Beware of quickfur

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Beware of quickfur

Postby 4Dspace » Thu Jul 19, 2012 4:49 pm

This is to alert the newcomers to the forum about quickfur, who has no understanding of the basic tenets of geometry, is generally confused and spreads his confusion around. The bottom line: you should take his answers about the 4D visualization with a huge grain of salt.

Yes, quickfur created a 4D website, in order to help himself understand 4D. Unfortunately, it did not help him understand nor see even the simplest objects, like a cube, in 4D. This fact is plainly apparent in the thread "Dimentional Baby Steps" http://teamikaria.com/hddb/forum/viewtopic.php?f=27&t=1705.

To spare you the necessity of wading through all 4 pages and over 100 posts in that thread (as of july 19 2012), below are the key quickfur's posts that show that not only he does not see 4D, but has trouble admitting his errors. Worse, he is stubbornly set into protecting his "reputation", which makes him not a contributor to the site, but a resident troll, seeking not knowledge but his own aggrandizement at the expense of the unsuspecting visitors.

Being confused is not a crime; it can happen to all. To spew one's own confusion to others and stubbornly insist on it is.

quickfur joined the site in 2004, which means that for nearly 8 years he was generously giving out wrong answers to people about the aspects of 4D visualization. If you bother to read over 1000 of his posts, you will see his arguments with people who disagreed with his wrong take on things. However, in absence of a moderator or another authority who could have set him right, he managed to "convince" those people that they were wrong and he right. His claim to authority is his website. But it did not help himself see 4D, so what is its value to others?

The forum suffered as the result. Unable to outargue him, people leave. Some leave convinced that they are unable to understand 4D, only because quickfur stubbornly imposed his personal misunderstandings on them.

And so, below are the quotes from the thread that plainly show that when it comes to 4D, quickfur is blind as a bat.

It started with ac2000 asking a simple question, if one writes on the faces of a cube, will the writing be visible in 4D:
ac2000 wrote:if I have a 3D cube and write a number on opposite sides of this cube, would it be possible for a 4D being to read both numbers from a single visual angle? Or couldn't it read any of the numbers at all because they are too flat and it can only perceive the sides of the cubes as edges?

The correct answer to this question is: all 6 faces of a cube are visible from 4D. However, from a given POV, 3 faces are viewed from 'outside' and 3 from 'inside'. Since the writing is on the outer side of the faces, it is visible only on those faces in 4D that show their 'outer' side to the given POV.

Our "expert" in 4D seeing quickfur answered that in 4D, the 2d-planes that comprise the faces of the cube are seen from both sides simultaneously, which violates the most basic tenet of Euclidean geometry, namely, that only one side of a plane is visible to a POV at any time:
quickfur wrote: Now the key here is to understand that every "voxel" in that 3D array is visible to the 4D being simultaneously. That is to say, they do not merely see the surface of a sphere or the surface of the cube; they see the entire 3D volume of both objects, every point on the surface, and every point the interior, all at the same time.

I objected to this wrong answer:
4Dspace wrote:This is wrong. Why are you stubbornly continue to spread this disinfo after the discussion that established that at any given moment, a 4Der sees only one side of the object, just like the rest of the NDers in all possible N-Universes?

The correct answer is: a 4Der will see only one side of each plane of the cube at a moment, but as he will change his POV, he will get to see the opposite sides as well. But not at the same time. Just like we have to turn the cube around to see its far face.

To which quickfur revealed his first misunderstanding :
quickfur wrote:What we consider as the "sides" of a cube has absolutely nothing to do with the "side" of the cube that the 4Der sees from her vantage point.

Which shows that, according to him, a cube stops being a cube once it is put into the 4D-space, as the planes that make up its faces apparently turn to mush. But the mush is not in geometry of 4D, the mush is in quickfur's head: he personally can't see the details and so he projects his lack of clarity to his mythical "4Der". But putting the cube in 4D does not make the panes that comprise its faces disappear. They still exist and relate to a given POV by showing only one of their side at a time.

And so, the argument between me and quickfur ensued that lasted for the following 4 pages, during which it turned out that quickfur lacked understanding of POV (point of view) in 4D and how it related to geometry in 4D, which, in turn, determines what aspects of a structure are seen in whatever D. And that is determined, first of all, by the line of sight set by the POV. Vision, first of all, is determined by a POV.

Which begs the question: Given pages and pages of quickfur's endless babble about the "4Der vision", what was that all about in absence of a clearly defined POV?

It turned out that quickfur got into his messy "4Der vision" by misusing the analogies, going from 2D to 3D to 4D. Going from 2D to 3D, he forgot that there is only 1 vector perpendicular to a plane in 2D, which coincides with the general line of sight from a POV in 3D (looking at 2D). There are 3 such vectors in 3D (as looked at from 4D), but still, always, only 1 line of sight, in any D. Thus he imbued his "4Der vision" with remarkable quality that allowed his mythical creature to capture the light going simultaneously in 3 orthogonal directions, which is impossible in principle, unless the "4Der's retina", instead of being confined to a POINT of view, surrounds the object instead.

By playing a bit stupid I managed to make him see this error. However, ever so mindful of his "reputation", quickfur could not admit it openly. He merely stopped painting me as dense as he paints his "2Ders" and stopped have-a-nice-day me. And just think how many people left the forum in the past under the similar circumstances!

And so it took another week-worth of posts to make him understand the basic tenet of Euclidean geometry, namely that only one side of a (hyper)plane is shown to a given POV, in any N-space. Which, to this moment, quickfur was not able to admit. Which means that he will stubbornly continue to give out wrong answers to the unsuspecting visitors of the site in regard to the aspects of the 4D space and 4D visualization.

His inability to admit his errors and trying to BS people, for whom geometry may be a novel thing, into seeing him as an authority on the subject (only because he put up a 4D site) is what makes quickfur a resident troll, detrimental to the success of the forum.

Unless he learns from our discussion and sorts out the mess in his head, I advise everyone to take his input with a huge grain of salt.

Good luck :D
Last edited by 4Dspace on Fri Jul 27, 2012 10:33 pm, edited 1 time in total.
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Re: Beware of quickfur

Postby wendy » Fri Jul 20, 2012 7:22 am

I have read all of quickfur's answers in that list, and have not found anything wrong with them. These are very similar to what i do, and the method i use to make six dimensions visible.

I have had a number of quite intelligent conversations with him.

Many persons do not have the ability to see four dimensions, and must rely on Abbot's Flatland or similar to draw the 2/3 to 3/4 dimensional analogy. When you look at a computer screen, you are not looking at three dimensions, but two. That means that renders of the surface a 4d person might see is actually produced not only as a solid object, but as one which is translucent to our vision. Yet the whole thing from what we see as side to side, is for the 4d as edge to edge.

One must understand that a good deal of the fault comes from the language. I have tried in some part to show in the polygloss, that one needs to shift the meanings of words into quite separate meanings, in order to grasp the higher dimensions. Side, for example, can mean the bounding surtope of a square or a cube or a tesseract. There are classes of polytope in hyperbolic space, where side is a collection of faces, that are connected to each other but not to any other set of faces that make a different side.

if I have a 3D cube and write a number on opposite sides of this cube, would it be possible for a 4D being to read both numbers from a single visual angle? Or couldn't it read any of the numbers at all because they are too flat and it can only perceive the sides of the cubes as edges?


The 4D can read all six sides of the cube in exactly the same way we see the four sides of the square. They are also to make out impressions in the faces, because they are neither inside or outside the square/cube, but in a space over (ie hyper) to it. They see the cube in all its glory in the same way we see a square. We can only see the interior of the cube if it is rendered translucent.

Now the key here is to understand that every "voxel" in that 3D array is visible to the 4D being simultaneously. That is to say, they do not merely see the surface of a sphere or the surface of the cube; they see the entire 3D volume of both objects, every point on the surface, and every point the interior, all at the same time.


You can indeed see every point of a square. The additional dimension granted is an other 'across dimension', so while we see on our table, the points of a square, in 4D, the table is still a plane, but the plane, for dividing 4D, is 3D, and every point therein can be directly connected to the eye without going through any other point on the table. [/quote]

To which you reply:
This is wrong. Why are you stubbornly continue to spread this disinfo after the discussion that established that at any given moment, a 4Der sees only one side of the object, just like the rest of the NDers in all possible N-Universes?

The correct answer is: a 4Der will see only one side of each plane of the cube at a moment, but as he will change his POV, he will get to see the opposite sides as well. But not at the same time. Just like we have to turn the cube around to see its far face.


Here you play on the meaning of 'side'. A sheet of paper has two sides, while a square has four sides. You can see only one side of a sheet of paper, but all four sides of the square. The actual field of vision is to give a plane, or a N-1 space, that is in triangular product with the eye. In short, light would climb the rays from the eye to a plane, so the plane must therefore divide space.

It turned out that quickfur got into his messy "4Der vision" by misusing the analogies, going from 2D to 3D to 4D. Going from 2D to 3D, he forgot that there is only 1 vector perpendicular to a plane in 2D, which coincides with the general line of sight from a POV in 3D (looking at 2D). There are 3 such vectors in 3D (as looked at from 4D), but still, always, only 1 line of sight, in any D. Thus he imbued his "4Der vision" with remarkable quality that allowed his mythical creature to capture the light going simultaneously in 3 orthogonal directions, which is impossible in principle, unless the "4Der's retina", instead of being confined to a POINT of view, surrounds the object instead.


The actual confusion is yours. There are three orthogonals in 3D, two lie in the plane, and one lies in the direction of the eye. In 4D, there are 4 orthogonals, of which one lies in the direction of the eye, and three lie orthogonal to it. It is quite possible to construct a figure in the space orthogonal to the eye-ray, and the being, whether 2D or 3D or 4D will see all of it, without any further crossing of the orthogonal space. The point is the 4D viewer can see us, what we see, and everything beyond it, in the manner that our eyes can see all the width of a film, without having to see through the charactors thereon.

And so it took another week-worth of posts to make him understand the basic tenet of Euclidean geometry, namely that only one side of a (hyper)plane is shown to a given POV, in any N-space. Which, to this moment, quickfur was not able to admit. Which means that he will stubbornly continue to give out wrong answers to the unsuspecting visitors of the site in regard to the aspects of the 4D space and 4D visualization.


Again, we see a confusion of terms. A hyperplane is all-space. hyper- means over, and plane means dividing space. All-space of N dimensions divides a space of N+1 dimensions, and therefore a hyperplane. You freely let 'plane' vary from 'two-dimensional' to 'dividing space' and back, simply to add confusion. The actual progression into higher dimensions involves also a clear mind of what is meant, whether it is 2 or N-1. You need to do this, because words for 3D freely vary across 2 and N-1, or 1 and N-2, etc, but in four or six dimensions, the spaces of 2 and N-1 now become 2 and 5 dimensions.

A square has four sides, a cube has six sides. Here we read side not as 1 or 2 dimensions, but as M-1 dimensions, where M is the solid dimension of the object. Since we can render the square as a thin slab prism in three dimensions, it has then 2 sides. Such occur, for example in coins, which have two sides (heads and tails), and twelve sides from their dodecagonal perimeter. It is wise to be wary of this.

Which shows that, according to him, a cube stops being a cube once it is put into the 4D-space, as the planes that make up its faces apparently turn to mush. But the mush is not in geometry of 4D, the mush is in quickfur's head: he personally can't see the details and so he projects his lack of clarity to his mythical "4Der". But putting the cube in 4D does not make the panes that comprise its faces disappear. They still exist and relate to a given POV by showing only one of their side at a time.


Side here has several different meanings, all being freely used. It does not matter whether side or face or whatever is meant. The dodecahedron has 12 sides, we can at any time see four or six of these at once. Close up, we can reduce this to one. The POV of a 4d person viewing a dodecahedral side of a twelftychoron, is to see something like sixty sides (faces), on the facing half of the polytope. Yet the full measure of the sides (faces) are revealed to a 4D person because the sides (faces) are all in the side (facing half) of the polytope. It's a confusion of terms that lawyers love to pick apart.

I rather that you take a better grasp of what is being shown and not let loose on the variations of words. One of the many faults with the higher dimensions, is simply the inadequaticy of words to show what is being said.
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Re: Beware of quickfur

Postby 4Dspace » Fri Jul 20, 2012 11:18 am

Thank you wendy for taking time to reply. I wish we had an opportunity to talk before, but, somehow, it did not happen.

wendy wrote:I have read all of quickfur's answers in that list, and have not found anything wrong with them. These are very similar to what i do, and the method i use to make six dimensions visible.

To me this means only one thing, namely that you'are just as unskilled at seeing 4D as he is. Or perhaps you did not understand what the issue is? It is the relationship of any plane --not just 2d-plane, but a 3d-hyperplane as well-- to a line of sight set by a POV, in any number of dimensions.

That's what the issue is. And according to quickfur, and now you, you can do the impossible, namely see planes from their both sides simultaneously in Euclidean spaces, lol. Since you two are the most regular contributors here, the so-called "experts", it makes this forum a sham.

What you and quickfur are saying is impossibility. It is contradictory to the notion of geometry.

wendy wrote:Many persons do not have the ability to see four dimensions, and must rely on Abbot's Flatland or similar to draw the 2/3 to 3/4 dimensional analogy.

I am not such a person. I see 4D very well.

wendy wrote:When you look at a computer screen, you are not looking at three dimensions, but two. That means that renders of the surface a 4d person might see is actually produced not only as a solid object, but as one which is translucent to our vision.

What 4d person? Who are those mythical 4d persons you're talking about here all the time?

wendy wrote: Yet the whole thing from what we see as side to side, is for the 4d as edge to edge.

I find that on this site you overuse analogies with other dimensions, which for most people, including you, it appears, turns out confusing in the end.

wendy wrote:One must understand that a good deal of the fault comes from the language. I have tried in some part to show in the polygloss, that one needs to shift the meanings of words into quite separate meanings, in order to grasp the higher dimensions. Side, for example, can mean the bounding surtope of a square or a cube or a tesseract. There are classes of polytope in hyperbolic space, where side is a collection of faces, that are connected to each other but not to any other set of faces that make a different side.

The meaning of "side" in the context of a (hyper)plane in relation to the POV is straightforward.

wendy wrote:
if I have a 3D cube and write a number on opposite sides of this cube, would it be possible for a 4D being to read both numbers from a single visual angle? Or couldn't it read any of the numbers at all because they are too flat and it can only perceive the sides of the cubes as edges?


The 4D can read all six sides of the cube in exactly the same way we see the four sides of the square. They are also to make out impressions in the faces, because they are neither inside or outside the square/cube, but in a space over (ie hyper) to it. They see the cube in all its glory in the same way we see a square. We can only see the interior of the cube if it is rendered translucent.

Who is this 4D who can read all six outer faces of the cube at once? There is a difference between the "sides" of the square and the faces of the cube. 2d-planes are not 1d-lines. Yet for you, in your misleading analogies, one turns to other when you go from one dimension to the next. This is wrong in principle. The fact that we can see a line in its entirety does not change the fact that only one side of a plane is visible to anyone in any dimension at a time. You are misled by the analogies you're using, when going from one D to another. This is the common problem on this forum.

A line is not a plane. Going from one dimension to another does not change the underlying structures of the object under examination. A plane remains a plane and a line remains a line. A plane does not turn into a line or vise versa, as your analogies on this forum often imply.

wendy wrote:You can indeed see every point of a square.

Correction. I can see every point on the plane of the square. And I see this plane only from one side.

wendy wrote:The additional dimension granted is an other 'across dimension', so while we see on our table, the points of a square, in 4D, the table is still a plane, but the plane, for dividing 4D, is 3D, and every point therein can be directly connected to the eye without going through any other point on the table.

Again, here you confuse points, which are dimensionless entities with planes, which are not. You cannot see points. You can see lines and planes. And while lines are one-dimensional and have no sides (something quickfur, by the way said many time, i.e. that lines have sides, lol) planes and hyperplanes do have sides, and they show only one to a POV.

I am rather surprised and taken aback that on this forum you do not appreciate these subtleties.

wendy wrote:To which you reply:
This is wrong. Why are you stubbornly continue to spread this disinfo after the discussion that established that at any given moment, a 4Der sees only one side of the object, just like the rest of the NDers in all possible N-Universes?

The correct answer is: a 4Der will see only one side of each plane of the cube at a moment, but as he will change his POV, he will get to see the opposite sides as well. But not at the same time. Just like we have to turn the cube around to see its far face.


Here you play on the meaning of 'side'. A sheet of paper has two sides, while a square has four sides.

I do not play on the meaning of side. I emphasize that a plane has sides, which are actually its directions, just like a line has directions. (line does not have sides, though). The 4 sides of a square are completely different thing. Those are the boundaries of a plane.

wendy wrote: You can see only one side of a sheet of paper, but all four sides of the square.

Again, you confuse yourself with wrong analogies. There is hardly any difference between a sheet of paper (presumably a representation of an infinite 2d plane) and a square, which is just a particular segment of the same plane. That the square is bounded and the sheet, presumably, not, is an irrelevant detail in our context. We are talking about the fact that any plane has 2 directions. Both a sheet and a square are planes.

wendy wrote: The actual field of vision is to give a plane, or a N-1 space, that is in triangular product with the eye. In short, light would climb the rays from the eye to a plane, so the plane must therefore divide space.

Is English your native tongue? Cause it's not for me. In any rate, to me, the way you presented it above, sounds like you perhaps drew your conclusions prematurely. That therefore part did not follow what you said.

wendy wrote:
It turned out that quickfur got into his messy "4Der vision" by misusing the analogies, going from 2D to 3D to 4D. Going from 2D to 3D, he forgot that there is only 1 vector perpendicular to a plane in 2D, which coincides with the general line of sight from a POV in 3D (looking at 2D). There are 3 such vectors in 3D (as looked at from 4D), but still, always, only 1 line of sight, in any D. Thus he imbued his "4Der vision" with remarkable quality that allowed his mythical creature to capture the light going simultaneously in 3 orthogonal directions, which is impossible in principle, unless the "4Der's retina", instead of being confined to a POINT of view, surrounds the object instead.

The actual confusion is yours.

Where is my confusion? Perhaps you misunderstood what I said? Because I do know what you are saying below and agree. So, where is my confusion? quickfur however, was confused by this. His confusion showed in how he described his "4Der vision", who was able to see a plane from both sides simultaneously, lol. That was the issue. You seem to be just as unclear on this aspect of geometry as he is.

wendy wrote:There are three orthogonals in 3D, two lie in the plane, and one lies in the direction of the eye. In 4D, there are 4 orthogonals, of which one lies in the direction of the eye, and three lie orthogonal to it.

Yes, this is obvious and is not the source of confusion, at least not for me. quickfur, going from 2D to 4D, forgot about the 3 orthogonals in 3D. All 3 merged into the line of sight of his "4Der", thus enabling his mythical creature to capture rays of light going in 3 orthogonal directions simultaneously. He called it "4Der vision". Lacking POV, and thus able to see everything from all sides simultaneously is the hallmark of his "4Der vision". Unfortunately, a vision without a POV is not a vision, but perhaps echo-location at best.

wendy wrote: It is quite possible to construct a figure in the space orthogonal to the eye-ray, and the being, whether 2D or 3D or 4D will see all of it, without any further crossing of the orthogonal space. The point is the 4D viewer can see us, what we see, and everything beyond it, in the manner that our eyes can see all the width of a film, without having to see through the charactors thereon.

Not sure what you mean here. I find frequent mention of mythical beings on this forum unnecessary. There are spaces of various dimensions though and a POV, to which the light converges. This is much simpler and straightforward in my opinion.

wendy wrote:
And so it took another week-worth of posts to make him understand the basic tenet of Euclidean geometry, namely that only one side of a (hyper)plane is shown to a given POV, in any N-space. Which, to this moment, quickfur was not able to admit. Which means that he will stubbornly continue to give out wrong answers to the unsuspecting visitors of the site in regard to the aspects of the 4D space and 4D visualization.


Again, we see a confusion of terms.

We being... who?

wendy wrote: A hyperplane is all-space. hyper- means over, and plane means dividing space. All-space of N dimensions divides a space of N+1 dimensions, and therefore a hyperplane.

No, I use the terms as they are used by most. A plane is a 2d plane, and a hyperplane is a 3-d plane. That's how it is used by most.

wendy wrote: You freely let 'plane' vary from 'two-dimensional' to 'dividing space' and back, simply to add confusion.

No, I don't. That's what you ascribe to me. What I am saying, merely, is that a plane (or a hyperplane) has 2 directions, which can be expressed as its chirallity, and that a (hyper)plane can show its only ONE SIDE to a given POV. Do you disagree with this statement?


wendy wrote: The actual progression into higher dimensions involves also a clear mind of what is meant, whether it is 2 or N-1. You need to do this, because words for 3D freely vary across 2 and N-1, or 1 and N-2, etc, but in four or six dimensions, the spaces of 2 and N-1 now become 2 and 5 dimensions.

Again, you speak of clear mind, yet your manner of expressing yourself does not support it. Perhaps English is not your native language?

wendy wrote:A square has four sides, a cube has six sides.

you confuse yourself with these sides. A cube has 6 faces. A square has one face. A cube is made of 6 planes, a square is made of one plane. Hope this is clear for you as it is for me.

wendy wrote:Here we read side not as 1 or 2 dimensions, but as M-1 dimensions, where M is the solid dimension of the object. Since we can render the square as a thin slab prism in three dimensions, it has then 2 sides. Such occur, for example in coins, which have two sides (heads and tails), and twelve sides from their dodecagonal perimeter. It is wise to be wary of this.

That's where your trouble lies. You change the nature of objects going from one dimension to another, as if this is the most natural thing to do. A square is still a square, no matter in what N-space you put it. Same for the cube. It will still be made of 6 planes, just as square will still remain a plane. It will not turn to prism.

This was the mistake quickfur was making all the time. Going from 1 D to another, lines turned to planes and planes to lines, faces to edges and back. This is crazy. No wonder you people here are so confused. You are confused by overuse of your analogies. An object remains what it is in whatever N-space you put it.

wendy wrote:
Which shows that, according to him, a cube stops being a cube once it is put into the 4D-space, as the planes that make up its faces apparently turn to mush. But the mush is not in geometry of 4D, the mush is in quickfur's head: he personally can't see the details and so he projects his lack of clarity to his mythical "4Der". But putting the cube in 4D does not make the panes that comprise its faces disappear. They still exist and relate to a given POV by showing only one of their side at a time.


Side here has several different meanings, all being freely used. It does not matter whether side or face or whatever is meant.

If you read my discussion with quickfur, you'd know that what I meant by the side of a plane was, first of all, its chirality, which is the plane's direction.

wendy wrote:The dodecahedron has 12 sides, we can at any time see four or six of these at once.

No, the dodecahedron has 12 faces.

wendy wrote:
Close up, we can reduce this to one. The POV of a 4d person viewing a dodecahedral side of a twelftychoron, is to see something like sixty sides (faces), on the facing half of the polytope. Yet the full measure of the sides (faces) are revealed to a 4D person because the sides (faces) are all in the side (facing half) of the polytope. It's a confusion of terms that lawyers love to pick apart.

I don't have this problem. It's you who is confused.

wendy wrote:I rather that you take a better grasp of what is being shown and not let loose on the variations of words. One of the many faults with the higher dimensions, is simply the inadequaticy of words to show what is being said.

"faults with the higher dimensions"? I do not assign faults with dimensions. The faults lie with faulty assumptions and lack of coherence when going from one D to another, which is a bad habit for many people on this board.
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Re: Beware of quickfur

Postby wendy » Sat Jul 21, 2012 9:57 am

There are some general comments, before we move onto specifics.

1. Euclidean geometry has no notion of 'sides'. What happens is that a 1-sphere has a surface of two points, and any subspace in a space that has a 1-sphere as its orthospace, is capable of dividing the space, and thus "have sides" in that space. In 4D, a hedrix or 2-space does not divide 4-space, and therefore does not have 'sides'.

Also, in euclidean geometry, all-space itself has no sides, since it does not substain a perpendicular vector.

2. The mythical 4D creature, and a POV are identical idioms. The 4D creature does provide the POV.

3. The path to higher dimensions is through a clear word-set. Many of the words in common use in the subject are misplaced idioms.

cells in common parlance means a solid element of a tiling, such as in cellular automata, and board games that are played on a tiled board. The general meaning is the same as 'bubble in a foam', and it is from various presentations of a surface of a 4D polytope that this word migrates. Using it as a specific meaning has the same effect as calling the squares of a tesseract 'cells', because the cells in Conway's game of Life are squares. In the PG, cell is restored to its general meaning.

plane has the general meaning of 'dividing space', specifically, something that supports against gravity etc. Along with face, this is restored to the meaning of 'dividing space'. Were one to follow the common meaning, 'face' could end up as 2D, while a 'facet' (little face) as 5D, and the 'facing side' as 5D. So go figure. You seem to be caught by the notion that a plane can be both 2D and a dividing space.

hyperplane has a respectable etymology, meaning 'above-plane'. Specifically, the meaning of hyperplane and hyperspace in the PG both expresses the correct etymology and correct use of these. What you are doing with it, is like saying 'the second floor is above us, and so is upstairs', and then applying 'upstairs' to the second floor when you're on the sixth one.

To me this means only one thing, namely that you'are just as unskilled at seeing 4D as he is. Or perhaps you did not understand what the issue is? It is the relationship of any plane --not just 2d-plane, but a 3d-hyperplane as well-- to a line of sight set by a POV, in any number of dimensions.

That's what the issue is. And according to quickfur, and now you, you can do the impossible, namely see planes from their both sides simultaneously in Euclidean spaces, lol. Since you two are the most regular contributors here, the so-called "experts", it makes this forum a sham.

What you and quickfur are saying is impossibility. It is contradictory to the notion of geometry.


If you wish to deal with so-called "experts", then i shall use the terminology of the PG, which is specifically designed for higher dimensions. It teases apart the meanings of words to seperate meanings.

A. By the rules of geometry, a hedrix can only have sides when embedded in a chorix, not in a terix. So there are no sides to a 2d space.

B. No contention exists that supposes that the POV needs to be in the space being viewed. Many of your comments suppose that the viewer must be in a chorix where the subject exists. If the POV exists outside a space, then any ray from the POV to the space only passes through one point of that space. A POV in four dimensions can resolve the entirity of a chorix and anything therein, say a cube, as readily as us, for not being in a hedrix, can see the entire hedrix, and anything therein.

Likewise, a line in 2D, such as a frontier between countries, has two sides. On a map, one is readily able to examine both sides of the line without having to flip it. The surface rendered is a hedrix (specifically, coordinates of the earth), and is perfectly rendered witlout loss on a sheet of paper. A hedrix has no sides, the paper has a hedrix on each side, and perfectly shows the hedrix without the need to flip.

What 4d person? Who are those mythical 4d persons you're talking about here all the time?

It's the same as your POV. We just make it solid relative to four dimensions, to avoid falling in your trap.

The meaning of "side" in the context of a (hyper)plane in relation to the POV is straightforward.


A space has no sides. You need to embed it in a space that it divides for it to 'have sides', and to place the POV in the containing space for the 'far side' to not be observable. It's a pretty simple concept really. In any case, the sides only exist when one is considering the embedding space, and in that case, the embedding space does not have sides.

Who is this 4D who can read all six outer faces of the cube at once? There is a difference between the "sides" of the square and the faces of the cube. 2d-planes are not 1d-lines. Yet for you, in your misleading analogies, one turns to other when you go from one dimension to the next. This is wrong in principle. The fact that we can see a line in its entirety does not change the fact that only one side of a plane is visible to anyone in any dimension at a time. You are misled by the analogies you're using, when going from one D to another. This is the common problem on this forum.

A line is not a plane. Going from one dimension to another does not change the underlying structures of the object under examination. A plane remains a plane and a line remains a line. A plane does not turn into a line or vise versa, as your analogies on this forum often imply.


Suppose one has a coordinate system in three dimensions, where the POV is (2,0,0). The square is a conventional coordinates in y,z, gives (0,±1,±1), Any line from the POV to the plane x=0 will pass through only point, and the only notion that the edges of the square has sides, comes from recognising the object as having that number of sides. Likewise, the POV (2,0,0,0), viewing the conventional cube (0,±1,±1,±1), can render all six sides of the cube, and the 'inside' and 'outside' of the cube in exactly the same manner.

In this sense, the sides of the cube only have meaning when these are rendered in a chorix. Since the cube is already chorid itself, it is feasable that it can both have 12 sides like the dodecahedral coin and heads-and-tails sides.

Again, here you confuse points, which are dimensionless entities with planes, which are not. You cannot see points. You can see lines and planes. And while lines are one-dimensional and have no sides (something quickfur, by the way said many time, i.e. that lines have sides, lol) planes and hyperplanes do have sides, and they show only one to a POV.


The meaning of words like 'deadline', 'line in a sand', 'front line', 'toe the line', all suggest that a line has sides, which has different conditions on each side. This is because line exists in a space where it divides, and the meaning is what is being divided. A dead line is something you step over and you're dead. A line in the sand is also a line to be crossed: that is, something is different on the other side.

In 4D, this sense is not preserved, since space, divided by gravity and a surface division, can never give a line.

I do not play on the meaning of side. I emphasize that a plane has sides, which are actually its directions, just like a line has directions. (line does not have sides, though). The 4 sides of a square are completely different thing. Those are the boundaries of a plane.


Lines do have bounding extents - they're called 'ends' or 'vertices'. Lines, like planes, are not vectors. They do not have directions, You need something else to provide a specific item. If you're going to be pedantic on keeping the same dimensional terminology throughout, if a square has sides in 3D, then it has sides in 4D, even though it is a side of a cube in 3D and 4D. In this sense, you are tying side to the meanings variously held by 'face' and 'margin' in the PG.

Again, you confuse yourself with wrong analogies. There is hardly any difference between a sheet of paper (presumably a representation of an infinite 2d plane) and a square, which is just a particular segment of the same plane. That the square is bounded and the sheet, presumably, not, is an irrelevant detail in our context. We are talking about the fact that any plane has 2 directions. Both a sheet and a square are planes.


The fact that a square can be rendered completely on one side of a sheet of paper blows apart your theory that a plane has two arounding-sides. It is sufficient to see the full extent and detail of a square from a single POV, even though the paper has two sides. The other side of the same paper can contain an entirely different view of a different plane. A plane, thus, has no side, as is evident from endoanalysis.

Yes, this is obvious and is not the source of confusion, at least not for me. quickfur, going from 2D to 4D, forgot about the 3 orthogonals in 3D. All 3 merged into the line of sight of his "4Der", thus enabling his mythical creature to capture rays of light going in 3 orthogonal directions simultaneously. He called it "4Der vision". Lacking POV, and thus able to see everything from all sides simultaneously is the hallmark of his "4Der vision". Unfortunately, a vision without a POV is not a vision, but perhaps echo-location at best.


The assumption here is that the POV is in the same chorix as the object. It isn't.

Not sure what you mean here. I find frequent mention of mythical beings on this forum unnecessary. There are spaces of various dimensions though and a POV, to which the light converges. This is much simpler and straightforward in my opinion.


A tennent of Euclidean geometry is that it is possible to draw a line between any two points. Analysis of this is that if one point lies in a space, and the second does not lie in that same subspace, then there is only one point in the subspace in the line. The whole point of moving the POV into hyperspace is to achieve the same effect that the view of a plane in 3d can be seen from some point in the hyperplane (ie chorix) that is not in 3D.

Likewise, the information in a map is a perfect representation of a hedrix, has no 'front and back', and is amply served on a single side of a page.

And so it took another week-worth of posts to make him understand the basic tenet of Euclidean geometry, namely that only one side of a (hyper)plane is shown to a given POV, in any N-space. Which, to this moment, quickfur was not able to admit. Which means that he will stubbornly continue to give out wrong answers to the unsuspecting visitors of the site in regard to the aspects of the 4D space and 4D visualization.


A plane object, such as a map, plan or picture, in 3d is perfectly rendered on a single side of paper, with little regard to what's on the other side of the same page, so it is inappropriate to speak of 'the other side' of a plane in the sense you are trying to do.

What is stubborn, is that you refuse to admit that the POV of space, for being in hyperspace, yields the entirity of space without any transcept of it.

No, I use the terms as they are used by most. A plane is a 2d plane, and a hyperplane is a 3-d plane. That's how it is used by most.


Which means that you have not got around to either using words in their etymological meanings, and have not got around to untangling meanings. You claim that only '(hyper)planes' can have sides. Firstly, this is incorrect, as i have shown that both points (eg point of no return), and lines can have bounding meanings and sensible meanings of 'sides', and that the meaning of 'side' exists only when the side exists in a space where its orthospace is a line: that is M-1 relative to M. A plane of 2d does not divide 4space.

No, I don't. That's what you ascribe to me. What I am saying, merely, is that a plane (or a hyperplane) has 2 directions, which can be expressed as its chirallity, and that a (hyper)plane can show its only ONE SIDE to a given POV. Do you disagree with this statement?


You confuse the function of hedrix (plane) and chorix (plane) in 4D. This equates to confusing the meaning of line and hedrix in 3D. Both of these are 'sides' in the sense that when gravity rules,a line suffices to divide the ground (which is what a line in the sand, a dead line, a front line do), and a side divides the faces of a cube, yet the cube has six sides, since the six sides divide it from the external space. In short a side supports an outvector.

A dividing space is only one side. There are two spaces on either side of it that may have different natures. Likewise, one does not have to use both sides of a page to represent a plane object, so it can hardly have more than one side from any POV.

you confuse yourself with these sides. A cube has 6 faces. A square has one face. A cube is made of 6 planes, a square is made of one plane. Hope this is clear for you as it is for me.


A cube is a chorid, which supports outvectors pointing in six different directions. In the chorix that it defines, these six boundaries are sides. A square is a hedrid, with four sides, or divisions in the hedrix it supports. This much is evident from endoanalysis. The hedric faces of a cube fail to support the chorid nature of it, as much as the choric nature of the cube fail to support the terid tesseract it is a face of.

This was the mistake quickfur was making all the time. Going from 1 D to another, lines turned to planes and planes to lines, faces to edges and back. This is crazy. No wonder you people here are so confused. You are confused by overuse of your analogies. An object remains what it is in whatever N-space you put it.


Get used to it, hon. The analogies used by quickfur are pretty much those used by Hutton and others.

If you read my discussion with quickfur, you'd know that what I meant by the side of a plane was, first of all, its chirality, which is the plane's direction.


A plane has no chirality. In any case, if a plane did have chiralty, so does a line and all space. In fact, this device is used in endoanalysis to construct a pseudovector which is normal to the chirality of the object, the vector has no real meaning.

"faults with the higher dimensions"? I do not assign faults with dimensions. The faults lie with faulty assumptions and lack of coherence when going from one D to another, which is a bad habit for many people on this board.


You suppose that both a hedrix and a chorix have sides in 4D, and that a POV in 4D is incapable of rendering a chorix without having to look through other parts of it. Further, you suppose that a plane, for dividing space, has several "sides". Yet recourse to simple examples will show that all of these are wrong, unless you suppose the 'view of 4D', is renedered in the same chorix that the POV exists. The terminology all suggest this.

For one that is supposed to view four dimensions, i suspect something entirely different is going on (like what is suggested above).

The lack of coherence is from taking words with loaded meanings, and applying them with gay abandon in higher dimensions, and to suppose that all of the loaded meanings continue to work. The standard terminology uses words with loaded meanings where the meanings no longer apply.
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Re: Beware of quickfur

Postby 4Dspace » Sun Jul 22, 2012 6:05 am

Hahahahaha! wendy, you are delusional. So, these are the "experts" of this board. One is incompetent at seeing a simple cube in 4D, and the other is a looney. This is so sad... I don't know, it's also hilarious.

You invented a crazy language, as if there is no over 200-year tradition of talking about structures in higher dimensions. Especially the 4th, which is so well explored and understood. Hey, we live in 4D. We may not know it, but that's the reality. Now, why do you think anyone would want to learn your crazy invention, where lines have sides, where basic structures of objects turn into different things altogether, only because you moved them from one N-space to the next? According to you post on another thread, you came up with your crazy "polygloss" over a liter of booze. Were you sober when you wrote the post above?

For your information, lines are 1-dimensional objects that do not have sides. Lines have directions. Same for planes. Planes too have directions and this direction is expressed as their chirality. For simplicity, we referred to plane's chrality as "sides", which, by the way has practical meaning even for such a simple thing as for viewing a cube in 4D. If the cube has a writing on its outer faces, i.e. "outside", in 4D what do you see? quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.

That's why this forum is a sham. It's run by a blind "expert" at seeing in 4D and a looney with crazy ideas. Both have mush in their heads. lol. I very much hope that gonegahgah will steer it in the right direction. Eventually. He is a bit slow for my taste, but, as they say, slow but steady. Hopefully, some intelligent people will come here eventually.

People! beware of regulars here, lol. :D
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Re: Beware of quickfur

Postby wendy » Sun Jul 22, 2012 7:20 am

It would not be the first time that a 200 year tradition of language has been overturned. Much the same happened in the world of electrics in the 1860's.

It's interesting to note that 4Dspace, for deriding such experts, has advanced nothing of note on the subject, save to posit that we're wrong. He states that the use of hyperspace to visualise 4D and the 2D/3D visualisation analogies are wrong, even though every tome i have read on this subject uses exactly these methods. He advances that that there is no POV in 4D, even though both quickfur and myself had provided this.

I suppose he is singularly silent on the ability for a line to divide space, and have sides, when he suggested otherwise.

I suspect that he supposes these 'flattened polytopes' or web of polyhedra really is the fourth dimension.

He admits to being lacking in the mathematical department, which supposes that he is not in a position to construct the necessary images to make 4d work. A trace of mathematics and anology goes a long way, yet neither of these are listed in his post, just reinterations that something like 'a plane has two sides, and you can't see both at once', is supposed to undo the work of hundreds of years.

In short, he talks the talk, but doesn't walk the walk. No alternate model of what '4d looks like' is advanced.

quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.


In the supposed terminology, the 'six faces of the cube' suddenly becomes the 'front and back of the hyperplane (chorix) that the cube is in 4D. The point is, that when one dismisses the notion that the plane has a front and back, there is nothing left here. Since one does not have to render front and back of the plane containing the square to cause it to be printed, the comment regarding the front and back of the hyperplane is moot, and the proposition is entirely left as (when the red herring is removed)

quickfur sees all 6 outer faces at once


Which is the exact premise that comes from POV

For your information, lines are 1-dimensional objects that do not have sides. Lines have directions. Same for planes. Planes too have directions and this direction is expressed as their chirality. For simplicity, we referred to plane's chrality as "sides"


One supposes that 'dead lines', 'front lines' and 'lines in the sand', are lines that have sides. The two sides of these have different meanings. So one might not wish to be standing on the side of a front line where the guns are pointing at, for example.

In any case, it is pretty easy to deduce from meaning, that 'side' only has meaning when the side is a division of space, that is, a space of M-1. When the side is 1D, the M=2, and we're talking about the ground. When the side is 2D, then M=3, and we're talking of the squares of a cube.

Even if one supposes that chiralty applies to a plane, it does not create 'sides', because the information is identical but reversed. You can still render the object on a single side of a sheet of paper, so there is only one layer.

That's why this forum is a sham. It's run by a blind "expert" at seeing in 4D and a looney with crazy ideas. Both have mush in their heads. lol. I very much hope that gonegahgah will steer it in the right direction. Eventually. He is a bit slow for my taste, but, as they say, slow but steady. Hopefully, some intelligent people will come here eventually.


I do not run this show, although i am acknowledged as an expert. When we start seeing practical demonstrations of your 4d vision, rather than rants against those who have, then we should take some notice of you. We don't want 'talk the talk', we want 'walk the walk'.
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Re: Beware of quickfur

Postby Ovo » Sun Jul 22, 2012 9:36 pm

4Dspace, where did you get that idea that a plane has two sides? Sources please.

As far as my intuition, my old geometry knowledge and the Wikipedia page for Plane and Euclidean geometry tell me, a plane has no sides. It separates a space in two halves, so a point in that space can be on one side or on the other side of the plane in that space (or it can be on the plane), but the plane itself has no sides or faces to speak of. If a point is on a plane, it can be seen from any POV in either half of the space that the plane sparates. Also, a polygon like a square is not a plane, it's a plane figure, a figure in a plane.

Haven't you been wrongly influenced by back-face culling in 3D applications?

4Dspace wrote:For your information, lines are 1-dimensional objects that do not have sides. Lines have directions. Same for planes. Planes too have directions and this direction is expressed as their chirality. For simplicity, we referred to plane's chrality as "sides", which, by the way has practical meaning even for such a simple thing as for viewing a cube in 4D. If the cube has a writing on its outer faces, i.e. "outside", in 4D what do you see? quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.

Refering to Wikipedia's definition of chirality, a plane is not defined by chirality. If we could say about a plane that it is chiral or achiral, it would be massively achiral anyway, as it has an infinite number of simmetry centers and axes.

So, no front and back on a plane. Or a hyperplane.
And a cube is not a hyperplane in 4D, it's a figure in a hyperplane. The space is a hyperplane in 4D.

I feel like this forum needs a lexicon reference.
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Re: Beware of quickfur

Postby 4Dspace » Mon Jul 23, 2012 11:43 pm

Ovo wrote:4Dspace, where did you get that idea that a plane has two sides? Sources please.

Dear Ovo, how about a source that water is wet? Have you got one for me? Of course, a plane in n-space where n>2 has sides. Thus you cannot see its both sides from the same POV. And chirality relates to the sides of a plane in a simple way: imagine you "hang a clock on a face of a cube". If you look at it from outside, how we normally see faces of a cube in our 3D, the hands of the clock run clockwise. If we look at the same face from inside the cube, the hands will run counterclockwise. Thus the two sides differ.

In Euclidean spaces, you can see only one side of a plane from a given POV. If you see both, this means that either the plane is twisted, or you're not in Euclidean space.

Ovo wrote:As far as my intuition, my old geometry knowledge and the Wikipedia page for Plane and Euclidean geometry tell me, a plane has no sides. It separates a space in two halves, so a point in that space can be on one side or on the other side of the plane in that space (or it can be on the plane), but the plane itself has no sides or faces to speak of.

see above

Ovo wrote:If a point is on a plane, it can be seen from any POV in either half of the space that the plane sparates. Also, a polygon like a square is not a plane, it's a plane figure, a figure in a plane.

No, a polygon is a bounded plane.

Ovo wrote:Haven't you been wrongly influenced by back-face culling in 3D applications?

no
Ovo wrote:
4Dspace wrote:For your information, lines are 1-dimensional objects that do not have sides. Lines have directions. Same for planes. Planes too have directions and this direction is expressed as their chirality. For simplicity, we referred to plane's chrality as "sides", which, by the way has practical meaning even for such a simple thing as for viewing a cube in 4D. If the cube has a writing on its outer faces, i.e. "outside", in 4D what do you see? quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.

Refering to Wikipedia's definition of chirality, a plane is not defined by chirality. If we could say about a plane that it is chiral or achiral, it would be massively achiral anyway, as it has an infinite number of simmetry centers and axes.

No one said that plane is defined by chirality. Chirality of a plane is like a direction of a line. Line has 2 directions and line is not defined by its directions. Line has directions. So does the plane. So, we spoke about "sides" of a plane informally, meaning its direction.

Ovo wrote:So, no front and back on a plane. Or a hyperplane.
And a cube is not a hyperplane in 4D, it's a figure in a hyperplane. The space is a hyperplane in 4D.

Really? Can you see both top and bottom of your kitchen table from the same POV?

Can you see what's written on all 6 faces of a cube from the same POV in 3D?

Guess what, neither in 4D.

That was the issue here.

By the way, ac2000 recommended a good link where you can see a torus rotate in 4D, which turns it inside out. Thus the authors of the film made sure to color its two hyper-sides differently.
http://www.dimensions-math.org/Download_Lyon.htm That's chapter 8.
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Re: Beware of quickfur

Postby Ovo » Tue Jul 24, 2012 12:07 am

Your condescending tone doesn't add any veracity to your statements. The only thing it does is to kill my will to agree with you and make me see you as an aggressor to fight against. Which is probably not what you want, deep down.
Though, I am self-trained to get over these destructive feelings and will try to answer objectively tomorrow.
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Re: Beware of quickfur

Postby 4Dspace » Tue Jul 24, 2012 12:44 am

wendy, this is the last time I answer your posts, since I do not see a point talking to you, a self-appointed expert in seeing higher dimensions, who is incompetent at visualizing a simple cube in 4D. This simple exercise revealed the truth. You claim that you "see up to 8D". Of course, no-one can get into your head and see what you see, but from what you posted above it appears that you are simply deluding yourself.

In addition, you have reading comprehension deficiencies, as indicated by the false statements that you ascribe to me:
wendy wrote:It's interesting to note that 4Dspace, for deriding such experts, has advanced nothing of note on the subject, save to posit that we're wrong. He states that the use of hyperspace to visualise 4D and the 2D/3D visualisation analogies are wrong, even though every tome i have read on this subject uses exactly these methods. He advances that that there is no POV in 4D, even though both quickfur and myself had provided this.

1. you forgot to put "experts" in quotes, for you are incompetent as a simple test revealed lol.

2. I never stated that "the use of hyperspace to visualise 4D and the 2D/3D visualisation analogies are wrong". I said that your visualization techniques are often misleading, resulting in mess in your heads. The result is that you cannot see a simple cube in 4D. Please.

3. Never have I said that "there is no POV in 4D". In fact, I was saying exactly the opposite, namely that quickfur has no idea of a POV in 4D.

wendy wrote:I suppose he is singularly silent on the ability for a line to divide space, and have sides, when he suggested otherwise.

I suspect that he supposes these 'flattened polytopes' or web of polyhedra really is the fourth dimension.

He admits to being lacking in the mathematical department, which supposes that he is not in a position to construct the necessary images to make 4d work. A trace of mathematics and anology goes a long way, yet neither of these are listed in his post, just reinterations that something like 'a plane has two sides, and you can't see both at once', is supposed to undo the work of hundreds of years.

In short, he talks the talk, but doesn't walk the walk. No alternate model of what '4d looks like' is advanced.

4. I never said that line cannot divide space. I said line has no sides, which was something you claimed.

5. I never spoke of "'flattened polytopes' or web of polyhedra". All this are your words which you ascribe to me.

6. I never "admitted to being lacking in the mathematical department". I have a degree in computer science, which, you may not know, is rather mathematical. In fact, my special interest in university was computer graphics and games. I wrote gaming and graphics programs. Alas, it turned out that I worked in financial industry designing databases. I excel in logic and analysis. (and by the way, have always graduated with honors from whatever schools I was in).

7. Whose work of hundreds of years? Not yours, for sure. You specifically can work for another thousand years, and still will not be able to see both sides of a (hyper)plane from the same POV in Euclidean space.

wendy wrote:
quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.


In the supposed terminology, the 'six faces of the cube' suddenly becomes the 'front and back of the hyperplane (chorix) that the cube is in 4D. The point is, that when one dismisses the notion that the plane has a front and back, there is nothing left here. Since one does not have to render front and back of the plane containing the square to cause it to be printed, the comment regarding the front and back of the hyperplane is moot, and the proposition is entirely left as (when the red herring is removed)

what?! What is this babble? The task was to visualize a cube in 4D with writings on its faces. What are you talking about here?

wendy wrote:
quickfur sees all 6 outer faces at once


Which is the exact premise that comes from POV

Which is exactly why I see no point talking to you or take your advice on visualization of any D. Again: seeing all 6 outer faces of a cube is equivalent to seeing both sides of a hyperplane from a single POV. The fact that you do not know such basics makes all your claims at expertise moot.

wendy wrote:
For your information, lines are 1-dimensional objects that do not have sides. Lines have directions. Same for planes. Planes too have directions and this direction is expressed as their chirality. For simplicity, we referred to plane's chrality as "sides"


One supposes that 'dead lines', 'front lines' and 'lines in the sand', are lines that have sides. The two sides of these have different meanings. So one might not wish to be standing on the side of a front line where the guns are pointing at, for example.

In any case, it is pretty easy to deduce from meaning, that 'side' only has meaning when the side is a division of space, that is, a space of M-1. When the side is 1D, the M=2, and we're talking about the ground. When the side is 2D, then M=3, and we're talking of the squares of a cube.

You're easily confused and taken off the track. It is geometry we are talking here.

wendy wrote:Even if one supposes that chiralty applies to a plane, it does not create 'sides', because the information is identical but reversed. You can still render the object on a single side of a sheet of paper, so there is only one layer.

8. I said several times in this thread and several times in the thread where the subject was raised that "sides" was the informal way to refer to the plane's direction, and that direction of a plane is its chirality.

wendy wrote:
That's why this forum is a sham. It's run by a blind "expert" at seeing in 4D and a looney with crazy ideas. Both have mush in their heads. lol. I very much hope that gonegahgah will steer it in the right direction. Eventually. He is a bit slow for my taste, but, as they say, slow but steady. Hopefully, some intelligent people will come here eventually.


I do not run this show, although i am acknowledged as an expert. When we start seeing practical demonstrations of your 4d vision, rather than rants against those who have, then we should take some notice of you. We don't want 'talk the talk', we want 'walk the walk'.

You the expert? You are delusional. A simple test revealed that you are incompetent at simplest things.
Besides, the 8 points of nonsense listed above that you ascribed to me are plenty for me to never bother talking to you again. There is no point talking to someone who lacks basic understanding and tends to misconstrue what is being said.

So, please never address me again and never talk about what I said.
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Re: Beware of quickfur

Postby 4Dspace » Tue Jul 24, 2012 2:04 am

Ovo wrote:Your condescending tone doesn't add any veracity to your statements. The only thing it does is to kill my will to agree with you and make me see you as an aggressor to fight against. Which is probably not what you want, deep down.
Though, I am self-trained to get over these destructive feelings and will try to answer objectively tomorrow.

Sorry, Ovo, I did not mean to sound condescending. I was merely mirroring your tone. Also, I admit, I got worked up by wendy's post above. Basically, you're right, if the object you're viewing is made of transparent material, then, of course you see all points. Not only in 4D. With a transparent object, you see it all in 3D as well. But the task was to see a cube made of solid planes with writing on its faces. Thus which side of the plane your POV reveals becomes relevant.
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Re: Beware of 4DSpace

Postby wendy » Tue Jul 24, 2012 7:18 am

1. you forgot to put "experts" in quotes, for you are incompetent as a simple test revealed lol.


No test has come from you. You have said nothing more than 'this am wrong because eggs are white". A page for having two sides, does not prevent one seeing the four sides of a square printed on one of them. This is where you could not see that the POV that both quickfur and myself had given you, allows one to see the six sides of a cube, on one side of a containing chorix.


3. Never have I said that "there is no POV in 4D". In fact, I was saying exactly the opposite, namely that quickfur has no idea of a POV in 4D.


Quickfur gives many pictures of 4d polytopes, as schegel diagrams or one-side views, which are perfectly consistant with a mapping of 4D to 2D, with an illusion of depth to allow the mind to create the image viewed orthogonally to the three-space the image represents.

You have given no image.

4. I never said that line cannot divide space. I said line has no sides, which was something you claimed.


This is terribly inconsistant with the notion that a plane has two sides because they divide space ('as seen from the other side'). A line can be seen from two different sides (exclusively), when the context is a plane.

5. I never spoke of "'flattened polytopes' or web of polyhedra". All this are your words which you ascribe to me.

(earlier) The correct answer to this question is: all 6 faces of a cube are visible from 4D. However, from a given POV, 3 faces are viewed from 'outside' and 3 from 'inside'. Since the writing is on the outer side of the faces, it is visible only on those faces in 4D that show their 'outer' side to the given POV.


But this is the geometric consequence of your comment that a (hyper)plane has two sides. The notion is that if the previous comment were true, then the resulting 4D would be the side-view of an orthogonal view, such as quickfur's renders of polytopes.

If you are seeing three from the inside, and three from the outside, then you are looking through a translucent cube, and therefore you must be in the same hyperplane as the cube. Therefore, if the cube is part of a tesseract, for example, you are looking at a flattened polytope. A view from the space not part of the hyperplane containing the cube, would make all six squares of the cube appear in exactly the same way we view a square on a plane, since there is a separate hyperplane containing the individual face of the cube, and the POV for each of the six planes. For the same reason, there is a separate plane for each side of the square and the POV. I'm pretty sure that your grasp of Euclidean geometry and spacial coordinates would grasp this concept.

4. I never said that line cannot divide space. I said line has no sides, which was something you claimed.

while leaving unsaid, instances in languages where lines do explicitly divide space, and has different things on different sides. In any case, lines do divide space: that's why we call them 'edges' of a cube.

6. I never "admitted to being lacking in the mathematical department". I have a degree in computer science, which, you may not know, is rather mathematical. In fact, my special interest in university was computer graphics and games. I wrote gaming and graphics programs. Alas, it turned out that I worked in financial industry designing databases. I excel in logic and analysis. (and by the way, have always graduated with honors from whatever schools I was in).


Code-bashing has very little to do with mathematics. In any case, this 'logic' is singularly lacking in parsing anything other than what you fancy is four dimensions.

In any case, you failed to grasp the coordinates given separately by quickfur and myself, regarding a POV that does not need to travel through the cube to see points inside it, or to see the six faces of the cube without passage through the cube. I mean, it's simple Euclidean geometry.

quickfur sees all 6 outer faces at once, and he, the "expert" does not even realize that this means that he is seeing both front and back of the the hyperplane, which a cube is in 4D.


I suppose your mathematical skills, have failed you here too. You can as readily see from a point not on the hyperplane, all points of the hyperplane. You can as readily see the six sides of a cube on a chorix as one can see the four sides of a square on a hedrix.

Again: seeing all 6 outer faces of a cube is equivalent to seeing both sides of a hyperplane from a single POV. The fact that you do not know such basics makes all your claims at expertise moot.


It's only true if your POV is part of the same hyperplane that the cube falls in. You can easily see all four sides of a square from a point not in the square's plane. Likewise, you can see all six sides of the cube from a point not in the cube's hyperplane. Since you don't admit this, (which is pretty ordinary coordinate geometry), then it becomes clear that your POV is in the plane of the cube, and hence you are looking at flattened polytopes incorrectly.

Here also, we switch meaning from seeing points on either side of a square in a hyperplane, (inside vs outside), suddenly to you can't see both sides of the hyperplane itself, because it "has two sides". In short, a slide on the meaning of 'side'.

You're easily confused and taken off the track. It is geometry we are talking here.


In the terms of the PG, a plane or face is one equal sign, a margin is two. That is, when you construct a plane in N dimensions, like x=0, there is only one equal sign, and the dimension (or number of free variables) is N-1. When you construct x=0, y=0, then there are two fixed, and N-2 free variables. The geometry is that a line divides, when the space is two dimensions.

8. I said several times in this thread and several times in the thread where the subject was raised that "sides" was the informal way to refer to the plane's direction, and that direction of a plane is its chirality.


The chiralty of an object is not a 'side'. Even lines can have chiralty (vectors). You can connect a vector-line into a chiral plane by the right-hand rule. It's the normal way, for example, of representing torque (a vector perpendicular and matching in chiralty to a rotation in a plane).

In any case, the POV no more has to resolve chiralty by observing both sides of the plane. Clocks work quite nicely, for being chiral. Still, that a 2-space and a 3-space may contain chiral objects, does not suppose that they divide space any more than a 1d object (where chiralty is the vector orientation).

So, please never address me again and never talk about what I said.


Are you scared of being shown as a one who 'does the talk, but not the walk'. In short, your argument has been found wanting, and your manner has been found to be stubborn and rude.
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Re: Beware of quickfur

Postby 4Dspace » Tue Jul 24, 2012 10:32 am

Oh, I see. Some invisible moderator changed the subject and perhaps posts as well. How clever.

Who is the moderator here?
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Re: Beware of 4DSpace

Postby wendy » Tue Jul 24, 2012 12:04 pm

Hahahahaha! wendy, you are delusional. So, these are the "experts" of this board. One is incompetent at seeing a simple cube in 4D, and the other is a looney. This is so sad... I don't know, it's also hilarious.


It does well to look for the colour that the user's name appears in, when making remarks like this. Purple means 'moderator'. Both quickfur and i are moderators. You should be aware that on many boards, the recieved experts, especially those who are generally polite, are given moderator powers. This is done by the owner of the board to trusted members. Normally, this power is used to remove spam articles, and to a lesser extent, trolls. Quickfur believed that you were trolling him, and i came to much the same conclusion myself.

In your particular case, I both removed a large post of mine appended as quote at the end of one of your posts.

Later on, after reading some of the interactions between you and quickfur, and generally agreeing with quickfur, ovo, and others, decided to change the title of this stream of messages to being beware of 4DSpace. What comes fair goes fair. Also, the comment above does not really help your case. There is a difference between disagreeing in subject, and to start personal attacks on individuals, specifically when experts are not 'self appointed', but are recognised from their imput.
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Re: Beware of quickfur

Postby Ovo » Tue Jul 24, 2012 3:51 pm

4Dspace wrote:Sorry, Ovo, I did not mean to sound condescending. I was merely mirroring your tone. Also, I admit, I got worked up by wendy's post above.
No problem, I know very well the feeling of frustration and anger towards someone who doesn't think the same as you. It's a human instinct but in the case of debating universal knowledge, this instinct has only negative effects (it reduces objectivity) and we all have to get over it, however difficult it can be. It's especially hard when you are the first to try to, but it's very rewarding when you manage to do it. What I am trying here is to help us do it together.

I haven't read your previous discussions with quickfur but in the context of this thread, you were the first to explicitly show these agressive emotions. You expressed them in your first post by the use of irony ('protecting his "reputation" ') and rude or denigrating expressions ("quickfur's endless babble", "the mush is in quickfur's head").
Now, as far as I can see, quickfur and wendy, as well as you and I, are not trolling purposedly. We are all honest people with a different POV on the same matter.
As with any scientific matter, we all agree that there is, or should be only one truth if we all start from the same base principles. So, some of us must be wrong. Or perhaps... we are not based on the same principles. Then we should solve that first.
And this is what we have to do because, obviously, we don't agree on what are the postulates of Euclidean geometry. And by consequence, on our deductions. (I do think that a 4D creature with a 3D retina can see the writings on all faces of a cube at once from a single POV away from the cube on the fourth axis.)

the most basic tenet of Euclidean geometry, namely, that only one side of a plane is visible to a POV at any time
Ok so first, vocabulary. As you pointed later on, "sides" is not a good term to represent what you mean, namely that when you look at a plane from a POV that is not on the plane, it will not be the same wether you see it from one half or the other of the space. You call it the "chirality of a plane". Right. I don't say it exists, but it's a less confusing term than "sides".

So let's reformulate with that new term:
the most basic tenet of Euclidean geometry, namely, that a plane is chiral and you don't see the same enantiomorph wether you look at it from one half or the other half of the space that the plane separates.
Is it a correct reformulation?
If so:
a) I don't see any hint of this in the postulates of the Euclidean geometry.
b) When I search for "chirality of a plane" on Google, it yields only one result. It looks like you're almost the only person in the world speaking of the chirality of a plane. ;)
c) When I look at the definition of chirality and plane on Wikipedia, I understand that a plane is not chiral. A plane is not a polygon and chirality only applies to figures.

So we actually have a deeper problem in the fact that we don't have the same definition for "plane".
If I look at Wikipedia's definition, a plane is not to confound with the figures that can be on a plane. The plane is a "place", it's not an object. A polygon is not a plane, we only say that it is in a plane.
So, a polygon (as well as some writing on the face of a cube) can be chiral, but not a plane.

Now that the vocabulary is sorted (at least, you have my definition of "plane"; wether you take it at yours or not won't prevent you to understand what follows), we can enter the technical details:
A writing on the face of a cube can be chiral, right, but only in a 2D space, not in 3D or higher dimensional spaces.
Reason? "In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral." Source: Wikipedia
In 3D, a flat figure always possesses a plane of symetry: the plane it is on. Then a polygon or any plane figure like those flat writings we are speaking of is not chiral in a 3D space.

That's about it.

So yes, I think that a 4D creature in a 4D space could see all the faces of an opaque cube, as well as all of its interior, all at once from a single POV outside of the cube's space. And if there was some writing on opposite faces of the cube, the 4Der would see one of the writings reversed but would only have to tilt its 4D head on the fourth axis to see it the opposite way.
The same way we can see a sequence of points on two opposite edges of a square (as well as its interior) all at once. And by tilting our head, we can see these sequences reversed.
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Re: Beware of quickfur

Postby 4Dspace » Tue Jul 24, 2012 8:31 pm

Ovo, what you're saying is the equivalent to seeing the whole cube in its entirety in 3D, including its writings, straight or reversed. Which means that your cube is transparent.

But at least you agree that even in 4D, you will see the same thing, except that "back faces" will not be obscured by the "front faces" as they are in 3D, as they all are visible from most locations in 4D in their entirety. What you're saying, again, is that your cube is transparent, thus you see the countercloskwise image, i.e. which is on the far side of the hyperplane, which a cube is in 4D, (a cube = a segment of a hyperplane).

Your view is different from quickfur's, who claims that writings on a solid cube in 4D are visible in its normal orientation on both sides.

Now, this bit of visualization is self-evident to me. I don't know how you arrive at your vision. I simply see it in my head. Just like I see in 3D, I don't need to do math to understand what I see. I employ math when there is a disagreement and I have to check what I see. Which, with this cube thing I did long time ago, which is posted on another thread where this issue came about.

Now, regarding your post:

Ovo wrote:I haven't read your previous discussions with quickfur but in the context of this thread, you were the first to explicitly show these agressive emotions. You expressed them in your first post by the use of irony ('protecting his "reputation" ') and rude or denigrating expressions ("quickfur's endless babble", "the mush is in quickfur's head").

Well, you should have read the whole thing, and then you would see what quickfur said (provided the posts are same as before, which you cannot say, when they were modified -- to me it appeared that some were fixed post factum as a means of damage control). You will see that quickfur was first to sound condescending and in fact, he insulted me. And not once. I thought he and wendy may be moderators here, but it does not say anywhere in FAQs and they could have had different color to nicknames after certain number of posts, as on other boards. So, I thought may be the board is mostly unsupervised.

Ovo wrote:Now, as far as I can see, quickfur and wendy, as well as you and I, are not trolling purposedly. We are all honest people with a different POV on the same matter.
As with any scientific matter, we all agree that there is, or should be only one truth if we all start from the same base principles. So, some of us must be wrong. Or perhaps... we are not based on the same principles. Then we should solve that first.
And this is what we have to do because, obviously, we don't agree on what are the postulates of Euclidean geometry. And by consequence, on our deductions. (I do think that a 4D creature with a 3D retina can see the writings on all faces of a cube at once from a single POV away from the cube on the fourth axis.)

Well, first, Euclidean geometry has no mention of 4D creatures nor their retinas. In fact, these mythical beings do not exist and all references to them and qualities of their vision are moot.

Second, the Euclidean space is "flat", in the mathematical sense, meaning that it does not curve anywhere, and all its postulates are based on this fact. One of the postulates of Euclidean space is that a line can intersect a plane only at one point. This is basic "Euclidean geometry", which we learned when we were kids. Agree?

So, when you collected definitions, you forgot that in general, a plane may exist in a non-Euclidean space, and while being considered flat from its own POV, it may turn out curved in some other N-space, because that space is not Euclidean (i.e. curved).

So, I already said this many times, in this thread included, that, just like a line, a plane too has directions. Since talking of a different color of these 2 directions confuses people into thinking that perhaps it's not a plane, since this would imply layers of paint in the direction a true 2d-object does not have, the chirality is another way of talking about the plane's direction. And, as you mentioned above, this fact is used in computer graphics when deciding whether a part of a model needs to be rendered for a given POV. If what is rendered is a simple cube, the same applies. You don't need to render the writings on the faces that are not visible in 3D. In CG this is determined by that plane chirality.

Now, in 4D, the same principle applies. If the hyperplane is a solid and not a transparent object, you will not see what's on its "other side" to your your POV. It does not matter if this is a 2d-plane or a 3d-plane or a n-hyperplane with n>2. The same principle applies no matter from where you look at it. You still see only one side at a time. If the plane is transparent, then you will see "the writings" on the other side counterclockwise, and if it is not transparent, you will not see them at all.

Exactly like you have a drawing on a sheet of paper, you can see what's on it only from one side and not the other. To me it's very, very strange that such an obvious, self-evident thing has to be defended.

Ovo wrote:So let's reformulate with that new term:
the most basic tenet of Euclidean geometry, namely, that a plane is chiral and you don't see the same enantiomorph wether you look at it from one half or the other half of the space that the plane separates.
Is it a correct reformulation?

No. The fact that only one side of a plane is visible to a POV in a Euclidean space is a basic fact that you can check yourself. A POV defines a line with direction. A line can intersect a (hyper)plane only once (in Euclidean spaces). Thus, you can see only one "side" of a (hyperplane), determined by the direction of the line from your POV.

Ovo wrote:If so:
a) I don't see any hint of this in the postulates of the Euclidean geometry.
b) When I search for "chirality of a plane" on Google, it yields only one result. It looks like you're almost the only person in the world speaking of the chirality of a plane. ;)
c) When I look at the definition of chirality and plane on Wikipedia, I understand that a plane is not chiral. A plane is not a polygon and chirality only applies to figures.

Not so. See above.

Ovo wrote:So we actually have a deeper problem in the fact that we don't have the same definition for "plane".
If I look at Wikipedia's definition, a plane is not to confound with the figures that can be on a plane.

Plane is a 2d space. A 2d figure is a "segment" of a plane. When you build your cube out of 6 squares, those squares are planes. Now, no matter how a plane is bounded, i.e. be it a triangle or a square or whatever form, the relationship of a line intersecting a plane from 3D and higher is still the same.

This too appears self-evident to me.

Ovo wrote: The plane is a "place", it's not an object. A polygon is not a plane, we only say that it is in a plane.
So, a polygon (as well as some writing on the face of a cube) can be chiral, but not a plane.

No, here we disagree. A polygon is a bounded plane. The boundary is the difference. The boundary has certain shape, like square or a circle, but it's still a plane. I.e. a bounded plane does not change into a prism or a segment of a line only because you moved your object from one N-space to the next.

When viewing a cube in 4D, we had to agree what this cube is actually made of, i.e. is it a segment of a 3d-space, or it is made of 6 square faces, i.e. planes. That is because the entirety of a cube is visible in 4D. If it is a solid thing with some structures within, then that is what is seen. You should have read the thread, this would help you understand what's the issue. The task was well defined: an opaque cube made of 6 squares (flat 2d things) with writings on its outer faces is viewed in 4D. What is seen?

Ovo wrote:Now that the vocabulary is sorted (at least, you have my definition of "plane"; wether you take it at yours or not won't prevent you to understand what follows), we can enter the technical details:
A writing on the face of a cube can be chiral, right, but only in a 2D space, not in 3D or higher dimensional spaces.
Reason? "In three dimensions, every figure which possesses a plane of symmetry or a center of symmetry is achiral." Source: Wikipedia
In 3D, a flat figure always possesses a plane of symetry: the plane it is on. Then a polygon or any plane figure like those flat writings we are speaking of is not chiral in a 3D space.

Here you appear to misunderstand what wiki is saying. But that's besides the point.

Ovo wrote:That's about it.

So yes, I think that a 4D creature in a 4D space could see all the faces of an opaque cube, as well as all of its interior, all at once from a single POV outside of the cube's space. And if there was some writing on opposite faces of the cube, the 4Der would see one of the writings reversed but would only have to tilt its 4D head on the fourth axis to see it the opposite way.

1. It would help greatly if you do not refer to mythical creatures when discussing geometry.(relevance)

2. Here you are saying the same thing I was saying all along. Namely, that the the opposite faces of the cube will show the writings in reverse to a given POV, in other words, you will see some faces from their "other side" or other "other direction". Absolutely agree with you here. And this is the crux of the matter, so we agree, regardless of our differences in definitions :D

3. Here you are also saying that the faces of the cube in viewing are made of transparent material, which allows you to see it in its both sides (front and back, even though back writings appear in reverse), just like you can tell what's on a glass table looking at it from above or below. But if the cube is made of opaque material, which shows writing only on one of its sides, then you will see what's written only looking at it from one direction, just like you do not see what's on an opaque table looking from below. I thought this was such a self-evident thing... :\


Ovo wrote:The same way we can see a sequence of points on two opposite edges of a square (as well as its interior) all at once. And by tilting our head, we can see these sequences reversed.

Here you are wrong. A square's edges are 1d lines, and as such, they " do not have sides" and are visible in their entirety from 3D. Here you're misusing the analogy. That's what I have been saying all along. Analogies, while being helpful in the initial steps in visualization, become the source of confusion once you start dealing with well-defined objects.

Granted, either in 3D or 4D, you can look at a plane edge on --i.e. from the same 2D space that plane is in-- in which case the plane will appear like a line. In this case you will not see what's written on either of this plane sides. You have to look at a plane from 3D or 4D or higher, in order to view what's written on it. And in 4D, just like in 3D, a plane is still a plane. And if to a given POV it appears like a plane, and not a line (edge-on, remember?) then, provided it is transparent, you can see what's written on it, either "straight-on" or "in reverse", depending on the relationship of your POV to the plane's directions. If the plane is not transparent, you see the writing only from a particular direction, just like with a drawing on a sheet of paper.

Well, :\ this was exhaustive. It is very tiring and absolutely not rewarding affair, trying to prove that water is wet. I wasted tons of time on this trivia and am leaving you to sort out the analogies from what is.
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Re: Beware of quickfur

Postby 4Dspace » Wed Jul 25, 2012 12:38 am

PS
So, Ovo, I had that "problem", i.e. visualize a cube in 4D defined much simpler than "writings on its outer faces". I simply colored the inside of its faces green and outside, red. Which, unfortunately, confused people into thinking that perhaps the 6 faces that make up the cube are not 2d-planes proper, but very thin prisms in disguise. Which steered us astray from what the crux of the matter was, and that was a trivially simple thing as, from what side do you see that plane?

Planes do have directions. Not only from a POV where n>2. Planes have directions (exactly 2) from their own 2D POV as well. You can draw a circle on a plane going in 2 opposite directions. Only because the result is the same, does it mean that we have to omit the direction in which it was made? That depends on how this is relevant to our aim at hand.

And so, planes do have directions. Exactly 2. Just like lines.

And so, returning to the "problem", i.e. a well-defined cube made of 6 square planes (the exact definition came about not from the start but in the process of discussion in that thread), the task was to see this cube, colored red outside and green inside, in 4D. Of course, in 3D, we cannot see that it is colored green inside. But, having moved our cube into 4D, we can easily see inside it and thus can tell that its 6 planes are colored green inside and red outside.

Outside to what, one may ask. Why, the answer is the same as in 3D: outside to the inner 3d-space this cube occupies. It is still there. It is not 0 as in 3D analogy.

Given the fact that all 6 faces of the cube are visible in their entirety from most positions in 4D, what color they appear to a fixed POV in 4D?

And here, I believe from what you posted above, you would say that some faces will be seen green (the counterclockwise aspect of a writing on its face), and some, red. Agree?

That's how I posited the problem originally. Writing on the outer faces of a cube is just another generalization of the same thing. Which, funny enough, still speaks of the plane's chirality (which way a circle is made on a plane tells about a distinct direction).

And so, how do you see the 6 faces of such a cube in 4D? I say, half are seen red and half, green. That's 3 and 3. The 3 'near' ones are red and 3 'far' ones are green.

Now, what's near and far? A hyperplane, which is a 3D object defined by 3 bounding 2d planes orthogonal to each other, separates 4D into 2 halves. It's a wall you cannot penetrate. If the wall is not infinite (as the case is with our cube == it's a bounded 3d subspace in 4D), then you can walk around it. But it's still a "wall" in the sense that you cannot walk through it, and, unless it is transparent, you can't see its other side. You POV determines which side is seen. One at a time.

So, a cube in 4D is bound by "2 parallel hyperplanes" (both parallel to each other and perpendicular to the POV). These two hyperplanes carve out a 3D subspace out of the 4D space they are in. If here we are to use an analogy with 3D, this would be equivalent to two 2d-planes sandwiching a section of 2D space between. Seems redundant, since the 2D space has neither direction nor length in the 3rd dimension (==from 3D POV). Yet, in this analogy that's how it is, a 0. And so, going out of the analogy into what is, we realize that 0 (which is the total volume a 2D plane occupies in 3D) is not equal to x cubed in 4D. Here we make a leap from 2D seen from 3D, to 3D as seen from 4D. There is no correspondence in this step. Here the analogy is misleading: A gazillion of 2d-planes will never amount to a cube in 3D. Simply cause 0 times a gazillion is still 0. But, funny enough (!) eight 3d cubes in 4D do in fact make up a tesseract, a bona fide, real, 4d-object.

See where and how analogies lead astray?
Last edited by 4Dspace on Fri Jul 27, 2012 10:34 pm, edited 1 time in total.
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Re: Beware of 4DSpace

Postby wendy » Wed Jul 25, 2012 6:48 am

The problem is that you accused quickfur publicly, without going through the correct protocols. It should have been brought to a moderator's attention. Now it has, the moderator has decided that quickfur's opinions and representations on 4D are closer to the truth. Since it you that are adding red herrings to the mix, it is appropriate to be wary of you, not quickfur.

quickfur is a member of the notables group, which means the powers that be decided that he had sufficient fluency in the subject.

The view that a plane has two sides has been severally dealt with quickview, ovo and myself. A plane divides a space of one higher dimension, so it can not divide a space of 4D. A plane divides space into two halves, and there might be two views that might be shoe-chiral, but this does not constitute two sides as commonly recieved. What exists on a plane may be perfectly represented on a single side of a page.

There exists POVs in 4D that can resolve the entirity of three dimensions (as far as the eye can see), without any passing through 3D. Quickfur and I both gave coordinates for an example. So it is as possible to see the cube in 4D, in exactly the same way that one can see a square in 3D. The notion of inside and outside only exists in the prospective of the space conatining the object, not in higher spaces. This is the distinction between /around/ and /surround/ in the PG.

It is readily demonstrated from the idioms and examples that you are giving, that you suppose that the various pictures and aminations that you are watching are a faithful representation of 4D, and that no higher representation exists. It's in the same league that because the maps in the atlases are flat, then the world is flat.

Regarding the quote about 'water is wet', there no doubt is on the wiki, a reference that water is wet. Helium-3 is super-wet, while mercury is dry, it has to do with the size and direction of the miniscus they produce.
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Re: Beware of 4DSpace

Postby wendy » Wed Jul 25, 2012 7:45 am

While chiralty is an important idea in mathematics, it's ability to determine a direction when one supposes that the conventional product of two chiral objects (which is the sum of dimensions) gives all-space, and one of the two chiral objects is a direction (ie a vector or line).

Vector-lines are indeed chiral, the direction of the ray can act in conventional methods to create chiral objects. The notion of circulation is that a vector around a closed group creates, with the vector-area so enclosed, a ray which represents the product of the vector-area and the circulating vector, which is the product of both. Any ring of N-2 does by its cancelling surface chiralty, and the vector (N-1)-space, does indeed produce such a measure. Examples of this are measures of torque, magnetic moment = current × area. The out-vector in endoanalysis uses surface chiralty extensively, including chiralty of lines.

On the other hand, it is never advanced that objects presenting chiralty explicitly divide all space. It only divides space where the space is N-1 dimensions, and for being in several different spaces, can produce unique directions in those M-spaces which are different in higher space. For example, a vector on an edge on a cube, can produce a vector 'to its left' for every plane that it falls on, but only when the 'up' side of the containing plane is also defined.

In any case, chiralty of space is never posited to divide space, nor does it provide 'different sides' of an object that elsewise has no different sides.

And here, I believe from what you posted above, you would say that some faces will be seen green (the counterclockwise aspect of a writing on its face), and some, red. Agree?


What is not guessed here is that the colour need not be either of these colours. A helix or screw, for example, is chiral, yet it offers no direction. It can be produced by rotating a vector around a point as the point advances. The exact colur might leave the plane as red or green, but could advance through the whole spectrum and around, so the colour observed from a point could be any other colour.

A similar thing happens with the seasons. In 3D, when it is summer in the south, it is winter in the north. Whatever it is in the south it is six months removed in the north. In four dimensions, the order of seasons is the full circle. There is no north-south axis. There is always somewhere in any place, and so one can not assume that only two specific seasons or month-weathers apply. This is a natural physical consequence of having two separate and orthogonal axies of rotations (clifford rotations). This is a direct anology to a pointer rotating against the sun, where only 0 or 180 is available, and the two times are 12 hours apart.

A POV is a point, not a line. That's what it says point of view. The geometric process of drawing lines from the POV (not part of a 3d-space), to points of the 3D space, will reveal to anyone, that there is no extra point of the 3-space involved in the line, so the opaqueness of the cube does not inhibit the view of that point from hyperspace. That's the whole point of hyperspace.

Supposing that one must have translucent cubes, and that one can see sides from the inside and outside specifically implies that the line containing the POV contains two other points of the space containing the cubes, that is what you are looking at is a flattened polytope in the space of flattening.

The notion that there might be 4D characters, that are solid in their space, and have retinas that are able to totally access what is geometrically possible from a POV, is simply giving person to the view. Where you read such things, you could place a POV. Nothing is detracted from calling a Point 'A' or 'Joe'. What is important here is that the image is resolved onto what might be expected to be seen with a 3d retina at such a point, which is the natural implications of supposing 4D and biology.

Regarding 'flat'. Euclidean space has 'zero curvature'. It is only 'flat' when that space is held in a higher space of 'zero curvature'. In hyperbolic space, Euclidean geometry is still zero curvature, but it's not flat. There are still less curved spaces, the flat space is the one that has the same (negative) curvature as all-space. So if you want to wrangle non-euclidean geometry, you must assume that Euclidean geometry, while being zero curvature, is no longer flat.

But, funny enough (!) eight 3d cubes in 4D do in fact make up a tesseract, a bona fide, real, 4d-object.


This view comes from looking at a squashed polytope too. No, it makes a hollow box or the surface. You need to add bulk or substance to it to make a real 4d object, just as you have to fill the six squares to make a cube. Otherwise, it's a drawing on a peice of paper.

So, a cube in 4D is bound by "2 parallel hyperplanes" (both parallel to each other and perpendicular to the POV). These two hyperplanes carve out a 3D subspace out of the 4D space they are in. If here we are to use an analogy with 3D, this would be equivalent to two 2d-planes sandwiching a section of 2D space between.


Two parallel hyperplanes do cut out a slab of 4-space, in the same way that two planes cut out a slab of 3-space. It's pretty ordinary euclidean geometry. I mean, that's the whole point of it.

The analogies you present are false, because you assume the various presentations of 4D into movies and pictures, works because 4D is actually squashed into 3D: that is, you have no perception of depth in 4D.

This leads me to struggle with how you can suppose that ( A ) computing involves mathematics (it doesn't), ( B ) that you are skillful at mathematics when even the simple coordinates that quickfur and i gave for a POV fail you, and ( c ) how you can suppose that that a plane has 'two sides', which is given entirely without supporting reason or argument (the chiralty argument works only when the plane divides space).

Still, i do programming. You don't need fancy mathematics to do it: just a clear head and specific understanding of the issues and outcomes. This is singularly lacking in your arguments.
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Re: Beware of quickfur

Postby Ovo » Wed Jul 25, 2012 4:49 pm

I thought he and wendy may be moderators here, but it does not say anywhere in FAQs
In most forum boards, go to the index, look around at the bottom of the page, you should see the color legend for the admins and other roles. Click on one of the roles to get the list of users in that group.

And so, returning to the "problem", i.e. a well-defined cube made of 6 square planes (the exact definition came about not from the start but in the process of discussion in that thread), the task was to see this cube, colored red outside and green inside, in 4D. Of course, in 3D, we cannot see that it is colored green inside. But, having moved our cube into 4D, we can easily see inside it and thus can tell that its 6 planes are colored green inside and red outside.
I don't know in what world you can color a single point with 2 colors. We are not speaking of the same thing.
Anyway, let's assume the normal vector to the cube's faces points outside of the cube, and let's assume we have some home cooked rule saying that those faces look green if we look at them in the direction of the normal vector (i.e. "from inside"), and red if you look at them in the direction opposite to the normal vector ("from outside").
Now we place this cube in a 4D space and we look at it from a POV outside of the hyperplan that the cube lies in. What happens ? Our line of sight is orthogonal to the vector normals of all the faces. As you didn't tell me what happens in this case, I can't tell you how it would look. Logically I would imagine that all the faces would look kind of brown (red + green), but maybe you have some special rule.
But again, we are not speaking of the same thing. It's useless to discuss consequences if we are not analysing the exact same causes.

Plane is a 2d space. A 2d figure is a "segment" of a plane.
Right. You can say "plane figure" for less confusion.

When you build your cube out of 6 squares, those squares are planes.
No! Squares are called "squares" or "regular quadrilaterals" or "plane figures", not "planes".
A tile on a floor, do you call it a floor?
"Hey, seen my new floor made of floors?"

Now, no matter how a plane is bounded
A plane is not bounded in Euclidean geometry, a plane is infinite. If you mean square, say "square", if you mean triangle, say "triangle", if you mean polygon, say "polygon", if you mean plane figure, say "plane figure".

A polygon is a bounded plane.
Polygon:
"A polygon is traditionally a plane figure that is bounded by a closed path." (Wikipedia)
"A closed plane figure bounded by three or more line segments." (The free dictionnary)
"A figure, especially a closed plane figure, having three or more, usually straight, sides. " (Dictionnary.com)
"A closed plane figure with straight edges" (Gellert et al. 1989, p. 162)
"A closed plane figure bounded by straight line segments as its sides" (Bronshtein et al. 2003, p. 137)
"A closed plane figure bounded by three or more line segments that terminate in pairs at the same number of vertices, and do not intersect other than at their vertices" (Borowski and Borwein 2005, p. 573)
"A geometric object consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points. In other words, a polygon is a closed broken line lying in a plane." (Coxeter and Greitzer 1967, p. 51)

Please acknowledge your mistake and use the same vocabulary as everyone, for the good of all.

No. The fact that only one side of a plane is visible to a POV in a Euclidean space is a basic fact that you can check yourself.
No, it's not a self-evident fact, it's a wrong fact for me and the other persons in this discussion, and I've spent a lot of time checking the basics of Euclidean geometry and couldn't find a single reference to this. Planes don't have sides with different things on them. Now, stop thinking that what you remember of what you have learned can only be the truth, check your own facts and give links to external sources (like I do) or make a proper demonstration (better than I do), thanks!

The task was well defined: an opaque cube made of 6 squares (flat 2d things) with writings on its outer faces is viewed in 4D. What is seen?
I don't call this well defined. It leaves a gigantic room to interpretation. If the question was asked genuinely by someone relatively new to 4D visualization, I understand what was meant (and this is what I based my answers on until now). Otherwise, it needs a lot more precision to be answered correctly.

Well, first, Euclidean geometry has no mention of 4D creatures nor their retinas. In fact, these mythical beings do not exist and all references to them and qualities of their vision are moot.
Euclidean geometry doesn't describe vision, colors, visibility or invisibility either.

It would help greatly if you do not refer to mythical creatures when discussing geometry.
See above. I am not discussing geometry, nor are you. We are discussing a concept similar to reality set in a Euclidean space. If you want to discuss 4D only on a mathematical standpoint, why are you talking about vision, colors and such?

Here you are saying the same thing I was saying all along. Namely, that the the opposite faces of the cube will show the writings in reverse to a given POV, in other words, you will see some faces from their "other side" or other "other direction". Absolutely agree with you here. And this is the crux of the matter, so we agree, regardless of our differences in definitions :D
Haha, maybe we should stop right here. ;) Except that I misused the term "reversed". I meant 'upside-down', rather 'counterclockwise'. In fact, we disagree both on definitions and on logical conclusions.

Well, :\ this was exhaustive. It is very tiring and absolutely not rewarding affair, trying to prove that water is wet. I wasted tons of time on this trivia and am leaving you to sort out the analogies from what is.
I'm starting to get tired too, I think I'll stop now. Thank you very much for the time and effort you poured into your answers, regardless of how frustrating they were too me.
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Re: Beware of quickfur

Postby 4Dspace » Wed Jul 25, 2012 7:34 pm

Ovo wrote:
4Dspace wrote:No. The fact that only one side of a plane is visible to a POV in a Euclidean space is a basic fact that you can check yourself.

No, it's not a self-evident fact, it's a wrong fact for me and the other persons in this discussion...

If that's what you think, then, alas, we have irreconcilable differences, lol. To me this is a self-evident fact out of water-is-wet category.

I cannot compromise on this. But I believe this can be proved. We start slowly.

So, we have a plane (a 2D space) and a line (1D space). Both are straight and the 3D space we view them in is flat as well. Everything is super-straight Euclidean, lol.

I believe that a line can intersect a plane only once. (special case, when the line is parallel to a plane, then its intersection with the plane divides the plane into two sections <-- this special case we ignore).
Do you, Ovo, think that a straight line, non-parallel to the plane, can intersect the plane only once? Or do you think a line can intersect a plane more than once in Euclidean 3D?

This is important.
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Re: Beware of quickfur

Postby Ovo » Wed Jul 25, 2012 8:27 pm

4Dspace wrote:Do you, Ovo, think that a straight line, non-parallel to the plane, can intersect the plane only once? Or do you think a line can intersect a plane more than once in Euclidean 3D?
Before I answer this, can you give me your definition of "plane"? Is a polygon still a plane for you? If you refuse to adhere to the common definition of one of the major actors in our topic of discussion, I doubt you can convince me of anything.
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Re: Beware of quickfur

Postby 4Dspace » Wed Jul 25, 2012 8:51 pm

Ovo wrote:
4Dspace wrote:Do you, Ovo, think that a straight line, non-parallel to the plane, can intersect the plane only once? Or do you think a line can intersect a plane more than once in Euclidean 3D?
Before I answer this, can you give me your definition of "plane"? Is a polygon still a plane for you? If you refuse to adhere to the common definition of one of the major actors in our topic of discussion, I doubt you can convince me of anything.

Ovo, when I said that a square or any polygon is a plane, what I meant that, regardless of the shapes of those figures, they abide by the... properties of a plane. Thus, each of them can be intersected by a non-parallel line only once. But you want to be specific and call a square not a plane but a plane figure. If that's what you prefer, I can easily go with that. :)

So, a plane -- whatever definition suits you best, please state it and I will accept it.

But, in this particular, very general case, this is a plane proper, exactly like you mean it, I believe. It is infinite in all directions and our line is also infinite (this is to make sure that, regardless of the angle between the line and the plane, they will intersect somewhere for sure, lol).
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Re: Beware of 4DSpace

Postby Ovo » Wed Jul 25, 2012 9:42 pm

Alright. So a plane is a 2-dimensional surface with zero thickness extending indefinitely.
A line too is by definition infinite. No need to precise that your line is infinite if you accept this definition.

And now to answer the question, I will cite the basic properties of planes in a 3D space listed on Wikipedia, which I obviously adhere to:
Two planes are either parallel or they intersect in a line.
A line is either parallel to a plane, intersects it at a single point, or is contained in the plane.
Two lines perpendicular to the same plane must be parallel to each other.
Two planes perpendicular to the same line must be parallel to each other.
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Re:Beware of quickfur

Postby 4Dspace » Wed Jul 25, 2012 9:50 pm

Ovo wrote:Alright. So a plane is a 2-dimensional surface with zero thickness extending indefinitely.
A line too is by definition infinite. No need to precise that your line is infinite if you accept this definition.

And now to answer the question, I will cite the basic properties of planes in a 3D space listed on Wikipedia, which I obviously adhere to:
Two planes are either parallel or they intersect in a line.
A line is either parallel to a plane, intersects it at a single point, or is contained in the plane.
Two lines perpendicular to the same plane must be parallel to each other.
Two planes perpendicular to the same line must be parallel to each other.


Alright. Do you Ovo agree with this: A line intersects a plane at a single point.== a line intersects a plane once.

We omit other cases for our purposes.
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Re: Beware of 4DSpace

Postby Ovo » Wed Jul 25, 2012 9:58 pm

Yes, I agree with this, a line cannot intersect a plane more than once. It is exactly what the line I put in bold says.
I'm going to bed so further replies will come later.
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Re: Beware of quickfur

Postby 4Dspace » Wed Jul 25, 2012 10:20 pm

Ovo wrote:Yes, I agree with this, a line cannot intersect a plane more than once. It is exactly what the line I put in bold says.
I'm going to bed so further replies will come later.

Good. We number this as 1. a line cannot intersect a plane more than once.

Now, do you agree that a line has 2 directions (+,-)?

And that if we mark a specific point on this line and call it POV, there is only one direction from this point along the line to the plane?

In other words, we put our plane between X,Z axes, and set our line on XY plane at some angle to the X axis. The upper right quadrant is traditionally (+). That's where we mark a point on our line. This way, in order to intersect our plane, we need to move from the point along our line in (-) direction. And going from this point in the (+) direction we will never meet the plane. Agree?


Another thing I would like you to answer is: Given a sheet of paper with writing on both sides: 'yes' on one side, 'no' on the other. in 3D, can you see both 'yes' and 'no' from a single POV? Or you can see only either one at a time?
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Re: Beware of 4DSpace

Postby Ovo » Thu Jul 26, 2012 12:55 pm

Now, do you agree that a line has 2 directions (+,-)?
Right

And that if we mark a specific point on this line and call it POV, there is only one direction from this point along the line to the plane?
Right

In other words, we put our plane between X,Z axes, and set our line on XY plane at some angle to the X axis. The upper right quadrant is traditionally (+). That's where we mark a point on our line. This way, in order to intersect our plane, we need to move from the point along our line in (-) direction. And going from this point in the (+) direction we will never meet the plane. Agree?
Yes.

Another thing I would like you to answer is: Given a sheet of paper with writing on both sides: 'yes' on one side, 'no' on the other. in 3D, can you see both 'yes' and 'no' from a single POV? Or you can see only either one at a time?
Given you are speaking of a scene set in reality, given that I don't have a mirror, given the sheet of paper doesn't let any light pass through it, given the sheet of paper is not curved, etc., I can see either "yes" or "no" from a single POV, not both.
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Re: Beware of quickfur

Postby 4Dspace » Fri Jul 27, 2012 11:07 pm

Sorry for delay. We got hit by lightning :D and it fried our router.

Ovo wrote:
Now, do you agree that a line has 2 directions (+,-)?
Right

And that if we mark a specific point on this line and call it POV, there is only one direction from this point along the line to the plane?
Right

In other words, we put our plane between X,Z axes, and set our line on XY plane at some angle to the X axis. The upper right quadrant is traditionally (+). That's where we mark a point on our line. This way, in order to intersect our plane, we need to move from the point along our line in (-) direction. And going from this point in the (+) direction we will never meet the plane. Agree?
Yes.

Another thing I would like you to answer is: Given a sheet of paper with writing on both sides: 'yes' on one side, 'no' on the other. in 3D, can you see both 'yes' and 'no' from a single POV? Or you can see only either one at a time?
Given you are speaking of a scene set in reality, given that I don't have a mirror, given the sheet of paper doesn't let any light pass through it, given the sheet of paper is not curved, etc., I can see either "yes" or "no" from a single POV, not both.

Well, good. Now that last question can save us tons of time. That's a real thing set in reality. Please do take a sheet of paper and write 'yes' on one side and 'no' on another. Look at it in 3D. No mirrors :). Now, imagine the same sheet in 4D. What do you see?

In the mean time, we do the same with our setup. Now where our infinite plane was, we put a sheet of paper. We orient it in such a way that 'yes' faces upwards, toward our POV somewhere on our line.

Would you agree that from the point on the line only 'yes' is seen. And that in order to see 'no', we would have to move the point to the negative side of the line and 'look' at the sheet in the (+) direction of the line?

Would you also agree that the line is representative of both our line of sight from POV to the sheet and also a ray of light that is reflected off the sheet and follows the (+) direction of the line toward the POV on it?

Would you also agree that the light reflected off the bottom of the sheet with 'no' on it, does not reach the point on the (+) side of the line that is piercing the sheet? In fact, all light reflected off the bottom of the sheet goes in completely 'wrong' direction from where our POV is.

Would you agree that our set up is pretty representative of visualizing a piece of paper with writings on its sides in 3D?
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Re: Beware of quickfur

Postby Ovo » Sat Jul 28, 2012 8:45 am

4Dspace wrote:Sorry for delay. We got hit by lightning :D and it fried our router.
No problem, science can wait. May router rest in peace. :)

Please do take a sheet of paper and write 'yes' on one side and 'no' on another. Look at it in 3D. No mirrors :). Now, imagine the same sheet in 4D. What do you see?
Me, I can't see in 4D, but a 4D an analog of me staring at the sheet of paper could see both "yes" and "no" from the same POV.

But seen our different understanding off 4D that shows up on your thread, it's no wonder that we don't come to the same conclusion here.

In the mean time, we do the same with our setup. Now where our infinite plane was, we put a sheet of paper.
A sheet of paper equals to a very rectangular thin cuboid. Should I imagine a very thin rectangular cuboid centered around the plane ?
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