1. A device for occupying a human with physical and mental activities comprising: (a) a human mountable object having a convex surface on which said mountable object can either rotate or rock; (b) a base assembly disposed underneath said convex surface; and (c) an object motion control assembly holding said convex surface on said base assembly by way of a strap arrangement, said strap arrangement being configured to hold said human mountable object on said base assembly at selectable tensions including: (i) a static mode preventing all rotation and rocking, (ii) a semi-dynamic mode allowing rotation and rocking on said base assembly when a force is applied to said object, and (iii) a fully-dynamic mode allowing resistance-free rotation and rocking on said base assembly, so as to enable said human mountable object to roll or to rotate on said base assembly in a controlled manner as a user mounted on said mountable object attempts to maintain a stable position on said mountable object in response to motion of said human mountable mounted object.