by quickfur » Thu Sep 19, 2024 5:25 pm
The surface of a 4D road has 3D extent, so steering on a 4D road is analogous to flying in space in a 3D rocket; the possible motions are identical. So in theory, any controls that parallel the controls of a 3D rocket would work.
This assumes, however, that 4D roads are built as 3D surfaces with 3 degrees of freedom. But the point of having a road (rather than an open field) is to direct vehicles to travel along a 1D direction, and only occasionally allow switching lanes and/or turning at a fork in the road. So you really only need the ability to turn in 2 degrees of freedom (since the cross-section of the road is 2D); the rest of the possible motions are superfluous. For this, a simple joystick-like steering would suffice.
Note that due to the extra dimension of space, we never actually need any intersections or elevated ramps. Intersections can be replaced with on-ramps and off-ramps that connect with the perpendicular road, and these ramps do not need to be elevated; they can be built entirely at ground level without intersecting each other. Thus, no intersections are needed, neither are traffic lights (except lights for controlling congestion when merging onto busy roads).
All of the above, however, assume a direct analogy with 3D roads. However, Keiji has discovered an alternative system with uniquely 4D properties: the planar rail system. This is a hybrid between a 3D railway track and an open road where you can turn wherever you want. Thanks to the extra dimension of space, you can have both properties at the same time. A planar rail road is one where one of the 3 degrees of freedom is constrained by a rail, so the vehicle ends up having only 2 dimensions of freedom, one for forward motion and one for lateral motion. This system is advantageous over a completely open 3D road because in an open road, you have 2 degrees of freedom of turning, which can be confusing because your orientation w.r.t. the road will change the meaning of the lateral dimensions. For example, if you approach a fork that splits left and right, the left turn may take you to city A and the right turn may take you to city B. But if you approach the road with a 180° rotated orientation, your left/right will be swapped, and turning left will take you to city B instead of city A. In a planar rail system, the rail can restrict the orientation of the vehicle so that it always approaches a fork in the same orientation. The vehicle will still be able to make turns because there's still an extra dimension to turn in, in addition to the forward direction. So you never have to worry about vehicles approaching a fork in the wrong orientation (think about how confusing road signs would be in that case!).
And for the planar rail road system, you don't need any special controls; a 2D steering wheel works just fine!
car_steering_only_roll_4d.jpg