Another observation that I have made related to this, is that when I am exploring an object with my finger, for example, it feels to me as though I am projecting myself onto the finger and in essence “walking around” on the object and building or recognizing a model of it much like exploring a room and building a model of it. There is a sense of a position on the object and a sense of a heading, both of which changes fluidly as I move my finger around in different directions.
To me, at least, the sensations of exploring a room and exploring an object are extremely similar, and the logical conclusion (to me) is that they must be sharing the same mechanics behind the scenes. An “allocentric” space when exploring an object is essentially the same as an “egocentric” space when exploring a room. The switch between the two spaces, I would theorize, is at least in part a function of attention
If this is true, then understanding how grid cells and head direction cells are used when navigating a room are directly applicable to how they are used when exploring an object. We had a discussion on this thread recently where some excellent references were given related to the nature of head direction cells when exploring a 3D room.
As an interesting side note, this would also explain how we are able to almost effortlessly control an avatar in a video game (compared to an RL algorithm, for example, which requires a ridiculous number of iterations) – we can essentially project ourselves onto the avatar and explore the game world as though we were actually in it.