[Ben Barker]

Am I the LAST person on Earth to know about these great things? I was talking with a friend about Salvador Dali and his hypercube/Jesus painting came up.


I was like, "Hypercubes? What is a hypercube?" Then I was just blown away.
The fourth dimension, what a fascinating subject for art. Maybe it's just me, I am a form&space, Escher nut. But I think these are the neatest shapes I've ever seen. Pretty hard to conceptualize, but still opened my eyes quite a bit.

Here is a page where I got the above pics, it does as good a job as any at trying to explain hypercubes. I'm just to stupid to even start trying to dissect hyperspheres, but this whole fourth dimension thing is incredible even if I am just a math-handicapped artist http://www.math.ohio-state.edu/~fiedorow/math655/hypercube.html

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Ben Barker

[aNoah]

Aghm... all this hypercube stuff is � I have no better words � BS!
The word hypercube is a simple mathematics term (like n^2: n squared; n^3: n cubed; n^4: n hypercubed).

It is IMPOSSIBLE to visualize, because we live in a 2d world. We do not fully understand the 3-dimentional world... and definitely don't know ANYTHING about the 4th dimention.

Anyone who talks of the 4th dimention is simply speculating.

Nuff SAID

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-aNoah
Current Project Snapshot
My Gallery

[coconutmonkey]

aNoah wtf are you talking about? Saying we live in a 2d world? Riiiiiiight. Maybe our ART is 2d but our world is at LEAST 3D. The one thing you are right about is that we dont know about the 4th diminsion. If there even is one.

[Ben Barker]

I thought we lived in a 3D world... please explain.
The way I was told was, an unfolded cube makes a 2D cross, where as an unfolded hypercube makes a 3D cross. The planar cross section of a hypercube is a 3D shape. The 4th dimensional axis on XYZ axes would be a point, and the axis is perpendicular to X, Y, and Z.
A cube drawn on a piece of paper if 3D squashed to 2D. This: http://dogfeathers.com/java/hyprcube.html
is a 4D hypercube squashed into 3D. If you draw one on paper (squash it into 2D) it is still a hypercube, with the same number of vertices and faces. So, how is this BS? The only way we can visualize it is "squashed" into a lesser dimension, but it still seems to be valid.
Again, I am still a little foggy on this. Please explain, if possible, how it is speculation.

[Lukias]

For a stupid bastard like self that makes as much sense as a turd on a biscycle.

I owe you thanks Ben, through your site i found this one.

Cheers


PS your quake dude was my desktop for a couple of months and still is at home.

[Ben Barker]

Heh, thanks. I'm glad my DAAP links page helped SOMEONE My classmates at the DAAP don't really use it.

[Visigoth]

Whoever said we exist in two dimensions is an idiot.

The first dimension is width, the second is breadth, the third is depth, the fourth is time. Since we are affected by all 4 of those, we are technically 4-dimensional beings.

~{V}~

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Your car is a fiberglass penis extension.

[coconutmonkey]

why is time considered a diminsion? It doesnt follow any of the rules that any other dimminsions do...?

[n8]

ooooo....i thought the forth dimension was time..??...heres an idea...try painting time...and dun gimme that clock stuff!!..hehe
yeah...ummm http://www.worldofescher.com
for escher stuffs.. =)

[IO_Error]

There are an infinite number of dimensions. All the different "squashings" of a 4D cube are better refered to as 3-D "shadows" or "projections". The most popular "hypercube shadow" I've seen or heard of is the cube inside a cube, connected to the outer cube at all its vertices.
aNoah: It HAS been proven that dimensions exist beyond the third. If you are truly interested in this subject, read into Quantum Mechanics.. it'll blow your mind.
I could ramble on forever about multiple dimensions and quantum mechanics, but this is already way outside the realm of Digital Art.



IO_Error

[waylon]

Hmm. I should try to develop the world's first 4D modeling package. Think it would sell?

[Zombie]

quote:

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Originally posted by waylon:
Hmm. I should try to develop the world's first 4D modeling package. Think it would sell?

---

well, if we assume the fourth dimension is time, than any 3d package that has animation capabilities is technically already a 4d package

any movement, by definition takes place over time. Unless of course the movement is so fast as to break the human "persistance of vision", at which point it would look like teleportation.......at least it makes sense to me

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mike hovland
3d artist
midway games

[eetu]

heh a hypercube aka a tesseract is a cube with 4 spacial dimensions.
and actually i think it has 8 3d-cubes as it's sides.

check out e.g. http://www.geom.umn.edu/docs/holt/tesseract/top.html

eetu.

[Frost]

I would suppose any number of dimensions could be made -- some things can be explained mathematically which we cannot begin to understand visually. Personally, I just like to remain in 3d or less. =]

Regarding those Dali paintings... I see nothing more than simple 1-point perspective with parralel planes in the top one and the jesus one is simply a 2 (perhaps 3) point... I fail to see the magic in it. (although he was a greatly mind-screwed painter that I sort of like).

[kig]

I'm visualizing 4D as an infinite number of 3D objects. Like, in 1D you have an infinitely thin line, in 2D you have an infinitely thin plane, which consists of an infinite number of infinitely thin lines and in 3D you have an infinite number of infinitely thin planes making up an infinitely dense 3D form.

Oh, and try visualizing bending space. Not bending air or water or any matter or light etc, but bending empty space. Fun fun


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[email protected]
http://kig.seire.org/
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datte?

[balistic]

quote:

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Originally posted by n8:
ooooo....i thought the forth dimension was time..??...heres an idea...try painting time...and dun gimme that clock stuff!!..hehe
yeah...ummm http://www.worldofescher.com
for escher stuffs.. =)

---

You've obviously never seen "Nude Descending a Staircase." Anyone have a link to that piece?

The amount of misinformation in this thread is rather alarming. Current science accepts the existance of about ten dimensions. Four of them (length, width, depth, and time)are readily observable, and the rest usually only come into play on sub-atomic levels.




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Brian "balistic" Prince
3D Artist
Eggington Productions
http://www.bprince.com

[Jaymo]

4D visualized would be 3d animation. and there IS a 4d package: cinema4D H H H
just my 2 pence

[Moonlord]

escher rulez.
he has drawn a lot of cool pictures that
play with your eyes.

concerning the dimensions aspect: a math teacher
once said to us "The first 3 dimensions are easy to visualize, the fourth (he didnt say its time) is understandable too but dont bother asking about the fifth or more dimensions cuz enough scientist are going mad at it" --He said it in German though.

[This message has been edited by Moonlord (edited November 02, 2000).]

[Transcendent]

There are more dimensions than 4, it's just our evolution which blinds us from perceiving the others.

Do animals perceive time ? Do amoebas perceive matter ?

[Nex]

Uhm..

"Dimension" in this context is meant in the technical/mathematical/geometrical way.

1st dimension: a constant - a line. 1st dimensional creatures (if they would exist) can go in two possible directions on that line, so along ONE axis.

2nd dimension: a plane - a function. 2nd dimensional creatures can move along 2 axes.

3rd dimension: 3d space. movement along 3 axes is possible.

The shadow (the projection) of an "N" dimensional Object is always "N-1" dimensional. so the shadow of a 3d object is 2 dimensional etc.

for the 4th dimension there are 2 approaches that are confused often:

1) mathematical: in this approach the 4th and any additional dimension is just another variable added to a geometrical formula. Its not possible to imagine a 4 dimensional figure. The PROJECTION of it however would be a "hypercube" for instance. The shadow of a cube in 4d would be a 3d figure.

2) physical: the 4th dimension is time here.
See Einstein, Hawking, etc. on this.
after THIS definition 4 dimensional beings would be able to move in time as well as in the 3 axes.

those two definations are not that different if you think of what a 3d creature would appear to look/behave like to a 2d creature.

1.) it could suddenly appear and dissappear (when it moves through the 2d creatures dimension)

2.) it can move normally in the dimension of 2d creatures.

3.) it could see things that the 2d creature could never because it does not have this point of view. etc.


If this interrests you I recommend reading "In Hyperspace" by Michio Kaku.

[This message has been edited by Nex (edited November 02, 2000).]

[This message has been edited by Nex (edited November 02, 2000).]

[Nightime]

quote:

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Originally posted by balistic:

You've obviously never seen "Nude Descending a Staircase." Anyone have a link to that piece?

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It's a wonderful painting, here is the link:
http://www.franceweb.fr/zumba/Duchamp/bio1.html#1912

Closer look:
http://www.barewalls.com/cgi-bin/clientdetails.exe?ItemID=544&zoom=1


-JJ



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JJ / Nightime
http://members.home.net/jeremy12/web/

[Starseed]

As I understand it, the current most acceptable and studied theory of extra dimensions (some think its a greator discovery than any of einsteins . . . infact it proves one of the relativities wrong, or at least a part of it . . . can't remember whether it is special or general) Anyway, it's called the superstring theory, and I think it suggests that there are 9-11 dimensions (one of those, can't rememeber, and I'm not home to look it up in the book I have, which, by the way is a great book called "The Elegant Universe" by Greene)

Anyone here read anything on superstrings?

Oh, and I agree that the visualization of what the 4th dimension would 'look' like as depicted in the art pieces is bs. That is someone's rendition in 2d, painted to look 3d, but nothing more than that, 4d is beyond our human forms perception, like some of you said.

Of course this is all just my opinion (based on some other respectable ones) . . . I could be wrong.

-mt

[This message has been edited by Starseed (edited November 02, 2000).]

[Sergenth]

I remember seeign something about a class in either Los Angeles or San Francisco that was all about visualizing high order math concepts... 4 dimensional among other things. The professor maintained that with proper training, we could imagine in 4d. I tend to think this is possible only because we are able to interpret 2 dimensional visual data as a 3d volumetric mental estimate. That's pretty fancy neurochemics and there's a good chance it's upgradeable.

Here is a good way to visualize time in a more physical way. Imagine that you are flying through space in a ship alongside a companion ship. You encounter a region of space... a sphere, that is distorted in the dimension of time. The distortion is outward.. as an explosion is outward. So you fly through this region of thick time... and your companion ship does not go through the region. Because the time has expanded... it will take you longer to travel through this region and it will seem as if your companion ship is flying ahead of you when you look out the window. Even though the space is still the same distance, the time dimension is affecting your rate of travel. So, it's all about thick and thin region of space...

gawd.. someone tell me if I'm spouting pure bullshit... I have no idea :P

Oh, and Frost, that top image Barker posted is an Escher pic.

[Frost]

( thanks =) )

[pierre]

There is often a belief that we, "humans", have a difficulty thinking in 3d. That is wrong, the case is totally the opposite. We have severe problems thinking in 2d because of the illusion that any visual appearance tend to have on us.

Draw a straight line on a piece of paper (yeah, or on your screen) and I can assure you that most people would see it as something lying on the "paper". That makes us instantly enter the world of 3d because an objekt ontop of the other needs a z axis.

if you draw a square you will most likely see it as a flat square shaped objekt lying ontop of the paper. Now, you could also see it as a hole, but the laws of "simplicity" makes the human brain choose the easiest way to interpret a visual appearance, and in this case it is easier to see it as a flat solid objekt lying ontop, rather than a grid objekt or a a holw in the paper.

if you place say a flat square shaped objekt ontop a flat circular objekt, letting some of the circel show. You will most likely see the continuing form of the cirkle as just a cirkle, even though we don't know what hides under the square. Laws of simplicity again.

The laws of simplicity makes us tend to think in 3d, because it is easier than 2d.

We live in an eucledian world of thinking. One objekt, with a certain size, has the same size, even though it is 10.000 miles away from you.
Would we live in a pyramidal world, that would not be the case. It would have the same measurements, but it would not be of the same physical size depending on the distance it would have to you. A feet is still a feet, but not of the same length in this type of world. And this is actually how we have to think when we try to depict something in our world of 3d on a flat (2d) piece of paper.

just my two cents. my fingers got tired pretty quick

pierre

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http://www.crosswinds.net/~pierrehannah

[Seraphire]

I don't think I have much more to add.

I do believe it is possible to imagine in the 4th. Being time.
And we do exist in at least 4. Though we can't percieve the fourth all at once. We have to view one section of it at a time. Which is being represented in that applet, posted earlier.

3d object, can have width, height, and time, but not length, can't it?

Starseed, I have read a little about superstring. Very little. It ties together quantum and reletivity, which don't work together, or something, like that. Memory has faded, and I could be completely wrong.

I don't think that the art is BS. It's an emotional visualization. Not a mathematical one. The idea isn't to accurately display what it looks like. Just to give the idea, and let the persons imagination take over.


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The Groove is in the Heart!

Seraphire
Michael Jon Birkhofer
Seraphire's Cafe/The Monochrome

[Zoogie]

quote:

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Anyway, it's called the superstring theory, and I think it suggests that there are 9-11 dimensions

Anyone here read anything on superstrings?

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Ack... IE ate my original post Anyway, here's a kinda interesting link about string theory, M-theory, and dualities: http://www.physics.ucsb.edu/~jpierre/strings/tutor.htm
I've kinda lost touch with string theory since reading "Hyperspace" by Michio Kaku (as someone mentioned earlier, it'll blow your mind) a few years ago. I think that "Beyond Einstein" (also by Kaku) touches on string theory a bit.

quote:

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Oh, and I agree that the visualization of what the 4th dimension would 'look' like as depicted in the art pieces is bs. That is someone's rendition in 2d, painted to look 3d, but nothing more than that, 4d is beyond our human forms perception, like some of you said.

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Heh, I had a class project a while back which involved describing a four-dimensional object produced by an expression we were given. Now that I think about it, it was probably a hyper-hyperboloid or something like that. I didn't do too well (and it left me with a splitting headache)

[This message has been edited by Zoogie (edited November 02, 2000).]

[sacrelicious]

I checked out the hypercube link in Ben's post (the dogfeathers one)... holy shit! I was looking at this stuff, my eyes crossed and feeling like an idiot, when all of the sudden the images just POPPED into focus. They appear 3D and are perfectly sharp, not at all blurry. Everyone should check it out, if only to go "holy shit!" like I did. Everything else important or interesting has already been said so... um... see ya!

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mmm... sacrelicious