Hypercube
Wednesday, March 31, 2004 by gizzimo | Discussion: WinCustomize Talk
Yeah i'm a real big nerd + fanatic about higher dimensions? (particularly the 4th). uh this isn't an opinion post about it (although you say whatever you want about it) but mainly a request. Would it be possible for me to ask one of the designers here to create a really cool wallpaper of a Hypercube? (the cube within a cube perspective) and like, use all ur cool..effects to make it look good and illusionegetic etc..? yeah, cool. thanks. seeya.
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werewolf
Reply #3 Wednesday, March 31, 2004 9:04 PM
Reply #3 Wednesday, March 31, 2004 9:04 PM
Actually, you might want to poke around the wallpaper section for some of the older walls. I believe someone actually *did* do a hyper cube.
crofttk
Reply #4 Wednesday, March 31, 2004 9:10 PM
Well, there's no way to represent a 3 dimensional object in one dimension, other than as a line which would imply 0 extent for one dimension of the three making it therefore only a two dimensional object represented in one dimension.
So, how in thunderation is one going to represent a FOUR dimensional object in the only TWO dimensional medium these artists work in ????
Coooome ooon, gimme a break !
Your Pal,
John Stossel
P.S. I think I did see this "picture" of a hypercube or something 4 dimensional in a Scientific American, or the like, sometime in the last several months. Couldn't make heads or tails of it.
[Message Edited]
Reply #4 Wednesday, March 31, 2004 9:10 PM
Well, there's no way to represent a 3 dimensional object in one dimension, other than as a line which would imply 0 extent for one dimension of the three making it therefore only a two dimensional object represented in one dimension.
So, how in thunderation is one going to represent a FOUR dimensional object in the only TWO dimensional medium these artists work in ????
Coooome ooon, gimme a break !
Your Pal,
John Stossel
P.S. I think I did see this "picture" of a hypercube or something 4 dimensional in a Scientific American, or the like, sometime in the last several months. Couldn't make heads or tails of it.
[Message Edited]
werewolf
Reply #5 Wednesday, March 31, 2004 9:12 PM
Reply #5 Wednesday, March 31, 2004 9:12 PM
I understand, but I really think that someone tried one.
crofttk
Reply #6 Wednesday, March 31, 2004 9:14 PM
Reply #6 Wednesday, March 31, 2004 9:14 PM
Yup, your jest a leettle ahead of me there wolfie !
(if I may call you that without offense
)
I would certainly encourage any attempts, regardless.
P.S. What I mean above is that I was composing my tongue-in-cheek tirade as citizen werewolf was making his suggestion. My longer post was NOT a response to his.
[Message Edited]
(if I may call you that without offense
)I would certainly encourage any attempts, regardless.
P.S. What I mean above is that I was composing my tongue-in-cheek tirade as citizen werewolf was making his suggestion. My longer post was NOT a response to his.
[Message Edited]
werewolf
Reply #8 Wednesday, March 31, 2004 9:45 PM
Reply #8 Wednesday, March 31, 2004 9:45 PM
whoa...a hypercube is a sunken square cutout with a raised square inside of that with a red x inside of that. My god, it's so simple. I totally get it now. Man, I can't believe I never saw that before.
CygnusXII
Reply #9 Wednesday, March 31, 2004 9:46 PM
Reply #9 Wednesday, March 31, 2004 9:46 PM
Tesseract: is what you are actually looking for.
The Tesseract (or Hypercube)
A guided demonstration
http://www.geom.uiuc.edu/docs/outreach/4-cube/
The Tesseract
A look into 4-dimensional space
http://pw1.netcom.com/~hjsmith/WireFrame4/tesseract.html
Tesseract Facts
http://mathworld.wolfram.com/Tesseract.html
The Tesseract (or Hypercube)
A guided demonstration
http://www.geom.uiuc.edu/docs/outreach/4-cube/
The Tesseract
A look into 4-dimensional space
http://pw1.netcom.com/~hjsmith/WireFrame4/tesseract.html
Tesseract Facts
http://mathworld.wolfram.com/Tesseract.html
paxx
Reply #10 Wednesday, March 31, 2004 10:30 PM
Reply #10 Wednesday, March 31, 2004 10:30 PM
OK, another try.
Here is the hypercube theory explained with an animation:
MindlessPuppet
Reply #12 Thursday, April 1, 2004 3:38 AM
Reply #12 Thursday, April 1, 2004 3:38 AM
I liked the movie Cube 2: Hyper Cube on the Sci-fi channel... It was cool...
paxx
Reply #13 Thursday, April 1, 2004 7:35 AM
Reply #13 Thursday, April 1, 2004 7:35 AM
Oh Cygnus, it's not from me. I grabbed it from a web site.
http://www.geocities.com/CapeCanaveral/7997/
All I did is turn the Flash into an animated GIF. :)
crofttk
Reply #14 Thursday, April 1, 2004 9:22 AM
That's good Paxx, thanks for digging that up.
Although I was tongue-in-cheek earlier, I had quite forgotten the technique of using another attribute, color being one of the most convenient, to represent an extra dimension. I should have known better, being and engineer and always having to cram mult-dimensional data onto 2 & 3-D charts.
[Message Edited]
Reply #14 Thursday, April 1, 2004 9:22 AM
That's good Paxx, thanks for digging that up.Although I was tongue-in-cheek earlier, I had quite forgotten the technique of using another attribute, color being one of the most convenient, to represent an extra dimension. I should have known better, being and engineer and always having to cram mult-dimensional data onto 2 & 3-D charts.
[Message Edited]
joetheblow
Reply #15 Thursday, April 1, 2004 10:10 AM
Reply #15 Thursday, April 1, 2004 10:10 AM
That is a Hypercube? So its a cube squared? I think that is cool. so how do you make such an opject in a 3 dimentional world?
gizzimo
Reply #16 Thursday, April 1, 2004 11:25 AM
Reply #16 Thursday, April 1, 2004 11:25 AM
Don't you have to ask for permission to use that animation? I was actually gonna use it myself but I didn't wanna play phlagerism. I've been interested in higher dimensions for years. The hypercube isn't a Tesseract by the way a tesseract is an unfolded hypercube (like the Net is an unfolded cube). Remember that the hypercube only looks like a cube within a cube from one four dimensional angle. Rotate around the hypercube 3 dimensionally and the cube will always have another smaller cube inside it connected to the vercities. Rotating 4 dimensionally is different. when you do so, you'll notice that the interior of the hypercube becomes the exterior. that's the 4th direction by the way
Up/down 1D
left/right 2D
forward/backward 3D
upsilon/delta 4D
In the 4th dimension, there is no exterior or interior. If you are contained inside a hypercube and you try and go out one side of the hypercube, you'll appear at the other side (the train station in the 3rd Matrix installation is a 4 dimensional realm, When neo exist one side, he enters at the other in essence, there is no such thing as Entrance or Exit in the 4th dimension.) I am digressing here now, sorry.
Anyways, visualising a hypercube in our 3rd dimension is practically impossible (a 2D person [[eg a shadow]] cannot see a cube, only one side) so we can only perceive 'one' side of the hypercube (the cube within a cube perspective) the other perspectives are fortified angles, they are 'slices' of a 4D cube.
If you're going to try and design it, don't bother think about how it will look, because it will only be a wallpaper right? which means its only appropriate you worry about making the cube-within-a-cube look cool since you can only really 'see' a 4D cube when it's in motion, preferably 4D motion (upsilon and delta).
If anyone's interested in the 4th dimension such as I am, and you wish to try and understand/visualise 4D space, try and put it into perspective of a 2D person transitioning into the 3rd dimension, he would grow proportion.
Edwin Abbott wrote the book Flatland, describing how a 2D person saw a sphere enter his world (obviously it entered in slices since the 3rd dimensional aspect of the sphere is cross-sectioned through the surface of Flatland)
http://roark.ry4an.org/flatland/
and here's a fictional interview conducted by a human, with a hyperbeing (4 Dimensional person)
http://web.mit.edu/maiki/www/stories/hexa.html
Thanks.
Up/down 1D
left/right 2D
forward/backward 3D
upsilon/delta 4D
In the 4th dimension, there is no exterior or interior. If you are contained inside a hypercube and you try and go out one side of the hypercube, you'll appear at the other side (the train station in the 3rd Matrix installation is a 4 dimensional realm, When neo exist one side, he enters at the other in essence, there is no such thing as Entrance or Exit in the 4th dimension.) I am digressing here now, sorry.
Anyways, visualising a hypercube in our 3rd dimension is practically impossible (a 2D person [[eg a shadow]] cannot see a cube, only one side) so we can only perceive 'one' side of the hypercube (the cube within a cube perspective) the other perspectives are fortified angles, they are 'slices' of a 4D cube.
If you're going to try and design it, don't bother think about how it will look, because it will only be a wallpaper right? which means its only appropriate you worry about making the cube-within-a-cube look cool since you can only really 'see' a 4D cube when it's in motion, preferably 4D motion (upsilon and delta).
If anyone's interested in the 4th dimension such as I am, and you wish to try and understand/visualise 4D space, try and put it into perspective of a 2D person transitioning into the 3rd dimension, he would grow proportion.
Edwin Abbott wrote the book Flatland, describing how a 2D person saw a sphere enter his world (obviously it entered in slices since the 3rd dimensional aspect of the sphere is cross-sectioned through the surface of Flatland)
http://roark.ry4an.org/flatland/
and here's a fictional interview conducted by a human, with a hyperbeing (4 Dimensional person)
http://web.mit.edu/maiki/www/stories/hexa.html
Thanks.
gizzimo
Reply #17 Thursday, April 1, 2004 11:42 AM
Reply #17 Thursday, April 1, 2004 11:42 AM
Oh and here's what happens when a hypercube moves 'through' our 3 dimensional world. (imagine a sphere plunging through flatland, the flatlanders would only see cross-sections of the sphere, meaning they would only see a circle suddenly appear growing larger until it dissappears)
http://cips02.physik.uni-bonn.de/ScienceSite/hypercubus/animator/main.html
http://cips02.physik.uni-bonn.de/ScienceSite/hypercubus/animator/main.html
Chris TH
Reply #19 Thursday, April 1, 2004 8:59 PM
Ooohh... be careful!! It would only look circular from the 3rd dimension (which flatlanders cannot move into)...
The following is from "Of the Nature of Flatland - Edwin A. Abbott (1838-1926)"
"Place a penny on the middle of one of your tables in Space
and leaning over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition of
the inhabitants of Flatland), and you will find the penny becoming
more and more oval to your view, and at last when you have placed
your eye exactly on the edge of the table (so that you are,
as it were, actually a Flatlander) the penny will then have ceased
to appear oval at all, and will have become, so far as you can see,
a straight line."
Reply #19 Thursday, April 1, 2004 8:59 PM
| (imagine a sphere plunging through flatland, the flatlanders would only see cross-sections of the sphere, meaning they would only see a circle suddenly appear growing larger until it dissappears) |
Ooohh... be careful!! It would only look circular from the 3rd dimension (which flatlanders cannot move into)...
The following is from "Of the Nature of Flatland - Edwin A. Abbott (1838-1926)"
"Place a penny on the middle of one of your tables in Space
and leaning over it, look down upon it. It will appear a circle.
But now, drawing back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition of
the inhabitants of Flatland), and you will find the penny becoming
more and more oval to your view, and at last when you have placed
your eye exactly on the edge of the table (so that you are,
as it were, actually a Flatlander) the penny will then have ceased
to appear oval at all, and will have become, so far as you can see,
a straight line."
Sput
Reply #20 Thursday, April 1, 2004 9:43 PM
Reply #20 Thursday, April 1, 2004 9:43 PM
Hang on...the flat landers would see it as a line from one side, but if they looked around it (or had "stereo scopic vision", they'd see it as rounded. Just as we see a sphere as a "sphere" even though when projected into 2d from one point of view it would appear as a flat circle. So, if we look as a sphere with just one eye and from one point in space then it looks like a circle, but we see it from 2 points at the same time with paralax, and can move to look around it too, so we perceive it as a 3d solid.
Thus, the flat liners would see a sphere passing through their plan as a curved "surface" getting bigger and then smaller again....but it wouldn't appear as a line if the could percieve "depth" from them to the "surface" as we do.
....I think
Thus, the flat liners would see a sphere passing through their plan as a curved "surface" getting bigger and then smaller again....but it wouldn't appear as a line if the could percieve "depth" from them to the "surface" as we do.
....I think
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Reply #1 Wednesday, March 31, 2004 7:57 PM