The qualia manifolds
Ever noticed implicit geometries in the structure of the qualia you deal with on a daily basis?
So here is one observation about our experience. Visual experience has two major dimensions and one minor one (depth). This sensory modality is experienced as either 2 or 3 dimensional (and ambiguous points in between are also instantiated at times). Now, it also has a specific kind of topological features. It seems that the edges of the visual field are the edges of a patch in Euclidean space. The edges are not connected to each other. At first, it might take you by surprise to consider hypothetical visual fields with edges that are actually connected. Maybe you could make it a torus, by connecting edges left and right as well as those at the top and the bottom of the visual field. It’ll make a manifold of experience. You may also twist it before connecting it, making a Klein bottle or a projective plane.
A common reaction to this idea is “it may be impossible to do that, maybe the geometry of our visual field is the only possible one.” Without actually going ahead and interfering with your mind and brain directly it is unlikely I’ll be able to show conclusively it is possible. But there is a strong intuition pump available to help you conceive of the possibility.
So, touch your arm. Your writs more specifically. Using a finger make a circle around the wrist. You end up where you started, and yet you only advanced in one direction.