In mathematics classrooms we most often consider shapes and surfaces extrinsically--looking at the object from the outside. This extrinsic perspective is inherent in our usual analytic descriptions which depend on an encompassing 3-space. In addition, when we do visualize or picture an object it is most often from an external (extrinsic) perspective. However, it is important for many parts of mathematics to be able to describe and visualize objects intrinsically--as a being living in (on) the object would experience it. For example, the great circle on a sphere are, from an extrinsic point of view, merely circles; however, from the intrinsic point-of-view of a bug whose universe is the sphere the great circles are experienced as straight. It is in this setting that spherical geometry most naturally exists. Intrinsic points-of-view are also important in understanding the possible shapes of our physical universe and many important parts of differential geometry. I would also say that intrinsic visualization is important in our understanding of other people (How is the world experienced and viewed by someone who is different than I?). I will describe (by as much as possible demonstrating!) Some of the activities that I have my students do in order to break their extrinsic habits.