Seeing into four dimensions

(detailed explanation is below)
Instructions: Try different shapes and stereo-viewing options by clicking on the buttons below, and seeing what happens. Use the mouse to rotate around your hyper-object as follows:

• To rotate into Z: drag with the left mouse button down (click to reset).
• To rotate into W: drag with the middle mouse button down, or left-drag while holding down the Alt key (click to reset).

 view shape curve(a,b) mono anaglyph cross uncross mirror thick lines arrow axes box corner diamond simplex knot ribbon torus klein bottle
 set a: set b: 2 3 5 8 13 21 34 2 3 5 8 13 21 34
Explanation:

This is a visualization of four dimensional objects, implemented in Java and Javascript, which lets you manipulate four dimensional shapes within a Web browser. It lets you play with hyper-cubes, hyper-simplices, hyper-octahedra, 4D knots, ribbons, tori, and other cool shapes. It's got an "open" API - you can use it to define your own 4D shapes directly within a Web document, without needing to do any Java programming.

The applet lets you manipulate the 4D objects, rotate them around, apply various rendering styles and stereoscopic viewing options, and in general have a grand old time. If you can completely understand what you are seeing, then you may be a mutant, and you will go far in the field of computer graphics.

I've designed this four dimensional viewer to make it as easy as possible for you to create your own 4D shapes. The actual objects are all described by simple JavaScript programs in this document. Feel free to grab this html file from your browser and hack on it to create your own shapes.

This work is part of a long-term research agenda of mine to figure out how the brain works. I have three conflicting hypotheses:

1. People just can't visualize in four dimensions. Oh well.
2. Sure they can, with the right practice and training.
3. They can all right, but only up to the age of (say) five. Then they lose those language acquisition skills, and the brain goes all hard and useless.
The answer is significant because of issues that go way beyond seeing in four dimensions. Is the brain a general purpose device, or are our perceptual abilities hopelessly wired in already, still making sure we can evade saber-tooth tigers? Here is a very concrete way to shed light on how flexible are our perceptual and learning abilities.