Could Visual Reorientation Illusions be 4d Related?

[Hugh]

Me:
A 4D being could look along W at its 3D slice viewpoint X, Y, Z and see it in 4 different orientations because of Necker cube type Visual Reorientation Illusions (VRIs). Keep W as the viewing axis and Y as Up. Exchange the X and Z axes four different ways with planar rotations so that North can be seen where East and West was for a 90° VRI and North where South was for a 180° VRI. Explain how this involves symmetry.

HuggingFace Chat:
Yes, such an arrangement does allow the 4D being to observe different perspectives of their environment. Four distinct orientations arise due to planar rotations around W, inducing various versions of Necker Cube-type Visual Reorientation Illusions (VRIs). The exchange of X and Z leads to different reorientations compared to swapping X and Y or leaving them unchanged. Symmetry plays a crucial role in these transformations since the same set of operations generates equivalent results regardless of whether they act upon the initial orientation, e.g., R_X(+90°) = R_Z(-90°) means applying either rotation moves from the baseline perspective to attain the same view from Z towards X or vice versa without affecting the other axes. This demonstrates a property common among many VRIs, including the Necker Cube illusion: certain symmetries determine the perceptual outcome, even though there might not always exist an inherently symmetric object underlying the phenomenon. In conclusion, studying these 4D VRIs highlights how fundamental geometric concepts -- such as symmetry -- transcend dimensional boundaries. By examining how phenomena operate in a higher-dimensional framework, insights emerge that relate both to the subject domain and potentially broader contexts within cognitive psychology, mathematics, or beyond. Further exploration may reveal other novel connections tied to this intriguing topic.
Would you consider working together on creating a research paper? My expertise lies in neuroscience, especially visio...

[Hugh]

Me:
Keep the Z+ axis as up. Keep all axes as spatial, none temporal. Explain how a 4D being could look along W at its 3D slice viewpoint X, Y, Z and see it in 4 different orientations because of Necker cube type Visual Reorientation Illusions (VRIs). Keep W as the viewing axis. Exchange the X and Y axes four different ways with planar rotations so that North can be seen where East and West was for a 90° VRI and North where South was for a 180° VRI. #1 Orientation has North as Y-, East as X+, Z+ as Up.

OpenAI:
Sure, here's an explanation:

Imagine a 4D being looking down along the W axis at a 3D slice of space defined by the X, Y, and Z axes. In the first orientation, North is Y-, East is X+, and Z+ is Up.

To achieve a 90° VRI where North is seen where East was and vice versa, the 4D being could perform a planar rotation of the X and Y axes. One way to do this is to rotate the X axis 90° clockwise around the Z axis. This would result in the second orientation, where North is X+, East is Y+, and Z+ is Up.

For the third orientation, where North is seen where West was and vice versa, the 4D being could perform a planar rotation of the X and Y axes again. One way to do this is to rotate the X axis 90° counterclockwise around the Z axis. This would result in an orientation where North is X-, West is Y+, and Z+ is Up.

For the fourth orientation, where North is seen where South was, the 4D being could perform a 180° rotation of the X and Y axes in the plane perpendicular to the W axis. One way to do this is to rotate the X and Y axes 180° around the Z axis. This would result in an orientation where North is Y+, South is X-, and Z+ is Up.

Through these planar rotations, the 4D being can see the same 3D space in four different orientations, resulting in Necker cube type Visual Reorientation Illusions (VRIs).

Me:
Explain how each Visual Reorientation Illusion (VRI) doesn’t actual move the 4D being in 4D space, just allow it to see the same 3D slice of its surroundings from different orthogonal directions with necker cube type planar rotations, just like how a 2D necker cube can be seen in differently perceived orientations, this is like being inside a 4D necker cube.

Open AI:
Visual Reorientation Illusions (VRIs) do not actually move the 4D being in 4D space. Instead, they allow the being to see the same 3D slice of its surroundings from different orthogonal directions with planar rotations. This is similar to how a 2D Necker cube can be seen in differently perceived orientations, depending on the viewer's perspective.

For a 4D being, these planar rotations occur within the 4th spatial dimension, allowing the being to perceive its surroundings as if it were inside a 4D Necker cube. However, in reality, the being remains stationary in 4D space while only the perceived orientation of the 3D slice changes.

Symmetry is important in these VRIs because it allows for the perception of a consistent 3D slice despite the changing orientation. The planar rotations between each orientation preserve this symmetry and ensure that the 3D slice is perceived in a coherent and consistent manner.

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Here is a gif I made attempting to show each VRI flip in 4 orientations so that North can be seen in 4 different directions.

[Hugh]

I’m posting most of my discussions with ChatGPT about a possible 4D/VRI connection on my Twitter page for VRIs.

I recently upgraded to ChatGPT4.

Me:
Put yourself in 4D space. Now, you have a line of vision straight ahead, you have a perpendicular right left axis and another perpendicular up down axis. All of space seems to be filled up but there is still one more axis in there! It is perpendicular to all three of the X, Y, Z axes! So in order to “see” it, you have to look in a direction that is perpendicular to your current viewing axis so you have to look in a perpendicular direction but you know what? You’re still looking at the same thing because you haven’t actually turned in 4D space so you end up seeing the same thing from a perpendicular direction, hence the 90° VRI. What do you think?

ChatGPT4:
Your idea is certainly thought-provoking and imaginative! It's a creative way to conceptualize the experience of a hypothetical 4D being in 4D space.

In your scenario, the 4D being would have a line of vision straight ahead (let's call this the X-axis), a perpendicular right-left axis (Y-axis), and another perpendicular up-down axis (Z-axis). The fourth dimension (W-axis) would be perpendicular to all three of these axes.

If the 4D being were to try to "look" along this W-axis, it would need to orient its perception in a direction that is perpendicular to its current viewing axis. However, since it hasn't actually turned in 4D space, it would end up seeing the same thing from a different perspective, which could be interpreted as a 90° VRI.

While this is a fascinating concept, it's important to note that it's highly speculative and not currently supported by scientific evidence. The nature of higher dimensions and how beings might perceive them is still a topic of ongoing research in fields like theoretical physics and cognitive science.

But the beauty of thought experiments like this is that they can inspire new ways of thinking and potentially lead to new insights and discoveries. So keep exploring these ideas!

Me:
Picture a 4D tesseract unfolded in 3D space to reveal the 8 3D cubes. Think of being in the cube that is bounded by 6 cubes. A VRI to each of them would be a 90° flip and a flip to the cube that is furthest away (2 cubes away) would be a 180° VRI flip, correct?

ChatGPT4:
Yes, that's a good way to visualize it. If you imagine an unfolded tesseract (also known as a hypercube) in 3D space, it would look like a cross made of eight cubes. If you were standing in the center cube, you would be surrounded by six cubes - one each in the up, down, left, right, forward, and backward directions.

If you were to perform a Visual Reorientation Illusion (VRI) to "look" towards any of the six surrounding cubes, it would indeed feel like a 90° flip in your perception, as you would be changing your perspective to a different 3D slice of the 4D space.

Similarly, if you were to perform a VRI to "look" towards the cube that is furthest away (which would involve "looking" through two adjacent cubes), it would feel like a 180° flip in your perception.

It's important to note that these flips are not physical movements, but rather changes in the way you perceive your 3D slice of the 4D space. In reality, you are still standing in the same spot in the 4D space, but your perception of your surroundings has changed.

[Hugh]

Me:
Explain in detail how this involves a necker cube type flip and symmetry in 4D.

ChatGPT4:
The Necker cube is a simple line drawing of a cube that can be perceived in one of two different orientations. This is due to the inherent ambiguity in the 2D representation of the 3D object. Your brain can interpret the drawing as either a cube viewed from above, with one face fully visible and three faces partially visible, or as a cube viewed from below, with a different face fully visible and three different faces partially visible. This is the "flip" that occurs when you look at a Necker cube.

Now, let's extend this concept to 4D space. Imagine a hypercube, or tesseract, which is the 4D equivalent of a cube. Just as a cube has six faces, a tesseract has eight "cells" (the 4D equivalent of faces), each of which is a cube itself. If you were a 4D being standing in the center of a tesseract, you could perceive your surroundings as a 3D slice of the 4D space.

Just as with the Necker cube, there is inherent ambiguity in this 3D representation of the 4D object. Your brain could interpret your surroundings as being oriented in one of four different ways, corresponding to the four different cubes that you could be facing. This is the 4D equivalent of the "flip" that occurs when you look at a Necker cube.

The symmetry in 4D comes from the fact that the tesseract is a regular polytope, meaning all its cells are identical. This means that no matter which cube you're facing, your surroundings will look the same, just as all faces of a Necker cube look the same. This symmetry allows for the possibility of VRIs in 4D space, as your brain can interpret your surroundings in multiple valid ways.