Warning: Here be spoilers. This is a brief description of how the 4th dimension works in my world for those coming in in the middle.
This is a 4th physical dimension, similar to that described in Flatland. In place of “up” or “down”, the other dimension has directions named “droit” and “widder.” Droid is from heraldry (and medieval Latin) meaning either “a right” or the right side of a crest, opposite to sinister. Widder comes from widdershins, an archaic word for counterclockwise, upstream, or the way it isn’ t usually done.
In the first book, I introduce the idea of the Hellians (and Mouse) having access to a 4th dimension. Mouse can use it to pass “over” walls, and the Hellians travel in ships that navigate it.
The second book takes place mostly on Hell, so I go much deeper into how it all works. Clempson has had three hundred years to figure out much from a piece of wood that Mouse gave him, and he used that understanding to build a mule-shaped homunculus.
The 3d space we live in is called the “nominal volume.” The Hellians only use the widder half of the 4th dimension because the droit volumes are full of space monsters. They call this widder-space. Everything that isn’t in the field of influence of a planet is a formless void that they call “the void,” and thus their ships are called voidships.
When things are thrown off of the nominal volume, they fall back onto it. This follows the normal Pythagorean formula for gravity. There is a transition cost when shifting from widder to droit, causing 4d motion to dampen instead of vibrating indefinitely.
If something “falls” onto solid material, it is blocked from entering the nominal plane and can get stuck. Air and water will just get out of your way. Hellians have figured out how to dislodge and displace solid material, but it’s like punching a brick wall. There is no air outside of the nominal volume. You’ll carry some with you if you’re thrown out, but otherwise, vacuum rules apply.
I’ll add more details if anyone asks.