xkcd

by **M.qrius** » Sat Jan 12, 2008 11:47 pm UTC

I just had a thought, that a 4-dimensional game would prove to be an interesting investigation in whether you can get used to 4d. I'm thinking about a 'simple' thing like a racing game (on your own, so time trial or something).
I've been looking around, but couldn't find anything of the sorts. Would it be a viable idea?

Some thoughts:
In 4d, gravity is still just in 1 direction.
Would you miss info because the world is mapped onto 2d instead of 3d? 4d beings would probably map the world on 3d with their eyes.
Would you interpret it as 3d areas stacked behind each other? If I imagine playing 4d tic tac toe, I have 3 blocks of 3d tic tac toe... (But 3+d tic tac toe is guaranteed win for first player anyway)

by **Berengal** » Sun Jan 13, 2008 12:25 am UTC

Racing games are highly 4d anyway, since time is such an important factor. Now, if we're talking 4 spacial dimentions, then things get a little more complicated.

Information is always lost when flattening a dimention. A sphere projected onto a 2d surface will always look like a circle to an objective observer (one can fool the brain by various, obvious methods like shading etc.) The problem with 4d is that us humans aren't used to viewing 4d objects, and thus it's impossible to use clever trickses to make us think a 3d object is 4d. A 4d sphere (hypersphere? I don't know the jargon here) will look like a 3d tube when flattened, and no amount of shading can make us think it's otherwise. I'm not saying such a game wouldn't be feasable, but for those of us not yet initiated into the secrets of 4d envisioning it would be rather freaky at first.

Mind you, it would probably be a rather interesting game if you could move on all four axises (up-down, left-right, forwards-backwards, ana-kata (Oh, how I've longed to use those terms)). One way to do it could be colours representing the fourth dimention, as I've tried to explain it to other people a couple of times before (Nevermind that googling for ana kata turns up a paper doing the exact same thing. I was onto this way before him!), but that would sort of ruin the illusion of the fourth dimention being a spatial one.

It'd be interesting to see if this is feasable. I for one like the idea, have thought of something somewhat similar in the past (not a racing game, but rather a puzzle game), but I've no idea how to project 4d to 3d (nor am I really that good at projecting 3d to 2d either, or at least the program's I'm working on to do that indicate).

by **eternauta3k** » Sun Jan 13, 2008 12:41 am UTC

Try to make a sketch of what it'd look like

by **M.qrius** » Sun Jan 13, 2008 1:12 am UTC

I disagree that a 4d sphere would always look like a tube. For example, if you have a solid hypercube, it wouldn't look like a cube. A 2d being would see 2 sides of a square (1 for x, 1 for y), a 3d being can see 3 sides of a cube (1 for x, 1 for y, 1 for z), and if I'm not mistaken a 4d being can see 4 cubes of a hypercube (1 for x, 1 for y, 1 for z and 1 for w).
To someone who wouldn't know what he was looking at, it would probably look like a partially see-through combination of cubes. See also this writeup which I wrote some time in the past. (For easily-bored people, scroll down to the picture which is actually not quite a hypercube.)

As for projecting 4d to lower, I'm not quite sure what it would look like either. That doesn't mean that it's impossible to code. It's just coding a normal x/y/z viewer from scratch, except you now have x/y/z/w. You don't have to be able to visualize is to be able to code it (Although it would help with bughunting). The mathematics aren't that hard, just non-intuitive.

Maybe I'll have a go at drawing a bit later, but it's quite hard...

Edit: Oh and to the first bit of text you find when you google ana kata: in lineland, you would be able to see the point, even though it has no height and width. We can see everything, and we don't have any 4th dimension width either. 2d people would be able to see stuff even though they have no thickness.
He makes some valid points otherwise, about being able to drink wine out of a bottle without opening it and such, but I don't like that he involves 'planes' in religion. It doesn't add much to the discussion of the abstract. I also don't think colors are a good analogy, because it doesn't really show the idea of a spatial 4th dimension.

by **Avram** » Sun Jan 13, 2008 3:33 am UTC

I had this idea a while back as well. I envisioned an FPS where moving in the 4th dimension would warp the environment. I don't know jack about geometry though, so I don't know what it would really look like or how it might work.

I think a game based on non-euclidean geometry would also be a great idea.

by **M.qrius** » Sun Jan 13, 2008 3:47 am UTC

Warping the environment is a nice idea as well, but it still only shows 3 dimensions. You can't see anyone approaching from the 4th dimension.

Portal has some form of wrapping, which might count as non-euclidean geometry...

by **Ubercomrade** » Sun Jan 13, 2008 4:51 am UTC

What if a first-person-shooter engine is used with this kind of game, which recycles its own time dimension:
Cursor*10
I don't think that would count as true 4D because time only goes cylindrically, like on a phonograph; in all other ways it would be a 3D game. I still think it would be fun, though.

Another thought:
The thing that defines 3D games is the geometry; with 4 dimensions, excluding time, the level geometry as we perceive it in 3D would have exist in every shape simultaneously. Change in position with respect to time, d<x,y,z>/dt, is velocity. Change in geometry (or position of geometry points) with respect to the extra dimension, d<x,y,z>/dw, would represent the rate at which the geometry changes as the player travels along the w axis. Thus, the entire level geometry would be a set of functions with respect to w. (I think I'm recycling time again... Oh well.) This could be tricky with moving brushes like doors and elevators, because their geometry would have to be defined as a function of not one but two independent variables. Vision would also be quite tricky to implement with 4 dimensions, because the player would have to see in each direction of the extra dimension. Perhaps if the background is black; the entire level within the present coordinate of w is rendered in a monochrome wireframe, in green; geometry as close to the player as the HUD is rendered #00FF00, while the geometry at the edge of the player's vision is rendered #000100; geometry in the positive w direction is rendered #AaBbCc, such that:
Aa = 0;
Bb + Cc = k₁ * ( ( geometry.x - player.x )² + ( geometry.y - player.y )² + ( geometry.z - player.z )² + ( geometry.w - player.w )² )^-0.5
and
Cc = k₂ / ( geometry.w - player.w )

Similarly, geometry in the negative w direction is rendered #AaBbCc, such that:
Cc = 0;
Aa + Bb = k₁ * ( ( player.x - geometry.x )² + ( player.y - geometry.y )² + ( player.z - geometry.z )² + ( player.w - geometry.w )² )^-0.5
and
Aa = k₂ / ( player.w - geometry.w )

In other words, everything is rendered in wireframes, the background is black, the player will see the current-w-coordinate geometry in green, geometry in the positive-w-direction in blue, geometry in negative-w-direction in red, and stuff farther is rendered darker. Alternatively, instead of re-rendering edges for every few intervals, the points of geometry could have a 3D parametric curve (with W as the independent variable, changing color from dark red, to green, to dark blue, with change in the positive w direction) along which the point would appear to flow as the observer traverses along the w axis.

Then there would be the physics interactions... If a ball bounces of a four-dimensional plane, it could get deflected along the w-dimension. Good luck finding it in a 4-dimensional level. :lol:

by **Antimatter Spork** » Sun Jan 13, 2008 5:00 am UTC

There are 4d and 5d Rubix Cubes.

by **Rysto** » Sun Jan 13, 2008 5:13 am UTC

Fonkey wrote:I think a game based on non-euclidean geometry would also be a great idea.

They made that. It's called Super Mario Galaxy.

by **Avram** » Sun Jan 13, 2008 5:32 am UTC

M.qrius wrote:Warping the environment is a nice idea as well, but it still only shows 3 dimensions. You can't see anyone approaching from the 4th dimension.

I can't really think of a way to do it that wouldn't warp the environment. 3D objects are generally depicted in 2 dimensions as collections of distorted 2D shapes, and as the object moves in 3D space, the shapes warp and move in 2D space.

But I think see what you mean about not being able to see into the 4th dimension. The system I was thinking of would only draw objects that are at the same position on the 4th axis as the player. Hmm, maybe objects could be rendered to the screen with their saturation and luminosity proportional to their proximity to your co-ordinates on the 4th dimensional axis? So someone approaching from the fourth dimension would gradually become brighter and more colorful. Or perhaps distant objects would be blurry, but become more clearly defined as they move closer.

On second thought, that would be really messy. A 4th dimension radar on your HUD, maybe?

by **lowbart** » Sun Jan 13, 2008 10:08 pm UTC

Berengal wrote: ana-kata (Oh, how I've longed to use those terms)

I remember that book! The boy who reversed himself? Is that what it was called?

by **Freakish** » Sun Jan 13, 2008 11:08 pm UTC

There are already a few 4d games. Time Shift and Blinx come to mind.

by **M.qrius** » Sun Jan 13, 2008 11:33 pm UTC

Freakish wrote:There are already a few 4d games. Time Shift and Blinx come to mind.

Please read the thread. I'm not talking about time as a fourth dimension. By your definition every 3d game is 4d, whether you can move backwards in time or only move forwards.

by **Berengal** » Sun Jan 13, 2008 11:35 pm UTC

And as I previously mentioned, most racing games depend on the most often experienced fourth dimention known as time. This is about 4 spacial dimentions, however.

I liked the Prince of Persia time rewinding much better than Time Shift's anyway.

Edit: Ninja'd

by **Narsil** » Mon Jan 14, 2008 12:07 am UTC

In the spirit of understanding a 4th dimension, could it be made up of any combination of higher dimensions?

Example, 2s can be either x & y, x & z, or y & z axes. Not sure that it would affect the game in any meaningful way, just curious.

by **Freakish** » Mon Jan 14, 2008 4:03 am UTC

M.qrius wrote:
Freakish wrote:There are already a few 4d games. Time Shift and Blinx come to mind.

Please read the thread. I'm not talking about time as a fourth dimension. By your definition every 3d game is 4d, whether you can move backwards in time or only move forwards.

I read the thread before posting, but time is the only way you going to get a 4d game. Anything else well only ever appear as 2/3d, however adding control over time highlights the dimension.

by **Matthias** » Mon Jan 14, 2008 6:06 am UTC

Maybe something akin to Soul Reaver or Prey, with a second world as an overlay to the regular one, with shadowy glimpses of whichever world you're not in? I think that counts as 4d. I mean, I know it's not exactly what you had in mind--you're really only taking a small step ana or kata--but there ya go.

by **M.qrius** » Mon Jan 14, 2008 6:50 am UTC

Freakish wrote:I read the thread before posting, but time is the only way you going to get a 4d game. Anything else well only ever appear as 2/3d, however adding control over time highlights the dimension.

A first person shooter doesn't look like 2d to me. If you map a 4d area onto a 2d plane, it won't look 2d or 3d. For example, we view a solid cube like this:

Code: Select all: E_______ F / /| / / | D ______ C | | | |G | | / | |/ A|______|B

It's missing the H point.
A 4d being would see a solid hypercube like this:

Code: Select all: EEE EE FFF FF E F EE FF E F EEE F ############################################################## ################################################################ #### ###### ####$ ####### ##### $ ######### ###### $ #####$ ### #### $ $ #####$$ ### ##### $$ $ #### $$ ### #### $$ $ CC CC #### $$ ### #### $ $ C #### $$ ### DD DD #### $ $ C ##### $$ ### D D ##### $$ $ C ##### $$ ### D D #### $$ $ CC ##### $$ ### DD ################################################################ $$ ### ################################################################ $$ ### #### $ $ #### $$ ### ### $ $ ##### $$ ### #### $$ $ ###### $$ ### #### $ $ ####### $$ ### #### $ $ ####### $$ ### ### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########$$$$ ### #### $$ $ EEE $ #### ###$$$$ FFF ### #### $$$ $ E $ #### ###$ $ F ### #### $$ $ EE $ ### ### $ FF ### #### $$$ $ E $ ### $### $ F ### ### $$ $ EEE $ ### $$$### $ F ### #### $$ $ $ #### $$ ### $ ### #### $$ $ $ #### $$$ ### $ ### #####$$ $ $ #### $$ ### $ ### ####$ $ $ #### $$ ### $ ### ####$ $ $ ###$$ ### $ ### #### $ $ ####$ ### $ ### ############################################################### CC ### $ ### ############################################################### C ### $ ### ############################################################## C ### $ ### ### DD $ $ ### C ### $ ### ### D D $ $ ### CC ### $ ### ### D D $ $ ### ### $ ### ### DD $ $ ### ### $ ### GG GG ### $ $ ### ### $ ### G ### $ $$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$### G GG ### $ $$ H H HH ### ### $ #### G G ### $ $$ H H ### ### $ ##### GG ### $ $$ HHHH ### ### $ ##### ### $ $$ H H ### ### $ ####### ### $ $$ H H ### ### $ ####### ### $ $ ### ### $ ######## ### $ $$ ### ### $ ######## ### $ $$ ### ### $ #### #### ### $ $ ### ### ##### #### ### $ $$ ### BBB BB### ##### #### ### $ $$ ### B B ### #### #### ### $ $$ ### BBB ####### ### ### $ $$ ### B B ##### $ #### ### $ $ ### BBB ### $ ### ### $ $ ### #### $ #### ### $ $ ### #### $ ### ### $$$ ### #### $#### ### $$ ### ### #### ### $ ### #### #### ### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$####$$$$##### GG ### $$ H H ### #### #### G ### $$ H H ### ### #### G GG ### $$ HHHH ### #### #### G G ### $$ H H ### #### ##### GG ### $$ H H ### ### #### ### $$ ### ### #### ### $$ ### ######## ### $$$ ### ####### ### $$ ######### ### $$$ ######## ###$$ ###### ################################################################ ############################################################### A BBB A A B B AAAAA BBB A A B B A A BBB

Note that this is not a hypercube. it's missing the point A' (More explanation on why is in the link I posted earlier)
So it's just not the same, and it wouldn't play the same either. I'm not sure if it would be playable. It might be.

Narsil wrote:In the spirit of understanding a 4th dimension, could it be made up of any combination of higher dimensions?

Example, 2s can be either x & y, x & z, or y & z axes. Not sure that it would affect the game in any meaningful way, just curious.

For it to be made up of a combination of directions, we'd need to have 5 or more dimensions. We don't actually have that, so we can't take 4 of that. Combining 2 or 3 of our dimensions won't create a 4th, since we need 4 lines which are all perpendicular too all of the others as axes. This is only possible in 4 or higher dimensions.

For the record, I think of 2 dimensions not in the way as outlined by flatland, but like a plane with a width and a height. This has the added value that you can add gravity to your 2d world without breaking it. (See this for more on what effects this would have.)

by **Marbas** » Mon Jan 14, 2008 8:14 am UTC

Do you have to make the 4th dimension visible on a single screen? Why not just it's effects? Or better yet, why not two screens? You could model the fourth dimension abstractly via computer programs, and give the user the ability to move through chunks of the 4th axis using a button command, the effects of this could then be observed by the player witnessing what happens to the 3-dimensional shapes in front of them. 4-dimensional walls and such could be modeled by something which prevents the player from using said command. Maybe some sort of box will help the user see what's on the 4th axis while omitting another one too.

Hell, an axis switch command would pretty cool as well, a sort of swap-out feature where one is moved to the HUD box and another is placed in front of you. The game would have to be pretty simple to compensate for this, but if you make the learning curve gentle enough I could see things getting complicated and interesting.

by **Berengal** » Mon Jan 14, 2008 9:00 am UTC

Marbas wrote:Do you have to make the 4th dimension visible on a single screen? Why not just it's effects? Or better yet, why not two screens? You could model the fourth dimension abstractly via computer programs, and give the user the ability to move through chunks of the 4th axis using a button command, the effects of this could then be observed by the player witnessing what happens to the 3-dimensional shapes in front of them. 4-dimensional walls and such could be modeled by something which prevents the player from using said command. Maybe some sort of box will help the user see what's on the 4th axis while omitting another one too.

Hell, an axis switch command would pretty cool as well, a sort of swap-out feature where one is moved to the HUD box and another is placed in front of you. The game would have to be pretty simple to compensate for this, but if you make the learning curve gentle enough I could see things getting complicated and interesting.

I've thought about this as well, and it does seem to be able to work, but only if the player exists in 3d pluss a point in the 4th dimention (with optional "flipping" of dimentions). This is basically what Soul Reaver and Prey did, only they only had two levels on the fourth dimention, not a continuum.

It doesn't quite work of the player is also fully 4d, though.

by **liquidpaper** » Mon Jan 21, 2008 7:37 am UTC

you could simply use hue (colours) to represent the place in the 4th dimension and transparency to show how close something is. the radar would have to be 3d and you could simply add just two keys to allow you to 'slide' through the 4th dimension. the ojects would need to be textured in order to keep the 3d look on the 2d screen. i think it would be really cool. the hardest part would be making the 4d map, since adding another dimension multiplies the size by however many points are in the new dimension. there would be many obstructions or it would be extremely difficult to follow something. while following something the hardest part would be to keep track of which colours were in what direction, so if the object you were following started turning green and fading you would need to be aware of what colour you were in and in what direction green was.

by **Brooks** » Mon Jan 21, 2008 7:47 am UTC

As stereoscopic displays become more commonplace, doesn't this get more feasible? Representing 4D in 3D has to be more intuitively grasp-able than representing 4D in 2D, right?

by **Eschatokyrios** » Mon Jan 21, 2008 8:44 am UTC

Metroid Prime 2, and any other game where you can move between multiple worlds is a 4d game, albeit with an extremely short 4th axis (there are only two occupyable positions on the 4th axis, dark world or light world). But you could conceivably have more. Add another "world" that you can shift to and that's 3 points. Or, extend the geometry of the game as non-discretely as possible in an analogous fashion to the light and dark worlds. You could move your character around normally with the control stick, and, say, hold L-shoulder and R-shoulder to shift in one direction or the other along the 4th axis.

by **zenten** » Mon Jan 21, 2008 11:20 am UTC

Berengal wrote:
It doesn't quite work of the player is also fully 4d, though.

I would assume any 4d programmer could do a better job with that than any of us.

by **SecondTalon** » Mon Jan 21, 2008 3:04 pm UTC

Anyone else thinking of something like Cursor*10?

Basic idea of that game is you control the action for a set amount of time... when time runs out, you start over controlling a second character while the first does whatever you did the first time around.

Repeat.. repeat... I think this game gives you 16 chances to work with yourself to get it right. Anyway, could craft a time-traveling game based on something like that.. you have to travel to 10:15am, enter the control room and hold the Open Door button for enough time to allow you to travel back to 10:15am and walk through the door....

by **thedufer** » Mon Jan 21, 2008 4:00 pm UTC

SexyTalon wrote:Anyone else thinking of something like Cursor*10?

Basic idea of that game is you control the action for a set amount of time... when time runs out, you start over controlling a second character while the first does whatever you did the first time around.

Repeat.. repeat... I think this game gives you 16 chances to work with yourself to get it right. Anyway, could craft a time-traveling game based on something like that.. you have to travel to 10:15am, enter the control room and hold the Open Door button for enough time to allow you to travel back to 10:15am and walk through the door....

Its 10 chances (thus Cursor*10), and 16 levels. And I believe its already been mentioned in this thread.

by **SecondTalon** » Mon Jan 21, 2008 4:08 pm UTC

by **Spoffin** » Mon Jan 21, 2008 4:32 pm UTC

There's a rubix cube in the 4th dimension. God knows how that works.

by **4=5** » Mon Jan 21, 2008 4:52 pm UTC

you use 3d glasses to get the 3 dimentional plain that you will represent the four dimentional objects on, it's actually fairly easy to program the distortions

by **liquidpaper** » Tue Jan 22, 2008 4:11 am UTC

Spoffin wrote:There's a rubix cube in the 4th dimension. God knows how that works.

there isn't a rubix cube in the forth or fifth dimension it is simply a 4x4x4 rubix cube (or 5x5x5 rubix cube). it still has only 3 dimensions.

by **Spoffin** » Tue Jan 22, 2008 5:01 am UTC

liquidpaper wrote:
Spoffin wrote:There's a rubix cube in the 4th dimension. God knows how that works.

there isn't a rubix cube in the forth or fifth dimension it is simply a 4x4x4 rubix cube (or 5x5x5 rubix cube). it still has only 3 dimensions.

Now, if I thought that a 4x4x4 rubix cube was a 4 dimensional rubix cube, I'd be incredibly stupid.

I admit I should have made more clear that its a computer model and not a physical object. But I did think we were talking about computer games

http://en.wikipedia.org/wiki/Rubik%27s_ ... e_software

by **meoiswa** » Thu Feb 18, 2010 4:46 am UTC

There IS a 4 spatial, 10 degrees of freedom game, its called Anachron and its available for Linux and Mac OS X, i dont know if its available for windows. This is an extract from the game's manual.
It is quite playable and interesting, but takes some time to actually understand "WTH!!!!" is happening
Enjoy reading:

Welcome to Adanaxis! The world’s first real-time shooter in four spatial dimensions. The game world has the usual three dimensions (left/right, up/down and forward/back) plus another new direction in space. We don’t have this dimension in our physical world but it’s possible to simulate a fourth dimension, so this is what Adanaxis does. The game takes a while to learn, but you can soon become a natural. It’s a bit like learning to play a first person shooter for the first time, and once you get it, you might not want to go back…
[...]
Technical Details
Instead of the usual six degrees of freedom in 3D there are ten in 4D; four directions and six rotations. Three directions are mapped onto the screen just like 3Dm and these are chosen so that the x axis is left/right, the y axis is up/down, and the w axis is away from you into the screen. There’s no direction left to use for the z axis, so the game represents z in three ways:
• Tinting the object red (negative z) or green (positive z) to show where it is in z.
• Using the three-dot markers to show where the object is in x, y and z.
• Fading objects as they move away from the view axis in z.
There’s also another reason for the last one, as it makes the z axis more consistent with x and y. You can’t see objects with large x or y values (compared to w, their distance away from you) because they go off the screen, and the fading does the same for z. The fading essentially gives you a viewing angle in the zw plane that is roughly the same as that in xw and yw.

by **SlyReaper** » Thu Feb 18, 2010 4:22 pm UTC

I'm pretty sure there are computer programs modelling 3x3x3x3 and 3x3x3x3x3 rubix cubes. Obviously such a thing could never exist physically, but it's doable on a computer. I don't think anyone has ever solved the 5D one.

by **SWGlassPit** » Thu Feb 18, 2010 5:15 pm UTC

meoiswa wrote:There IS a 4 spatial, 10 degrees of freedom game, its called Anachron and its available for Linux and Mac OS X, i dont know if its available for windows. This is an extract from the game's manual.
It is quite playable and interesting, but takes some time to actually understand "WTH!!!!" is happening
Enjoy reading:

Welcome to Adanaxis! The world’s first real-time shooter in four spatial dimensions. The game world has the usual three dimensions (left/right, up/down and forward/back) plus another new direction in space. We don’t have this dimension in our physical world but it’s possible to simulate a fourth dimension, so this is what Adanaxis does. The game takes a while to learn, but you can soon become a natural. It’s a bit like learning to play a first person shooter for the first time, and once you get it, you might not want to go back…
[...]
Technical Details
Instead of the usual six degrees of freedom in 3D there are ten in 4D; four directions and six rotations. Three directions are mapped onto the screen just like 3Dm and these are chosen so that the x axis is left/right, the y axis is up/down, and the w axis is away from you into the screen. There’s no direction left to use for the z axis, so the game represents z in three ways:
• Tinting the object red (negative z) or green (positive z) to show where it is in z.
• Using the three-dot markers to show where the object is in x, y and z.
• Fading objects as they move away from the view axis in z.
There’s also another reason for the last one, as it makes the z axis more consistent with x and y. You can’t see objects with large x or y values (compared to w, their distance away from you) because they go off the screen, and the fading does the same for z. The fading essentially gives you a viewing angle in the zw plane that is roughly the same as that in xw and yw.

Came for this, leaving happy. It's in the Fedora repositories and it can be found at http://www.mushware.com/

by **Josephine** » Thu Feb 18, 2010 5:31 pm UTC

google Adanaxis.

by **Not A Raptor** » Thu Feb 18, 2010 8:06 pm UTC

SlyReaper wrote:I'm pretty sure there are computer programs modelling 3x3x3x3 and 3x3x3x3x3 rubix cubes. Obviously such a thing could never exist physically, but it's doable on a computer. I don't think anyone has ever solved the 5D one.

O RLY?

by **_MC_** » Fri Feb 19, 2010 1:08 am UTC

I imagine a fourth spacial dimension as being an infinite set of "parallel" universes in the same 3d space. However, since we're not talking about Star Trek and instead about continuous functions in four dimensions, the transition as you move along the fourth spacial axis would make objects appear to fade in or out as you move towards or away from them in 4d space. Similar to how distant objects appear small or unclear, objects approaching along the fourth dimension would seem to fade in until they have the same fourth-dimensional position as you do.

*EDIT*

Looks like people beat me to it.

by **wst** » Fri Feb 19, 2010 1:40 am UTC

Firstly - As much as I understand of 4 dimensions is basically from this and this will be referred to in this post

In the above video, the square and the apple can see inside flatlanders and closed rooms when the apple pushes the square into the third dimension. When the apple intersects flatland, only that immediate slice can be seen.

So, I think, as it's going to be brain-breakingly-impossible to render (imho, or at least to view), dimensions will be more like, seeing through things. As you travel through the 4th dimension, objects without the same co-ordinates in this 4th dimension get less visible.

Think back to the video-flatland, and the way the square appears in mid-air when he returns from 'updown'. This effect, but in three dimensions.

This means that you have a problem - infinite universes, or something. How will you ever meet anyone else and shoot them?

1) Heat/air currents, gravity, maybe minor optical lensing effects - these might be able to propagate through the 4th dimension somewhat and lead a 3d-clue to someone's location. Just move yourself and your weapon in the 4th dimension to the same co-ordinates and fire

Etcetc. I hope I've sparked some useful thoughts.

by **TheAmazingRando** » Fri Feb 19, 2010 1:48 am UTC

I also had the fade in/out dimension shifting theory, but I realized this is still pretty limited as far as 4-dimensional motion is concerned. It's effectively the same as taking cross-sections of a 3-dimensional object in order to represent it in two dimensions. And it makes pretty good sense, intuitively. But if you wanted true 4-dimensional gameplay, you'd need to include rotations. And I'm not sure there's a way to do that that would make any intuitive sense to the player. I've looked at 3-dimensional projections of them while reading about what it is I'm seeing, and I still can't seem to understand them.

by **Toeofdoom** » Fri Feb 19, 2010 4:43 am UTC

Heh, a guy at my uni made a game with what he calls 4D space... I personally think it's just non-euclidean and uses a bunch of portals. Really good game anyway, but not 4D.

Anyway, you could definitely make it, but I don't know why anyone would want to work with 4 dimensional rotation matrices. Quaternions apparently only work in 3 and 7 dimensions, as well.

And I'm pretty sure no matter what section of a hypersphere is overlapping our dimension, you'll see a sphere. Think about it: You'll never see anything but a circle if you take a planar cross-section of a regular sphere.

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