If one of the spatial dimensions wrapped around, how would architecture be different?

Following the same geometry as this question, how would architecture be different? To review, when go east or west 5 feet, you end up back where you started.

Is there a way to make structures feel roomier, despite the fact the wrap around thing (say, by connecting rooms in a certain way).

How would this affect structural integrity? How would the building be built different to deal with and/or take advantage of this.

How would you attach structures to themselves ("wrapped around")?

Anything else of note?

• using 2 piece of mirrors in parallel should make your structures feel roomier I think – user6760 Oct 16 '15 at 3:25
• Thinking about this geometry reveals some interesting effects... like angular momentum is only conserved along the axis parallel to the wrapping direction; and $1/r^2$ forces turn into $2/r$ forces over distances more than the wrapping distance. (On a related note, I know know what string theorists are talking about when they refer to "small extra dimensions".) – 2012rcampion Oct 16 '15 at 6:35

A nice way to think about this type of thing is to imagine a bunch of $\infty\times\infty \times 5$ ft blocks stacked next to each other, with the same stuff in each block. So if you were in one block, looking into another, you would see another copy of yourself and the room you are in, and another one beyond that, and so on, repeating infinitely. In math, this is called a covering space. I will refer to the strange space you describe as cylindrical space.

Something interesting about this space is that it is not simply connected. Imagine you had a string in normal space. You could tie the ends together, and then do whatever you wanted with it. You could wad it up and put it in your pocket, for instance. But in this space, you could tie one end of your string in one of the blocks to the other end in the next block, and you would suddenly have an infinite strand which you could not wad up without breaking! Moving down from the covering space to cylindrical space, it would look like a an infinitely long piece of string. This is a really weird concept which is not true in normal space.

Everything, obviously, would have to fit in this very narrow space. There is really no way around this. Every room only has two walls (unless you want it to be even narrower), so all the electricity and plumbing has to run to these two walls, or through the floor. Also, all things we normally put on walls, like TVs, paintings, mirrors, etc,... would have to go on these two very narrow walls. An architect would have to take advantage of vertical space to make lots of rooms. Beds would have to lie in the infinite direction because nobody taller than $5$ ft could lie down in the $5$ ft direction. Nevertheless, skinny houses and buildings are possible. Something like this narrow house might be what you get.

It's not all bad. Even though the room is narrow, you don't have to worry about everybody seeing the TV; there are a whole array of TVs, one in each copy of the universe all stacked next to each other. Since you only need two walls, the building will be stronger. Also, you don't need so many mirrors in the bathroom because it is really easy to see the back of your head. There would be more advantages, I think if the universe were a little wider. Say, $30$ ft. Then you could take advantage of the cylindrical properties to have hallways that wrap around. Then, instead of two rooms being at opposite ends of the hall $30$ ft apart, the furthest apart they can be is $15$ ft. The same advantage applies to lots of application where minimizing distance is an issue.

Some things could seem infinite, like beds or bathtubs five feet wide. That would be pretty cool.

All in all, this would be a pretty weird place to live.

• If rooms didn't align east west, couldn't they connect to other rooms instead of themselves? – PyRulez Oct 16 '15 at 3:38
• Maybe, but you would have to be really clever about it for that to be useful with only five feet in one direction. With more space, that would be more useful. – Alex S Oct 16 '15 at 3:40
• Or, similarly, construct a room in such a way that it wraps around twice or more before connecting to itself. – PyRulez Oct 16 '15 at 3:42
• Building my last comment, you could have a situation where you walk through a door in a square room into a different square room, and then turn right, walk through a different door and end up back in the room you started in. As for wrapping more than once, this is not possible in the topology of the cylindrical space. – Alex S Oct 16 '15 at 3:54
• 5' is short enough that you could reach out and touch yourself. Would be weird for us but the inhabitants would be used to it. – Tim B Oct 16 '15 at 9:08

You'd only need one side wall to support your structure. It would be pressed on from both east and west and therefore resist from both east and west. Of course, with a front and back wall, you could forego the side wall entirely.

Your world would have to build up and down a lot, but you'd still be constrained by gravity. I'm not sure how gravity would be affected, but it would change the density of stars and planets.

I'd imagine you'd have a lot of hobbit-type holes. People would live underground (or at least under roofs) and pathways would be built on top of them. You could build above the pathways, but since buildings are heavy and people are not it would make more sense to put the lightweight things on top.

If you came to a bridge that's out, there'd be no way to bypass it. But because water can't travel sideways particularly, there probably wouldn't be many wide chasms to begin with.

The world would have a lot less water, or there'd be no dry land. On the other hand, if there's less gravity (not sure that's true), the mountains would be much taller, so you could have really deep lakes and oceans and still have dry land.

Weather patterns would change dramatically. There would be no way for pressure to move sideways, so tall buildings might be out of the question, although there's still some limited room to build pipes between floors to allow air pressure to flow north to south.

Sideways momentum would be weird. If you came across other planetary systems, you'd have to add a sideways vector. I don't know that it's terribly complex, but it would be different since you can't orbit along that axis, just move.