Well, I have to admit, this is the one of the most interesting and hilarious threads Wolfire has ever had.
I'm reminded of the old story about the blind men and the elephant.
After examining the elephant (by touch alone, obviously), they all were convinced they knew what an elephant was like. One said it was like a snake, one said it was like a tree trunk, one said it as like a wall, one said it was like a palm frond.
They were all right, and all wrong. None could comprehend the whole elephant. The best one was the guy who insisted it was like a rope, hanging down from heaven: you pull it, and the sky opens up with waste.
But I know graphics, and you can represent a four dimensional object in two dimensions. It's the same way you represent a three dimensional object in two dimensions: with Cartesian coordinates.
Orthographic projection allows you to show the three essential views of any objects: plan, front elevation and side elevation. It's based on an X, Y and Z axis.
Descriptive Geometry, using the same axes, allows you to determine the true size and shape of any face of any object graphically, whether it is linear, planar, spherical or anything in between.
Adding a horizon and vanishing points allows you, using the same axes, to portray in two dimensions the way objects look to your eyes.
Drawing two versions of the same object in either of the above systems, directly on top of one another but rotated by 5 degrees (about the separation between your eyes) allows you to see them in 3-D (actually, you just trick your brain and eyes) using either the red-green or red-blue trick or the mirror trick.
You can also represent an object in three, four or any number of dimensions, with he correct number of coordinates: 2 for 2-D, 3 for 3-D, etc.
This is based on a simple progression:
- A Zero dimension object is a point; when a point moves in space, it sweeps out a line, a 1-D object.
- When a line moves in space, it sweeps out a plane, a 2-D object.
- When a plane moves in space, it sweeps out a solid, a 3-D object. If the plane is square, and moves a distance equal to its sides, it sweeps out a cube.
- When a cube moves in space, it sweeps out a hypercube, a 4-D object.
Here's an example: a hypercube drawn on four axes. If you look at it correctly, you'll see 4 pairs of connected cubes.
If you're good, you can make two 3-D versions of the hypercube, connected together, separated by 5 degrees of rotation, one painted red, one painted green or blue. Put it on a slowly rotating turntable, put on your special glasses, watch it turn itself inside out, then puke if you watch too long.
Want more info? Here's a start
Even more? Try this
As for God, I take my lead from Pierre-Simon Leplace, a French cosmologist, who wrote one of the earliest books on the topic. He was introduced to the Emperor Napolean, who had been given Leplace's book.
Napoleon said, "You have written this huge book on the system of the world without once mentioning the author of the universe."
Laplace replied, "Sire, I had no need of that hypothesis."
Later when told by Napoleon about the incident, Louis-Joseph Lagrange (who correctly predicted what became known as Lagrange points in planetary orbits) commented, "Ah, but that is a fine hypothesis. It explains so many things."
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