Don't try to visualize the unvisualizable. Our brains are built for 3D space visualization.

or are they?

are brains are not built for 3D space visualization. What we see is 2D, or what some may argue is 2.5D, but certainly not 3D. Can you visualize volumetric data? No, we see 2D projections of 3D data, but cannot visualize the 3D volumetric data itself. Can you visualize the entire volume of things, such as an apple? No, we see a perspective. To see inside the apple, we must slice it, but we cannot visualize the apple in 3D, even in our mind's eye. All we see are 2D projections or perspectives of 3D, but not the 3D itself.

The discussion is about visualization, at least my contribution to it, so it's not necessarily about optometry. It may be a rare talent, but I actually do visualize in three dimensions. It helps me with mechanical invention, for one thing. I have several mechanical patents pending and a trade secret. I also hold a patent in computer science for a sorting algorihtm, something that has nothing at all to do with spatial dimensions.

I think I read that somewhere in Carl Sagan's "Cosmos".

Now, that would be a neat trick out of the hat. I can't even tell a hollogram from the real thing.

but you can't do 3D volumetric visualization

Why not?

because that is not the way we visually perceive the world. We perceive volumes through slices and slice planes. It is impossible to perceive the volume in it's entirety in a single mental image. Our mental thoughts and imagery are based on our senses, and our eyes use a 2D receptor array (the retina), which renders full volumetric visualization impossible.

computing in 3D and navigating in a 3D environment are different from mentally visualizing 3D volumes in their entirety.

For example, open any book and you'll find that all figures are 2D; they may be 2D projections of 3D data, or perspective shots, but their still 2D. Our retina is a 2D sheet of photoreceptors. Yes, we see stereoscopically, which only means we see in depth, but this is not the same as volumetric visualization. We do not see 3D volumes; we only see our 2D perspectives of an arguably 3D environment.

I would challenge you to examine any 3D object and try to visualize its 3-dimensionality in it's entirety. You may try to imagine the object is partially transparent to facilitate this, but try as you might, you cannot visualize the entire 3-dimensionality of the object, since to do so would imply invariance of perspective, and we always visualize objects with some perspective, since that is the nature of our perception of objects, for better or worse.

To the point where even in those of us with monocular vision (due to accident of disease), our brains will find ways to enhance the visual experience from the 2 dimensional plane it is percieving. There are many one-eyed (monocular) depth perception cues that allow us to make reasonably accurate depth judgements: perspective, overlay, shadowing, aerial perspective (color of the sky), relative motion, relative size, etc.

so all make believe? otherwise "War of the Worlds" actually happened.

Watch a pigeon (and some other birds) walk sometime. It will move its head in a jerky stop-motion, in order to generate synthetic stereovision. The brain receives an image from an eye on one side of its head, and a fraction of a second later it receives another image from a point a few inches in advance along the bird's walking path. It generates 3D models of the world on both sides of its head that way. Some robots also generate stereovision with a single camera by moving it to a new position for an additional image.