03 / A STEP ALONG W

Translations through the unseen

A translation changes position without changing orientation. In four dimensions, its offset has four components.

A new direction around a wall.

A wall can block every route within one slice yet have a finite extent along W. Move outside that extent, pass its side, then return. You have gone around the obstacle in four dimensions.

The slice has a normal.

The game stores four perpendicular basis vectors. Three span the visible slice. The fourth, b₃, is its normal. Translation along the normal changes position by:

After you rotate, b₃ need not match the original global W axis. “Depth” therefore means distance along the current slice normal. The movement controls in later realms follow that local normal.