Abstract
Whether mathematical and linguistic processes share the same neural mechanisms has been a matter of controversy. By examining various sentence structures, we recently demonstrated that activations in the left inferior frontal gyrus (L. IFG) and left supramarginal gyrus (L. SMG) were modulated by the Degree of Merger (DoM), a measure for the complexity of tree structures. In the present study, we hypothesize that the DoM is also critical in mathematical calculations, and clarify whether the DoM in the hierarchical tree structures modulates activations in these regions. We tested an arithmetic task that involved linear and quadratic sequences with recursive computation. Using functional magnetic resonance imaging, we found significant activation in the L. IFG, L. SMG, bilateral intraparietal sulcus (IPS), and precuneus selectively among the tested conditions. We also confirmed that activations in the L. IFG and L. SMG were free from memory-related factors, and that activations in the bilateral IPS and precuneus were independent from other possible factors. Moreover, by fitting parametric models of eight factors, we found that the model of DoM in the hierarchical tree structures was the best to explain the modulation of activations in these five regions. Using dynamic causal modeling, we showed that the model with a modulatory effect for the connection from the L. IPS to the L. IFG, and with driving inputs into the L. IFG, was highly probable. The intrinsic, i.e., task-independent, connection from the L. IFG to the L. IPS, as well as that from the L. IPS to the R. IPS, would provide a feedforward signal, together with negative feedback connections. We indicate that mathematics and language share the network of the L. IFG and L. IPS/SMG for the computation of hierarchical tree structures, and that mathematics recruits the additional network of the L. IPS and R. IPS.
Highlights
One of the fundamental properties common to language and mathematics is the critical involvement of tree structures in those comprehension and production processes
Sentences consist of hierarchical tree structures with recursive branches [1,2], and mathematical calculations can be expressed by hierarchical tree structures [3], which may derive from the unique and universal property of recursive computation in humans [4]
We apply the computational concept of Degree of Merger (DoM) to tree structures in mathematical calculations, and we hypothesize that the DoM represents specific loads in the computation of hierarchical tree structures in mathematics
Summary
One of the fundamental properties common to language and mathematics is the critical involvement of tree structures in those comprehension and production processes. Sentences consist of hierarchical tree structures with recursive branches [1,2], and mathematical calculations can be expressed by hierarchical tree structures [3], which may derive from the unique and universal property of recursive computation in humans [4] This point provides a good motivation for the theoretical and experimental approaches advocated in the present study. Among various models that may possibly quantify the complexity of tree structures, ‘‘number of nodes’’ would be a straight-forward model, counting the total number of non-terminal nodes (branching points) and terminal nodes of a tree structure This model cannot capture hierarchical levels within the tree (sister relations in linguistic terms), whereas the DoM plays a critical role in measuring hierarchical levels of tree structures, such that the same numbers are assigned to the nodes with an identical hierarchical level [8]. We apply the computational concept of DoM to tree structures in mathematical calculations, and we hypothesize that the DoM represents specific loads in the computation of hierarchical tree structures in mathematics
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