Four spatial dimensions

[Lachlan Easton]

As part of my individual research assignment I am doing for my diploma I plan on creating a 4D app (wow that's 1 more than 3D!). The plan for the final product is to have a 4D puzzle-like maze. Not really sure why I started this thread. I guess it would be fun to discuss higher dimensions and how you would represent them programmaticaly (totally a word)

I'll be post updates of my still to be fully conceived app on my blog. Which currently has some information on 4D space so I don't sound like a loony http://cephalopodmagic.blogspot.com.au/2012/04/thinking-in-four-dimensions.html

[hamsterman]

I've been meaning to write a program that would do with 4d vectors what the video card does with 3. It's very straightforward, really. Programmatically I don't see anything that is good with 3d but hard with 4. You'd better concentrate on how you're going to represent them visually.

[Gaminic]

Mathematically (and thus, programmatically), there is nothing impressive about 4D (or 5D, or 5000D). The maze example is pretty cool though, because it relies more on conceptualizing than just the math behind it.

[Pravesh Koirala]

just to be clear, by 4D you mean 4D-and-not-including-time-dimension type of 4D. am i right?
Coz, I've always been fascinated by higher dimensions. I mean, I can't even begin to conceptualize how it may look like. How are you supposed to program an 4D app? I mean, what about the graphics?? I'm really looking forward to the development of this thread.
cheers!!

[chrisname]

I've heard of a 4D puzzle game before. ( edit: here it is: http://marctenbosch.com/miegakure/ ).

@hamsterman,
Doesn't OpenGL actually use 4D vectors internally?

[hanst99]

OpenGL uses whatever vectors you tell it to internally. That is, 2, 3 or 4 dimensional ones. Most people go for 4 dimensional vectors in 3D because it's more convenient for matrix multiplications though.

Coz, I've always been fascinated by higher dimensions. I mean, I can't even begin to conceptualize how it may look like. How are you supposed to program an 4D app? I mean, what about the graphics?? I'm really looking forward to the development of this thread.

I'm still trying to figure out how and WHY one would want a fourth spatial dimension in a game. As if 3 weren't bad enough.

[ne555]

Vectors in the projective space. Now a translation can be computed as a matrix multiplication.

[Lachlan Easton]

As many have stated before me it turns out that under the hood 4D maths is no more complex than 3D (other than the cross product and the fact that all your vectors have an extra number... No wait technically that is more complex).

just to be clear, by 4D you mean 4D-and-not-including-time-dimension type of 4D. am i right?

Yes, you would be right.

better concentrate on how you're going to represent them visually

Yes I admit I'm quite torn between doing a full 4D projection (meaning the whole game world will look something like this http://www.youtube.com/watch?v=t-WyreE9ZkI) or doing it like miegukure (see chrisname's link) where you only ever view 3 dimensions and swap out which three you're viewing.

[LB]

http://www.youtube.com/watch?v=M9sbdrPVfOQ therefore your arguments are invalid.

[Lachlan Easton]

therefore your arguments are invalid.

... What arguments?

[LB]

There were some implications that time was the fourth dimension. How would we know it wasn't the first? Just swatting away the implications before they materialized.

[Lachlan Easton]

I don't plan on treating time as a dimension.

[hamsterman]

@chrisname, OpenGL uses 4D vectors, but that 4th number is mostly there to make a translation matrix possible. It does not represent a position. Naturally, I'd be using 5D vectors.