Dimensional Discourse

I just felt I should elaborate on how one might retrain himself to be able to visualize 4D without the aid of virtual reality since I may have focused too much on VR in my last post.First of all, a hypothetical 4D analog of a human would have a basically 3D retina, just as a normal human's retina is basically 2-dimensional. The trick is to be able to form a 3D image in your mind where you can "see" every point in the image, including the back, the front, and every internal point, all simultaneously. This should take a while to master, though. It might help at first if you make the image "transparent" so you can see all the points at once, or maybe just imagine one slice at a time of the image. As for depth perception, you could either try to picture 2 individual 3D retinas and try to apply parallax shift, or just use something like color-coding to assign depth (This is all still in your mind).Now, about rotating objects in 4D. There are actually 6 rotational "axes" in the 4th spatial dimension, not 5. It's probably better to think in terms of planes of rotation rather than in terms of rotating around an axis, as an "axis" is 2D in the 4th dimension. You can find the number of rotational planes with the formula r = (n^2-n)/2, where r is the number of rotational planes and n is the number of dimensions.I'll try to help you visualize 4D rotation.

      __________        /|     |     |\        __________
|          |      / |     |     | \      |          |
|          |     |  |     |     |  |     |          |
|          |     |  |     |     |  |     |          |
|          |     |  |     |     |  |     |          |
|__________|      \ |     |     | /      |__________|
\|     |     |/

Above is as good a picture I can do of a square rotating in the 3rd dimension. As you can see, one side "grows" as the other "shrinks," and they appear to come closer together until you're seeing the square on edge; then the process reverses. Keep in mind that this is only an apparent distortion of the square.For rotation of a cube in 4D, first imagine just a plane cube. Now distort it similar in fashion to how I distorted the square, only "shrink" one face while "enlarging" the opposite face, at the same time, bringing the two opposite faces closer together. This should look like the cube distorting into a frustum and finally flattening into a square, the square being the "edge-on" view of the cube.I hope this helps.

Again, as others have...you assume direction is applicable.
Did it ever occur to you that visualization is intrinsic to 3 dimensions? To think of visualization limits you. Did it ever occur to you that a fourth dimension may be beyond physical? All we know to be physical lies in our 3 dimensional world. I do find it curious that many discuss 4th or greater dimensions with seriousness as if they exist and many of the same people have a real problem with any other similarly non provable myths.

Many people, when they first hear that a fourth spatial dimesion means a space that can include 4 mutually perpendicular lines, think that it is impossible because neither can they visualize it, nor can they point in this new direction. One reason you cannot visualize such a space is that you have never directly experienced anything like it, so you assume direction is not applicable.Visualization is not intrinsic to 3D. Imagine a Flatlander; he could only see a line in front of him. He would not be able to visualize 3D because he had never experienced it, nor could he ever consider shapes like circles or squares to be flat, since they have both width and depth. Similarly for us, we might not be able to imagine a 4th spatial dimension, but that does not make one impossible. I believe an intuitive grasp of higher spatial dimensions is only a matter of training. Of course. It's not impossible to conceive that there could exist an extra "spiritual" dimension. However, as I believe someone else has mentioned before on this thread, we would not call it a fourth dimension if it had nothing in common with the three below it. For instance, even though time is a dimension, we do not call it the fourth dimension because it is so different in nature from the three spatial dimensions. Thus, even if there is another dimension "beyond physical," I would not call it the fourth dimension; it would be just another dimension in its own category. I would not dismiss the existance of higher dimensions so quickly. String theory, which has mathematically reconciled relativity and quantum mechanics, may very well be true, though scientists are still not sure whether they can test for it. If it does turn out to be true, then there are actually higher dimensions, only curled up very tightly so as to be shorter than the width of a proton.Now don't think I believe there is an actual fourth spatial dimension of macroscopic scale "somewhere out there." Probably very few people believe one actually exists. But being able to visualize higher dimensions would certainly be useful in the real world, especially when trying to understand the relationships between many variables and to more intuitively see trends among them. Economics, for instance, often involves many more variables than three, so being able to visualize higher spatial dimensions would allow an economist more readily to notice trends in the data than by simply looking at numbers (think about graphing on a 4D coordinate system).Again, a macroscopic fourth spatial dimension probably doesn't exist, but a theoretical fourth dimension certainly has its applications.

Yes I would have to agree with you. A new way to see things often offers us something of value. A fresh perspective. It is far to often though, that a fourth or greater dimension is discussed as if there is such a thing.

quote:

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1. Does anyone have any suggestions on visualizing/perceiving 4D, or any of its properties, beyond mere 3D analogues?

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I wish i could help, iv been trying figure out how to create
4d image on a computer useing the program language called visual basic and vector math with no success. I can only create 3d projections of the 4d object on the 2d screen.
That means the image is projection of a projection of the 4d object.
This problem gets worse when u try to express objects of increasing greater dimensions as projections on the 2d screen.
Maybe if i had a holographic projector i could do 4d projections in 3d but even with that a don't think the projector would be capable of creating a 4d image.
Not including time there's length, width and depth.
I just cant think what the fourth one would be with out resorting
to 3D analogues,all though iv been trying to for 15yrs

quote:

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3. Is the concept of a spacetime (not ours; just hypothetically) with more than one temporal dimension possible? If so, what would be the properties of such a universe? What would life there be like? Could anything even exist in it or would causality fragment into chaos?

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Like time moveing at differant rates in differant parts of the universe?
and or
Mabey time moveing backwards in one place and forwards somewhere else?

quote:

---

1. Does anyone have any suggestions on visualizing/perceiving 4D, or any of its properties, beyond mere 3D analogues?

---

I wish i could help, iv been trying figure out how to create
4d image on a computer useing the program language called visual basic and vector math with no success. I can only create 3d projections of the 4d object on the 2d screen.
That means the image is projection of a projection of the 4d object.
This problem gets worse when u try to express objects of increasing greater dimensions as projections on the 2d screen.
Maybe if i had a holographic projector i could do 4d projections in 3d but even with that a don't think the projector would be capable of creating a 4d image.
Not including time there's length, width and depth.
I just cant think what the fourth one would be with out resorting
to 3D analogues,all though iv been trying to for 15yrs

quote:

---

3. Is the concept of a spacetime (not ours; just hypothetically) with more than one temporal dimension possible? If so, what would be the properties of such a universe? What would life there be like? Could anything even exist in it or would causality fragment into chaos?

---

Like time moveing at differant rates in differant parts of the universe?
and or
Mabey time moveing backwards in one place and forwards somewhere else?

quote:

---

1. Does anyone have any suggestions on visualizing/perceiving 4D, or any of its properties, beyond mere 3D analogues?

---

I wish i could help, iv been trying figure out how to create
4d image on a computer useing the program language called visual basic and vector math with no success. I can only create 3d projections of the 4d object on the 2d screen.
That means the image is projection of a projection of the 4d object.
This problem gets worse when u try to express objects of increasing greater dimensions as projections on the 2d screen.
Maybe if i had a holographic projector i could do 4d projections in 3d but even with that a don't think the projector would be capable of creating a 4d image.
Not including time there's length, width and depth.
I just cant think what the fourth one would be with out resorting
to 3D analogues,all though iv been trying to for 15yrs

quote:

---

3. Is the concept of a spacetime (not ours; just hypothetically) with more than one temporal dimension possible? If so, what would be the properties of such a universe? What would life there be like? Could anything even exist in it or would causality fragment into chaos?

---

Like time moveing at differant rates in differant parts of the universe?
and or
Mabey time moveing backwards in one place and forwards somewhere else?

quote:

---

Visualization is not intrinsic to 3D. Imagine a Flatlander; he could only see a line in front of him. He would not be able to visualize 3D because he had never experienced it, nor could he ever consider shapes like circles or squares to be flat, since they have both width and depth. Similarly for us, we might not be able to imagine a 4th spatial dimension, but that does not make one impossible. I believe an intuitive grasp of higher spatial dimensions is only a matter of training

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An interesting problem, he can look side to side and forward and back
but not up and down because that's not a possibility for him in his 2d world.
So the question i have to ask is this,
if i can look side to side and forward and back AND
up and down, what is that other direction to look
in that's not a possibility for me to perceive because i am a 3d lander.
"I've been trying to figure this out for the last 15yrs."

quote:

---

Visualization is not intrinsic to 3D. Imagine a Flatlander; he could only see a line in front of him. He would not be able to visualize 3D because he had never experienced it, nor could he ever consider shapes like circles or squares to be flat, since they have both width and depth. Similarly for us, we might not be able to imagine a 4th spatial dimension, but that does not make one impossible. I believe an intuitive grasp of higher spatial dimensions is only a matter of training

---

An interesting problem, he can look side to side and forward and back
but not up and down because that's not a possibility for him in his 2d world.
So the question i have to ask is this,
if i can look side to side and forward and back AND
up and down, what is that other direction to look
in that's not a possibility for me to perceive because i am a 3d lander
"I've been trying to figure this out for the last 15yrs."

Direction may have nothing to do with it. The concept of direction is a 3d concept.

You have limited yourself to understanding a higher dimension with only one of the five senses. You are assuming that a higher dimension involves a physical direction. An idea is not a physical direction. I did not say that math was not a usefull tool. Just not in this instance. Again you go on the assumption that a higher dimension has physical direction and that it can be visualized.
I am saying we experience a higher dimension already. We just do not see it for what it is.