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[PHeMoX]

The player exists in four space, but may only interact with a single 3D projection at any given time. Interaction with the exatra dimension is accomplished through rotations in four space.

Sounds easier than it is. For example, in case of Fez how would you make it 4 dimensional? By rotating it's already 3D, which makes up for áll 6 degrees of freedom actually, right?

[Corpus]

He means rotation in the fourth dimension, which is different to rotation in the third dimension and which I cannot grasp mentally.

[Inane]

He means rotation in the fourth dimension, which is different to rotation in the third dimension and which I cannot grasp mentally.

Seriously. What the fuck is that shit?

[Chris Whitman]

It's just a math trick, basically.

Instead of representing points in space with an ordered pair, as in two dimensions (e.g. [1,2]) or an ordered triplet, as in three dimensions (e.g., [1,2,3]), four dimensional points can be represented by ordered quadruplets, [1,2,3,4].

Since we can't render a three dimensional object on a computer screen, of course, we do a two dimensional projection (sometimes called a subspace projection) to give the appearance of looking through the screen into a three dimensional scene. The same math can be extended into higher dimensions to give the projection of a four dimensional scene onto the two dimensional screen. Since you have an extra dimension, meaning you have an extra direction which is 'perpendicular' (mathematically, of course, its perpendicularity has no real geometric meaning) to the normal three basis directions in three dimensional space, you have an additional axis to 'rotate' through, by extending the definition of rotation arbitrarily into higher spaces.

The idea sounds cool to oversized-glasses-wearing nerds, but in practice it's extremely counterintuitive and difficult to grasp. You're basically just generalizing the math used in three dimensional modelling into another mathematical dimension. It isn't much more than a neat toy.

[PHeMoX]

mathematically, of course, its perpendicularity has no real geometric meaning

Right, which is why, unless we're talking about 'time' as the fourth dimension, any higher dimensional space in games would be a bit pointless don't you think? Being a math trick anyway, I don't see how rotating beyond the 3rd dimension would make sense. As in, in Fez it makes perfect sense to rotate a 2D image into a 3D one, back into a 2D one. I don't quite see how this would work beyond the 3rd dimension (minus time). Bút I guess I simply can't grasp 4D very well. 

[deadeye]

I simply can't grasp 4D very well.

What a noob.  Even my elderly grandma can rotate in four dimensions and she's in a wheelchair.

[ithamore]

There was this post in the "Post games you want to see on TIGSource!" thread . I was thinking of front-paging it, but decided not to after finishing the demo.

Here is the text to save you the trouble of clicking:

Adanaxis from Mushware is one of those first-person zero-gee interstellar space shoot 'em games.  You know, blow up the other fleet, protect the convoy, etc, etc.  The physics aren't real flight physics: you go as long as you hold the button down, you stop when you let it up, there's no acceleration or momentum.

There is, however, flight through four spatial dimensions.  My attempts to explain aren't working very well at the moment, so I suggest you just go download the demo.  (Or watch a gameplay movie.)

Found on http://happypenguin.org.  available for WinXP, OS X, and Linux.  Shareware.

I thought the it might be interesting, but, once I found it to be a game that merely requires the play to adjust the controls to group together the 3 colored markers related to an enemy ship at the top of the cursor, it no didn't feel like I was flying through 4D: I was only playing a 3D space shooter with overly simplified (non-spacial) scrolling requirement that had to be met to determine weather or not a shot could make a hit. You fly to a ship, group up the colors, and then you shoot.

Once I have my (x,y,z) locked, what am I doing on that extra axis, which is only presented to me abstractly? Moving along the w-axis, moving along a scale of how pretty the object being viewed is, or moving along the spectrum of current US politics that some how coincide with the object? It's too arbitrary and ambiguous in terms of 4D.

[PHeMoX]

I simply can't grasp 4D very well.

What a noob.  Even my elderly grandma can rotate in four dimensions and she's in a wheelchair.

True, you sure got me there, but there's a difference between rotating while not knowing that you are rotating and consciously rotating in the 4th dimension. Okey, perhaps that was a bit mean, sorry.

[deadeye]

True, you sure got me there, but there's a difference between rotating while not knowing that you are rotating and consciously rotating in the 4th dimension. Okey, perhaps that was a bit mean, sorry.

I was just kidding.  My grandma's dead, she can't rotate for shit.

[Melly]

True, you sure got me there, but there's a difference between rotating while not knowing that you are rotating and consciously rotating in the 4th dimension. Okey, perhaps that was a bit mean, sorry.

I was just kidding.  My grandma's dead, she can't rotate for shit.

Does it make me an asshole if I laugh out loud to that?

[shinygerbil]

True, you sure got me there, but there's a difference between rotating while not knowing that you are rotating and consciously rotating in the 4th dimension. Okey, perhaps that was a bit mean, sorry.

I was just kidding.  My grandma's dead, she can't rotate for shit.

She's be spinning in her grave if she could hear you now.

[Jrsquee]

I rotated your grandma last night.



Yeah, I went there. 

[ithamore]

Making a game with 4 spacial dimensions is possible, though. One would simply have to look back at old 3D games for insight. What I'm really suggesting is using 3D "slices" of 4D objects.

Early 3D games merely enlarged or reduced vectors and sprites to immerse the player in a 3D world. The vector polygon enlargements are better examples of the mathematical idea I want to discuss. A sphere can be understood as a series of infinite, parallel circles aligned uniformly from a point through a series of growing circles to a great circle to a series of shrinking circles to a point. So, a simple 3D game would have a sphere appearing as a larger or smaller circle as you move toward it or away from it.

The same can be applied to 3D "slices" of 4D objects. As one zooms in toward or away from an object it changes along an extra axis (which we'll call the 'a-axis'), a circle would appear larger, smaller, or more like another shape instead of a circle).

The player will only see 3D "slices" of the 4D object, but they will enable the player to visualize and build together the object and its extra-environment.

[bigbossSNK]

That is both a very concise explanation and an interesting idea! I can certainly see the puzzle element of a game based on this.