Are numbers special?: The comparison systems of the human brain investigated by fMRI
Introduction
Are numbers special? Are they represented by a unique brain system? Many accounts of number processing stress the central role of the IPS for number processing (Dehaene, Dehaene-Lambertz, & Cohen, 1998; Dehaene, Piazza, Pinel, & Cohen, 2003). This view is based on patient studies (Dehaene & Cohen, 1997; Lemer, Dehaene, Spelke, & Cohen, 2003) emphasizing the necessity of the IPS of the dominant hemisphere, particularly for number comparison. In addition, electrophysiology studies on monkeys (Nieder & Miller, 2004; Sawamura, Shima, & Tanji, 2002) and neuroimaging studies on humans (Pesenti, Thioux, Seron, & De Volder, 2000; Pinel et al., 1999; Pinel, Dehaene, Rivie’re, & LeBihan, 2001) revealed bilateral IPS activation during number processing and numerical comparison. Yet, other evidence has suggested that the IPS does not serve as a specialized module for number comparison but is designed to subserve other cognitive processes as well, such as visuospatial analysis (Simon, 1999) or a general magnitude comparison (Walsh, 2003). Moreover, its activity has been reported to be modulated by general task difficulty (Göbel, Johansen-Berg, Behrens, & Rushworth, 2004).
Numbers are claimed to be represented in an abstract fashion on an analogue mental number line (Barth, Kanwisher, & Spelke, 2003; Dehaene et al., 1998; Zorzi, Priftis, & Umilta, 2002). This idea is supported by the numerical distance effect, a fundamental behavioral effect that is observed when subjects perform the number comparison task. The distance between two stimuli influences the comparison of the stimuli; the larger the distance between two stimuli, the easier the decision will be and the shorter the reaction time (RT) (Moyer & Landauer, 1967). The number line is generally held to be compressive (Dehaene, 2002, Dehaene, 2003) because comparison times are better predicted when the distance between the two compared numbers are measured on a logarithmic rather than on a linear scale.
However, it is important to note that the reaction time data for the comparison of physical magnitudes across a wide range of domains (e.g., line length, pitch, weight) show exactly the same effects as the comparison of numerical size. Accordingly, the RT profiles for the comparison of both numerical and physical magnitudes are best described by the same logarithmic equation (Welford, 1960). This has led some authors to argue that the mechanism for comparing numerical magnitudes is equivalent to that for the comparison of physical stimuli (Gallistel and Gelman, 1992, Gallistel and Gelman, 2000; Moyer & Landauer, 1967), a view that is further supported by simulations of number comparison with a recent computational model (Zorzi & Butterworth, 1999).
Therefore, the activation found for number comparison might indicate the operation of a magnitude comparison network rather than a specific numerical network. No study that investigated IPS involvement in number comparison, neurophysiological and neuropsychological alike, examined this possibility. A few recent imaging studies attempted to address the question of whether the way in which the human brain represents numbers is similar to the way in which physical features (Fias, Lammertyn, Reynvoet, Dupont, & Orban, 2003) or other semantic information (Le Clec’H et al., 2000) are represented. Yet, none of these studies manipulated the to-be-compared features (e.g., numerical and physical) and their distances within the same experimental design. Only the latter approach, as taken in the present study, can control for the non-specific activations of other brain areas due to attention, difficulty, semantic content, and the like. For example, Wiese (2003) suggested that language and numerical abilities are dependently linked. Thus, one may suggest that the differences between comparisons are not due to the comparison per se, but are due to the content of the stimuli that are presented. In order to determine commonalities and differences between the numerical and physical comparison systems it is essential to adopt such a design that will manipulate and combine the comparison type and distances. We manipulated three different features, numerical value, luminance, and size, of similar stimulus material and varied the distance in each of these features. Pinel, Piazza, Le Bihan, and Dehaene (2004) addressed the same question with a similar design. They scanned normal subjects with fMRI while they compared size, number, and luminance, which varied orthogonally. They found the expected behavioral interference effect and, in their brain activation data, distributed and overlapping cerebral representations for size, number, and luminance. However, their results could have been influenced by the processing of the irrelevant features that were manipulated as well. Our design was different in that, for each manipulation, we kept the other features constant (e.g., all stimuli for the numerical comparison had the same size and luminance) in order to avoid interference effects and thus be more sensitive to effects specific for the respective comparison. Note that Stroop-like interference between physical size and numerical values (Henik & Tzelgov, 1982; Schwarz & Ischebeck, 2003; Tzelgov, Meyer, & Henik, 1992), and luminance and numerical values (Cohen Kadosh & Henik,submitted for publication) has been documented in previous work. Accordingly, in the current experiment, any overlap between comparison conditions in brain imaging data would then indicate a common magnitude comparison network rather than reflect the implicit and automatic processing of the irrelevant magnitude.
We expected that task-specific1 areas would show increasing activity with decreasing distance, corresponding to the increasing difficulty (cortical “distance effect”). On the basis of the clinical studies, we expected the cortical specific-distance effects for numbers in the parietal lobe to be unilateral (in the dominant hemisphere) rather than bilateral. Hence, we hypothesized that while a widespread network of areas would be commonly activated by all comparison tasks, a subset of them, particularly along the left IPS, would show a task-specific modulation by number comparison.
Section snippets
Subjects
Fifteen subjects (eight males, twelve right-handed) with mean age of 27.8 years (S.D.: 4.8 years) were recruited from an academic environment. The study was approved by the local ethics committee. Subjects had no history of neurological or psychiatric disorder and gave written informed consent for participating after the nature of the study had been explained to them.
Behavioral task
A computer display stimulus consisted of two digits that appeared at a distance of 14 cm from the subject, at the center of a
Behavioral data
For every subject in each condition the mean RT was calculated for correct trials only. These means were subjected to a two-way analysis of variance (ANOVA) with comparison and distances as within subject factors.
All main effects were significant. Participants responded faster to a large distance than to a small distance [F(2,28) = 121.35, M.S.E. = 475, p < 0.001]. Participants also responded faster to the luminance and size comparison than to the numerical comparison [F(2,28) = 3.72, M.S.E. = 1.917, p <
Discussion
We addressed the question whether numerical comparison is specifically subserved by a distinct neural circuit or region, supposed to be centered on the left IPS. We analyzed brain activation in response to three different comparison tasks (numerical, size, and luminance) and found a largely overlapping network of frontal, parietal, and occipitotemporal areas of both hemispheres, thus confirming the view that many of the neural resources used for number comparison are shared by other comparison
Acknowledgments
This work was partly supported by grants to R.C.K. from the German Academic Exchange Service (DAAD, Research Grants for Doctoral Candidates and Young Academics and Scientists), the Kreitman Foundation and the Max Planck Society (Minerva Seed Grant) and by a grant to A.H. from the Israel Science Foundation, funded by the Israel Academy of Sciences and Humanities. The authors are grateful to Jan Lammertyn for his helpful comments and to David Prvulovic, Kathrin Cohen Kadosh and Christoph
References (44)
- et al.
The construction of large number representations in adults
Cognition
(2003) The neural basis of the Weber–Fechner law: A logarithmic mental number line
Trends in Cognitive Sciences
(2003)- et al.
Cerebral pathways for calculation: Double dissociation between rote verbal and quantitative knowledge of arithmetic
Cortex
(1997) - et al.
Abstract representations of numbers in the animal and human brain
Trends in Neurosciences
(1998) - et al.
Preverbal and verbal counting and computation
Cognition
(1992) - et al.
Non-verbal numerical cognition: From reals to integers
Trends in Cognitive Sciences
(2000) - et al.
Distinct cortical areas for names of numbers and body parts independent of language and input modality
NeuroImage
(2000) - et al.
Approximate quantities and exact number words: Dissociable systems
Neuropsychologia
(2003) - et al.
The topography of high-order human object areas
Trends in Cognitive Sciences
(2002) - et al.
Modulation of parietal activation by semantic distance in a number comparison task
NeuroImage
(2001)