Neuropsychologia (xxxx) xxxx–xxxx

Contents lists available at ScienceDirect

Neuropsychologia journal homepage: www.elsevier.com/locate/neuropsychologia

Are numbers grounded in a general magnitude processing system? A functional neuroimaging meta-analysis H. Moriah Sokolowskia, Wim Fiasb, Chuka Bosah Ononyea, Daniel Ansaria, a b



University of Western Ontario, London, Ontario, Canada Ghent University, Ghent, Belgium

A R T I C L E I N F O

A BS T RAC T

Keywords: Numerical magnitude Non-numerical magnitude Neural specialization Functional magnetic resonance imaging Symbolic Nonsymbolic

It is currently debated whether numbers are processed using a number-specific system or a general magnitude processing system, also used for non-numerical magnitudes such as physical size, duration, or luminance. Activation likelihood estimation (ALE) was used to conduct the first quantitative meta-analysis of 93 empirical neuroimaging papers examining neural activation during numerical and non-numerical magnitude processing. Foci were compiled to generate probabilistic maps of activation for non-numerical magnitudes (e.g. physical size), symbolic numerical magnitudes (e.g. Arabic digits), and nonsymbolic numerical magnitudes (e.g. dot arrays). Conjunction analyses revealed overlapping activation for symbolic, nonsymbolic and non-numerical magnitudes in frontal and parietal lobes. Contrast analyses revealed specific activation in the left superior parietal lobule for symbolic numerical magnitudes. In contrast, small regions in the bilateral precuneus were specifically activated for nonsymbolic numerical magnitudes. No regions in the parietal lobes were activated for non-numerical magnitudes that were not also activated for numerical magnitudes. Therefore, numbers are processed using both a generalized magnitude system and format specific number regions.

1. Introduction For decades, researchers have canvassed the brain in search of neural responses associated with abstract representations of numerical magnitudes (i.e. the quantity of a discrete set of items) (Brannon, 2006; Cantlon et al., 2009a, 2009b; Dehaene et al., 1998, 2003; Piazza et al., 2007). Empirical neuroimaging studies, like prior neuropsychological studies (Cipolotti et al., 1991; Dehaene et al., 2003), have consistently implicated regions along the bilateral parietal lobes and particularly, the intraparietal sulcus as important for processing numerical magnitudes (for reviews see: Ansari, 2008; Brannon, 2006; Dehaene et al., 2003; Nieder, 2005). 1.1. A general magnitude system A longstanding view in the field of numerical cognition is that number operates within its own domain (Brannon, 2006; Dehaene et al., 1998, 2003; Piazza et al., 2007). However, researchers have consistently documented striking behavioural similarities between estimating numerical quantities and non-numerical magnitudes such as space and time (Cantlon et al., 2009b; Cohen Kadosh et al., 2008; Moyer and Landauer, 1967). Because of this, it has been fiercely



debated whether the human brain contains a number module that is specialized for representing numerical magnitudes or if numerical processing operates within a more general system used to process both numerical and non-numerical magnitudes (Cantlon et al., 2009b; Cohen Kadosh et al., 2008; Simon, 1999; Walsh, 2003). A nonnumerical magnitude refers to the size or extent of a continuous dimension such as space, time or luminance. Recent innovations in neuroimaging techniques have allowed researchers to explicitly test whether number is processed using a generalized magnitude system or a specific number system. Several studies asked participants to make comparative judgments on different kinds of numerical and non-numerical magnitudes (e.g. Cohen Kadosh et al., 2005; Dormal et al., 2012a; Dormal et al., 2012b; Fias, Lammertyn et at., 2003; Pinel et at., 2004). The majority of these studies have found both distinct and overlapping neural populations for numerical and non-numerical magnitudes (Cohen Kadosh et al., 2008). The first empirical paper that studied brain activation during numerical and non-numerical magnitude processing used positron emission tomography (PET) to examine neural activity while subjects compared line lengths, angle size and numerical magnitude of two digit Arabic number symbols (Fias et al., 2003). This study found that the left intraparietal sulcus responded to both numerical and non-numer-

Correspondence to: Numerical Cognition Laboratory, Department of Psychology, Westminster Hall, Western University, London ON, Canada N6A 3K7. E-mail address: [email protected] (D. Ansari).

http://dx.doi.org/10.1016/j.neuropsychologia.2017.01.019 Received 10 November 2016; Received in revised form 17 January 2017; Accepted 18 January 2017 0028-3932/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Sokolowski, H.M., Neuropsychologia (2017), http://dx.doi.org/10.1016/j.neuropsychologia.2017.01.019

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are said to have an abstract (i.e. format-independent) quality. This has driven numerical cognition researchers to hypothesize that symbolic and nonsymbolic numbers have the same underlying representations (e.g. Dehaene et at., 1998). To empirically evaluate this hypothesis, researchers have investigated neural responses that are activated by both symbolic and nonsymbolic processing in order to determine regions associated with abstract representations of numerical magnitudes (Brannon, 2006; Cantlon et al., 2009a, 2009b; Dehaene et al., 1998, 2003; Piazza et al., 2007). Although a large body of research has identified brain regions that respond to numerical magnitudes across stimulus formats (Dehaene et al., 1998; Eger et al., 2003; Holloway et al., 2010; Piazza et al., 2007), many studies, including a recent quantitative neuroimaging meta-analysis (Sokolowski et al., 2016) have also reported striking differences between brain regions that support symbolic and nonsymbolic numerical magnitudes (Ansari, 2007; Cantlon et al., 2009a, 2009b; Cohen Kadosh et al., 2011; Holloway et al., 2010; Piazza et al., 2007; Venkatraman et al., 2005). Notably, this previous quantitative meta-analysis (Sokolowski et al., 2016) only examines numerical magnitude processing; it does not include nonnumerical magnitude processing. Specifically, Sokolowski et al. (2016) revealed overlapping and distinct regions of activation for symbolic and nonsymbolic number processing. However, it remains unclear whether the regions associated with abstract number processing (i.e. the overlapping regions) or the format-dependent regions (i.e. the distinct regions) are rooted in a general magnitude system. Understanding the relations between the general magnitude system and symbolic and nonsymbolic number processing will help to illuminate the mechanism used to process numbers at the neural level. The important distinction between symbolic and nonsymbolic processing at the neuronal level reported in Sokolowski et al. (2016) suggests that symbolic and nonsymbolic numbers may be differentially related to a general magnitude system. Relatedly, several theoretical and empirical papers have highlighted that estimating discrete quantities (i.e. numerical magnitudes) in nonsymbolic arrays is inherently confounded by continuous non-numerical properties of the arrays, such as area, density, or circumference (Gebuis et al., 2014; Gebuis and Reynvoet, 2012; Henik et al., 2012; Leibovich and Henik, 2013). In other words, a change in a nonsymbolic numerical magnitude is inherently correlated with non-numerical properties. Several researchers have indicated that it is not possible to control for all continuous properties of a nonsymbolic numerical magnitude (Gebuis and Reynvoet, 2012; Leibovich and Henik, 2013). Consequently, this behavioural confound of non-numerical magnitudes during nonsymbolic numerical magnitude processing suggests that perhaps nonsymbolic numerical magnitudes will relate more closely to non-numerical magnitudes than symbolic numerical magnitudes at the neural level. This converging evidence suggests that when examining overlapping and distinct brain regions associated with numerical and non-numerical magnitudes, it is important to examine symbolic and nonsymbolic numerical magnitudes separately. To date, the distinction between the relationships between non-numerical magnitudes and both symbolic and nonsymbolic number processing, has only been examined in one empirical neuroimaging paper (Chassy and Grodd, 2012), and has never been studied at the meta-analytic level. This further motivates the need to quantify studies exploring the relationship between non-numerical magnitude processing and both symbolic and nonsymbolic numerical magnitude processing at the meta-analytic level. Overall, research studying the neural overlap of numerical and nonnumerical magnitudes has produced three major findings. First, convergent and distinct brain regions support numerical and nonnumerical magnitude processing. Second, the bilateral intraparietal sulcus is implicated as a brain region that underpins magnitude processing. Third, regions along the right intraparietal sulcus underlie general magnitude judgments and the left intraparietal sulcus is specialized for processing numerical magnitudes. These conclusions, which arise from studies using magnitude comparison tasks, are

ical magnitude comparison tasks, supporting the hypothesis that different magnitudes are represented by a common mechanism. However, they also found greater activation for number processing compared to non-numerical magnitude comparison in a site anterior to the left intraparietal sulcus (Fias et al., 2003). Similarly, functional magnetic resonance imaging (fMRI) experiments have revealed brain activation in a widespread cortical network, including the bilateral intraparietal sulcus, recorded while subjects compared the numerical magnitude, physical size, and brightness of Arabic number symbols (Cohen Kadosh et al., 2005; Pinel et at., 2004). More specifically, Pinel et al. (2004) found that number and size engaged a common parietal network and size and luminance shared occipito-temporal perceptual representations. Similarly, Cohen Kadosh et al. (2005) found that regions in the left intraparietal sulcus were activated during processing of number, size, and luminance. Number-specific activation was found in the left intraparietal sulcus and right temporal regions (Cohen Kadosh et al., 2005). These pioneering studies, all of which used a symbolic number format (e.g. 2 or two), suggest that common and distinct neural populations support symbolic number processing and non-numerical magnitude processing (Cohen Kadosh et al., 2005; Fias et al., 2003; Pinel et al., 2004). Distinct and overlapping brain regions for number and nonnumerical magnitudes were also revealed when number was represented nonsymbolically, as a discrete array (e.g.••). This has been studied both in humans and in non-human primates. For instance, Castelli et at. (2006) found more bilateral intraparietal sulcus activation during processing of discrete, non-symbolic stimuli compared to processing of continuous stimuli in humans. In a similar vein, Dormal and Pesenti (2009) examined brain regions associated with discrete nonsymbolic numbers compared to continuous magnitudes (line length). They reported overlapping activation for numerical and nonnumerical stimuli in the right intraparietal sulcus. Additionally, they revealed distinct activation in the left intraparietal sulcus during nonsymbolic number processing. The notion that the right intraparietal sulcus underlies a common magnitude system was further supported by Dormal et al. (2012a) who examined neural activation during nonsymbolic number processing compared to duration processing. This idea that nonsymbolic numbers and non-numerical magnitudes share overlapping representations has also been reported in nonhuman primates (e.g. Tudusciuc and Nieder, 2007). Specifically, single neurons within the intraparietal sulcus in rhesus monkeys encode numerosity, length, or both numerosity and length (Tudusciuc and Nieder, 2007). These data lend additional support to the notion that the parietal lobe may support both numerical and non-numerical magnitude presentations. Only one study to date has examined overlapping and distinct neural representations underlying all three formats of magnitude representation: symbolic (positive and negative integers) numbers, nonsymbolic numbers (dot arrays) and non-numerical magnitudes (disk size) (Chassy and Grodd, 2012). Specifically, this study used fMRI with human subjects to examine the distinction between brain activation patterns during processing of dots and disk size compared to symbolic (positive and negative digit) formats. In accordance with previous research, the right intraparietal sulcus was activated during processing of dots and disk size as well as during processing of symbolic numbers. Additionally, symbolic number processing was correlated with activation in the left intraparietal sulcus (Chassy and Grodd, 2012). Taken together, these studies suggest that the right intraparietal sulcus underlies a common magnitude system and additional brain regions, such as the left intraparietal sulcus, exhibit activation that is specific to number processing. 1.2. Numerical magnitudes Since different formats of numerical magnitudes (symbolic and nonsymbolic) can represent the same quantity, numerical magnitudes 2

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brain activation that correlate with non-numerical and numerical magnitude processing. ALE meta-analyses quantify the spatial convergence of a group of independent empirical neuroimaging studies. Specifically, ALE extracts 3D-coordinates (foci) from all included empirical studies. The ALE algorithm models Gaussian probability distributions that are centered on the foci. ALE produces whole brain, statistically thresholded maps that represent the reliable unification of these probability distributions across all included independent empirical studies (Eickhoff et al., 2012, 2009a, 2009b, 2009c; Laird et al., 2005; Turkeltaub et al., 2012, 2002). The present study is the first to use this technique to provide a statistically based overview of brain regions that are activated by nonnumerical and numerical magnitudes across 93 empirical neuroimaging papers. First, the present meta-analysis examined overlapping and distinct brain activation patterns for numerical and non-numerical magnitude processing to determine whether number is processed using a specific number processing system or if number is rooted in a general magnitude processing system. Following this, the numerical magnitude ALE map was split into symbolic numerical magnitude processing and nonsymbolic numerical magnitude processing. Symbolic and nonsymbolic ALE maps were each compared to the non-numerical ALE map in order to determine whether overlapping and distinct regions supporting numerical and non-numerical magnitude processing are formatdependent.

further supported by studies using other paradigms such as estimation tasks (Leroux et al., 2009; Vogel et al., 2013), ordinal tasks (Fulbright et al., 2003; Lyons and Beilock, 2013), and identification tasks (Cappelletti et al., 2010; Eger et al., 2003). 1.3. Qualitative meta-analyses This consensus, discussed in several review papers (Cantlon et al., 2009b; Cohen Kadosh et al., 2008; Walsh, 2003) is however qualitative in nature. Quantitative statistics that evaluate the consistency across different findings have thus far not been used to probe this conclusion. Two qualitative meta-analyses used Caret software (Van Essen, 2012; Van Essen et al., 2001) to examine brain activation patterns underlying magnitude processing across studies (Cantlon et al., 2009b; Cohen Kadosh et al., 2008). Caret software is a qualitative meta-analytic tool that is commonly used to visualize neuroimaging data. This software projects the coordinates of brain activation onto a population-averaged brain template (Van Essen, 2012; Van Essen et al., 2001). Qualitative meta-analysis by Cantlon et al. (2009b) and Cohen Kadosh et al. (2008) used Caret software to depict brain activation patterns from multiple studies that examined different kinds of magnitudes (e.g. number, space, time, luminance, pitch). The spatial distribution of intraparietal sulcus activation across empirical studies illustrates that the intraparietal sulcus hosts overlapping domain-general and domain-specific neural populations for numbers compared to non-numerical magnitudes (Cantlon et al., 2009b; Cohen Kadosh et al., 2008). Although this qualitative method of visualizing data has been the most common approach used to synthesize data across studies (Turkeltaub et al., 2002), this method requires subjective judgments to evaluate the extent of overlap. This subjectivity is problematic for rigorous assessments of whether neuroimaging data across studies converge. In view of this, it is critical to use quantitative meta-analytic tools, such as activation likelihood estimation (ALE) to synthesize neuroimaging data with variable methods and unreliable findings (Eickhoff et al., 2009b; Turkeltaub et al., 2012, 2002). While converging evidence indicates that numerical and nonnumerical magnitude processing rely on distinct and overlapping brain regions, this data has never been synthesized, quantitatively. Specifically, previous meta-analyses qualitatively mapped brain activation patterns, but did not statistically test for the convergence of activation reported on these maps. Therefore, it remains unclear which brain areas underlie general magnitude processing and which specifically support number processing. Additionally, these previous qualitative meta-analyses grouped symbolic and nonsymbolic numerical stimuli into a general term: number (Cantlon et al., 2009b; Cohen Kadosh et al., 2008). Therefore, previous meta-analyses were unable to determine whether overlapping and distinct brain activation patterns for non-numerical and numerical magnitude processing differ based on number format (i.e. symbolic vs. nonsymbolic). Due to marked differences in neural correlates of symbolic and nonsymbolic numerical magnitude processing, as revealed in a recent meta-analysis (Sokolowski et al., 2016), it is critical to separate symbolic and nonsymbolic numerical stimuli. Importantly, Sokolowski et al. (2016) do not compare brain regions associated with symbolic and nonsymbolic numbers to non-numerical magnitudes. Therefore, it is critical to conduct a quantitative meta-analysis that builds upon Sokolowski et al. (2016) to compare both symbolic and nonsymbolic numerical with non-numerical magnitudes.

2. Methods 2.1. Literature search and article selection All relevant experimental research articles were identified using a stepwise process. First, standard searches databases, PsychInfo (http:// www.apa.org/psychinfo/), and PubMed (http://www.pubmid.gov) were used to search the literature. The following key terms, “number*,” “numeral,” “symbol*” “nonsymbolic,” “magnitude,” “fMRI,” “PET,” “functional magnetic resonance imaging,” “positron emission topography,” “neuroimag*,” “imaging,” “congruent,” “incongruent,” “stroop,” “quantity,” “amount,” “physical size,” “numerical size,” “object size,” “size,” “size interference,” “length,” “duration,” “distance,” “area,” were entered into both databases. Second, the reference sections of the relevant papers obtained during the first step were reviewed. Studies were considered for inclusion if they contained a numerical magnitude processing task and/or a non-numerical magnitude processing task. The following symbolic and nonsymbolic numerical magnitudes were considered for inclusion: Arabic digits, verbal numbers, arrays of objects (e.g. dots). The following non-numerical magnitudes were considered for inclusion: size (specifically, area/length/height), luminance/brightness, weight, duration/time. Importantly, only studies in which the numerical or non-numerical magnitude were cognitively evaluated by the participants were considered for inclusion. The term ‘study’ denotes the paper and the term ‘contrast’ refers to an individual contrast reported within a study. 2.2. Inclusion/exclusion criteria The following inclusion and exclusion criteria were taken from Sokolowski et al. (2016). 1. Studies must use at least one of the following tasks: comparison, discrimination, passive viewing, estimation, categorization, target detection, matching, mapping, ordering, counting, naming, size congruity. Tasks that required higher level cognitive processing (such as calculation) were excluded in order to constrain the brain activation to be specifically related to magnitude processing. 2. Studies must have contrasts with active control conditions.

1.4. The present meta-analysis



Quantitative meta-analytic tools that use statistical coordinatebased methods to determine the convergence of empirical neuroimaging data (Eickhoff et al., 2009b; Turkeltaub et al., 2012, 2002) are ideal for determining trends across independent studies, while minimizing subjectivity. The present study uses ALE to identify patterns of 3

4

2009

2015

2009

Chouinard P A

Coull J T

Dormal V

Social Cognitive and Affective Neuroscience

25

fMRI

fMRI

23

10 25F

Physical Size Comparison Height Comparison

2014

17

7F 10M

Kedia G

Neuroreport

31

2006

fMRI

Kaufmann L

17

2005

fMRI

Physical Size Comparison

Judgement Comparison Adaptation

Length Comparison

Judgement

Area Comparison Physical Size Comparison Luminance Judgment Physical Size Comparison Physical Size Comparison Weight Comparison

Tasks (s)

Kaufmann L

4

7F 8M

15M 14F 12M

14M

1F 15 M

5F 7M

6F 3M

15F 11M

16M 8F 6M

Gender

Physical Size Comparison Physical Size Comparison

Journal of Cognitive Neuroscience NeuroImage

28

21

26

26

21

20 21

Mean Age

2007

fMRI

fMRI fMRI fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI fMRI

Imaging Method

Kadosh R C

15

15 26 15

14

16

12

9

26

16 14

N

Luminance Judgment

Neuropsychologia

Human Brain Mapping Journal of Neuroscience European Journal of Neuroscience

Human Brain Mapping

Journal of Cognitive Neuroscience

NeuroImage

PLoS ONE

PLoS ONE

Brain Research NeuroImage

Journal

Kadosh R C

2005

2007

Cavina-Pratesi C

Kadosh R C

2014

Attout L

2012 2013 2009

2006 2006

Ansari D Ansari D

Dormal V Hayashi M J Jacob S N

Year

1st Author

Table 1 Studies included in the Non-numerical Meta-Analysis.

Nonnumerical 3 Nonnumerical 5 (continued on next page)

Main effect of judgment: Height > Control condition Main effect of judgment: Height > Beauty comparison

9

Nonnumerical

1

5

2

1

1

2

5 3

3

25

5 15 1

9 3 1

2 1 7 2 3 1 2 1

7

1

5

4

0

1 21

Foci

Distance effect in height conditions

Nonnumerical

Nonnumerical

Numerical comparison (incongruent trials > congruent trials) Physical Comparison Close Distance > Physical Comparison Far Distance

Nonnumerical

Physical comparison (Distance 1 > Distance 4, only neutral trials)

Nonnumerical

Nonnumerical

Luminance Distance Triangle comparison task: Incongruent vs. Congruent

Nonnumerical

Nonnumerical Nonnumerical

Size vs. luminance Size Distance Luminance vs. size

Nonnumerical

Nonnumerical

Adaptation to Line Proportion Size vs. numerical

Nonnumerical Nonnumerical Nonnumerical

Duration vs. Reference for Duration Main Effect of Duration Task Line Proportion full brain analysis

Nonnumerical Nonnumerical Nonnumerical

Nonnumerical Nonnumerical Nonnumerical Nonnumerical Nonnumerical Nonnumerical Nonnumerical Nonnumerical

Spatial dynamic -Temporal dynamic (Block 2 only) Static - Dynamic Spatial static - Temporal static Time x Duration Space x Distance Spatial dynamic -Temporal dynamic (All blocks) (Space x Distance) - (Time x Duration) (Time x Duration) - (Space x Distance) Discrete Length vs. Reference for Discrete Length Continuous Length vs. Reference for Continuous Length Conjunction of Discrete Line and Continuous Line

Nonnumerical

Nonnumerical

Different weight > Same weight Temporal static - Spatial static

Nonnumerical

Nonnumerical

Nonnumerical

Nonnumerical Nonnumerical

Magnitude Type

Different size > Same size

Size > Pattern

Distance effect of luminance judgment

Area Change Effect Main effect of congruity (incongruent > congruent)

Contrast Name

H.M. Sokolowski et al.

Neuropsychologia (xxxx) xxxx–xxxx

5

2006

2013

Vogel S E

2004

Pinel P

Tang J

2015

Monaco S

1997

2006

Melcher T

Schacter D L

2006

Liu X

2015

2003

Lewis P A

Robertson B D

2016

Leibovich T

2005

2015

Leibovich T

Pouthas V

Year

1st Author

Table 1 (continued)

Journal of Cognitive Neuroscience Neuropsychologia

Neuroreport

NeuroImage

Human Brain Mapping

European Journal of Neuroscience Neuron

Journal of Cognitive Neuroscience Brain Research

Journal of Cognitive Neuroscience Neuropsychologia

Neuropsychologia

Journal

14

18

12

16

6

15

11

9

12

8

19

20

N

fMRI

fMRI

PET

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

Imaging Method

25

25

23

23

22.3

24

32

26

26

22

24

Mean Age

7F 7M

7F 11M

12F

8F 8M

3F 3M

5F 6M

7F 5M

3F 5M

12F 7M

8F 12M

Gender

Judgement

Comparison

Size Comparison

Comparison

Duration Estimation

Physical Size Comparison

Adaptation

Stroop

Comparison

Duration Estimation

Comparison

Comparison

Tasks (s)

3

Nonnumerical

Brightness > Control

Numerical Task Conflict Trials > Numerical Task Non-Conflict Trials

Size change - New object Size change - Passive viewing

Control - Congruent contrast Main effect of physical size difference: (Far - Close) Close - Far contrast Close - far correlation

11

1 4

24 22 36 6

6

Nonnumerical 10 (continued on next page)

Nonnumerical

Nonnumerical Nonnumerical

Nonnumerical Nonnumerical Nonnumerical Nonnumerical

Nonnumerical

5 8

Nonnumerical Nonnumerical

Long duration estimation trials vs. Short duration estimation trials

3

Nonnumerical

9

11

Nonnumerical

Nonnumerical

10

Nonnumerical

Estimation Trials vs. Control Trials

2 1 7

Nonnumerical Nonnumerical Nonnumerical

Size Comparison with numerical stimuli vs Luminance comparison Size comparison with numerical stimuli vs size comparison with letter stimuli Size Comparison (numbers) Small Distance vs Size Comparison (numbers) Large Distance Size comparison (letters) small distance vs Size comparison (letters) large distance Size Comparison (all stimuli) small distance vs. Size Comparison (all stimuli) large distance Incongruent vs. Congruent Trials: Physical Size Interference (Numerical Comparison) Size and Luminance Distance Effects (Close - Far Trials) Luminance Comparison Small Distance vs Luminance Comparison Large Distance Incongruent vs. Congruent Trials: Physical Size Interference (Luminance Comparison)

1

7

14 11

Nonnumerical

Nonnumerical

Nonnumerical Nonnumerical

16

13 7 7 2

20

5

3 1

Foci

Size Comparison with numerical stimuli vs Numerical Task

Adaptation effects

Stroop-incongruency (Stroop-incongruency vs. Stroop-congruency) Stroop-incongruency in contrast with word oddball (Stroop incongruency > Word oddball)

Incongruent vs. Congruent

Nonnumerical

Nonnumerical Nonnumerical Nonnumerical Nonnumerical

Length 3.0 s Length (Mean of 0.6 and 3.0 s) Length, 0.6 > 3.0 s Length, 3.0 > 0.6 s

Time Time Time Time

> > > >

Nonnumerical

Nonnumerical

Nonnumerical Nonnumerical

Magnitude Type

Time > Length 0.6 s

Task effect: Non-numerical > Numerical

CN group: Congruent continuous task > Congruent numerical task CN group: Incongruent continuous task > Incongruent numerical task

Contrast Name

H.M. Sokolowski et al.

Neuropsychologia (xxxx) xxxx–xxxx

Neuropsychologia (xxxx) xxxx–xxxx

7 Nonnumerical

3. 4.

5.

6. 7. 8.

1. Reported coordinates that were contrasted against baseline, rest, or fixation were excluded. Studies must include a sample of healthy human adults. Studies must use fMRI and/or PET brain imaging techniques. This is because these imaging methods (PET and fMRI) have similar spatial uncertainty (Eickhoff et al., 2009a). Studies must use whole-brain group analyses. 1. Contrasts that used region of interest (ROI) analyses were excluded. 2. Contrasts that used multivariate statistics were excluded. Stereotaxic coordinates must be reported in Talairach/Tournoux or Montreal Neurological Institute (MNI) space. Studies must have more than five participants. Studies must be written in English.



Ninety-three studies were included in the meta-analyses. Data from 201 contrasts from studies that met the inclusion criteria were included in the meta-analyses. Overall, 1433 healthy adult human participants were included in the final sample. All included studies contained either a numerical and/or a non-numerical magnitude-processing task. Across all studies, 1117 activation foci were reported. Tables 1, 2 report descriptive information for the included studies. The Lancaster transformation (icbm2tal) was used to transform studies from MNI into Talairach space when the stereotaxic coordinates were reported in MNI space (Laird et al., 2010; Lancaster et al., 2007). Foci, number of foci reported in contrast; fMRI, functional magnetic resonance imaging; PET, positron emission tomography; N, sample size of each study; M – Male, F – Female.

Foci, number of foci reported in contrast; fMRI, functional magnetic resonance imaging; PET, positron emission tomography; N, sample size of each study; M – Male, F – Female.

9 Nonnumerical 2016 Wen X

Brain Structure Function

28

fMRI

21

14F 14M

Physical Size Comparison

Distance effect in the size comparison [(size comparison of scenes low distance-size comparison of scenes high distance) + (size comparison of faces low distance-size comparison of faces high distance)] Distance effect in the size comparison (Response Time covariate) [(size comparison of scenes low distance-size comparison of scenes high distance) + (size comparison of faces low distance-size comparison of faces high distance)]

0 Nonnumerical Brightness Specific Activation

Year 1st Author

Table 1 (continued)

Journal

N

Imaging Method

Mean Age

Gender

Tasks (s)

Contrast Name

Magnitude Type

Foci

H.M. Sokolowski et al.

2.3. Analysis procedure The present meta-analysis used GingerALE, the revised ALE algorithm developed by Brainmap (http://www.brainmap.org) to compute quantitative, coordinate based meta-analyses (Eickhoff et al., 2012, 2009a; Eickhoff et al., 2009b, 2009c; Turkeltaub et al., 2012). ALE assesses the convergence of foci across many contrasts from independent studies. Specifically, the ALE algorithm models the coordinates of the foci as Gaussian probability distributions centered on coordinates to create a modeled activation (MA) map (i.e. a probabilistic map of activation) for each construct of interest (e.g. numerical magnitude processing). The ALE algorithm produced a nulldistribution map by randomly distributing all foci included in the experimental analysis across the brain. To statistically identify meaningful convergence of activation across studies, the MA map is compared to the null-distribution map. This identifies whether the clustering of activation in the ALE activation map is greater than activation from random clustering (i.e. noise), produced by the ALE null-distribution map. As most empirical studies include one participant group that completes many tasks, activation patterns from multiple contrasts within a single study do not represent independent observations. To account for this issue, the Brainmap development team developed a modified ALE algorithm and a method of organizing datasets by subject group (rather than by contrasts) (Eickhoff et al., 2009a, 2009b, 2009c; Turkeltaub et al., 2012). The present meta-analyses were conducted using both the modified ALE algorithm and subject grouping. This ensured that subject groups with more reported contrasts do not influence the MA more than subject groups with fewer reported contrasts (Turkeltaub et al., 2012). For the first analysis, two ALE maps were created: One for nonnumerical magnitude processing and one for numerical magnitude processing. Single dataset ALE maps determined convergent brain activation during each of numerical (both symbolic and nonsymbolic) magnitude processing and non-numerical magnitude processing. A conjunction ALE analysis was run to identify convergent brain regions during both numerical and non-numerical magnitude processing. Contrast analyses comparing numerical and non-numerical maps were 6

Year

2006 2006 2007

2005

2006

2007 2014 2006 2006

2012

2007

1999

2013

2014

2009

2012

2010

1st Author

Ansari D Ansari D Ansari D

Ansari D

Ansari D

Ansari D Attout L Cantlon J F Castelli F

Chassy P

Chen C

Chochon F

7

Damarla R

Demeyere N

Dormal V

Dormal V

Dormal V

NeuroImage

Human Brain Mapping

Human Brain Mapping

Human Brain Mapping

Human Brain Mapping

Journal of Cognitive Neuroscience

Neuroreport

Cerebral Cortex

Journal of Cognitive Neuroscience PLoS ONE PLoS Biology Proceedings of the National Academy of Sciences

NeuroImage

Neuroreport

Brain Research Journal of Cognitive Neuroscience Journal of Cognitive Neuroscience

Journal

Table 2 Studies included in the Numerical Meta-Analysis.

15

15

14

12

10

8

20

16

13 26 12 12

14

12

16 9 13

N

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI

fMRI fMRI fMRI fMRI

fMRI

fMRI

fMRI fMRI fMRI

Imaging Method

21

21

21

26

25.5

22.7

28

21.5 21 25 24

21

19

20.4 19.8 21.5

Mean Age

15M

15M

14M

9F 3M

7F 3M

4F 4M

10F 10M

16M

15F 11M 5F 7M 4F 8M

8F 6M

16M 6M 3F

Gender

Numerosity Categorization

Numerosity Categorization Numerosity Categorization

Passive Viewing

Passive Viewing

Delayed-numbermatching Naming Comparison

Comparison

Comparison Order Judgment Passive Viewing

Comparison Size Congruity Comparison Size Congruity

Passive Viewing Comparison Comparison

Tasks (s)

3 4

Nonsymbolic Nonsymbolic

Nonsymbolic Nonsymbolic

[Sequential Numerosity]-[Reference Sequential Numerosity] [Simultaneous Numerosity-Reference Simultaneous Numerosity][Sequential Numerosity-Reference Sequential Numerosity]

6 4

6

1

5

(continued on next page)

Nonsymbolic

Nonsymbolic

(Numerosity - Reference for Numerosity) - (Duration vs Reference for Duration) [Simultaneous Numerosity]-[Reference Simultaneous Numerosity]

Nonsymbolic

9

1 9 14

Nonsymbolic Nonsymbolic Nonsymbolic

Nonsymbolic

4

6 2

2 13 1

8

1 1

2 2

8 7 2 7

7

10

12

4 7 1 2 3

Foci

Nonsymbolic

Nonsymbolic Symbolic

Symbolic Symbolic Symbolic

Symbolic

Numerosity vs. Reference for Numerosity

Numerosity Processing - Reference for Numerosity

Adaptation to categories (repeated categories pairs vs. different categories pairs) Repetition of small category versus large category (large < small) Repetition of small category versus large category (small < large) Numerosity specific repetition [Repetition-Category > (Repetitionnumerosity + Repetition-Exact)] Interaction Small/Large with Category/Numerosity/Exact Small numerosity < Small category

Stable Parietal lobe voxels in Pictoral Mode Stable Parietal lobe voxels in Digit-object mode

Digit Naming vs. Control Comparison vs. Control Comparison vs. Digit Naming

Unmatched Numbers > Matched Numbers

Nonsymbolic Symbolic

Nonsymbolic Nonsymbolic

Difficulty Effect While Estimating Numerosity: In Space Difficulty Effect While Estimating Numerosity: In Time Disk > Dots Positive Integers < Negative Integers

Symbolic Symbolic Nonsymbolic Nonsymbolic

Symbolic

Main effect of distance in the neutral condition (small > large) Conjunction of Small and Large symbolic number Distance effect of numerical order judgment Number > Shape (Adults) Estimating Numerosity: In space and time

Symbolic

Symbolic

Nonsymbolic Nonsymbolic Nonsymbolic Nonsymbolic Nonsymbolic

Magnitude Type

Main effect of distance (small > large)

Distance effect (small > large) adults

Number Change Effect Distance Effect - Adults Small Nonsymbolic > Large Nonsymbolic Large Nonsymbolic > Small Nonsymbolic Conjunction of small nonsymbolic and large nonsymbolic

Contrast Name

H.M. Sokolowski et al.

Neuropsychologia (xxxx) xxxx–xxxx

8

2003

2003 2007

2009

2003

2013 2013

2013

2010 2013 2010 2013 2009

Eger E

Fias W Fias W

Franklin M S

Fulbright R K

Hayashi M J He L

He L

Holloway I Holloway I Holloway I Holloway I Jacob S N

Kadosh R C

2011

2009

Eger E

D D D D

Year

1st Author

Table 2 (continued)

Frontiers in Human Neuroscience

NeuroImage Journal of Cognitive Neuroscience NeuroImage Journal of Cognitive Neuroscience European Journal of Neuroscience

Cerebral Cortex

Journal of Neuroscience Cerebral Cortex

American Journal of Neuroradiology

Journal of Cognitive Neuroscience

Journal of Cognitive Neuroscience Journal of Neuroscience

Neuron

Current Biology

Journal

19

19 26 19 26 15

20

27 20

19

17

18 17

9

10

N

fMRI

fMRI fMRI fMRI fMRI fMRI

fMRI

fMRI fMRI

fMRI

fMRI

PET fMRI

fMRI

fMRI

Imaging Method

26.3

23.5 25 23.5 25

21

21

24

21.8

23

27.9

23

Mean Age

9M 4M 9M 4M

12F 7M

10F 22F 10F 22F

8F 12M

14F 12M 8F 12M

8F 11M

10F 7M

18M 9F 8M

5F 4M

5F 5M

Gender

Passive Viewing

Comparison Passive Viewing Comparison Passive Viewing Passive Viewing

Comparison

Comparison Comparison

Order Identification

Ordering Task

Comparison Comparison

Target detection

Comparison

Tasks (s)

Magnitude Change Dots Magnitude Change Dots > Digits

(nonsymbolic - control) - (symbolic - control) Nonsymbolic Comparison (symbolic - control) - (non-symbolic - control) Adaptation to Hindu-Arabic Numerals for both groups Dot Proportion full brain analysis Adaptation to Dot Proportion Numerosity full brain analysis

Symbolic > Nonsymbolic Digit-digit > cross notation trials Overlap between (Symbolic > nonsymbolic) and (small > large)

Main Effect of Numerosity Task Nonsymbolic > Symbolic Dot-dot > cross-notation trials Overlap between (nonsymbolic > symbolic) and (large > small)

Number vs Shapes Far Order Number vs. Near Order Number

Number comparison vs Nonsymbolic Stimuli Comparison (Number comparison-number dimming) - (letter comparison-letter dimming) Magnitude Near > Far (common regions with Order Near > Far) Order Far > Near (common regions with Magnitude Near > Far) Magnitude Near > Far (Unique regions) Order Far > Near (Unique regions)

Modality-related effects: Auditory Numbers > Visual Numbers (fixed-effect) Modality-related effects: Auditory Numbers > Visual Numbers (random-effect) Modality-related effects: Visual Number > Auditory Number (fixedeffect) Modality-related effects: Visual Number > Auditory Number (random-effect) Number > Letter and Colour (fixed-effect) Number > Letter and Colour (random-effect) Number > Letter (fixed-effect) Number > Letter (random-effect) Number > Colour (fixed-effect) Number > Colour (random-effect)

5 4 4 2 2 2 4 3

Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic

10 6

7 6 2 2 1 27 1

2 1 2

13 8 4 6

0 0

1 1 3 1

(continued on next page)

Nonsymbolic Nonsymbolic

Nonsymbolic Nonsymbolic Symbolic Symbolic Nonsymbolic Nonsymbolic Nonsymbolic

Symbolic Symbolic Symbolic

Nonsymbolic Nonsymbolic Nonsymbolic Nonsymbolic

Symbolic Symbolic

Symbolic Symbolic Symbolic Symbolic

13 3

4

Symbolic

Symbolic Symbolic

2

8 10 Symbolic

Nonsymbolic Nonsymbolic

3

Nonsymbolic

Number Comparison Same List Number Comparison Different List

3

Nonsymbolic

[Sequential Numerosity-Reference Sequential Numerosity][Simultaneous Numerosity-Reference Simultaneous Numerosity] [[Sequential Numerosity]-[Reference Sequential Numerosity] and [[Simultaneous Numerosity]-[Reference Simultaneous]]

Foci

Magnitude Type

Contrast Name

H.M. Sokolowski et al.

Neuropsychologia (xxxx) xxxx–xxxx

2012 2000 2002

2004 2006

Piazza M Piazza M

2009

Leroux G

Park J Pesenti M Piazza M

2016 2015

Leibovich T Leibovich T

2010 2011 2011

2006 2000

Kaufmann L Le Clec'H G

Meintjes E M Naccache L Notebaert K

2007 2005

Kadosh R C Kaufmann L

2013

2011

Kadosh R C

Lyons IM

2007

Kadosh R C

2006 2013

2005

Kadosh R C

Liu X Lyons IM

Year

1st Author

Table 2 (continued)

9

Neuron Brain Research

Journal of Cognitive Neuroscience Journal of Comparative Neurology NeuroImage

Magnetic Resonance Imaging Cerebral Cortex Journal of Cognitive Neuroscience

Journal of Cognitive Neuroscience

Journal of Cognitive Neuroscience Journal of Cognitive Neuroscience

Developmental Science

Journal of Cognitive Neuroscience Neuropsychologia

Neuroreport NeuroImage

Journal of Cognitive Neuroscience NeuroImage

Frontiers in Human Neuroscience

Neuron

Neuropsychologia

Journal

12 10

20 8 9

18 9 13

35

23 33

9

19 20

17 5 6

4 17

19

17

15

N

fMRI fMRI

fMRI PET PET

fMRI fMRI fMRI

fMRI

fMRI fMRI

fMRI

fMRI fMRI

fMRI fMRI fMRI

fMRI fMRI

fMRI

fMRI

fMRI

Imaging Method

23

29

23.4

11 26

23

22 24

10 37 27

31

26.3

31

28

Mean Age

3F 7M

11F 9M 8M 9M

2F 7M 6F 7M

16F 17M

7F 5M 16F 17M

9M

12F 7M 8F 12M

10M 7F 5M 3F 3M

7F 10M

12F 7M

7F 10M

7F 8M

Gender

Passive Viewing Estimation Counting

Visual matching task Comparison Count

Comparison Comparison Passive Viewing

Comparison

Number-length interference Stroop Comparison

Comparison Comparison

Physical Comparison Compare to 12 Compare to 12

Comparison Stroop

Passive Viewing

Stroop

Comparison

Tasks (s)

Regions Responding to Deviations in Number Estimation > Matching Counting > Matching Counting > Estimation

Number > Letter Comparison > Numbers All 6–9 > All 1–4 6–9 Random > 1–4 Random 6–9 Canonical > 1–4 Canonical

Proximity Judgment > Proximity Judgment Control Repeated vs. Congruent Non-Repeated Ratio 1.25 Below > Ratio 1 (Habituation) Ratio 1.5 Below > Ratio 1 (Habituation) Ratio 2 Below > Ratio 1 (Habituation) Ratio 2 Below > Ratio 1.25 Below Ratio 1.5 Above > Ratio 1 (Habituation) Ratio 2 Above > Ratio 1 (Habituation) Ratio 2 Above > Ratio 1.25 Above

Symbolic:Number Ordinal > Luminance Symbolic Ordinal Symbolic Ordinal > Luminance Ordinal (symbolic) and Symbolic Cardinal > Luminance Cardinal (Symbolic)

Task effect: Numerical > Nonnumerical Numerical then Continuous group: Congruent numerical task > Congruent continuous task (Interference-Reference interference) AND (Covariation-Reference Covariation) Distance of 18 vs. Distance of 27 Nonsymbolic: Number Ordinal > Luminance Nonsymbolic Ordinal Dot Ordinal > Luminance Ordinal (dot) and Dot Cardinal > Luminance Cardonal(Dot)

Physical Comparison (maximal interference > minimal interference) Numbers > Body Parts (Block) Numbers > Body Parts (ER)

Numerical comparison task: Incongruent vs. Congruent Numerical comparison > physical comparison Numerical comparison (Distance 1 > Distance 4, only neutral trials) Physical comparison (incongruent trials > congruent trials)

Magnitude Change Digits Magnitude Change Digits > Dots

Notation Adaptation Quantity Adaptation Notation x Adaptation

Numerical vs. Size Numerical vs. Luminance Numerical Distance

Contrast Name

1 7 8 6 5

17 2 1 1 1 1 1 1 1

3 10

6 7 10

10

2 4

3 4 3

2 5 5 0

10 3

2 1 1

7 8 3

Foci

Nonsymbolic 7 Nonsymbolic 9 Nonsymbolic 14 Nonsymbolic 7 (continued on next page)

Symbolic Symbolic Nonsymbolic Nonsymbolic Nonsymbolic

Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic Symbolic

Symbolic Symbolic

Symbolic Nonsymbolic Nonsymbolic

Nonsymbolic

Nonsymbolic Nonsymbolic

Symbolic Symbolic Symbolic

Symbolic Symbolic Symbolic Symbolic

Symbolic Symbolic

Symbolic Symbolic Symbolic

Symbolic Symbolic Symbolic

Magnitude Type

H.M. Sokolowski et al.

Neuropsychologia (xxxx) xxxx–xxxx

2001

2004

2011

2015 2011

2010

2004

2006

Pinel P

Pinel P

Price G R

Robertson B D Roggeman C

Santens S

Shuman M

Tang J

2013

1999

Pinel P

Vogel S E

Year

1st Author

Table 2 (continued)

Neuropsychologia

Journal of Cognitive Neuroscience

Neuron

Cerebral Cortex

NeuroImage Journal of Neuroscience

NeuroImage

Neuron

NeuroImage

Neuroreport

Journal

14

18

9

16

16 23

19

15

13

11

N

fMRI

fMRI

fMRI

fMRI

fMRI fMRI

fMRI

fMRI

fMRI

fMRI

Imaging Method

25

25

22.2

23 25.8

22.17

24

26

Mean Age

7F 7M

7F 11M

2F 7

1F 13M

8F 8M 23M

6F 13M

18F 6M

2F 9M

Gender

Number line estimation

Comparison

Comparison

Match-to-numerosity

Comparison Passive Viewing

Passive Viewing

Stroop

Comparison

Compare to 5

Tasks (s)

10

Number > Control Number Specific Activation

conjunction: (Large numerosity > Medium numerosity) and (Medium numerosity > Small numerosity) Experiment 1: Nonsymbolic number comparison > Nonsymbolic colour comparison Numerical > Physical Physical Task Conflict Trials > Physical Task Non-Conflict Trials

(conjunction) Arabic digits > Letters and Arabic digits > Scrambled digits Incongruent - Congruent contrast Large vs. Small Numerical Deviants Far vs. Close Numerical Deviants

Number Comparison vs. Size Comparison Number Comparison Small Distance vs. Number Comparison Large Distance

Verbal vs. Arabic Arabic vs. Verbal Distance Effect

Arabic Number > Verbal Number Close Distance > Far Distance Far Distance > Close Distance

Contrast Name

Symbolic Symbolic

Symbolic Symbolic

Nonsymbolic

Nonsymbolic

Symbolic Nonsymbolic Nonsymbolic

Symbolic

Symbolic Symbolic

Symbolic Symbolic Symbolic

Symbolic Symbolic Symbolic

Magnitude Type

10 5

10 1

2

6

43 2 1

1

5 3

3 6 7

1 1 1

Foci

H.M. Sokolowski et al.

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H.M. Sokolowski et al.

performed using an uncorrected threshold of p < 0.001 with 5000 threshold permutations and a minimum volume of 50 mm3. Results from both of these methods for thresholding are reported. Conjunction analyses were computed to quantitatively determine which brain regions are activated by two single dataset ALE maps. The conjunction map was created using the voxel-wise minimum value of the single dataset ALE map. If both single dataset ALE maps have significant activation in a particular voxel, then that voxel is considered to have significant conjunction between the two maps. The following ALE conjunctions were computed: (1) non-numerical and numerical, (2) non-numerical and symbolic, (3) non-numerical and nonsymbolic. Contrast analyses were computed to identify brain regions that were specifically activated by the non-numerical magnitude map and the numerical magnitude maps. Contrast analyses are computed by subtracting one single dataset ALE map from the other. Specifically, the contrast analysis algorithm pools the foci from the two single dataset ALE maps being compared, and then randomly separates the two foci into two groups. The two groups have the same number of foci as the two single dataset ALE maps. This creates simulated null data that corrects for unequal sample sizes. The single dataset ALE maps are contrasted and compared to the contrast of the two groups of null data. This identifies which voxels in the single experimental map differ significantly from the distribution of values within that voxel. The data are converted to Z-scores. The following ALE contrasts were computed: (1) non-numerical > numerical, (2) numerical > non-numerical (3) non-numerical > symbolic, (4) symbolic > non-numerical, (5) nonnumerical > nonsymbolic, (6) nonsymbolic > non-numerical.

computed to determine which regions were specifically activated by numerical and by non-numerical magnitude processing. Subsequently, numerical magnitude processing was split into symbolic and nonsymbolic numerical magnitude processing, creating two additional ALE maps (symbolic numerical magnitude and nonsymbolic numerical magnitude). Conjunction and contrast analyses were computed to compare symbolic and nonsymbolic numerical magnitude processing to non-numerical magnitude processing. 2.4. Single dataset ALE maps First, two ALE meta-analyses were conducted to identify convergent regions of activation for: (1) non-numerical magnitude processing, and (2) numerical magnitude processing. The numerical magnitude processing ALE map included contrasts with both symbolic and nonsymbolic stimuli. Following this, two additional ALE meta-analyses were conducted to identify convergent regions of activation for: (1) symbolic number processing, and (2) nonsymbolic number processing. Scribe (version 2.3 or 3.0.8) was used to input studies into the brainmap database. Sleuth (version 2.4) was used to compile coordinates and compute the Lancaster transformation. GingerALE (version 2.3.6) was used to compute the single file ALE meta-analyses, conjunction analyses, and contrast analyses. Out of the 93 included studies, 28 were used to create the non-numerical magnitude map of activation (418 subjects, 70 contrasts, 457 foci) and 65 were used to create the numerical map of activation (1015 subjects, 131 contrasts, 660 foci). Of the 65 papers included in the numerical magnitude map, 37 were used to create the symbolic map of activation (576 subjects, 77 contrasts, 341 foci) (cf. Table 1), and 28 were used to create the nonsymbolic map of activation (439 subjects, 54 experiments, 319 foci) (cf. Table 2). The symbolic and nonsymbolic numerical ALE maps use all papers included in Sokolowski et al. (2016) as well as eight additional papers that have been published since. The symbolic numerical ALE map includes six additional papers and the nonsymbolic ALE map includes two additional papers. Numerical search terms for years 2014–2016 and non-numerical magnitude search terms were used to identify these additional papers. All ALE analyses were thresholded using a cluster-level correction of 0.05 with a clusterforming (uncorrected) threshold of p < 0.001, generated from 1000 threshold permutations. This recently developed correction provides a faster and more rigorous analytical solution to address the issue of false positives driven by multiple-comparisons (Eickhoff et al., 2012).

2.6. Anatomical labeling Anatomical labels were produced automatically using GingerALE software. A label was produced for each of the peak ALE locations within each cluster. Anatomical labels are reported in Tables 3–7. 3. Results The results will be presented in the following order. First, the results are presented for the non-numerical magnitude map and the numerical magnitude map. Following this, the numerical magnitude map will be split into symbolic numerical magnitudes and nonsymbolic numerical magnitudes. Then the results of the symbolic numerical magnitude map and the nonsymbolic numerical magnitude map will be presented. This will be followed with the results of the conjunction and contrast analyses revealing overlapping and distinct brain regions for: (1) non-numerical and numerical, (2) non-numerical and symbolic, and (3) non-numerical and nonsymbolic.

2.5. Conjunction and contrast analyses Conjunction and contrast analyses were conducted to identify overlapping and distinct brain regions for non-numerical and numerical magnitude processing. Conjunction and contrast analyses were also computed to examine overlapping and distinct brain activation for nonnumerical compared to symbolic numerical magnitude processing and for non-numerical compared to nonsymbolic numerical magnitude processing. Conjunction and contrast analyses were performed using an uncorrected threshold of p < 0.01 with 5000 threshold permutations and a minimum volume of 50 mm3. An uncorrected threshold was used because the optimal cluster-level correction used to create the single data ALE analyses (Eickhoff et al., 2012) is not yet available for conjunction and contrast analysis. Although false discovery rate (FDR) thresholding is available to use for the conjunction and contrast analyses it, is not recommended because ALE models the foci as 3D Gaussian distributions (Chumbley and Friston, 2009). An uncorrected threshold of p < 0.01 is appropriate for the conjunction and contrast analyses. This is because the conjunction and contrast analyses use clusters from the single dataset ALE maps that have already passed the strict threshold (cluster-level p < 0.05, uncorrected p < 0.001). In order to identify brain regions that exhibited the strongest level of metaanalytic convergence, contrast and conjunction analyses were also

3.1. Single dataset meta-analyses (numerical and non-numerical) Single dataset ALE meta-analyses were computed to examine converging foci for non-numerical magnitude processing, and numerical magnitude processing. 3.1.1. Non-numerical ALE map The non-numerical single dataset ALE map revealed convergent regions of brain activation that support non-numerical magnitude processing (Fig. 1, Table 3). Convergent regions of brain activation across 28 studies (Table 1) were in the left superior parietal lobule, bilateral inferior parietal lobules, right inferior frontal gyrus, medial frontal gyrus, and bilateral superior frontal gyri. Additionally, there was convergent activation in the left precentral gyrus, left fusiform gyrus, and bilateral insula. 3.1.2. Numerical ALE map The numerical single dataset ALE map revealed convergent regions of brain activation that support numerical magnitude processing 11

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inferior parietal lobule, bilateral precuneus, bilateral medial frontal gyri, right insula, right precentral gyrus, and middle occipital gyrus. 3.3. Conjunction and contrast analyses 3.3.1. Conjunction ALE map (non-numerical and numerical) A conjunction analysis was computed to identify which brain regions were activated by both the non-numerical and the numerical magnitude single dataset ALE maps. Significant clusters of brain activation for non-numerical and numerical magnitude processing converged in the bilateral inferior parietal lobules, left superior parietal lobule, bilateral insula, right inferior frontal gyrus, right medial frontal gyrus, left superior frontal gyrus, and left fusiform gyrus (Fig. 2, Table 5). All brain regions reported in this conjunction analysis were significant at p < 0.01, and p < 0.001 with a minimum cluster size of 50. 3.3.2. Contrast ALE maps (non-numerical and numerical) Contrast analyses that compared the single dataset ALE maps were conducted to reveal which brain regions were specifically activated by non-numerical magnitude processing and numerical magnitude processing. The contrast analyses revealed that the left precentral gyrus was specifically activated by non-numerical > numerical, and the left superior parietal lobule was specifically activated by numerical > nonnumerical (Fig. 2, Table 5). All brain regions reported in these contrast analyses were significant at p < 0.01, but not at p < 0.001 with a minimum cluster size of 50. 3.3.3. Conjunction ALE map (non-numerical and symbolic) A conjunction analysis was computed to identify which brain regions were activated by both the non-numerical and the symbolic numerical magnitude single dataset ALE maps. Significant clusters of brain activation for non-numerical and symbolic numerical magnitude processing converged in the bilateral inferior parietal lobules, left superior parietal lobule, right medial frontal gyrus, and right claustrum (Fig. 2, Table 5). All brain regions reported in this conjunction analyses were significant at p < 0.01, and p < 0.001 with a minimum cluster size of 50.

Fig. 1. : Single Dataset ALE maps of non-numerical, numerical, symbolic, and nonsymbolic number processing. The ALE analyses revealed significant clusters of convergent brain clusters (cf., Table 1, Table 2). Activations were identified using a cluster-level threshold of p < 0.05 with 1000 threshold permutations and an uncorrected p < 0.001. Brain surface maps sliced at Z=48 and Y =− 48 are shown in Talairach space.

(Fig. 1, Table 3). Convergent regions of brain activation across 65 studies (Table 1) included the bilateral inferior parietal lobules, superior parietal lobules, bilateral precuneus, right medial frontal gyrus, right inferior frontal gyrus, bilateral middle occipital gyri, left inferior occipital gyrus, bilateral insula, and left superior temporal gyrus.

3.3.4. Contrast ALE maps (non-numerical and symbolic) Contrast analyses that compared the single dataset ALE maps were conducted to reveal which brain regions were specifically activated by non-numerical magnitude processing and symbolic numerical magnitude processing. The contrast analyses revealed that the left precentral gyrus, right insula, left superior frontal gyrus, left medial frontal gyrus, and left inferior frontal gyrus were specifically activated by nonnumerical > symbolic. The brain regions that are specific to nonnumerical > symbolic were significant at p < 0.01, but not p < 0.001 with a minimum cluster size of 50. The left superior parietal lobule was specifically activated by symbolic > non-numerical (Fig. 2, Table 6). Activation in the left superior parietal lobe for symbolic > non-numerical was significant at p < 0.01, and at p < 0.001 with a minimum cluster size of 50.

3.2. Single dataset meta-analyses (symbolic numerical and nonsymbolic numerical) The foci included in the numerical map were categorized as symbolic or nonsymbolic. Separate single dataset ALE meta-analyses were computed to examine converging foci for symbolic numerical magnitude processing, and nonsymbolic numerical magnitude processing. 3.2.1. Symbolic ALE map The symbolic single dataset ALE map revealed convergent regions of brain activation that support symbolic magnitude processing (Fig. 1, Table 4). Convergent regions of brain activation across 37 studies (Table 1) were in the left superior parietal lobule, bilateral inferior parietal lobules, bilateral precuneus, left middle temporal gyrus, right superior frontal gyrus, right cingulate gyrus, and right claustrum.

3.3.5. Conjunction ALE map (non-numerical and nonsymbolic) A conjunction analysis was computed to identify which brain regions were activated by both the non-numerical and the nonsymbolic numerical magnitude single dataset ALE maps. Significant clusters of brain activation for non-numerical and nonsymbolic numerical magnitude processing converged in the right inferior parietal lobule, left superior parietal lobule, right insula, right inferior frontal gyrus, bilateral medial frontal gyri, and right superior frontal gyrus (Fig. 2, Table 5). All brain regions reported in this conjunction analyses were significant at p < 0.01, and p < 0.001 with a minimum cluster size of 50.

3.2.2. Nonsymbolic ALE map The nonsymbolic single dataset ALE map also revealed convergent regions of brain activation that support symbolic magnitude processing (Fig. 1, Table 4). Convergent regions of brain activation across 28 studies (Table 1) were in the bilateral superior parietal lobules, right 12

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Table 3 Single Dataset Analyses (Non-numerical, Numerical). Hemisphere

Brain Area

Non-Numerical L L R R L L L R L R R L Numerical R R R R R R R L L L L L R R R L L L L L L R

BA

X

Y

Z

ALE

Vol/mm

Superior Parietal Lobule Inferior Parietal Lobule Inferior Parietal Lobule Insula Precentral Gyrus Precentral Gyrus Fusiform Gyrus Inferior Frontal Gyrus Superior Frontal Gyrus Medial Frontal Gyrus Superior Frontal Gyrus Insula

7 40 40 13 6 6 19 9 6 32 8 13

−32 −36 36 30 −40 −48 −46 42 −8 2 6 −32

−52 −50 −44 20 −6 0 −68 6 10 10 16 22

46 50 44 6 32 28 −10 28 48 46 50 2

0.0219 0.021 0.0304 0.0321 0.0239 0.0168 0.0238 0.0261 0.021 0.0154 0.0137 0.0225

2008

Inferior Parietal Lobule Superior Parietal Lobule Precuneus Superior Parietal Lobule Middle Occipital Gyrus Middle Occipital Gyrus Middle Occipital Gyrus Superior Parietal Lobule Superior Parietal Lobule Precuneus Inferior Parietal Lobule Superior Temporal Gyrus Medial Frontal Gyrus Insula Inferior Frontal Gyrus Middle Occipital Gyrus Middle Occipital Gyrus Middle Occipital Gyrus Middle Occipital Gyrus Inferior Occipital Gyrus Insula

40 7 31 7 19 19 18 7 7 39 40 39 32 13 9 18 18 19 19 19 13

38 30 26 18 30 34 34 −28 −26 −30 −34 −34 4 30 44 −38 −26 −28 −32 −42 −32 38

−44 −58 −72 −64 −78 −78 −84 −54 −60 −64 −36 −50 10 20 4 −84 −86 −88 −84 −68 18 32

44 46 26 52 18 10 2 44 44 36 42 24 46 6 28 −2 2 18 8 −6 4 24

0.0549 0.0379 0.0379 0.0307 0.0238 0.0238 0.02 0.0525 0.0473 0.0362 0.0217 0.0194 0.0515 0.0513 0.0514 0.0269 0.026 0.0235 0.0222 0.0433 0.0299 0.0279

17360

1968 1720 1512 1360 1144 1000

920

14240

4992 2544 2432 2208

1144 1096 952

particular, Cantlon et al. (2009b) concluded that the intraparietal sulcus is recruited during both numerical and non-numerical magnitude processing. Similarly, Cohen Kadosh et al. (2008) concluded that the intraparietal sulcus hosts overlapping domain general and domain specific neural populations associated with numerical and non-numerical magnitudes. However, these previous conclusions were inferred by spatially mapping coordinates onto a template brain (Cantlon et al., 2009b; Cohen Kadosh et al., 2008; Van Essen, 2012). In contrast, the current quantitative meta-analysis evaluated the data using quantitative statistics. Moreover, unlike the previous qualitative studies, the current study allowed for the implementation of conjunction and contrast analyses to quantitatively evaluate overlapping and distinct brain regions that support symbolic, nonsymbolic, and non-numerical magnitude processing. In what follows, this discussion will outline several important research findings that arose from these conjunction and contrast analyses and discuss how these findings relate to prominent theoretical frameworks.

3.3.6. Contrast ALE maps (non-numerical and nonsymbolic) Contrast analyses that compared the non-numerical and nonsymbolic single dataset ALE maps were conducted to reveal which brain regions were specifically activated by non-numerical magnitude processing and nonsymbolic numerical magnitude processing. The contrast analyses revealed that no regions were specifically activated by non-numerical > nonsymbolic. Small regions in the bilateral precuneus were specifically activated by nonsymbolic > non-numerical (Fig. 2, Table 5). All brain regions reported in these contrast analyses were significant at p < 0.01, but not p < 0.001 with a minimum cluster size of 50.

4. Discussion The present study examined the neural bases of the ability to process numerical and non-numerical magnitudes at the meta-analytic level. Specifically, quantitative meta-analytic techniques were implemented to examine two questions. First, this study examined whether number is processed using a specific number processing system or if number is rooted in a general magnitude processing system used to process both numerical and non-numerical magnitudes. Second, this study looked at whether these overlapping and distinct brain regions for non-numerical and numerical magnitudes depend on the format of the numerical magnitude. This finding from the single file ALE maps that overlapping and distinct activation (particularly in regions along the intraparietal sulcus) support numerical and non-numerical magnitude processing, provides statistically quantified support for previous qualitative metaanalyses (Cantlon et al., 2009b; Cohen Kadosh et al., 2008). In

4.1. Numerical vs. non-numerical A prominent discussion in the field of numerical cognition concerns whether numbers are represented using an approximate number system, specifically used to process numerical magnitudes (Cicchini et al., 2016; Odic and Halberda, 2015), or a general magnitude system used to process both numerical and non-numerical magnitudes (Cantlon et al., 2009b; Cohen Kadosh et al., 2008; Simon, 1999; Walsh, 2003). It is also possible that numbers are processed using both number specific and general magnitude cognitive systems. In the current study, conjunction analyses were used to quantitatively identify 13

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Table 4 Single Dataset Analyses (Symbolic Numerical, Nonsymbolic Numerical). Hemisphere

Brain Area

BA

X

Y

Z

ALE

Vol/mm

Symbolic Numerical L L L L L L L R R R R R R R R

Superior Parietal Lobule Precuneus Inferior Parietal Lobule Inferior Parietal Lobule Inferior Parietal Lobule Inferior Parietal Lobule Middle Temporal Gyrus Inferior Parietal Lobule Precuneus Precuneus Precuneus Precuneus Superior Frontal Gyrus Cingulate Gyrus Claustrum

7 19 40 40 40 40 39 40 19 31 7 7 6 32

−26 −30 −34 −42 −40 −38 −34 36 30 26 26 20 2 4 28

−60 −64 −52 −44 −46 −50 −54 −44 −64 −72 −50 −52 10 18 20

42 38 36 38 46 50 26 42 38 26 46 46 48 42 4

0.0308 0.0307 0.0237 0.0199 0.0199 0.0192 0.0146 0.0406 0.0303 0.021 0.0177 0.0173 0.021 0.0165 0.0257

8272

Nonsymbolic Numerical R R R R R R R L L L L R L R R L L

Superior Parietal Lobule Inferior Parietal Lobule Superior Parietal Lobule inferior Parietal Lobule Precuneus Middle Occipital Gyrus Precuneus Superior Parietal Lobule Precuneus Precuneus Precuneus Medial Frontal Gyrus Medial Frontal Gyrus Insula Precentral Gyrus Middle Occipital Gyrus Middle Occipital Gyrus

7 40 7 40 7 19 31 7 7 19 7 32 32 13 6 19 19

18 44 28 38 28 34 28 −30 −20 −26 −22 4 −4 32 42 −32 −26

−64 −38 −58 −48 −48 −78 −72 −54 −62 −70 −64 10 10 20 2 −84 −88

52 46 46 48 48 10 24 46 46 30 36 46 44 8 28 8 18

0.03 0.0296 0.0265 0.0264 0.0261 0.0228 0.0176 0.0319 0.0224 0.0188 0.0179 0.0331 0.0243 0.0338 0.0364 0.0204 0.0189

11720

7504

944 920

6064

4496 2032 1816 1544

reflected in the overlapping regions in the current ALE meta-analyses. Although the current available meta-analytic methods cannot confidently conclude that regions in the brain that are engaged during both numerical and non-numerical magnitude processing host a general magnitude system, it can highlight which brain regions distinctly support numerical and non-numerical magnitudes. Contrast analyses were used to reveal brain regions that were specifically activated by non-numerical compared to numerical magnitude processing. Subtracting the non-numerical map from the numerical map revealed activation in regions typically associated with number processing (Ansari, 2008; Cantlon, 2012; Dehaene et al., 2003; Nieder and Dehaene, 2009). Specifically, the contrast numerical > non-numerical revealed specific activation in the left superior parietal lobule. Importantly, no brain regions in the parietal lobe were found to be specifically activated by non-numerical magnitude processing. Specifically, the contrast non-numerical > numerical revealed that activation in the left precentral gyrus, a region in the primary motor cortex that has been associated with movement (Buccino et al., 2004), was related to non-numerical magnitude processing. Therefore, numbers are processed using the combination of all brain regions found to support non-numerical magnitude processing and a brain region that is specific to numerical magnitudes.

regions that were overlapping for non-numerical and numerical magnitude processing in order to determine whether brain regions used to process number are specifically associated with number, or if these regions process magnitude more generally. Conjunction analyses revealed that several regions including the bilateral inferior parietal lobules, left superior parietal lobule, right claustrum and right medial frontal gyrus were consistently activated by both numerical and nonnumerical stimuli. Therefore, this study is first to provide quantitative meta-analytic support for the hypothesis that regions along the parietal and frontal cortex host a general magnitude processing system. It is important to acknowledge that ALE methodology does not discriminate between patterns of activation within the overlapping regions of a conjunction analysis. This limitation of coarse spatial resolution suggests that while overall activation may overlap in a specific region, the pattern of this activation may differ. This means that the overlapping regions revealed in conjunction analyses for numerical and non-numerical magnitudes may be overlapping due to domain general processes such as decision-making or response selection rather than general magnitude representations. However, all contrasts that were included in the current meta-analyses were contrasted against a control condition. Therefore, it is less likely that overlapping activation was due to domain general process rather than to basic magnitude processing because the selection criteria should have minimized domain-general factors such as response selection. Moreover, a previous quantitative meta-analysis examining symbolic and nonsymbolic numerical magnitude processing specifically examined brain regions activated during passive numerical tasks (such as passively viewing Arabic digits) (Sokolowski et al., 2016). In this study, the passive ALE map aligned closely to the larger ALE map that included both passive and active contrasts (Sokolowski et al., 2016). This finding supports the idea that it is not task-related activity that is

4.2. Symbolic and nonsymbolic vs. non-numerical Previous empirical papers as well as a quantitative meta-analysis have indicated that common and distinct brain regions support symbolic and nonsymbolic numerical magnitude processing (e.g Fias et al., 2003; Holloway et al., 2010; Lyons et al., 2014; Piazza et al., 2007; Sokolowski et al., 2016). However, no study to date has examined whether the overlapping and distinct brain regions support14

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Fig. 2. ALE maps of the conjunction and contrasts. Conjunction and contrast of A) non-numerical and numerical single dataset ALE maps (described in Table 3, Fig. 1). The ALE conjunction analysis revealed significant clusters of convergence between non-numerical and numerical (gold). ALE contrast analyses reveal specific activation for numerical > nonnumerical (purple) and non-numerical > numerical (green). B) non-numerical and symbolic numerical single dataset ALE maps (described in Table 3, Table 4, Fig. 1). The ALE conjunction analysis revealed significant clusters of convergence between non-numerical and symbolic numerical (gold). ALE contrast analyses revealed specific activation for symbolic > non-numerical (red) and non-numerical > symbolic (green). C) non-numerical and nonsymbolic numerical single dataset ALE maps (described in Table 3, Table 4, Fig. 1). The ALE conjunction analysis revealed significant clusters of convergence between non-numerical and nonsymbolic numerical (gold). ALE contrast analyses revealed specific activation for nonsymbolic > non-numerical (blue). No regions were activated for non-numerical > nonsymbolic. All conjunction and contrast analyses were conducted using an uncorrected p < 0.01 and p < 0.001 with 5000 permutations and a minimum volume of 50 mm3. All regions in the conjunction analyses were significant at p < 0.001. For the contrast analyses, only the brain region from the contrast of symbolic > nonsymbolic (B) was significant at p < 0.001. Regions from all other contrast analyses were significant at p < 0.01, but not p < 0.001. Brain slices are shown along the Z-plane in Talairach space. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

inferior frontal gyrus, left medial frontal gyrus and right superior frontal gyrus). Contrast analyses were used to reveal brain regions that were specifically activated by symbolic versus non-numerical magnitude processing and nonsymbolic versus non-numerical magnitude processing. Subtracting the non-numerical map from the symbolic and nonsymbolic numerical maps respectively, revealed activation in regions typically associated with number processing (Ansari, 2008; Cantlon, 2012; Dehaene et al., 2003; Nieder and Dehaene, 2009). Specifically, the contrast symbolic > non-numerical revealed activation in the left superior parietal lobule. Notably, the left superior parietal lobule was also activated for numerical > non-numerical, but not nonsymbolic > non-numerical. Contrasting nonsymbolic > non-numerical revealed activation in the bilateral precuneus. The bilateral

ing numerical and non-numerical magnitudes differ as a function of number format. The current meta-analysis was the first study to separately compare symbolic and nonsymbolic numerical magnitudes to non-numerical magnitudes to determine whether the common and distinct regions depend on number format. Conjunction analyses revealed similarities and differences for the overlap between symbolic and non-numerical compared to nonsymbolic and non-numerical. Both symbolic and nonsymbolic numerical magnitudes overlapped with non-numerical magnitudes in the parietal and frontal cortex (specifically, the right inferior parietal lobule, left superior parietal lobule, and right medial frontal gyrus). However, symbolic and non-numerical maps also overlapped in a left lateralized parietal region, whereas nonsymbolic and non-numerical maps also overlapped in multiple regions in the frontal lobe (specifically, the right 15

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Table 5 Conjunction and Contrast Analyses (Non-numerical, Numerical). Hemisphere

BA

X

Y

Z

ALE

Vol/mm

Sig.

Non-Numerical and Numerical R Inferior Parietal Lobule L Superior Parietal Lobule L Inferior Parietal Lobule R Insula R Inferior Frontal Gyrus L Superior Frontal Gyrus R Medial Frontal Gyrus R Superior Frontal Gyrus L Fusiform Gyrus L Insula

40 7 40 13 9 6 32 8 19 13

36 −32 −36 30 42 −6 2 6 −46 −32

−44 −52 −50 20 6 10 10 16 −68 22

44 46 50 6 28 48 46 50 −10 2

0.0304 0.0219 0.021 0.0321 0.0261 0.0205 0.0154 0.0137 0.0238 0.0225

1960 1824

**

1552 1112 792

**

712 528

**

Numerical > Non-numerical L Superior Parietal Lobule

7

−32

−66

44

2.9478

264

*

Non-numerical > Numerical L Precentral Gyrus L Precentral Gyrus

6 6

−40 −36

−8.5 −4

35 34

3.3528 3.2389

808

*

* **

Brain Area

**

** **

**

significant at the p < 0.01 level. significant at the p < 0.001 level

influenced by non-numerical magnitude processing than those specifically activated by symbolic number processing. An alternate possible explanation for the finding that regions specifically activated by symbolic > non-numerical are more significant than those for nonsymbolic > non-numerical is that the symbolic ALE map is more reliable than the nonsymbolic map (Sokolowski et al., 2016). Importantly, no parietal brain regions were specifically activated in non-numerical magnitude processing. In particular, the contrast nonnumerical > symbolic revealed activation in the frontal lobe and the insula. No regions were specifically activated by non-numerical that were not also activated by nonsymbolic. Notably, the right insula and medial frontal gyrus were activated in the non-numerical > symbolic contrast and in the conjunction of non-numerical and nonsymbolic (Fig. 2). This suggests that these regions support overlap between nonnumerical magnitudes and numerical magnitudes in the nonsymbolic format but not the symbolic format. Overall, the results of the nonnumerical > symbolic and non-numerical > nonsymbolic contrasts showed that non-numerical magnitude processing did not specifically activate any parietal number regions that were not also activated by number processing. Together these findings suggest that symbolic and nonsymbolic numbers are processed using the general magnitude

precuneus was not significantly activated by numerical > non-numerical or symbolic > non-numerical. The finding that the left superior parietal lobule was specifically activated by numerical > non-numerical, and symbolic > non-numerical but not nonsymbolic > non-numerical suggests that this numerically specific region is driven by symbolic stimuli. Moreover, activation in the left superior parietal lobule for symbolic > non-numerical is the only region from a contrast analysis that was found to be significant at both p < 0.01 and p < 0.001. One interpretation for this finding is that perhaps nonsymbolic numerical magnitude processing is more similar to non-numerical magnitude processing than symbolic numerical magnitude processing. This notion is supported by the large body of research that shows that estimating the amount of dots (i.e. the numerical magnitude) in a nonsymbolic dot array is inherently confounded by non-numerical (e.g. area and density) properties of the array (Henik et al., 2012; Leibovich and Henik, 2013). In other words, if a quantity of a nonsymbolic numerical magnitude changes, the non-numerical properties associated with that quantity also change. Despite researchers' best efforts, it is not possible to control for all of these continuous properties (Gebuis and Reynvoet, 2012; Leibovich and Henik, 2013). Therefore, perhaps the regions specifically activated by nonsymbolic number processing are more

Table 6 Conjunction and Contrast Analyses (Non-numerical, Symbolic Numerical). Hemisphere

Brain Area

BA

X

Y

Z

ALE

Vol/mm

Sig.

40 7 40

−44 −52 −50 20 10

44 44 50 4 46

0.0304 0.0187 0.0186 0.0257 0.0154

1528 1256

**

744 256

**

Non-numerical and Symbolic Numerical R Inferior Parietal Lobule L Superior Parietal Lobule L Inferior Parietal Lobule R Claustrum R Medial Frontal Gyrus

32

36 −30 −38 28 2

Symbolic Numerical > Non-numerical L Superior Parietal Lobule

7

−32

−66

44

3.5401

576

**

Non-numerical > Symbolic Numerical L Precentral Gyrus L Precentral Gyrus R Insula L Superior Frontal Gyrus L Medial Frontal Gyrus L Inferior Frontal Gyrus

6 6 13 6 32 47

−42 −40 36 −8 −8 −30

−8 −10 12 14 14 25

38 34 4 50 46 −2.7

2.6197 2.5622 2.6356 2.5899 2.4573 2.4181

344

*

96 64

*

56

*

* **

significant at the p < 0.01 level. significant at the p < 0.001 level.

16

**

**

*

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Table 7 Conjunction and Contrast Analyses (Non-numerical, Nonsymbolic Numerical). Hemisphere

Brain Area

Non-numerical and Nonsymbolic Numerical R Inferior Parietal Lobule R Insula L Superior Parietal Lobule R Inferior Frontal Gyrus L Medial Frontal Gyrus R Medial Frontal Gyrus R Superior Frontal Gyrus Nonsymbolic Numerical > Non-numerical R Precuneus L Preuneus

BA

X

Y

Z

ALE

Vol/mm

Sig.

40 13 7 9 32 32 8

40 32 −32 42 −6 2 6

−44 20 −52 6 10 10 16

44 6 46 28 46 46 50

0.0245 0.0302 0.0219 0.0261 0.0205 0.0154 0.0137

1568 1288 1208 960 792

**

7 7

18 −26

−58 −46

48 38

3.2389 2.5241

184 56

*

** ** ** **

*

Non-numerical > Nonsymbolic Numerical * **

significant at the p < 0.01 level. significant at the p < 0.001 level.

regions as well as adjacent language areas that may support the mapping of symbols onto magnitudes. Research examining the neural correlates of ordinal processing of symbols have implicated the intraparietal sulcus as important for processing both magnitude and ordering of number symbols (Franklin and Jonides, 2008). Therefore, it is also likely that the symbolic specific regions support ordinal components of symbolic number processing. In accordance with the neuronal recycling hypothesis and Rozin (1976), perhaps symbolic numbers are processed with a general magnitude system as well as symbolic specific brain regions that are specialized for processing different aspects of symbolic numbers such as linguistic or ordinal components (Dehaene and Cohen, 2007; Rozin, 1976). The analogous nonsymbolic contrast, namely nonsymbolic > non-numerical, revealed that the bilateral precuneus is specifically activated by nonsymbolic numbers. Research has implicated the precuneus (along with the transverse parietal sulcus and the posterior inferior parietal sulcus) as important for tactile and visual object processing in both humans and macaques (Culham et al., 1998; Culham and Kanwisher, 2001; Grefkes and Fink, 2005). Consequently, it is likely that the specific nonsymbolic activation in the bilateral precuneus was related to the processing of the objects in a nonsymbolic array. Overall, these contrasts supported the idea that both symbolic and nonsymbolic numbers are processed using a general magnitude system as well as format specific number regions, rather than an approximate number system.

processing system (i.e. all regions that were significantly activated by non-numerical magnitude processing) and additional brain regions that are correlated with the format of the numerical magnitude (i.e symbolic and nonsymbolic numbers). The finding that symbolic specific regions remained significant at a stricter p-threshold, and that several regions were activated by non-numerical > symbolic, but not non-numerical > nonsymbolic suggest that there is stronger specificity for symbolic than for nonsymbolic numerical magnitude processing.

4.3. Neuronal recycling hypothesis The finding that numerical magnitudes activate the same neural regions as non-numerical magnitudes lends support to the neuronal recycling hypothesis (Dehaene and Cohen, 2007). The neuronal recycling hypothesis states that culturally acquired skills such as reading and math use a set of evolutionarily ancient circuits that are sufficiently similar to the required function and have sufficient neural plasticity to support processing of novel cultural abilities (Dehaene and Cohen, 2007). In accordance with this hypothesis, the data from the current meta-analyses indicate that the culturally acquired ability to process numbers may have invaded cortical regions dedicated to the evolutionarily older general magnitude processing system. Notably, the data in this meta-analysis also support a related hypothesis proposed by Rozin (1976) that the process of evolution drives evolutionarily older systems to adapt so that existing processing capabilities can be applied to novel abilities. Specifically, this theory suggests that the evolutionarily older system that originally evolved to process magnitudes became accessible to other systems used to process numbers through the process of evolution (Henik et al., 2012; Rozin, 1976). The current data cannot determine whether the system hijacked the general magnitude system (Dehaene and Cohen, 2007) or if the general magnitude system became accessible for number processing through evolution. However, these results do reveal that symbolic and nonsymbolic numbers activate a general magnitude system as well as additional seemingly format-specific regions. Interestingly, symbolic numbers specifically activated the left superior region of the parietal cortex and nonsymbolic numbers specifically activated the bilateral precuneus. This suggests that the brain regions that are format-dependent (i.e. differentially activated by symbolic and nonsymbolic numbers) were distinct and lateralized within the parietal cortex. Given the involvement of the left temporal and parietal cortex in language abilities (Price, 2000), it is possible that the regions along the left parietal lobule that are specifically activated by symbolic numbers may reflect the verbal semantic processing of number symbols. Therefore, it is likely that symbolic numerical representations are processed using general magnitude processing

4.4. The Frontal Lobes The importance of the frontal lobes for processing number has often been overlooked in empirical research on numerical and nonnumerical magnitude processing, due to the intense focus on activation in the parietal lobes supporting number processing (Cappelletti et al., 2010, 2009; Cohen Kadosh et al., 2007; Eger et al., 2003; Fias et al., 2003; Göbel et al., 2004; Holloway et al., 2010). However, many neuroimaging studies, as well as a recent quantitative meta-analysis, have reported consistent activation in the frontal cortex that is specific to number processing (Cohen Kadosh and Walsh, 2009; Cohen Kadosh et al., 2007; Dormal and Pesenti, 2009; Dormal et al., 2012b; Eger et al., 2003; Franklin and Jonides, 2008; Hayashi et al., 2013; Sokolowski et al., 2016). For a more detailed review of frontal brain activation supporting numerical magnitude processing see Sokolowski et al. (2016). The current meta-analysis helps to clarify the role of frontal brain regions in the processing of numerical magnitudes. Specifically, results revealed consistent activation in frontal regions during symbolic, nonsymbolic and non-numerical magnitude processing. Moreover, 17

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neuroimaging studies, which is a strong potential driver of conflicting findings between studies. Second, the massive cost associated with conducting neuroimaging means that the majority of empirical neuroimaging studies have extremely small sample sizes. A major advantage of ALE is that the algorithm groups many different studies, and consequently increases sample sizes. This convergence across methodologies combined with an increased sample size allows researchers to address broader theoretical questions and have more confidence in converging patterns of findings.

results showed that neural activation in response to both numerical and non-numerical magnitude processing is no less consistent in the frontal cortex compared to the parietal cortex. In particular, frontal activation was found in numerical and non-numerical single dataset ALE maps, the conjunction analysis of non-numerical and nonsymbolic magnitudes, as well as in the contrast of non-numerical > symbolic numerical magnitudes. This indicates that perhaps the frontal regions support the processing of non-numerical and nonsymbolic magnitude processing, but not symbolic magnitude processing. A potential explanation for the finding that frontal regions are shared by non-numerical and nonsymbolic magnitude processing, but not symbolic magnitude processing, is that non-numerical magnitude processing inherently confounds nonsymbolic numerical magnitude processing. Specifically, perhaps these frontal regions support the processing of the correlation between the numerical and non-numerical properties associated with nonsymbolic arrays. Another body of research has indicated that the ability to inhibit visual perceptual aspects of nonsymbolic dot arrays relates to the processing of nonsymbolic numerical magnitudes (Bugden and Ansari, 2016; Gebuis et al., 2016). Based on these recent findings, it is possible that the consistent frontal activation present during the processing of nonsymbolic numerical magnitudes supports the role of attentional selection or inhibition. Ultimately, since frontal regions are consistently engaged during basic number processing, even at the meta-analytic level, it is critical to begin to unpack the ways that these frontal regions support number processing.

4.6. Conclusions This study revealed that overlapping and distinct regions across the brain are activated by non-numerical magnitudes, symbolic numerical magnitudes, and nonsymbolic numerical magnitudes. These patterns of activation revealed the specific roles of parietal and frontal regions supporting numerical magnitude processing. Based on the finding that all forms of magnitudes activate the right inferior parietal lobule, a general magnitude processing system may be located in the right inferior parietal lobule. This study also highlights the lateralization of symbolic and nonsymbolic number processing within the parietal lobes. Specifically, as reported in Sokolowski et al. (2016), the left superior parietal lobule is potentially important for processing symbolic numerical magnitudes, while the bilateral precuneus may be important for processing nonsymbolic sets of items. However, the current findings extend this to show that not only is symbolic leftlateralized compared to nonsymbolic, but it is also left lateralized when compared to non-numerical magnitude processing. This lateralization in the brain supporting symbolic and nonsymbolic numerical magnitudes, as well as non-numerical magnitudes is an important avenue for future empirical research. The contrasts non-numerical > symbolic and non-numerical > nonsymbolic revealed no regions of activation in the parietal lobes that are specific to non-numerical magnitudes. This suggests that while there is specialization for symbolic and nonsymbolic numerical magnitude processing in the parietal lobules, the areas involved in non-numerical magnitude processing completely overlap with those engaged by numerical magnitude processing within the parietal cortex. However, frontal regions were activated by both nonnumerical and nonsymbolic numerical magnitudes, but not symbolic magnitudes. This suggests that these frontal regions may support the processing of non-numerical properties of nonsymbolic arrays. Overall, the present meta-analysis extends our understanding of the brain regions that support numerical compared to non-numerical magnitude processing and sets a foundation for future research to explore neural mechanisms that underlie basic number processing.

4.5. Advantages and limitations of ALE The present meta-analysis focused on brain regions that support non-numerical and numerical magnitude processing by quantitatively synthesizing results from 93 empirical papers. This study identified brain regions that were consistently activated across studies with varying methodologies and contrasts. Importantly, the numerical ALE maps were generated using a set of contrasts that were fairly homogeneous. In particular, the majority of the contrasts used data from number discrimination paradigms where the participant compared either Arabic digits for symbolic numbers or dot arrays for nonsymbolic numbers. However, the contrasts that comprise the nonnumerical magnitude ALE map were relatively heterogeneous. For example, contrasts comparing physical size, duration, and luminance were all included as contrasts in the non-numerical magnitude ALE map. Although ALE is a valuable methodology that can synthesize many different studies with different methods and techniques, it is important to be cognizant of the fact that the homogeneity of the contrasts within the three maps being compared are not equivalent. Additionally, ALE methodology has several specific limitations. First, counter-intuitively, the cluster-level algorithm leads to an increase in cluster sizes when the foci are closer in proximity. Second, the way that the algorithm creates Gaussian models of the data causes experiments with fewer subjects to produce more extensive clusters than experiments with more subjects. Finally, even though the modified ALE algorithm corrects for the confound of within-experiment clustering (Turkeltaub et al., 2012), there is still the potential for some influence of closely clustered foci from a specific experiment (for a detailed discussion see: Eickhoff et al. (2012)). Notwithstanding these limitations, ALE has several essential benefits as a tool for quantitatively synthesizing neuroimaging data. First, the algorithm supporting ALE can synthesize data with varying methodologies. Specifically, ALE can account for methodological differences across studies (such as the smoothing kernel and the statistical threshold used) by evaluating the spatial distribution of the foci reported within each experiment, while simultaneously preventing within-experiment coherence of several foci from over-influencing the results (Turkeltaub et al., 2012). Therefore, ALE is an invaluable tool because it accounts for the diversity of methodologies across empirical

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