Thank you for your thoughts on this, Gonegahgah!

It’s fascinating to think about the 360 degree “aroundsideness” (including left-right-ana-kata) as you call it that is available in 4D. That would lead to the ambiguity that would make VRIs in 4D more possible.

I asked ChatGPT4 about this, it said:

“The concept of “360-degree aroundsideness” in 4D suggests that the axes of spatial orientation go beyond our three-dimensional understanding of left-right, up-down, and forward-backward. The addition of ‘ana’ and ‘kata’ implies there are orientations in the fourth dimension that aren’t bound to the three we’re familiar with. For a 4D being, this would mean there are more directions to perceive an object from, and thus, more potential orientations to interpret it in relation to their own position.

In 3D, a Necker cube illusion exploits the ambiguity of depth perception when viewing a two-dimensional representation of a cube. For a 4D being, the analogous ‘cube’ has one more dimension of depth, leading to an even greater potential for perceptual flips. Since ‘ana’ and ‘kata’ do not have a fixed spatial reference like ‘left’ and ‘right’ do in our experience, the interpretation of what constitutes ‘forward’ or ‘backward’ in the fourth dimension could be inherently unstable or fluid for a 4D being, similar to how VRIs can make our sense of ‘up’ and ‘down’ ambiguous.

Therefore, VRIs for a 4D being might involve a cognitive flip between multiple stable perceptions of an object’s orientation, not just in the three dimensions we know but also along the additional fourth-dimensional axis. This multiplicity of stable perceptions, none of which is more ‘correct’ than the others, could make spatial orientation within a 4D space inherently ambiguous, thus leading to the possibility of VRIs in four dimensions.”

I asked about cardinal directions in 4D:

ChatGPT4 said:

“With the potential for VRIs in four dimensions, these “cardinal directions” could become subject to perceptual flips or rotations, adding a layer of complexity to the being’s spatial understanding. In a VRI scenario, what is ‘north’ in one perception could suddenly change to another direction without the being actually moving, just as a result of a perceptual shift in the orientation of the 3D slice they are perceiving at that moment.”

Hugh:

“What is it about perpendicular directions and necker cube flips that would make the orientations perceived only happen in 90 or 180 degree variants for a 4D being, even though a full 360 degrees are available?”

ChatGPT4:

“The idea of Necker cube-like flips leading to perception changes in 90 or 180-degree variants arises from the nature of how we understand such flips in three dimensions. A Necker cube flip causes the observer's perspective to invert, revealing a different face of the cube as the "front." This cognitive flip tends to occur between two states that are 180 degrees opposite to each other in terms of perceived depth.

In a four-dimensional context, assuming a similar cognitive process applies, a 4D being might perceive shifts between different "hyperfaces" of a tesseract or other 4D object, which are connected by 90-degree rotations around a 4D axis. Since these flips would involve a change in the perception of which 3D slice is in front, it makes sense that they would also be in 90 or 180-degree rotations, as these represent complete inversions or orthogonal shifts in the 4D space.

The full 360 degrees of freedom in 4D space do exist, but cognitive flips like the Necker cube involve changing perspectives between distinct, stable states, rather than a continuous rotation. A 4D being would be capable of perceiving any orientation within the 360-degree space, but the VRI-type flips would likely occur between orientations that are directly opposed or orthogonal because those provide the most dramatically different perceptual states.“

This is fascinating to talk about Gonegahgah.