quickfur wrote:It seems we have inadvertently derailed the discussion about gonegahgah's method of 4D visualization. Here's my feeble attempt at bringing things back on track.

Hi QuickFur, no worries, I've just been so busy the last few days. I'll get back here later and read what has been added. Haven't had a chance. No time to even review yet atm.

I was just finishing typing the following to add which I had started to type up a few days ago:

wendy wrote:In 4-dimensions, the around-space is 2d, so even this space would support rotation. The effect of rotation here is that the 'left-right' axis would rotate! What this means, is that if you're rolling along on your wheel, and your axle is rotating around the wheel, it would be harder to turn (since the across-clock-face is turning, and if you're trying to turn to '3-oclock', it's no comfort if the 3-oclock becomes 4-oclock or whatever. This is why, in higher dimensions, it's not a really good idea to imagine wheels having rotations in the across-space.

I'm tending to think this way too. I'm getting the feeling that it is more about rotating the drive mechanism within the wheel so that a particular angle of sideways is the one currently driving the forward motion. This would then give control to turning in a particular angle of the 360° of extra sideways to the current orientated angle hopefully. I'll keep plugging away and see what I can grow to understand of this along the way.

I've come to realise, QuickFur, that there is a distinction between representation and physical layout. The following could also be used to represent a sphere for a 2Der:

So every cross section of the circle is spun around the cross section's centre point into the 4th dimension to produce the sphere.

The following is just spread a bit more apart to allow more of the detail to show.

In all the images I've also shown the ground rotated into the 4th dimension and this is what makes each of these representations equivalent.

So just here I have shown the following representations:

1. Rotating circle around centre diameter line into the 4th dimension.

2. Rotating circle around a point where it meets the ground into the 4th dimension.

3. Rotating circle cross sections around their centre points into the 4th dimension.

All of these are equivalent which is shown by the ground following the same rotation pattern into the 4th dimension.

As I've realised here, with the example QuickFur provided me with of the tiger, there are other direct ways things can uniformly form shapes into the 4th dimension beside simple rotation and extrusion.

Understanding this now, which I did a couple of days ago but I've been too busy to write, then it should be easier to match what I was wanting with one of the simpler shapes that QuickFur was demonstrating for me earlier. I've got to go out so I'll try to work that out later.