hypercube

Fun With Hypercubes! Here is a little animation I created for my upcoming RPG game called 'ELSEWHERE'. This Role Playing Game for Win 95 is a project I have been waiting 14 years to get to make! The actual animation will take about 42 seconds to load in with a 28k modem. I really think you will find it quite something to see, and worth the wait. Here is why:

I have always had a facination about the fourth dimension, and higher dimensions in general.

In creating a luggage for use in my game 'Elsewhere', I decided that four dimensional luggage would be grand.

I do not refer to the fourth dimension as 'time' here, as it would be in a discussion of Einsteinian relativity. I mean a fourth PHYSICAL dimension, to which time is external, yet one more dimension up. Time then becomes the fifth dimension in this case.

What do I mean by a fourth physical dimension?

Well, we have three observable dimensions to our reality, excluding time. Three directions to point to, three directions of motion and freedom. These are our three physical dimensions.

There is length, and width. If you prefer you can call them side-to-side, and front-to back. On a map, north-&-south, and east-&-west. With these two dimension you can locate any spot on a flat plain. You can say the oil spot on the driveway is "four feet to the front of you and two feet to the left". These two dimensions are at 90 degrees to each other, if you drew them as lines, they would form a cross on the floor. They are perpendicular to each other.

There is another dimension, height. Up-and-down. With this dimension, now you can say that a butterfly is hovering above the oil spot on the driveway. The butterfly might be, say, "four feet to the front of you and two feet to the left, then one foot straight up!".

That makes three physical dimensions, and with them, we can state the exact position of absolutely anything in our universe at any given moment, from a butterfly, to a galaxy. Three coordinates, three numbers, three dimensions.

Now, about this fourth direction...

Think about something simple. A line. It is easy to imagine a horizontal line, say on a sheet of paper.

Now, imagine that you could magically make that horizontal line move up the paper, drawing as it went. It would paint a square. A line, which is one direction, moving 90 degrees to itself -in a new direction- can paint a square.

So now we have a square, stretched out of a line. The line moved perpendicular to itself, and thus we now have a square.

Now, imagine that we can make our magic square rise up out of the paper! Imagine that we can move it up, out of the paper at 90 degrees to the surface of the paper. It would form a cube, of course. A square, given thickness, becomes a cube. Just like the line made a square, the square moving in a new direction perpendicular to what has come before, makes a cube.

Three directions. First east-&-west, then north-&-south, then up-&-down.

We made a cube.

Now, let's take our magic cube and move it 90 degrees. Let's move it perpendicular to all that has gone before. We will move the whole of it into a new direction, a fourth place to point, a fourth dimension of motion.

The brain boggles. It halts. Huh? HOW?

It's called ANA and KATA. Ana-&-kata are the names of the new direction. Just as we have up-and-down, now we have ana-and-kata.

If we move our cube ana...or kata...we get a hypercube. A hypercube is the logical progression of line, square, cube, hypercube. A square has four sides, a cube has six sides, and a hypercube has 16 sides.

The hypercube, also called a tesseract, has a proud usage in fiction and media. Dr. Who's Tardis is a hypercube, and the Starship Enterprise has warp drive that travels in the fourth physical dimension. Most warp drive uses the fourth physical dimension, and any time you see a science fiction show where there is instantaneous travel or a structure that is larger on the inside than on the outside, then you can be sure higher dimensions are involved.

The neat thing about dimensions is that there is more room available for every new dimension you add. If you are a living two-dimensional square, and you want to hide stuff, you could store it above or below you, in the mysterious third dimension.

If you are a science fiction character, and you want to make things appear from nothing and return to nothing, the fourth dimension is just the same situation.

What better kind of luggage than 'Tesseract Luggage' then? You can store lots of stuff, mountains of stuff, seemingly inside a space much too small for all of that stuff.

Indeed, the author Robert A. Heinlein already thought of this, in his wonderful book, 'Glory Road', with a little four dimensional suitcase called a 'Foldbox'. In my game I want to honor my favorite author, and so I present my own take on the idea, with my Tesseract Luggage. Let the animation run a few times, and try to get the full feeling of a fourth dimension, a fourth direction ana or kata to anything you know.

This animation is correct, by the way, representing accurately what a hypercube would look like, if it rotated in only one direction through our three dimensional space. This hypercube has one of its side MUCH larger than the others, which is why it seems to increase and decrease in size. Like a cube with one face really wide, and the others distorted in relation.

Even so, this is what it would actually look like. Enjoy!

And here is a rough demo pic from ELSEWHERE itself...

Jennifer Diane Reitz

Oct. 29th, 1998