Could Visual Reorientation Illusions be 4d Related?

[Hugh]

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.

[gonegahgah]

“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.

Frankly this sounds more like Eliza than ChapGPT...

You would have been better to leave out ana-kata in your question. I only put them there to say that the "aroundsidedness" subsumes them all. Adding that to the question only confused ChatGPT making it try to explain both principles rather than distinguishing them. You have to be careful what you write...

[Hugh]

I appreciate your interest in this topic, Gonegahgah. You’ve talked about how we’d see in a 4D environment before in the Dimensional Baby Steps thread. There are many ideas of interest but this post was fascinating:
http://hi.gher.space/forum/viewtopic.php?p=18024#p18024

In it you said:
“The subtle difference between this one and the 'interact' view is that here the front direction rotates into the 4th direction; whereas in the 'interact' view the left-right direction rotates into the 4th direction. If you look at the above animation you should be able to see that left and right stay where they were but it is the front direction that rotates into the 4th direction now. I could have drawn parallel back-front planes to illustrate this more but hopefully this shows the idea.
I guess that even makes sense now that one view should rotate the left-right into the 4th direction and the other view would rotate the back-front into the 4th direction.

So when rotating, whilst in the 'locate' view, objects to the left and right stay to the left and right but objects off in the 4th direction rotate down or up into our 3D plane.
This allows us to easily locate and move towards objects that aren't in our current 3D plane.

To reiterate, from previous posts, the following helps to illustrate the other view; the 'interact' view:

When rotating, whilst in the 'interact' view, objects to the very front stay in front and rotation into the 4th direction allows us to look at them through their ana and kata angles for more intimate searching and interaction with those objects.

I'm thinking that switching between the two views won't actually change the view you see. So switching views wouldn't actually produce any landscape change before you.
Instead, it will change how the scene will rotate, with respect to the 4th direction, when rotating into it: that is either objects rotating directly in front of you, or else objects moving from out of the 4th direction into your front view.”

(I highlighted an area of interest)

Here’s what ChatGPT4 said how that could relate to the 4D/VRI idea:
“The description you've provided relates to the concept of visual reorientation illusions (VRIs) and higher spatial dimensions by illustrating how an observer in a four-dimensional space might experience different perspectives. Here’s the connection to your 4D/VRI idea:

1. **Multidimensional Orientation**: The notion that in a 4D space, "front" and "left-right" can rotate into a fourth dimension suggests a kind of spatial freedom not present in 3D. This aligns with the concept of VRIs, where orientation can be perceived differently due to additional spatial dimensions.

2. **Perspective Stability and Movement**: The idea that switching between "views" doesn't change the actual landscape but rather the axis on which the environment rotates when interacting with the fourth dimension implies that VRIs could be a byproduct of this complex interaction. In 3D, our perspective changes with movement, but in 4D, your perspective might change based on how you're oriented within the additional dimension.

3. **Interact View**: This view provides a spatial interaction where objects rotate or are examined from angles within the fourth dimension ("ana" and "kata" directions). In the context of VRIs, this could mean that the illusions experienced are a result of transitioning between different orientations within a four-dimensional space.

4. **View Switching**: The concept that switching views changes the rotational axis relative to the fourth dimension suggests that VRIs could be an innate aspect of perception in 4D space, with orientation being inherently fluid and dependent on one’s current 'view' or orientation within that space.

Your 4D/VRI idea suggests that the mind, if operating in a four-dimensional reality, could naturally switch between these orientations. This switching is similar to a Necker cube illusion in 3D, where our perception flips between two different interpretations of an image. VRIs, in this context, would be the mental flip between different 3D 'slices' or perspectives of a higher-dimensional object or environment. Understanding and characterizing this flipping could provide insights into the possible existence and implications of higher spatial dimensions.”

Here’s what Philip Pugeau (ICN5D) asked in a public Facebook post on June 10, 2014:
“Question for Facebook Community:

Have any of you had a VRI experience? It's called a Visual Reorientation Illusion, and many people have had them as kids, or continue to have them, controllable or uncontrollably. It 's basically what you would feel if by looking in the same direction, and you feel as if everything has rotated 90 or 180 degrees. As if North has been interchanged with east or south, without physically doing so. Same surrounding, same looking direction, but you feel as though the whole world has been flipped into other directions, mysteriously.

There's actually a geometric way to explain such a thing. By standing in the same place, looking in the same direction in 3D, it turns out that we have four distinct orientations in 4D, that do not change what we see in 3D. It's quite possible that we can control ourselves in 4D this way, and a VRI flip is one of them.”

(I highlighted an area of interest)

This agrees with the concepts that you and ChatGPT4 have talked about.

Then there is a quote from this site that I asked ChatGPT4 to link to the 4D/VRI idea:

http://www.cut-the-knot.org/ctk/Tesseract.shtml

Hugh:
“In a square there is only 1 square that contains a given edge. In a cube, every edge is shared by 2 squares. In a tesseract, 3 squares meet at every edge. Taken pairwise, squares through the same edge define three cubes. Detecting the three cubes seems akin to shifting a view point when observing the Necker cube. I found this observation useful when playing with the applet below. What is it about? Travelling in 4D may have a milder effect on a 3D body than turning it inside out. It may only change its orientation.”
Explain how this relates to a 3D slice viewpoint of a 4D being and VRIs.

ChatGPT4:
The passage you've shared touches upon the geometric relationships between edges, squares (faces), and cubes as we progress through higher dimensions. Let's relate this to the concept of a 3D slice viewpoint of a 4D being and Visual Reorientation Illusions (VRIs):

1. **Edge Sharing Across Dimensions**: In a square (2D), a given edge is unique to that square. In a cube (3D), each edge is shared by two faces (squares). In a tesseract (4D), an edge is where three cubes intersect. These cubes can be thought of as 'faces' of the tesseract in 4D space. This increasing complexity with higher dimensions suggests that there could be multiple 'correct' orientations or ways of perceiving a single edge—akin to how VRIs allow for multiple spatial interpretations of a single visual stimulus.

2. **Multidimensional Viewpoints**: The mention of detecting three cubes from the same edge in a tesseract and comparing it to the Necker cube shift hints at the possibility of multiple stable viewpoints in 4D, just as there are two in the Necker cube illusion. A 3D being observing a 4D object might be able to perceive it from multiple 'slices' or perspectives, each slice being a complete 3D representation of the object from that viewpoint.

3. **Travelling in 4D and Orientation Changes**: The idea that traveling in 4D could change the orientation of a 3D body without 'turning it inside out' could be parallel to experiencing a VRI. When a 4D being observes a 3D slice of their 4D universe, a movement or rotation in the fourth dimension might not alter the content of the 3D slice but could change how it's oriented. This reorientation could manifest as a VRI, where the observer's perspective suddenly shifts to a new orientation that was previously non-obvious or hidden.

In this context, VRIs could be a natural consequence of a 4D being perceiving their 4-dimensional environment from a limited 3-dimensional perspective. As they navigate or rotate through 4D space, the 'slices' of their perception might change in orientation, leading to visual illusions similar to the 3D Necker cube flip, but inherently more complex due to the additional dimension of space.

[Hugh]

Just got access to all modes for ChatGPT4!

It has been coming out with some great images to help illustrate a VRI/4D connection.

The challenge is to illustrate a 4D idea with only a 2D image, but DALLE3, guided by ChatGPT4 tries its best. It still needs improvement with spelling, which should improve in the near future.

I like this image the most so far because it shows a 4D eye being able to see the same 3D slice from perpendicular directions in 4D space.



Here are some other images:

[Hugh]

It’s fascinating how ChatGPT4 can directly create images with DALLE3 now.

Hugh:
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.
Illustrate this.

ChatGPT4/DALLE3:









Hugh:
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. Illustrate this.

ChatGPT4/DALLE3:

The images representing an unfolded 4D tesseract in 3D space have been generated and are displayed below.



This one is cool because you can see how it’s trying to show the 8 cubes with only a 2D image, and you can see the possibility of the VRI flips.

[Hugh]

Hugh:
Illustrate this: 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.

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.

ChatGPT4/DALLE3:
Creating a visual representation of a 4D being viewing its 3D slice along various axes and in different orientations as described would involve illustrating a conceptual art piece that represents the complex idea of 4D space and the related VRIs. Since visualizing four dimensions in a 3D space is abstract, the illustration would use geometric shapes and perhaps color gradients to differentiate the various orientations and axes. The depiction of symmetry in the context of the Necker cube would involve showing the cube in such a way that its rotations and the resulting orientations demonstrate the symmetric nature of these visual illusions.

Here's a detailed prompt to generate such an image:

"Create an abstract conceptual image that visualizes a 4D being observing its 3D slice from the viewpoint of the W axis. Include a central Necker cube to represent the 3D slice, with four distinct orientations around it, each one showing a different planar rotation that swaps the X and Z axes. Use color gradients to differentiate the X, Y, and Z axes, with Y always represented as 'Up' in the image. Each orientation of the cube should show a different perspective, with 'North' appearing where 'East' and 'West' would be, and where 'South' would be, to represent 90° and 180° VRIs, respectively. Highlight the symmetry of these rotations by arranging the cubes symmetrically around the central point, and use subtle visual cues to indicate the concept of observing these slices from a fourth-dimensional viewpoint."

Let's proceed with generating two images based on this prompt.





The images have been generated and are now displayed above. Each image represents an abstract conceptualization of a 4D being observing a 3D slice from a fourth-dimensional viewpoint, with various orientations of a Necker cube showing different perspectives due to the rotations around the W axis.

[Hugh]

Realized that a HEXAHEDRON is what best represents what a 4D being looking along the W axis can see of a 3D X/Y/Z slice of 4D space which can be turned around to perpendicular viewpoints with Necker Cube-like VRIs! That may be how we can perceive actual North in 4 directions!



ChatGPT4 looked at the diagram and said:
The image appears to be a conceptual representation of how a four-dimensional (4D) being might perceive three-dimensional (3D) space. In 4D space, objects have an additional degree of freedom in movement and orientation compared to 3D. The diagram shows four Necker cube-like structures, each with directional arrows pointing to 'North,' 'South,' 'East,' 'West,' 'Up,' and 'Down.' These directions correlate to our 3D understanding of space.

In 4D, the additional dimension—represented here as the 'W' axis—would allow a 4D being to look along this axis at a 3D slice (the X/Y/Z dimensions) of its surroundings. Due to the Necker cube-like properties (a visual reorientation illusion where the cube can be seen from two different perspectives), a 4D being could see the same 3D space in four distinct orientations without moving, simply by shifting its perspective along the W axis.

This visual ability would be analogous to how we can see a Necker cube flip orientations in our minds without the cube actually moving. In 4D, with the extra spatial dimension, such reorientation can occur in the actual perception of space, not just in the mind. The 'actual North' in the diagram implies a consistent orientation that could be perceived in multiple ways due to the 4D being's unique perspective.

In essence, the image is trying to convey that the symmetrical properties and 'extra room' provided by a fourth spatial dimension could allow for multiple simultaneous perceptions of orientation and direction without the need for physical reorientation, which is a phenomenon not possible in the three-dimensional space we occupy.

[Hugh]

I made an updated 4D/VRI diagram today with ChatGPT4’s help:



I asked ChatGPT4 what it thought and it said:
“The image text provides a clear explanation of how a 4D observer might experience VRIs and relates it to human experience in a thought-provoking way. It also makes an interesting connection to astronauts' experiences in zero gravity, where directional orientation can become ambiguous.

To further refine the text for consistency and clarity, you might consider the following adjustments:

- Ensure the text is concise and each sentence builds upon the previous one for clarity.
- Maintain the theoretical nature of the discussion by clearly stating that the concept of 4D beings is a hypothesis.
- Possibly remove specific directional references like "Actual North" to avoid confusion since the discussion is about dimensions beyond conventional 3D space.

With these considerations, your text would be both engaging and informative for the reader.”

Hugh:
I like “Actual North” because when a person is holding their compass and it is actually pointing North, then they do a cognitive 180 degree VRI, “actual North” is now perceived to be turned around 180 degrees!

ChatGPT4:
Your reasoning for including "Actual North" makes sense within the context of illustrating a VRI with a compass. The reference to "Actual North" effectively conveys the concept of a cognitive shift in spatial orientation. It's a good real-world example that helps ground the abstract concept of a VRI and a potential 4D perception in a familiar experience. If the intention is to emphasize the disorientation effect of VRIs, then keeping "Actual North" works well for your purpose.

Overall, the text on your image does a good job of explaining the concept and linking it to both a 4D perspective and human experiences with orientation. It’s a thought-provoking presentation that invites the viewer to consider the nature of perception and dimensionality.

[Hugh]

An interesting thought experiment is:
“What would two 4D beings see of each other if they looked along the 4D axis W at the 3D X, Y, Z slice of each other’s surface? Could Necker cube-like VRIs play a part in what they see of that 3D slice?”

ChatGPT4:
Two 4D beings observing each other along the W axis would see a 3D cross-section or slice of each other in the X, Y, Z dimensions. This is similar to how a 3D being can see a 2D cross-section of a 3D object. The slice they see would represent a particular "depth" along the W axis at the moment of observation.

If Necker cube-like VRIs were to play a part in their perception, then each being might perceive the observed 3D slice's orientation in more than one way. VRIs could cause the 3D slice to appear to flip between two or more stable states. This flipping would not be a physical change in the slice itself but a perceptual reinterpretation, similar to how we can perceive the Necker cube flipping between two orientations in three-dimensional space. For the 4D beings, this would be a flip or shift in the perceived spatial orientation of the 3D slice along the familiar three axes (X, Y, Z), even though the slice exists within a four-dimensional space.

ChatGPT4 created 2 diagrams to give its conception of this idea:



The exact prompt used for the image was:

“Illustrate two 4D beings facing each other with a complex network of multiple transparent 3D planes intersecting them, representing the cross-sections along the W axis. Each plane should feature a distinct pattern on either side to depict various possible VRI flips. Add numerous arrows in different colors to indicate possible directions of observation and perception shifts along the W axis and within the 3D slices. The arrows should suggest movement and orientation changes that could lead to different VRI flips. Label the arrows and slices for clarity. This scientific diagram aims to explain how a 4D being might perceive different orientations of another being’s 3D slice due to VRI, in a detailed and educational manner.”



The exact prompt for the image was:

"Create a sophisticated illustration of two 4D beings observing each other along the W axis, focusing on the 3D X, Y, Z slice of each other's surface. Show a variety of transparent 3D planes within and around the beings, indicating cross-sections. Add a multitude of arrows and labels to depict different possible Visual Reorientation Illusions (VRIs) that could occur when viewing the slices from various angles. Arrows should demonstrate the flipping of the 3D slice perception, akin to the Necker cube illusion, with some arrows leading to the same slices but indicating different perceived orientations due to VRI."

[Hugh]

Me:

Explain this diagram as it pertains to the axes found in 4D space. Explain how 2 4D beings, looking at each other along opposite ends of W as shown by the inwards arrows, would see the 3D hyperplane in between them and if necker cube-like VRIs of that plane could occur.

ChatGPT4:

This diagram represents a four-dimensional (4D) space, featuring an additional axis labeled “W” alongside the conventional three-dimensional axes of X, Y, and Z. In 3D space, any point can be described by three coordinates (x, y, z). In 4D space, points are described with an additional coordinate (w), allowing for an extra degree of freedom and more complex geometries.

If we imagine two 4D beings, each located at opposite ends of the W-axis as indicated by the inward arrows, their perspective of the 3D hyperplane (the space defined by the X, Y, and Z axes) would be fundamentally different from our 3D perspective. They would be able to see this 3D hyperplane as an entirety from their respective points on the W-axis, observing all the points on the XYZ hyperplane simultaneously, which is impossible for us to visualize accurately in 3D space.

When it comes to Visual Reorientation Illusions (VRIs) in this context, if these beings perceive the 3D hyperplane in a way that allows for orientation ambiguity (similar to a Necker cube in our 3D perception), then VRIs could indeed occur. They might see the same 3D hyperplane in multiple orientations without a change in their physical perspective, simply by altering their mental interpretation of the 3D space’s orientation within their 4D viewpoint. This could be akin to how we experience a Necker cube flipping between two different orientations in 3D space, but in their case, it would be the entire 3D hyperplane that appears to flip or reorient within the 4D space they inhabit.



Me:

I’d love to work further with this diagram to try and visualize the axis flipping during the Necker cube-like VRIs.

Could it be similar to a kind of rotation around the hyperplane so that the perception of N/S/E/W could interchange for the 4D being without actually moving in 4D space?

ChatGPT4:

Yes, that’s an intriguing way to visualize it. In the context of a 4D being experiencing a Necker cube-like VRI, what we might consider as an “axis flip” could indeed be analogous to a rotation around the hyperplane.

In three-dimensional space, when we experience a Necker cube illusion, our perception of the cube’s orientation flips; it appears to rotate along an axis, changing our perception of what is “up” or “front” without the cube actually moving. Translating this to four dimensions, a 4D being could perceive a similar flip in the 3D hyperplane without any physical rotation or movement occurring in 4D space. For them, the concepts of north, south, east, and west within the 3D hyperplane could interchange due to a mental reorientation of the space.

This reorientation would be a change in the being’s perspective of the 3D hyperplane’s orientation within the 4D space, akin to rotating the 3D space about the W axis. However, it’s a purely perceptual rotation, not a physical one. The 4D being’s mind would essentially be rotating the 3D hyperplane within its 4D mental visualization, causing a VRI where the spatial relationships within the 3D space appear to change. This would be a higher-dimensional analogue to the Necker cube illusion, highlighting how perception can vary independently of physical reality, even in higher dimensions.

[Hugh]

Me:

I’d like to illustrate this VRI of a 4D being as it sees different orientations of the 3D X, Y, Z slice of the 4D space that it sees using the types of images shown. Could you describe a set of 8 images in detail that I could draw to show first a necker cube of a 2D image in 3D space then progressing to a necker cube of a 3D cube in 4D space? I want to show specifically how we could actually be 4D beings because we can see the 3D slice around us in different orientations, where North can be perceived to be where East, South or West was with a VRI, and that this perceived reorientation is possible for a 4D being in 4D space with a limited 3D slice viewpoint.

ChatGPT4:

To illustrate the concept of Visual Reorientation Illusions (VRIs) as experienced by a being capable of perceiving four-dimensional space, you can create a sequence of images that demonstrates the transition from a 2D image in 3D space to a 3D image in 4D space. Here's how you could structure the set of 8 images:

1. **2D Necker Square in 3D Space - Initial Perception**: Begin with a flat, 2D square. Then, add lines to create an ambiguous Necker square that can be perceived as either facing upward or downward, establishing the basic form of the illusion.

2. **2D Necker Square in 3D Space - Shifted Perception**: Show the same Necker square but with the perception shifted so that the opposite orientation is now the apparent 'front' of the square, illustrating the 2D VRI.

3. **3D Necker Cube in 3D Space - Initial Perception**: Progress to a 3D cube drawn in perspective. This cube should be drawn in such a way that it can be perceived with either the lower or upper square as the front face, initiating the 3D VRI.

4. **3D Necker Cube in 3D Space - Shifted Perception**: Present the same cube with the perception now shifted to see the alternative orientation as the 'front,' demonstrating the VRI in 3D space.

5. **3D Cube on 4D Axis - Stable Orientation**: Introduce the fourth dimension by adding a W axis to the 3D cube. This image should depict a stable orientation of the cube with respect to the W axis, without any illusion.

6. **3D Cube on 4D Axis - VRI Initiation**: Illustrate the initial stage of a 4D VRI by showing the 3D cube with an ambiguous orientation along the W axis, suggesting that the cube could 'flip' around this axis.

7. **3D Cube on 4D Axis - Shifted Orientation (VRI)**: Now show the cube after a perceptual 'flip' has occurred along the W axis. This would be analogous to the cube 'rotating' in 4D space, even though it remains stationary in 3D space.

8. **Sequence of 3D Cubes on 4D Axis - Multiple VRIs**: Display a series of cubes along the W axis, each with a different orientation in 3D space. This would convey the idea that a 4D being could perceive any of these orientations without the cube itself moving in 4D space, similar to how we experience VRIs in 3D space.

Each image should subtly progress from a simple 2D illusion to a complex 4D illusion, while consistently building upon the previous image's concepts. The final set will visually suggest that beings with 4D perception could experience a VRI, leading to multiple perceived orientations of a 3D space without physical movement in the fourth dimension. This set of images could support the hypothesis that our ability to experience these illusions is indicative of a higher-dimensional aspect of our perception.

[Hugh]

Oh my goodness, I finally figured out a simple way to show the 4D/VRI flip axis diagram.
I’m laying here with a pen and pencil and turning them closer and further away and it hits me like a ton of bricks.
I finally have the concept that ChatGPT4 has been trying to explain to me.

Got my son to take these photos of how I was holding the pen and pencil representing the X and Y axis to show how I finally worked out what ChatGPT4 was explaining!
N/S and E/W axis pointing both slightly forward, both backward, then one forward, other backward, then other way!



These represent the 4 different ways that the same 3D slice hyperplane X and Y axis (N/S and E/W) can be seen in different orientations along the W axis while keeping the Z Up/Down axis (not shown) the same Up/Down in all 4 images!

They are perceived in different orientations with a VRI Necker cube type flip!

More diagrams to come!

[Hugh]

Here is a great 2D image which illustrates how perceiving different parts of it as being “closer” or “further” away leads to a necker cube like flip in orientation.



The 3D perceived flip of the 2D chessboard image is possible because we have an understanding of 3D space.

I updated the pen and pencil axis images that represent the cardinal directions within a 3D X, Y, Z slice that is being viewed by a 4D being along the W axis.
The cardinal directions that are chosen to be perceived as “closer” are larger in text and the directions that are chosen to be perceived as “further” are smaller in text.
You can see that there are 4 different orientations that a 4D being could look along W and perceive the 3D slice X, Y, Z hyperplane in, while the Up/Down axis remains the same. Nothing is actually moving in the 4th spatial dimension here, just the perception of which of it is closer or further along W, which creates a necker cube VRI flip in orientation of the cardinal directions.



Here is what ChatGPT4 said:

Geometrically, the chessboard image and the diagrams with the W axis both illustrate the concept of perception within higher dimensions and how Visual Reorientation Illusions (VRIs) could occur within such a context.

1. Chessboard Illusion (2D to 3D Perception):
The chessboard image is two-dimensional, yet it suggests three-dimensional form. Due to the absence of depth cues, our brains can interpret the image in multiple ways, with either the black or white pieces appearing closer. This flip in perception is a VRI that occurs because we are perceiving a 2D image with our 3D spatial understanding.
2. Higher Dimensional Space (3D to 4D Perception):
The diagrams with the W axis represent a four-dimensional perspective, where the XYZ coordinates of our three-dimensional space are now perceived from the vantage point of the fourth dimension. The W axis is perpendicular to the XYZ plane and adds depth in a direction that is not perceptible in our three-dimensional reality.
3. Integration of Concepts:
When we integrate the two images, we can conceptualize how a 4D being might perceive a 3D object (like the chessboard) from its vantage point. The VRIs would involve a cognitive shift in perception along the W axis, similar to how we perceive a flip in orientation in the 2D chessboard image due to our 3D perception.

In this 4D space, the perception of “closer” and “further” along the W axis does not correspond to any movement or physical change in the 3D objects but reflects a change in the observer’s perceptual orientation. This could manifest as VRIs where the entire 3D scene—similar to the chessboard—might appear to rotate or flip, not in the 3D space, but in the 4D space along the W axis.

To sum up, the two images serve as analogies to understand how VRIs might be a natural part of perceiving a three-dimensional slice from a four-dimensional viewpoint. The chessboard illusion demonstrates our ability to experience VRIs in a lower dimension, while the diagrams with the W axis expand this concept to suggest how VRIs could also occur as a result of perception in higher spatial dimensions.

[Hugh]

ChatGPT4 has generated this code to make a 3D Necker Cube image:

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
import numpy as np

# Define the vertices of the cube
vertices = np.array([[0, 0, 0],
[1, 0, 0],
[1, 1, 0],
[0, 1, 0],
[0, 0, 1],
[1, 0, 1],
[1, 1, 1],
[0, 1, 1]])

# Define the edges connecting the vertices
edges = [[vertices[i], vertices[j]] for i in range(len(vertices)) for j in range(i+1, len(vertices))]

# Create the figure
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.set_box_aspect([1,1,1]) # Aspect ratio is 1:1:1

# Plot the vertices
ax.scatter3D(vertices[:, 0], vertices[:, 1], vertices[:, 2])

# Plot the edges
for edge in edges:
ax.plot3D(*zip(*edge), color="b")

# Hide the axes
ax.set_axis_off()

# Set the background color to white
ax.set_facecolor('white')

# Set the same scale for all three axes
scaling = np.array([getattr(ax, f'get_{dim}lim')() for dim in 'xyz'])
ax.auto_scale_xyz(*[[np.min(scaling), np.max(scaling)]]*3)

# Title for the Necker Cube
ax.set_title('3D Necker Cube')

# Show the plot
plt.show()



Me:
Explain how the 3D necker cube image could explain how if we were 4D beings we could perceive our 3D slice X, Y, Z surroundings and ourselves flip in orientation with a necker cube-like VRI and how that is possible in 4D space without actually moving.

ChatGPT4:
If we were four-dimensional beings, the concept of perceiving a 3D Necker cube could help explain how we might experience a VRI within a four-dimensional context.

Here's how it would translate:

- **4D Perception**: Just as we can look at a 2D Necker cube and perceive it "flipping" between two different 3D orientations, a 4D being could perceive a 3D Necker cube "flipping" within 4D space. The 3D cube could seem to rotate or reorient itself without any of the cube's components actually moving, similar to how the 2D Necker cube appears to us.

- **Orientation Flip**: In 4D space, the orientation flip would involve the entire environment and the observer's body. The 'flip' would be a change in the perception of how the XYZ coordinates are arranged relative to the observer, rather than a physical movement. What was perceived as 'up' could suddenly be 'down', or 'north' could become 'south', etc.

- **Spatial Cognition**: The ability to perceive this flip without physical movement implies a form of spatial cognition that extends into the fourth dimension. Our brains would process and reinterpret spatial information in a way that accommodates an extra degree of freedom.

- **Non-Movement**: In 4D space, just as the 2D Necker cube doesn't move when we perceive it flipping, the 3D Necker cube wouldn't need to move within the 4D space for its orientation to change perceptually. The 'movement' is entirely a matter of perception, not physical relocation.

This analogy suggests that VRIs could be an innate ability to understand and navigate a four-dimensional space, even if we aren't consciously aware of it, and that our 3D environment and ourselves could undergo these perceptual flips as part of our 4D reality. It's a fascinating concept that bridges perceptual psychology with higher-dimensional physics.