4D Non-Euclidian Game

[Mr Skeptic]

This bit taken from another thread, gave me this idea. I've heard these analogies before, but never with a comparison to computer games.

 

What Sisyphus was describing was a toroidal 3D universe. Like PacMan 2D square with opposite edges identified but the whole 2D world jacked up one dimension. So a PacMan 3D cube with opposite faces identified. Try daydreaming that you live in such a thing. A room where you can pass out thru the east wall and the arm you stick thru the wall comes in from the west wall.

 

In cosmology one doesn't hear very much about the toroidal 3D topology. But it is a workable example of closed 3D space, which is how S. used it in his post. It's the surface of a donut, jacked up one dimension.

 

The more usual case is the socalled hypersphere or S3. This is the surface of a balloon, jacked up one dimension more.

A balloon surface is S2 the socalled "two-sphere". It doesn't have to have a surrounding 3D space but can exist on its own as a closed 2D world. (That's important to realize.)

 

The corresponding thing in one higher dimension also does not have to have a 4D surrounding---it can exist on its own. That's probably the most important thing to realize in all of differential geometry. Geometries can be experienced from within, curvature can be defined and measured from within---so they don't have to be embedded in higher dimensional surroundings.

 

Use your imagination and try first to have the experience of a 2D creature living in the two-sphere. Slide around on the surface of a balloon. Go exploring.

 

Then use your imaginatin and try to experience what it would be like to live in a reasonable size three-sphere. One not too large. So that you could circumnavigate.

 

 

So my question now is, how hard would it be to have a non-euclidian game universe? Say, a first person shooter with 3 space dimensions, 1 time dimension, and a closed space-time? Would people get the hang of warped space? Or would they get incredibly annoyed? Could one of the physics/graphics engines be modified for this purpose or would you have to start from scratch? Would graphics cards be useless for this?

[ydoaPs]

Most video games are non-euclidean(you fall down if you walk off a cliff)

[forufes]

Portal!!!

Edited January 31, 2010 by forufes
why can't i write fully in CAPS?

[insane_alien]

forufes, in reposnse to your reason for editing, you cannot post fully in caps because it is against forum etiquette, so we made it impossible.

[Sisyphus]

This bit taken from another thread, gave me this idea. I've heard these analogies before, but never with a comparison to computer games.

 

So my question now is, how hard would it be to have a non-euclidian game universe? Say, a first person shooter with 3 space dimensions, 1 time dimension, and a closed space-time? Would people get the hang of warped space? Or would they get incredibly annoyed? Could one of the physics/graphics engines be modified for this purpose or would you have to start from scratch? Would graphics cards be useless for this?

 

Not that I'm entirely up on gaming, but it is weird that I can't think of any, since the 2D equivalent is so common. The example given was Pacman, but I think Asteroids is an even better example, if you're familiar with that. I guess 2D is inherently easy with a 2D display (objects that "go off the screen" in one direction emerge on the other side). You could have the same thing with a 3D display, I suppose, but it probably wouldn't be as seamless with a 2D rendering of a 3D space. A 3D FPS would have interesting effects. Like, if there was a clear viewpoint all the way across the map, you could see your own back in the distance.

 

That kind of thing could really help people visualize the "finite but unbounded" concept, I imagine.

[forufes]

but as i said, there IS a game, called portal, you open two portals in any place, go through one and you're out the next, you can use the holes as mirrors to see your back, you can make one in the ceiling and one in the ground where you'll drop and keep falling to the depths of eternity, you can use them as catapults because they conserve momentum, the game is funny like hell, the setting unorthodox, and the puzzles are pure mind blowing..

a favorite to who ever plays it.

highly advise buying it, here are some spoilers:

http://en.wikipedia.org/wiki/Portal_%28video_game%29

[Mr Skeptic]

Portal is a fun game, but it is 3D with teleporters is all. No bent spacetime to be seen.

[Sisyphus]

Portal is a fun game, but it is 3D with teleporters is all. No bent spacetime to be seen.

 

I don't know whether it's "bent," but from the description it does sound at least partially what we're talking about. A straight line passing through a portal continues out the other side.

 

If, for example, you made a cube, then made each pair of opposite edges portals to one another, then you've got yourself a torroidal universe, right?

[Mr Skeptic]

Well, I suppose you could say that such games have flat space with occasional infinitely curved space.

 

Easy way to tell, are the sum of the angles of a triangle 180 degrees? If so, you space is flat, boring, Euclidean space. If not, you have curvature of some kind.

 

All I ever have seen is flat space, though in 1D you would not be able to tell (there's no triangles).

[Mr Skeptic]

Well I found something similar. Miegakure: it claims to be a 4D platform jumping puzzle game. http://marctenbosch.com/miegakure/. Found it thanks to xkcd.

[AJBonkoski]

Wow! That looks like an awesome game. Looks like the project was just started this month one year ago! I'm looking forward to it. It should be pretty sweet.

[mano]

This bit taken from another thread, gave me this idea. I've heard these analogies before, but never with a comparison to computer games.

 

Another fascinating 3D drag & drop programming language is Mama, which was designed to improve students' analytical and logical skills, while creating 3D animations and games. Mama programming language home page: http://en.eytam.com/mama

[Sir_Oblivious]

I don't know for sure if this is 4D Non-Euclidian, but it is Non-Euclidian. It is called Antichamber. Here is the link. http://www.antichamber-game.com/

[Mr Monkeybat]

There is a UDK demo called Hazard the Journey of Life. It has euclidean geometry but all sorts of impossible spaces.

[Mr Monkeybat]

Another free game here shows what it would be like if the speed of light was at walking speed:

http://gamelab.mit.edu/games/a-slower-speed-of-light/

 

All screens games and cameras introduce some distortion as the FOV of the camera rarely matches the FOV of your monitor so you could say that no screens display undisturbed euclidion geometry.