Data on foliation intersection and/or inflection axes preserved in porphyroblasts (FIAs) indicate that no porphyroblast rotation occurs during ductile deformation relative to spatial coordinates. This contrasts with 99% of investigations of “rigid” objects in non-coaxially deforming media where the objects rotate. When anastomosing shear zone formation around relatively strong objects in a weaker matrix is modeled, no “porphyroblast” rotation occurs. Formation of these anastomosing zones controls the development of this phenomenon, called gyrostasis. If such zones are absent, porphyroblasts rotate. In weak materials the gyrostatic situation arises because the superposition of simple shearing deformation normal to initial coaxial shortening results in only small rotations of principal axes of stress. Since shear zones are controlled by the orientations of principal axes of stress, initial anastomosing zones retain their orientations and positions during subsequent non-coaxial deformation. The porphyroblast is isolated from the embedding non-coaxially deforming matrix, but this material close to the porphyroblast continues to deform coaxially; no local rotation occurs. This has major tectonic significance because, allowing for the effects of rotation due to brittle deformation, porphyroblasts can now be routinely used to access lengthy structural and/or metamorphic histories destroyed in the matrix by reactivation such as movement directions, shear senses, and extended pressure-temperature-time paths.