Edited by: Angela Dorkas Friederici, Max Planck Institute for Human Cognitive and Brain Sciences, Germany
Reviewed by: Angela Dorkas Friederici, Max Planck Institute for Human Cognitive and Brain Sciences, Germany; Paul Summers, University of Modena, Italy
*Correspondence: Stefan Heim, Department of Psychiatry, Psychotherapy, and Psychosomatics, Medical School, RWTH Aachen University, Pauwelsstraße 30, 52074 Aachen, Germany. e-mail:
This is an open-access article distributed under the terms of the
The neural bases for numerosity and language are of perennial interest. In monkeys, neural separation of numerical Estimation and numerical Comparison has been demonstrated. As linguistic and numerical knowledge can only be compared in humans, we used a new fMRI paradigm in an attempt to dissociate Estimation from Comparison, and at the same time uncover the neural relation between numerosity and language. We used complex stimuli: images depicting a proportion between quantities of blue and yellow circles were coupled with sentences containing quantifiers that described them (e.g., “most/few of the circles are yellow”). Participants verified sentences against images. Both Estimation and Comparison recruited adjacent, partially overlapping bi-hemispheric fronto-parietal regions. Additional semantic analysis of positive vs. negative quantifiers involving the interpretation of quantity and numerosity specifically recruited left area 45. The anatomical proximity between numerosity regions and those involved in semantic analysis points to subtle links between the number system and language. Results fortify the homology of Estimation and Comparison between humans and monkeys.
No species but ours can pride itself in the possession of both mathematical and linguistic abilities. Some primates possess numerical abilities, but only we humans can talk about what we count. Are these two abilities governed by the same principles and supported by the same neural structures? Philosophers from Plato to Frege have pondered the relation between mathematical and natural languages, as these seem to share properties, having alphabets and combinatorial rules, allowing for recursion, as well as ambiguous expressions. Chomsky (
We report an fMRI experiment that addressed the language/math question from a new angle, and helped uncover the anatomical loci of linguistic and numerical operations. Our behavioral and imaging data seem to provide a fresh perspective on this perennial debate. Guided by current models of linguistic and mathematical capacity, we separated the neural underpinnings of complex language processes from those of numerosity-related ones. Within the latter, moreover, we were successful in identifying two distinct neural systems (one for quantity estimation, the other, for comparison). This three-way distinction between neurocognitive components emerged as subjects were evaluating linguistic statements about quantity against visual scenarios. Critically, it emanated from analyses of data from a single cross-modal parametric fMRI experiment that concomitantly probed numerical cognition and language.
The current view on numerical cognition and its brain basis is rather refined (Dehaene and Cohen,
The implementation of tasks that require the estimation of
In humans, bilateral parietal and frontal regions modulated by numerical distance have also been identified, and shown to have similar properties: in a seminal study by Piazza et al. (
For language to be directly related to numerical cognition, aspects of language processing that pertain to quantity would be expected to have a role in numerical cognition. Past studies have either investigated linguistic and arithmetical abilities separately Dehaene et al.,
We probed circuits for linguistic and mathematical processing in healthy participants in an fMRI experiment whose design featured two parameters, one that served as a proxy for numerical estimation, and the other, for comparison. It also featured a linguistic contrast that was orthogonal to numerosity (Polarity, the difference between positive quantifiers like
A parametric proportion paradigm (PPP henceforth) was introduced: participants were asked to verify auditory sentences about proportion against visual scenarios that contained two quantities of objects, and do so under time pressure. The relevant meaning representations were created through the inclusion of a proportional (or degree) quantifier in each sentence, which was either positive, e.g.,
The PPP design systematically varied the proportion between the colors across scenarios. Participants thus judged each sentence against eight different scenarios (created in Mathematica™), each with a different blue/yellow proportion (Figure
This design allows correlating the BOLD response separately with two parameters, and one contrast:
The Estimation parameter
The Comparison parameter RT: The closer
The Semantic Polarity contrast: linguistic stimuli were divided along a clear non-numerical axis that related to their meaning – Polarity, characterized by whether or not the meaning representation of the quantifier contained a negation (cf. The Meaning of the Proportional Quantifiers Used in Supplementary Material for details). Half of the quantifiers were positive (
The experimental goal, then, was to obtain a three-way dissociation within the same fMRI data set. This goal was accomplished by identifying voxels responding to the one or the other of the uncorrelated parameters (
The present design differs from previous numerosity experiments, and experiments that used linguistic stimuli to study numerical cognition (Cohen and Dehaene,
Quantifier | Polarity |
---|---|
Viele = many | Positive |
Wenige = few | Negative |
Die meisten = most | Positive |
Die wenigsten = very few | Negative |
Mehr als die Hälfte = more-than-half | Positive |
Weniger als die Hälfte = less-than-half | Negative |
All procedures were approved by the ethics committee of the Medical School at RWTH Aachen University.
Participants performed a truth-value judgment task, indicating by pressing the left or right response button whether an auditory sentence with a quantified subject matched a subsequently presented visual array of blue and yellow circles. Each sentence was presented 24 times, with one picture at a time. The 24 repetitions result from systematically combining each sentence with three different pictures for each of the eight different proportions of blue/yellow circles (see below). Stimulus presentation was controlled by a computer placed in the control room using Presentation 11.0 software (Neurobehavioral Systems, Albany, CA, USA), and each participant received a different pseudo-randomization of sentence–picture pairings.
Stimuli were constructed of auditory sentence–visual image pairs (cf. Figure
The trial schema (Figure
The fMRI experiment was carried out on a 3-T Trio scanner (Siemens, Erlangen, Germany). A standard birdcage head coil was used with foam paddings to reduce head motion. The functional data were recorded from 40 axial slices using a gradient-echo EPI sequence with echo time (TE) = 30 ms, flip angle = 90°, and repetition time (TR) = 3 s. The field of view (FOV) was 256 mm, with an in-plane resolution of 3 mm × 3 mm. The slice thickness was 3 mm with an inter-slice gap of 1 mm. A time series containing a total of 684 images was recorded, amounting to a total functional scanning time of 34 min.
Data analysis was performed using SPM5 (Wellcome Department of Cognitive Neurology, UK) running on MATLAB 7 (The Mathworks Inc., Natick, MA, USA). Pre-processing involved the standard procedures of realignment to the mean image of the EPI time series, normalization of functional data to the MNI template using the unified segmentation procedure provided in SPM5, spatial smoothing with a Gaussian kernel of 8 mm FWHM, and highpass filtering at 1/128 Hz in order to correct for slow drifts in the BOLD signal.
Each of the different processing steps involved in quantification, i.e., Composition, Estimation, and Comparison, was addressed by its own event-related analysis (note that the differential analysis of the auditory phase vs. the visual phase in a trial is enabled by the temporal spacing of the onset times of more than 1 s: Boynton et al.,
In a first analysis for Composition, the set of brain regions was assessed which was activated while listening to the auditory sentence that contained the quantifying expression and building up a semantic representation of the according scenario (data type: beta estimates of BOLD amplitude during the auditory presentation phase).
The next, parametric, analysis was run for Estimation, i.e., coding the circles in the
The third, again parametric, analysis was done for Comparison, i.e., coding for numerical distance between |
Composition (i.e., creation of a semantic representation) refers to the first, auditory phase of the trial when subjects listened to a sentence containing a quantifier expression. There were six conditions, i.e., one for each quantifier.
At the first level, an event-related general linear model (GLM) analysis was performed. The duration for each condition was set to 2.8 s, beginning with sentence-onset and covering the entire auditory phase. Each condition was convolved with the canonical hemodynamic response function (HRF) and its first temporal derivative. For subsequent ANOVA at the second level, the beta weights for the six Composition conditions were contrasted against the implicit resting baseline by calculating contrasts of the type
At the second (group) level, the random-effects repeated-measures 1 × 6 ANOVA was calculated in order to obtain an
Estimation refers to the visual phase in a trial when the display containing yellow and blue circles was presented after the subject listened to the sentence in the auditory Composition phase. In particular, the Estimation effect is operationalized as linear increase in BOLD signal with linear increase of the number of circles of the
At the first level, the parametric increase of the BOLD signal with increasing number of circles of the respective color-of-mention was assessed separately for each quantifier on a trial-by-trial basis. The event-related GLM analysis for individual data sets involved 12 (2 × 6) orthogonal conditions, one for each color-of-mention (2) and quantifier (6). For each condition, a stick function (i.e., duration = 0, onset time = trial onset) was convolved with a canonical HRF and its first temporal derivative. Stick functions with duration = 0 were chosen in order to analyze the initial matching of the visual scenario with the mental representation generated in the auditory Composition phase before, and to address this process in the GLM independently of the actual duration of this matching process (this latter aspect relates to processing difficulty and is addressed with the analysis described next).
In order to model the parametric BOLD increase as a function of the number of circles (i.e., the data relevant for subsequent analysis), the percentage of circles in the
At the second level, these individual contrast images were submitted to a random-effects analysis, realized as a repeated-measures 1 × 6 ANOVA. In order to assess which brain regions uniformly responded with increasing activation to increasing numerosity, the
Comparison is a process that calculates the numerical distance between the number of
Thus, the Comparison effects mainly reflect regions parametrically responding to increasing RT. Technically, identification of the Comparison was achieved as follows.
At the first level, a stick function (duration = 0) for each of the six conditions (one for each quantifier), was convolved with a canonical HRF and its first temporal derivative.
Additionally, for each trial, the RT for the
At the second level, these individual contrast images were submitted to a random-effects analysis, realized again as a repeated-measures 1 × 6 ANOVA. The
In order to identify those voxels that were commonly involved in semantic Composition and responded to semantic processing difficulty (RT regressor), the
We used a set of quantifiers for the present study that we classified along the semantic dimension of Polarity, the absence or presence of linguistic negation. Negation is absent in positive quantifiers (
Effects of Semantic Structure – Polarity – can be examined in all three sets of parameters, i.e., Composition (the auditory sentence conditions), Estimation (the monotonic parameter of numerosity), and Comparison (the non-monotonic parameter of RTs). Reliability and robustness of effects of Semantic Polarity can thus be assumed if they are present in a given voxel not only for one but for all three parameter sets. Accordingly, the same contrast for Polarity was computed in each of the three parameter sets. Subsequently, the three
For the anatomical localization of the activations we used cytoarchitectonic probability maps, which are based on an observer-independent analysis of the cytoarchitecture in a sample of 10 post-mortem brains (Zilles et al.,
The following behavioral results were found: First, participants’ responses (truth-value judgments) presented a step-function along the “yes–no” axis (where “yes” indicates a sentence-scenario match, Figure
Brain regions responsive to Estimation were identified via the monotonic parameter
Cluster size (voxels) | Local maximum in macroanatomical structure | Percent of cluster volume in cytoarchitectonic area | |||||
---|---|---|---|---|---|---|---|
Cluster 1 (1930) | Left inferior parietal lobule (cluster extends into IPS) | −45 | −53 | 57 | 5.30 | 32.2 | hIP1 |
Cluster 2 (1685) | Left medial frontal gyrus | 0 | 24 | 44 | 4.99 | 16.6 | hIP3 |
Cluster 3 (1404) | Left precentral gyrus (cluster extends into IFG) | −39 | 5 | 33 | 6.77 | 43.2 | Area 44 |
16.8 | Area 45 | ||||||
Cluster 4 (373) | Right middle frontal gyrus | 39 | 14 | 38 | 4.46 | ||
Cluster 5 (364) | Left inferior frontal gyrus | −48 | 20 | 8 | 5.18 | 56.9 | Area 44 |
15.1 | Area 45 | ||||||
Cluster 6 (304) | Right supramarginal gyrus (cluster extends into right angular gyrus and IPS) | 48 | −42 | 45 | 4.76 | 48.4 | PFm |
19.1 | PF | ||||||
13.8 | hIP2 | ||||||
Cluster 7 (291) | Left inferior frontal gyrus | −53 | 41 | −8 | 6.02 | ||
Cluster 8 (232) | Right angular gyrus | 36 | −60 | 45 | 3.94 | 27.6 | PGa |
13.8 | hIP3 | ||||||
Cluster 9 (223) | Left middle temporal gyrus | −51 | −38 | −8 | 4.21 | ||
Cluster 10 (159) | Right inferior occipital gyrus | 32 | −95 | −11 | 4.52 | 69.2 | hOC3v |
26.4 | Area 18 | ||||||
Cluster 11 (139) | Left inferior occipital gyrus | −26 | −98 | −11 | 4.18 | 48.9 | hOC3v |
41.7 | Area 18 | ||||||
Cluster 12 (82) | Right medial frontal gyrus | 8 | 48 | 44 | 4.15 | ||
Cluster 13 (74) | Left middle occipital gyrus | −32 | −69 | 32 | 4.17 | ||
Cluster 14 (58) | 44 | 17 | −15 | 3.70 | |||
Cluster 15 (36) | Right middle orbital gyrus | 27 | 41 | −14 | 3.94 | ||
Cluster 16 (36) | Right cerebellum | 21 | −86 | −35 | 3.65 | ||
Cluster 17 (26) | Left SMA | −15 | 3 | 65 | 3.51 | 96.2 | Area 6 |
Cluster 18 (21) | Left superior frontal sulcus | −21 | 42 | 18 |
Regions responsive to Comparison were identified via the RT parameter. It varied non-monotonically and was made a regressor for the BOLD fMRI response Responses to Comparison also involved a bilateral fronto-parietal set of regions. Parietal effects included bilateral IPL, bilateral IPS, and left SPL. Frontal regions comprised bilateral IFG and SMA. In addition, the putamen was activated (Figure
Cluster size (voxels) | Local maximum in macroanatomical structure | Percent of cluster volume in cytoarchitectonic area | |||||
---|---|---|---|---|---|---|---|
Cluster 1 (6059) | Left SMA | −5 | 6 | 53 | 7.72 | 28.0 | Area 6 |
18.3 | Area 6 | ||||||
Cluster 2 (4124) | Right putamen | 20 | 14 | −5 | 7.36 | ||
Cluster 3 (3964) | Left putamen (cluster extends into IFG) | −18 | 17 | −8 | 6.44 | 10.4 | Area 44 |
Cluster 4 (2163) | Right inferior parietal lobule | 63 | −42 | 17 | 7.16 | 24.6 | PFm |
13.2 | PF | ||||||
Cluster 5 (831) | Left inferior parietal lobule (cluster extends into IPS) | −48 | −47 | 50 | 4.29 | 23.0 | hIP2 |
20.6 | hIP1 | ||||||
19.6 | hIP3 | ||||||
18.9 | PF | ||||||
Cluster 6 (571) | Right precentral gyrus | 41 | 0 | 50 | 4.53 | 29.1 | Area 6 |
Cluster 7 (317) | Right middle frontal gyrus | 38 | 42 | 27 | 4.14 | ||
Cluster 8 (184) | Left supramarginal gyrus (cluster extends into left angular gyrus) | −57 | −41 | 27 | 4.38 | 77.2 | PF |
22.8 | PFcm | ||||||
Cluster 9 (177) | Left middle temporal gyrus | −56 | −50 | 9 | 4.27 | ||
Cluster 10 (163) | Left inferior frontal gyrus | −41 | 42 | 15 | 4.27 | ||
Cluster 11 (119) | Left calcarine sulcus | −23 | −71 | 8 | 4.21 | 41.2 | Area 17 |
Cluster 12 (110) | Right inferior frontal gyrus | 44 | 8 | 24 | 3.88 | 54.5 | Area 44 |
Cluster 13 (92) | Right inferior frontal gyrus | 56 | 11 | 20 | 4.01 | 98.9 | Area 44 |
Cluster 14 (90) | Left thalamus | −8 | −8 | 3 | 3.68 |
Quantifier | ||
---|---|---|
Few | −0.825 | <0.001 |
Fewest | −0.849 | <0.001 |
Less-than-half | −0.822 | <0.001 |
Many | 0.869 | <0.001 |
More-than-half | 0.884 | <0.001 |
Most | 0.869 | <0.001 |
Few | 0.043 | 0.531 |
Fewest | 0.108 | 0.114 |
Less-than-half | −0.096 | 0.158 |
Many | 0.263 | <0.001 |
More-than-half | 0.184 | 0.007 |
Most | 0.097 | 0.157 |
Few | −0.002 | 0.972 |
Fewest | −0.043 | 0.531 |
Less-than-half | 0.135 | 0.047 |
Many | 0.178 | 0.009 |
More-than-half | 0.198 | 0.003 |
Most | 0.126 | 0.064 |
Although both the Estimation effect and the Comparison effect recruited fronto-parietal regions, they overlapped only in part having centroids that were separate in each region (Figure
We compared the fMRI effect of Polarity (negative > positive quantifiers) in all three sets of parameters, i.e., for the non-monotonic Comparison parameter, for the monotonic Estimation parameter, and also for the BOLD signal in the auditory phase of the trial when the quantifier sentence was presented. Consistency of a Polarity effect in all three parameter sets was tested with a conjunction analysis revealing only voxels responding (at
The separation between semantic Polarity, numerical Estimation, and numerical Comparison was achieved via decisions that participants made on visual scenarios in which numerosity (and subsequently proportion) was parameterized. These scenarios were presented in contrasting linguistic contexts. Though embedded in a tightly controlled design, the PPP was implemented in a rather naturalistic verification task: we verify sentences daily, in communicative acts that require us to answer a yes/no question. These can range from the most mundane topics (
There are two novel aspects here: First, these data were obtained for the first time from the same set of subjects in a single study, instead of merging together disparate studies of different scopes and quality. Second, and most importantly, it is the spatial relation of the semantic Polarity regions to the arithmetical parts, exposed through the parametric analyses of the
Our study relates to the hypothesis by Dehaene et al. (
We thus found a potential human/monkey homology for successive steps of numerosity assessment, but moreover, established a direct connection to language. At the same time, we provided evidence for the neural modularity of language and arithmetic, revealed through a task that matches linguistic representations with numerical ones. Such matching has been used before to distinguish numbers from numerosities (Cohen and Dehaene,
Interestingly, functional division between Estimation and Comparison similar to that in parietal cortex was also found in both frontal lobes. Likewise, the semantic Polarity analysis was prominent in the left frontal lobe in area 45. Evidence for frontal involvement in numerical cognition has been available (Piazza et al.,
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The Supplementary Material for this article can be found online at
Properties of the images and how they were created.
The mapping between the current PPP and standard numerosity experiments.
The meaning of the proportional quantifiers used.
Correlations between the proportion parameter
We are grateful to Danny Fox, Israel Nelken, Yonatan Loewenstein, Lew Shapiro, and Michael Wagner for their incisive and helpful comments. Furthermore, we wish to thank Peter Pieperhoff, Berhard Schwarz, and Andrea Santi for advice on methodology. Partial support for this project was provided by an Alexander von Humboldt Foundation Research Award (Yosef Grodzinsky) and by NIH (grant #00094), as well as SSHRC (standard grant #410-2009-0431) and Canada Research Chairs (Yosef Grodzinsky).
1In order to fully appreciate the effects of the monotonic regressor for Estimation and the non-monotonic RT regressor for Comparison, these two effects were assessed in two separate GLM analyses for each subject at the first level. Effects due to shared variance of the two regressors, if present, are identified as overlaps of the resulting