Surface of the Side of an Opaque 4D Cube

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Surface of the Side of an Opaque 4D Cube

Postby PatrickPowers » Wed Jan 06, 2016 4:10 pm

What would the surface of a side of an opaque 4D cube look like if it were to appear in our 3D world? It would be a cube, and it would have all the visual properties of a flat surface. These properties are

    From a suitable vantage point, every point on the surface is visible.
    The surface may be colored.
    The surface may reflect light.
    The surface may be shiny
    It is not possible to see through the surface

The basic problem with a 4D surface in a 3D world is reconciling the first proposition with the last. There is a solution. Imagine an empty box with a lid, like the ubiquitous cardboard box. Open the lid, and it is possible to see five of the six sides of a cube, the sixth side being the open lid. The entire 3D volume is visible, but it is not possible to see beyond it. Perfect.

Given this basic idea, the enclosed volume may be colored and reflect light. It would reflect it in an unusual way. An object is shiny if its surface is somewhat reflective, like a low-quality mirror. What would a reflection in a 3D mirror look like?
PatrickPowers
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