The Role of the Inertia Tensor in Proprioception
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Recent research has identified the inertia tensor I, a parameter comprising both principle moments of inertia and principle axes of inertia, as the relevant mechanical quantity to which perceiving properties of hand-held objects by dynamic touch (e.g., wielding) is tied. In the light of this research, a useful summary (see Pagano & Turvey, 1992) is that I provides the domains for two sets of functions, one consisting of the principal moments of inertia or eigenvalues, which map onto perceived "magnitudes," such as object length (e.g., Solomon & Turvey, 1988), and one consisting of the principal axes of inertia or eigenvectors, which map onto perceived "directions," such as the orientation of an object in the hand (e.g., Turvey, Burton, Pagano, Solomon, & Runeson, 1992). The understanding of dynamic touch summarized in this manner may apply not only to how one perceives "attachments to the skin," such as tools and instruments, but also to the very traditional concern of how one perceives the body itself. Because the body, its limbs, and its limb segments, are describable through I, it can be hypothesized that a person's knowledge about the dimensions and directions of his or her body and its appendages is given continuously by the eigenvalues and eigenvectors of the respective tensors. This hypothesis stands in contrast to traditional theories of proprioception-which propose acquired or innate mechanisms (e.g., body scheme; knowledge of limb lengths and joint angles}-by implicating an 'on-line' means of knowing about the dispositions of one's limbs through invariants within the patterning of forces acting upon tissues of the body during self-induced movement.