.

[GIO888]

I'm completely lost.

Can I go to hell in a rowboat or not?

 

[Palantir30]

I'm completely lost.

Can I go to hell in a rowboat or not?

Nope, you need a handbasket to ride in. Alternately, you could use a boat, but it's not rowed, it uses a pole. Bring exact change.

 

[Barmer]

He said that since our world is 3D, we need another point. As I said before, our world isnt 3D. As I just repeated, the Civ world isnt 3D .... Again, we're not in 3D space, no matter which universe we're talking about.

You seem pretty sure that our world isn't 3D. Couldn't it be that our perception is limited by the Civ coordinate system? Have you ever been to -2147483647:-2147483647? I was there once(using a 64 bit processor -- a 32 bit processor gets confused by the minus sign ) and didn't see any wounded units. So it must be that, once units arrive there, they can then move --on their own-- anywhere along any of the infinite number if intinitely long lines that pass through that point. They are no longer constrained by the whims of the PLAYER nor, therefore, by the the Civ coordinate system. Each unit can go to any unoccupied point to lick its wounds in privacy .

BD - knowing things

 

[Zombie69]

Either a third coordinate is insufficient or it's imaginary and meaningless.

Just because there are more than 3 dimensions doesn't necessarily mean that 3 coordinates are insufficiant. For instance, the 4th dimension in our universe is time. If we assume heaven and hell to be eternal, than the 4th coordinate is irrelevant. Every point on that coordinate is a fit. Mathematically speaking, this coordinate doesn't need to be given. The same could be said for every other dimension after the 3rd one.

However, unless you want heaven and hell to be located along an infinite line in space, you need a 3rd dimension!

However no matter whether we are in a 2D, 3D, 4D or any other kind of universe except one, a point does not describe a line, no matter how many coordinates comprise that point. A single point is part of an infinite number of lines that include that point. To describe a line, you need a second point, a second group of coordinates. Only then would you have described an infinitely long line.

This is totally wrong. To define a line in a 3D system, if that line is parallel to one of the 3 axis, all you need is to specify the coordinates on the other 2 axis, as has been done in this thread. For example, x = 1 and y = 2 is a set of equations that describes an infinite line going through every point in space whose coordinates are (1,2,z), for all z, and running parallel to the z axis.

You should review your basic math courses before posting stuff like this.

 

[Palantir30]

Just because there are more than 3 dimensions doesn't necessarily mean that 3 coordinates are insufficiant.

Yes, yes it does. In four dimensions, you need four coordinates to define a point. It really doesnt get any more basic than that.

For instance, the 4th dimension in our universe is time.

This is not universally accepted, nor does it imply the contents of your next paragraph.

If we assume heaven and hell to be eternal, than the 4th coordinate is irrelevant. Every point on that coordinate is a fit. Mathematically speaking, this coordinate doesn't need to be given.

That is an assumption that I dont share, nor do most theologians. Many religions consider Hell to be temporary. One of the Christian variants holds that Hell is destroyed during the rapture. So at most, you're talking about a line segment, not a line. I demand that fourth coordinate.

The same could be said for every other dimension after the 3rd one.

Only if you continue to make undisclosed, undefendable oversimplifications.

This is totally wrong. To define a line in a 3D system, if that line is parallel to one of the 3 axis, all you need is to specify the coordinates on the other 2 axis, as has been done in this thread. For example, x = 1 and y = 2 is a set of equations that describes an infinite line going through every point in space whose coordinates are (1,2,z), for all z, and running parallel to the z axis.

Again, you're falsely assuming 3 dimensions. Again, you're making the assumption that the line is always paralel to any axis (which is even sillier, since you're the one assuming a third dimension). Those are unfounded assumptions, and the cause of your falsely drawn conclusion.

You should review your basic math courses before posting stuff like this.

Our math isnt the cause of the difficulty here, our differing conceptualization of the problem is where the issue lies. You're doing the math fine, you're just solving a different question than the one that was descirbed by the language used by Olleus. And since that is the question I was responding to, your classification of my argument as 'wrong' in the context of that question, is inaccurate. Should I insult you by telling you to review basic language and logic courses before posting stuff like this?

 

[petertr2000]

Do we really need to state that we are assuming cartesian coordinates?

 

[Zombie69]

Yes, yes it does. In four dimensions, you need four coordinates to define a point. It really doesnt get any more basic than that.

To define a point, yes. But we're not defining a point here, we're defining a line. And this can just as easily be done with 2 coordinates in a 3D environment.

This is not universally accepted, nor does it imply the contents of your next paragraph.

It's an example, not an all-encompassing statement. Jeez. I guess you should review logics as well as math.

That is an assumption that I dont share, nor do most theologians. Many religions consider Hell to be temporary. One of the Christian variants holds that Hell is destroyed during the rapture. So at most, you're talking about a line segment, not a line. I demand that fourth coordinate.

I don't care what you or any theologian think. The point is that we don't know what heaven is or if there even is one, so mathematically it can be assumed to be infinite in time if that dimension isn't provided.

Again, you're falsely assuming 3 dimensions.

No i'm not. I'm assuming that the other dimensions are irrelevant, which is totally defensible mathematically.

Again, you're making the assumption that the line is always paralel to any axis (which is even sillier, since you're the one assuming a third dimension). Those are unfounded assumptions, and the cause of your falsely drawn conclusion.

First of all, the line will always be parallel to an axis if you define your coordinate system to make it so, which you can since there is no universal 3D coordinate system to define the universe.

Also, i'm not making the assumption that the line is parallel to an axis. The given set of equations makes it so! I'm just reading and interpreting them, that's all.

Interestingly, if we assume that the coordinate system isn't cartesian, then the line may not be parallel to an axis at all. In fact, it may not even be a straight line, or even infinite for that matter. For example, take a 3D system described by an axis going through an origin, a distance x from the origin, a y angle around the axis and a z angle up and down the axis. Given a known x (e.g. 1) and a known z (e.g. 2), then (1, y, 2) describes a circle around the only axis in the system, rather than a straight line parallel to an axis.

Our math isnt the cause of the difficulty here

Oh, but i think it is.

 

[Meffy]

didn't see any wounded units

Ya silly! Just take off the crazy shades with the moving LED effect. ;-)

I'm completely lost.

Can I go to hell in a rowboat or not?

If we call this thread a rowboat then yes, just stay aboard. :-D

 

[Bushface]

Bonus points will be given to the first person who can describe the ONLY circumstances where one given point will describe an infinite line.

Given a universe of three dimensions, of which two (let's call them the x and y ones) have a unique value of zero, then any point with coordinates (0, 0, z) - that is, any point in this limited system - defines the unique straight line through the origin. Or a one-dimensional universe, if you prefer so to call it, in which only one infinite line can exist and which is uniquely defined by any point upon it.

And has anybody here considered the postulated universes which have an irrational, imaginary or fractal number of dimensions ?

 

[Zombie69]

And has anybody here considered the postulated universes which have an irrational, imaginary or fractal number of dimensions ?

I never have, but it's a very interesting concept!

I don't even know how you could have a non integer as the number of dimensions. Can you have 2 and a half dimensions for instance? How does that work?

 

[Danghis Khan]

Perhaps it is a n-dimesional heaven/hell that is an intersection of all the games played on that particular install. In which case you could argue for a sort of reincarnation of dead units (which would be just fine with me, I could finally get some of my tanks back.)

 

[Breunor]

According to my calculation this comes out to be..... Detroit Michigan..... Coincidence? I think not.

Is that why the Pistons are having such a good year?

Breunor

 

[Meffy]

I don't even know how you could have a non integer as the number of dimensions. Can you have 2 and a half dimensions for instance? How does that work?

Welcome to the world of fractals: http://math.rice.edu/~lanius/fractals/dim.html

They're pretty, but they're also mathematically interesting. [note that the link above is at a very elementary level, but it does get right to the point without any heavy mathematics]

 

[karadoc]

That's like a zillion times bigger than what a double can hold in C.

A double could easilly hold a number that big, or even much bigger. Remember that a 'double' in C is a floating point number.

 

[Prince James I]

Not wishing to interrupt, I'd just like to announce that this is the best internet thread ever. Anywhere.



(Mathematical Philosophy... Who'd a thunk it?)

 

[Bevertje]

Wow, that map would contain 4,611,686,014,132,420,609 squares. So, 4.6 x 10^18.

I only play on that big maps... Little maps suck

 

[Meffy]

There is no Z dimension in Civ IV. It's meaningless to talk about a third spatial dimension in the Civ universe, as the game engine doesn't implement any such thing. No unit is capable of storing a z coordinate, and no tile has more than two coords. (If someone can demonstrate otherwise I'll gladly retract this but it seems to be the case.)

Heaven/hell is within the plane, as you originally reported, Olleus, one cell in from the southwestern corner of the map's coordinate system -- not in any third dimension. This can be verified by re-examining the logfile you cited in your original post.

The origin is tile (0, 0). My guess would be that this is the lower-left corner of the actual map (which, of course, doesn't fill the entire coordinate system... but it's fun to pretend it might).

In the cartesian plane it's traditional for X to be the "horizontal" dimension so it is probably east-west, with coord values increasing toward the east. By the same reasoning I think it likely that the Y dimension runs north-south, increasing toward the north -- though it might increase toward the south instead, as when numbering display pixels.

To verify (or disprove) my guesses you could have a look at your logfile again; I haven't bothered yet.

 

[Dianthus]

There is no Z dimension in Civ IV. It's meaningless to talk about a third spatial dimension in the Civ universe, as the game engine doesn't implement any such thing. No unit is capable of storing a z coordinate, and no tile has more than two coords. (If someone can demonstrate otherwise I'll gladly retract this but it seems to be the case.)

There *is* a third dimension for tiles, though it is limited to just 4 values. It's called elevation and has the values Mountain, Hill, Flat Land, Water .

 

[Meffy]

That's at best a pseudo-dimension. For it to constitute a meaningful dimension, it would have to be possible to travel from, for instance, tile (3, 8, flat) to tile (3, 8, hill) to (3, 8, mountain).

But it's interesting just the same. Is this elevation used when submerging tiles as global warming progresses?

 

[warpus]

Let us start with the assumption that the universe is 3d

Technically the universe has 4 dimensions.. or 11, if string theory is to be believed. The 4th dimension you're forgetting is time.

If you're strictly talking about civ, yes, there are 3 dimensions in the game: 2 of space and 1 of time.

I haven't read much of this thread so I'm not sure how much discussion there has been about the 3rd spatial dimension in the CIV4 universe.

There isn't one. Every single location in the game can be referenced using 3 values: 2 for space and 1 for time. This implies that the CIV universe is composed of 3 dimensions. If we needed a minimum 4 values to reference a location, then we'd have 3 spatial and 1 time = 4 dimensions.