So far, the differences I've found between a 3D and 4D world are:

• Planes no longer divide space into two parts, in the same way that a line doesn't divide 3D space into two.
  
• A line won't generally intersect (touch) a plane, in the same way that two lines won't genrally intersect in 3D.
  
• A face of an object will extend in three dimensions and not two. An (infinite) face extending in three dimensions does divide space into two, so objects and light don't go through it.
  
• There are six independent planes xy, xz, xw, yz, yw, zw
  
• Planes can be orthogonal (at right angles to each other).
  
• Rotations work differently. There is no axis of rotation like 3D. A general rotation rotates in two orthogonal planes, and the angle of rotation in each is independent.
  
• Huygen's principle doesn't work; the maths can't be solved in the same way.
  

Some tips for Adanaxis: I've noticed that if an enemy is behind, you can rotate about three planes (instead of just two axes) to face him.

Action:	Rotates plane: Game label:	Rotates about:
Aim L/R	XW	YZ
Aim D/U	YW	XZ
Aim hidden axis	ZW	XY
Universe L/R	XZ	YW
Universe D/U	YZ	XW
Universe roll	XY	ZW

For movement, note that the W-axis is back (+) and forwards (-). The Z-axis is the "hidden axis".

Question: Can anyone give a good explanation about why the universe seems to revolve about some point in the distance when the player rotates *about* the YW and XW planes?

Random comment: the captcha required for every post is a bit annoying, but I have a feeling that the mental arithmetic it involves helps maintain the quality of the posts...

Quick tip, because it took me a while to realize: Just like you strafe around X by doing an XW rotation one direction while moving along X in the other, you can strafe around Y or Z by doing a YW or ZW rotation one way while moving the other way through Y or Z. Strafing along multiple axes at once is the only way I've been able to evade the fire of the beam ships at close range.

ChaimLeib wrote (View Post): › Question: Can anyone give a good explanation about why the universe seems to revolve about some point in the distance when the player rotates *about* the YW and XW planes?

To me it really looks more like the whole world rotating around a point. The way I think of it is, instead of having vision represented by a series of planes decreasing in scale with depth, you have a series of cubes. What you're actually seeing is the third axis of each cube rotating. But note that you're still looking at the same things at the end, which would not be the case if you were doing an XW, YW, or ZW rotation. Note that these two rotations are analogous to the familiar XY rotation.

Oh, you mean a bunch of cubes stacked on top of each other in the 4th dimension? That makes sense. Thanks!

ChaimLeib wrote (View Post): › Oh, you mean a bunch of cubes stacked on top of each other in the 4th dimension? That makes sense. Thanks!

Yep! And even if that's not how it's being visualized, that is basically what you'd actually be seeing as a 4D person, assuming you have cube pupils. Like some kind of hypergoat.