Assume a Spherical Chicken: Analytic Constraints, Inertia Tensor Information, and Wielded Rod Length Perception

Abstract

Information associated with the inertia tensor is the preeminent explanation for haptic perception of object properties, notably wielded rod length. Critics counter that tensorial-based information requires non-tensorial supplementation (mass, torque). However, those critiques omit important constraints. With relevant constraints included, the inertia tensor alone completely specifies rod length. I list constraints inherent (but tacit) in haptic rod length perception, and show that object properties associated with the inertia tensor are invariant, even with constraints removed, by involving (a) longitudinal moment equivalents for rod mass and (b) derivatives of moments with respect to varying rotation axes. Analytic outcomes show tensorial-based information is a robust basis for wielded rod length perception, and suggest open questions for empirical exploration.

Keywords:

• dynamic touch
• rod length
• wielding
• information analysis
• inertia tensor

Acknowledgment

I thank Michael Turvey for encouraging me to write this paper. However, I take personal responsibility for the ideas presented.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Notes

1 This expression more generally also invokes the rod’s angle relative to gravity. Here, for the sake of simplifying the derivation, we take that angle to be zero (i.e., horizontal).

2 Clearly, ethical concerns regarding participant and experimenter safety would have to be observed quite carefully with any procedures involving objects near maximal human capabilities.