Making games in 11 dimensional space.

[Saktoth]

Just some musings ive been having that i have nowhere better to put (Oh my god im turning into Caydr/AF >_>). Id put this in games/mods but it doesnt really pertain to spring so much, so its here.

Ive been thinking recently a little bit about string theory. No im not going to bore you with amateur prattling about its implications, i know i could not possibly understand string theory, but the idea of 11 dimensional space (The number of dimensions required for string theory to work) has intrigued me, specifically how to represent dimensions beyond 3 (4, strictly) in an easily understandable context.

Naturally i tried to think how to apply this to a game or simulation. Tesseracts are one way to represent a 4d object in 3d, but thats just too difficult to process, especially for a game.

So. Say we have a finite space, X Y and Z ranging from 0 to 100. Im sure you can visualize this easily enough. Collisions of objects in the space occur when they all share the same X Y and Z coordinates. Add more variables and we can track an object in an arbitrary number of dimensions, and thus an object must also share the A B and C values to collide, as well as the XYZ. But how could we represent this visually?

One way could be to use colour. Light to dark for the 4th dimension, with red blue and green increasing the number of dimensions to 7. Objects can move along these spaces in the same way they move along the first 3 dimensions, with velocities and trajectories. Thus, you have two objects sharing the same X Y and Z coordinates, but one is Dark Blue while the other is Light Red (Assume the same greenspace). You throw the Dark Blue object down the Blue Dimension and up the Red and Light dimensions. If it intersects the same place as the Light Red object, a collision occurs- though the objects do not move in X Y and Z (they have no velocity in those dimensions), rather they are sent hurtling away from eachother in Light and Red space.

Objects can also have sizes within these dimensions, an object occupying 10 units of the 100 unit Red space might be coloured in a gradient of the section of the space it is occupying.

Assuming the object doesnt rotate in the first 3 dimensions (say, it is a point or a sphere) we add rotation to this to give us more dimensions. Say, the object is represented by an arrow (though physically it is a sphere) and an object at a 90 degree y rotation will pass right through an object of 160 degree y rotation, even if it shares the same space in the first 7 dimensions. Using rotation, we can add up to 3 extra dimensions, bringing us to 10.

The 11th is, of course, time. Time works just like any other dimension- if it is a scale from 0 to 100, an object will only collide with another if it shares all the other coordinates as well as the time coordinate. The only difference is that time moves at a constant speed in a single direction and the fact its visualization is made up of a distinct set of instances rather than all time information being displayed at once (though im sure you can visualize all time instances of an object being displayed at once).


This brings up another interesting way you could visualize additional dimensions in the same way you visualize time. You visualize time by taking several instances (in this case, 100) and displaying them one after the other. If each instance consisted of 3 seperate images of the same object, with each instance showing the 3 of 9 dimensions the object is in at one time (by displaying them as regular xyz), an object would only collide with another if they were in the same position in all three images at once.

An easier way to do this would be to have a red object, a green object and a blue object (Ignore the earlier use of the red-green-blue spectra as dimensional locations, this is a new visualization). The three different objects are actually displaying the location of single a 9 dimensional object, by rendering it in 3 seperate instances of 3 dimensions but all at the same time, by colour-coding them. The red, blue and green versions of an object must be colliding with the red blue and green versions of another object in order for collision to occur.

The downside of this representation is that each object must have a distinct shape or signifier to let you know which r-b-g objects are related. So lets discard these models in favour of the first one.

If you've followed me this far, you realise how absurdly difficult it would be to hit anything with objects moving in 11 dimensions. In truth, we have trouble hitting objects moving in 3 dimensions. 2 dimensional collisions are much easier to predict and manipulate (pool, say).

Which brings me to the role of gravity. In Spring, the third dimensions effect on the space a projectile can occupy is reduced because all ballistic projectiles ultimately come back to rest at a single point in the y dimension. This is the ground, which can vary in height, but for our purposes we will call this 0.

Gravity can be represented by a constant force that is applied to an object, bringing it back to 0 on that dimension. If Redspace and Bluespace also had gravity, an object thrown up the blue and red space would slow, stop, turn around and fall back to 0 on the blue and red space, thus making it more likely for these objects to collide (Though this is mostly just a cute thought experiment).

So, what sort of game could actually benefit from being made in 11 dimensional space? Ive no idea. Im sure there have already been games made with similar concepts, with coloured objects only colliding similarly coloured objects, etc, though velocity along a colour dimension is not something i can say ive seen. Most likely, this wouldnt actually make a 'fun' game, and you probably wouldnt get much more than an 11-dimensional bouncing particle screensaver out of the idea.

[Evil4Zerggin]

You could consider Set a 4-dimensional game (that doesn't use the time dimension).

In any case, if you take a broad definition of "dimension", you could argue that most RTS are already functioning in high numbers of dimensions, as you could assign a dimension to each variable describing a unit's state, such as position, hit points, weapon reload state, experience, etc.

[Saktoth]

I was thinking something similiar- but hp, weapons, special damage categories, they dont describe position, and you dont 'move' through them. I suppose it can be said that you move through hp by being pushed down it by weapons, but there are certainly no 'collision' points (other than one, with the ground, at 0, which kills you).

Take say, air and subs in most spring games or even RTS's. You can only hit air with AA weapons, and subs only with anti-sub weaponry. I suppose that can be seen as a dimension with a distance of 1-3 (though objects might be able to have a 'size' of 2, and occupy 2 spaces in the dimension at once), but thats a very short dimension and you dont move along it so much as occupy one space within it and shoot into an adjacent space.

The point of this isnt so much to add a bunch of arbitrary states that form a sort of matching game. I mean, its not to apply multidimensional ideas in an effort to foster understanding of matching and 'collisions' along values and colours (honestly thats taking a simple idea and making it more complex...), its to apply values and colours to representing movement in multiple dimensions.

So, the point of this is to really create a framework for representing movement through an arbitrary number of dimensions (or as many as you can find representations for) of arbitrary length (as long as the length is finite, thats necessary when you have an 'end' to say, colour spectrum).

Its probably not practical or useful, just an idea i wanted to get out of my head. Its easier to understand movement through colourspace than it is to understand what the hell is going on when you are looking at this: http://www.youtube.com/watch?v=FXKe0SiATwQ

[Elkvis]

how about this, as a four dimensional game.

2 have time time zones, Now and some time in the past. You have to fight in both time zones. Although you cannot stop fighting in the present, because you need energy to control the past and if the enemy defeats you there, you cannot get back to influencing the past in the first place.

Events in the past influence the present..

Hohoho; can you imagine how complex that would be. I'd have to be turn based as you would need a super computer to calculate the cause and effect possibilities in anything like real time. And the present would change hugely from turn to turn. Each present setting would be like a mini game, where you struggle for the ability to control the past (and to what extent).

[Machiosabre]

just make 11 one dimensional games and stick em together, next topic!

[Erom]

There is a 4 spacial dimension + time space shooter in development. Google mushware.

It's pretty weird looking.

[Pxtl]

The 4D fighter game is called Adanaxis. Haven't tried it personally.

[KDR_11k]

Highest I've seen is Frequon Invaders.

[manored]

I think a game with 11 dimensions would be too headaching to be fun :)
Also, I cannot think of a way of representing more than 3 spacial dimensions in a pratical manner (I dont think colors would work well) except by having one 3 dimensional space for ever possible combination of the other dimensions... like, if you had 5 dimensions with the last 2 ones having 3 instances, you would use 9 3 dimensional spaces to represent it... Also, I think that we would need a direct brain connection to be able to perceive and understand other dimensions... like, the game socking it straigh in your mind :)

By the way, has anyone ever imagined how chess would be with more dimensions? I already imagined it with 3 and 4 dimensions for some odd reason :)

[Peet]

[quote="KDR_11k"]Highest I've seen is [url=http://arch.robison.home.comcast.net/~a ... equon.html]Frequon Invaders[/url].[/quote]
This game froze me up twice >:(

[Teutooni]

First, solve this damn thing and think about an 11 dimensional game after, ok?

[Panda]

Its probably not practical or useful, just an idea i wanted to get out of my head. Its easier to understand movement through colourspace than it is to understand what the hell is going on when you are looking at this: http://www.youtube.com/watch?v=FXKe0SiATwQ

I remember a trick that you can do with bubbles that resembled that video.

The Steven Spielberg game, Boom Blox, is a fun game for the Wii that can help you understand movement through 4 dimensions. There are some wicked looking little creatures in it that you get to blow up by throwing bowling balls at jewel blocks at different angles. There are also Jinga-like levels availible.

I like your movement through colourspace explanation. It reminds me of whats going on near the event horizon of a black hole and it's pretty.

[AF]

Wow that cliffs inside a giant bubble

[Caydr]

Me too.

[Saktoth]

Highest I've seen is Frequon Invaders.

Wow thats really interesting, its odd when your brain clicks in and starts finding the pattern. Im still seeing black lines moving around the screen as i move my eyes.

As a game, its not much, just find-the-dot. As an... experience thats... really interesting *blink blink* *rubs eyes*... the lines are still there.

The 4d shooter looks interesting, though it looks like the 4th dimension seems kinda optional (I need to play it...). Ultimately though, it is viewing the 4th dimension within the same space as the first 3, so thats gonna be confsing. However, the truth is all computer games are actually in 2d- navigating a 3d space on a computer screen is ultimately just a trick of your mind in translating 2d data into 3d. It would be utterly fascinating to see if we can program our brains to translate 2d data into 4d data.

In the end though thats sort of what im trying to avoid. By having objects shaded in different colours and what have you, you dont have to confuse the 3d data with the data from any of the other dimensions- your brain doesnt have to sift through a jumbled up 2d image and retranslate it. Thats why i posted this idea, because i see the idea of colourspace as something so much easier to grasp than the movement of a tesseract.

Actually, if you think about it, in a first person game such as a space shooter like Adanaxis, you are really translating the world as 2 dimensional, with depth or distance to an object being represented by the objects size. Thats an interesting idea, that you're only seeing 2 dimensions and the third is shown as object size (im sure we've all seen simple starfield simulators with objects flying from the centre of the screen and growing larger as they do). But then, you can re-orient yourself within that space to face different axes, to fly in different directions.

So, if translating it to a space shooter such as Adanaxis, you'd have to think about orientation in colourspace. I suppose if you represented colourspace as a spectral ring, like the Frequon radar, you could shift your orientation to be facing more towards one colour, allowing you to change orientation in 2 colour dimensions... So you might have red at 0, blue at 90, green at 180, black at 0.

I dont know how you'd represent that other than a 'colour orientation indicator' though, or several colour orientation bars to represent your position or orientation in colourspace seperately from the visualization of an objects colour. It would be easy enough to represent your position in 11 dimensions as 11 different bars, as machio said, 11 one dimensional games, which sort of defeats the point.

[Teutooni]

Don't forget that all dimensions are identical and orthogonal. You can't have a color ring. You'd also need to link the colors into classic spatial dimensions, like being able to swap from looking in the direction of positive x to looking to positive red, for example.

This could be done by taking for example red, green and blue, thinking them as the classical dimensions, all identical and orthogonal (not a ring) and the classical x, y and z. Then, you could turn the camera to different vectors, and the spatial dimensions would swap to colorspace dimensions and the other way around accordingly. It's quite hard to explain without illustrations. A 6D version of swinging camera around. In any case, I don't see how this is any easier to grasp than the tesseract.

You think there's some kind of a shortcut to representing multiple dimensions in 2D in a way easily understandable. This might be possible, at least with severe limitations like fixed camera angle, essentially stripping it down to 11 bars, but that'd kinda make it pointless imo.

If you plan to emphasise time being an essential gameplay feature as a dimension, how do you plan to illustrate it? Most games have a time dimension, but it's more or less tied to the time dimension in the real world (REAL TIME strategy, anyone? ) and isn't really worth much discussion, it's obvious.

[Crayfish]

I don't think it's possible to portray extra (spatial) dimensions. If we're unable to percieve them in the real world, I just don't see a two dimensional computer monitor managing to convey them.

Could be wrong though. Hope I am, it's a cool idea.

[Panda]

Holographic principal says that the universe can be seen as a "two-dimensional information structure "painted" on a boundary surface, and that the three dimensions we observe are illusory".- Wikipedia - http://en.wikipedia.org/wiki/Holographic_principle

Like in Bombshell:
http://www.youtube.com/watch?v=qS1sOWvo97s

These concepts would be good to know if you wanted to go into holographic game design along with helping you understand how the universe works.

[manored]

He wants eleven dimensions tough, and I dont think it will be possible for a human being to understand and manage that big load of information in time to react to something, or, in case of a really slow/pausable/turn based game, before he runs out of patience towards the game :) Maybe after we get our brains tugged into computers.

[Peet]

It's easy, just visualize N-dimensional space and set N to 11!