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Getting a Grip on Numbers: Numerical Magnitude Priming
in Object Grasping
Oliver Lindemann
Radboud University Nijmegen and University of Groningen
Juan M. Abolafia
Radboud University Nijmegen
Giovanna Girardi
University of Rome “La Sapienza”
Harold Bekkering
Radboud University Nijmegen
To investigate the functional connection between numerical cognition and action planning, the authors
required participants to perform different grasping responses depending on the parity status of Arabic
digits. The results show that precision grip actions were initiated faster in response to small numbers,
whereas power grips were initiated faster in response to large numbers. Moreover, analyses of the
grasping kinematics reveal an enlarged maximum grip aperture in the presence of large numbers.
Reaction time effects remained present when controlling for the number of fingers used while grasping
but disappeared when participants pointed to the object. The data indicate a priming of size-related motor
features by numerals and support the idea that representations of numbers and actions share common
cognitive codes within a generalized magnitude system.
Keywords: numerical cognition, action planning, generalized magnitude system, common representation,
object grasping
In the last few decades, many authors have emphasized that
cognitive representations of perceptual and semantic information
can never be fully understood without considering their impact on
actions (Gallese & Lakoff, 2005). In this context, interactions
between perception and action have been extensively studied (for
review, see, e.g., Hommel, Mu¨sseler, Aschersleben, & Prinz,
2001). More recently, researchers also started to focus on the
interactions between language and action (e.g., Gentilucci, Be-
nuzzi, Bertolani, Daprati, & Gangitano, 2000; Glenberg & Kas-
chak, 2002; Lindemann, Stenneken, van Schie, & Bekkering,
2006; Zwaan & Taylor, 2006). However, a cognitive domain that
has hardly been investigated in respect to its impact on motor
control is the processing of numbers. This is surprising since
information about magnitude plays an important role in both
cognition and action. Accurate knowledge about size or quantity is
required not only for high-level cognitive processes such as num-
ber comprehension and arithmetic (Butterworth, 1999; Dehaene,
1997) but also for the planning of grasping movements (Castiello,
2005; Jeannerod, Arbib, Rizzolatti, & Sakata, 1995). Since mag-
nitude processing in mathematical cognition and magnitude pro-
cessing in motor control have typically been studied independent
of each other, little is known about possible interactions between
these two cognitive domains.
Interestingly, some authors have recently argued that the coding
of magnitude information may reflect a direct link between num-
ber processing and action planning (Go¨bel & Rushworth, 2004;
Rossetti et al., 2004; Walsh, 2003). This idea is so far primarily
based on neuroimaging studies that have found an overlap in
activated brain areas during processes related to numerical judg-
ments and those related to manual motor tasks. In particular, the
intraparietal sulcus has been suggested to be the locus of an
abstract representation of magnitude information (for review, see
Dehaene, Molko, Cohen, & Wilson, 2004). At the same time, it is
widely agreed that this particular brain region, as part of the dorsal
visual pathway, is also concerned with visuomotor transformations
and the encoding of spatial information required for motor actions
(see, e.g., Culham & Valyear, 2006). On the basis of these find-
ings, Walsh (2003) proposed a neuropsychological model of mag-
nitude representation that states that space and quantity informa-
tion are represented by a single generalized magnitude system
located in the parietal cortex. Such a system may provide a
common metric for all sorts of magnitude information, whether
this information relates to numerical quantities in counting or to
physical sizes of objects in the performance of grasping actions. In
other words, the model claims that number cognition and action
planning are linked by a shared abstract representation of magni-
tude, which is strongly connected with the human motor system.
Oliver Lindemann, Nijmegen Institute for Cognition and Information,
Radboud University Nijmegen, Nijmegen, the Netherlands, and Graduate
School of Behavioral and Cognitive Neuroscience, University of Gro-
ningen, Groningen, the Netherlands; Juan M. Abolafia and Harold Bek-
kering, Nijmegen Institute for Cognition and Information, Radboud Uni-
versity Nijmegen; Giovanna Girardi, Department of Psychology,
University of Rome “La Sapienza,” Rome, Italy.
Juan M. Abolafia is now at the Instituto de Neurociencias de Alicante,
Miguel Herna´ndez University–CSIC, Alicante, Spain.
We thank Albert-Georg Lang for his consulting help in the statistical
power analysis.
Correspondence concerning this article should be addressed to Oliver
Lindemann, Nijmegen Institute for Cognition and Information, Radboud
University Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, the Netherlands.
E-mail: o.lindemann@nici.ru.nl
Journal of Experimental Psychology: Copyright 2007 by the American Psychological Association
Human Perception and Performance
2007, Vol. 33, No. 6, 1400 –1409
0096-1523/07/$12.00 DOI: 10.1037/0096-1523.33.6.1400
1400
Indirect behavioral evidence that symbolic magnitude informa-
tion interferes with motor processes has been provided by
language-based studies. For example, Gentilucci et al. (2000)
reported that grasping actions are affected by words representing
size-related semantic information (see also Glover & Dixon, 2002;
Glover, Rosenbaum, Graham, & Dixon, 2004). Gentilucci et al.
required participants to grasp objects on which different word
labels had been attached, and they observed that the word large
leads to a larger maximum grip aperture when reaching out for the
object than does the word small. This finding indicates that the
processing of size-related semantic information interferes with
action planning. However, as demonstrated by behavioral, neuro-
psychological, and animal research, semantic knowledge about
magnitudes constitutes a very domain-specific cognitive ability
that does not require any verbal processing but is based on a
language-independent abstract representation of quantity and size
(e.g., Brannon, 2006; Dehaene, Dehaene-Lambertz, & Cohen,
1998; Gallistel & Gelman, 2000). Consequently, the findings of an
interference effect between semantics and action can hardly be
generalized to the domain of numerical cognition, and it remains
an open question whether number processing interferes with action
planning, as would be predicted by the notion of a generalized
magnitude system.
A characteristic property of nonverbal number representations is
the direct coupling of magnitude information with spatial features
(Fias & Fischer, 2005; Hubbard, Piazza, Pinel, & Dehaene, 2005).
Such an association between numbers and space is nicely demon-
strated by the so-called SNARC effect (i.e., the effect of spatial–
numerical associations of response codes), which was first re-
ported by Dehaene, Bossini, and Giraux (1993). These authors
required their participants to indicate the parity status of Arabic
digits (i.e., odd or even) by left and right keypress responses, and
they observed that responses with the left hand were executed
faster in the presence of relatively small numbers as compared
with large numbers. Responses with the right hand, however, were
faster in the presence of large numbers. The SNARC effect has
been interpreted as evidence that numerical magnitude is spatially
represented, an idea that has often been described with the meta-
phor of a “mental number line” on which numbers are represented
in ascending order from the left side to the right. Although the
origin of spatial numerical associations is still under debate (see
Fischer, 2006; Keus & Schwarz, 2005), there is growing evidence
suggesting that SNARC effects do not emerge at the stage of motor
preparation or motor execution. For example, it is known that
spatial–numerical associations are independent from motor effec-
tors, because they can be observed for different types of lateralized
responses such as pointing movements (Fischer, 2003), eye move-
ments (Fischer, Warlop, Hill, & Fias, 2004; Schwarz & Keus,
2004), and foot responses (Schwarz & Mu¨ller, 2006). Addition-
ally, it has been shown that numbers not only affect the initiation
times of lateralized motor response but can also induce attentional
(Fischer, Castel, Dodd, & Pratt, 2003) and perceptual biases (Ca-
labria & Rossetti, 2005; Fischer, 2001). These findings suggest
that space–number interferences occur during perceptual process-
ing or response selection but not in later, motor-related stages of
processing. Recently, this interpretation received direct support
from electrophysiological experiments on the functional locus of
the SNARC effect (Keus, Jenks, & Schwarz, 2005). Regarding the
idea of a generalized magnitude system, SNARC and SNARC-like
effects can be considered evidence that numbers and space are
coded on a common metric, but it appears to be unlikely that they
reflect an interaction between number processing and motor con-
trol.
However, if numerical cognition and motor control share a
cognitive representation of magnitude, numerical information
should affect the preparation or execution of motor response. In
other words, effects of numerical magnitude should be present not
only in movement latencies but also in the kinematic parameters of
an action. Moreover, the notion of a generalized magnitude system
implies that numerical stimulus–response compatibility effects are
not restricted to associations with spatial locations as indicated by
the SNARC effect and, rather, predicts a direct interaction between
numerical and action-related magnitude coding. Consequently, the
processing of numerical magnitudes should affect the program-
ming of size-related motor aspects—an effect that could be de-
scribed as a within-magnitude priming effect of numbers on ac-
tions (Walsh, 2003). Initial supporting evidence for this hypothesis
has come from the observation of an interaction between number
processing and finger movements recently reported by Andres,
Davare, Pesenti, Olivier, and Seron (2004). In this study, partici-
pants were required to hold the hand in such a way that the
aperture between index finger and thumb was slightly open. Then
participants judged the parity status of a visually presented Arabic
digit and indicated their decision by means of a flexion or exten-
sion of the two fingers (i.e., a closing or opening of the hand).
Electromyographic recordings of the hand muscles indicated that
closing responses were initiated faster in the presence of small
numbers as compared with large numbers, whereas opening re-
sponses were faster in the presence of large numbers. This inter-
action between number size and finger movements constitutes an
interesting example of a numerical priming of size-related action
features. Andres et al. (2004) argued that the performed move-
ments may represent mimicked grasping actions and supposed that
the observed interaction may point to an interference between
number processing and the computation of an appropriate grip
aperture needed for object grasping. However, to date, there has
been little empirical evidence that numerals affect reach-to-grasp
movements. To test this hypothesis directly, we decided to inves-
tigate natural grasping movements that involve, in contrast to
finger movements, a physical object and that comprise a reaching
phase, which is characterized by both an opening and a closing of
the hand (see Castiello, 2005).
Thus, the present study investigated the effects of number pro-
cessing on the planning and execution of prehension movements to
test the hypothesis that numerical cognition and motor control
share a common representation of magnitude. As mentioned
above, previous research has demonstrated that reach-to-grasp
movements are sensitive to abstract semantic information (Genti-
lucci et al., 2000; Glover & Dixon, 2002; Glover et al., 2004).
Considering this and the fact that the planning to grasp an object
depends to a large extent on magnitude processing, since it re-
quires a translation of physical magnitude information (i.e., object
size) into an appropriate grip aperture, grasping responses ap-
peared to us to be promising candidates to study the presumed
functional connection between numbers and actions. To be precise,
we expected that the processing of Arabic numbers could prime
the processing of size-related action features (i.e., a within-
magnitude priming effect; see Walsh, 2003) and, consequently,
1401
GETTING A GRIP ON NUMBERS
affect the initiation times and movement kinematics of reach-to-
grasp movements.
Experiment 1
Experiment 1 investigated whether processing of numerical
magnitude information affects the response latencies and move-
ment kinematics of grasping movements. Participants had to judge
the parity status of visually presented Arabic digits. Decisions had
to be indicated by means of two different reach-to-grasp move-
ments toward a single target object placed in front of the partici-
pants. Specifically, participants were required to grasp the object
with either a precision grip (i.e., grasping the small segment of the
object with the thumb and index finger) or a power grip (i.e.,
grasping the large object segment with the whole hand). If mag-
nitude representations for numerical cognition and action planning
have a common basis, we expected to find a stimulus–response
compatibility effect between number magnitude and the prehen-
sion act. Thus, power grip actions should be initiated faster in
response to relatively large numbers, and precision grip actions
should be initiated faster in response to relatively small numbers.
Since it is known from research on eye– hand coordination that
participants tend to fixate a to-be-grasped object before initiating
the reach-to-grasp movement (Land, 2006), we obscured the right
hand and the object from the view of the participants and trained
them to grasp the object correctly without visual feedback. There
were two major reasons for the use of memory-guided grasping
actions in this paradigm: First, if actions have to be executed
without visual feedback, participants’ visual attention remains
constantly directed toward the parity judgment task until the move-
ment is executed and does not alternate between the to-be-grasped
object and the monitor. The task requirements as well as the
reaction time (RT) measurements are therefore comparable to
those in classical number processing experiments using button-
press responses. Second, online adjustments of memory-guided
actions are more difficult to perform than are adjustments of
visually guided actions (e.g., Schettino, Adamovich, & Poizner,
2003). As a result, participants are less prone to execute the
reaching movements before they have completed their judgment
and selected the required grip. This control is crucial for our
paradigm, because the hypothesized response latency effects can
be only detected if number processing and grip selection are fully
completed before the initiation of the reach-to-grasp movement.
With respect to the measurement of the maximum grip apertures,
it is noteworthy to mention that several studies have shown that
hand kinematics during memory-guided grasping actions do not
differ from those found during visually guided actions (Land,
2006; Santello, Flanders, & Soechting; 2002; Winges, Weber, &
Santello, 2003). It seems, therefore, to be unlikely that the absence
of visual feedback influences the appearance of potential number
magnitude effects in the grip aperture data.
Method
Participants. Fourteen students of Radboud University Nijme-
gen, Nijmegen, the Netherlands, participated in the experiment in
return for €4.50 (U.S.$6) or course credit. All were naive regarding
the purpose of the study, had normal or corrected-to-normal vision,
and were free of any motor problems that would have influenced
their performance on the task.
Setup and stimuli. Participants sat in front of a computer
screen (viewing distance: 70 cm) and were required to grasp a
wooden object consisting of two segments: a larger cylinder (di-
ameter: 6 cm; height: 7 cm) at the bottom and a much smaller
cylinder (diameter: 0.7 cm; height: 1.5 cm) attached on top of it
(see Figure 1). The object was placed at the right side of the table
behind an opaque screen (height: 44 cm; width: 45 cm), allowing
a participant to reach it comfortably with his or her right hand but
without the possibility of visual control (see Figure 1A). At a
distance of 30 cm from the object center, we fixed a small pin
(height: 0.5 cm; diameter: 0.5 cm), which served as a marker for
the starting position of the reach-to-grasp movements.
As stimuli for the parity judgment task we chose the Arabic
digits 1, 2, 5, 8, and 9 printed in a black sans serif font on a light
gray background. They were displayed at the center of the com-
puter screen and subtended a vertical visual angle of approxi-
mately 1.8°.
Procedure. At the beginning of the experiment, participants
were required to practice grasping the object with either the whole
hand at its large segment (i.e., power grip) or with thumb and index
finger at its small segment (i.e., precision grip). Figure 1B illus-
trates the two required responses in the experiment. Only if par-
Figure 1. Basic experimental setup. A: Participants sat at a table with a computer screen and a manipulandum.
An opaque screen obscured the to-be-grasped object and the right hand from view. B: The object consisted of
two segments: a large cylinder at the bottom affording a power grip and a small cylinder at the top affording a
precision grip.
1402
LINDEMANN, ABOLAFIA, GIRARDI, AND BEKKERING
ticipants were able to perform the grasping movements correctly
and fluently without vision was the experimental trial block
started.
The participant’s task was to indicate as soon as possible the
parity status of the presented Arabic digit (i.e., even vs. odd) by
means of the practiced motor responses. That is, depending on the
parity status, the participant was required to reach out and grasp
the object with either a power or a precision grip. However, in the
case of the digit 5, participants were required to refrain from
responding. This no-go condition was introduced to ensure that
reaching movements were not initiated before the number was
processed and the parity judgment was made.
Each trial began with the presentation of a gray fixation cross at
the center of the screen. If the participant placed his or her hand
correctly at the starting position, the cross turned black and dis-
appeared 1,000 ms later. After a delay of random length between
250 ms and 2,000 ms, the digit was presented. Participants judged
its parity status and executed the corresponding grasping move-
ments. The digit disappeared with the onset of the reach-to-grasp
movement or after a maximal presentation time of 1,000 ms. After
an intertrial interval of 2,000 ms, the next trial started. If partici-
pants moved their hands before the digit was shown or if they
responded on a no-go trial, a red stop sign combined with a
4400-Hz beep sound lasting 200 ms was presented as an error
signal.
Design. The mapping between digit parity and required grasp-
ing response was counterbalanced between participants. That is,
half of the participants performed a power grip action in response
to even digits and a precision grip action in response to odd digits.
For the other half, the stimulus–response mapping was reversed.
The digits 1, 2, 8, and 9 were presented 50 times. The experi-
ment thus comprised 100 power grip responses and 100 precision
grip responses, whereas each grip type had to be performed toward
both small and large digits. Additionally, there were 25 no-go trials
(i.e., digit 5). All trials were presented in a randomized sequence.
The experiment lasted about 45 min.
Data acquisition and analysis. An electromagnetic position-
tracking system (miniBIRD 800, Ascension Technology Corpora-
tion, Burlington, VT) was used to record hand movements. Two
sensors were attached on the thumb and index finger of the
participant’s right hand. The sampling rate was 100 Hz (static
spatial resolution: 0.5 mm). The movement kinematics were ana-
lyzed offline. We applied a fourth-order Butterworth lowpass filter
with a cutoff frequency of 10 Hz on the raw position data. The
onset of a movement was defined as the first moment in time when
the tangential velocity of the index finger sensor exceeded the
threshold of 10 cm/s. We used reversed criteria to determine
movement offset. For each participant and each experimental
condition, we computed the mean RT (i.e., the time elapsed
between onset of the digit and the onset of the reaching movement)
and the mean maximum grip aperture (i.e., average of the maxi-
mum Euclidean distances between thumb and index finger during
the time between reach onset and offset).
Anticipation responses (i.e., responses before onset of the go
signal and RTs ⬍ 100 ms), missing responses (i.e., no reactions
and RTs ⬎ 1,500 ms), incorrect motor responses (i.e., all trials on
which participants failed to hit the object or stopped their reaching
and initiated a new reach-to-grasp movement), and incorrect parity
judgments were considered errors and excluded from further sta-
tistical analyses. In all statistical tests, a Type I error rate of ␣⫽
.05 was used. To report standardized effect size measurements, we
calculated the parameter omega squared (
2
), as suggested by Kirk
(1996).
Results
Anticipations and missing responses occurred on 0.3% of trials;
2.7% of the grasping responses were performed incorrectly. The
error rate for the parity judgments was 2.2%.
The mean RT data were submitted to a two-way repeated
measures analysis of variance (ANOVA) with the factors number
magnitude (small magnitude: 1 and 2; large magnitude: 8 and 9)
and type of grip (power grip, precision grip). Figure 2 depicts the
mean RTs. Power grip responses (605 ms) were initiated faster
than precision grip responses (621 ms), F(1, 13) ⫽ 5.17, p ⬍ .05,
ˆ
2
⫽ .13. Most important, however, the analysis yielded a signif-
icant Number Magnitude ⫻ Type of Grip interaction, F(1, 13) ⫽
7.13, p ⬍ .05, ˆ
2
⫽ .10. That is, precision grips were initiated
faster to small numbers (612 ms) than to large numbers (631 ms),
t(13) ⫽⫺2.30, p ⬍ .05. This difference appeared to be reversed
for the power grip responses, for which actions were initiated
faster to large (600 ms) than to small numbers (609 ms). This
contrast, however, failed to become significant, t(13) ⫽ 1.10,
p ⫽ .32.
The mean maximum grip apertures were analyzed with the same
two-way ANOVA as used for the RT data (see Table 1 for means).
The main effect of type of grip was significant,F(1, 13) ⫽ 376.50,
p ⬍ .001, which reflects the trivial fact that maximum grip aper-
ture was larger for the power grip responses (120.0 mm) than for
the precision grip responses (75.0 mm). Interestingly, we also
found a main effect of number magnitude, F(1, 13) ⫽ 5.31, p ⬍
.05, ˆ
2
⫽ .13. This finding indicates that grip apertures were
somewhat larger in the context of large numbers (97.8 mm) than in
the context of small numbers (97.2 mm). The Type of Grip ⫻
Number Magnitude interaction did not reach significance, F(1,
13) ⫽ 3.80, p ⫽ .08.
Discussion
Experiment 1 demonstrates a magnitude priming effect of nu-
merals on grasping latencies. That is, the grasping responses to
Figure 2. Mean response latencies in Experiment 1 as a function of
number magnitude and type of grip.
1403
GETTING A GRIP ON NUMBERS
small digits were initiated faster if the object had to be grasped
with a precision grip, and responses to large numbers were rela-
tively faster if a power grip was required. In addition, we found
that number magnitude affected the grasping kinematics (i.e., the
maximum grip apertures were enlarged when the object was
grasped in presence of a large number). Although the Type of
Grip ⫻ Number Magnitude interaction was not significant, the
mean maximum grip apertures seem to suggest that the main effect
of number magnitude was restricted to the precision grip actions.
A possible reason for this dissociation is the fact that many
participants had to open their hand to a maximum degree to
perform the power grip response and clasp the bottom cylinder,
which had a large diameter. Under these circumstances, the pro-
cessing of large numbers can hardly result in a further enlargement
of the grip aperture. The number magnitude effect on the grasping
kinematics is therefore less pronounced, for it could be observed
for precision grip actions.
The magnitude priming effect on grasping latencies and the
number effect on grip aperture indicate that the processing of
numbers has an impact on prehension actions. Both findings are in
line with the hypothesis that numerical cognition and action plan-
ning share common cognitive codes within a generalized system
for magnitude representation (Walsh, 2003). A possible objection
to the interpretation that the numerical magnitudes primed the
size-related motor features of the grasping actions is that the two
responses not only varied with respect to the required grip size
(i.e., precision or power grip) but were also directed toward dif-
ferent parts of the object. That is, each precision grip was directed
toward the small top segment, whereas each power grip was
directed toward the large bottom segment. Therefore, the possibil-
ity cannot be excluded that the observed response latency differ-
ences reflect a compatibility effect between numerical magnitudes
and spatial response features along the vertical direction. That is,
it might be possible that responses to the top were facilitated for
small numbers and responses to the bottom were facilitated for
large numbers. Such SNARC-like effects for the vertical direction
have been previously shown by different researchers (e.g., Ito &
Hatta, 2004; Schwarz & Keus, 2004). However, such studies
consistently suggest spatial–numerical associations of upward
movements with large numbers and downward movements with
small numbers. Although we observed the opposite pattern of
effects in Experiment 1, we cannot exclude at this point the
possibility that the differences in the latencies of the grasping
response might have been driven by a reversed vertical SNARC
effect. A second possibility to account for the data of Experiment
1 is the assumption of correspondence effects between the numer-
ical size and the size of the object segment to which the action is
directed. That is, reach-to-grasp responses toward the small or
large segment could be facilitated in response to small or large
numbers, respectively. This possible association between abstract
magnitude information and physical object properties would also
argue against our interpretation of numerical priming effects on
grasping actions. To evaluate these alternative explanations, we
conducted a second experiment.
Experiment 2
The aim of Experiment 2 was to control for a possible confound
of the required grip size and the relative vertical goal location of
the reaching movements in Experiment 1 and, thus, to exclude the
possibility that the observed response latency effects were driven
by a spatial association between numerical magnitudes and the
vertical dimension (e.g., a vertical SNARC effect). To do so, we
required the participants in Experiment 2 to merely reach out for
the object without grasping it (i.e., pointing movement). That is,
the parity status of Arabic digits had to be indicated by means of
pointing movements toward the small top or large bottom segment
of the object. If our previous findings reflected a reversed vertical
SNARC effect or a compatibility effect between number size and
the size of the object segments that served as goal locations for the
response, the same response latency effects should be present in
pointing movements. However, if the effects reflected a priming
effect of aperture size, the intention to grasp should be crucial to
finding stimulus–response compatibility effects between numeri-
cal information and object-directed actions. In that case, we would
expect pointing responses to be unaffected by the presented digits.
Method
Participants. Twenty-two students of Radboud University
Nijmegen participated in Experiment 2 in return for €4.50 (U.S.$6)
or course credit. None of them had taken part in the previous
experiment. All were naive regarding the purpose of the experi-
ment and had normal or corrected-to-normal vision.
Setup and stimuli. The experimental setup and stimuli were
identical to those of Experiment 1.
Procedure. The procedure and the design were virtually the
same as in Experiment 1. The only modification was that instead
of the previous grasping movements, participants performed point-
ing movements. That is, depending on the parity status of the
presented digit, the participants were required to point either to the
small top or to the large bottom segment of the object. Since the
pointing movements needed to be performed accurately without
sight, the responses were again practiced at the beginning of the
experiment.
Design. Half of the participants had to point to the small top
segment in response to even digits and to the large bottom segment
in response to odd digits. The other half were given the reverse
stimulus–response mapping. The experiment again comprised 225
trials (50 repetitions of the digits 1, 2, 8, and 9 plus 25 no-go trials
Table 1
Mean Maximum Grip Aperture (in Millimeters) During Reach-
to-Grasp Movements in Experiments 1 and 3 as a Function of
Number Magnitude and Type of Grip
Grip Small number Large number
Experiment 1
Precision 74.6 75.9
Power 119.6 119.7
M 97.2 97.8
Experiment 3
Precision 73.7 74.2
Power 116.3 117.0
M 95.0 95.6
1404
LINDEMANN, ABOLAFIA, GIRARDI, AND BEKKERING
with the digit 5) presented in a random order and lasted about 30
min.
Data acquisition and analysis. An electromagnetic motion-
tracking sensor was attached to the participant’s right index finger
and used to record the pointing trajectories. Movement onsets were
determined and analyzed as described in Experiment 1. In addi-
tion, we calculated for each pointing trajectory the path curvature
index (PCI), which was defined as the ratio of the largest deviation
of the pointing trajectory from the line connecting the movement’s
start and end locations to the length of this line (see Desmurget,
Prablanc, Jordan, & Jeannerod, 1999).
Trials with incorrect parity judgments were excluded from the
RT analysis. To increase the chance of finding an effect of number
magnitude on pointing, we also considered movements with
strongly curved trajectories (i.e., movements with a PCI larger than
.50) to be incorrect responses, because in these cases participants
may have initiated the pointing movement before having com-
pleted their parity judgment, or they may have corrected their
judgment during the movement.
Results
Anticipation and missing responses occurred on 0.4% of trials;
2.6% of the pointing movements were performed incorrectly (i.e.,
PCI ⬎ .50).
1
The average error rate for parity judgments was
1.1%.
We applied a two-way repeated measures ANOVA with the
factors number magnitude (small, large) and pointing goal location
(small top segment, large bottom segment) to the RT data (see
Figure 3) and the PCI data (see Table 2 for means). Pointing
movements toward the small top segment (530 ms) were initiated
faster than were movements to the large bottom segment (543 ms),
F(1, 21) ⫽ 4.80, p ⬍ .05, ˆ
2
⫽ .08. Responses to small numbers
(541 ms) were faster than responses to large numbers (531 ms),
F(1, 21) ⫽ 7.38, p ⬍ .01, ˆ
2
⫽ .12. Most important, however, the
analysis did not show a significant Number Magnitude ⫻ Pointing
Goal Location interaction, F(1, 21) ⬍ 1, even though the statistical
power
2
of the performed ANOVA was sufficient to detect an
interaction effect that was only half the size of the effect found in
Experiment 1—that is, (1 ⫺) ⫽ .83 for an expected
2
⫽ .05 and
an assumed population correlation between all factor levels of ⫽
.75 (conservatively estimated from the observed empirical corre-
lations).
The analysis of the PCI data revealed that pointing movements
toward the top segment (PCI ⫽ .29) were more curved than the
movements toward the bottom segment (PCI ⫽ .20), F(1, 21) ⫽
26.98, p ⬍ .001. Importantly, there were no significant effects of
number magnitude or the Number Magnitude ⫻ Pointing Goal
Location interaction, both Fs(1, 21) ⬍ 1.5, which shows that
number processing had no impact on the pointing kinematics.
Discussion
If participants made pointing instead of grasping movements,
the interaction between numerical magnitudes and motor re-
sponses disappeared. Likewise, the analysis of movement curva-
ture data failed to reveal any influence of numerals. This absence
of numerical magnitude effects on the pointing movements ex-
cludes the possibility that the priming effects observed in Exper-
iment 1 were driven by spatial associations between numbers and
relative vertical locations or by associations between number mag-
nitude and physical object size. Since other authors have reported
numerical associations with locations along the vertical axis, it is
possible that the absence of effects for pointing movements was
caused by two opposite effects resulting from contrary associations
of numerical magnitude with vertical space (i.e., a vertical SNARC
effect) and with physical object size (i.e., an association between
number and size of object segment). Independent of this specula-
tion, however, the outcome in Experiment 2 shows clearly that
numerals did not affect motor actions if responses did not involve
a grasping component and consisted only of a pointing movement.
Taking these together with the results of Experiment 1, we can
conclude therefore that the intention to grasp is a prerequisite for
the presence of numerical magnitude priming of actions, which in
turn indicates that the observed interference effects must have
emerged during the selection and preparation of the grip.
Nevertheless, our interpretation of a within-magnitude priming
effect between numerical cognition and action planning could still
be questioned. The reason is that the motor responses in Experi-
ment 1 differed not only with respect to the size of the required
1
A two-way repeated measures ANOVA with the factors number mag
-
nitude (small, large) and pointing goal location (small top segment, large
bottom segment) on the error data (i.e., amount of incorrect performed
motor response) yielded no significant effects (all ps ⬎ .20).
2
The statistical power analysis was conducted using the G*Power 3
program (Faul, Erdfelder, Lang, & Buchner, in press).
Figure 3. Mean response latencies in Experiment 2 as a function of
number magnitude and pointing goal location.
Table 2
Mean Path Curvature Indices for Pointing Movements in
Experiment 2 as a Function of Number Magnitude and Pointing
Goal Location
Segment Small number Large number
Small top .29 .29
Large bottom .20 .21
M .24 .25
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GETTING A GRIP ON NUMBERS
grip but also with respect to the number of fingers that had to be
used for grasping. That is, precision grips always implied grasping
movements with two fingers (e.g., only thumb and index finger),
whereas power grips always involved the use of all five fingers of
the hand. Therefore, we cannot exclude the possibility that our
findings were driven by the different number of fingers involved in
the grasping responses. Such an explanation is not farfetched, and
it appears to be even plausible to assume that there is a strong
association between the fingers of the hand and the semantic
knowledge about numerical magnitudes (see, e.g., Di Luca, Grana,
Semenza, Seron, & Pesenti, 2006). This connection is, for in-
stance, nicely illustrated by children’s use of finger-counting strat-
egies when learning to deal with abstract quantities. And in fact,
empirical evidence for this relation comes from developmental
studies indicating that the performance of a child in a finger
agnosia test is a good predictor for later numerical skills (Noel,
2005). Moreover, neuropsychological research has shown that
symptoms of finger agnosia are often associated with symptoms of
dyscalculia (so-called Gerstmann’s syndrome; Mayer et al., 1999).
Consequently, we conducted a third experiment to control for the
number of fingers involved in the grasping responses.
Experiment 3
In Experiment 3, we sought to provide further evidence that
number processing interferes with the processing of action-coded
magnitude information for motor preparation, and we aimed to
exclude the possibility that this compatibility effect was caused by
overlearned associations between numbers and the fingers of the
hand. To do so, we tested whether magnitude priming effects of
numerals could also be found in grasping movements that required
a fixed number of fingers for both required types of grip. As in the
first experiment, participants grasped the object in different ways
to indicate the parity status of Arabic digits. Now, however, power
and precision grips both had to be performed with the thumb and
index finger only. Consequently, the two grasping responses dif-
fered only in aperture size.
3
To ensure that the ring, middle, and
little fingers were not used to grasp the target object, we required
participants to hold a little stick with these three fingers. If the
response latency differences in Experiment 1 were driven by a
number–finger association, we should not observe any magnitude
priming effects. If, however, they reflected a magnitude priming of
size-related response features of the grasping action, we should be
able to replicate our previous findings.
Method
Participants. Eighteen students of Radboud University Nijme-
gen, none of whom had participated in either of the previous
experiments, took part in Experiment 3. The participants were paid
€4.50 (U.S.$6) or received course credits. All were naive regarding
the purpose of the study and had normal or corrected-to-normal
vision.
Setup and stimuli. The experimental setup and stimuli were
identical to those of Experiment 1.
Procedure and design. The procedure and the experimental
design were virtually identical to those of Experiment 1. Again,
participants were required to indicate the parity status of the
presented digits by performing different types of grasping re-
sponses with the right hand. However, in contrast to Experiment 1,
the object had to be grasped with thumb and index finger only.
That is, depending on the presented digits, participants grasped the
object with two fingers either at the large segment (i.e., power
grip) or at the small segment (i.e., precision grip). To ensure that
no other finger of the right hand were used for grasping, partici-
pants had to hold a little stick (length: 5 cm; diameter: 1.5 cm)
during the experiment between their right middle, ring, and little
fingers.
Data acquisition and analysis. Data acquisition and analysis
methods were identical to those used in Experiment 1. An addi-
tional motion-tracking sensor was mounted inside the stick and
used to make sure that participants held the stick in their right hand
during all trials.
Results
Anticipations and missing responses occurred on 0.7% of trials;
only 0.9% of the grasping movements were performed incorrectly.
The error rate for the parity judgments was 1.6%.
The RT and grip aperture data (see Figure 4 and Table 1) were
analyzed as in Experiment 1. The 2 (number magnitude: small vs.
large) ⫻ 2 (type of grip: precision grip vs. power grip) ANOVA of
the RTs revealed no main effects (both Fs ⬍ 1). Importantly, a
significant Number Magnitude ⫻ Type of Grip interaction was
found, F(1, 17) ⫽ 5.46, p ⬍ .05, ˆ
2
⫽ .06. Post hoc t tests
indicated that the precision grip RTs were shorter to small numbers
(556 ms) than to large numbers (571 ms), t(17) ⫽⫺2.13, p ⬍ .05,
whereas for the power grips, there was a nonsignificant trend
toward the reversed effect—that is, shorter RTs to large (560 ms)
than to small numbers (571 ms), t(17) ⫽ 1.95, p ⫽ .058. The
two-way ANOVA on the mean maximum grip apertures revealed
a main effect of type of grip, F(1, 17) ⫽ 292.76, p ⬍ .001, which
showed that the grip apertures were larger for power grip actions
(116.7 mm) than for precision grip actions (73.9 mm). Although
the mean grip aperture difference between responses toward small
and large numbers was identical to the main effect observed in
Experiment 1, the factor number magnitude did not reach statisti-
cal significance, F(1, 17) ⫽ 2.11, p ⫽ .16.
Discussion
Experiment 3 replicated the RT effect of Experiment 1 and
showed an interaction between numbers and grasping actions that
involve a fixed number of fingers. These findings exclude the
possibility that the observed response latency effects were driven
by an association between numbers and the fingers of the hand,
and they provide additional support for the idea of numerical
priming of size-related motor features.
In contrast to Experiment 1, the size of the maximum grip
apertures did not differ for small and large numbers. A possible
reason for this might be that the grasping responses in Experiment
3 had to be performed in a rather unnatural manner. Since partic-
ipants were required to hold a stick with the three remaining
3
For reasons of simplicity, we keep the label power grip here for the
grasping of the large segment with the thumb and index finger, although
the term is usually reserved for grasping actions with all fingers of the
hand.
1406
LINDEMANN, ABOLAFIA, GIRARDI, AND BEKKERING
fingers while grasping the object with the thumb and index finger,
the responses were certainly more difficult to perform and might,
thus, have been more disturbed than those in Experiment 1. Evi-
dence for this is provided by the observation that the within-
subject confidence interval for the grip aperture data was larger for
Experiment 3 than for Experiment 1.
4
It is therefore likely that the
increased movement complexity was responsible for the absence
of grip aperture effects when objects had to be grasped with two
fingers only.
General Discussion
The present finding of an interaction between representations of
numerical information and representations of action-coded magni-
tude information for grasping provides evidence for a close link
between numerical cognition and motor control. We asked partic-
ipants to indicate the parity status of visually presented Arabic
digits by means of different reach-to-grasp movements (Experi-
ments 1 and 3) and observed that precision grip actions were
initiated faster in response to relatively small numbers, whereas
power grip actions were initiated faster in response to large num-
bers. This finding indicates a magnitude priming of grasping
actions by Arabic numerals. Besides this, we observed that numer-
ical magnitude also had an impact on grip aperture kinematics.
With both effects, we provide behavioral support for the idea that
number processing and action planning share common cognitive
codes within a generalized system for magnitude representation
(Walsh, 2003).
Interestingly, the present study indicates that intention to grasp
the object was crucial for the interference between number pro-
cessing and action planning. Numerical magnitudes did not affect
actions if they involved no grasping component and consisted
merely of a reaching movement (i.e., pointing response) toward the
smaller or larger (respectively, upper or lower) part of the object
(Experiment 2). This finding clearly excludes the possibility of a
compatibility effect between numbers and the reaching component
of actions—an effect that could have been caused by an associa-
tion of number size with the size of to-be-grasped object part or
with the end position of the reaching movement along the vertical
dimension (a vertical SNARC effect; see Ito & Hatta, 2004;
Schwarz & Keus, 2004). In addition, we excluded the possibility
that interactions between grasping actions and number magnitude
were driven by the different number of fingers involved in the two
different grasping responses, because the priming effects of the
Arabic numerals were also present when the grasping actions were
performed with two fingers only (Experiment 3).
Arabic numerals not only affected the time to plan and initiate
the grasping action but also influenced the way in which the action
was performed. That is, when participants grasped the object
without any restrictions concerning the fingers to be used, maxi-
mum grip apertures were enlarged in the presence of large num-
bers. Taking these results together, we conclude that the process-
ing of numerical magnitude information somehow biased the
processing of size-related motor features in the preparation of
grasping responses. It is possible that this effect originated from
processes in the dorsal pathway, where magnitude information
needed to select an appropriate grip aperture is computed and
represented (see Castiello, 2005).
The present magnitude priming effect in object grasping sub-
stantially extends previous findings of numerical stimulus–
response compatibility effects caused by an association between
numbers and spatial locations. The most prominent example of this
relationship is the SNARC effect, reflecting the tendency to re-
spond quickly with a left-side response to small and a right-side
response to large numbers (Dehaene et al., 1993; for review, see
Hubbard et al., 2005). So far, SNARC effects have been shown for
several types of lateralized motor responses (Fischer, 2003;
Schwarz & Keus, 2004; Schwarz & Mu¨ller, 2006). It is important,
however, to note that in the present study, the grasping actions did
not differ with respect to a lateralized left–right response feature.
Instead, participants always moved with the same hand toward the
same object at the same location. Consequently, the observed
differences in the latencies of reaching responses cannot be ex-
plained by an association between numbers and spatial response
features. Rather, our data reveal an interaction between numerical
magnitude information and size-related features of the motor re-
sponse (i.e., the grip aperture). Thus, the demonstrated magnitude
priming of grasping actions shows also that numerical stimulus–
response compatibility effects are not restricted to an association
between numerical values and spatial locations along the mental
number line (e.g., Dehaene et al., 1993).
The experiments reported here represent a direct behavioral test
of the idea of a generalized magnitude system for number process-
ing and action planning. Importantly, the present findings go
beyond the number–finger-movement interaction previously
shown by Andres et al. (2004). Although these authors also spec-
ulated that the compatibility effects observed between numbers
and the extension/flexion of the index finger might be the result of
a common representation involved in number processing and hand
aperture control, the reported evidence for this was quite indirect
in that the task did not require any grasping action. For example,
it cannot be excluded that the effects in the study of Andres et al.
were the results of an association between numbers and space
along the sagittal axis, because each response comprised an index
4
The within-subject confidence intervals (cf. Loftus & Masson, 1994)
for the mean maximum grip apertures in the presence of small and large
numbers were ⫾0.56 in Experiment 1 and ⫾0.91 in Experiment 3.
Figure 4. Mean response latencies in Experiment 3 as a function of
number magnitude and type of grip.
1407
GETTING A GRIP ON NUMBERS
finger movement either toward or away from the body. The find-
ings could be therefore also explained in terms of the more
classical idea of the mental number line. Moreover, the assumed
connection with grasping behavior appears to be problematic, not
only because the actions did not involve objects but also because
an opening or closing of two fingers differs in several crucial
motor features from natural grasping movements. As is known
from several studies of motor control, reach-to-grasp movements
always consist of both an opening and a closing of the hand rather
than a single change of the grip aperture (for review, see Castiello,
2005). Since hand preshaping is strongly linked to the transport
phase of the hand, we argue that magnitude effects in grasping
actions cannot be investigated appropriately without considering
the whole reaching movement. It is thus important to notice that,
in contrast to previous work, the present findings were not driven
by finger movements per se and reflect an effect on reach onset
times and grasping kinematics during reaching out for the target
object. Since the observed numerical magnitude priming is an
effect of the intended end postures of the grasping actions, our
results indicate that the size of the required grip aperture at the end
of reaching is the crucial motor feature responsible for the ob-
served cognitive interference. This interpretation is in line with
recent theories in the field of motor control, assuming that the
motor planning is guided mainly by the desired end postures of a
goal-directed movement (Rosenbaum, Meulenbroek, Vaughan, &
Jansen, 2001). Taking our results together, the major advance
made by studying number effects on natural grasping actions is
that our findings provide clear-cut evidence for the presence of
within-magnitude priming between numbers and size-related mo-
tor features, and they demonstrate furthermore that these effects
emerge during action planning well before the object is actually
grasped.
Since, broadly speaking, Arabic digits represent an instance of
symbolic semantic information, our findings may also contribute
to research investigating the relationship between semantic pro-
cessing and motor actions. Similar to the current number effect on
the grasping kinematics, an impact of word meanings on the grip
aperture has been demonstrated in several studies (Gentilucci et
al., 2000; Glover & Dixon, 2002; Glover et al., 2004). For exam-
ple, semantic action effects have been found for words represent-
ing categorical magnitude relations (e.g., small, large) as well as
for words denoting objects that are associated with a specific
physical size (e.g., grape, apple) and, therefore, also with a spe-
cific type of grip (Tucker & Ellis, 2001). The present study extends
these findings and provides the first empirical evidence for a
comparable grip aperture effect of Arabic numerals. This shows
that semantic effects on motor actions are not restricted to words
representing physical or relative magnitudes but can be also elic-
ited by stimuli representing knowledge about abstract and absolute
magnitudes. Glover and Dixon (2002) performed a very detailed
analysis of grip aperture kinematics and found that semantic ef-
fects of word reading are only present very early on in the reach.
As the hand approaches the target object, this effect gradually
declines. These authors concluded that semantic information in-
terferes with motor planning but not with processes of movement
control, which become effective only after an action has been
initiated. Following this reasoning, it is likely that the present
kinematic effects of numbers also occurred during motor prepara-
tion. We assume, therefore, that the grip aperture effects of nu-
merals originated from the same cognitive interference during the
stage of action planning as the magnitude priming effect found in
the reaching latencies.
Several authors have suggested recently that semantic process-
ing and action planning should be understood as two mutually
dependent processes (e.g., Gallese & Lakoff, 2005; Glenberg &
Kaschak, 2002). This idea implies not only that semantic process-
ing affects action planning but also that action planning may affect
semantic processing. Evidence for this has been provided recently
by the observation that the planning and execution of an action can
facilitate semantic judgments on the meaning of action-related
words or sentences (Lindemann et al., 2006; Zwaan & Taylor,
2006). Whether such a reversed effect of action planning on higher
cognitive processes also exists for the processing of numbers is an
intriguing, open question for future investigations.
In sum, not much is known about the role of magnitude infor-
mation in the coupling of motor control and other cognitive pro-
cesses. The present study indicates the existence of a functional
connection between numerical cognition and action planning. As
the magnitude priming of grasping actions by Arabic digits shows,
the coding of numbers interferes with the coding of size-related
response features. This finding suggests that number processing
and motor preparation share common cognitive codes (Hommel et
al., 2001), and it supports in particular the idea of a generalized
magnitude system (Walsh, 2003) in which representations of num-
bers and actions are linked by a common metric for size and
quantity information.
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Received August 27, 2006
Revision received December 13, 2006
Accepted February 11, 2007 䡲
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