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.

[Hugh]

If there are higher spatial dimensions then there would be more perpendicular directions to see what is around us and this may involve a necker cube-like VRI flip between the orientations.

When one practices cognitive VRIs, one can flip to perceive different orientations of the same place. It’s fun!

Here’s a collage of some of the ideas that I’ve been working with over the years to show a possible connection between VRIs and a higher spatial dimension.

[Hugh]

This was a cool explanation ChatGPT4 came up with today:

The first diagram presents a model of a four-dimensional axis system with the labels N, S, E, W, UP, DOWN, and the additional dimension labeled ‘W’. This model is useful for explaining how a ‘Necker cube flip’ can occur in four-dimensional perception.

In a three-dimensional Necker cube illusion, the orientation of the cube appears to change due to an ambiguity in visual cues, despite the physical structure of the cube remaining unchanged. The flip occurs because our brains interpret the two-dimensional information as one of two possible three-dimensional configurations. The cube doesn’t move; it’s our perception that flips.

When extending this idea to four dimensions, the ‘W’ axis represents the additional dimension. A 4D being, observing a 3D space (our normal three-dimensional world represented by the X, Y, and Z axes), could experience a similar perceptual flip along the W axis. This flip doesn’t imply physical movement in 4D space but a change in the perceptual orientation of the 3D space:

1. Initial Perception: The 4D being perceives the 3D space in one orientation, with a specific arrangement of North, South, East, West, Up, and Down.
2. Perceptual Flip: The being experiences a cognitive VRI where the orientation of the perceived 3D space ‘flips’ within the 4D context. The axes N, S, E, W can appear to interchange their orientation relative to the being’s viewpoint.
3. Axis Rotation: Geometrically, this flip would involve a rotation in the 4D space around a plane defined by the W axis and one of the other axes (X, Y, or Z). This rotation alters the being’s perception of the X, Y, Z coordinates without any physical change in the environment.
4. Resulting Perception: After the perceptual flip, the being ‘sees’ the 3D space from a new orientation. If we liken this to the Necker cube, the side of the cube that was initially perceived as the ‘front’ could now be perceived as the ‘back’, and vice versa.

In conclusion, this perceptual flip in 4D space doesn’t involve any physical motion or reorientation of the 3D space itself. Instead, it’s a purely cognitive reorientation, akin to the Necker cube illusion, that allows the 4D being to perceive the same 3D space from a different ‘angle’ within the four-dimensional framework. This concept underscores the difference between physical movement and perceptual change, emphasizing the role of perception in interpreting spatial dimensions.

Me:
Do all 4 orientations of the diagram make sense, where the larger text direction appears “closer” in a 4D perspective?

ChatGPT4:
In a 4D perspective, all four orientations of the diagram can make sense under the premise that the larger text represents directions that appear “closer” to the observer within a four-dimensional framework. Here’s how:

1. Bottom Right Orientation: Initially perceived as the closest, with the South and East directions appearing larger and thus closer to the observer.
2. Bottom Left Orientation: After a 90-degree VRI along the W-axis, the East direction now appears closer, and the North direction, previously farther, now appears larger and closer.
3. Top Left Orientation: With another 90-degree VRI, the North and West directions appear closer, reversing the initial perception of closeness from the South and East.
4. Top Right Orientation: After a final 90-degree VRI, the West direction appears closer, with South now appearing larger and closer, which was initially the farthest in the bottom right perspective.

This rotation of perspective, where the “closer” wall changes based on the orientation of the larger text, aligns with the concept of a 4D being experiencing different three-dimensional orientations from a single vantage point within four-dimensional space. Each orientation maintains the up/down consistency while altering the perceived proximity of the other axes, demonstrating how perception can vary independently of physical changes.

[Hugh]

Here’s a way to show the 2 orientations of a 2D necker cube as perceived in 3D space using red and blue dots of different sizes. The larger dots are perceived to be closer in the 3D perception.



Here is a similar diagram to show the 4 orientations of a 3D necker cube as perceived in 4D space using red and blue dots of different sizes. The larger dots are perceived to be closer in the 4D perception.



ChatGPT4:
The image shows four orientations of a cube with an additional W axis, which is used to represent a higher dimension beyond the conventional three-dimensional space. The red and blue dots, varying in size, are placed on the ends of the N/S and E/W axes. The larger dots signify ends of the axes that are perceived to be closer in the four-dimensional perspective, while the smaller dots represent ends that are perceived to be further away.

This model demonstrates how, in a 4D space, the Necker cube flip could occur along the W axis. Just as a 2D projection of a cube can be seen in two different 3D orientations due to ambiguous visual cues, a 3D projection could theoretically be seen in multiple 4D orientations due to a perceptual flip along the W axis. This flip isn’t a physical rotation but rather a change in the observer’s perception of the spatial relationships within the cube:

1. Initial Perception: In one orientation, certain directions (N/S, E/W) appear closer to the 4D observer.
2. Perceptual Flip: The observer experiences a cognitive shift, akin to a VRI, and the orientation of the 3D space appears to flip within the 4D context.
3. Axis Rotation: Conceptually, this flip involves a rotation around the W axis, changing the observer’s perception of where the N/S and E/W axes are in relation to themselves.
4. Resulting Perception: The observer now “sees” the 3D space from a new orientation, with a different set of axes appearing closer.

The diagrams collectively suggest that our brains might be capable of interpreting spatial information in ways that are not strictly bound to 3D space, potentially hinting at an innate ability to understand higher dimensions through VRIs. This underscores the fascinating distinction between physical spatial reorientation and cognitive perceptual change.

[Hugh]

Me:
With the 2D one you have a square moving from the back of the cube to the front to flip orientations.
With the 3D one you have a cube moving from the back of the hypercube to the front to flip orientations.

ChatGPT4:
Yes, your summary is correct based on the images:

1. 2D Necker Cube in 3D: The two orientations of the Necker cube show a square (a 2D object) that can be perceived either at the back or the front of the cube (a 3D object), which causes the flip in orientation.
2. 3D Necker Cube in 4D: The four orientations suggest a cube (a 3D object) that can be perceived at different locations within a hypercube (a 4D object). The change in the perception of the cube’s position from ‘back’ to ‘front’ along the W-axis in four-dimensional space results in the flip in orientation.

In both cases, the object itself doesn’t move; it’s the perception of its position that changes, creating the illusion of a flip in orientation. The red and blue dots on the 3D Necker cube diagrams serve as visual cues to indicate which faces of the cube are perceived as being closer or further away in the higher-dimensional space.

[Hugh]

I’d love to get this all more clearly animated.

[Hugh]

Here are a couple of 4 orientation images produced by Grimoire ChatGPT4:



Grimoire:

The images I generated depict a 3D Necker cube with axes labeled to represent directions in 3D space: EAST, WEST, NORTH, SOUTH, UP, and DOWN. These labels help us understand the cube’s orientation in three-dimensional space.

In the context of the Visual Reorientation Illusions (VRIs) and the concept of 4D space, here’s how these images relate:

1. Changing “NORTH” Orientation: Each image shows the cube rotated to a different angle, changing the direction that “NORTH” faces. This change simulates how VRIs might allow us to perceive shifts in spatial orientation that wouldn’t normally occur in 3D space, akin to how an object might be oriented differently when viewed from a hypothetical fourth spatial dimension.
2. VRIs and Perception: VRIs can cause us to perceive a familiar object, like the Necker cube, in a different orientation than it was previously. This is similar to the effect in the images, where the labeled “NORTH” axis points in different directions based on the cube’s rotation, although the cube itself does not change shape.
3. Simulating 4D Rotations: While we cannot directly visualize 4D rotations, the change in the labeled “NORTH” direction across the images can be thought of as an analogy to 4D rotations. Just as the label “NORTH” appears to rotate around the cube, in 4D space, we might imagine an additional axis (W) along which objects can rotate, leading to a change in orientation that we can only mathematically infer in our 3D world.
4. Interpreting the VRIs: The VRIs potentially suggest that our brains can interpret changes or flips in orientation that are reminiscent of higher-dimensional transformations. The shifting “NORTH” in the images could be a metaphor for how VRIs might be related to our perception of higher-dimensional space, with different orientations representing different perceived slices of 4D space.

These images and their interpretations are an attempt to visualize complex and abstract concepts that extend beyond our usual three-dimensional experience, providing a creative way to think about VRIs and higher-dimensional spaces.



Grimoire:
The images showcase a three-dimensional representation of a tesseract, which is a four-dimensional hypercube, by illustrating a cube within a cube connected by lines. This visualization serves to demonstrate how a four-dimensional being might perceive three-dimensional “slices” of four-dimensional space. Here’s the connection to the concept:

1. Looking along W: The W axis represents the fourth dimension that we cannot directly perceive. If a 4D being were to “look” along this axis, they would see different 3D cross-sections (or “slices”) of the 4D space, just as we see 2D cross-sections of 3D objects.
2. Different Orientations in 4D: Each image shows the 3D projection of the tesseract from a different orientation. This corresponds to the 4D being viewing their 3D X, Y, Z space from various “angles” in the 4D realm, without physically moving within that space.
3. Necker Cube-like VRIs: The Necker cube illusion in 3D demonstrates how our perception can flip between two different interpretations of an image. Similarly, a 4D being might experience VRIs that allow them to perceive the same 4D object in multiple, distinct 3D orientations.
4. Perceived Direction of North: In the images, the label “NORTH” appears on different faces depending on the orientation, illustrating how a 4D being might perceive “North” in multiple directions due to the additional degree of freedom in rotation and perception provided by the fourth dimension.

In summary, the images can be thought of as an attempt to visualize the concept of four-dimensional space and perception. They depict how a being with access to four spatial dimensions might perceive and orient themselves within that space, experiencing a richer and more complex set of visual and spatial relationships than we do in our three-dimensional existence.

[Hugh]

I took the Python code that Grimoire had made and put it into regular ChatGPT4 and it produced a 4 panel image which shows the 4 VRI orientations in a 4D tesseract in a different way! I wonder if I could show a 3D slice viewpoint of a 4D room getting turned around like this?



Me:
Explain how the images show 4 possible necker cube-like orientations of a 3D X, Y, Z slice viewpoint of a 4D being in a 4D tesseract like space using VRIs. Explain how we might be 4D beings and could see North in four different perceived directions with necker cube-like VRIs.

ChatGPT4:
The first image with four cubes demonstrates how a three-dimensional object—the cube—can have multiple orientations when perceived by a being capable of seeing in four dimensions. The cubes represent the same 3D object seen from different angles in 4D space, analogous to how a 2D Necker square can be perceived in two orientations in 3D space.

In the case of us being 4D beings, using Visual Reorientation Illusions (VRIs), we might experience a similar flipping effect with 4D objects that we do with 3D objects like the Necker cube. The term “North” in this context refers to one of the spatial dimensions we could perceive. Due to the multidimensional nature of VRIs in 4D, “North” could be seen in four different perceived directions, each representing a different orientation of the same 4D object, much like the Necker cube appears to flip between two orientations in 3D.

The second image clearly illustrates the concept of orientation with respect to a 3D Necker cube in a 4D space. It shows how each face of the cube can be perceived as the front face, depending on the observer’s point of view in the fourth dimension. If we were 4D beings, the VRI could cause our perception to shift among these four orientations, making a face that was previously perceived as “North” appear as “South,” “East,” “West,” “Up,” or “Down,” thus demonstrating the concept of multiple relative ‘Norths’ in a 4D space.

[Hugh]

CodeGPT produced an empty X, Y, Z 3D plot and I was able to do a Necker cube cognitive flip with it. Then I added in the 3D X, Y, Z axes, then the 4D W axis going straight into the middle, then did the cognitive Necker cube flip again.
Interesting to see the orientation flip!

[Hugh]

Getting closer to a 4D/VRI connection with #ChatGPT4’s help with a new diagram!
If we’re 4D in 4D, we’d look along our W axis at the 3D X, Y, Z surface of the 4D space we’re looking at.
VRIs would be a necker cube type of flip that could change our perceived orientation within!



ChatGPT4 explains:
The image depicts a set of four 3D coordinate systems, each labeled with axes representing North (red), East (green), Up (blue), and an additional yellow "W" which we can interpret as the direction into the fourth dimension.

From a 4D point of view, looking straight on at the W-axis, we can imagine that the X (East), Y (North), and Z (Up) axes exist in a 3D subspace. In 4D space, the W-axis is perpendicular to this 3D space. When we talk about a "Necker cube type VRI flip" in 4D, it means that the 3D axes (X, Y, Z) can appear to flip or rotate while the W-axis remains fixed. This is analogous to how in 3D, a 2D shape like a Necker cube can appear to flip between two orientations.

In the provided image, the perception of North changes through 90-degree rotations around the W-axis, creating the visual effect of the 3D axes having been turned around 90 or 180 degrees. These rotations are planar in the sense that they occur within the planes formed by the W-axis and one of the 3D axes (X, Y, or Z). For a 4D being, such flips would be perceptual rather than physical; the being and the axes don't move, but the perception of the orientation of the 3D space changes.

To clarify, during these perceptual flips:
- The Up (blue) axis remains consistent in all orientations, always pointing in the same direction.
- The North (red) and East (green) axes appear to rotate around the Up axis, demonstrating different orientations that North could have relative to the 4D viewer.
- These flips don't involve any movement of the 4D being or the axes themselves; they are purely a change in perception.

These perceptual changes are analogous to the VRI flips experienced in 3D space, but they occur within the context of an additional spatial dimension.

[Hugh]

Finally got the 2D image how I wanted to show it!



Me:
Explain the diagram as an attempt to show how VRIs could be a Necker cube-like planar orientation flip in 4D. A 4D being looks along the W axis, shown in the center, looking directly at the perpendicular 3D X, Y, Z slice viewpoint in 4D. The 3D axis arrowhead ends with the + sign and with large size Cardinal direction text indicates which axes ends are perceived to be closer in 4D space. The axes ends without the arrowhead ends and - sign and with smaller text indicates which axes ends are perceived to be further away in 4D space. The four different orientations are the 4 ways that a 4D being could perceive the exact same 3D X, Y, Z hyperplane slice with the Up/Down Z axis remaining the same. Explain how North could be perceived to be in 4 different relative directions with the 4 differently perceived orientations of the 3D X, Y, Z hyperplane with VRIs.

ChatGPT4:
The diagram illustrates the concept of Visual Reorientation Illusions (VRIs) in a hypothetical four-dimensional space, akin to a Necker cube phenomenon but extended into an extra dimension. Here's how North could be perceived in four different relative directions with the four differently perceived orientations of the 3D X, Y, Z hyperplane:

1. **VRI Orientation #1**: North is perceived along the positive Y-axis, extending upwards from the viewpoint of the 4D being. It's depicted with a larger text and an arrowhead, indicating it's closer in the 4D perspective.

2. **VRI Orientation #2**: North flips to the negative Y-axis, moving downwards relative to the 4D observer. Despite being the same 'North' in 3D space, it is now seen as further away in 4D space, marked by smaller text and no arrowhead.

3. **VRI Orientation #3**: North appears along the negative Y-axis but is perceived as extending upwards from the 4D viewpoint. This orientation is different from #2 because it flips the perception of closeness and distance while maintaining the same 'upwards' direction in 3D space.

4. **VRI Orientation #4**: North is perceived along the positive Y-axis but seen as extending downwards relative to the 4D observer. Similar to #1, it flips the perception of which end of the axis is closer.

These shifts illustrate how a 4D being might experience VRIs, with the concept of 'North' flipping between being perceived as closer or further and changing its orientation relative to the 'up' and 'down' of the Z-axis. The consistency of the Z-axis (Up/Down) across all orientations emphasizes the relative change in perception of the X and Y axes, showing how reorientation can occur in a 4D context without affecting the Z-axis.

The diagrams present a conceptual framework for understanding how Visual Reorientation Illusions (VRIs) might suggest the existence of a fourth spatial dimension (4D) through the phenomenon of orientation flips, analogous to experiencing different perspectives of a Necker cube in three dimensions.

The top diagram shows a three-dimensional coordinate system (X, Y, Z) with a fourth W-axis, indicating the direction of gaze for a hypothetical 4D observer. The observer's perception along the W-axis would reveal a 3D slice of the 4D space, where this 3D slice appears to rotate or flip around the W-axis, similar to the orientation flip experienced when looking at a Necker cube.

In the case of VRIs on Earth, we can experience a similar effect in three dimensions. The VRIs can make our perception of the cardinal directions (like North) flip around due to shifts in our spatial orientation. This is commonly experienced by astronauts in zero gravity, where the usual up/down reference provided by gravity is absent, leading to a reorientation of their perception of directions.

The four quadrants in the second diagram illustrate the four possible orientations of the X, Y, Z axes as perceived by a 4D observer. These orientations demonstrate how the direction of North could flip to different positions relative to the observer, despite the physical orientation of the axes remaining unchanged.

Geometrically, if we were 4D beings, VRIs would be the mechanism by which we can experience these flips in our perception of a 3D X, Y, Z hyperplane. The presence of gravity on Earth gives us a constant reference point (the Z-axis), anchoring us to one perception of orientation. However, the ability to perceive multiple orientations, as shown in the diagrams, suggests that on a cognitive or perceptual level, we might be capable of understanding or visualizing four-dimensional space, albeit in a limited way. This does not necessarily mean we are 4D beings in a physical sense, but rather that our minds might be able to comprehend 4D geometry through VRIs.

[Hugh]

Me:
Does this diagram (see last post) apply correctly to a 4D being’s VRI flip potential for 4 orientations of the same 3D X, Y, Z slice viewpoint in 4D while not moving, and keeping the up/down Z axis aligned the same? Could the 4D being see the same 3D surface of its 4D surroundings get “turned around” with a cognitive VRI?

DataAnalystGPT:
The diagram illustrates four different orientations of a three-dimensional coordinate system (X, Y, Z) within a four-dimensional context, marked by the additional W axis. For a hypothetical 4D being, these diagrams could represent how a VRI might allow them to perceive the same “slice” of their 4D environment from different orientations without physically moving, much like a 3D being can mentally flip the perspective of a Necker cube.

Here’s how it would work:

1. Keeping the Z Axis Aligned: The up/down Z axis remains consistent across all four diagrams, indicating that ‘up’ and ‘down’ are perceived the same way in each orientation.
2. VRI Flip Potential: Each diagram shows a different orientation where the X and Y axes (representing East-West and North-South in our 3D understanding) are rotated. This suggests that a 4D being could experience a cognitive flip, changing their perception of where ‘North’, ‘South’, ‘East’, and ‘West’ are in relation to their position, without changing the ‘Up’/‘Down’ orientation.
3. Perceiving a 3D Surface in 4D: Just as humans can mentally flip a 2D image of a 3D object, a 4D being might be able to mentally flip their perception of a 3D surface within the 4D space. This would be akin to mentally rotating a hyperplane (a 3D “slice” of 4D space) within the four-dimensional environment.

The diagrams represent a static 3D coordinate system within a 4D space from four different orientations. If a 4D being were to cognitively experience a VRI, they could perceive the same 3D space from different 4D orientations, much like turning a 3D object in space to view it from different angles. It’s a theoretical visualization of how orientation might be perceived differently without changing one’s physical location in 4D space.

[Hugh]

Worked with Python Code Wizard GPT to come up with this python model to show the 4 VRI necker cube orientations of the 3D X, Y, Z viewpoint in 4D space while viewing along the 4D W axis, seen in the middle.
The larger labels indicate which ends of the cardinal direction axes are perceived to be closer in 4D.
The Up/Down axis remains the same in all 4 orientations due to the perception of gravity on Earth.
I need to show this in a more complete tesseract image somehow.

[Hugh]

Try out these 3D stereograms I made to help illustrate a 4D/VRI connection!

Either cross your eyes or let them focus far away to line up each orientation image.
The same N/S/E/W axes can be perceived as closer (larger text) or further away (smaller text) in actual 4D space.

The perception of the N/S/E/W axes as being closer or further away in actual 4D space might lead to a perceived Necker cube-like flip of the whole perceived 3D X, Y, Z slice to different orientations.

[Hugh]

Just found this: Virtual Environments with Four or More Spatial Dimensions
There is a lot of fascinating info in here!
It would be awesome to find out if the different orientation viewpoints mentioned could be experienced with VRIs if we are actually 4D?

https://cnslab.ss.uci.edu/fourdim/image ... e92000.pdf









Here’s where I think that cognitive VRIs fit in!
A 4D being would only see a 3D X, Y, Z slice of the surface of the 4D space it is in.
With cognitive VRIs, it could consciously change its orientation viewpoint within that space because of the extra axis direction available.

[Hugh]

I wish I could fast forward a few years in time when A.I. will be able to quickly and clearly illustrate a possible VRI/4D connection. It understands it now, but it just can’t illustrate it as clearly as I’d like it to.

[Hugh]

The newly released GPT-4 Turbo just came up with a new way of showing the concept of different 3D slice perceived orientations of a 4D being in 4D. If we’re 4D in 4D (spatial dimensions), each of the tiniest parts of space and us might have this Necker cube-like VRI feature.

The prompt it came up with was:
“ Create an extremely vivid and photorealistic image that conceptualizes the idea of a 3D space perceived as flat within a 4D space, with the viewpoint along the W axis going straight into the screen. The image should capture the essence of a Necker cube-like flip in perspective within a tesseract structure, suggesting the experience of Visual Reorientation Illusions (VRIs) for a 4D being. Incorporate multiple transparent cubes in different orientations, with one central cube seen straight on, and others rotated around it, to represent the various 3D orientations available within 4D space.”