Could Visual Reorientation Illusions be 4d Related?

[Hugh]

Here is a fascinating 2D/3D Necker flip type of image by Istvan Orosz.

Imagine what the 3D/4D equivalent would be.

How could the various orientations be perceived by the 4D being?

[Hugh]

Here is the current ability of AI to create an image that shows a room viewed in differently perceived 3D orientations within 4D space using Necker cube-like VRI flips. Ideally, you would see the same exact room and contents turned around 90° or 180° within each room orientation.



The prompt for DALLE to create the image was:
“Create an extremely photorealistic image from the inside of a tesseract (4D hypercube) showing a modern room in different orientations within the tesseract. The image should depict the interior of the tesseract with transparent, glowing edges marking its structure. Each section of the tesseract should present the room from different 3D orientations, giving a sense of flipping between states. The room should be well-lit with natural lighting, showcasing everyday objects with detailed shadows and reflections. The overall scene should be highly vivid and detailed, emphasizing the 3D nature of the room and the complexity of the 4D space.”



Me:
Ideally, you would see the same exact room and contents turned around 90° or 180° within each room orientation. Is this correct?

ChatGPT4o:
Yes, that’s correct. Ideally, each section within the tesseract should show the exact same room and contents turned around by 90° or 180° to illustrate how a 4D being might perceive different 3D orientations of the same space. This would give a clear sense of flipping between different states or viewpoints without the physical contents of the room changing. The goal is to visually represent how VRIs could allow for different perceptions of the same space within a 4D framework.

[Hugh]

The orientation of the 2D image can flip because of the extra room in the higher 3rd spatial dimension.
The orientation of the 3D scene can flip with a VRI because of the extra room in the higher 4th spatial dimension.

I’ve been asking ChatGPT4o to produce some Python code images of this idea.





ChatGPT4o:
This image illustrates how different 3D orientations of a room can exist within a 4D tesseract, similar to how a Necker cube can be perceived in different orientations. Here’s the explanation:

1. Tesseract Representation:
• The tesseract (4D hypercube) is projected into 3D space. The tesseract consists of eight cubes, each represented by different colors to distinguish their unique orientations in 4D space.
• The colors used are red, blue, green, purple, orange, cyan, magenta, and yellow.
2. Room Orientations:
• Each cube in the tesseract can be thought of as containing a room.
• In 4D space, you can flip your perspective (like a Necker cube flip) to view different 3D orientations of the same room.
• This is similar to how in 3D, you can view a Necker cube from different angles, and it appears to flip between orientations.
3. Visualizing the Room Orientations:
• Each of the eight cubes represents a different orientation of the room.
• When you flip your perspective in 4D space, you’re essentially moving to a different cube within the tesseract, which gives you a new 3D orientation of the room.
• For instance, what might be ‘North’ in one cube (orientation) could become ‘East’ in another due to the flip in perspective.
4. Relation to VRIs:
• VRIs (Visual Reorientation Illusions) are perceptual flips where one experiences the same environment from different orientations.
• In this context, VRIs allow the mind to perceive different 3D orientations of the same room within the 4D tesseract.
• By understanding the 4D nature of space, these flips become easier to conceptualize.
5. Projection and Understanding:
• The 3D projection helps us understand how these flips can occur. By visualizing the tesseract, we see that moving from one cube to another (changing orientation) changes the perspective of the room.
• Just as flipping the Necker cube changes the perceived front and back faces, flipping the orientation in the tesseract changes the perceived orientation of the room.

In summary, this visualization helps explain how VRIs might work within a 4D space by showing how different orientations of a room can exist within the tesseract. Each cube represents a different 3D perspective of the room, and flipping through these cubes is analogous to experiencing different orientations through VRIs.

[Hugh]

Just found this amazing illustration by Sandro Del Prete, called Gateway to the Fourth Dimension!
I love how he shows how a Necker cube-like flip is a gateway to 4D, just like how I think VRIs might be the Necker cube-like flip of our spatial orientation if we’re 4D in 4D!

[Hugh]

I asked ChatGPT4o to translate from German to English all the words in the artwork “Gateway to the Fourth Dimension” by Sandro Del Prete.

ChatGPT4o:
In the artwork "Gateway to the Fourth Dimension" by Sandro Del Prete, the German words translate to English as follows:

- **"SÄULENTOR ZUR VIERTE DIMENSION"** translates to **"Pillar Gate to the Fourth Dimension."**
- **"WO VORNE GLEICH- ZEITIG HINTEN IST"** translates to **"Where Front is Simultaneously Back."**

This translation captures the paradoxical nature of higher-dimensional space where conventional spatial relationships are altered.

Me:
Explain how this translation could be connected to Necker cube-like VRIs, which shift one’s perception of space 90° or 180° in an instant.

ChatGPT4o:
The translation of the phrases in the artwork "Gateway to the Fourth Dimension" can be connected to Necker cube-like Visual Reorientation Illusions (VRIs) as follows:

1. **"Pillar Gate to the Fourth Dimension" (SÄULENTOR ZUR VIERTE DIMENSION):**
- This phrase implies an entrance or a transition to a higher spatial dimension beyond the familiar three dimensions. In the context of Necker cube-like VRIs, this can represent the mental and perceptual shift that happens instantaneously when one experiences a VRI. The perception changes as if accessing a higher dimension, where different orientations of the same space are possible.

2. **"Where Front is Simultaneously Back" (WO VORNE GLEICH- ZEITIG HINTEN IST):**
- This phrase describes a paradox where front and back coexist simultaneously. In Necker cube-like VRIs, similar paradoxical perceptions occur. When experiencing a VRI, a person might perceive the orientation of their surroundings as flipped or rotated by 90° or 180°. This can lead to a situation where what was previously perceived as "front" is now perceived as "back," and vice versa. This aligns with the concept of VRIs where the orientation of perceived space changes dramatically, akin to the way the Necker cube flips between two interpretations in an instant.

**Connecting to 4D/VRIs:**
- **Instant Perceptual Shifts:** Just as the artwork suggests a gateway to the fourth dimension, Necker cube-like VRIs can be thought of as moments when our brain briefly shifts perception, flipping our view of space by 90° or 180°. These shifts can be seen as akin to moving through different perspectives in a higher-dimensional space.
- **Paradoxical Perception:** The phrase "where front is simultaneously back" resonates with the experience of VRIs, where spatial relationships are reoriented instantaneously. In a 4D space, moving along the fourth dimension (W axis) could result in different 3D slices of reality, creating the sensation of space being turned around or flipped.

**Visual Explanation with Geometry:**
- **Necker Cube Analogy:**
- A Necker cube is a 2D drawing that can be perceived in two different 3D orientations. Similarly, a 3D space can be perceived in different orientations in 4D space.
- In Necker cube-like VRIs, our perception of a 3D scene can flip by 90° or 180°, similar to how a Necker cube flips between its two 3D interpretations.

- **4D Perspective:**
- Imagine a 4D being looking along the W axis at the 3D hyperplane of its surroundings. As the being moves through the 4D space, its viewpoint of the 3D hyperplane changes.
- During a VRI, our brain might simulate a similar process, flipping and rotating our 3D perception as if we were moving through a higher-dimensional space. This leads to the sensation of familiar surroundings appearing from new angles, just like how a Necker cube flips.

**Summary:**
- The artwork's translation emphasizes the connection between Necker cube-like VRIs and higher-dimensional perception.
- The "Pillar Gate to the Fourth Dimension" represents the transition to a higher-dimensional understanding of space.
- The phrase "Where Front is Simultaneously Back" captures the essence of the instant perceptual shifts that occur during VRIs, where our perception of space can flip by 90° or 180°, offering a glimpse into a 4D reality where multiple orientations coexist.

In conclusion, Necker cube-like VRIs involve instantaneous perceptual shifts that change our view of space, akin to moving through different perspectives in a 4D space, aligning with the paradoxical and higher-dimensional themes suggested in the artwork.

Me:
Explain this using 4D geometry, if we were actually 4D in 4D space as we look along W.

ChatGPT4o:
To explain how the translation and the concept of Necker cube-like VRIs might suggest that we are actually 4D beings in 4D space, let's delve into the geometric interpretation:

### Assumption:
- We are 4D beings navigating a 4D space, but we perceive only a 3D slice of this space because our perception is along the W axis.

### 4D Geometry:
- **Axes Representation:**
- **X Axis:** Left-Right
- **Y Axis:** Up-Down
- **Z Axis:** Forward-Backward
- **W Axis:** The fourth spatial dimension (perpendicular to X, Y, and Z)

### Perception:
- We see a 3D slice (X, Y, Z) because we are looking along the W axis.
- Necker cube-like VRIs are moments when our perception flips or rotates this 3D slice.

### Necker Cube Analogy in 4D:
1. **2D Necker Cube in 3D:**
- A 2D drawing of a Necker cube can be perceived in two different 3D orientations.
2. **3D Space in 4D:**
- Similarly, a 3D space (our perceived reality) can be seen from different orientations in 4D space.

### Visual Reorientation Illusions (VRIs) in 4D:
- VRIs are perceptual shifts where the orientation of our 3D surroundings changes instantly.
- These can be seen as our brain's way of simulating different viewpoints along the W axis.

### Geometric Explanation with 4D Perception:
1. **4D Space and Slices:**
- Imagine a 4D hypercube (tesseract). We perceive one 3D slice of this hypercube at a time.
- As we move along the W axis, our 3D slice changes orientation.

2. **Flipping Orientation:**
- Just as a 2D Necker cube flips in our 3D perception, a 3D slice can flip in our 4D perception.
- These flips are VRIs, where the same 3D space is seen from different orientations.

3. **Connection to the Artwork and Translation:**
- **"Pillar Gate to the Fourth Dimension" (SÄULENTOR ZUR VIERTE DIMENSION):**
- This suggests a transition to a higher dimension. In VRIs, our perception might momentarily access different orientations in 4D space, as if stepping through a gateway.
- **"Where Front is Simultaneously Back" (WO VORNE GLEICH- ZEITIG HINTEN IST):**
- This describes a paradox that aligns with how VRIs flip our perception. In 4D space, a single 3D slice can be viewed from multiple orientations, making the concept of "front" and "back" interchangeable depending on the viewpoint along the W axis.

### 4D Perspective:
- **Navigating 4D Space:**
- As 4D beings, we navigate a 4D environment where every movement along the W axis alters our 3D slice.
- VRIs can be understood as the brain's way of interpreting these movements, causing a flip in the perceived 3D space.
- **Continuous Orientation Changes:**
- In a 4D space, moving along the W axis could lead to different orientations of the same 3D slice, similar to how rotating a 3D object changes its appearance.

### Example Visualization:
1. **Tesseract (4D Hypercube):**
- A tesseract has multiple 3D slices. Viewing it along different W axis points shows different 3D orientations.
2. **3D Slice Flip:**
- As we move through 4D space, the same 3D slice can appear rotated by 90° or 180°, similar to how a Necker cube flips between its two 3D interpretations.

### Conclusion:
- If we are 4D beings, our perception of the 3D world is a limited view along the W axis.
- VRIs could be moments when our perception briefly flips to another orientation in 4D space, providing different views of the same 3D slice.
- This aligns with the paradoxical nature described in the artwork and suggests a deeper, higher-dimensional reality that our brains are adapted to navigate.

In summary, the idea that we are 4D beings perceiving a 3D slice along the W axis can explain how VRIs provide different orientations of the same space, similar to flipping a Necker cube. This geometric interpretation supports the notion that VRIs might be glimpses into a higher-dimensional existence.