How do you call higher dimensional axes?

[daemonflower]

In 3D we've got the x, y and z axes. The fourth axis is usually called the w axis, or the t axis if you're talking about time.

Is there any wide-spread convention how to call the fifth, sixth, ... spatial axis? Or do I have to invent one myself?

[bo198214]

in the n dimensional case the coordinates are usually called x₁, ..., x_n

[daemonflower]

in the n dimensional case the coordinates are usually called x₁, ..., x_n

Hm, not so beautiful... but I guess I could live with x, y, z, x₄, ...

[bo198214]

XD *I dont have seen this!*

[daemonflower]

Yeah, but calling the axes "x₁, x₂, x₃" in the three dimensional case, which is what users would normally see, would be nonstandard and confusing... anyway, thanks, I'll think of something!

[wendy]

w,x,y,z is the usual set.

z is height, and y is forward. Everything else is across.

W

[PWrong]

I've used x, y, z, w, u, v before, in that order. If I had to, I might use x, y, z, w, u, v, p, q, r, s. I'd order them that way because that's the way the alphabet tends to get divided up in maths, for whatever reason.
But if I got that high, I'd prefer to use x₁, ... ,x_n or x¹, ... ,xⁿ.

[bo198214]

but x,y,z,w,u,v is not lawful, rather x,y,z,w,v,u

I mean it makes anyway only sense (to use non-indexed variables) if you want to describe things that are particularly valid in that 4,5 or 6 dim space (for us humans it makes sense to have different words for depth, breadth and hight, but if you dont live in 6 dim space, why would you give the directions independent names/variables?). Usually in 5 or 6 dimensions one anyway tends to formulate things that are valid also in n dimensions and this is quite easier to formulate with indexed variables (for example matrices etc).

[houserichichi]

It's just semantics at this point...anybody versed in what you're talking about will get the gist of whatever you decide to label the axes. After three, however, it is most aesthetically pleasing and less cumbersome to use x_i for Euclidean axes.

x₁ = x
x₂ = y
x₃ = z
x₄ = w (or whatever letter you'd like to choose)
ad infinitum.

[daemonflower]

It's just semantics at this point...

That's true.

anybody versed in what you're talking about will get the gist of whatever you decide to label the axes.

With my program I aim at people who do not necessarily know what we're talking about here... educational purposes, if you wish.

I've decided on the following scheme. In the three-dimensional case, I'll just label the axes x, y, z. In the higher dimensional case, I'll have a different set of labels: x₁ (x), x₂ (y), x₃ (z), x₄ (w), x₅, x₆, ... This seems pretty clear to me.

It's mainly academic for dimensions higher than four, as I guess everybody will get lost anyway...

[bo198214]

With my program I aim at people who do not necessarily know what we're talking about here... educational purposes, if you wish.

So what is your program?
At least you audience seems sufficiently educated to know x,y,z, otherwise I can barely imagine how to convey the idea of higher dimensions ...

[daemonflower]

I am working on a three dimensional Go game (http://sourceforge.net/projects/go-3/), which I plan to extend to n dimensions - simply because I can, because I have found an elegant solution to create a n+1-dimensional Go board from an n-dimensional one.

I don't expect many people to want to play Go in more than three dimensions (it's hard enough in two, after all). But I want to give them the possibility, and I want some consistency there.

The project of going from three to n dimensions is still in its early stages. I was coding some user interface elements when I stumbled across the naming problem.

I will post a link to my n-dimensional Go game on this forum when it is ready to be reviewed - which may take some time, I have other things to do too

[pat]

Care to describe your "elegant solution to create a n+1-dimensional Go board from an n-dimensional one"?

And, for my vote... I use x, y, z, w, u, v. If I need u or v for something else or need more than six dimensions, I switch to x₁, x₂, ...

[pat]

w,x,y,z is the usual set.

z is height, and y is forward. Everything else is across.

For me, I use x is forward, z is height. The reason that I use x is forward is that there is always a forward (or, more to the point, I want there to always be a forward), even in one dimension.

My raytracer does x₁ is forward, x₂ is left-to-right, x₃ is top-to-bottom, x₄ is left-to-right across slices of x_1,2,3, x₅ is top-to-bottom across slices of x_1,2,3,4, x₆ is left-to-right across slices of x_1,2,3,4,5, x₇ is top-to-bottom across slices of x_1,2,3,4,5,6, etc. I recently added an option though that will start x₄ as top-to-bottom instead of left-to-right. This makes it easier for me to make stereo-pairs of renderings of 4-d scenes.

For some n-dimensional games that I've started working on, I've used x is forward, y is left-to-right, z is the other left-to-right, and w is top-to-bottom with gravity pushing things in the -w direction.

[Keiji]

Eh, I always use y as the axis of gravity, z as the axis of sight, and x as the axis that's perpendicular to both of those.

When it comes to 2D, I generally dismiss the z direction, as I don't imagine being in the plane, rather looking at the plane...

[pat]

Eh, I always use y as the axis of gravity, z as the axis of sight, and x as the axis that's perpendicular to both of those.

When it comes to 2D, I generally dismiss the z direction, as I don't imagine being in the plane, rather looking at the plane...

Scratches head... if you dismiss z, and z is your line of sight, then you're not looking anywhere? I mind not having a line of sight, and so use x in all dimensions.

[Keiji]

No, I mean that on a sheet of paper for instance, the axes would be x and y, without z.

[daemonflower]

Care to describe your "elegant solution to create a n+1-dimensional Go board from an n-dimensional one"?

Basically it's the old way to construct an n-dimensional hypercube: Take an n-1 dimensional hypercube of size a, then move it a units along the nth axis. You can do the same with a grid with 19 (or, more generally, m) crossing points.

The point I really like about my idea is that I use generic programming to define an n-dimensional grid and project it to n-1-dimensional space (and so on, until you've reached 3 dimensions). I'd post a simple code example for a hypercube here, but I have discovered that the code I already have is too complex to boil it down to a few lines... at least it would take me more than a few minutes to do it. I'll post it in the "Programming" forum when I find the time.