Fourth Dimension
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# Basic Information

The Fourth Dimension can refer to either the Time Dimension or an additional Spatial Dimension. The majority of this page is about the spatial dimension.

## Time Dimension

In Spacetime and Relativity, the Fourth Dimension is Time. Three Dimensional Objects have Length, Width, and Breadth. Knowing coordinates for those three dimensions allows you to locate exactly where a point (or object) is. Knowing the time, or where it is, is like a fourth coordinate that helps identify the precise location in both time and space.

## Spatial Dimension

Most people "get" time pretty intuitively, but a fourth spatial dimension gets a little tricker. At it's simplest, it's that coordinate concept. There's a fourth axis that defines where things are in 4D space. But there's many implications stemming from that concept. The fourth dimension may prove an important part of an Alien Geometry or how Hyperspace works in your setting, so knowing a few tricks about it might be helpful.

A lot of science is based on the theory of the existence of multiple dimensions beyond those we can perceive. Kaluza-Klein theory uses a fourth spatial dimension to integrate gravity and electromagnetism (including visible light) as a single force. String theory says there'll be exactly 10 dimensions. To be honest, most of it is way over my head, but I've been reading up and trying to extract the useful parts of Dimensional Theory for gaming.

As you've no doubt experienced in your life, a three dimensional object casts a two dimensional shadow. Likewise, a two dimensional object casts a one-dimensional shadow, which can be illustrated if you hold a sheet of paper edge-wise towards a source of light. (The shadow it will cast is shaped like a line.) Extrapolating from this, we can assume that the shadow of a fourth-dimensional object will be a three-dimensional shadow. Weird, huh?

### Bounding Volumes:

A two-dimensional square has 4 one-dimensional lines for it's outermost surfaces. A three-dimensional cube has 6 two-dimensional sides for it's outermost surfaces. Again, we can assume a four-dimensional object will have three-dimensional surfaces defining it's boundaries.

### Visual Capability:

As three-dimensional beings, we humans can see in two-dimensions. Our steroscopic eye configuration gives us depth perception, but it doesn't let us see around corners. Dimensional theory, however, suggests that a fourth-dimensional being would be able to see in three dimensions. It could see the inner surfaces of three-dimensional objects, see behind things, etc.

### Perpendicularity:

In flat two dimensional space, there's only one way that two lines can be perpendicular. Once you add a third dimension, there's a way to fit in a third line that's perpendicular to both the existing lines. By extension, in four dimensions, it's possible to draw a fourth line that is perpendicular to all three existing lines. Somehow, that line will be at a 90o angle to all three previous lines. Don't spend too much time concentrating on how that works, our brains are pretty well wired for three-dimensional space.

### Length, Area, Volume:

Let's crack out our old friend, the Pythagorean Theorem. Remember A2+B2=C2? On a right triangle, if you know the length of the two short sides, A and B, you can add their squares to determine the length of the long side, C, also known as the hypotenuse. If you need to know the length of diagonal of a rectangle, the Pythagorean Theorem enables you to calculate it using the triangle that is 1/2 the square's area. This is a fundamental concept in geometry, engineering and architecture, helpful in knowing how long you need to make a support beam or other structure.

It can also be applied to three dimensions. If you need to know the length of D, the diagonal of a cube is A2+B2+C2=D2. A, B, and C are the lengths of three adjacent sides that share a corner. By extension, the length of the diagonal of a fourth-dimensional object, it would be A2+B2+C2+D2=E2. We can see that as you add more dimensionality, the object gets correspondingly "larger".

If you've ever read Flatland, you'll recall how the three-dimensional sphere could alter the size of the circle that he manifested as in the two-dimensional world. His volume remained constant, it's just that only a portion of it was present in flatland at any given moment. So, again, this implies that a fourth-dimensional object would appear to be able to change it's size, volume, and mass simply by moving more or less of it's body into the region of our dimensional coordinates.

### It's Simpler Up There

One of the neat things about higher dimensional theory is that the universe gets simpler from the higher perspective. The more dimensions you can perceive the more elegant the world becomes. This goes beyond simply the perspective of being able to look down on the poor Flatlanders. For example, one theoretical explanation is that light is vibration in a higher dimension. Quantum uncertainty may be tied into this as well. If you were a fourth-dimensional being, perhaps you might be able to see all the places that a photon or subatomic particle occupied at once.

## Sources

Bibliography
3. Book: Hyperspace by Michio Kaku
4. Fiction: "— And He Built a Crooked House" by Robert Heinlein (short story). An architect designs a house based on a hypercube. What could go wrong?

# Game and Story Use

• To make a Monster or Alien really creepy or, well, alien, make it fourth dimensional.
• See also Fourth-Dimensional Lifeform, where we explore the ramifications of what a 4D monster (or sentient being) can do to poor little 3D us's.
• The fourth dimension might explain other phenomena such as reincarnation, ghosts, or ESP. It may be that the soul is fourth dimensional, and only bound to three dimensions by the bodily manifestation. If we (or our perceptions) transcend our body, we can be fourth-dimensional beings ourselves. Or so says the NPC philosopher-priest.
• The fourth dimension may be how you explain hyperspace or warp in your setting. By pushing your way into a higher dimension, you are able to shortcut across the galaxy. See Spacetime, Closed Timelike Loop, Riemann's Bookworms, and Wormhole.
page revision: 14, last edited: 27 Oct 2010 02:02