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The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling?

The Relation between Finger Gnosis and Mathematical Ability: Can we Attribute Function to Cortical Structure with Cross-Domain Modeling? Marcie Penner-Wilger (Marcie.Penner-Wilger@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Michael L. Anderson (michael.anderson@fandm.edu) Department of Psychology, Franklin & Marshall College, Lancaster, PA 17604 USA Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742 USA anatomically distinct brain areas (Bergeron, 2008). As such, workings are neither consciously available nor describable with higher-level psychological vocabulary. Therefore, in contrast to the current practice in cognitive neuroscience, workings should be described using domain-independent vocabulary. Here, we adopt a vocabulary drawn from information processing theory, although certainly other possibilities (e.g. dynamic systems theory) may turn out to be more appropriate to the task (Anderson, 2007a). According to the Massive Redeployment Hypothesis (MRH; Anderson, 2010, 2007a,b) multiple workings, in concert, compose higher-level cognitive uses, and a typical brain area will contribute to many cognitive uses, across domains, but perform the same working across uses (Anderson, 2010). MRH straddles the middle ground between localization and holism in that, although parts of the brain are specialized (i.e., they always perform the same working), this specialization is at the lower-order level of cognitive workings (e.g., computations or transformations) rather than that of higher order cognitive uses. Anderson (2007a, p. 339) uses the analogy of “finding the right letter to go into a box on a (multidimensional) crossword puzzle” to describe the task of determining a shared cognitive working. Thus, knowing the many cognitive uses that a brain area supports will help to determine what that brain area does. Both Anderson (2010, 2007a,b) and Bergeron (2008) advocate for the determination of shared cognitive workings within and across domains as a method to advance our understanding of high-level cognition and to achieve the interdisciplinary goals of cognitive science. The methodology of looking across domain boundaries to determine the working of a brain area is not common in cognitive neuroscience; activations are generally attributed to processes specific to the domain under investigation (Cabeza & Nyberg, 2000). Cabeza and Nyberg conclude, in a review of 275 imaging studies, “it would be useful to systematically compare functional neuroimaging data in different cognitive domains and to develop general theories that account for the involvement of brain regions in a variety of cognitive tasks” (Cabeza & Nyberg, 2000, p. 31). One such working was proposed by Hubbard et al. (2005): a computational transformation for spatial updating implemented within the parietal sulcus. This cognitive working is also thought to play a role in another cognitive use: shifting attention along the mental number line. It is hypothesized that the SNARC effect— Abstract This paper details and applies a novel method for assigning function to local cortical structure. Imaging results from multiple cognitive domains were used to investigate what a shared neural substrate could be contributing to two apparently different domains: finger and number representation. We identified a region within the left precentral gyrus contributing to both tasks; identified, across several cognitive domains, other cognitive uses to which the ROI may have been put; and looked across these cognitive uses to ascertain the functional contribution of the ROI. The result of this process is a proposed local working—an array of pointers—that can be tested empirically and will allow for further elaboration of the redeployment view of the relation between finger and number representations. This work is significant for understanding the relationship between finger gnosis and math, and for introducing cross-domain modeling as a new empirical method. Keywords: number representation; finger representation; neural substrate; exaptation; function-structure mapping; localization; cross-domain modeling. The Redeployment View Finger gnosis or “finger sense” (indexed by the ability to distinguish which fingers have been lightly touched without visual feedback) is related to math ability (Fayol, Barrouillet, & Marinthe, 1998; Noel, 2005; Penner- Wilger et al., 2007). In Penner-Wilger and Anderson (2008) we elaborated a novel hypothesis regarding the observed predictive relation between finger gnosis and mathematical ability. In brief, we suggested that these two cognitive capacities have overlapping neural substrates, as the result of the re-use (“redeployment”) of part of the finger gnosis circuit for the purpose of representing number. On this redeployment view, the neural circuitry shared between finger gnosis and number representation forms one part of the functional complex necessary for number representation. Along with the neural circuit shared with finger gnosis, additional neural circuits (with additional abstract functional capacities) are expected to combine in support of the capacity for number representation. The crucial question that a shared neural circuit raises is: What is the shared circuit doing for the different functional complexes of which it is a part? What is the working of this circuit that allows it to support tasks in such apparently different cognitive domains? In the framework we adopt here, workings represent low-level operations that are performed by small,