Is there a generalized magnitude system in the brain? Behavioral, neuroimaging, and computational evidence

Some 10 years ago, it was proposed that different quantities, including time, space or number, are processed by a common mechanism (Walsh, 2003; Pinel et al., 2004; Cohen Kadosh et al., 2005), henceforth called generalized magnitude system (GMS). This presented an important attempt at theoretically integrating data across various literatures, and became very influential (e.g., Burr et al., 2010; Lourenco and Longo, 2011; Bonato et al., 2012). However, in this paper we will evaluate the concept in a critical way. We first argue that such a mechanism faces conceptual difficulties. Second, we look at empirical findings that were proposed to support a GMS and will offer a different explanation of these findings based on computational modeling and recent empirical observations. Third, we review positive evidence in favor of distinct magnitude mechanisms. We discuss alternatives for a GMS in a final paragraph. A first difficulty a GMS faces is the metric to code different types of magnitudes. What common metric allows comparing the loudness of a tone to the duration of a stimulus or the meaning of an Arabic digit? In other words, what is the scale factor that relates one magnitude dimension to another? One strong interpretation of the GMS would imply that there is a single common currency on which all dimensions can be mapped. Early studies addressed this issue for one particular pair of dimensions, namely event counts and time (duration). A scale factor of 1:5 was obtained, in which the representation of one count is equivalent to 200 ms of time (Meck and Church, 1983). However, it was demonstrated that a single scale factor fails to explain all observations (e.g., Balci and Gallistel, 2006). Furthermore, numerical effects on the magnitude of grip aperture are flexibly modulated by the relative magnitude of the numbers on a specific trial (Chiou et al., 2012). In other words, the scale factor by which one magnitude is mapped to another can change on a trial-by-trial base. To fit the framework of a GMS, the common metric thus has to be sensitive to the relative magnitude in a specific context. This flexibility of the scaling factor violates the prediction from a GMS for a common monotonic mapping of quantities (Bueti and Walsh, 2009). Another difficulty for a common monotonic mapping concerns metathetic dimensions, i.e. magnitude dimensions that lack an intrinsic polarity (Stevens, 1957). What is, for example, the larger magnitude when judging luminance? If luminance is defined with respect to black, increasing darkness then increases the magnitude. On the other hand, if luminance is defined with respect to white, magnitude should decrease with increasing darkness. Another issue concerns the specific problem the brain faces when representing numbers. From a computational point of view, representing numbers is inherently different from representing other magnitude dimensions, such as luminance, surface area, or weight. A problem specific for processing numerosity is that it requires the individuation of objects independent of their nonnumerical features. How the brain represents numbers is therefore likely to depend on a unique set of neural properties. These unique properties to encode discrete numerosities could be the reason why differences in processing between discrete and continuous magnitudes have been observed (Castelli et al., 2006). Concerning the second argument, much of the evidence in favor of a GMS comes from the observation that behavioral effects can be very similar across stimulus types, or that they interact with each other. One important behavioral effect that has often been used to argue along these lines is the comparison distance effect (CDE). The CDE indicates a decrease in response times when the magnitude between two stimuli that need to be compared increases (Moyer and Landauer, 1967). The presence of a CDE when comparing different types of stimuli, such as numbers, luminance, weight and even social status, has led to the suggestion that the representations of these stimuli must overlap (e.g., Moyer and Landauer, 1967; Chiao et al., 2004). However, as we have demonstrated before (Verguts et al., 2005; Van Opstal et al., 2008) the CDE can originate from the pattern of connections from input coding neurons to the decision and response neurons, relevant for the magnitude comparison task (e.g., “Left stimulus is larger”). In particular, the CDE may result from a competition in the decision process that is determined by the monotonically increasing pattern in these connection weights (see Van Opstal et al., 2008 for full details). In fact, this connectivity pattern automatically develops from the requirements of a magnitude comparison task, and a CDE will thus be observed for any stimulus type trained on this task. Therefore, the presence of a CDE across stimulus types does not imply a common representation or dedicated magnitude processing system. Instead, similar effects may arise from similar computational constraints across tasks. For a similar argument in the context of the size congruity effect, see Santens and Verguts (2011). Similarly, if the CDE does not originate from stimulus representation, brain activity that correlates with the CDE is