Hypercube Transcript: http://4d.shadowpuppet.net
version: 3.2 2005.05.05

Ascii art in Lucida Console font: Regular 10pt


0D:

1.	We begin with a zero dimensional point.

2.	A point has no mass, and its size is undefined.
	
3.	A point is one vertex, representing a position in space.

	.

Interactive Mode:
	Click the mouse on the screen to relocate the zero dimensional point.

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1D:

1. 	Conecting 2 points in space, creates an edge.

2.	with one dimension, a point has one set of independent directions, which I will arbitrarily call Up and Down.

3.	We can now measure this space, and again arbitrarily call it Length.

	._____________.

Interactive Mode:
	Click and drag the point, forward and back, along the edge. This is a one dimensional plane.

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2D:

1.	In 2 dimensional space, an edge may move to make a square.

2.	We can now measure this space in a second way. This time WIDTH.

3.	Now we have 2 sets of independent directions, which we can call UP/DOWN & LEFT/RIGHT.

4.	These 2 sets can be combined to form an infinite set of dependant directions.

	._____________.
	|             |
	|             |
	|             |
	|             |
	|             |
	|             |
	|_____________|

Interactive Mode:
	Use the arrow keys to move up, down, right, and left. This is a 2-dimensional world, the same as a nintendo video game.
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3D:

1.	In 3D, a Square may expand FORWARD and BACK to make a cube.

2.	Now we have DEPTH and 3 sets of independent directions.

	     7-----------4
	    /|          /|
	   / |         / |
	  /  |        /	 |
	 /   |       /   |
	3-----------0	 |
	|    |	    |	 |
	|    |	    |    |
	|    |	    |    |
	|    6------|----5
	|   /       |   /
	|  /        |  /
	| / 	    | /
	|/	    |/
	2-----------1


Interactive Mode:
	You may use the mouse to click the buttons on the screen to rotate or resize the cube. Alternatively, you may press the following buttons:

	l = rotates left
	r = rotates right
	u = rotates up
	d = rotates down
	z = rotates forward
	x = rotates backward

	+ = zoom in
	- = zoom out

You may also hold multiple keys or hold a key while clicking a button to move in a combination of directions.

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4D:

1.	In 4d, we have a new set of indepedent directions, which I will call ANA and KATA

2.	Duplicating a cube in this way gives us a hypercube.

3.	I will call this measurement Spassitude.

4.	Just as a Cube has a volume of one, a hypercube has hypervolume of one. And as a CUBE contains 6 sqaures, a Hypercube contains 8 CUBES.

5.	Just as with a cube, each angle is 90 degrees, which is an imperfect illusion in this 2d sketch.

			     15----------------12
			    /|		       /|
			   / |		      / |
			  /  |               /  |
			 /   |              /   |
			/    |             /    |
		       /     |            /     |
		      11-----------------8      |
		      |	     |		 |	|
	       7------|-----------4	 |	|
	      /|      |	     |	 /|	 |	|
	     / |      |	     | 	/ |	 |	|
	    /  |      |      14/--|------|-----13
	   /   |      |     / /   |	 |     /
	  /    |      |    / /    |	 |    /
	 /     |      |   / /     | 	 |   /
	3------------------0      |	 |  /
	|      |      | /  |      |   	 | /
	|      |      |/   |      |	 |/
	|      |      10---|-------------9
	|      | 	   |      |
	|      6-----------|------5
	|     /	           |	 /
	|    /	      	   |	/
	|   /              |   /
	|  /               |  /
	| /  	    	   | /
	|/	    	   |/
	2------------------1

Interactive Mode:
	You may use the mouse to click the buttons on the screen to rotate or resize the cube. Alternatively, you may press the following buttons:

	l = rotates left
	r = rotates right
	u = rotates up
	d = rotates down
	z = rotates forward
	x = rotates backward
	a = rotates ana
	k = rotates kata

	+ = zoom in
	- = zoom out

You may also hold multiple keys or hold a key while clicking a button to move in a combination of directions.

Click on the Model buttons to change the starting form of the Hypercube.
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the only way to truly see four dimensional space is to overcome the mental conditioning that space only has 3 dimensions.


5.1	over 500 years ago, we decided the world was round. We see and feel a sphere, but we only see and feel 3d of space. Someday we may interact with more spacial layers and see that from a certain perspective, the world was flat all along.