There are well-known procedures for tricking human brains into assigning 3-dimensional perspective to 2D images. Some, like 3D glasses in a theater, work without effort, while others, like the stereogram of a galloping horse below, require some training and many people cannot do it at all:
We have a good mathematical understanding of 4D, and we routinely use computers to handle calculations in N-dimensional spaces. The problem is that our brain is adapted to create a 3D pseudoemulation. If you think about it, it's created by neurons spiking: nothing intrinsically 3D about it, rather us Earth-mammals adapted to use 3D because it's useful in a 3D environment.
Now I want to be in a place where a human girl, aged about 12, is able to "see" in 4D. More specifically, I want her to achieve 4D perspective on a 3D object. Assume that a device exists to grant that information to her if she can understand it. It may require effort, like the stereogram, work for a limited 'volume', and she may only be able to sustain it for a brief time (or it may come as natural as breathing).
I know of no human who claims to be able to do this, so this poses a bit of a problem. While it may come down to the wiring of our brain, I'm trying to think of a training program (for the child or even for the infant she once was if we want to take advantage of extra neuroplasticity of newborns) that would engender and boost this ability. I'm thinking computer simulations, minor brain surgery, etc.
How could we train/modify people to see in 4D?