Tesseract

[edit]

Reason: I nominated this animation because in really helped me visualize a tesseract. Compare with still tesseract image. The colors are clear and make it stand out nicely.
Articles this image appears in: Tesseract
Creator: Jason Hise
Nominator: Leon math

Support — Leon math 23:41, 11 January 2007 (UTC)[reply]
Strong Support I love this animation. It is so cool. --Midnight Rider 00:30, 12 January 2007 (UTC)[reply]
Support Beautiful. TimVickers 00:33, 12 January 2007 (UTC)[reply]
Support Though strictly speaking it is an animation of a 2D projection of a 3D projection of a rotating tesseract. —Dgies^t c 00:33, 12 January 2007 (UTC)[reply]
- Should I then change the caption? Leon math 00:39, 12 January 2007 (UTC)[reply]
  - Nah, I'm just being pedantic. —Dgies^t c 05:19, 12 January 2007 (UTC)[reply]
Support This makes me think. --Arad 00:56, 12 January 2007 (UTC)[reply]
Support Very interesting and unique, higly enc. Arjun 01:33, 12 January 2007 (UTC)[reply]
Support soooo enc and this picture is worth a book worth of words. I wish I could find the question on the reference desk that I asked about 4 dimensional space; somebody linked to a fascinating picture like that one.. IIRC a 4 dimensional pyramid moving through 3 dimensional space --⁪froth^{T C} 01:52, 12 January 2007 (UTC)[reply]
Support, I found that this image illustrated the concept better to me, but this is nevertheless also an excellent illustration. Noclip 02:04, 12 January 2007 (UTC)[reply]
- Another thing that helped me visualize 4 dimensions is taking cross sections. For example, the cross sections of a hypershere would be spheres getting larger and larger but then shrinking, just like the cross section of a sphere. The cross sections of a tesseract are just a sequence of cubes, but that wouldn't make for a very good image. Leon math 02:23, 12 January 2007 (UTC)[reply]
  - Wouldn't it just be a cube that appears and disappears? --⁪froth^{T C} 04:01, 12 January 2007 (UTC)[reply]
  - The cross-section would only be a cube in special cases. Otherwise it can be a variety of shapes, as this 3D projection shows. — BRIAN0918 • 2007-01-12 21:35Z
  - This image does not show cross sections, but instead shows a projection. And true, if you cut it at an angle the cross section wouldn't be a cube.Leon math 21:45, 12 January 2007 (UTC)[reply]
    - If you had a 4 dimensional cube moving straight through 3 dimensional space (straight on, not at any funky angles or anything) then I'm quite sure it would be a single cube that poofs into existance and then disappears --⁪froth^T 23:02, 12 January 2007 (UTC)[reply]
      - That doesn't sound right. If you have a cube, and you move it through a 2D plane, it could show up as a square and then disappear immediately, but that's only if one of the cube's surfaces is parallel to the plane. Otherwise (ie, the more likely case), you're going to see an object with sides that change in length. For a hypercube it'll produce even more complicated results. — BRIAN0918 • 2007-01-18 23:15Z

Support Oh boy that confuses me. That would definetly make a great screensaver. It tis be a winner. Why1991 02:40, 12 January 2007 (UTC)

Support That's cool --Fir0002 02:57, 12 January 2007 (UTC)[reply]

Support I've been trying to picture this since I was a kid. Noraad 03:00, 12 January 2007 (UTC)[reply]
Strong Support It suddenly makes sense! --Iriseyes 03:08, 12 January 2007 (UTC)[reply]
Support - a lovely illustration of a projected rotation - does anyone know a well-established mathematician who has claimed to be able to visualize 4 spatial dimensions without tricks such as projection or cross-sectioning? I seem to recall hearing that no mathematician has ever claimed that. Debivort 05:36, 12 January 2007 (UTC)[reply]
- We have 2D computer displays. An animation can be seen as having 3 dimensions, the two of the screen, plus time. The domain of animations on computer screens could therefore be considered to be ${\displaystyle \mathbb {R} ^{3))$ ${\displaystyle \mathbb {R} ^{3))$ . Since an ${\displaystyle \mathbb {R} ^{4))$ ${\displaystyle \mathbb {R} ^{4))$ domain is not a subspace of ${\displaystyle \mathbb {R} ^{3))$ ${\displaystyle \mathbb {R} ^{3))$ , the only way it can be converted to ${\displaystyle \mathbb {R} ^{3))$ ${\displaystyle \mathbb {R} ^{3))$ is through a map, such as ${\displaystyle \mathbb {R} ^{4}\rightarrow \mathbb {R} ^{3))$ ${\displaystyle \mathbb {R} ^{4}\rightarrow \mathbb {R} ^{3))$ . Projections and cross-sections are just types of maps. You could come up with other maps but you still couldn't "see" the whole shape at once since your animation only has a domain of ${\displaystyle \mathbb {R} ^{3))$ ${\displaystyle \mathbb {R} ^{3))$ . For a static image, you have only an ${\displaystyle \mathbb {R} ^{2))$ ${\displaystyle \mathbb {R} ^{2))$ domain available. Therefore you would need a ${\displaystyle \mathbb {R} ^{4}\rightarrow \mathbb {R} ^{2))$ ${\displaystyle \mathbb {R} ^{4}\rightarrow \mathbb {R} ^{2))$ map, such as the projection you see in a single frame of this animation. What you're asking for is sort of like the vector space version of saying "Has any mathematician found a way to make 4=3?" Hope that helps. —Dgies^t c 06:01, 12 January 2007 (UTC)[reply]
  - While a nice explanation and use of notation, it doesn't really help because I was just curious if anyone with mathematical clout had ever historically claimed to be able to visualize it. I've had some pothead buddies say they could visualize 4 spatial dimensions, that doesn't carry much weight. Debivort 07:16, 12 January 2007 (UTC)[reply]
    - This is nothing any mathmatician could do for us. To visualize four spatial dimensions you'd have to overcome the limitations of your own mind, which is from birth on conditioned to three spatial dimensions. Interesting question whether this limitation is intrinsic, or environmental. Fact is, we have two 2D organs, which deliver just enough information to generate a pseudo 3D image in your mind. Even if reality would have more than three spatial dimensions there is no way we could see 4D. --Dschwen 12:17, 12 January 2007 (UTC)[reply]
      - You guys are sure answering a historical question with a lot of certainty. One could imagine a flatlander claiming to be able to visualize something in 3D, and I could similarly imagine a person claiming to be able to see 4. I just wonder whether it has happeened or not. Debivort 13:43, 12 January 2007 (UTC)[reply]
        Yeah yeah, and if a tree falls and nobody is around to hear it, does it make a sound?. I'm not answering the historical question with certainty. However I'm answering your question with the certainty that the math of sub-spaces and projections gives me. And furthermore it should be obvious that I'm in no way certain about the role the brain plays in the apparent (?) limitation to 3 dimensions. --Dschwen 15:47, 15 January 2007 (UTC)[reply]
    - OK, so perhaps there was a misunderstanding. I thought you were asking if there was a way of visualizing in terms of images and videos without using a projection or slicing technique, and showed why that's not possible. You were really asking if someone can see higher-dimensional objects in their mind's eye. I don't think it's a topic of serious mathematical discussion as it is not verifiable by anyone else. —Dgies^t c 16:43, 12 January 2007 (UTC)[reply]
      - Yes I could definately visualize 4 dimensions after first reading Flatland. I couldn't see anything in the fourth dimension of course since there's nothing to see but I could clearly visualize 4D "spheres" and "pyramids" moving through 3 dimensional space. --⁪froth^T 23:05, 12 January 2007 (UTC)[reply]
        Wow, I definately couldn't after reading either that or Sphereland. It was required to do a project on it in geometry in 6th grade, so I drew a little town on posterboard. Clearly such art has evolved... --Iriseyes 00:04, 13 January 2007 (UTC)[reply]

Support per all above. Krowe 06:27, 12 January 2007 (UTC)[reply]

Support per above — Lycaon 07:17, 12 January 2007 (UTC)[reply]
Support just for the beauty of it and before trying to analize its logic. To understand the kind of difficulty we are dealing with try to imagine what a rotating 3D cube looks like by observing its projection into a one-dimensional space (a straight segment, for example). As far as I know no one ever claimed to have visualized a 4D hypercube. The best we can do is to construct an intelectual model of it - Alvesgaspar 08:32, 12 January 2007 (UTC)[reply]
Support Mmmmm a 2D representation of a 3D representation of a 4D cube... Now what does a 5D cube look like... --antilived^{T | C | G} 10:25, 12 January 2007 (UTC)[reply]
Oppose I don't like moving pictures. Having a moving picture as Picture of the Day would make it annoying to try to read anything else on the Main Page. Otherwise, very interesting picture. (Could buttons be added to make it start and stop moving?) --Coppertwig 13:28, 12 January 2007 (UTC) Never mind, I understand a still picture would be shown on the main page with a link like "view the animation". Objection withdrawn. Nifty picture, anyway. --Coppertwig 02:34, 14 January 2007 (UTC)[reply]
- There are plenty of animated FPs, and they are often Picture of the Day. There is usually a link that says "view animation"--Bridgecross 15:02, 12 January 2007 (UTC)[reply]
Oh and Support per Mrs Whatsit. --Bridgecross 15:09, 12 January 2007 (UTC)[reply]
Support Somehow, "WOW!" just doesn't quite say it. TomStar81 (Talk) 19:03, 12 January 2007 (UTC)[reply]
Support Very cool. FP quality all the way. S h a r k f a c e 2 1 7 20:33, 12 January 2007 (UTC)[reply]
Weak oppose. If you can add some information to the caption indicating how the tesseract is rotating, I'd support. Right now, it makes people think that tesseracts rotating in 4 dimensions will always give that appearance, which is not true. Any sort of addition to the caption would be an improvement. — BRIAN0918 • 2007-01-12 21:33Z
Support. Definitely makes me want to learn more. --Tewy 01:52, 13 January 2007 (UTC)[reply]
Support not much to say besides 'awesome'. I used to have a screensaver of a hypercube, until I caught myself deliberately not working so it'd come on. Opabinia regalis 03:03, 13 January 2007 (UTC)[reply]
Support. Great FP stuff. To quote Chris Rock: "It's spinnin', nigga, it's spinnin'!" :)). - Darwinek 00:41, 14 January 2007 (UTC)[reply]
Support. Great!-Ran da l l l in 03:03, 14 January 2007 (UTC)[reply]
Strong Support! Wikipedia rarely gets images as good as this one! Wow! This is great! Ilikefood 02:11, 15 January 2007 (UTC)[reply]
Support. This image gives information that would really be impossible to absorb simply by reading text. --Dante Alighieri | Talk 20:13, 15 January 2007 (UTC)[reply]
Support Awesome geek porn. ~ trialsanderrors 22:34, 15 January 2007 (UTC)[reply]
Support That's very interesting and adds what can't be explained in text. Darth griz⁹⁸ 01:47, 16 January 2007 (UTC)[reply]
Support, Wow, I've been staring at this for 10 minutes. It's really pretty! --Tohru Honda13^{Talk•Sign here} 04:49, 16 January 2007 (UTC)[reply]
Support ??? ;-) | AndonicO ^{Talk · Sign Here} 13:50, 16 January 2007 (UTC)[reply]

Support Great picture. Well done! --vineeth 06:16, 17 January 2007 (UTC)[reply]
Support Helps me visualize a tesseract, where can I find a still to compare? Photonikonman 13:41, 18 January 2007 (UTC)[reply]
- Check the article; it has several examples. --Tewy 20:17, 18 January 2007 (UTC)[reply]

Promoted Image:Tesseract.gif --KFP (talk | contribs) 00:06, 19 January 2007 (UTC)[reply]