So I've seen visualisations of objects with four spatial dimenions (e.g. a hypercube), and these are typically done as a wireframe representation. Although interesting, I was wondering if there are any attempts at visualising a 3D object from a 4D perspective. I think Cixin Liu in his book Death's End describes the idea quite well:
A person looking back upon the three-dimensional world from four-dimensional space for the first time realized this right away: He had never seen the world while he was in it. If the three-dimensional world were likened to a picture, all he had seen before was just a narrow view from the side: a line. Only from four-dimensional space could he see the picture as a whole. He would describe it this way: Nothing blocked whatever was placed behind it. Even the interiors of sealed spaces were laid open.
I'm especially interested in how the interiors of sealed spaces can be seen from a 4D perspective. Take for example, a 2D scenario, where a solid square is inside a circle with some thickness.
From our (3D) perspective, we can easily see the square and the circle, essentially, seeing the whole picture. However, a 2D observer on the plane of the circle and square would only be able to see the outside of the circle, and would have no way of knowing what the interior looked like.
Similarly, when a 3D observer looks at a 3D object such as a block of reinforced concrete, they have no way of knowing what the interior looks like, but a 4D observer would be able to see the whole interior simultaneously. The position of the reinforcing bars, their interior, and the interior of each individual piece of aggregate would just be able to be, seen, by the observer, somehow.
I've tried looking for visualisations of this effect, but can't find any. So has this simply never been attempted, are the result incomprehensible, or is there something fundamental here I don't understand that prevents a visualisation?
