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Fourth Dimension

Started by Omnimmotus Sep 3, 2006 at 2:13 AM 12 replies 2.3k views
Original Post
Omnimmotus
Omnimmotus
Due to idle curiosity, I decided to look up information on the fourth spatial dimension. Online, there are plenty of flash animations of hyper-cubes, but, to be honest, I just don’t understand them. I know that on a 2D projection like that of a computer screen, it has to go through a loss of two dimensions, but I still feel like I should be able to have a better understanding. Recently, there was a topic on if there were any 1D games. I wish to make the opposite proposal, would it be possible, (and would the result be playable) to make a 4D game? It seems simple enough to me, just as for 3D space every component has three spatial position values (x,y,z) and three spatial rotation values, (pitch, yaw, roll) it seems all you would need to do is add that final dimension and then act is if it’s the same. (x,y,z,h) The only problem is, we don’t have any idea how this fourth dimension would act. In the third dimension, gravity takes hold. Most first person shooters have you move with the WASD keys in the X and Y axis, while jumping provides movement in Z. Same with rotation, The mouse rotates your view along the X and Y axes, while the Z axis is entirely untouched. Therefore, wouldn’t it be logical to say in a 4D game, you add an extra axis of rotation into the mix? (Z would follow, but I feel like that wouldn’t do enough.) Is anyone interested in programming a test for this? I would use the mouse for rotation, and the mouse-wheel for rotation along an additional axis. Since 4D space is so difficult to understand, it might be best to have the computer generate the level algorithmically. I can’t offer much more help than that. Thanks in advance, and good luck. (You’ll need it.)
dao ke dao, fei chang daoming ke ming, fei chang ming
Oluseyi
Oluseyi
Quote:
Original post by Omnimmotus
The only problem is, we don’t have any idea how this fourth dimension would act.

Yes, we do.

(There's also a 5D version of that linked from that page, as well as 3D and 2D decompositions to help you better understand what's going on.)
Omnimmotus
Omnimmotus
Excellent. That's exactly what I was talking about. I should have checked more. I'm about to begin testing that, to see if it helps at all.

I am curious, though, how far we can take this. Could you make a 4D game with textures, enemies, guns, and puzzles? What would that be like? What is AI programming like in 4D? Also, would textures have to be in 3D?

EDIT: Also, when I said we don't have any idea how it would act, I meant on a person or object. Is there some sort of gravity in the fourth dimension? Could you "jump"? (I guess it would be a "hyper jump" so to speak.)
dao ke dao, fei chang daoming ke ming, fei chang ming
Robin S
Robin S
Since the existence of a macroscopic (large-scale) fourth dimension is purely hypothetical, it's difficult to say what physics would be like if we had one. In fact, the laws of physics are almost certainly dependent on more than just the number of macroscopic dimensions we have, so it is perfectly plausible to have completely nonsensical laws of physics in a 3D universe, let alone a 4D one. If, however, you are interested in making life simple for yourself, it might be an idea to extend the number of dimensions but leave everything else as similar to or analagous to our own universe as possible. For example, gravity would still exist - but its strength would be determined by an inverse cube law, not an inverse square one. Things like that.
PhilMorton
PhilMorton
Our universe has 11 dimensions, or even 26 depending on who you ask...
http://en.wikipedia.org/wiki/String_theory
http://en.wikipedia.org/wiki/Superstring_theory


"Dimensions" dont really exist, they are just ideas to help us understand things.

So as for "we don’t have any idea how this fourth dimension would act", that just means you havnt made up a definition for the fourth dimension yet.
If you define the fourth dimension as time, then everyone suddenly understans "how it would act" - objects move along this dimension at a rate proportional to time (which, according to relativity is proportional to the objects velocity - the rate of change in the other three dimensions).
Allways question authority......unless you're on GameDev.net, then it will hurt your rating very badly so just shut the fuck up.
dwarfsoft
dwarfsoft
I play 4D games all the time... 3 Dimensions I interact directly with, and the fourth I experience throughout the game as I play it.

Seriously though, wouldn't having something that abstract represented in 2D on a screen be completely impossible for the player to understand/interact with?

And with regard to 1D games... do Text based adventure count? They don't really classify as 2D or 3D in the traditional spacial sense :P
Farraj
Farraj
Isn't the 4th dimension (in real life) is the 'time' dimension?? how would you use that in a game?

And I dont think that there is a 1D game :/ if there was it would only be .... a line???

If we really think about it, 3D games aren't really "3D". They're jsut 2D that give the illusion of 3D. If it was really 3D, it wouldn't be on the screen. It would be like some holigraphic image floating in mid air (that would be nice :P).

I don't think 4D is even possible to view, is it??
Robin S
Robin S
Just to clear things up a bit, speaking as a mathematician:

There is no one "the" fourth dimension. Any variable can be considered as a dimension, including time, colour, sound intensity, the value of a particular share in the stock market and anything else you want. According to current attempts by physicist to create a "theory of everything" describing all of the fundamental laws of the universe, it seems to be convenient for there to be 10, 11 or 26 physical, spatial dimensions. However, most of these dimensions (all except for the three we experience first-hand) are "rolled up" extremely small - far smaller than it could physically be possible to detect - and to all intents and purposes, merely account for some of the properties of matter.

What Omnimmotus is asking about here is clear. He wants to know what a game would be like which featured a fourth spatial dimension; one which had an actual effect on the game, so a macroscopic one. For these purposes, what I mentioned was relevant. Concepts of time as a fourth dimension, or of extra, undetectably small extra spatial dimensions, while interesting, are irrelevant to the discussion.

I hope this helps to clarify the situation for at least some people. :)
Farraj
Farraj
I agree to what 'Robin S' said. If your going to add a dimension it should be "one which had an actual effect on the game".
Iron Chef Carnage
Iron Chef Carnage
I'm a huge fan of this, and a couple years ago I made a thread that went on for quite some time about it.

I use the hypercube idea similar to the one in Heinlein's short story, "And He Built a Crooked House", where the tesseract is a 4d solid and the game is played on the three-dimensional "surface" of it. Imagine a 2D game being played on the surface of a cube, such that when you reach an edge of a face, you "turn the corner" and keep going, but never really perceive the change. It get really awkward for navigation and orientation, and the corners of the cube freaky in terms of how you get around.

Just extrapolate that effect into four dimensions, so you can get all turned around by going from cube to cube, because they're joined together at seemingly impossible angles. I'm all about that and I'm confident that the technology in games like "Portal", using the Source engine, are capable of pulling it off.

My dream is an Escher-inspired puzzle game where you can throw a rock on the ground, tie a rope to it, walk through a few doors, fish the rope off the ceiling and carry the rock around like a helium balloon.
Robin S
Robin S
The physics of that last one could be quite tricky...

A game played on the surface of a hypercube wouldn't differ in any respects that I can think of from a game played on the surface of a hyersphere, since the two are topologically identical. All such a game would involve would be some kind of "wrapping round" so that if you travel far enough in any direction, you end up back where you started. A sort of mini-cosmos (assuming our Universe is indeed representable as the surface of a hypersphere, as many people believe it is). I'm not sure whether this has been done before, but the type of game where I can imagine it having the most application would be strategy games, where it might be quite useful to have what are effectively multiple routes to the same destination (a la Pacman).
JasonHise
JasonHise
That's funny Iron Chef, I thought I had started that thread a couple years ago ;) It seems to have vanished so I guess there is no way to know.

Anyhow, I think that portals and local gravity are the best ways to handle a game played on a four dimensional surface, and I think that one played on the surface of a hypercube could be great fun. In a story based puzzle game I am planning, I plan to have a level where a labratory has collapsed into a hypercube. The only way out will be through a portal into the past, and the only way to get to it will be by cleverly choosing which doors to go through in which order to manipulate your own personal gravity.

Example of gravity manipulation with 2D world on the surface of a 3D object: Imagine mario on the side of a cube, where each face on the cube is a room. If he goes through the door to his right, then through a trap door to the room below, then goes through the door on his left, he will be emerging from a trapdoor in the floor of the original room, but with his gravity now pointed toward that room's left wall.
Almonsin
Almonsin
I think a 4 dimensional point could be projected into 3d (similarly to projecting from 3d to 2d), and then it could be projected onto the screen. And you could make polygons of these points, and view a 4d object on your screen.

Also, gravity could be calculated from the distance of objects in 4d.

What do you think?

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