## Windscreen Wipers...

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.

### Windscreen Wipers...

Not sure if this situation has been raised before?
How would windscreen wipers work on a 4D car? Any thoughts?
gonegahgah
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### Re: Windscreen Wipers...

A 4D windshield would have to span a 3D hyper-area, so the analog of a windshield wiper would have to sweep out a 3D region. So my expectation is that the wipers would span 2D areas, so that when they sweep across the windshield they would clear away a 3D region of water. As to the exact shape and number of the wipers, that would depend on the shape of the windshield, which in turn depends on how the car is designed.
quickfur
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### Re: Windscreen Wipers...

Cool. That makes sense and provides food for thought.
Thanks quickfur.

I guess they could also even possibly spin as long as the spin describes a swiping process?
Perhaps like some sort of spinning offset plane?
Would that work?
gonegahgah
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### Re: Windscreen Wipers...

Spinning is a swiping/sweeping process. Think, for example, about surfaces of revolution in 3D that are commonly used in undergrad calculus classes. A wiper could be for example a square hinged on the X axis, say, so that it rotates around the X axis when activated. It would thus sweep out the volume of a 3D cylinder. So if a 4D windshield were in the shape of a cube, say, the wiper could be attached to one side, with the X axis running down the middle of a square face and the wiper being a rectangle occupying half of the square, then when it rotates it would sweep out a half-cylindrical region on the windshield.

You could also put the axis in the middle and have the wiper continuously sweep out a cylindrical region in the middle of the windshield (like extruded radar ); that would work if the driver's seat is offset to one side of the windshield, as would be the case in a wide, multi-seat vehicle. Less desirable for single-seat configurations because you'd have the wiper axle sticking through the middle of your view.
quickfur
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### Re: Windscreen Wipers...

Opens up possibilities...
Maybe you could also have multiple triangular blades that rotate themselves while also following each other around in a circle so that we don't get that unmoving centre?
I guess like 3 spinning planets in the same orbit around the sun, but with the planets being flat and wider (wider than where the sun would lay) with three different orientations so that they don't collide?
Wish I could animate that easily with the triangles.
gonegahgah
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### Re: Windscreen Wipers...

IMO that'd be too distracting to the driver.
quickfur
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### Re: Windscreen Wipers...

I was then also thinking about the windscreen shape...
Apart from the forward direction it could basically just form a cylinder to provide maximum view.
I then though maybe the sideways orientation of the driver wouldn't matter...
... but then I realised the driver would still need to have instruments close to each hand.

So would the windscreen be somewhat triangular then? Or, still cylindrical in the sideways direction?

The indicator would probably allow for different directions to be indicated so that you could indicate to turn into a particular sideways direction.
One hand could control that with a joystick style indicator.
The windscreen wipers would also be controlled by a separate hand; just like we do.
But what would an extra hand do? I'm guessing drivers would have preferred orientations to these controllers.

Seats we sit on tend to have a little hill between the legs for greater comfort so I guess there would still be a little hill between each of the legs of a 4D person.
The feet would have accelerate, brake, but perhaps also rotate?
gonegahgah
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### Re: Windscreen Wipers...

To sweep a chorid (3d solid) with wipers, you need the wiper to be hedrid (2d).

Given that the intent of wipers is to throw the water off some forward area, including a solid block where the driver sits, the motion would prolly be a prism-version of the 3d wiper, ie a square or something swept side to side in an arc. The driver's attention would then follow behind the sweep of the blade, where the view is clearest.
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wendy
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### Re: Windscreen Wipers...

I want to add, that in ordinary cars you often have 2 overlapping windscreen wipers. In 4d, the window is approximately shaped like a rectangular prism. You could then have a planar windscreen wiper in the (left-right) middle which sweeps the 3d volume of a cylinder(axis of cylinder parallel to the ana-kata axis) . You could then have another windscreen wiper whose plane is always parallel to the first, but who is positioned on the left bottom edge of the windscreen. Then both windscreen wipers could sweep in parallel, like they do in real life.
DonSoreno
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### Re: Windscreen Wipers...

DonSoreno wrote:I want to add, that in ordinary cars you often have 2 overlapping windscreen wipers. In 4d, the window is approximately shaped like a rectangular prism. You could then have a planar windscreen wiper in the (left-right) middle which sweeps the 3d volume of a cylinder(axis of cylinder parallel to the ana-kata axis) . You could then have another windscreen wiper whose plane is always parallel to the first, but who is positioned on the left bottom edge of the windscreen. Then both windscreen wipers could sweep in parallel, like they do in real life.

Aha, in other words, it's an extrusion of 3D wipers into 4D, right?
quickfur
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### Re: Windscreen Wipers...

quickfur wrote:
DonSoreno wrote:I want to add, that in ordinary cars you often have 2 overlapping windscreen wipers. In 4d, the window is approximately shaped like a rectangular prism. You could then have a planar windscreen wiper in the (left-right) middle which sweeps the 3d volume of a cylinder(axis of cylinder parallel to the ana-kata axis) . You could then have another windscreen wiper whose plane is always parallel to the first, but who is positioned on the left bottom edge of the windscreen. Then both windscreen wipers could sweep in parallel, like they do in real life.

Aha, in other words, it's an extrusion of 3D wipers into 4D, right?

Yes.
DonSoreno
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### Re: Windscreen Wipers...

gonegahgah wrote:I was then also thinking about the windscreen shape...
Apart from the forward direction it could basically just form a cylinder to provide maximum view.
I then though maybe the sideways orientation of the driver wouldn't matter...
... but then I realised the driver would still need to have instruments close to each hand.

So would the windscreen be somewhat triangular then? Or, still cylindrical in the sideways direction?

The indicator would probably allow for different directions to be indicated so that you could indicate to turn into a particular sideways direction.
One hand could control that with a joystick style indicator.
The windscreen wipers would also be controlled by a separate hand; just like we do.
But what would an extra hand do? I'm guessing drivers would have preferred orientations to these controllers.

Seats we sit on tend to have a little hill between the legs for greater comfort so I guess there would still be a little hill between each of the legs of a 4D person.
The feet would have accelerate, brake, but perhaps also rotate?

I think that windscreen would be rectangular prisms, as that would be easier to manufacture, and would fit to a tesseractoid (?) vehicle shape. They wouldn't need extra features for the windscreen wipers, and perhaps they would need 4 different turn signals. The road grid would resemble a 3d lattice, so you need 4 turn signal. There would be no need for train crossings.
DonSoreno
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### Re: Windscreen Wipers...

Road structures have been discussed at length before on this forum. The general consensus is that multi-way intersections are not necessary, and in fact, would not be preferred, because of the inherent risks of accidents and traffic congestion. Instead, the most likely structure would be a highway-like structure where main roads pass near each other but don't intersect, with a system of on-ramps and off-ramps connecting them. Just like multi-level highways in 3D, except that in 4D no elevation is required and the entire structure can be built on flat ground.

Furthermore, no pedestrian crossings are ever necessary, because one can always just walk "around" the road to reach the other side! Likewise, bridges to connect buildings across roadways would never be necessary: you'd just build around the road to connect opposite sides instead. Bridges over rivers would also be unnecessary, since the road could just wind around it. But bridges across lakes that are wide in at least 2 dimensions would be necessary, since then you couldn't just go around it easily.

A more interesting possibility arises in 4D that has no direct correspondence with 3D structures: Keiji's "planar rail" system. Basically, it's a cross between a railroad and an unconfined wheeled-vehicle road. Vehicles would be confined in 1 dimension, like trains are confined on train tracks, but the track itself extends in 2 dimensions simultaneously, so you could still have free steering (while being confined at the same time!). The confinement in 1 dimension lets you build roads that are inherently safe: vehicles cannot accidentally drive off the road and cause havoc. At the same time, they still retain a limited amount of freedom -- the same degree of freedom 3D cars have, which is in 2 dimensions. This lets vehicular controls retain the direct analogue of the 3D steering wheel: you only ever have to turn left or right, never into the extra set of directions in 4D, thus simplifying car control and reducing the risk of accidents due to overly-complex controls. The planar rails that confine vehicles can gently twist in 3 dimensions as you go along, allowing roads to orient vehicles in any direction needed to orient them in the direction of travel and merge with other roads via connecting ramps.

The combination of all of the above gives you a uniquely 4D road system that has (1) no need of traffic lights; (2) has no intersections, only on/off ramps; (3) confines vehicles only to road surfaces; (4) yet has enough freedom of movement so that at junctions no complex rail-switching track system (like in 3D) is needed; and (5) can be built entirely on a flat surface with no elevated structures.
quickfur
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### Re: Windscreen Wipers...

Wipers: I've tried to come up with something clever without success. It seems to me that the basic wiper concept remains the same in N dimensions. You have an N-2 dimensional triangleoid wiper that moves semicircularly in two dimensions. The open question is, how many such wipers is best?

Side windows: The side windows are an N-2 sphere. In 3D we get the unusual discontinous 1-sphere.

Turn signals : The directions in which one may turn may also be found on an N-2 sphere. Turn signals also lie on an N-2 sphere, presumably discretized as a matter of practicality. What about the turn signal control? For N>3 I'd say it would be a single lever that can be moved to point any direction within an N-2 sphere. A slick feature would be maintaining that direction relative to the Earth as the vehicle rotates. Is anyone clever enough to come up with a way to do that with Model T era technology?

On-off ramps : Would be much cheaper in N>3 because no need to build a bridge or tunnel, hence much more common. There would remain plenty of ordinary intersections, as this is unbeatably compact and cheap and is safe enough for low traffic/low speed locations.
PatrickPowers
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### Re: Windscreen Wipers...

PatrickPowers wrote:[...] There would remain plenty of ordinary intersections, as this is unbeatably compact and cheap and is safe enough for low traffic/low speed locations.

I question that. In 3D, intersections are inevitable because two arbitrarily-drawn straight lines on the 2D surface of the planet would almost always intersect unless they are parallel. That is to say, if there are two nearby roads that are approximately straight and they aren't parallel, then an intersection is pretty much guaranteed. So if there are a bunch of nearby destinations and people start buliding roads between arbitrary pairs of them, then intersections naturally arise because they are inevitable.

On the 3D surface of a 4D planet, though, two random straight line segments, even nearby ones, are much more unlikely to intersect. If you have a bunch of nearby destinations and build some number of roads between arbitrary pairs of destinations, they would almost always never intersect. The expectation is rather that they would pass nearby each other but not intersect; the region around the point of closest proximity would be the ideal region for building connecting ramps. The only case where you might have intersections is if there's a common landmark roughly situated in the middle of the cluster of destinations where people would naturally congregate, then people would naturally build roads towards that landmark, and they would intersect there. Even then, I'd imagine the roads would simply end at the landmark without intersecting each other, and connecting streets built between these endpoints around the landmark. So you'd end up with a polyhedral cage sort of configuration around the landmark, where each vertex is the endpoint of an incoming road, and some subset of edges (potentially all?) would serve as connecting streets. The vertices would then be intersections, I suppose. But they'd be more like the higher-dimensional equivalents of T junctions than cross-shaped intersections.

What would be an interesting experiment, is if we wrote a Monte Carlo simulation of road-building in a settlement, that can reproduce road structures similar to what we observe in the real-world, then run the same simulation in 4D to see what kind of structures it comes up with.
quickfur
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### Re: Windscreen Wipers...

My idea is that roads would tend to intersect because the drivers want them to intersect, in order to get from one road to the other. Limited access roads are the exception.

In the old days roads have random layouts. You still see this in European cities. The grid layout is fairly recent. Washington DC may have been the first such.

Getting back to windshield wipers, in 4D you would get a square wiper that pivots on one edge. In ND you get a (N-2)D cube that still has a 2D pivot. The 1D pivot is unique to our 3D world.
Last edited by PatrickPowers on Thu Jun 23, 2022 12:59 pm, edited 1 time in total.
PatrickPowers
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### Re: Windscreen Wipers...

You just have to look at things like the blood system to get something that goes everywhere and crosses nowhere.

As for wipers, you can still use something like a half-cylinder here, just by adding an extra dimension to all parts of the wipers. Running in unison, they can intersect each other's space but at different points of the cycle. You need n-2 dimensions for the blade, which is to be expected.
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wendy
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