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 Jenny
part of thewhole
 
Registered: 06/02/00
Posts: 5,614
Loc: Columbus, OHIO
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 hypercubes 
#2228223 - 01/08/04 12:23 PM (20 years, 3 months ago) |
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as i haven?t taken any physics classes, this whole 4th dimension idea i stumbled apon in the book i?m reading perked my curiousity, so i read up about in on the good old world wide web.
(btw i did not write this)
I began to wonder if I could perhaps visualize a four-dimensional shape...something I?d been trying to do for years. This train of thought was prompted by a mental exercise in which I attempted to unfold a cube into panels, then fold it back up again.
As I mentally considered the unfolded cube, I remembered a graphic from a book I own called The Fourth Dimesion, by Rudy Rucker; the graphic shows a three-dimensional unfolded cube. Holding this figure in my mind as clearly as I could, I attempted to "fold it up" into a hypercube.
I let the figure do what it wanted to in my mind?s eye--shift and bend and change its orientation several times. I could practically feel the gears grinding in my brain, but for some reason I felt fairly confident that something would come of this visualization exercise.
For one brief, shining second, what I consider to be a glimpse into the fourth dimension became available to me.
I was basing my visualization on the three dimensional analogy: if you look at a cube from the vantage point of the third dimension from one side, you see a two-dimensional square. Therefore, I figured that if you looked at one "side" of a hypercube from the vantage point of four-dimensional space, you might see a three-dimensional cube--but you?d see every surface of this cube simultaneously. (Kinky!)
My little splinter of enlightened vision showed me a glowing figure, one with astonishing depth yet still somewhat out-of-focus. This doesn?t sound all that spectacular, but the actual experience was one of the most bizarre things I?ve ever felt. The hypercube faded in my mind?s eye after a moment.
I have read that if one is trying to visualize in four dimensions, a sphere -- actually, a hypersphere, is easier than a cube to get a decent mental picture of. In my exercise, I tried to consider what a hypersphere might look like. In my calculus book, there?s a chapter on three-dimensional surfaces being used to represent four-dimensional shapes.
I was just curious if this makes sense to any of you and if you have had a similar experience. I guess i sort of have a good understanding of the 4th dimension but trying to visualize it is hurting my brain!
The 3d picture above shows, to my eyes, a cube inside of another cube. How is this representing 4D? Can one of you smartypants out there help me out?
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Mindfulness is the aware, balanced acceptance of the present experience.
It isn't more complicated than that.
It is opening to or recieving the present moment, pleasant or unpleasant, just as it is,
without either clinging to it or rejecting it.
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 daba
Stranger
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 Re: hypercubes [Re: Jenny]
#2228235 - 01/08/04 12:27 PM (20 years, 3 months ago) |
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I'm trying to see a side of a 4-D hypercube, but I just can't visualize every side of a cube being seen without making it transparent.
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Frog
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Re: hypercubes [Re: daba]
#2228260 - 01/08/04 12:34 PM (20 years, 3 months ago) |
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That was my gut reaction, and based on what the article said:
"I was basing my visualization on the three dimensional analogy: if you look at a cube from the vantage point of the third dimension from one side, you see a two-dimensional square. Therefore, I figured that if you looked at one "side" of a hypercube from the vantage point of four-dimensional space, you might see a three-dimensional cube--but you'd see every surface of this cube simultaneously. (Kinky!)
My little splinter of enlightened vision showed me a glowing figure, one with astonishing depth yet still somewhat out-of-focus. This doesn't sound all that spectacular, but the actual experience was one of the most bizarre things I've ever felt. The hypercube faded in my mind's eye after a moment."
Maybe I'm still limited by my 3D vision, or mind-set, but it would be either like seeing the image as a transparancy, or like being on all sides of the image at once, which of course wouldn't be possible.
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The day will come when, after harnessing the ether, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, man will have discovered fire. -Teilard
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
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Re: hypercubes [Re: Jenny]
#2228353 - 01/08/04 12:59 PM (20 years, 3 months ago) |
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My avatar is a hypercube projected into 2D...
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infidelGOD
illusion
Registered: 04/18/02
Posts: 3,040
Loc: there
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Re: hypercubes [Re: Seuss]
#2228366 - 01/08/04 01:03 PM (20 years, 3 months ago) |
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hypercube (as seen on a computer screen):
a 2 dimensional "drawing" of a 3 dimensional "drawing" of a 4 dimensional object.
it's true nature is impossible to visualize in a normal state of mind.
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Frog
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Re: hypercubes [Re: Seuss]
#2228372 - 01/08/04 01:05 PM (20 years, 3 months ago) |
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See, the examples in the first post, and in your post, Seuss, are all transparent. If you can't see all things at all times, and you want to be able to see all sides, the object at which you are looking would have to be transparent.
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The day will come when, after harnessing the ether, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, man will have discovered fire. -Teilard
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
Loc: Caribbean
Last seen: 2 months, 6 days
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Re: hypercubes [Re: Frog]
#2228401 - 01/08/04 01:13 PM (20 years, 3 months ago) |
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I wrote a java applet years ago that I used to create my avatar. It spings forever, where my avatar is only a few seconds. The java applet no longer runs under the newer version of java, or I would post it. I will play with it and see if I can get it working again and post a link.
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Just another spore in the wind.
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Frog
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Registered: 10/22/03
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That makes sense.
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The day will come when, after harnessing the ether, the winds, the tides, gravitation, we shall harness for God the energies of love. And, on that day, for the second time in the history of the world, man will have discovered fire. -Teilard
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gnrm23
Carpal Tunnel
Registered: 08/29/99
Posts: 6,488
Loc: n. e. OH, USSA
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Re: hypercubes [Re: Jenny]
#2228515 - 01/08/04 01:46 PM (20 years, 3 months ago) |
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und so:
get ye a short story by robert a heinlein entitled: "and he built a crooked house-"
(for a view of a tesseract, well, from the inside, hehheh...)
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old enough to know better
not old enough to care
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Yarry
Old Timer
Registered: 01/04/04
Posts: 23,762
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Re: hypercubes [Re: gnrm23]
#2228545 - 01/08/04 01:53 PM (20 years, 3 months ago) |
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bah i thot this was a thread about big cubensis! lol
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Grumpy Old Man.
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trendal
J♠
Registered: 04/17/01
Posts: 20,815
Loc: Ontario, Canada 
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Re: hypercubes [Re: Jenny]
#2228549 - 01/08/04 01:54 PM (20 years, 3 months ago) |
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A hypercube, usually refering to a 4-D cube (4 spatial dimensions), can be displayed in 3-D in several forms. A hypercube is actually an n-dimensional cube, though as I said it is most likely to be a 4-D cube.
The first is the picture you have at the top and bottom. These are 3-D "shadows" of a hypercube. Think of what a cube (clear sides) would be like if you cast its shadow onto a 2-D surface. It would look like a large square with a smaller square inside it, with the four corners of the small square connected out to the four corners of the larger. Extrude this into 3-D and you have the shadow of a hypercube.
There is another way to display the hypercube in 3-D, and that is by unfolding it. If you "unfold" a cube you end up with a 2-D cross made of six identical squares (think of those cardboard dice you have to cut out and fold up). If you unfold a hypercube you end up with a 3-D shape which is a kind of 2-way cross made up of 8 identical cubes.
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Once, men turned their thinking over to machines in the hope that this would set them free.
But that only permitted other men with machines to enslave them.
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gnrm23
Carpal Tunnel
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Re: hypercubes [Re: Yarry]
#2230436 - 01/09/04 05:26 AM (20 years, 3 months ago) |
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heh...
in that wacky heinlein story, a california architect cons his buddy into letting him build a house shaped like an unfolded tesseract (4 stories tall, with the second floor havinng 4 rooms coming off of each face...) but the morning after a minor earthquake, the house seems to be only one cube - until you walk in the front door & up the stairs... but there doesn't seem to be a way back out again...
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old enough to know better
not old enough to care
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EvilGir
Im the on coming storm
Registered: 11/26/01
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Re: hypercubes [Re: gnrm23]
#2230445 - 01/09/04 05:42 AM (20 years, 3 months ago) |
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Hey a little bit of topic but, anyone here seen the movie Cube 2 Hypercube.
I think there a weird animation thing in there.
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Fighting the man the best way I can.
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Seuss
Error: divide byzero
Registered: 04/27/01
Posts: 23,480
Loc: Caribbean
Last seen: 2 months, 6 days
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Re: hypercubes [Re: EvilGir]
#2230474 - 01/09/04 06:11 AM (20 years, 3 months ago) |
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> A hypercube, usually refering to a 4-D cube
There is also an older class of super computers call hypercubes that were produced by Intel back in the late 80's and early 90's. The name came from the topology of the communications bus between the different nodes (cpus) in the computer. If you allocated 16 nodes, each node could talk to four other nodes in a 4n hypercube configuration. If you allocated 32 nodes, each node could talk to five other nodes in a 5n hypercube configuration.
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Just another spore in the wind.
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VirtBlu
Flouronaught
Registered: 01/06/04
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Re: hypercubes [Re: Jenny]
#2234051 - 01/10/04 11:12 PM (20 years, 3 months ago) |
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