Touch perception reveals the dominance of spatial over digital representation of numbers.
ABSTRACT We learn counting on our fingers, and the digital representation of numbers we develop is still present in adulthood [Andres M, et al. (2007) J Cognit Neurosci 19:563-576]. Such an anatomy-magnitude association establishes tight functional correspondences between fingers and numbers [Di Luca S, et al. (2006) Q J Exp Psychol 59:1648-1663]. However, it has long been known that small-to-large magnitude information is arranged left-to-right along a mental number line [Dehaene S, et al. (1993) J Exp Psychol Genet 122:371-396]. Here, we investigated touch perception to disambiguate whether number representation is embodied on the hand ("1" = thumb; "5" = little finger) or disembodied in the extrapersonal space ("1" = left; "5" = right). We directly contrasted these number representations in two experiments using a single centrally located effector (the foot) and a simple postural manipulation of the hand (palm-up vs. palm-down). We show that visual presentation of a number ("1" or "5") shifts attention cross-modally, modulating the detection of tactile stimuli delivered on the little finger or thumb. With the hand resting palm-down, subjects perform better when reporting tactile stimuli delivered to the little finger after presentation of number "5" than number "1." Crucially, this pattern reverses (better performance after number "1" than "5") when the hand is in a palm-up posture, in which the position of the fingers in external space, but not their relative anatomical position, is reversed. The human brain can thus use either space- or body-based representation of numbers, but in case of competition, the former dominates the latter, showing the stronger role played by the mental number line organization.
- SourceAvailable from: Edward Michael Hubbard[Show abstract] [Hide abstract]
ABSTRACT: Abstract The SNARC effect refers to faster reaction times for larger numbers with right-sided responses, and for smaller numbers with left-sided responses (Dehaene et al., 1993), even when numerical magnitude is irrelevant. Although the SNARC is generally thought to reflect a mapping between numbers and space, the question of which spatial reference frame(s) are critical for the effect has not been systematically explored. We propose a dynamic hierarchical organization of the reference frames (from a global left-right frame to body- and object-related frames), where the influence of each frame can be modulated by experimental context. We conducted two experiments based on predictions derived from this organizational system. Experiment 1 compared instructions that differed only in focusing participants' attention on either the response buttons or the hands. Instructions focusing on a hand-based reference frame eliminated the SNARC. Experiment 2 provided the opportunity for an object-centered reference frame to manifest itself in the SNARC. Although we did not observe an effect of an object-centered reference frame, we observed the influence of other reference frames in a context where an object-centered reference frame was emphasized. Altogether, these results support the proposed organization of the reference frames.Quarterly journal of experimental psychology (2006) 02/2014; · 1.73 Impact Factor
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ABSTRACT: Recent research in cognitive sciences shows a growing interest in spatial-numerical associations. The horizontal SNARC (spatial-numerical association of response codes) effect is defined by faster left-sided responses to small numbers and faster right-sided responses to large numbers in a parity judgment task. In this study we investigated whether there is also a SNARC effect for upper and lower responses. The grounded cognition approach suggests that the universal experience of "more is up" serves as a robust frame of reference for vertical number representation. In line with this view, lower hand responses to small numbers were faster than to large numbers (Experiment 1). Interestingly, the vertical SNARC effect reversed when the lower responses were given by foot instead of the hand (Experiments 2, 3, and 4). We found faster upper (hand) responses to small numbers and faster lower (foot) responses to large numbers. Additional experiments showed that spatial factors cannot account for the reversal of the vertical SNARC effect (Experiments 4 and 5). Our results question the view of "more is up" as a robust frame of reference for spatial-numerical associations. We discuss our results within a hierarchical framework of numerical cognition and point to a possible link between effectors and number representation. (PsycINFO Database Record (c) 2014 APA, all rights reserved).Journal of Experimental Psychology Human Perception & Performance 04/2014; · 3.11 Impact Factor
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ABSTRACT: This paper elaborates a novel hypothesis regarding the observed predictive relation between finger gnosis and mathematical ability. In brief, we suggest that these two cognitive phenomena have overlapping neural substrates, as the result of the re-use ("redeployment") of part of the finger gnosis circuit for the purpose of representing numbers. We offer some background on the relation and current explanations for it; an outline of our alternate hypothesis; some evidence supporting redeployment over current views; and a plan for further research.Frontiers in Psychology 01/2013; 4:877. · 2.80 Impact Factor
Touch perception reveals the dominance of spatial
over digital representation of numbers
Claudio Brozzoli*†‡, Masami Ishihara§, Silke M. Go ¨bel¶, Rome ´o Salemme*†, Yves Rossetti*†, and Alessandro Farne `*†‡
*Institut National de la Sante ´ et de la Recherche Me ´dicale, Unite ´ Mixte de Recherche-S 864 ‘‘Espace et Action,’’ F-69500 Bron, France;†Universite ´ Claude
Bernard Lyon I, F-69000 Lyon, France;§Department of Psychology, Max Planck Institute for Human Cognitive and Brain Sciences, 04103 Leipzig, Germany;
and¶Department of Psychology, University of York, York YO10 5DD, United Kingdom
Edited by Dale Purves, Duke University Medical Center, Durham, NC, and approved February 14, 2008 (received for review September 6, 2007)
We learn counting on our fingers, and the digital representation of
numbers we develop is still present in adulthood [Andres M, et al.
(2007) J Cognit Neurosci 19:563–576]. Such an anatomy–magnitude
association establishes tight functional correspondences between
fingers and numbers [Di Luca S, et al. (2006) Q J Exp Psychol 59:1648–
1663]. However, it has long been known that small-to-large magni-
[Dehaene S, et al. (1993) J Exp Psychol Genet 122:371–396]. Here, we
investigated touch perception to disambiguate whether number
representation is embodied on the hand (‘‘1’’ ? thumb; ‘‘5’’ ? little
finger) or disembodied in the extrapersonal space (‘‘1’’ ? left; ‘‘5’’ ?
right). We directly contrasted these number representations in two
experiments using a single centrally located effector (the foot) and a
simple postural manipulation of the hand (palm-up vs. palm-down).
We show that visual presentation of a number (‘‘1’’ or ‘‘5’’) shifts
attention cross-modally, modulating the detection of tactile stimuli
delivered on the little finger or thumb. With the hand resting palm-
down, subjects perform better when reporting tactile stimuli deliv-
‘‘1’’ than ‘‘5’’) when the hand is in a palm-up posture, in which the
position of the fingers in external space, but not their relative
anatomical position, is reversed. The human brain can thus use either
space- or body-based representation of numbers, but in case of
competition, the former dominates the latter, showing the stronger
role played by the mental number line organization.
mental number line ? tactile perception
by virtue of learning processes such as counting on fingers. Such an
embodied finger-counting strategy, developed during numerical
acquisition in childhood, might result in a finger–number associa-
tion still present in adulthood when the same numerical manipu-
the precentral gyrus and parietal areas participating in hand-
shaping control and finger movements (3) are commonly reported
during numerical tasks (4–9) and have been suggested to underlie
implicit finger-counting strategies (4–6). Neuropsychological stud-
ies of Gerstmann’s syndrome (10, 11) and transcranial magnetic
stimulation (TMS) approaches in healthy subjects (3, 12, 13) have
also suggested tight functional correspondences between fingers
and numbers. However, a disembodied form of numerical repre-
sentation is also well established: Numbers are represented in a
spatial format along the so-called ‘‘mental number line,’’ whereby
smaller numbers occupy relatively leftward locations compared
known as the spatial numerical association of response codes
(SNARC) effect, suggests that magnitude information may be
analogically arranged from left to right (in most Western cultures):
In parity judgment tasks, large numbers are responded to faster
with the right hand (and small numbers faster with the left hand)
number on the mental number line and the location of the correct
t has long been considered that literate humans associate num-
bers (e.g., ‘‘1’’ and ‘‘5’’) with fingers (e.g., thumb and little finger)
response effector in external space. Neuropsychological evidence
from neglect patients and TMS studies on subjects bisecting nu-
merical intervals has further supported the left-to-right spatial
organization of numbers (16–21). Moreover, visual attention and
action can be enhanced according to the magnitude of a visually
presented number, larger numbers boosting performance on the
attempts to contrast hand-/finger-based (embodied) and space-
results. Dominance of the space-based representation has been
suggested by Dehaene et al. (14), who asked subjects to perform a
crossed-hand version of their original parity-judgement task and
identity but the left–right hand location in the response space. In
Author contributions: C.B. and A.F. designed research; C.B. performed research; R.S.
S.M.G., Y.R., and A.F. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
‡To whom correspondence may be addressed. E-mail: firstname.lastname@example.org or farne@
This article contains supporting information online at www.pnas.org/cgi/content/full/
© 2008 by The National Academy of Sciences of the USA
front of them with their middle finger aligned with the central fixation point
on the monitor. After a fixation period of 500 ms, a number appeared for 300
ms in the center of the monitor. A tactile stimulus was delivered either to the
thumb or the little finger at a variable interval from number onset: four SOAs
were possible in the first experiment (550, 800, 1,050, or 1,300 ms after onset
of the task-irrelevant number) and two in the second experiment (250 ms or
550 ms after onset of the task-irrelevant number). The subjects were in-
structed to respond to the tactile stimulus as quickly as possible, by pressing a
centrally located pedal with their right foot.
Experimental setup and procedures. The subjects’ right hands lay in
April 8, 2008 ?
vol. 105 ?
contrast, finger-based dominance has been suggested by Di Luca et
was congruent with the prototypical finger-counting strategy. In
addition, a certain degree of flexibility in number representation
has been recently suggested (25–28), because the mapping between
numbers and space can vary to some extent with instructional
context (25) and task demands (17).
Previous findings are thus not definitive with regard to number
representation, because both the embodied and the disembodied
hypotheses have received empirical support. In this study, we used
a previously undescribed approach to disambiguate between such
representations within a corporeal modality, by investigating the
delivered to the fingers. A postural manipulation of the hand
(palm-up vs. -down) allowed us to directly contrast the embodied
and disembodied representations of numbers. A further manipu-
lation was critically introduced to avoid any left–right arrangement
in the response space, potentially favoring a space-based represen-
tation, and any motor bias in the response effector, potentially
favoring a finger-based representation: Subjects had to respond to
tactile stimulation by pressing a centrally located pedal with the
Results and Discussion
Participants performed a simple tactile detection task by making
speeded foot-pedal responses to a tactile stimulus delivered to
either the thumb or little finger of their right (preferred and
counting) hand. Tactile intensity was set in a previous session to
obtain an equal detection probability for the two fingers [see
supporting information (SI) Experiment 1, Supporting Procedures
and Supporting Results, Table S1, and Fig. S1]. In the first experi-
ment, the task instructions were given as to emphasize the fingers
(i.e., ‘‘you will feel a touch on either your thumb or little finger’’).
At a variable stimulus onset asynchrony (SOA), an electrocutane-
ous stimulus followed the presentation of a task-irrelevant number
tactile task was performed with the unseen hand passively resting
either in a palm-down or -up posture.
Two main results were found: First, visual presentation of a
number cross-modally affects tactile performance. Second, this
numerical cueing of touch does not follow a number–finger asso-
emphasis on fingers. (a) Regression lines of the inverse efficiency score as a
Visual numerical cueing of touch is modulated by hand posture:
the averaged data in each image. Performance for the thumb (blue) in
palm-down posture (Upper), decreased as a function of number magnitude
the pattern is opposite for the same stimulus on the same thumb but in
palm-up posture (Lower, y ? ?2.0x ? 430, r2? 0.65). Little-finger results
(yellow) mirror those for the thumb (y ? ?4.6x ? 437, r2? 0.39, palm-down
posture, Upper; y ? ?3.7x ? 425, r2? 0.77 palm-up posture, Lower). (b) Beta
values of the regression lines (mean ? SEM) relating the inverse efficiency
score to number magnitude are presented for the palm-down (left side of the
graph) and the palm-up posture (right side) for little finger (yellow bars) and
posture modulates the visual numerical cueing of touch. Indeed, for stimuli
applied to the thumb, positive beta values in the palm-down posture become
negative in the palm-up posture (?5.94 ? 2.10 vs. ?2.04 ? 2.53, respectively).
The opposite is true for the little finger (?0.55 ? 1.95 vs. ?3.70 ? 2.58,
respectively). (c) Time course of the visual numerical cueing of touch. Inverse
efficiency scores (mean ? SEM) for stimuli to the little finger (yellow) and
thumb (blue) after presentation of number ‘‘1’’ (black bars) and ‘‘5’’ (green
bars) are presented for each SOA (550, 800, 1,050, and 1,300 ms). The spatial
bias induced by the number is not modulated by time: in the palm-down
finger was better after number ‘‘5’’ than number ‘‘1,’’ whereas performance
‘‘5.’’ The reversed pattern is observed in the palm-up posture (Lower), irre-
spective of the SOA.
Brozzoli et al.
April 8, 2008 ?
vol. 105 ?
no. 14 ?
conditions including all of the numbers (‘‘1,’’ ‘‘2,’’ ‘‘4,’’ and ‘‘5’’) is
provided by Fig. 2a. When the right hand was in the palm-down
posture, placed centrally with the middle finger aligned with the
applied to the little finger improved as a function of the preceding
number magnitude. The larger the number, the better the perfor-
mance in terms of inverse efficiency (IE) score, jointly indexing
accuracy, and response latency. The opposite pattern of results was
found when the same little finger was stimulated with the hand in
actually decreased as the preceding number increased. The statis-
tical comparison showed a significant finger ? posture interaction
[F(1,13) ? 9.80; P ? 0.01]: Fig. 2b shows that for stimuli applied on
the little finger, a difference was present between the slopes of IE
respectively; P ? 0.05; Fig. 2b, yellow bars). Results for the thumb
mirrored those for the little finger (Fig. 2b, blue bars). When the
hand was in the palm-down posture, subjects’ detection improved
the preceding number, the better the performance, because the
was in the palm-up position, subjects’ detection of brief stimuli on
the thumb tended to worsen with decreasing magnitude of the
presented number (?5.94 vs. ?2.04 for the palm-down and -up
postures, respectively; P ? 0.053, Fig. 2b).
To further establish the dominant role played by the space-based
organization of numbers, an additional analysis of tactile perfor-
mance was run by focusing on those conditions with presentation
four-way ANOVA revealed a significant main effect of SOA on
tactile performance [F(3,39) ? 15.35; P ? 0.01]. Newman–Keuls
posthoc test revealed that subjects’ performance was worst in the
longer SOA (1,300 ms), compared with shorter ones (550, 800, and
was not involved in any significant interaction (Fig. 2c). The
hypothesis of an embodied representation of numbers predicts that
the thumb is more closely associated with, and thus would be more
efficiently primed by, number ‘‘1’’ than number ‘‘5,’’ independently
of the hand’s posture, with the opposite association for the little
finger. Contrary to these predictions, a significant posture ?
finger ? number interaction [F(1,13) ? 14.43; P ? 0.01] confirmed
that the numerical cueing of touch is mapped in extrapersonal
Visual numerical cueing of touch is modulated by hand posture:
score as a function of number magnitude for all conditions. Regression
equations reflect the averaged data in each image. Performance for the
thumb (blue) in palm-down posture (Upper), decreased as a function of
number magnitude from the smallest (‘‘1’’) to the largest (‘‘5’’) number (y ?
?23.2x ? 446, r2? 0.97); the pattern is opposite for the same stimulus on the
same thumb but in palm-up posture (Lower, y ? ?3.4x ? 505, r2? 0.39).
0.91, palm-down posture, upper row; y ? ?12.1x ? 484, r2? 0.41 palm-up
posture, Lower). (b) Beta values of the regression lines (mean ? SEM) relating
the inverse efficiency score to number magnitude are presented for the
palm-down (left side of the graph) and palm-up postures (right side) for little
finger (yellow bars) and thumb (blue bars) [finger ? posture interaction,
F(1,12) ? 6.02; P ? 0.03]. Hand posture modulates the visual numerical cueing
of touch, also when emphasis in task instruction is given to the side (left or
?3.4 ? 4.9, respectively). The opposite is true for the little finger (?1.69 ? 7.3
vs. ?12.12 ? 6.6, respectively). (c) Time course of the visual numerical cueing
of touch. Inverse efficiency scores (mean ? SEM) for stimuli to the little finger
(yellow) and thumb (blue) after presentation of number ‘‘1’’ (black bars) and
‘‘5’’ (green bars) are presented for each SOA: 250 ms (i.e., during number
presentation) and 550 ms (i.e., after number presentation). Even at the
shortest SOA, the spatial bias induced by the number on tactile perception
shifts according to whether the hand is in the palm-down (Upper), or the
palm-up posture (Lower).
www.pnas.org?cgi?doi?10.1073?pnas.0708414105 Brozzoli et al.
space. Subjects’ performance was better in perceiving a touch on
score: 447 vs. 470 ms, respectively; P ? 0.05), but the opposite
tendency was obtained when the hand posture was reversed (IE
score: 428 vs. 417 ms, respectively). Similarly, when considering the
little finger, subjects’ performance mirrored that of the thumb: In
the palm-down posture, stimuli on the little finger were detected
posture, in which performance was better when touches were
0.05). The same significant pattern of results was also obtained
when subjects’ accuracy was separately tested, and response laten-
cies showed the same tendency. In other words, the same touch
delivered to the same little finger was better perceived if preceded
by number ‘‘5’’ than ‘‘1’’ in the palm-down posture but was better
perceived if preceded by number ‘‘1’’ than ‘‘5’’ in the palm-up
To further explore the potential role played by instructional
and task-setting variables, we performed a second experiment
whereby tactile stimuli were always delivered on the thumb or
little finger, but the side of the hand was stressed (i.e., ‘‘you will
feel a touch on either the left or right side of your hand’’).
effect of numerical cueing of touch, a shorter SOA was tested:
tactile stimuli were delivered either 550 ms (i.e., as the shortest
SOA in the first experiment) or 250 ms after number onset (i.e.,
when the task-irrelevant number was still present on the screen;
see Methods for details).
Results replicated the findings of the previous experiment. As
shown in Fig. 3b, tactile performance was cross-modally affected
by the visual presentation of a number, and numerical cueing of
touch again followed a number–space association, as revealed by
the significant finger ? posture interaction [F(1,12) ? 6.02; P ?
0.03]. In the palm-down posture, subjects’ tactile detection at the
little finger improved with increasing number magnitude; the
opposite pattern was observed in the palm-up posture. For
stimuli applied on the little finger, the slopes of IE regression
lines in the palm-down and -up position differed (?1.69 vs.
?12.12, respectively; P ? 0.04; Fig. 3b, yellow bars). Again,
results for the thumb mirrored those for the little finger (Fig. 3b,
blue bars). When the hand was in the palm-down posture,
subjects’ detection improved with decreasing number magni-
tude; the opposite tendency was present when the hand was in
the palm-up position (?23.22 vs. ?3.35 for the palm-down and
-up postures, respectively; P ? 0.07; Fig. 3b). When considering
only the numbers ‘‘1’’ and ‘‘5,’’ the ANOVA revealed a signif-
0.01], which further confirmed that the numerical cueing of
touch was mapped in extrapersonal space. Fig. 3c illustrates that
this effect was also present at the shortest SOA, because neither
was this variable significant nor was it involved in any interaction
(Fig. 3c), thus suggesting a rather early space-based mapping of
The findings of both experiments clearly demonstrate that the
human brain takes into account magnitude information pre-
sented in the visual modality when processing tactile stimuli at
the fingers, but in so doing, it refers to an extrapersonal spatial
representation of numbers. Indeed, very similar and consistent
results were observed both when task instructions emphasized
the (left or right) sides of the hand (second experiment), and the
(little finger or thumb) fingers of the hand (first experiment), as
common SOA (550 ms from number onset), whereby the be-
tween-subject variable emphasis was not involved in any inter-
action. Therefore, even when emphasis was given to fingers and
might have in principle favored a finger-based numerical repre-
sentation, the results were clear in showing a space-based
dominance in number representation. When compared with
previous studies, it is noteworthy that the present findings were
obtained within a best-suited approach to disambiguate between
number representations: First, number magnitude was totally
task-irrelevant, at odds with previous visuomotor number-finger
mapping task (24); second, a single centrally located effector was
used, at variance with SNARC tasks whereby two left–right
horizontally aligned effectors are typical used (14, 17); finally,
the foot was used as response effector, i.e., a body part that is not
used to learn counting.
Here, the case for a connection between space and numbers (29)
was studied in direct reference to the body. Our manipulation of
reference frames in which tactile perception is biased by numerical
we not only show that number-based attentional cueing crosses
sensory modalities but also demonstrate that number-based tactile
priming is early mapped according to an extrapersonal spatial
representation, thus providing a compelling support for the dom-
inant role played by the spatial representation of numbers known
as the ‘‘mental number line.’’
Subjects. The first experiment was run on 14 (7 female, mean age 30.9; SD 10.1,
29.3; SD 8.1, range 21–51 years) healthy subjects participated in the second
experiment. Three subjects took part in both experiments. All participants gave
ethics committee. They were asked to show how they usually count with their
fingers, without specifying in the request which hand to use first. However, to
induce subjects to use both hands, they were asked to count up to ‘‘8.’’ Only
subjects who used the conventional (for Italian and French subjects) counting
thumb were admitted to the experimental session. Subjects were all right-
handed according to the Edinburgh Handedness Inventory. They had normal or
corrected visual acuity, reported no somatosensory problems, and were naı ¨ve as
to the purpose of the study.
Apparatus and Procedure. Both experiments were run with the same setup and
procedures were identical, unless otherwise stated. A personal computer (Dell,
Optiplex GX270, Intel Pentium 4) equipped with a visual stimulus generator
and response collection. Arabic numerals (‘‘1,’’ ‘‘2,’’ ‘‘4,’’ or ‘‘5’’) were presented
800 ? 600 pixels; refresh rate, 160 Hz), located 57 cm from the subjects’ eyes,
subtending 1 ? 1° of visual angle. Subjects’ right hidden hands lay in front of
fixation and eye movements were constantly monitored throughout each trial
via an eye-tracking system (Cambridge Research Systems; 250 Hz). After the
subject succeeded in keeping the fixation within a (nonvisible) circular window
centered on the fixation point (2.5° side by side) for 500 ms, one of the four
equiprobable numbers (‘‘1,’’ ‘‘2,’’ ‘‘4,’’ or ‘‘5’’) appeared (300 ms). In the first
experiment, a brief (100-?s) electrocutaneous stimulus was equiprobably deliv-
ered via self-adhesive disposable electrodes (Neuroline 700-K, Ambu) to the
thumb or little finger at one of four possible SOAs (550, 800, 1,050, or 1,300 ms).
In the second experiment, the electrocutaneous stimulus was equiprobably de-
foot-pedal response. If central fixation was broken at any time during the trial,
obtain ?80% correct detections for both fingers with a titration procedure that
was run in a preexperimental session (see SI Experiment 1 and SI Experiment 2).
Each stimulator (DS7A, Digitimer) current was varied independently for each
Brozzoli et al.
April 8, 2008 ?
vol. 105 ?
no. 14 ?
task. To ensure that number magnitude was processed (see SI Experiment 1 and
SI Experiment 2, Number Magnitude, and Table S2), they were also told they
could be asked without warning which number appeared in the immediately
to combine RT and accuracy data into a single performance measure, computed
number (‘‘1’’ vs. ‘‘5’’) as variables. Each posture was further analyzed by a three-
calculated and submitted to a three-way ANOVA with SOA, posture, and finger
as within-subject variables. Significant sources of variance were explored by
Newman–Keuls posthoc tests and planned comparisons.
ACKNOWLEDGMENTS. We thank F. Frassinetti, N. Holmes, F. Pavani, and A.
Roy for thoughtful discussions and comments on an earlier version of the
manuscript. This work was supported by the European Mobility Fellowship,
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