What happens when a 4 dimensional being views a 4 dimensional object in 3 dimensions?

Viewing a 3 dimensional object in 2 dimensions

Consider the following well-known illusion which I scribbled out very quickly: cube.gif (2121 bytes)If you gaze at it, you may notice that it appears to change. It appears in one way and then in another. It also has other effects. The essential idea is that this illusion appears to change when you gaze at it, although in truth it doesn't change.

I will call this figure 'the cube' although it is a rough drawing of a cube.

At one moment, it can appear that you are looking down on the figure, and at another moment, it appears you are looking at it from underneath.

The figures is a 2 dimensional representation of a 3 dimensional object. Or we think it is!

Because it could be the drawing of at least 2 objects then the drawing changes.

The 4 dimensional being views a 4 dimensional object

The 4 dimensional being is a viewpoint of 3 dimensions. The viewpoint takes up one dimension. So when the being views a 4 dimensional object, it cannot view more than 3 dimensions at a time. The four dimensions are represented by 3 dimensions, which like the figure above, begin to change.

The beings scans the 4 dimensional object in sections (of 3 dimensions) so that there is the apparency of change.

We can understand the above sentence by likening it to the cube. We are 4 dimensional beings. We view the 2 dimensional picture of the cube in 3 dimensions. (We view the world in 3 dimensions, even 2 dimensional objects).

When the cube changes there is the impression of movement. When we view a 4 dimensional object (such as our world) from a viewpoint in 3 dimensions we see the 3 dimensional representation of a 4 dimensional object. Like the cube in 2 dimensions, the hyper-world in 4 dimensions appears in apparently changing 3 dimensional scenes. Or as 3 dimensions with time.

This is exactly what our world appears to be.