What does a 4D "cube" look like?

[dark_energy]

I can't imagine something with more than a length, width, and height... <div class="Discussion_UserSignature"> </div>

 

[yevaud]

Try this like for an introduction to Tesseracts.<br /><br />http://www.geom.uiuc.edu/docs/holt/tesseract/top.html <div class="Discussion_UserSignature"> <p><em>Differential Diagnosis:  </em>"<strong><em>I am both amused and annoyed that you think I should be less stubborn than you are</em></strong>."<br /> </p> </div>

 

[bobw]

Here's a link to my favorite picture of a hypercube. Get out your 3-D glasses!<br /><br />http://dogfeathers.com/java/hyprcube.html <div class="Discussion_UserSignature"> </div>

 

[vogon13]

How about a mobius strip in the fourth dimension?<br /><br />Think about it. <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[vogon13]

I thought of klein bottle, too, but figured more folks had seen and played with the mobius strip.<br /><br />Could someone post one of Eschers neat mobius prints? The one with the ants on it is really intense. <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

 

[Leovinus]

Since you can only see 3 dimensions, anything will more than 3 dimensions can't be "looked" at and so can't "look like" anything. <div class="Discussion_UserSignature"> </div>

 

[tom_hobbes]

Yeah, but can somebody do a diagram? <img src="/images/icons/wink.gif" /> <div class="Discussion_UserSignature"> <p><font size="2" color="#339966"> I wish I could remember<br /> But my selective memory<br /> Won't let me</font><font size="2" color="#99cc00"> </font><font size="3" color="#339966"><font size="2">- </font></font><font size="1" color="#339966">Mark Oliver Everett</font></p><p> </p> </div>

 

[kmarinas86]

A 4-D cube would appear to change shape in a 3D representation as you rotate it like how a 3-D shape appears to change shape on 2-dimensional paper as you rotate. A cube seen in a 2D representation is a sum of crossections like how a 1D representation is a sum of crossections of a 2D object laid perfectly flat. A 0D representation of a line is a sum of cross sections of a line. If we were to have a 4D object, we could make a 3 dimensional crossection of it. Every crossection of a 3D object gives us a 2D shape. Of every 2D shape a 1D line. Of every 1D line, a 0D point. A 0D point cannot have a crossection. There is no -1st dimension.<br /><br />The notion of a 5th dimension violates the law of conservation of energy. The 4th dimension is not spatial at all - it is time. Object A can only exist with Object B if they are on the same time. It would violate the law of conservation of energy for two seperate times to collide at a certain present just as how two points on a line can never meet each other. Time is not spatial - it is instantaneous.

 

[main_sequence]

width, height, and length moving through time...

 

[harmonicaman]

A nice Wikipedia tesseract page.<br /><br />You can make a model of a hypercube at home by dipping a wire cube into a soap solution.

 

[tplank]

Just a bump because I think Escher is cool. <div class="Discussion_UserSignature"> <p>The Disenfranchised Curmudgeon</p><p>http://tonyplank.blogspot.com/ </p> </div>

 

[smartie]

Could someone please explain to me clearly why an object can not be described to have a forth spatial dimension of scale. <br /> With the lenght dimension I can move left and right. With the width dimension I can move forward and backwards. With the height dimension I can move up and down. With a forth spatial dimension I would be able to move in and out. Unfortunately I'm not permitted to move freely through it, but I have been growing into it since I was a concieved. <br /> Does'nt the 4D hypercube demonstrate this forth spatial dimension of scale. Imagine a cube expanding and contracting. http://en.wikipedia.org/wiki/Tesseract <br /><br />

 

[smartie]

Could someone tell me how to add an image to my posts. I keep trying

without much success. Any ideas?

 

[najab]

Because of 'questionable' images posted in the past you aren't allowed to link directly to images. All images have to be uploaded via the "Preview post" screen so that they can be approved.

 

[bobw]

When you make a post there is a check box under the text window where you type. Make sure it is checked to preview your post. Under the preview window there is a blank space with a browse button. Click browse and select the picture from your computer. When you submit the post the image file is uploaded along with the text. The picture has to be approved by moderators before it will show up. Until then there is a message in its place which says "image waiting for approval". They stopped letting people attatch files with the hypertext commands when someone posted a bunch of porn. <br /><br />Edit: sorry I was slow, dial-up <img src="/images/icons/frown.gif" /> <div class="Discussion_UserSignature"> </div>

 

[najab]

Your explaination was way better than mine anyway! <img src="/images/icons/smile.gif" />

 

[raghara2]

Actually there was some picture at MS research. It depends on definitions of view transforms. 4D in space defined (axis aligned) cube could be translated into 2D image in 4 different ways. One of them is square.<br /><br />If you will look at wolfram research, there are some 2D p-p images of rotating 4D objects as well. http://mathworld.wolfram.com<br /><br />That 4D 120 and 600 vertices objects are particulary nasty.<br /><br />

 

[harmonicaman]

Cool webpage! Some of the infinitely connected periodic minimal surfaces pictured there were discovered by Physicist Dr. Alan Schoen, SIU-C. He's a great violin player and we've jammed together at various events...

 

[yanks1419]

I think a 4D cube doesnt make sense. In the picture with the ants on the 1st page, I think that is cool but yet impossible. Excuse me for my lack of imagination, but if 4D was like the ants in the picture then wouldn't that be defying the laws of gravity?

 

[dark_energy]

It's not a 4D "cube" per se. It's a tesseract or 4D shape that you can construct with 3D figures as the shape's net, in contrast to 2D shapes being used as a net for a 3D shape. <div class="Discussion_UserSignature"> </div>