[gekko]

Get joining. Err... I'll post some of it here.

Everyone knows about 3D theory. Height, width, and depth are the defining characteristics of objects in our everyday lives. But then, we often here of a fourth dimension, time.

Let's suppose you wish to calculate how much volume a gas will occupy as it is poured into an object at an ever-decreasing rate. When you set up the calculus for such an equation, there are 4 major variables: height, length, width, and time. The same occurs in many problems. This is why time has become casually referred to as the fourth dimension.

Also:

Area = Width x Length
Length = Velocity x Time

Einsteine himself proposed that time was a fourth dimension at one point -- I don't recall if he stuck to that claim or not.

In physics, time is a crucial concept that is treated linearly, and works much like the three dimensions. There are (or at least were) plenty or reasons to refer to time as the fourth dimension, but the truth is that it isn't, and can't be. It isn't constant.


Discounting of Time:
Time isn't a defining characteristic, wheras an objects length in a particular dimension is. Let's suppose that you have two clocks, both of wich tell time perfectly. If you synchronize them, send one around the globe a few times (increase it's velocity), then check the times, the clocks will not read the same time any more. Time is relative -- yup, Einsteins theory of relativity deals with all that.

If you take two pencils, move one at the speed of light for a little while, then check them, they will still be the same length.

Intro to fourth spatial dimension:
OK, so there's a fourth spatial dimension, sure whatever, right? Well the proof is all mathematical mumbo jumbo that is far beyond what I understand or care about, but I can provide some examples of how to look at 4D, and how it may effect us.

Image a 2D world. Everything in this world moves in just 2 dimensions, we'll call it flatland. People in flatland can only percieve 2 dimensions: length and depth (no width). If you were to shove a pencil through their world, the would only see the cross-section of it (and only the outer edge at that, they wouldn't be able to tell if it was solid or a ring).

Just as baffled as the would be at something the could somehow have "width," the notion of something having space in a 4th dimension is ludicrous to us. Mathematical theory and physics both seem to back it up, though.

I'm going to stop there, as most of you probably already think I'm insane. If physics and/or hyperspace theory interests you, there is a great book called "Hyperspace," I believe that Author is Michio Kaku. It's a great read, and doesn't get all into math or physics.
Edit:His website.


So what the hell does all this have to do with gaming? I'm not going to start flaming every person that called time the fourth dimension, that'd be setting myself up for pain.

But for those of us that at least know of these theories -- even if you don't buy into them -- I just ask that you specify what you mean when you say 4D, time or space.

If you've made it this far, do youself a favor and pick up the book, you'll love it. Oh, and you're officially a geek.

Thanks for reading.

--Fidd

Wow, I'm not alone in my recognition that TIME is NOT under ANY circumstances the 4th dimension.

It is a completely independent entity.

It is not dependent on the other dimensions....the other dimensions are all defined using each other for assistance, without one it is pointless trying to define the others.....

Anyway, since it is completely independent of space, time cannot by definition be the 4th dimension. Because we can define our existence using time and space one is inclined to make the assumption that they are related while in fact, as you said, time is RELATIVE.

More of an idea than a fact if you will....

You guys are acting as if the definition of the 4th dimension is open to interpritation. Its not. I may be a bit nebulous, because we cannot experience it like we can with the three other space dimensions, but its identity is just as solid.

Mathematicians actually have built computer models that replicate 4D movements, via the 4D rotation of a "hypercube", or 4D cube.

Imagine we are a 2D species trying to comprehend the third dimension. Our brains simply cannot process this 3D information, but what we CAN do is study the 2D "Shadows" of a cube. Whenever we look at a computer monitor or a geometry textbook, we are extracting 3D information from a 2D medium. Therefore, it is possibly for our theoretical 2D minds to study 3D structure.

The same principal can be applied to our world. We can study 3D Models of 4D hypercube "shadows".

Now, this begs the question, can actual 4D engines be effective used in games?

It would probably baffle the player at first, but if we gave them 4D control of a hypercube based object, it might be possible for them to gain an understanding about how these objects behave.

It would probably be a bit too odd for an entire game, but I think it might have some potential as a minigame, or subgame (like, say, the Chocobo game from FFIX). It may be worth a try.

Implementation wold be difficult, however. Controls must be programmed for the new axis, which may be difficult to effectively incorporate with stardard conrtol inputs (but its still feasible.)

Also, the physical makeup of the objects would be different. They would have to be made up of something above polygons ("superpolygons" maybe? Im not sure if they have a name already or not...) In any even, programming, these structural and behavioral changes will be difficult to say the least. Programmers will be working blind, trusting their math, to construct things that they cannot see or touch or even imagine. Even if these massive programming hurdles were to be overcome, the hardware may not be able to facilitate this type of madness untill the next generation.

Just some more things for you guys to think about.

Why is it that people ignore my post? I'm repeating over and over there is already an existing game with the definite use of a 4th spatial dimension.

Also, it's almost obvious we can't control the 4th dimension directly, at least not yet. The limit is the controller here. Think of it. A joystick is barely able to control 2D. There's literally no device able to control all 3 dimensions, unless you can name me a single useable control that could handle Descent, a game that actually used all 3 dimemsions (rotate and move along all three dimensions, unlike FPS, which limit your movement a lot). So we have practically no controller capable of 4 dimensions. That's why the 4th dimension will most likely be done within the game, like with "gates" or similar.

The "hyperpolygons" barely make sense to me. Especially since no graphics card could handle a 4D vertex. In the example of Soul Reaver they reduced the 4D space to a "temporary 3D space", and these 3 dimensions are handled normally by the graphics card. This sounds like a reasonable approach. First you "project" the fourth dimension on a 3D space, and what's left is handled by the graphics card.

"When asked about a fourth dimension, people for some reason remain thinking in coordinate terms."

By definition that IS a dimension.

Are we talking pointless physical rambling here, or are we talking exact (math) definitions?

Math is the science that invented "Dimensions", every other science (including physics) is just (ab)using it.

The guy who wrote that 4D array is kinda right, by definition the 4th dimension is like the three others.

The "coordinate" is kinda wrong description for a dimension, since a coordinate is a number, no dimension and nothing. It's more like a "coefficent of a base dimension". For example the point [1,0] is 1 unit in x-direction from zero away, the point [2,0] is two units in x-direction from zero away. 1 and 2 are both just numbers, no dimensions.

Since we're talking about the "expansion of 3D" we need to look at the definition of 3D space. Again, I am not into relative physics rambling, I go by the definitions that coined the term dimension.
You are referring to the physical space here. The physical space has a math definition though. When we talk about 3D space, we always talk about a right angled, euclidic coordinate system with 3 axes/dimensions.
This means:
I) Every dimension is linear and can be represented by a vector/arrow
II) Every dimension is linear independent, that means it can't be created out of the other dimensions.
III) Every dimension is vertical to all other dimensions. This is also because of point II
Now we can create the mathematic definition of a 4D space.
You start with one dimension (vector/arrow) and add a second in a right angle to it. The result is like two connected edges of a square.
Now we add a third dimension. By definition again a straight arrow, in the right angle to all other dimensions. The only way to do it is, making it stick out of the square vertical. the three dimensions now describe three connected edges of a cube, each pointing into a different direction.

Again, I can't stress this often enough, since this point has been missed in lots of posts before: We are mathematical here. There's no physics involved. Math defined the dimensions, the physics are only abusing it.

As I said, we have three dimensions now. By definition the fourth is added as arrow, in the right angle to all other (3) dimensions. You won't be able to do this in a model, and the reason is our perception. Since this is already physics we can't continue there.

But we still have the definition from up there. Even though we can't visualize this 4D system, it is defined, so we can calculate with it.

Ok, now we have a correctly defined eucledian, right angled 4D system, and the task is now to apply this to reality somehow. All four dimensions look the same, by definition. The fourth is nothing special, just like a possible 5th, 6th, 7th etc.
Since, by physics definition the first 3 are spatial dimensions, the 4th has to be spatial as well. The definition doesn't allow the fourth dimension to be a "special case".
Of course you can project time on a timeline, and this way create a "4th dimension" when you visualize stuff. However this contradicts the definition of the 4D system, so what you have is no 4D system then.

I'm lacking pictures here. It's easier to show and describe with pictures, but I hope you get the idea.
Don't get lost in physical ramblings. There is a clear and unequivocal definition of dimension, space and such things. Learn to handle these, before you go the next step and try to apply it to physics.

Like I said, nerdy. But it brings back the whole point about advertising Blinx as a true 4D game. Is Blinx really a "true 4D game," I hight doubt it, it's an marketing phrase.