & Basili, A. (1985). Cognitive mecha-nisms in number processing and calculation: Evidence from dyscalculia.Brain and Cognition, 4, 171–196. doi:10.1016/0278-2626(85)90069-7

Merfeld, D. M., Priesol, A., Lee, D., & Lewis, R. F. (2010). Potentialsolutions to several vestibular challenges facing clinicians. Journal ofVestibular Research: Equilibrium & Orientation, 20, 71–77.

Mergner, T., Schweigart, G., Muller, M., Hlavacka, F., & Becker, W.(2000). Visual contributions to human self-motion perception duringhorizontal body rotation. Archives Italiennes de Biologie, 138, 139–166.

Miles, L. K., Karpinska, K., Lumsden, J., & Macrae, C. N. (2010). Themeandering mind: Vection and mental time travel. PLoS One, 5, e10825.doi:10.1371/journal.pone.0010825

Miles, L. K., Nind, L. K., & Macrae, C. N. (2010). Moving through time.Psychological Science, 21, 222–223. doi:10.1177/0956797609359333

Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments ofnumerical inequality. Nature, 215, 1519–1520. doi:10.1038/2151519a0

11WHOLE-BODY MOTION AND NUMERICAL COGNITION

tapraid5/zfn-xhp/zfn-xhp/zfn00112/zfn2749d12z xppws S�1 12/7/11 3:41 Art: 2011-0371

Presson, C. C., & Montello, D. R. (1994). Updating after rotational andtranslational body movements: Coordinate structure of perspectivespace. Perception, 23, 1447–1455. doi:10.1068/p231447

Probst, T., Straube, A., & Bles, W. (1985). Differential effects of ambiv-alent visual-vestibular-somatosensory stimulation on the perception ofself-motion. Behavioural Brain Research, 16, 71–79. doi:10.1016/0166-4328(85)90083-X

Ratcliff, R. (1993). Methods for dealing with reaction-time outliers. Psy-chological Bulletin, 114, 510–532. doi:10.1037/0033-2909.114.3.510

Rode, G., & Perenin, M. T. (1994). Temporary remission of representa-tional hemineglect through vestibular stimulation. Neuroreport: An In-ternational Journal for the Rapid Communication of Research in Neu-roscience, 5, 869–872. doi:10.1097/00001756-199404000-00004

Rorden, C., Karnath, H.-O., & Driver, J. (2001). Do neck-proprioceptiveand caloric-vestibular stimulation influence covert visual attention innormals, as they influence visual neglect? Neuropsychologia, 39, 364–375. doi:10.1016/S0028-3932(00)00126-3

Rossetti, Y., Jacquin-Courtois, S., Rode, G., Ota, H., Michel, C., &Boisson, D. (2004). Does action make the link between number andspace representation?: Visuo-manual adaptation improves number bisec-tion in unilateral Neglect. Psychological Science, 15, 426–430. doi:10.1111/j.0956-7976.2004.00696.x

Sagiv, N., Simner, J., Collins, J., Butterworth, B., & Ward, J. (2006). Whatis the relationship between synaesthesia and visuo-spatial numberforms? Cognition, 101, 114–128. doi:10.1016/j.cognition.2005.09.004

Salillas, E., Grana, A., Juncadella, M., Rico, I., & Semenza, C. (2009).Leftward motion restores number space in neglect. Cortex: A JournalDevoted to the Study of the Nervous System and Behavior, 45, 730–737.doi:10.1016/j.cortex.2008.09.006

Schwarz, W., & Keus, I. M. (2004). Moving the eyes along the mentalnumber line: Comparing SNARC effects with saccadic and manualresponses. Perception & Psychophysics, 66, 651–664. doi:10.3758/BF03194909

Simons, D. J., & Wang, R. F. (1998). Perceiving real-world viewpointchanges. Psychological Science, 9, 315–320. doi:10.1111/1467-9280.00062

Soyka, F., Robuffo Giordano, P., Beykirch, K., & Bulthoff, H. H. (2011).Predicting direction detection thresholds for arbitrary translational ac-celeration profiles in the horizontal plane. Experimental Brain Research,209, 95–107. doi:10.1007/s00221-010-2523-9

Suzuki, M., Kitano, H., Ito, R., Kitanishi, T., Yazawa, Y., Ogawa,

T., . . . Kitajima, K. (2001). Cortical and subcortical vestibular responseto caloric stimulation detected by functional magnetic resonance imag-ing. Cognitive Brain Research, 12, 441– 449. doi:10.1016/S0926-6410(01)00080-5

Umilta, C., & Nicoletti, R. (1990). Spatial stimulus-response compatibility.In R. W. Proctor & T. G. Reeve (Eds.), Stimulus-response compatibility:An integrated perspective (pp. 89–116). Amsterdam, the Netherlands:North-Holland.

Valjamae, A. (2009). Auditorily induced illusory self-motion: A review.Brain Research Reviews, 61, 240 –255. doi:10.1016/j.brainresrev.2009.07.001

Vuilleumier, P., Ortigue, S., & Brugger, P. (2004). The number space andneglect. Cortex: A Journal Devoted to the Study of the Nervous Systemand Behavior, 40, 399–410. doi:10.1016/S0010-9452(08)70134-5

Walsh, E. G. (1961). Role of the vestibular apparatus in the perception ofmotion on a parallel swing. The Journal of Physiology, 155, 506–513.

Wang, R. F., & Spelke, E. S. (2000). Updating egocentric representationsin human navigation. Cognition, 77, 215–250. doi:10.1016/S0010-0277(00)00105-0

Wood, G., & Fischer, M. H. (2008). Numbers, space, and action—fromfinger counting to the mental number line and beyond. Cortex: A JournalDevoted to the Study of the Nervous System and Behavior, 44, 353–358.doi:10.1016/j.cortex.2008.01.002

Zorzi, M., Priftis, K., Meneghello, F., Marenzi, R., & Umilta, C. (2006).The spatial representation of numerical and non-numerical sequences:Evidence from neglect. Neuropsychologia, 44, 1061–1067. doi:10.1016/j.neuropsychologia.2005.10.025

Zorzi, M., Priftis, K., & Umilta, C. (2002). Brain damage: Neglect disruptsthe mental number line. Nature, 417, 138–139. doi:10.1038/417138a

Zupan, L. H., & Merfeld, D. M. (2003). Neural processing of gravito-inertial cues in humans: IV. Influence of visual rotational cues duringroll optokinetic stimuli. Journal of Neurophysiology, 89, 390–400.doi:10.1152/jn.00513.2001

Zupan, L. H., & Merfeld, D. M. (2008). Interaural self-motion linearvelocity thresholds are shifted by roll vection. Experimental BrainResearch, 191(4), 505–511. doi:10.1007/s00221-008-1540-4

Received September 13, 2011Revision received November 7, 2011

Accepted November 14, 2011 �

12 HARTMANN, GRABHERR, AND MAST

AQ: 1

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