4D cars

[Keiji]

I've given a lot of thought to this lately, especially towards the problem of orientation (being able to steer with 2 degrees of freedom). So, here's what I've come up with - and it's actually /easier/ than 3D driving.

Firstly, the car would be restricted to the surface of a plane just like 3D cars are, using a planar "rail", as in 4D, planes can be hooked on to. The hook would only be a half hook, like an upside down U attached to the bottom of the car, as gravity would see to the vertical dimension, and having a full hook would mean it could bash into the rail supports, which wouldn't go very well (also, a half hook lets you raise the car off the road vertically for maintenance etc.)

The tyres would now meet with the surface of this planar rail, just like 3D tyres. Steering would therefore work like it does in 3D, which eliminates orientation problems.

To turn a bend along the plane formed by the frontal axis and the axis perpendicular to the rail (e.g. if the rail was in the xz axes and you were travelling along the x axis, the bend would be in the xw axes), you would not need to steer, as you do not need to move along the z axis (think of it as going up or down a hill in 3D, except no gravity is involved). To turn a bend along the plane of the rail itself, there are 2 options for road designers. The road could roll such that the bend is now in the first situation, meaning again no steering is required, or if there is no space for that, the road could just bend as it does in 3D, requiring steering. On motorways, the second option would not be allowed, so that steering would only ever be required for lane changes.

At junctions, crossings would never be necessary given sufficient space - only splits and merges, as roads can just go around each other in the three non-vertical dimensions available. This can all be done without bridges. Again, each lane could potentially roll in a different way, taking them to different destinations without requiring steering.

As a final note, roads would not divide land areas. Land areas would be divided using planes like the walls, floors and ceilings of a 3D building, and roads would run within these divisions like the electrical cables and pipes fitted inside those walls.

Discuss!

[PWrong]

Firstly, the car would be restricted to the surface of a plane just like 3D cars are, using a planar "rail", as in 4D, planes can be hooked on to. The hook would only be a half hook, like an upside down U attached to the bottom of the car, as gravity would see to the vertical dimension, and having a full hook would mean it could bash into the rail supports, which wouldn't go very well (also, a half hook lets you raise the car off the road vertically for maintenance etc.)

I'm not sure I get it. It sounds dangerously like riding a bike on a rope, with a hook on the bike in case you fall off. Or is it more like a train?

To turn a bend along the plane formed by the frontal axis and the axis perpendicular to the rail (e.g. if the rail was in the xz axes and you were travelling along the x axis, the bend would be in the xw axes), you would not need to steer, as you do not need to move along the z axis (think of it as going up or down a hill in 3D, except no gravity is involved). To turn a bend along the plane of the rail itself, there are 2 options for road designers. The road could roll such that the bend is now in the first situation, meaning again no steering is required, or if there is no space for that, the road could just bend as it does in 3D, requiring steering. On motorways, the second option would not be allowed, so that steering would only ever be required for lane changes.

I don't see how the first option gives drivers a choice. If the road bends in such a way to allow me to go where I want, what if you want to go a different way?

[wendy]

To get an idea of transport in four dimensions, it is best to start off with something like "Thor's wheel" (from the B.C. cartoons). This is basically a wheel and axle, the rider stands on the axle.

As in three dimensions, you have gravity and motion (time), which creates the plane of the wheel. Dividing space by these leave the 'across' space. In three dimensions, this is a line, with left-right axies. You basically can push a lever left or right to steer the thing.

In four dimensions, the across space is a full plane, and there is nothing to fix any given direction (kind of like putting clocks on the floor: there is no reason for all of the 12's to point the same way!) Basically, 4-space divided by height would give 3d space (eg the room), and divided by time [ -> 3d height] gives the floor. Clocks (ie riders in 4d), do not have to orientate themselves in any particular direction to travel forward (ie go from the floor to the roof). This is where things like left/right and ana/kata fail: nothing drives this.

The thing becomes rather hard to steer if we suppose rotation in the across-space, even though four dimensions allows it. You make moves to steer to your 12, and rotation puts you at 1 or 2.

A car, like an animal, consists of several sections each with a number of 'feet' or wheels. The sections each correspond to the across-space, (left-right) and the placement of sections to motion (front/back). You might have 3 or 4 or 5 wheels per section, and two sections. In the plan, the wheels correspond to the vertical lines of a prism. You could drive either by turning the whole base of the prism around (as animals and rigid-wheel vehicles do), or by turning the lines to point to the new direction (basically, the height of the prism), as cars do.

Roads need not cross, although ye still need merging traffic. It's kind of like the blood/digestive/spleen/breathing systems. They go around without need for level crossings.

[Keiji]

I'm not sure I get it. It sounds dangerously like riding a bike on a rope, with a hook on the bike in case you fall off. Or is it more like a train?

Yes, it's like a train. In 3D cars are restricted to a plane via gravity. In 4D, restricting them to a plane would require the second lateral to be removed, which is what my rail/hook does. However, even though the car is hooked to a rail, it can still steer left and right arbitrarily because there is still one lateral left.

I don't see how the first option gives drivers a choice. If the road bends in such a way to allow me to go where I want, what if you want to go a different way?

The road-bending stops you from "falling off the road" in the second lateral; as mentioned above you can still steer left and right to change lanes. Where space is available the only steering you would need would be to change lanes, and the lane would guide you through the junction to where you wanted to go. Going "a different way" would essentially be driving off the road.

This of course is necessary for certain purposes (farm vehicles, for instance), but for getting from A to B it's sufficient to be restricted to the road. Thus the hooks could be mechanically powered to unhook themselves where necessary. Once unhooked, travel would be equivalent to that of a spacecraft in 3D.

[PWrong]

It seems to me that a planar train track would take a long time to build, especially in sparse areas between cities. If you have two cities in 4D, you don't need a planar road to connect them. Even with 10 cities, assuming they're far apart and not all in the same plane, it would be easier to build 45 linear roads than however many planar rails.

The planar rail might be more efficient for cars within a large city or in the suburbs. I'm not sure how it would work without intersections though.

We'd probably have a combination of linear roads and planar roads, as well as offroad vehicles that can drive anywhere.

[Keiji]

The planar rail is equivalent to the surface of our roads - so it'd only be as wide as our roads are.

[PWrong]

Oh! That makes a lot more sense. That would certainly make the cars easier to design, at least for us. I wonder if 4D people would actually do it that way though.

[Keiji]

Probably - the choice is:
a) do it my way and end up having to construct rails and hooks which is a bit more difficult than just roads and tyres, or
b) end up with vehicles whose steering is equivalent to piloting a 3D spacecraft; you'd have planar steering not to mention circular orientation.

Either way's more intricate than 3D vehicles, but I'd hazard a guess that a) would be a lot easier, safer, and space-saving for a tetronian.

[PWrong]

It's possible that your way might take some innovation, they might use (b) for a long time before someone invented (a), or had the resources to pull it off.

Let's assume that travel technology in tetraspace begins with walking on foot, followed by, say, a "trorse and cart". Roads would be designed for use by pedestrians and a trorse and cart. Would your rail system work for a trorse and cart?

It might be like forcing a horse to stay on a train track. You could do it, but not without steering him.

[Keiji]

It wouldn't be that difficult to adapt an existing realmic road to the planar rail system.

[PWrong]

Probably not.

Apparently there used to be trains pulled along by horses on rails. I don't know if they used to steer them the way you steer a normal horse and cart, or if they had some other way of keeping them on the rail.

[Halfbaker]

So... Why can't 4D cars just drive on the 4D equivalent of normal roads? Meaning basically pavement organized like a circulation system on which hypercars drive along by rotating there wheels?

[Keiji]

Because their steering wheels would have two degrees of freedom, unlike ours which only have one. It would be quite difficult to steer straight.

[anderscolingustafson]

One way for a 4d car to be stabilized would be for it to be built in such a way that it corkscrews as it drives as the spinning would allow for more control and allow it to go in a strait line. A 4d car could still be stable to spite moving along a 3d realm if it was to corkscrew wile moving. It's sort of like how a bullet moving through the air can be stabilized if it spins.

[PWrong]

That would be pretty cool. That might make it hard to turn when you want to.

[Keiji]

Surely you would get rather dizzy like that?

[Halfbaker]

Trionian airline pilots steer just fine in three dimensions every day...

My cursor also has two degrees of freedom, I have no difficulty pointing it where I want, do I?

[anderscolingustafson]

Trionian airline pilots steer just fine in three dimensions every day...

True but trionian planes are also effected by gravity so it is slightly easier for them to go down in the up down dimension than up although in the left right dimension it is there is no real difference between the two directions in terms of which is easier to go in. A 4d car would be more like a 3d space ship or a 3d bullet and so it would probably need to spin in order to remain stable.

[Mrrl]

If your car has three front dirving wheels, it will be stable enough. The best form is duocylinder (small circle is the rotational biaxis), steering is two-dimensional. In first versions we can use some form of 3D joystick instead of steering wheel (maybe with non-linear reaction). Problem with straight steering may be solved the same way ad in 3D cars - all three wheels should be slightly directed inside, to the car axis.

[Keiji]

Trionian airline pilots steer just fine in three dimensions every day...

They don't have winding roads or (much) other traffic to contend with, though.
You try to imagine flying a plane when there are a thousand more in all directions around you, and cylindrical lanes somehow marked out in the sky.
Yeah, that's quite a bit more difficult...

My cursor also has two degrees of freedom, I have no difficulty pointing it where I want, do I?

That's because it doesn't need very much accuracy. Now try making pixel art... at 1:1 zoom.

[Mrrl]

You try to imagine flying a plane when there are a thousand more in all directions around you, and cylindrical lanes somehow marked out in the sky.
Yeah, that's quite a bit more difficult...

No, lanes must have square section. I thought that hexagonal lanes will work, but there will be problem with changing of lanes... But if cars are small enough, hexagonals (with triangluar free zones between) will be better.

[wendy]

Consider first 4-space. You have gravity + motion + across-space. Gravity and motion are each 1d, and across-space is N-2 dimensions (here 2d). Cars are things for getting from A to B, and have a dimension of time (ie length).

Roads are, as in three dimensions, latriform (eg linear). Unlike 3d, a latriform does not divide space, so one does not have to cross roads anywhere (or railways etc). More over, the worst one has to deal in 4d on the level is merging traffic: intersections are not required here.

The wheels of the car obviously spin in the directions of gravity and motion, just as they do in three dimensions. Steering amounts to a matter of turning the wheel so it points to a direction in the across-space, with direction and intensity (eg hard left in 3d).

The steering ring would be a sphere, mounted on a stick. As in three dimensions, it's in across-space, with the default position of straight ahead, maintained by way of springs. The steering of a car is then a matter of rotating this sphere so that the direction position is moved from the top in the angle and intensity of the desired motion.

One should also note that while one could have a rotation in the across-space, this is sort of like steering a plane that's going in a continual spin (where the steering space is across+gravity, does admit a rotation).

[Mrrl]

In 3D cars it's enough to have joystick with one degree of freedom (left/right) instead of steering wheel. Usage of the wheel has additional prorety that angle of it's rotation is much more than actual angle of the tyres turn: you can rotate the whell to 540 degrees, and tyres will turn on 15 degrees only. It helps to get very high accuracy of the turn angle/radius.
With spherical steering wheel it will be difficult to get the same effect: when you turn it in some position, result will depend on the "trajectory" of its twist. But probably it's not a big problem, and may be solved by some gearing.
And yes, spinning rotation of the car may be useful in case when driver position is not in the center, but at some side of the car. Of when you want to park the car with the partucalr door to curbside.

[Mrrl]

My concept of 4D car:

It is six-wheeled open car with one row of three passenger seats. Steering sphere is not ready now

Side (horizontal) view:



Top view (plan):



Front view:



Intermediate view 1 (between side and top):



Intermediate view 2 (from the wheel side). All three seats are visible:



One more view:



You can download complete 4D model from here: http://astr73.narod.ru/4DView/Examples/4DCar/4DCar.zip

Viewer for it is here: http://astr73.narod.ru/4DView/4DView.zip . Navigation is easy: by combinations of Ctrl and Shift keys with left or right mouse buttons. Help/Help menu item gives description of commands.

[Keiji]

Hey, cool concept
I hadn't thought of a hexagonal arrangement like that.

How did you make the model file?

[Mrrl]

Manually I've used calculator to find coordinates of vertices and small program that generates ridges structure for duoprisms. And Windows Notepad for the rest. That was enough. But it took two days to "draw" this small model, and I'm not sure how long it'll take to add spherical cylinders for the steering ring.