Imaging Informational Conflict: A Functional - Ricerca sull'intelligenza artificiale specializzata al MIT

Imaging Informational Conflict: A Functional
Magnetic Resonance Imaging Study of
Numerical Stroop

J. Tang, H. D. Critchley, D. E. Glaser, R. J. Dolan, and B. Butterworth

Astratto

& We employed a parametric version of the comparison
Stroop paradigm to investigate the processing of numerical
magnitude and physical size under task-relevant and -irrelevant
conditions to investigate two theoretical issues: (1) What is the
fate of task-irrelevant information? (2) What is the
neural
neural basis of the resolution of the conflict between task-
relevant and -irrelevant information? We show in 18 healthy
adults that numerical magnitudes of numbers call for higher
processing requirements than physical sizes. The enhanced

activation elicited by numerical magnitudes is not modulated
by task relevance, indicating autonomous processing. More-
Sopra, the normal behavioral distance effect when the numerical
dimension is task relevant and reversed distance effect when it
is not show that autonomous processing fully encodes
numerical magnitudes. Conflict trials elicited greater activation
in bilateral inferior frontal gyri, right middle frontal gyri, E
right superior frontal gyri. We postulate two sources to the
conflict, namely, at cognitive and response levels. &

INTRODUCTION

Task-irrelevant information can interfere with perform-
ance. This was classically demonstrated by Stroop
(1935), using a task where naming the ink color of a word
is more error prone and slower when the word is a con-
flicting color word, Per esempio, where the word GREEN
is printed in red. This is now known as the ‘‘Stroop
effect.’’ Nevertheless, the majority of responses in Stroop
task performance are correct, indicating appropriate res-
olution of the conflict between task-relevant and task-
irrelevant information (Derbyshire, Vogt, & Jones, 1998;
Carter, Mintun, & Cohen, 1995; George et al., 1994; Bench
et al., 1993; Pardo, Pardo, Janer, & Raichle, 1990).

Functional neuroimaging experiments of Stroop inter-
ference effects potentially provide insight into two im-
portant general theoretical questions: (1) What is the
neural fate of task-irrelevant information? More specifi-
cally, are there qualitative or quantitative differences in
the activation patterns that can be assumed to imply
different cognitive processing, or is the processing of the
stimulus dimensions autonomous so that task does not
modulate neural activity? (2) What is the neural basis of
the resolution of the conflict between task-relevant and
-irrelevant information?

We suggest that the classical color-word task is not
well suited to answering these questions because the
competing dimensions are unbalanced. Although words

University College London, UK

interfere with color naming, color has little effect on
word naming: There is rarely a significant slowing when
naming the word ‘‘GREEN’’ printed in red, even when
color information has been manipulated to precede the
word by 400 msec (Glaser & Glaser, 1982). Inoltre,
it is impossible to order color names on a continuum, so
even if one is able to parametrically vary the hue of a
colore, it is impossible to have a parametric modulation
on the color name dimension.

The number Stroop task provides a more appro-
priate alternative, as described originally by Besner and
Coltheart (1979), and uses the dimensions numerical
magnitude and physical size. In a typical experiment,
both numerical magnitudes and physical sizes of the
numbers displayed vary; subjects have to select the
larger number in either the numerical or the physical
dimension. Trials may be congruent, where the nu-
merically larger number is physically larger (per esempio., 3 5);
incongruent, where the numerically larger number is
physically smaller (per esempio., 3 5); E, in some experiments,
neutral where the numbers are displayed in the same
size (per esempio., 3 5) for the numerical comparison task and
where the same numbers are displayed in different sizes
(per esempio., 3 3) for the physical comparison task. The Stroop
effect manifests as interference (an increase in reaction
time and/or error rate in incongruent trials compared
with neutral trials) and/or facilitation (a decrease in
reaction time and/or error rate in congruent trials
compared with neutral trials) (per esempio., Girelli, Lucangeli,
& Butterworth, 2000; Tzelgov, Meyer, & Henik, 1992;

D 2006 Istituto di Tecnologia del Massachussetts

Journal of Cognitive Neuroscience 18:12, pag. 2049–2062

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Foltz, Poltrock, & Potts, 1984; Henik & Tzelgov, 1982;
Besner & Coltheart, 1979). Facilitation is always sub-
stantially smaller than interference (for a review, Vedere
MacLeod, 1991).

A further advantage of the number Stroop task is that
it provides a metric for processing ‘‘refinement’’: IL
numerical distance effect (Moyer & Landauer, 1967).
This effect,
like other symbolic and nonsymbolic dis-
tance effects, means that it is harder to discriminate
similar stimuli than dissimilar stimuli. In caso di
numbers, similarity is on the semantic dimension of
numerical magnitude. Comparison times are inversely
related to the numerical distance between two numbers,
so that, Per esempio, 3 4 takes longer to compare than 3
5 (Moyer & Landauer, 1967), E, generally, compari-
sons times are well captured by the Welford function
(Zorzi & Butterworth, 1999, and see below). The dis-
tance effect holds for written number words (Foltz et al.,
1984) and dot patterns (Buckley & Gillman, 1974). Così,
the presence of a distance effect shows that processing
has gone beyond a mere large–small categorization and
that the numbers have been processed to a semantic
level that discriminates between the magnitudes of each
number (Tzelgov et al., 1992).

The effect can be observed in numerical Stroop
compiti (Pinel, Piazza, Le Bihan, & Dehaene, 2004; Fias,
Lammertyn, Reynvoet, Dupont, & Orban, 2003; Pinel,
Dehaene, Rivie`re, & Le Bihan, 2001; Foltz et al., 1984;
Hinrichs, Yurko & Eh, 1981; Duncan & MacFarland,
1980), but when physical size is manipulated as the
task-relevant dimension and numerical magnitude as
the task-irrelevant dimension, the numerical distance
effect can vanish (Rubinsten, Henik, Berger, & Shahar-
Shalev, 2002) or even reverse (Girelli et al., 2000; Henik
& Tzelgov, 1982). See below for an account of the
reversed distance effect.

In this study, we further examined the autonomous
aspect of numerical information processing. Autonomy,
by definition, is a property of automatic processes, Quello
È, processes that are fast, effortless, and unconscious
(per esempio., Logan, 1980; Shiffrin & Schneider, 1977; Posner &
Snyder, 1975). Here we use the concept autonomous to
refer to a process that takes place even when it is
irrelevant to the task at hand, so that it begins and runs
to completion without intention (Zbrodoff & Logan,
1986). The number Stroop paradigm is particularly well
suited to investigate the depth of processing because it
uses the distance effect and the reversed distance effect
as metrics.

A reversed distance effect in the task-irrelevant di-
mension (per esempio., Girelli et al., 2000; Henik & Tzelgov,
1982) does not necessarily suggest that information is
processed differently in the task-irrelevant channel. Fol-
lowing Girelli et al. (2000),
if both dimensions are
processed autonomously, conflict will arise only when
competing outcomes are simultaneously active. It takes
less time to generate a candidate response when the

distance is greater. Così, this candidate response in the
task-irrelevant dimension will be generated more quickly
to interfere with the generation of the task-relevant
risposta. Per esempio, selecting the numerically larger
item will be slower for 3 5 di 3 5 because it will
be quicker to resolve the size difference in the first
case. Infatti, the reversed distance effect, like the nor-
mal distance effect, can be construed as evidence that
the processing of numerical information has continued
autonomously to its normal completion.

There is already considerable evidence as to where
semantic processing of numbers is expressed in the
brain. Pinel et al. (2001) has described two distinct
stages of numerical processing, namely,
identification
and semantic processing. The ventral occipitotemporal
areas are activated bilaterally by the visual shapes of
Arabic numerals (Dehaene & Cohen, 1995) during the
identification process. Word identification is thought to
be strictly left lateralized and to rely on the left ‘‘visual
word form area,’’ a region of the left fusiform gyrus that
is involved in the recognition of visual words (Shallice,
1988). Tuttavia, Pinel and colleagues (Pinel et al., 2001;
Pinel et al., 1999) have provided evidence that the right
fusiform gyrus is implicated in the identification of
Arabic numerals.

Several studies implicate the parietal lobes in support-
ing a notation-independent semantic representation of
quantities (see Dehaene & Cohen, 1995, for a review).
More specifically, the intraparietal sulcus and the pre-
cuneus have been implicated in the comparison process
of numbers, and the activity of these regions is modu-
lated by the numerical distance effect—smaller numer-
ical distances associated with high activation levels (Pinel
et al., 2001). Pinel et al. (2004) extended these findings
to other nonsymbolic continua, such as physical size and
luminance. By using a number Stroop paradigm, Essi
reported that during the numerical comparison task, IL
numerical distance effect was associated with enhanced
bilateral activity of the horizontal segment of the intra-
parietal sulci and the left precentral gyrus. In contrasto,
during physical size comparisons with number stimuli,
correlates of the physical distance effect were found
predominantly in the right hemisphere, in particular the
right prefrontal and occipital cortices and much of the
right intraparietal sulcus. Intersections of the correlates
between numerical magnitude and physical size distance
effects were observed in bilateral regions of the anterior
intraparietal sulcus. The authors concluded that during
comparative judgements, these continuous quantities
are engaged in common parietal representations.

It is important to note that the studies by Pinel and
colleagues (Pinel et al., 2004; Pinel et al., 2001) rest on the
basic assumption that for any given task, the first stage
is to translate the input into the appropriate representa-
zione, and in the case of comparison, the stimuli are con-
verted to analogue representations of quantity (Dehaene,
1992). Although Pinel et al.’s (2004) findings support

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common parietal representations in processing numer-
ical magnitude and physical size, it was also observed
that comparative judgements of numerical magnitudes
yielded larger activation in several parietal regions (bilat-
eral inferior parietal foci and the left intraparietal sulcus)
than those of physical sizes. No explanation was provided
by the authors for such a difference.

Problems with Previous Studies
of Numerical Stroop

In previous number Stroop studies, the attended and
unattended dimensions are not properly balanced. For
esempio, nine numbers have been used to create two
levels of numerical distance, distant and close pairs (In
addition to distance 0 for neutral pairs), whereas three
physical sizes were often employed to create large,
piccolo, and neutral stimuli; hence, only one level of
physical distance (in addition to distance 0 for neutral
pairs) was used. This meant that the two competing
dimensions were not appropriately matched,
limiting
the inferences about the amount of information avail-
able in the task-relevant and -irrelevant channels (per esempio.,
Girelli et al., 2000; Henik & Tzelgov, 1982). Rubinsten
et al. (2002) used three levels of numerical distance
and two levels of physical distance, E, more recently,
Pinel et al. (2004) varied both numerical distance and
physical distance, but the stimuli were grouped in the
analyses, so that the factor distance consisted of only
two levels (distant and close pairs). With such a design,
Pinel et al. failed to observe any distance effect in either
numerical magnitude or physical size when they were
task irrelevant.

In the present experiment, we parametrically varied
both numerical distance and physical distance and test-
ed for distance effects under both task-relevant and
-irrelevant conditions. Here, we viewed distance effects
as indicators for refined information processing; Questo
contrasts with the coarse large–small dichotomous clas-
sification implicated by the Stroop effect.

Neural Basis of Conflict Resolution

Specific brain regions have been implicated in process-
ing and resolution of informational conflict from task-
irrelevant features. In particular, enhanced activation in
the anterior cingulate cortex (ACC) has been reported in
color-word Stroop tasks where subjects have to name
the color of a conflicting color word, Per esempio, IL
word GREEN printed in red, compared to a noncon-
flicting stimulus (per esempio., Derbyshire et al., 1998; Carter
et al., 1995; George et al., 1994; Bench et al., 1993;
Pardo et al., 1990). Allo stesso modo, greater ACC activation has
also been observed during incompatible compared to
compatible trials, in flanker tasks (per esempio., Durston et al.,
2003; Bunge, Dudukovic, Thomason, Vaidya, & Gabrieli,
2002; van Veen, Cohen, Botvinick, Stenger, & Carter;

2001; Casey et al., 2000; Hazeltine, Poldrack, & Gabrieli,
2000; Botvinick, Nystrom, Fissell, Carter, & Cohen,
1999). These findings have been interpreted as suggest-
ing a role in conflict resolution.

Tuttavia, more recent research has indicated that the
precise function of the ACC rests in the detection of
conflict, rather than in the resolution of conflict per se.
The model proposed by Botvinick, Braver, Barch, Carter,
and Cohen (2001) assumes that conflict monitoring
(per esempio., detection) influences cognitive control. In partic-
ular, during a period of high conflict, more attention is
directed to the relevant task, and if another conflict
follows close in time, less interference is expected due to
the already heightened state of the system. In other
parole, the model predicts that not only behavior, Ma
also ACC activation would be affected by (1) variations
in trial type frequency and (2) the preceding trial’s
trial type.

Evidence to support Botvinick et al.’s (2001) modello
has come from various types of interference tasks. In a
color-word Stroop task, Carter et al. (2000) reported
that ACC activation during incongruent trials was higher
when such trials were infrequent than when they were
frequent, paralleling the behavioral finding that incon-
gruent trials induced more conflict when such trials
were rare. Allo stesso modo,
in a flanker task, greater ACC
activation was observed in incompatible trials that fol-
lowed compatible trials than those that followed incom-
patible trials (Botvinick et al., 1999), a finding replicated
and extended by Durston et al. (2003). Inoltre, in un
go/no-go task, the increase in ACC activation to a no-go
trial is a function of increasing number of preceding go
trials (Durston et al., 2002). All these findings are
consistent with the involvement of the ACC in conflict
detection and support Botvinick et al.’s (2001) proposal
that high ACC activation triggers an increased attention
on the relevant task, leading to less interference in cases
where conflicts are frequent or consecutive.

Another well-established finding is that ACC activity has
been associated with error commission (per esempio., Critchley,
Tang, Glaser, Butterworth, & Dolan, 2005; Braver, Barch,
Gray, Molfese, & Snyder, 2001; Menon, Adleman, White,
Glover, & Reiss, 2001; Falkenstein, Hoormann, Christ,
& Hohnsbein, 2000; Kiehl, Kiddle, & Hopfinger, 2000;
Carter et al., 1998; Gehring, Goss, Coles, Meyer, &
Donchin, 1993; for a review, see Botvinick, Cohen, &
Carter, 2004). Behavioral and electromyographic obser-
vations indicate that errors in speeded response tasks
are frequently associated with response conflict (Yeung,
Botvinick, & Cohen, 2004). The reason that errors are
committed even when there is a conflict detection system
is that even as an error response is being executed,
ongoing processing of the stimulus often leads to a
belated activation of the correct response, giving rise to
a transient period during with both correct and incorrect
responses are activated. Così, ACC activation during er-
rors reflects the detection of a postresponse conflict.

Tang et al.

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Conflict can occur at numerous levels of information
processing, ranging from perceptual representation to
response selection. Several studies have reported that
the ACC is engaged most strongly during conflicts at
the level of response selection (Milham, Banich, &
Barad, 2003; Nelson, Reuter-Lorenz, Sylvester, Jonides,
& Smith, 2003; Weissman, Giesbrecht, Song, Mangun, &
Woldorff, 2003; Bunge et al., 2002; Milham et al., 2001;
van Veen et al., 2001). D'altra parte, there was a
lack of substantial ACC activation when comparing be-
tween conflict and nonconflict trials in a color-word
matching Stroop task (Zysset, Mu¨ller, Lohmann, & von
Cramon, 2001). Invece, Zysset et al. (2001) observed
enhanced activation in regions along the left inferior
frontal sulcus (IFS) during conflict trials compared to
nonconflict trials (neutral and congruent trials) and con-
cluded that ‘‘regions along the IFS appear to be involved
in solving interference effect and task management.’’

Research employing other paradigms supports this.
Go/no-go and stop-signal tasks require subjects to per-
form speeded responses on ‘‘go’’ trials and to inhibit
their response on ‘‘no-go’’ or ‘‘stop’’ trials. Such re-
sponse inhibition has been reported to activate regions
along the right inferior frontal gyrus in neuroimaging
studies (per esempio., Bunge et al., 2002; Durston et al., 2002;
Menon et al., 2001; Garavan, Ross, & Stein, 1999; Rubia
et al., 1999; Konishi, Nakajima, Uchida, Sekihara, &
Miyashita, 1998, 1999). In some studies, enhanced acti-
vation was observed bilaterally (per esempio., Menon et al., 2001).
The idea that ACC activation is associated with conflict
detection suggests an effect on attentional allocation (for
a review, see Botvinick et al., 2004). D'altra parte,
there is evidence to suggest that regions in the inferior
frontal cortex are responsible for inhibiting prepotent
responses (per esempio., Bunge et al., 2002; Durston et al., 2002;
Menon et al., 2001; Garavan et al., 1999; Rubia et al., 1999;
Konishi et al., 1998, 1999) and are perhaps involved in
conflict resolution (Zysset et al., 2001). More recently,
van Veen and Carter (2005) reported distinct neural sub-
strates for cognitive (semantic) interference and response
conflict in a modified color-word Stroop task. Bilateral
middle frontal gyri, right superior frontal gyrus, and the
ACC were activated in response to cognitive interference.
Response conflict activated the bilateral middle/inferior
frontal gyri and a more anterior region in the ACC. Contro-
junction analysis revealed no overlap in activation be-
tween the two contrasts.

The present study investigates the neural fate of task-
irrelevant information using a modified version of the
number Stroop paradigm with two comparable dimen-
sions, namely, numerical magnitude and physical size.
The parametric design allows us to vary and measure
systematically the amount of interference exerted by
the task-irrelevant channels during conflict trials in
each of the comparison tasks, and hence characterize
the information-processing fate of task. A reversed nu-
merical distance effect in physical comparisons would

indicate that exact numerical values had been com-
puted despite task irrelevance (Girelli et al., 2000; Henik
& Tzelgov, 1982). Inoltre, the current design al-
lows us to test, for the first time, for a reversed physical
distance effect in numerical comparisons (cioè., task-
irrelevant condition). The reversed effects are indicators
for autonomous information processing.

In terms of brain activation, parietal activation levels
were predicted to be inversely related to numerical
distance in line with previous findings (Pinel et al.,
2004; Pinel et al., 2001). The key issue in the experiment
was whether task relevance modulates parietal activity. If
the fate of task-irrelevant information in this task was
autonomous processing, then an absence of a modula-
tion would be suggestive. The second key issue was to
identify the neural basis of the resolution of the conflict
between task-relevant and irrelevant information. Again,
balanced dimensions in a parametric design could reveal
activations specific to conflict and to errors arising from
conflict. We expected that conflict and errors would
modulate activity in frontal rather than parietal regions
where numbers and size are primarily represented.

METHODS

Tasks

The two tasks were numerical magnitude and physical size
comparisons. Subjects had to select the larger number
numerically or physically according to the task require-
ment. Subjects responded by pressing the left or right
button to indicate the side of the larger relevant attribute.
Reaction times and responses were recorded. A program
written in Cogent (which runs on a MATLAB Version 6.1
platform; The MathWorks, Natick, MA) was used.

Stimuli

The stimuli, presented on a screen situated outside
the scanner, were reflected onto a mirror (of size 20 (cid:1)
9 cm2) placed inside the scanner. In each trial, two di-
gits appeared simultaneously in white on a black back-
ground. Each presentation lasted 1000 msec with an
interstimulus interval of 3000 msec.

The stimuli were Arabic digits (1 A 9) in Arial font.
Each digit might appear in one of the nine different sizes
(subtending from approximately 3.88 A 9.78 with a mean
ratio of 1.1 between adjacent sizes). Four numerical
distances (ND = 1, 2, 3, E 4) and four physical
distances (PD = 1, 2, 3, E 4 units) were used. IL
pairs used were as follows: 2 3, 3 4, 6 7, 7 8 (for ND of 1);
1 3, 2 4, 6 8, 7 9 (for ND of 2); 1 4, 2 5, 5 8, 6 9 (for ND of
3); 1 5, 2 6, 4 8, 5 9 (for ND of 4). The equivalent physical
sizes were used to systematically vary PD.

There were three experimental conditions: congru-
ent, when the numerically larger digit was physically
larger (per esempio., 2 6); incongruent, when the numerically

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larger digit was physically smaller (per esempio., 2 6) or vice
versa; and neutral, when the two digits were of the
same physical size in the numerical comparison task
(per esempio., 2 6) or when the same digit appeared in different
sizes in the physical comparison task (per esempio., 2 2).

The total number of trials in each task was 217 (cioè., 64
congruent + 64 neutro + 64 incongruent + 25 blank =
217 trials). Stimuli were presented in a pseudorandom
order to avoid carryover effects.

Subjects

There were 18 right-handed subjects (11 men and 7
women), aged 21 A 38 years (M = 25.0 years, SD =
4.01 years). They performed two tasks (numerical and
physical comparison tasks); half of them participated in
the numerical task first, and the other half in the phys-
ical task first. All subjects had normal or corrected-to-
normal eyesight.

Scanning Procedures and Imaging
Data Processing

Whole-brain functional magnetic resonance imaging
(fMRI) data was acquired on a 1.5-T Magnetom VISION
system (Siemens Sonata, Erlangen, Germany). Function-
al
images were obtained with a gradient-echo-planar
sequence using blood oxygenation level-dependent
(BOLD) contrasto, each comprising a full-brain volume
Di 28 contiguous axial slices, 3.5-mm thickness). Vol-
umes were acquired continuously with a repetition time
(TR) Di 2.52 sec. A total of 275 scans were acquired for
each participant in two sessions (approximately 10 min
each), with the first six volumes subsequently discarded
to allow for T1 equilibration effects. During fMRI scan-
ning, pupil diameter was recorded online by an in-
frared eye tracker. The data were analyzed using SPM2
(Wellcome Department of Imaging Neuroscience; www.
fil.ion.ucl.ac.uk/spm) implemented in MATLAB 6.1.0.450
Release 12.1. Individual scans were realigned, slice time
corrected, normalized to the MNI template with voxels
Di 2 (cid:1) 2 (cid:1) 2 mm3 and spatially smoothed by an 8-mm
full width half-maximum (FWHM) Gaussian kernel using
standard SPM methods.

Event-related activity for each voxel, for each condi-
tion and each subject was modeled using a canonical
hemodynamic response function plus temporal and
dispersion derivatives. Statistical parametric maps of
the t statistic (SPM{T}) were generated for each subject
and the contrast images were further smoothed by an
8-mm FWHM Gaussian kernel.

At the second-level random-effects analysis, UN 2 (cid:1) 4
analysis of variance (ANOVA) model was applied; IL
factors were task (numerical comparison task and phys-
ical comparison task) and trial type (congruent, neutro,
incongruent, and error trials). Congruent and incon-

gruent trials were modeled parametrically with respect
to task-relevant and task-irrelevant distance, and neu-
tral trials were modeled parametrically with respect
to task-relevant distance. This allowed us to construct
t contrasts to test specifically for distance-modulated ac-
tivities. Our model was optimized to detect linear in-
crease/decrease in activities related to numerical and/
or physical distance. In the present study, congruent
and neutral trials were classified as nonconflict trials,
whereas incongruent trials were conflict trials. To com-
pare between conflict and nonconflict trials, and error
and correct trials in each task, t contrasts were con-
structed. Threshold significance was set at .001 uncor-
rected for multiple comparisons.

RESULTS

Behavioral Data

Errors were incorrect responses made in the compari-
son tasks, questo è, trials where subjects pressed the
wrong key. Reaction time outliers were identified by
the standard SPSS procedure (values that lay more than
1.5 times the interquartile range above the third quartile
O 1.5 times the interquartile range below the first
quartile) and removed. ANOVAs were used to analyze
mean error rates and mean reaction times, and when-
ever Mauchly’s test of sphericity assumption was violat-
ed, the Greenhouse–Geisser epsilon was used to correct
the degrees of freedom. UN 2 (cid:1) 3 repeated measures
ANOVA was conducted on mean error rates. The factors
were task (numerical comparison task and physical
comparison task) and congruent (congruent, neutro,
and incongruent). The ANOVA revealed a significant
main effect of congruity, F(1,22) = 38.10, p = .001; UN
nonsignificant main effect of task, F(1,17) = 3.34, ns;
and a nonsignificant Task (cid:1) Congruity interaction,
F(1,21) < 1, ns. Tests of within-subjects contrasts re- vealed a significant difference in error rates between incongruent and neutral trials, F(1,17) = 52.00, p < .001, and a nonsignificant difference between neutral and congruent trials, F(1,17) < 1, ns. The mean error rates were 11.55%, 4.43%, and 3.95%, respectively. A 2 (cid:1) 3 repeated measures ANOVA was conducted on mean reaction times. The factors were task (numerical and physical comparison tasks) and congruent (congru- ent, neutral, and incongruent). The ANOVA revealed a significant main effect of task, F(1,17) = 16.55, p = .001, a significant main effect of congruity, F(2,34) = 156.62, p < .001, and a significant Task (cid:1) Congruity interaction, F(2,34) = 8.07, p = .001. The mean reaction times for numerical and physical comparison tasks were 617 and 570 msec, respectively. Considering only the numerical comparison task, the main effect of congruity was significant, F(2,34) = 112.52, p < .001. Tests of within-subjects contrasts revealed a significant difference between congruent Tang et al. 2053 D o w n l o a d e d f r o m l l / / / / / j f / t t i t . : / / D h t o t w p n : o / a / d m e i d t f p r o r m c . h s i p l v d e i r r e c c h t . a m i r e . d c u o m o / c j n o a c r n t i c / a e r - p t d i c 1 l 8 e 1 - 2 p 2 d 0 f 4 / 9 1 8 1 / 9 1 3 5 2 6 / 8 2 7 0 4 o 9 c / n 1 2 7 0 5 0 5 6 9 1 9 8 9 / 1 j 2 o 2 c 0 n 4 . 9 2 p 0 d 0 6 b . y 1 g 8 u . e 1 s 2 t . o 2 n 0 0 4 8 9 S . e p p d f e m b b y e r g 2 u 0 e 2 s 3 t / j t . . . . . f o n 1 8 M a y 2 0 2 1 and neutral trials, F(1,17) = 47.84, p < .001, and between the latter and incongruent trials, F(1,17) = 81.60, p < .001. The mean reaction times were 585, 614, and 652 msec, respectively. Similarly for the phys- ical comparison task, the main effect of congruity was significant, F(2,34) = 41.62, p < .001. Tests of within- subjects contrasts revealed a significant difference be- tween congruent and neutral trials, F(1,17) = 5.16, p < .050, and between the latter and incongruent trials, F(1,17) = 56.16, p < .001. The mean reaction times were 553, 564, and 593 msec, respectively. Further analyses were conducted on mean reaction times to test for distance effects in both the task-relevant and -irrelevant dimensions for each task focusing on incongruent trials, because only here was there infor- mational conflict. For the numerical comparison task, a 2 (cid:1) 4 repeated measures ANOVA was conducted on mean reaction times of the incongruent trials. The fac- tors were task relevance (task-relevant and -irrelevant) and distance (1, 2, 3, and 4). The ANOVA revealed a significant Attention (cid:1) Task Relevance interaction, F(3,51) = 13.02, p < .001. There was no significant main effect (all nonsignificant). Further analyses were conducted at each level of task relevance. At the task-relevant level, the factor distance (in this case, the numerical distance) showed a significant main effect, F(3,51) = 8.61, p < .001. Tests of within-subjects contrasts revealed a significant negative linear trend for this factor, F(1,17) = 19.20, p < .001 (see Figure 1). No other trend was significant. At the task-irrelevant level, the factor distance (in this case, the physical dis- tance) showed a significant main effect, F(3,51) = 4.78, p = .005. Tests of within-subjects contrasts revealed a significant positive linear trend for this factor, F(1,17) = 7.51, p < .050 (see Figure 1). No other trend was significant. When considering the physical comparison task, we conducted a 2 (cid:1) 4 repeated measures ANOVA on mean reaction times of the incongruent trials. The factors were task relevance (task-relevant and -irrelevant) and dis- tance (1, 2, 3, and 4). The ANOVA revealed a significant main effect of task, F(1,17) = 19.11, p < .001, a Figure 1. Distance effects in task-relevant and -irrelevant dimensions of the numerical magnitude comparison task. Figure 2. Distance effects in task-relevant and -irrelevant dimensions of the physical size task. significant main effect of distance, F(3,51) = 16.26, p < .001, and a significant Attention (cid:1) Task Relevance interaction, F(3,51) = 55.58, p < .001. Further analyses were conducted at each level of task relevance. At the task-relevant level, the factor distance (in this case, the physical distance) showed a significant main effect, F(2,33) = 53.49, p < .001. Tests of within-subjects contrasts revealed a significant negative linear trend, F(1,17) = 96.44, p < .001, and a significant quadratic trend, F(1,17) = 8.98, p < .010, for this factor (see Figure 2). At the task-irrelevant level, the factor distance (in this case, the numerical distance) showed a signifi- cant main effect, F(3,51) = 7.59, p < .001. Tests of within-subjects contrasts revealed a significant positive linear trend, F(1,17) = 30.95, p < .001 (see Figure 2). No other trend was significant. In summary, during conflict trials, the task-relevant dimension showed a classic distance effect (indicated by a negative linear trend), whereas the task-irrelevant dimension showed a reversed distance effect (indicated by a positive trend), regardless of task. Functional Imaging Data Functional imaging data analysis at the first level allowed for neural responses associated with congruent, neutral, incongruent, and error trials to be modeled indepen- dently. Second-level t contrasts were constructed to test for brain regions associated with the parametric modu- lation of numerical distance and physical distance during neutral conditions. An F contrast was then constructed to compare processing of the two dimensions. Analysis on the conflict trials allowed us to test for a Task (cid:1) Distance interaction. To identify regions involved in conflict and error trials, t contrasts were used. Conjunc- tion analyses by inclusive masking were also performed to identify common regions for conflict and error pro- cessing across numerical and physical comparison tasks. Brain activations are summarized in Tables 1–3. Voxels reported are in Talairach coordinate space. In neutral trials, distance only varied parametrically in the task-relevant dimension, that is, only numerical 2054 Journal of Cognitive Neuroscience Volume 18, Number 12 D o w n l o a d e d f r o m l l / / / / / j f / t t i t . : / / D h t o t w p n : o / a / d m e i d t f p r o r m c . h s i p l v d e i r r e c c h t . a m i r e . d c u o m o / c j n o a c r n t i c / a e r - p t d i c 1 l 8 e 1 - 2 p 2 d 0 f 4 / 9 1 8 1 / 9 1 3 5 2 6 / 8 2 7 0 4 o 9 c / n 1 2 7 0 5 0 5 6 9 1 9 8 9 / 1 j 2 o 2 c 0 n 4 . 9 2 p 0 d 0 6 b . y 1 g 8 u . e 1 s 2 t . o 2 n 0 0 4 8 9 S . e p p d f e m b b y e r g 2 u 0 e 2 s 3 t / j t . . . . . f o n 1 8 M a y 2 0 2 1 distance was manipulated in the numerical task, and only physical distance in the physical task. No parietal region parametrically modulated by numerical distance or physical distance during these trials were revealed by t contrasts. However, the F contrast (see Table 1) comparing the processing of numerical distance and physical distance during neutral trials revealed several parietal regions that showed enhanced activation in processing numerical relative to physical distance in- cluding the right inferior parietal lobule [40 (cid:2)39 42], right precuneus [22 (cid:2)64 42], right inferior parietal lobule [32 (cid:2)56 45], and left superior parietal lobule [(cid:2)22 (cid:2)66 46], as well as the bilateral inferior frontal gyri and right temporal and occipital regions (see Table 1 and Figure 3). Small volume correction searches (5-mm radius) were performed with reference to Pinel et al. (2004) and revealed that the right inferior parietal lobule [38 (cid:2)41 43] also showed enhanced activation processing numerical distance compared to physical distance. No enhanced activation was observed processing physical distance relative to numerical distance. Conjunction by inclusive masking across the two tasks revealed no commonly activated voxel. However, the parietal regions that showed enhanced activation processing numerical relative to physical dis- tance were not affected by task requirement during conflict trials. The F contrast constructed to test for a Task (numerical task and physical task) (cid:1) Dimension (numerical distance and physical distance) revealed no significant difference in parietal activation. To test for differences in brain activity between con- flict and nonconflict trials, t contrasts were constructed (see Table 2). In the numerical task, enhanced activation in conflict trials compared to nonconflict trials was observed in right inferior frontal [44 9 31] and middle frontal [36 52 (cid:2)14] gyri, left fusiform gyrus [(cid:2)44 (cid:2)49 (cid:2)13], right occipital lobe [34 (cid:2)76 (cid:2)1], and various other regions. In the physical task, enhanced activation in conflict trials was observed only in the left inferior frontal gyrus [(cid:2)40 30 8]. Conjunction by inclusive masking across the two tasks revealed no commonly activated voxel. To test for differences in brain activity between error and correct trials, t contrasts were con- structed (see Table 3). Conjunction by inclusive masking (corrected for familywise error at 0.05) was performed across task and revealed enhanced activation in error trials compared to correct trials in bilateral inferior frontal gyri: left [(cid:2)32 17 (cid:2)11] and right [42 27 (cid:2)6], and several regions along the bilateral superior temporal gyri (see Table 3). DISCUSSION In the present experiment we examined processing of numerical magnitude and physical size using bidimen- sional stimuli. By varying the two dimensions, we were able to create conflicting situations as well as systemat- ically vary the amount of interference for each of task- relevant dimensions. We made efforts to match the two Table 1. An F Contrast Revealed Regions that Showed Enhanced Activation when Processing Numerical Distance Compared with Physical Distance Talairach Coordinates Voxels z Score x y z Brain Area F contrast (numerical distance > physical distance)

758

169

501

23 (SVC)

4.72

3.86

3.69

3.68

3.53

3.45

3.39

3.22

3.67

(cid:2)36

(cid:2)22

(cid:2)77

(cid:2)39

(cid:2)64

(cid:2)56

(cid:2)53

(cid:2)61

(cid:2)66

(cid:2)41

(cid:2)3

(cid:2)9

Right frontal lobe; inferior frontal gyrus; white matter

Left frontal lobe; inferior frontal gyrus; gray matter; BA 47

Right occipital lobe; middle occipital gyrus; white matter

Right parietal lobe; inferior parietal lobule; gray matter; BA 40

Right parietal lobe; precuneus; white matter

Right parietal lobe; inferior parietal lobule; white matter

Right temporal lobe; subgyral; white matter

Right occipital lobe; subgyral; white matter

Left parietal lobe; superior parietal lobule; gray matter; BA 7

Right inferior parietal lobule

No significant voxel was found in the opposition direction. Regions that showed enhanced activation under task-relevant conditions compared
with task-irrelevant conditions with respect to increasing distance in numerical and physical distance were revealed by t contrasts. BA =
Brodmann’s area; SVC = small volume correction.

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Figura 3. Parietal regions showing enhanced activation when processing numerical distance relative to physical size (clockwise from top
left: regions in the right inferior parietal lobule ([40 (cid:2)39 42] E [32 (cid:2)56 45]), right precuneus [22 (cid:2)64 42], and left superior parietal
lobule [(cid:2)22 (cid:2)66 46]).

dimensions by difficulty. In terms of error commission,
the two tasks did not differ in either rate or pattern.
Tuttavia, with respect to reaction times, the physical
comparison task was significantly faster than the numer-
ical comparison task. Such a difference could be ex-
plained by the different nature of these tasks—physical
size comparisons require processing at the perceptual
level, whereas numerical magnitude comparisons re-
quire higher cognitive processing. On this basis, it is

not surprising that processing time was shorter for
the former. It is important to note that the two tasks
showed the same reaction time patterns with respect
to congruity—significant interference and facilitation in
both numerical and physical tasks; in other words, IL
classical Stroop effect. Although not perfectly matched
in terms of reaction time, the Stroop effect was observed
in both tasks, indicating that two directions influenced
one another and, hence, the present paradigm is a more

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Volume 18, Numero 12

Tavolo 2. Regions Revealed by t Contrasts Showed Enhanced Activation during Conflict Trials Compared with Nonconflict
Trials in Numerical and Physical Comparison Tasks

Voxels

z Score

sì

Brain Area

Numerical task conflict trials > numerical task nonconflict trials—t contrast

Talairach Coordinates

224

112

613

4.32

4.08

3.93

3.60

3.73

3.66

3.43

3.42

3.28

3.25

(cid:2)10

(cid:2)22

(cid:2)44

(cid:2)48

(cid:2)5

(cid:2)17

(cid:2)76

(cid:2)49

(cid:2)14

(cid:2)1

(cid:2)13

Right superior parietal lobule; BA 7

Left superior frontal gyrus; BA 6

Right thalamus; ventral anterior nucleus

Right sublobar; lentiform nucleus; putamen

Right sublobar; caudate; caudate head

Right superior frontal gyrus

Left sublobar; extranuclear

Right middle frontal gyrus

Right occipital lobe; subgyral

Left fusiform gyrus

Right inferior frontal gyrus

Physical task conflict trials > physical task nonconflict trials—t contrast

3.20

(cid:2)40

Left inferior frontal gyrus

suitable choice for studying informational conflict than
the traditional color-word task in which direction of
influence is unidirectional—from word to color.

The Stroop effect we observed is consistent with the
number Stroop literature (Girelli et al., 2000; Tzelgov
et al., 1992; Foltz et al., 1984; Henik & Tzelgov, 1982;
Besner & Coltheart, 1979). Così, subjects were unable
to ignore the irrelevant information regardless of task.
Facilitation was reflected by reaction times but not error
rates, consistent with the general finding in the Stroop
literature that facilitation is virtually always substantially
smaller than interference (see review, MacLeod, 1991).
Distance effects (indicated by negative linear trends)
were observed in task-relevant channels, questo è, numer-
ical distance effect in the numerical task and physical
distance effect in the physical task. Reversed distance
effects were observed in both tasks, questo è, a reversed
numerical distance effect in the physical task (consistent
with Girelli et al., 2000; Henik & Tzelgov, 1982) and the
novel finding of a reversed physical distance effect in the
numerical task. Because distance effect was used as an
indicator of refined information processing, the ob-
served reversed distance effects under task-irrelevant
conditions suggest that numerical distance and physical
distance are processed in an autonomous fashion, sim-
ilar to task-relevant processing.

As proposed in the Introduction, the reversed dis-
tance effect can be explained in terms of amount of
interference. Information that would normally require

little effort to process under task-relevant conditions
(per esempio., the salient difference between two numbers with
a large physical distance) is harder to ignore under
task-irrelevant conditions (per esempio.,
in numerical compari-
figlio). In contrasto, information that requires more effort
to process under task-relevant conditions (per esempio., numer-
ical comparison of two numerically close numbers)
would exert little interference when such information
is to be ignored under task-irrelevant conditions (In
physical comparison).

Our brain imaging data revealed that when the task-
irrelevant dimensions were kept constant (cioè., in neutral
trials), the parietal lobes (regions in the right inferior
parietal lobule, right precuneus, and left superior pari-
etal lobule) showed enhanced activation when process-
ing numerical distance compared to physical distance.
This extends the findings of Pinel et al. (2004) who
observed enhanced activation in parietal lobes (regions
in bilateral
inferior parietal foci and left intraparietal
sulcus) during numerical comparisons compared to
physical comparisons, implying a processing difference
between numerical and physical dimensions.

Although there was no evidence to suggest that
processing numerical magnitude and physical size acti-
vated different parietal regions, the enhanced activa-
tion when processing numerical distance relative to
physical distance indicates a quantitative difference in
the processing of these two dimensions. This is consist-
ent with (although does not demonstrate) the distinction

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Tavolo 3. Regions Revealed by t Contrasts Showed Enhanced Activation during Error Trials Compared with Correct Trials
in Numerical and Physical Comparison Tasks

Voxels

z Score

sì

Numerical task error trials > numerical task correct trials—t contrast

Talairach Coordinates

2107

1200

619

3058

341

127

392

166

6.88

5.52

5.32

3.99

4.93

4.66

4.56

4.47

4.08

4.13

4.03

3.70

3.65

3.46

3.34

3.25

3.17

(cid:2)32

(cid:2)51

(cid:2)4

(cid:2)18

(cid:2)50

(cid:2)46

(cid:2)26

(cid:2)59

(cid:2)42

(cid:2)26

(cid:2)46

(cid:2)15

(cid:2)77

(cid:2)22

(cid:2)2

(cid:2)5

(cid:2)31

Physical task error trials > physical task correct trials—t contrast

1807

1837

909

335

149

5.83

5.08

5.00

4.43

4.89

4.15

4.04

(cid:2)34

(cid:2)16

(cid:2)42

(cid:2)27

(cid:2)73

(cid:2)35

(cid:2)7

(cid:2)11

(cid:2)29

(cid:2)6

(cid:2)29

(cid:2)25

(cid:2)19

(cid:2)18

(cid:2)5

(cid:2)9

(cid:2)11

(cid:2)25

(cid:2)35

Brain Area

Right superior temporal gyrus

Right temporal subgyral

Left inferior frontal gyrus; BA 47

Left superior frontal gyrus

Right inferior frontal gyrus

Right inferior frontal gyrus; BA 45

Right superior temporal gyrus

Right thalamus; medial dorsal nucleus

Left thalamus; medial dorsal nucleus

Left postertior lobe; uvula

Interhemispheric

Right brainstem; pons

Left precentral gyrus; BA 6

Right temporal subgyral

Left frontal subgyral

Left inferior parietal lobule

Right superior temporal gyrus

Right middle temporal gyrus

Right inferior frontal gyrus

Right inferior frontal gyrus; BA 47

Left inferior frontal gyrus; BA 47

Left posterior lobe; uvula

Right brainstem; medulla

Conjunction by masking across tasks (error trials > correct trials), corrected for family wise error at .050

715

181

6.88

5.52

5.32

4.93

4.66

(cid:2)32

(cid:2)51

(cid:2)42

(cid:2)26

(cid:2)46

(cid:2)7

(cid:2)11

(cid:2)6

Right superior temporal gyrus

Right superior temporal subgyral

Left inferior frontal gyrus; BA 47

Left superior temporal gyrus

Right inferior frontal gyrus

A conjunction (by inclusive masking) across the two tasks revealed regions that were commonly activated during error trials.

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made by Zorzi and Butterworth (1999) between numer-
ical magnitudes that are conceptualized as ‘‘discrete
numerosities’’ and physical sizes that are represented
in an analogue (or continuous) fashion, and with the
suggestion that comparative judgements on discrete
numerosity representations evoked by numbers call for
higher processing requirements compared with those
on analogue representations evoked by physical sizes.
We postulate that the processing streams of these two
types of representation converge at a cognitive level
(where conflict occurs when the streams of information
are incompatible).

In line with our a priori prediction, the parietal
regions (in right inferior parietal lobule, right precuneus,
and left superior parietal lobule) that showed enhanced
activation processing numerical relative to physical dis-
tance were not affected by task requirement in conflict
situations. In other words, these parietal regions were
equally active whether or not required by the task to
process numerical magnitudes. The lack of difference in
parietal activation level across numerical and physical
comparison tasks provides a strong evidence for auton-
omous processing of numerical magnitude.

È interessante notare, we found no evidence to suggest that
parietal activation was parametrically modulated by ei-
ther numerical or physical distance. This appears in-
consistent with numerical-distance-modulated parietal
regions identified by Pinel and colleagues (Pinel et al.,
2004; Pinel et al., 2001). Tuttavia, a closer look their
findings suggests that the numerical-distance-modulated
parietal activation might not be as robust as the authors
claimed. In the Pinel et al. (2001) study, numerical
distances were not modeled parametrically. The re-
ported distance-modulated parietal activation was in fact
a main effect of distance (across three levels) piuttosto che
a significant linear decrease in activation with increasing
numerical distance. When masking the main effect of
distance for close > medium and medium > far, IL
only surviving significant region was in the precuneus.
Inoltre, the reported numerical distance-modulated
parietal regions in the bilateral intraparietal sulci and the
right precuneus were from a single-subject analysis. Of
the four subjects tested, only two showed these effects;
one failed to show any strong correlation between brain
activation and numerical distance. The inconsistent find-
ings cast doubts on whether parietal activation is truly
modulated by numerical distance.

The current paradigm is arguably more complex than
that used by Pinel et al. (2001), and this could mean that
any numerical-distance-modulated parietal activation was
less likely to emerge. Pinel et al. (2001) used a compar-
ison task to a fixed reference, in which subjects had to
judge whether a visually presented number was smaller
or larger than the reference (65). Such a task is probably
easier than the current paradigm that involves comparing
bidimensional stimuli. Because Pinel et al.’s stimuli only
varied in one dimension (numerical magnitude), there

was neither irrelevant information nor conflict to influ-
ence subjects’ judgements, and the subjects were likely to
perform the task without much difficulty.

When confronted with a conflict, subjects had to
inhibit the task-irrelevant information in order to per-
form the task correctly. The enhanced activation in the
right inferior frontal gyrus in conflict trials compared to
nonconflict trials during numerical comparisons is con-
sistent with findings in go/no-go and stop-signal tasks
(per esempio., Bunge et al., 2002; Menon et al., 2001; Garavan
et al., 1999; Rubia et al., 1999; Konishi et al., 1998, 1999).
In Durston et al.’s (2002) go/no-go task, activity associ-
ated with successful response inhibition extended to the
right middle frontal gyrus. In the current experiment,
enhanced activation in this area was also observed in
conflict trials during numerical comparisons. The cur-
rent findings provide support for the suggestion that
regions in the inferior frontal cortex are responsible for
inhibiting prepotent responses and perhaps even con-
flict resolution.

The left fusiform gyrus showed enhanced activation in
conflict trials relative to nonconflict trials during numer-
ical comparisons. Such activation does not only reflect
the recognition of the visual shapes of the numbers, Ma
also suggests that the computation over the perceptual
properties of the numbers interacted with the semantic
processing of the numbers during numerical compari-
sons. This suggestion is further supported by the en-
hanced activation in the right occipital lobe—an area
involved in visual processing—in conflict trials during
numerical comparisons.

During physical comparisons, enhanced activation
in the left inferior frontal gyrus was observed in conflict
trials relative to nonconflict trials, but there was no evi-
dence to suggest that differential activity in the visual
cortex, supporting the idea that the source of inter-
ference comes from higher cognitive processing of the
numbers.

There was also evidence to suggest that conflict may
also occur at the response level. In van Veen and
Carter’s (2005) study, bilateral middle frontal gyri and
right superior frontal gyrus were activated in response to
cognitive interference, whereas response conflict acti-
vated the bilateral middle/inferior frontal gyri. The acti-
vations observed in this study—bilateral inferior frontal
gyri, right middle and right superior frontal gyri—imply
that there were two sources to the conflict, namely, at
cognitive and response levels.

No evidence was found to support an involvement of
the ACC in conflict resolution. Small volume correction
searches (5-mm radius) were performed with reference
to ACC coordinates identified by Menon et al. (2001),
van Veen et al. (2001), Bush et al. (1999), and Barch et al.
(1997), but no significant voxel was found. This appears
inconsistent with van Veen and Carter’s (2005) trovare
that different parts of the ACC were involved in cognitive
interference and response conflict. Tuttavia, in a related

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article using the present paradigm (Critchley et al.,
2005), we constructed a model optimized for the detec-
tion of ACC activation and reported such an activation
during conflict trials. Critchley et al. (2005) reported a
region in the ACC [6 22 38] very close to that reported
by van Veen and Carter during semantic conflict [7 18
42]. This provides strong evidence for a semantic level
conflict. Nonetheless, we have stated earlier that there
was another possible source of conflict, namely, at the
response level, which has been reflected by the activa-
tion in bilateral inferior frontal gyri.

Inoltre, we found no evidence to support the in-
volvement of the ACC in error commission. We per-
formed small volume correction searches (5-mm radius)
with reference to ACC coordinates identified by Menon
et al. (2001), who reported its associated activity with
error processing and found no significant effects. Noi
have proposed an alternative explanation that the
ACC acts as an interface between cognitive and bio-
behavioral systems based on evidence that its activation
strongly predicted trial-by-trial variability in autonomic
response magnitude (reflected by changes in pupil size)
that peaked during error trials (Critchley et al., 2005).

In summary, we set out to investigate whether nu-
merical magnitude and physical size are processed in an
autonomous fashion. By parametrically varying the
amount of interference exerted by the task-irrelevant
dimension on the task-relevant one in either task, UN
reversed distance effect—the indicator of refined infor-
mation processing—was observed in each of the dimen-
sions when these were task irrelevant. Such a novel
finding strongly supports autonomous, refined infor-
mation processing in both dimensions. The reversed
distance effect appears to be a robust indicator of
information processing and may prove to be a more
sensitive measure than the Stroop effect itself in Stroop
variants where an interference effect is not easily elic-
ited. Parietal regions have been described as compris-
ing a notation-independent representation of their
semantic content as quantities (Dehaene & Cohen,
1995). We found no evidence to suggest that parietal
regions were modulated by numerical distance. How-
ever, we provided strong evidence for the autono-
mous processing of numerical magnitude. Finalmente, we
conclude that prefrontal regions, especially bilateral
inferior frontal and right middle frontal gyri, are asso-
ciated with conflict resolution when these sources of
conflict could come from both cognitive and response
levels.

Ringraziamenti

This research was supported by the Wellcome Trust via a
program grant to H. D. C. and R. J. D.

Reprint requests should be sent to Joey Tang, Institute of
Cognitive Neuroscience, Alexandra House, 17 Queen Square,
London WC1N 3AR, UK, or via e-mail: joey.tang@ucl.ac.uk.

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2062

Journal of Cognitive Neuroscience

Volume 18, Numero 12 Imaging Informational Conflict: A Functional image

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