by 개구리 » Sun Aug 16, 2020 2:59 pm
You are only ever seeing a slice of the table at a time. In 3D, the top surface of tables are sections of planes, usually of the plane XZ if you consider Y to be the vertical direction of gravity. In 4D, the top surface of tables are sections of realms, usually of the realm XZW. In the game, there is a four dimensional space XYZW, but you are taking XYZ slices of the world along W, so you will always see the table "block" surface as just an XZ plane section. However, the rest of the "block" surface still exists, and since W is as perpendicular to gravity as X and Z, there is nothing stopping the polychoron from rolling to W, out of your XYZ viewing slice, which you see as it "disappearing". Really, it is just somewhere else on the "block" surface.
If you switched your view so that you were taking XZW slices along Y, then you would see something much different. At Y's minimum, you would see the surface of the 4-table, which would be a solid block filling the whole XZW slice. If you could see inside the solid block, you would see something like a point, line, disk, or some polygon "floating" inside of it. This is the point of contact of the polychoron that is sitting on this 3D surface. As you increased the Y of your slices, the "block" surface would suddenly disappear all at once, and you would see a small 3D slice of the polychoron in empty space, and as Y increased further, the polychoron would disappear (you reached past its height) and you would be left with only empty space as you approached the maximum of Y.
When you deal with slicing visualizations, you must always remember to "stack" everything that you see, even things that are not the polychoron that you are analyzing.
So when you have a glome in your XYZ view of XYZW, sitting on the 3D surface of a "hypertable", you simply see a sphere, that can roll around like an ordinary sphere in X and Z, but can also roll "away" in W, which you see as shrinking and disappearing. If you switched your view to XZW so that you see the whole "block" surface of the table at the same time, the glome would appear as a single point inside the block, and it could move around freely within the whole block, like a "fly" flying around a room. The glome hasn't disappeared to anywhere.
As a bonus, if you have a spherinder, then its point of contact in the block surface would be a line, and this line could move around freely except in any direction along its length (this is the spherinder rolling). The spherinder can even be "stood up" on the table, and its point of contact would be a sphere, which wouldn't move at all. If you had a cubinder on its side, then you would see its point of contact as a square, and when the cubinder rolls, the square point of contact would slide back and forth normal to its face. When the cubinder is stood up, its point of contact in the block would be a cylinder, which also doesn't move. So a glome can roll freely in three ways, a spherinder can roll freely in two ways, and a cubinder can only roll in one way.
One last thing to be noted is that the point of contact of a spheritorus would be a "fly", just like the glome, but this fly can only crawl around in one way, otherwise the spheritorus falls over and the fly becomes a circular point of contact (just the edge of the circle, not a disc).