ChatGPT and its Misunderstanding of 4D

[gonegahgah]

And again from ChatGPT...

We can apply a similar concept to a spherinder—a spherical cylinder—or, more specifically, a cylinder that is rotated into 4D, creating a shape that exhibits its "bulk" in a circular path.
Likewise, we can perform this operation on a simple cylinder.

Rotating the Spherinder and Cylinder
When we rotate these objects into 4D, their behaviors differ:

Spherinder (Left): When rotated around a plane into 4D, the spherinder appears as a cylinder at each step of its rotation.
Cylinder (Right): Rotating a cylinder into 4D has a similar effect to rotating a sphere. The cylinder seems to disappear from our 3D view, leaving behind only an ultrathin intersection that persists in our 3D space.
Now, let’s relate this to anatomy:

Human legs: Our upper and lower legs are roughly cylindrical, though they have irregularities caused by muscles, bones, and other internal structures.
4D beings’ legs: For a hypothetical 4D being, their upper and lower legs would be analogous to spherinders but would also feature "4D bumps" around their perimeter.
Feet: Our feet are more flattened and resemble ovoid cylinders, rather than perfect ones.
Next, I'll discuss the orientation of these shapes and the effects that orientation has.

My Addendum
I did describe the feet a little too ambiguously in my last post so I understand ChatGPT's mistake above. I've improved that now.
Feet: Our feet are more flattened and almost resemble ovals across, so a 4D being's feet would almost resemble ovoid cylinders across, rather than perfect ones.

[gonegahgah]

Let's just let ChatGPT rewrite the words for me...

This time, I’m exploring the effects of positioning and orienting the "plane of rotation" differently within our 3D slice, around which a 4D object is rotated.

First, I’ve rotated the object itself while keeping it aligned with the original plane of rotation.

Object Rotated Differently Within the Same Plane

Rotating the Object

3D Centred Axle.jpg (43.84 KiB) Viewed 114 times

Left: The original example demonstrates how the spherinder reveals a cylinder at every angle of rotation.
Right: Here, the spherinder is rotated to a different angle, though it still bisects the same plane of rotation. Even so, it continues to reveal a cylinder at every angle of rotation.
This means that if the upper leg were positioned at any angle and bisected by the same plane of rotation, it would remain fully visible through that plane.

Next, let’s see what happens when the plane of rotation itself is repositioned.

Plane Reoriented but Still Bisecting the Object

3D Other Axles

3D Other Axles.jpg (44.9 KiB) Viewed 113 times

Left: The plane of rotation is now tilted, running high at the back and low at the front. Rotating the spherinder around this plane still reveals a cylinder at every angle of rotation.
Right: Even with this unusual orientation, the spherinder continues to reveal a cylinder during rotation at every angle.

Now, let’s draw a parallel with how a 2D being might try to understand a 3D sphere.

3D Axle Reoriented

2D Angled Axles

2D Axle Angles.jpg (43.69 KiB) Viewed 114 times

Left: In the original example, a 2D being observes similar circles when rotating their 2D world around an axle pointed directly at them.
Right: If the angle of rotation is altered by tilting the axle, the 2D being still sees circles at every angle of rotation.

This demonstrates that rotation can occur around any linear or planar axle orientation without causing distortion, making it possible to observe the true shape of an object.

Why Does This Matter?
We’ll explore this further by examining the leg as a series of spherinders connected end-to-end and consider how this impacts the movement of the knee—and the slightly flatter structure of the foot.

Addendum:
In the second dual diagram I should have changed the angle of the cylinder arrows depicting 4D rotation because the rotations are no longer sideways.
None-the-less the results are as described, even if the plane of rotation is not sideways, as long as it bisects and rotates around that plane.
Now fixed!

[gonegahgah]

Here's my comparison depicting a similar process for a 4D leg as it rotates (or as we rotate) sideways into 4D:

Rotating around 4D Leg

4D Leg.jpg (44.12 KiB) Viewed 42 times

Left: This shows a spherinder (spherical cylinder) rotating (or being rotated) sideways in 4D. At each rotation, it appears as a cylinder.
Right: The same principle applies to a 4D leg, provided it is bisected by the plane of rotation.
This is a simplified model of a 4D leg.
Just as a 3D leg has variations in width and surface features (like bumps for muscles, bones, and tendons), a 4D leg would also have similar undulations and variations. However, much like we can consider a 3D leg to be generally cylindrical, a 4D being's leg can be thought of as generally spherindrical.

The fact that the leg bends does not affect the rotation, as long as it remains similarly bisected by the plane, regardless of the angle—whether bent or straightened.
This just demonstrates the natural thing that the 4D knee is solid in nature and even under rotation into a 3D slice.
Which leads us to the biopic of the knee...