4-D wheels

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Re: 4-D wheels

Postby wendy » Fri Jan 31, 2014 7:14 am

You could have the vehicle recieve pulses from the road, and steer itself thus. It's the same sort of thing that is proposed in some 3d thing.

Alternately, there is the O-Bahn, which does this sort of thing in 3d (for busses). Instead of the vehicle having flanges, the road has the flanges, and the vehicle is carried on it.
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Re: 4-D wheels

Postby Keiji » Fri Jan 31, 2014 7:25 am

wendy wrote:You could have the vehicle recieve pulses from the road, and steer itself thus.


That would be a bit too hi-tech. ;)

Perhaps if the rail flanges aren't enough (since they can only cover the same width as the individual rails themselves, which is not much!) there could be an additional guide wheel in the front middle of the vehicle, which would extend lower than the rail-wheels, so that wider flanges could be used to guide this wheel into the correct place before getting to the actual rail flanges.
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Re: 4-D wheels

Postby wendy » Fri Jan 31, 2014 8:33 am

You could look at the O-bahn for inspiration.
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Re: 4-D wheels

Postby anderscolingustafson » Tue Mar 04, 2014 10:49 pm

Many 3d structures including trees, the blood stream, the lungs, and the nervous system, have a fractal structure. Having a fractal structure with side tubes branching off a main tube is often times the most efficient way to allow things to flow. In 4d road systems would be 3d structures and so they might have a fractal structure similar to that of a tree as that would be the most efficient way to have traffic flow. The roads leading into towns and cities could be the widest of the roads and they could have roads branching off of them and those branches could have branches coming off of them and each road could be more narrow than the road it branches off of and the parking spaces and drive ways could be the narrowest.
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Re: 4-D wheels

Postby Keiji » Wed Mar 05, 2014 7:02 am

That's already how roads work in our world you know :)

(well, unless you live in one of the USA's many grid-based cities)
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Re: 4-D wheels

Postby quickfur » Wed Mar 05, 2014 3:22 pm

Keiji wrote:That's already how roads work in our world you know :)

(well, unless you live in one of the USA's many grid-based cities)

Even in grid-based cities, you still have a similar structure: freeways/highways, for travelling long distances; major roads ("arteries") for intra-city long distances, minor roads (still relatively big, but less frequented), streets (getting around in residential neighbourhoods), lanes (small roads within a community, that often don't span more than a block). You don't need 4D to have this kind of structure. :)

What 4D gives you that you can't have in 3D, is the ability to have disconnected road systems cover the same geographical area by interlocking each other without intersecting. Conceivably, such a system might be desirable for, say, emergency vehicles to never have to contend with local traffic to get where they need to. (However, one could object that this is not viable economically because you're essentially duplicating the public road system for a far less-frequently used purpose.) Or perhaps such disconnected systems might arise during the transition from "spaceship-steering" vehicles to planar rails -- the planar rail roads can be completely independent of the existing road systems, and both can co-exist simultaneously until the latter becomes obsolete (and may turns into pedestrian paths or tourist attractions, I don't know).
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Re: 4-D wheels

Postby Keiji » Wed Mar 05, 2014 5:44 pm

Disconnected road systems would be brilliant for separating pedestrian paths, cycle paths, roads (planar rail), true railways, canals, airport runways and even utilities like electricity, gas, telecoms etc. so that the roads do not have to be dug up every time they want to change something!!
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Re: 4-D wheels

Postby anderscolingustafson » Wed Mar 05, 2014 6:26 pm

Sometimes the place an emergency vehicle needs to get to might be in the main road system. For instance if there was a car accident then the emergency vehicles would still need to be able to get to it even if they had their own road system. Also if a criminal was trying to get away using the main road system the police would need to be able to get to him/her. So I think it would be a good idea to have the main road system connected to the road system for emergency vehicles so that police would be able to get to it if they need to.
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Re: 4-D wheels

Postby quickfur » Wed Mar 05, 2014 6:48 pm

Keiji wrote:Disconnected road systems would be brilliant for separating pedestrian paths, cycle paths, roads (planar rail), true railways, canals, airport runways and even utilities like electricity, gas, telecoms etc. so that the roads do not have to be dug up every time they want to change something!!

Speaking of electricity, the biggest advantage of 4D is that your wires will never get tangled up! I mean, they will, but a gentle tug should disentangle them easily, unlike in 3D where they form knots that no amount of tugging will undo.

I also get the feeling that in 4D, things will tend to be mainly built on the ground, rather than stacked over each other like in 3D where you have roads and pedestrian walkways side-by-side, and bridges are necessary when a crossing is needed; and electric cables and telephone poles have to criss-cross each other and hang over roads, etc.. In 4D, since there is so much ground space, you could in theory lay all these things out on the ground without intersecting each other, that you hardly need to build very much above ground level. There will also be markedly less need for bridges and overpasses (if at all!), since there's space to just walk around the obstruction instead. And skyscrapers will probably be unnecessary (not to mention extremely expensive to build!) since each additional floor introduces so much more floor space that having many floors seems extravagant. Also, since the weight of the upper floors increase cubically, it may not be feasible to build very high without risking collapse.

anderscolingustafson wrote:Sometimes the place an emergency vehicle needs to get to might be in the main road system. For instance if there was a car accident then the emergency vehicles would still need to be able to get to it even if they had their own road system. Also if a criminal was trying to get away using the main road system the police would need to be able to get to him/her. So I think it would be a good idea to have the main road system connected to the road system for emergency vehicles so that police would be able to get to it if they need to.

Good point.
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Re: 4-D wheels

Postby wendy » Thu Mar 06, 2014 7:51 am

Even though the floors might increase cubically, the wall area also increases, this time by the square. The amount actually held is then roughly a matter of simple L (ie area divided by margin). You can build into four dimensions, multi story buldings, but the real end is that the density of roads on a linear system is pretty much being fed by a cubic, rather than a square layout.

For example, here where i live, the road out the front takes up a chain or half-chain of frontage. That means, for a typical quarter-acre block, the road frontage is 1/7 of the total perimeter of the land. In four dimensions, you take a block, say a chain * chain * 2 chains. You put a road down in front of the place. The whole public easement might be a chain square, (running lanes, services, footpaths, etc), so that's one sq chain on a block that's got a margin of 10 sq chains. You can stack four of these blocks around a street front, so there are four houses per chain of road.
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Re: 4-D wheels

Postby anderscolingustafson » Sat Mar 08, 2014 5:37 pm

Although skyscrapers would be much greater in 4d than in 3d skyscrapers would also have a much greater surface area to help support the weight so they might still be able to get to be very tall without collapsing under their own weight do to the extra surface area to help support the extra weight. In fact with higher dimensions there is more surface area per volume so it may even be easier to build skyscrapers very tall without risking collapse in higher dimensions considering the added surface area to support the weight.
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Re: 4-D wheels

Postby ubersketch » Sun Dec 24, 2017 2:29 pm

arkmioh wrote:whould anyone who is smart enouf to understand four-dimentional wheels share what they know with me. For example what is a spherindrical wheel? And how many other kinds of wheels are there?

Here's what we have.
Cubinder - Cube extruded into the 4th dimension,
Spherinder - Sphere extruded into the 4th dimension,
Duocylinder - Uhhhh
Polytwisters/Hopf Polyhedra - UHHHHHHH
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Re: 4-D wheels

Postby Mercurial, the Spectre » Sun Dec 24, 2017 8:01 pm

ubersketch wrote:
arkmioh wrote:whould anyone who is smart enouf to understand four-dimentional wheels share what they know with me. For example what is a spherindrical wheel? And how many other kinds of wheels are there?

Here's what we have.
Cubinder - Cube extruded into the 4th dimension,
Spherinder - Sphere extruded into the 4th dimension,
Duocylinder - Uhhhh
Polytwisters/Hopf Polyhedra - UHHHHHHH

Duocylinders are just circle-circle duoprisms - they are the limit of the n-m duoprisms as both values reach infinity.
The polytwisters are curved shapes formed from combining swirl tori derived from a base polyhedron's faces, its simplest parts are curved planes that act like Mobius strips. The duocylinder's symmetry is just a subset of polytwister symmetry in which the base polyhedron has a prismatic subsymmetry.
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Re: 4-D wheels

Postby ubersketch » Mon Dec 25, 2017 3:41 pm

I already know, it's just they are kind of hard to explain.
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