Linear Algebra Map (6-dimensional vector space)

Mr Tumbler · Post by **Mr Tumbler** » Mon Feb 11, 2008 11:25 am

What if we could have a map that required (or taught) knowledge in linear algebra. Instead of just a cube (3-dimensional vector space), we could have 8 2x2x2 cubes (mini-cubes), the 8 cubes arranged like a cube (totally 64 territories). So each mini-cube would have 3 dimensions (say t,u,v), and the cubes would be arranged in 3 other dimensions (say x,y,z). This would span a 6-dimensional vector space (discrete vector space since each territory would be a discrete point).

The bonuses could for an example be received for occupying a 3-dimensional or 4-dimensional (more bonus) vector space in the 6-dimensional space.

Possible movements and bonuses could be expressed in different linear algebra terms.

Is this completely geeky, insane or impossible to play, OR is it an original challenging idea?

whitestazn88 · Post by **whitestazn88** » Mon Feb 11, 2008 1:27 pm

see hypercube?

i dont have the link, and im too lazy, but look it up

bryguy · Post by **bryguy** » Mon Feb 11, 2008 3:55 pm

whitestazn88 wrote:see hypercube?

i dont have the link, and im too lazy, but look it up try here: http://conquerclub.com/forum/viewtopic.php?t=35587

InkL0sed · Post by **InkL0sed** » Mon Feb 11, 2008 4:45 pm

I can barely tell the connections in the Hypercube map. I barely comprehend the existence of a fourth spatial dimension. Do you expect anyone to be able to understand a 6-dimensional map? If you do, you're nuts.

Sorry to suppress the geekiness, I normally support it fully.

onbekende · Post by **onbekende** » Mon Feb 11, 2008 4:55 pm

hypercubus is just 4

to do 6 dimensions, you need not only higher math, you need a server just for the calculations of the correct graphical represintation

pepperonibread · Post by **pepperonibread** » Mon Feb 11, 2008 5:08 pm

InkL0sed wrote:I can barely tell the connections in the Hypercube map. I barely comprehend the existence of a fourth spatial dimension. Do you expect anyone to be able to understand a 6-dimensional map? If you do, you're nuts.

Sorry to suppress the geekiness, I normally support it fully.

Hypercube (the map) is really only 3 dimensions, but the name Hypercube just sounds cool.

Mr Tumbler · Post by **Mr Tumbler** » Mon Feb 11, 2008 7:02 pm

It's not as complicated at is it sounds. I will come again tomorrow with a visualisation, both how a 6 dimensional vector space can look and how a 3-dimensional and 4-dimensional vector space within that space can look.

InkL0sed · Post by **InkL0sed** » Mon Feb 11, 2008 9:27 pm

pepperonibread wrote:
InkL0sed wrote:I can barely tell the connections in the Hypercube map. I barely comprehend the existence of a fourth spatial dimension. Do you expect anyone to be able to understand a 6-dimensional map? If you do, you're nuts.

Sorry to suppress the geekiness, I normally support it fully.
Hypercube (the map) is really only 3 dimensions, but the name Hypercube just sounds cool.

Yes, but my point was that it's hard even with 3 dimensions.

Mr Tumbler · Post by **Mr Tumbler** » Tue Feb 12, 2008 5:18 pm

Here is the visualization I promised. The problem with visualizing a continous 4 dimensional vector space (i.e. the hypercube) is that between any 2 points you have an infinite number of points. But with the discrete vector spaces you only have a finite number of points. It can be viewed as a photography series over time, so you only need to have a limited list of photographs.

I limit the number of discrete points in each dimension of the 6 dimensional cube to 2. The first 3 dimensions will then span a 2x2x2 "mini-cube". So I only need to repeat the mini-cube twice for the 4th dimension. The 5th will result in an area of 2x2 mini-cubes and the 6th dimension will result in a 2x2x2 super-cube of mini-cubes:

onbekende wrote:hypercubus is just 4

to do 6 dimensions, you need not only higher math, you need a server just for the calculations of the correct graphical represintation

As you can see, you can both visualize and understand the 6-dimensional vector space.

Movement
For moving/attacks we could allow movement along any of the dimensions (axises of the 6 dimensional coordinate system). So within the mini-cube, we allow a move either along the t, u or v dimension/axis, but not diagonally. Or the movement could go to the same point in another mini-cube that is located one step away along the x, y or z dimension/axis.

Bonuses
A bonus can be given for holding a full 3 dimensional or 4 dimensional vector space "cut" within the 6 dimensional vector space.

Lets express the full 6 dimensional vector space as t+u+v+x+y+z. A 1 dimensional cut/selection, e.g. along the t axis, could be expressed as t. A 2 dimensional cut/selection along t and u axises is expressed as t+u.

A 3 dimensional cut selection along t, u and v axises is expressed as t+u+v and can be visualized as:

A 3 dimensional cut selection along x, y and z axises is expressed as x+y+z and can be visualized as:

A 4 dimensional cut selection along t, u, y and z axises is expressed as t+u+y+z and can be visualized as:

Ogrecrusher · Post by **Ogrecrusher** » Tue Feb 12, 2008 5:25 pm

I'm a final year physics student and this map would confuse me

Mr Tumbler · Post by **Mr Tumbler** » Tue Feb 12, 2008 5:39 pm

Ogrecrusher wrote:I'm a final year physics student and this map would confuse me

Well, the confusing part makes it challenging for the ones looking for it

The good thing about having only 2 points in each axis, is that you always have exactly one movement along each axis. The bad thing is that having 6 dimensions/axises results in exactly 6 neighbours for each terretory. Well it's not worse than the "Cube Map" and the so called "Hyper Cube" suggestions, and maybe its needed for a challanging play on this map.

whitestazn88 · Post by **whitestazn88** » Wed Feb 13, 2008 12:57 am

this looks just like hypercube, except not everything is touching.

Mr Tumbler · Post by **Mr Tumbler** » Wed Feb 13, 2008 2:54 am

whitestazn88 wrote:this looks just like hypercube, except not everything is touching.

Except that this map is an actual 6 dimensional "hypercube". You can move in all 6 directions/dimensions. There is no real good way to draw all the connections

FreeMan10 · Post by **FreeMan10** » Wed Feb 13, 2008 4:45 pm

Mr Tumbler wrote:Except that this map is an actual 6 dimensional "hypercube". You can move in all 6 directions/dimensions. There is no real good way to draw all the connections

OK, the picture I can follow, moving in all 6 dimensions is gonna cause people to blow mental circuits. This will definitely need BOB!

john9blue · Post by **john9blue** » Wed Feb 13, 2008 11:52 pm

I think it sounds interesting, but the problem will be mass appeal. I tried making a dodecahedron map a while ago, but people were just too confused. Unfortunately, this site has an abnormally high percentage of 'non-geeks'... if it didn't, then we'd see a lot more abstract geometrical maps like this.

Mr Tumbler · Post by **Mr Tumbler** » Thu Feb 14, 2008 9:49 am

FreeMan10 wrote:OK, the picture I can follow, moving in all 6 dimensions is gonna cause people to blow mental circuits. This will definitely need BOB!

BOB?

FreeMan10 · Post by **FreeMan10** » Thu Feb 14, 2008 12:20 pm

Mr Tumbler wrote:BOB?

http://www.conquerclub.com/forum/postin ... &p=1127405

Mjinga · Post by **Mjinga** » Mon Feb 25, 2008 7:18 pm

I'm taking graduate courses in math and it took me a sec to understand the bonuses.

Sweet idea, though.

Out of curiosity, what field of science do/did you study?

fumandomuerte · Post by **fumandomuerte** » Mon Feb 25, 2008 7:34 pm

I like the idea.
A Chemical Engineer here

.

Stoney229 · Post by **Stoney229** » Thu Feb 28, 2008 4:30 am

FreeMan10 wrote:
Mr Tumbler wrote:BOB?
http://www.conquerclub.com/forum/postin ... &p=1127405

lol. try this.

FreeMan10 · Post by **FreeMan10** » Thu Feb 28, 2008 9:34 am

Stoney229 wrote:
FreeMan10 wrote:
Mr Tumbler wrote:BOB?
http://www.conquerclub.com/forum/postin ... &p=1127405
lol. try this.

D'oh! thanks for picking up the pieces for me.

Ditocoaf · Post by **Ditocoaf** » Mon Mar 03, 2008 7:49 pm

I get this, but that's because I'm in the habit of playing four-dimensional tic-tac-toe. It's a cool concept, but I think it's a little further than most people here will want to go.

Mr Tumbler · Post by **Mr Tumbler** » Wed Mar 12, 2008 9:17 am

Stopped playing for good now (at least I think so

). So if anyone likes this idea just take it over and continue.