> 4D Maze Game
In the Maze
The Fourth Dimension
Can You See It?
The Tesseract, Part Two
How Much Space Is There?
How to Point
How to Orient Yourself
VolumesWhat I want to talk about here is the concept of volumes. The concept is implicit in all the pages of the guided tour that deal with passages, notably the one about the forward passage, but somehow it never came through as clearly as I wanted it to. So, let's go back and work through one of the examples again.
The example I have in mind is the first of the forward side passages, the one that went forward and then right. To construct it, we started with a forward passage.
Then we removed the right wall and saw the back wall of the new square. Let's not do that yet, though. Instead, let's look more closely at that right wall.
Now, as I said back when I was explaining the idea, the three-dimensional retina really ought to be displayed as a solid block of color. In particular, the wall we're looking at really ought to be a solid block of purple.
Now that we know the wall is a tangible three-dimensional object, let's remove it.
That empty space is an example of the kind of volume I'm talking about.
Finally, we can see what's behind the right wall. The back wall of the new square is in the middle; around it are parts of four other walls (up, down, in, and out).
The spaces that those walls and parts of walls occupy are also volumes.
Now maybe the following generalities will make some sense.
Let's call a volume unoccupied if it is not occupied by the wall that defines it.
Can You See It?
Walls Are Opaque