Orientation

[Prashantkrishnan]

This is a continuation from viewtopic.php?f=3&t=2043

How do we define the orientation of the axes in flunespace? I have an intuition that the sense of "sense" or "orientation" is a wrong notion in itself, and not properly defined. Define right or left. We might say that left is the side where our heart is located. But a rotation in 4D would change this, and then the rotated person would think that the rest of the realm has rotated. This person's sense of orientation would be opposite to ours.

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http://cache1.asset-cache.net/gc/101864 ... 2BsWm2A%3D[/img]

This is a situation that I was inspired to consider after reading some old discussions between quickfur and 4DSpace.

Here we see a man looking at some clocks on a plane. Supposing that he is a completely normal man (with heart tilted to the left) and the clocks are our usual clocks (running clockwise), he sees them to be running clockwise. If he were to be rotated in flunespace around the plane of the clocks, after half a rotation, he would be on the other side of the clocks, with a laterally inverted body. He would still be facing the clocks, but from the back side. Now suppose that the back of the clocks are transparent so that he can see the hands. Would they seem to him to rotate clockwise or anticlockwise?

A mistake that one can make here is to think that they appear to rotate anticlockwise, since from the opposite side they seemed to rotate clockwise. This would bring about the following questions: At what point did he start seeing it rotating anticlockwise? Note that he has been facing the plane of the clocks throughout the rotation and we cannot arbitrarily chose a point where the sense suddenly changes. If at all the sense changed, the change should have been continuous. So if the sense gradually changed from clockwise to anticlockwise, how would he see it after rotating 90^o?

After pondering on this, I arrived at an explanation:- Even though he is standing on the opposite side, he sees the hands of the clock to be rotating clockwise. This is from the back of the clocks. This means that if he walked around (in his own realm) to see the front side, he would see the hands to be rotating anticlockwise. Note that if we (normal humans) were in his position, all these would not happen. With respect to us, he has an inverted body. This means that from our POV, his heart is on the right side. 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.

Now we might consider the rest of the situation: Suppose, as an inverted human being, he faces the front side of the clocks and observes the hands to be rotating anticlockwise. Now rotate him in the flune around his plane of symmetry. This would invert him back to a normal human being. Now his position has not changed, since he has undergone a bisecting rotation. He faces the front side of the clocks and sees the hands to be going clockwise.

Isn't that paradoxical? Now how, when and where did the sense change on rotation? How did he see the clocks after rotating 90^o?

It turns out that there is no paradox. True, he is facing the same direction throughout his rotation, but the planes he sees are different from every angle. There are two conditions for him to be able to properly see a plane:
It should be normal to his line of sight.
It should be in the same realm as him.
From most of the angles, the plane in question satisfies the first condition but not the second one. There are only two positions from which both are satistfied: after 0^o rotation and after 180^o rotation. These being opposite positions, show him the hands of the clock going in the opposite sense.

Thus all the paradoxes related to orientation are resolved.

The notion of "right" and "left" varies from person to person and frame to frame. We have been able to choose a convention because all human beings (as far as I know) can be translated into one another without rotation in 4D (ignoring their details, of course).

[Hugh]

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.

Hi Prashantkrishnan. I find your quote here very interesting, as it may apply to an idea that I've been discussing in another thread. If you're interested, you can check it out and reply in that thread.

Here is a link to a post there that describes how others have experienced a rotation of their orientation in real life, and I think that it may be related to the possible existence of higher dimensions of ourselves, and the universe. http://hddb.teamikaria.com/forum/viewtopic.php?p=21513#p21513

You can also check out my youtube channel describing VRIs, link below.

Thanks.

[Prashantkrishnan]

I have read your thread on Visual Reorientation Illusion. It seems quite interesting, and the nearest I can map to the experience is when I am inside a car. I first look outside the window and observe my surroundings, then close my eyes and after some time open them again. During the interval, the car turns right without my knowledge and I see the surroundings in a different orientation. This has happened to me many times, though only with the cause of the turning of the car. I don't think that is like rotating in 4D and turning into your mirror image. From the pictures I saw in the thread, they all seemed to be 3D rotations, as is the situation of a car turning.

[Hugh]

During the interval, the car turns right without my knowledge and I see the surroundings in a different orientation.

It's great to hear you've experienced VRIs Prashantkrishnan, and that you've seen your surroundings in a different orientation than normal. For me, it's like seeing everything "from a different dimension."

Thank you for your thoughts on this idea.

[Prashantkrishnan]

For me, it's like seeing everything "from a different dimension."

I don't understand how VRIs make you see things from a different dimension. From what I understand of VRIs, these are some of the orientations that can be caused by VRIs:






Note that these require only rotation in 3 dimensions. On the other hand, rotation in 4 dimensions of the same system might make it look like this:




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).

...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.

I have quoted this from your thread on VRIs and I am replying to it here because I felt that it would be appropriate to reply to this along with your comment about the different dimension.

You say here that 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. If here what you meant was that lateral directions remain lateral, then I agree with this. But right doesn't remain the same direction and neither does left. Observe the animation at 180^o and you find that the orientation is impossible for a normal human being. This is what rotation in 4D does but VRIs in 3D cannot do. In 3D, the closest you can get to this is to imagine the following situation: Suppose you walked into a street upside down. Right turns would become left turns and vice versa even though forward and backward remain same. This happens because axes always invert in pairs (i.e. rotation requires two dimensions.) If, instead of turning upside down, you turned "anaside kata", it would amount to the same. Now, forward and backward, as well as up and down, remain the same. Two axes have inverted, but you are infinitely thin with respect to one of those. So you percieve it as a lateral inversion. The rotation was around the forward/backward-up/down plane.

How is this related to the Necker Cube?

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.

A plane has a circle of normals from a single point lying on the plane, but only one normal from a point lying outside it. So light from a plane reaches the 4D beings eye only through one direction. However, this 4D being can see both halves of the realm normal to its line of sight as the plane divides the realm. There exists a unique realm normal to the line of sight of the 4Der where this plane lies in flunespace.

[Hugh]

Thank you for your thoughts on this idea.

Your knowledge of the math of dimensions is very appreciated, and it is far above my own.

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.

I appreciate the effort that you have taken to read and try to understand what I've said, and am very grateful for any effort to see if this can somehow work. All input is welcome.

--------------------

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]

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.

Yes now I see what you meant We can see the Necker Cube from two different viewpoints. This is very much similar to the 180^o rotation in four dimensions. Here's another picture of the Necker Cube (actually it's the same one you posted, but I highlighted three more vertices ):



Here red, blue, grey, white is the order we get in the clockwise sense from our viewpoint. If this is the near face, we see it from outside and if it is the far face, we see it from inside. From inside clockwise means from outside anticlockwise in our realmic world. This means that one orientation of the Necker Cube cannot be turned into the other by a three dimensional rotation. But this is done in a four dimensional rotation. (You must have seen some of those videos of a cube that seems to morph into a frustum and turn inside out).

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.

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.

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.

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.

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.

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.

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.

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?

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".

[Prashantkrishnan]

As for the mathematical part of my post, if you meant this:

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).

I was just referring to the vector product of two vectors. Curling the fingers of your right hand from the x-axis to the y-axis would have your right thumb pointing in the +Z direction. This is our convention for naming the axes. A 4D rotation of the coordinate system would reverse this.

[Hugh]

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!

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?

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.

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.

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".

By "3D slice viewpoint", I mean the whole 3D viewpoint around us, which is represented in our brain as a 3D cube with up/down, right/left and forward/backward. With Necker Cube type VRIs, one can interchange the axes with each other to see different orientations, each being a different viewpoint.

On Earth, one can only do 4 different viewpoints with VRIs because of what we perceive as the "down" direction of gravity, but up in space, astronauts can consciously do VRIs around to every orientation possible, which is 4 orientations for each of the 6 sides of a cube (4X6) which is 24.

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]

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!

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.

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?

If you, as a 4D being, are looking at a cube directly, perpendicular to its realm, the image of the entire cube is formed in your 3D retina. Your brain does not have to infer the depth of the cube or the position of the vertices any more than what is already detected by the eye. The question of Necker Cube type illusion comes only when your eyes detect only a projection and your brain has to infer the depth. If the brain can infer it in two ways, then you get reorientation flips. We 3D beings have no reorientation flips when we look at a square. But if a square had transparent edges, then probably a 2D being would have reorientation flips while looking at it. This situation is mentioned by Rudy Rucker in "The Fourth Dimension" in Puzzle 4.3. 4D beings can, of course, have these flips while looking at a tesseract.

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.

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.

Where I said that "he would not notice any change in himself", I was talking about the man who rotated in 4D while his surroundings remained as they were. He would think that he has not changed, but all the objects around him have become their mirror images. If we saw him, we would think that he has turned into his mirror image. If our surroundings also rotated, then there would be no observation of objects"becoming mirror images".

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.

How are we 4D? Are you saying that we have been trapped in this 3D realm by some barriers in 4D, like quickfur's glass slab in http://hddb.teamikaria.com/forum/viewtopic.php?f=27&t=1705&p=17303#p17307?

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.

If you mean the Necker Cebe VRI, then that does not happen when we can see "all around" an object. This happens when we see only "in front of" an object. And it happens only with a projection of the wireframe of a cube drawn without back face culling. If you mean the theatre VRI, then do we actually see something after the VRI which we could not see before the VRI? Isn't it just that you see the same thing in the same way, but you think you are seeing it from a different direction?

And 3D is actually flat to a 4D being. It is right that 3D objects still remain 3D and solid, but for the 4D observer, they are infinitely thin in a direction. That is what we mean by "flat". We call 2D objects flat because they are infinitely thin in one of the directions that we are aware of.

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!"

I just now read about this in "The Fourth Dimension" I didn't actually make the Neck-A-Cube, but I visualised what would happen if we did as in the instructions. This is one corner of a cuboid which we turn inside out. The same thing would happen if we rotated that Neck-A-Cube in 4D. If we took a whole cuboid and tried to pull at the vertices to perform this transformation, we would not succeed unless the surfaces can pass through each other. However, the 4D rotation would perform this function.

[Hugh]

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.

When it happens, it's like someone has picked up the entire world, including you, and turned it 90 or 180 degrees, and put it back down all in an instant. Something has been rotated, our viewpoint of ourselves and our surroundings. My thought has always been, could it be that we're seeing everything from another possible angle of direction?

Aale de Winkel made an interesting point in the "Flaw in Flatland" thread from this Tetraspace forum on Dec. 4, 2003 when he said: "I doubt very much that tetra-vision would be the same as x-ray-vision.
Tetronians will not be able to see within a trionian body, they see the lightrays reflecting off a body just in a direction more then we trionians do!"

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. Like when one looks at each of the four different movie theater orientations, one at a time. By the way, would you be able to try doing the movie theater flip yourself? I'd like to hear the result of your experimenting.

4D beings can, of course, have these flips while looking at a tesseract.

This is what I'm thinking we might be doing, with VRIs, if we are actually 4D beings looking at our 4D surroundings.

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.

This is what I'm thinking actually is happening in 4D, with our 4D selves in our 4D universe.

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).

Looking at the picture of the tesseract in my avatar, it looks so familiar to me in a way, because there are all these different 3D cube viewpoints possible, and that's what I can see when I do my conscious VRIs all around. It's like there are all these different Necker Cube VRI flips that I can do, which happen instantaneously, just like in the 2D Necker Cube flip, and I'm wondering how it is actually scientifically possible that we can do this.

I thank you for your time Prashantkrishnan in looking into this idea, it has always fascinated me...

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]

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.

That makes your point much clearer You say again that the entire universe rotates in 4D during VRI, including the observer, and that we can actually feel some difference.

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.

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?

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).

A theoretical 2D being sees only a 1D line, but he does not think that he sees nothing. If you go by that logic, then dionians cannot exist because they have no thickness. We can justify their existence in two ways:
By admitting that objects without 3D thickness can exist.
By ascribing quantum thickness to the dionians.
Similarly, the fact that they do see something around them can be justified in two ways:
By admitting that projections without 2D thickness are visible to dionians
By ascribing quantum 2D thickness to their linear vision.

Also, dionians can see only 1D but can feel 2D. As for us trionians, we can see 2D and feel 3D. Hence, we are indeed only 1 dimension above a 2D being. And there must definitely 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?

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 180^o VRIs are easier than 90^o or 270^o VRIs. This might be because 180^o VRIs return the universe to the same realm, inverted, while 90^o and 270^o VRIs take us to a different, orthogonal realm.

[Hugh]

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?

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.

We look in one direction, let's say it's axis z, forward.

Axis x is across right and left, and axis y is up and down, which gives a plane of vision in front of us.

If there is a 4th axis w, it has to be somewhere. As I've thought about this, I've realized that it is also perpendicular to the x and y plane axes in front of us, and to z as well. How this fits in with the VRI is that the same x,y plane of vision can be seen from different orthogonal axes; z or w.

The available range of w to z forms a full circle in a sense all the way around the plane of vision.

The VRIs result from a Necker Cube effect of being able to see the same plane of vision from different orthogonal directions, but only from one directional axis at a time.

Our brain has evolved the ability to focus on which of the available directions we want to at any time.

Well that's the way I have thought it could be 4D related...

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 180^o VRIs are easier than 90^o or 270^o VRIs. This might be because 180^o VRIs return the universe to the same realm, inverted, while 90^o and 270^o VRIs take us to a different, orthogonal realm.

I don't think there are any different 3D realms involved, it's all just one big higher dimensional universe, with more directions available to look in and explore than we currently think, with our higher dimensional eyes and bodies.

On a side note, there is a quote by Michio Kaku that I have quoted in other threads on here about how the existence of higher dimensions would allow us to unite all the forces of physics. I'm wondering if VRIs could help by showing how we may really be higher dimensional, which would make the universe's physics easier to understand...

Here's Michio Kaku's quote:

Field Theory in Higher Dimensions

To see how higher dimensions helps to unify the laws of nature, physicists use the mathematical device called “field theory.” For example, the magnetic field of a bar magnet resembles a spider’s web which fills up all of space. To describe the magnetic field, we introduce the field, a series of numbers defined at each point in space which describes the intensity and direction of the force at that point. James Clerk Maxwell, in the last century, proved that the electro-magnetic force can be described by four numbers at each point in four dimensional space-time (labeled by A _ 1, A _ 2 , A _ 3 , A _ 4 ). These four numbers, in turn, obey a set of equations (called Maxwell’s field equations).

For the gravitational force, Einstein showed that the field requires a total of 10 numbers at each point in four dimensions. These 10 numbers can be assembled into the array shown in fig. 3. (Since g _ 12 = g _ 21 , only 10 of the 16 numbers contained within the array are independent.) The gravitational field, in turn, obey Einstein’s field equations. The key idea of Theodore Kaluza in the 1920s was to write down a five dimensional theory of gravity. In five dimensions, the gravitational field has 15 independent numbers, which can be arranged in a five dimensional array (see fig.4). Kaluza then re-defined the 5th column and row of the gravitation al field to be the electromagnetic field of Maxwell. The truly miraculous feature of this construction is that the five dimensional theory of gravity reduces down precisely to Einstein’s original theory of gravity plus Maxwell’s theory of light. In other words, by adding the fifth dimension, we have trivially unified light with gravity. In other words, light is now viewed as vibrations in the fifth dimension. In five dimensions, there is “enough room” to unify both gravity and light.

This trick is easily extended. For example, if we generalize the theory to N dimensions, then the N dimensional gravitational field can be split-up into the following pieces (see fig. 5). Now, out pops a generalization of the electromagnetic field, called the “Yang-Mills field,” which is known to describe the nuclear forces. The nuclear forces, therefore, may be viewed as vibrations of higher dimensional space. Simply put, by adding more dimensions, we are able to describe more forces. Similarly, by adding higher dimensions and further embellishing this approach (with something called “supersymmetry), we can explain the entire particle “zoo” that has been discovered over the past thirty years, with bizarre names like quarks, neutrinos, muons, gluons, etc. Although the mathematics required to extend the idea of Kaluza has reached truly breathtaking heights, startling even professional mathematicians, the basic idea behind unification remains surprisingly simple: the forces of nature can be viewed as vibrations in higher dimensional space.

[Prashantkrishnan]

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.

Why do you think that this is so? Why is our viewpoint limited? If we are 4D, then why don't we percieve it?

[Hugh]

Why do you think that this is so? Why is our viewpoint limited? If we are 4D, then why don't we percieve it?

I feel we do actually perceive it, when we experience VRIs, we see things "from another dimension", another direction.

In a quote from here: http://hddb.teamikaria.com/forum/viewtopic.php?p=21513#p21513 , badenver, who hadn't experienced a VRI before said "it was like being in the twilight zone, truly, it was like entering a whole new dimension where everything looks the same but feels different and is in a different place" I experience this every day, and can make it happen just by thinking it.

Astronauts, outside of the confines of gravity up in space, can do VRIs at will to interchange all three perceived spatial axes with each other, so that not only the walls can interchange subjective orientational identities (like here on Earth with N/S/E/W), but also the ceiling and floor can be interchanged as well. They can feel that they are floating "above the Earth" with the Earth "below" them, then, with an instant VRI, they can feel they are floating "below the Earth", with the Earth "above" them.

One Skylab crewmember described it this way: “It was a strange sensation. You see brand-new things… It’s really like a whole new room that you walk into… with the lights underneath your feet, and it’s just an amazing situation to find yourself in”. Another noted “All one has to do is to rotate one’s body to [a new] orientation and whammo ! What one thinks is up is up”. “It’s a feeling as though one could take this whole room and, by pushing a button, just rotate it around so that the ceiling up here would be the floor. It’s a marvelous feeling of power over space – over the space around one”

This is a power that I can consciously feel all the time, except I'm limited to rotating around the walls only (N/S/E/W) here on Earth.

As quoted above, Michio Kaku says that existence of higher dimensions would make things easier to explain with regards to the physics of the universe.

I'm hoping that someone out there can find a way to somehow put all of this together to make it all work out.