Prashantkrishnan wrote:But not from his POV. All his neurons and his entire brain would also have been rotated. This means that he would not notice any change in himself. He would think that his heart is on the left, and ours is on the right. With respect to him, the entire realm would have been rotated in a flune.
Prashantkrishnan wrote:During the interval, the car turns right without my knowledge and I see the surroundings in a different orientation.
Hugh wrote: For me, it's like seeing everything "from a different dimension."
Hugh wrote:gonegahgah wrote:
...The left will always fall to our left and the right will always fall to our right.
...The key thing with this view is that anything in front of you stays directly in front of you even as you rotate into the ana or kata directions.
This is an interesting picture you've created from the Dimensional Baby Steps thread gonegahgah.
I hope you don't mind that I'm responding to it in here, but it has a possible relevance to the VRI.
The key things from my perspective is that you said that forward stays in front of you and left/right stays the same relative to you as you rotate through ana/kata.
This is similar to the VRI flips. What is in front of you stays in front of you and what is to your right and left stays to your right and left.
What happens with VRIs is that there is a perceived rotation though, and this fits in with the rotation shown with your picture.
It seems that at times when the ana/kata rotation is at 90, 180 and 270 degrees that there is a lining up of axes that might enable somewhat of a perceived Necker Cube effect.
Again, the idea here in this thread is that it is a 4D being experiencing this VRI, there isn't any actual rotation involved, but the perceived possible angles that the light can reach the 4Der's eyes is from more directions than what would be available in only 3D.
Hugh wrote:You asked how VRIs are related to a Necker Cube, here is an explanation: http://hddb.teamikaria.com/forum/viewtopic.php?p=18002#p18002
It seems to me that VRIs are kind of like being "inside" a Necker Cube, that's how it feels to me as I consciously flip from viewpoint to viewpoint in a movie theater, to all four different facing views.
A 2D Necker Cube can instantly flip to two different orientations within perceived 3D space, and I'm thinking that a 3D cube viewpoint (as in the entire movie theater room itself) can be instantly flipped to many different viewpoints within possible 4D or higher space.
When I see the tesseract in each of our avatars, it looks and feels like what I can see of our world in totality when I consciously make VRIs happen!
It's like there are all these other viewpoints that I can see, all these other angles available, and I've thought since I was young that there might be a higher dimensional explanation for it.
If there are actual higher dimensions to ourselves and the universe, then there would be all these other directions that light can travel in, and we would be able to see light coming from those other directions as well.
Here is another angle to look at things (I'm thinking outside the tesseract.).
What if we actually are 4D beings, in a 4D universe, but can only see a 3D world around us because of our limited viewpoint?
(Take for example a theoretical 2D being that looks along his plane universe "along the edge", which is only a 1D line, which cannot be actually seen at all because it is infinitely thin, so it has a very limited viewpoint.)
What if it's the same for us, and we can only see a 3D "slice" of the 4D universe around us?
The big question is, what other types of 3D "slice" viewpoints would be available in that 4D space, with our 4D eyes?
Prashantkrishnan wrote:Try the right hand thumb rule. For the first four systems (after VRI) , you will get i x j = k (according to our convention), while for the last two (after 4D rotation) you will get i x j = -k (violating our convention).
Prashantkrishnan wrote:Does the movie theatre really give the feeling of a lateral inversion? I have not observed them much, and I will have to observe the kind of VRI we get in a movie theatre to properly understand what you are saying.
Prashantkrishnan wrote:A 4D being would be able to see the cube from two different viewpoints outside the realm of the cube. A viewpoint in flunespace for a 3D cube would thus give as many different orientations as our viewpoint could give for a 2D square. If you mean rotating a cube in four dimensions and looking at it from the same realm, we get the Necker Cube itself. I'm not sure whether this is what you mean here when you say "3D cube viewpoint". I'm not much familiar with the movie theatre room If you mean a 4D analogue of this, something like a 'Necker Tesseract', then here's an imprecise drawing (I use paint, and I'm not experienced with various softwares) of a 2D projection of how a tetronian would see it from my new website:
The 4D creature would see the red vertex as the nearest and the blue vertex as the farthest as one orientation and the other way round as another orientation. The remaining vertices all lie on the projection envelope, so there are no more orientations for this. These two rotations can be rotated into each other around their realm of symmetry in 5D.
Prashantkrishnan wrote:I believe you mean that you can spot each surcell of the tesseract and visualise it as a cube when you 'look at it that way'. Looking at the entire tesseract that way is what causes the problems we get trying to visualise 4D. We have to imagine all the details we know about the tesseract and feed them into the projection (all in our head) and this requires immense concentration. I have never been able to do it. I have tried to visualise a dichoral angle, which is the simplest 4D structure we need to be familiar with to try to visualise anything else. I can't say I have succeeded.
Prashantkrishnan wrote:I have often wondered why we cannot see objects outsidde our realm even if there is an unobstructed path for light from them to our retina. I think that since we have a 2D array of cells in our retina, only a single plane normal to our line of sight can be visible to us at a time. Our retina does not have enough space for 3D images. When light from our realm enters our eye and hits the retina at a spot, while at the same time another ray of light from outside our realm hits the same spot, the one from our realm passes through our eye lens while the other one does not. I think that because of this, our eye might give preference to the former ray, as both images cannot be stuffed into the same spot.
Prashantkrishnan wrote:If we are actually 4D beings, we ought to be able to move out of this realm. We may at most be thin 4D prisms confined to a realm by some solid barriers which prevent us from moving out of the realm. This model has been mentioned by quickfur in the thread 'Dimensional Baby Steps'. And we don't actually see 3D slices, we see 2D projections of 3D objects. (You may call them 3D slices if you think of them as small prisms, of course). If we had the freedom to move around in a flune, then we could have infinitely many 3D "slice" viewpoints. I'm not sure what you mean by "types of 3D slice viewpoints".
Hugh wrote:Prashantkrishnan wrote:Does the movie theatre really give the feeling of a lateral inversion? I have not observed them much, and I will have to observe the kind of VRI we get in a movie theatre to properly understand what you are saying.
Here's the video that I made about the Movie Theater VRI Flip to explain how one can get their orientation easily turned around inside of one. This happens to a lot of people, and they find that when they leave the theater, they start heading for the exit in the "wrong" direction because they got "turned around" with a VRI during the movie, but didn't realize it. Things normally flip "back to normal" after a short time. What I find interesting is to consciously do a VRI flip while in a movie theater, which is the easiest place for me to do them. I can mentally turn the theater around to each of the four orientations quite easily. Actually, one can learn to do this wherever they are with practice.
https://www.youtube.com/watch?v=xETQaPrDeQQ
After seeing the video, does this make the VRI flip there more understandable? It would be interesting if you could try doing the VRI flip yourself in a movie theater the next time you go, I would very much like to hear if you can do the flip there yourself!
Prashantkrishnan wrote:A 4D being would be able to see the cube from two different viewpoints outside the realm of the cube. A viewpoint in flunespace for a 3D cube would thus give as many different orientations as our viewpoint could give for a 2D square. If you mean rotating a cube in four dimensions and looking at it from the same realm, we get the Necker Cube itself. I'm not sure whether this is what you mean here when you say "3D cube viewpoint". I'm not much familiar with the movie theatre room If you mean a 4D analogue of this, something like a 'Necker Tesseract', then here's an imprecise drawing (I use paint, and I'm not experienced with various softwares) of a 2D projection of how a tetronian would see it from my new website:
The 4D creature would see the red vertex as the nearest and the blue vertex as the farthest as one orientation and the other way round as another orientation. The remaining vertices all lie on the projection envelope, so there are no more orientations for this. These two rotations can be rotated into each other around their realm of symmetry in 5D.
That's a really interesting 4D Necker Cube picture! Thank you.
When you say "A 4D being would be able to see the cube from two different viewpoints outside the realm of the cube" this is fascinating to think about and try to understand...
Within actual 4D, wouldn't there would be multiple 3D cubes, each with its own Necker Cube type of reorientation flip possible, in all those different directions?
Prashantkrishnan wrote:I believe you mean that you can spot each surcell of the tesseract and visualise it as a cube when you 'look at it that way'. Looking at the entire tesseract that way is what causes the problems we get trying to visualise 4D. We have to imagine all the details we know about the tesseract and feed them into the projection (all in our head) and this requires immense concentration. I have never been able to do it. I have tried to visualise a dichoral angle, which is the simplest 4D structure we need to be familiar with to try to visualise anything else. I can't say I have succeeded.
This is why I feel there is still hope that this phenomenon can somehow be shown to be 4D related, because we find it so hard to think about actually visualizing 4D, that the actual experience of it may be something we don't really expect, like how the VRI appears to us as something like a simple 3D rotation, but in actuality may be much more complex. When I talked to Rudy Rucker about the VRI, he said that if we got turned around in 4D we'd turn into our mirror image, but I asked what if both we and our surroundings got turned around in 4D together, and then he understood what I was trying to say... Then it's like you said in your original post that "he would not notice any change in himself" and I think his surroundings too, except for a change in orientation.
The idea I'm proposing is that we're not just 3D ourselves getting turned around in 4D space, but we're 4D in 4D space, with the ability to see all those other directions, but only in 3D at a time because of our limited viewpoint.
Prashantkrishnan wrote:I have often wondered why we cannot see objects outsidde our realm even if there is an unobstructed path for light from them to our retina. I think that since we have a 2D array of cells in our retina, only a single plane normal to our line of sight can be visible to us at a time. Our retina does not have enough space for 3D images. When light from our realm enters our eye and hits the retina at a spot, while at the same time another ray of light from outside our realm hits the same spot, the one from our realm passes through our eye lens while the other one does not. I think that because of this, our eye might give preference to the former ray, as both images cannot be stuffed into the same spot.
It's interesting to think about what a 4D being would experience with a 3D retina, then it would be able to see from more directions within that 4D space... Another thing that I've thought about is that 3D isn't "flat" to a 4D being, it is still 3D, with each angle at 90 degrees to all the other ones, so a 4D being with a 3D limited viewpoint would see a 3D cube "all around itself", not just "in front of itself", which is like what we see, and what I'm thinking is that the VRI is a result of us being higher dimensional, because we can see what appears to be 3D around us, from different directions, because our retinas are actually 3D, and can look in all those other directions too.
It would be interesting for you to make a Neck-A-Cube and see how it relates to what I'm saying about the VRI connection.
On this page, it explains How Does One Obtain the Ability to "See" in Four Spatial Dimensions? and it has an explanation for making a Neck-A-Cube, designed by Rudy Rucker.
http://128.143.168.25/classes/200R/Projects/fall_1999/fourdim/how.html
On this page, there is Appendix C, which contains a larger version of the Neck-A-Cube to make an actual model for yourself to experiment with:
http://128.143.168.25/classes/200R/Projects/fall_1999/fourdim/app.html
Mathematician and writer Rudy Rucker adapted this design for use in helping visualize four dimensions. The following are his directions in making what he calls a Neck-A-Cube (Figure 9):
1. Trace figure.
2. Cut out around outline.
3. Crease line AC, and then crease line DE. Each time crease by folding the marked surfaces together.
4. Slit from A to B.
5. Slide one of the upper “squares” behind the other to make something like the corner of a room where walls meet ceiling. Cup the object in your right hand.
6. Close one eye and stare at the corner. “Pull” at the corner till Necker reversal takes place.
7. Once the object is solidly reversed, try moving your hand around.
8. If you have trouble getting the illusion, make sure that the model is uniformly lit (so that shadows don’t provide depth cues); and make sure to hold it still until Necker reversal has taken place.
This is kind of what the VRI does with our orientational viewpoint, except that it is "all around us", we are "inside the cube itself!"
Prashantkrishnan wrote:Here, since the entire system (along with the observer) rotates, there is actually no rotation. I suppose that's why you call it an illusion: We percieve that something has rotated even though nothing has rotated.
Prashantkrishnan wrote:4D beings can, of course, have these flips while looking at a tesseract.
Prashantkrishnan wrote:Now that's where we connect 4D rotations to VRI in 3D! If we and our surroundings together were rotated in 4D, there would actually be no change in our realm, but there has been a rotation. Similar to what I think about the movie theatre.
Prashantkrishnan wrote:How are we 4D? Are you saying that we have been trapped in this 3D realm by some barriers in 4D
Hugh wrote:So tetronians can see light reflecting off of things from more directions, so I'm thinking that with VRIs we can see the light reflecting off of things from more directions, so that might make us, and everything else, possibly tetronian.
The extra directions are orthogonal, so we can't see each of them at the same time with our limited 3D viewpoint, so that's where the VRI comes in, where we can see each of the other possible directions, one at a time by consciously choosing to look in those directions.
Prashantkrishnan wrote:How are we 4D? Are you saying that we have been trapped in this 3D realm by some barriers in 4D
This realm may not actually be 3D, it appears to be 3D but I'm thinking that it is at least 4D, and we are at least 4D.
A theoretical 2D being looks around itself and only sees a 1D line, which he can't see because it is infinitely thin, so he actually sees nothing around himself, 0.
We are supposedly only 1 dimension above a 2D being, yet see and feel a 3D world around us.
I'm thinking that there might be more there than meets the eye (at a glance).
Do you think there is any way possible that it might be 4D related, or there is no way at all that it can be related to higher dimensions?
Prashantkrishnan wrote:Do you mean that even though we are infinitely thin in one of the four orthoganal directions in tetraspace, we can perform rotations in 4D with the entire universe (VRIs) when you say that we are 4D?
After reading what you said about rotations and the drastic increase in the number of viewpoints with dimension, I would think that it is 4D related, though I don't see how mentally visualising and creating a VRI can cause a rotation of the whole universe in 4D. Though it all makes sense, considering that 180o VRIs are easier than 90o or 270o VRIs. This might be because 180o VRIs return the universe to the same realm, inverted, while 90o and 270o VRIs take us to a different, orthogonal realm.
Hugh wrote:I'm thinking if we are 4D, we are full 4D, not infinitely thin in any of the dimensions
What may make the dimensions seem infinitely thin is our limited viewpoint.
Prashantkrishnan wrote:Why do you think that this is so? Why is our viewpoint limited? If we are 4D, then why don't we percieve it?
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