Could Visual Reorientation Illusions be 4d Related?

[PatrickPowers]

You might enjoy this vid I made before I had ever heard of a VRI.
https://youtu.be/n0fdKTaTfdM

[Hugh]

You might enjoy this vid I made before I had ever heard of a VRI.
https://youtu.be/n0fdKTaTfdM

Well that was fun. Well done.

I’ve seen some of your other videos with regards to 4D animations on your other YouTube channel: https://www.youtube.com/channel/UCoFTI5DQgTCSm-Lz-VI8JKQ

It would be awesome to see some sort of an animation which would show a VRI and how it could be 4D related.

The turn is an instantaneous one. It is like looking at a Necker Cube flip, but one is actually inside the cube, and it is 3D all around you.

I made a picture kind of explaining it:



If we are actually 4D or higher, and we are surrounded by 4D or higher, but could only see a 3D “slice” of our surroundings at any time, but could see that 3D slice from different directions because of those other available directions, could VRIs be the way that we can do that? Rudy Rucker created a Neck-A-Cube model that would help to peer into 4D and it relies on a necker cube type of “twinkling arrangement” similar to the VRI.

VRIs made the news recently in this article:

https://www.universetoday.com/149559/since-theres-no-up-or-down-in-space-how-do-our-brains-deal-with-this/

If that universetoday link didn’t work, this might:

https://www.sciencetimes.com/articles/29132/20210115/up-down-direction-space-research-reveals-brains-deal.htm

I’m hoping that someone can help to put all the pieces together and explain how VRIs and higher dimensions could be related.

[Hugh]

I joined Twitter yesterday to learn more about VRIs.

As far as I know, VRIs involve the firing of Head Direction cells in the brain.

I have been following researchers in the field of spatial navigation and hope to learn more about the phenomenon.

https://twitter.com/VRIs_Hugh

[Hugh]

Is there a way to show or animate this fascinating higher dimensional VRI explanation by Phil?

“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.”



Does the answer involve something from this?



I got that from this site:

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

[ICN5D]

Well, maybe, it could be animated. Or, illustrated to some degree which still requires a bit of handwaving and declaring where the analogy works and fails. Maybe the 3D projection of a 3d shape revolving around in 4d? Like a torus, for instance. As the torus revolves, it flattens down to a 2d image at 2 points of the rotation, and expands fully at two other opposing points. Maybe drawing on the idea that the 2d image stays constant, while the rest of the 3d-ness of the shape transforms, sort of shows us how we can revolve around stationary 2-planes like a flag pole. It's a stretch, I dunno ....

[Hugh]

Well, maybe, it could be animated. Or, illustrated to some degree which still requires a bit of handwaving and declaring where the analogy works and fails. Maybe the 3D projection of a 3d shape revolving around in 4d? Like a torus, for instance. As the torus revolves, it flattens down to a 2d image at 2 points of the rotation, and expands fully at two other opposing points. Maybe drawing on the idea that the 2d image stays constant, while the rest of the 3d-ness of the shape transforms, sort of shows us how we can revolve around stationary 2-planes like a flag pole. It's a stretch, I dunno ....

Interesting possibilities, ICN5D!

The actual flip is like a Necker cube and is instantaneous, so there is less of a revolution and more of an axis interchange.

Like when you see a Necker cube flip it does it all at once and there is no halfway.

Maybe there is a way to show 3 axes of a “3D slice viewpoint” flip various ways to line up with the 4 axes.

I’m thinking we only have a 3D slice limited viewpoint of all higher dimensions because we look along one axis, along with the other two, up/down and right/left so all higher dimensions must be accessed by flipping around the whole of those 3 dimensions as a slice to a whole new orientation at once, with a VRI.

I’m thinking a 90 degree VRI is to an adjacent cube viewpoint and a 180 degree VRI is to the opposite cube viewpoint.



I would love to see this more clearly somehow.

[Hugh]

If this is a 2D representation of a perceived 3D Necker Cube which flips orientation along common 1D lines...

I need to show a 3D representation of a 4D Necker Cube which flips orientation along common 2D planes.

Any ideas?

[Hugh]

Imagine being 4D in a 4D tetracube, with only a “one 3D slice cube” limited viewpoint of that space. There are all these other different cube viewpoints available within that same space, but they are each only from different directions.

[Hugh]

In the movie Interstellar, Murphy’s bedroom is shown in the tesseract with time as the 4th dimension. If you substitute space as the 4th dimension, you get a hint at what being inside 4D space with a 3D slice view is like. Kind of like the totality of what you can see with VRIs.

[Hugh]

https://blogs.scientificamerican.com/roots-of-unity/nothing-is-more-fun-than-a-hypercube-of-monkeys/



This sculpture is called More Fun than a Hypercube of Monkeys and is explained in the article above.

There is a monkey at the centre of each of the 8 cubes of a tetracube.

As it is rotated, you can see how the monkeys are being rotated around to all of the possible positions within that space.

If we are 4D (or higher) ourselves, in a 4D (or higher) universe, but we only have a limited “3D slice” viewpoint of that space, this is how that 3D slice viewpoint could be turned around within that space to see the various orientations of perceived 3D things from different directions with VRIs.

The idea is that we’re the 4D creature in 4D space but because of our limited 3D viewpoint we can see that perceived 3D space from other directions, and this sculpture shows what the other directions would be which is other orientations of our perceived 3D slice viewpoint with a Necker Cube type of VRI flip.

[Hugh]

We sit in what appears to be a 3D room as we look all the way around it, but what if there is a higher dimension to it, how would it appear to us? Perhaps if we were to look at it from that higher dimension, we would see it from that other, new direction.

[Hugh]

I’ve been working on a better way to show how we might be seeing higher dimensions when we experience VRIs. We can see the same thing from different directions! It has always amazed me how that is even possible. What drives me to continue is an effort to help science.

[Hugh]

Could this be a way to show the 4 orientations in 4D that do not change what you see in 3D that ICN5D was talking about?

[Hugh]

https://twitter.com/VRIs_Hugh/status/16 ... 2758484992

There is a great animation here of a sphere being reversed in a hypersphere. http://matematita.science.unitn.it/4d/i ... ex_en.html

“To describe the hypersphere, the 4D analogon to the sphere, we can think of two solid tori that are glued together in such a way that the meridians on the surface of one torus coincide with the parallels on the surface of the other one, and viceversa. In the animation meridians and parallels are painted with different colours to emphasize the identification.

A sphere, painted blue outside and pink inside, is in the hypersurface of the hypersphere, inside one torus. We inflate the sphere till it touches the surface of the torus in a meridian. Since the surfaces of the tori are identified, the sphere appears also on the other torus, along a parallel.

We inflate the sphere further and the part on the surface of the tori passes entirely inside the second torus, till the sphere is represented by two disks (in the first torus) which are adjacent to an annulus (inside the second torus).

Now we can deflate the sphere symmetrically and it returns inside the torus where it was at the beginning, but painted pink outside. In other words, it is reversed: the inside surface is now outside and viceversa.”

This kind of reminds me of a 3D slice viewpoint of a 4D being looking at different orientations “all the way around” of that 4D space.