Talk:Five-dimensional space

Suggest to establish an answer and/or to add an expiration date, if appropriate.

Move to "Five-dimensional space"? (No - see reason, expiration: none)
This article seems to be written from the perspective that there's a preferred coordinate system (starting with "up/down, left/right and forwards/backwards"), with respect to which a fifth dimension might be identified. This is certainly not the favored approach of contemporary geometers. I suggest a move to Five-dimensional space and a corresponding overhaul of the article. --Trovatore 18:43, 16 November 2005 (UTC)

Reason for 'no': In addition to geometrical dimensions there are also physical dimensions, which are already height, width, depth and time (multiplied by velocity of light). Candidates for an additional 5th physical dimension are e.g. mass and probability.--Turul2 18:48, 04 December 2008 (UTC)

Volume? (fixed, expiration: none)
This article contains a formula to find out the volume of a 5 dimensional circle. Surely volume is not the correct word to describe the amount of space contained inside this 5d shape - just like area does not describe the amount of space inside a 3d object. Volume is measured in m3, which only describes 3 dimensions, the 5d objects amount of internal space would be measured in m5. —Preceding unsigned comment added by 86.134.9.179 (talk • contribs) 09:01, 17 June 2006


 * The generic term is content. Will fix.  &mdash;Tamfang 17:45, 17 June 2006 (UTC)


 * Has been fixed to hypervolume. No appropriate article content. &mdash;Turul2 19:11, 04 December 2008 (UTC)

Time as one of the 5 dimensions?
This article talks about the 5th dimension as an additional spatial dimension beyond the 4th, which it identifies as time. First of all, I don't think time can be regarded as a spatial dimension (at least, I doubt such an assumption is commonly accepted). Second of all, if the 5th dimension is merely another spatial one and non-temporal, then it is exactly like what the Fourth dimension article is talking about (4 spatial dimensions, potentially with one additional temporal one), except that the dimensions are labelled differently. In which case, I'm not sure I see the justification for a separate article. On the other hand, this article appears to be focusing on the geometry of 5 spatial dimensions, as it refers to 5D polytopes, and so it should not confuse the issue by labelling one of the dimensions as time. Besides, 4D space-time as defined by General Relativity is Minkowskian, not Euclidean, and as far as we know, the universe is by no means Euclidean with or without additional dimensions, so the discussion of polytopes doesn't really work in that context. I think this article should focus on 5D Euclidean space, and not try to rationalize it in terms of space-time.&mdash;Tetracube 00:36, 2 November 2006 (UTC)


 * I whole heartedly agree! You have expressed this extremely well. Borg Master (talk) 09:41, 10 December 2023 (UTC)

both space and time are the 4th dimension, known as the spacetime dimension —Preceding unsigned comment added by 24.189.153.102 (talk) 13:10, 8 June 2008 (UTC)

Selector as the 5th dimension
As discussed in theory on the 4th dimension, time or speed is accepted as the 4th dimension. We have length, depth and height as the three other dimensions. So what is the 5th dimension? Is it a selector of the property of the 4th dimension? Lets just play with the thought and say that a value of 1 in the 5th dimension represents the property of time in a certain point in the 4th dimensional space, therefore the given value in the 4th dimension represents the time at which the 3rd dimensional image is given. This would mean that the image is moving according to the value in the 4th dimension.

The thing is that the value in the 5th dimension points to every possible version of the 4th dimension. The 5th dimensions give the 4th dimension all possible properties of the physical universe, probably also the abstract universe. In the 4th dimension we observe time when the value of the 5th dimension is 1. When the 5th dimension value is 2 it can represent atomic mass. Value 3 can represent taste. The value N represents all properties given in the relative universe of this specific case.

The full aspect of the 5th dimension is unthinkable to us, other than from a mathimatical point of view, as pain is for a rock.


 * Daniel Holth, Norway 2nd November *

(Grammar edited by Dennis Standing)

One particular variant of Kaluza–Klein theory is induced matter theory and this theory relates the 5th dimension to mass and momentum along it to charge (see discussion item 4 and space-time-matter consortium). --Turul2 (talk) 17:44, 18 August 2008 (UTC)

10th dimension link
I think the link to "Imagining 10th dimension" should be removed, since it's mostly science fiction and nothing to do with current scientific concensus. —The preceding unsigned comment was added by 80.222.116.225 (talk) 12:39, 23 December 2006 (UTC).
 * Seconded. \Mike(z) 17:40, 5 January 2007 (UTC)

mistake
I myself, studying dimensional theories, must disagree with the hypercube theory. Though it present an exceptional understanding of the dimensional pattern which my work is highly dependant on. It forgets that a line, one dimensional, extends infinitley. The square does NOT define two dimensional space. A parallelogram is the correct symbol. The parallelogram represents a plane once again extending infinitely. The cube, I will except as the symbol for three dimensional due to lack of excepted geometric symbol. The cube you must remember, as a representation of three dimensional, extends infinitely in all directions. Due to that fact the point, the line, the plane, and the cube are all co-cubular (lack of better word once again) so the hyper cube etc. are also co-cubular and not a shape exceeding the third dimension.

p.s. sorry for poor wording but mathmaticians have not yet had reason to define one where my words lack.

p.s.s. The person who orginated this theory was Intelligent and deserves credit. His theory is perfect in all ways except using a line segment in the stead of a line.

--Leon vautour 23:42, 6 January 2007 (UTC)Leon X Vautour

confusion
From the article: "Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated"

Isn't the 5th dimension sound? Imagine:
 * 1)  a line
 * 2)  a plane
 * 3)  a shape
 * 4)  a shape rotating/moving through space
 * 5)  a shape rotating/moving through space and speaking.... ? (e.g., a holographic talkie, or a memory projection)

Which would make the 6th dimension "energy" transferred from one shape to another... ? --Renice 13:34, 24 March 2007 (UTC)

Btw, this would also mean that Jedi knights are able to think in the 7th dimension -- the ability to force a 6th dimensional object to exert energy through suggestion. --Renice 14:20, 24 March 2007 (UTC)

This would also suggest that astroplaning may be a form of 7th dimensional thought. --Renice 14:42, 24 March 2007 (UTC)

The Hypercube...
The fifth dimesnion is described by some scientists as the 3rd dimension wrapping around itself. Look closely at the net of the hypercube and the resultant hypercube. The net is obviously 3-dimensional, unlike normal geometrical nets. In order to form the hypercube, the net appears to wrap around itself, joining the opposite ends of the net together, providing a visual representation of the 5th dimension. —The preceding unsigned comment was added by 64.149.188.82 (talk) 01:13, 10 May 2007 (UTC). angelic conscioussness is not numeric —Preceding unsigned comment added by 77.165.5.122 (talk) 19:36, 28 February 2009 (UTC)

There is no 5th dimension
As far as spatial and temporal dimensions are concerned, the four are length, breadth, height, and time. The myth that there is a 5th seems to stem from the 60s pop group. I read here about some silly suggestion that the Star Wars 'Force' could be a dimension. That is not related to time (it does not interfere with it) or space (there are still 3 dimensions). These four dimensions can't be interfered with in any way in the real world, and they are all, by definition, infinite. Therefore, there is no 5th dimension. Gravity does not interfere with these dimensions, and it varies on location [the moon has less of a pull]. The physics view of a 5th dimension is complete myth.

In geometry, there are only 3 dimensions, except in the real world where the 4th may manipulate the other 3. The other 'dimensions' are just combinations of 2 of the 3 dimensions.

The article's neutral stance is unjustified because it has been acknowledged almost universally by the scientific community that there are only 4 dimensions.

4th dimension is spacetime, so it does exist and is its own dimension, the 5th dimension theory could be possible, as there may be infinite dimensions. ex: 1st dimension a line 2nd dimension a line squared= a square 3rd dimension a square squared=cube 4th dimension cube squared= tesseract. possibility of a penatract. each dimension shows a side: the 1st is a line, so no sides, 2nd is a square showing 1 side, 3rd is a cube showing a full 6 sided view. 4th is spacetime and a tessaract showing many sides i havent counted yet. but the possibility of something past spacetime is low. there so far is a magnetic pole, a cosmic string, a domain wall, something about the 3rd dimension, and a spacetime tesseract. if there is a 5th dimension, it is impossible to find out what it is, except for the fact that it is a penatract24.189.153.102 (talk) 13:26, 8 June 2008 (UTC)

@24.189.153.102 You know what I think, the fifth dimension is probably a plane where objects travel far faster than light, which would mean that we are unable to see objects within it, even if it existed. I suspect if a type of "ghost" were real that it would live in that dimension. There are endless possibilities in this universe, you will never know all of what is out there. ~ali31 173.85.202.240 (talk) 18:43, 18 April 2011 (UTC)

Describing five dimensions with mathematical equations
this section uses stuff like "we" and "lets" and "(you) think" that makes it kind of personal and should be fixedSoyseñorsnibbles 01:52, 28 September 2007 (UTC)

Smallville
Has a fifth dimension ever been actually mentioned in Smallville (TV series); can you name the episode? If not, I think it should not be listed here, even if some people speculate on the Mxyzptlk connection. 213.216.199.6 (talk) 13:15, 5 January 2008 (UTC)
 * I find the whole popular culture section rather pointless really since only a few of the references really address the actual concept of a fifth dimension. Anything to do with comics books generally use the word "dimension" as a synonym to some alternate plane of existence and therefore irrelevant to the subject of the article. Takeshi357 (talk) 14:44, 1 February 2009 (UTC)

The 5th dimension in Biology
Kodjo and Togbey, (2000?), proposed that 4/5 is the exponent that represents allometric scaling of the brain. They reasoned that 5 is the natural extension of 1/2, 2/3, and 3/4 exponential (fractal) scaling laws of tissues. Since they found a close 4/5 scaling factor for neurons, and 5 is the denominator of that, they reasoned that the 5th dimension is that of thought. [Note: allometric scaling is non-linear variation of morphology based on mass or size, or other measurement of an organism or organ.] http://www.unomaha.edu/wwwmath/OurArchive/KerriganMinigrants/2006_2007/KodjoTogbeyReport.pdf for details. 74.195.25.78 (talk) 01:10, 8 January 2008 (UTC)

Five-dimensional equations
Any equation or set of equation whose exponents sum to 5 may be said to be 5-dimensional. Of course there are some sets of equations found in chemistry and mechanical engineering books that extend to 20 dimensions. Also, if E=mc^2 is correct, and c is not necessarily constant, then Energy (not the relationship between energy and what else) is five-dimensional. [c^2 would equal distance^2 / time^2; 2+2 = 4 (dimensions)] 74.195.25.78 (talk) 01:19, 8 January 2008 (UTC)

Editing the first paragraph (Intro)
The word space has been relinked form vector space to Euclidean space. This is a restriction, because there are also Hilbert-spaces and Riemannian manifolds. As the following sentence says, the the 5th dimension will be the whole space, but it should be a line of all locations, where the first 4 components remain constant and the fifth varies.

Suggestion: link space instead to euclidean space to Riemannian manifold etc. and reformulation of the definition, what a 5th dimension is.

Why has the reference to fourth dimension been removed ?

--17:25, 22 August 2008 (UTC)~ Turul2


 * I know that Euclidean space is more restrictive, but this article mainly focuses on Euclidean space (e.g., 5-polytopes), so I thought it was more appropriate. The Euclidean space article is also easier for the general reader to grasp, whereas Vector space (the original link target) is much more abstract. From the POV of a casual reader, it would be quite difficult to understand how exactly the vector space article explains the word "space" in the intro.


 * Also, I removed the reference to fourth dimension because it didn't seem to be directly pertinent to this article. Feel free to put it back if you feel otherwise.


 * Anyway, I was just trying to make the article more readable to the casual reader. If you think that is detrimental, please feel free to rework it.&mdash;Tetracube (talk) 18:21, 22 August 2008 (UTC)

5 dimensional stellations
Out of curiosity: are there stellated shapes in 5 (and higher) dimensions - and what would they project as in our 3D world? Would they be 'chandelier-crystals-like' or 'coral-like'? Jackiespeel (talk) 15:39, 17 January 2013 (UTC)
 * Yes, but none of them are regular. You can see cross-sections of some of them at Jonathan Bowers' website. Double sharp (talk) 15:45, 17 January 2013 (UTC)
 * So would they be 5D versions of the images in crystal growth? How would 'polyhedra, simple or complex, stellated or otherwise, flexagons and other geometric objects' in general be seen in 'our' 3D world - and would there be 'seemingly disconnected objects that would move as a whole if you picked up one of them'? Jackiespeel (talk) 22:12, 20 January 2013 (UTC)
 * To understand how we see a 5D object psas through our 3D space, we need to do a little more dimensional analogy than we usually have to do for 4D objects. A 5D object forms a cross-section on a 4D plane if you stick the 4D plane through the 5D object. A 3D plane can be stuck through this 4D cross-section, creating a cross-section of a cross-section, otherwise known as a poke-section. (You could extend this down another dimension by sticking a 2D plane through this 3D poke-section, creating a jab-section, and so on until you hit the bottom.)
 * On your last question, yes there would – consider the outermost poke-sections of the quasitruncated penteract. (Poke-sections are cross-sections of cross-sections. A cross-section of a poke-section is called a jab-section.) You could pick up any one of the eight apparently disconnected shapes arranged like the vertices of a cube, and they would move together, for they are part of the same 5D object.
 * How each object will be seen in your 3D world depends a lot on the shape itself and at what angle you poke it into our 3D world. Double sharp (talk) 16:08, 10 April 2014 (UTC)

Putting it another way, as many of us cannot visualise 5D space:

The prongs of a 3D rake in Flatland would appear as a set of oblongs or circles (depending upon the intersection plane) which would move together 'for no apparent reason.' If it fell on its side it would 'somehow' become a single L shape.

How would the equivalent part of a 5D rake appear in our 3D space (one object or several, or 'depends upon the way it is positioned') - and what happens when 'it falls on its side' and several parts move out of our set of three dimensions? Jackiespeel (talk) 16:50, 21 January 2013 (UTC)
 * It depends on what you think a 5D rake looks like. Since there is AFAIK no such thing, I do not really know what kind of object you are thinking of.
 * What intrigues me is your use of Flatland as an analogy. Flatland is 2D, so you're going down one dimension, but your proposed 5D-to-3D goes down two dimensions. Perhaps it would be a better analogy to imagine a 3D rake passing through Lineland, or a 4D rake (tetraspace objects have been a lot more thought about because they're the simplest to visualize for all dimensions higher than 3!) passing through Flatland, if you want to understand how your proposed 5D rake would pass through our universe. Double sharp (talk) 16:08, 10 April 2014 (UTC)
 * The 'issue' is the visualisations. We are all familiar with the 3D world and 'shadows, cross-sections and conic sections' - with rakes, doughnuts, stellations and other 'complex shapes' having different cross sections, possibly 'a group of linked but disconnected shapes' (rake, potato stamp, stellation of the stellation etc). That a 4D+ 'object' would have a 3D 'conic section' appears perfectly logical (even if it is difficult to visualize the object).
 * Indeed a 4D object would have a 3D cross section, but I don't see how a 5D object would have a 3D cross section. In the same way, a 2D object has a 1D cross section, but a 3D object doesn't have a 1D cross section. You can take the cross section of its 2D cross section, however, and that would be 1D. Similarly, an nD object has an (n − 1)D cross section. Double sharp (talk) 11:57, 11 April 2014 (UTC)

Another way - taking List of Wenninger polyhedron models - with 4D+ 'polyhedron of some form' or other objects would there be equivalents of the Fourth stellation of the cuboctahedron where the 3D 'facets/components' are likewise separate as we see them, but which would move as a single object? Jackiespeel (talk) 17:51, 10 April 2014 (UTC)
 * Those facets are not disconnected as we see them, nor are they 2D. It is just that they intersect each other and pass through the inside of the polyhedron, so that you can only see the externally visible parts. As another example, in the small stellated dodecahedron, you can only see the spikes of each pentagrammic face, and the internal pentagonal areas of the stars are not visible from the outside.
 * Nonetheless, if you mean a self-intersecting polytope (which would have areas of facets invisible to a viewer of the same dimensionality, because they are inside the polytope), quite a lot of the known nonconvex uniform polytopes (the gocco family seems a good candidate, starting og, gocco, gittith, ginnont, goxaxog, gososaz, gook, ganinov, godedak, gafefer, gizazac, etc.) Double sharp (talk) 12:03, 11 April 2014 (UTC)
 * I did ask the question a while back, and this is getting slighty outside my area of knowledge of the subject.

The question more generally is/was how would 'a five dimensional object appear in a particular 3D space as it moves through that space' (on a graph the x, y, z axes)? Going back to the 3D-2D analogue, the rake would present different shapes in Flatland as it rotates - would a 4D/5D/other D object do the same in our 3D universe? Alternatively - consider the inhabitants of a '3D aquarium' in a 5D (v, w, x, y, z) world rolling 3D dice that can move in all 5 dimensions - would the dice at times appear to be only 'flat surfaces (eg lying along v, y, z axes) or lines (v, w, x) - and in a 6D universe would the dice sometimes 'disappear' entirely (being aligned u, v, w)? Jackiespeel (talk) 21:19, 11 April 2014 (UTC)

Removed section: In popular culture
This section was removed, and I have no problem with the removal, except eventually someone will start adding things back. So any debate can go on talk, and this section below can be a references. Tom Ruen (talk) 22:09, 4 December 2014 (UTC)

In popular usage, the "fifth dimension" is often used to refer to unexplored or unknown aspects of the universe, and not necessarily to the mathematical concept of a 5-dimensional space.
 * In popular culture


 * For example, the opening narration of The Twilight Zone begins: "There is a fifth dimension, beyond that which is known to man."
 * In the fictional universe of DC Comics, the "fifth dimension" is said to be the place from which Mister Mxyzptlk, a Superman villain, comes.
 * The 1965 Lost in Space TV show episode "Invaders from the Fifth Dimension" features hostile aliens from the fifth dimension, and the Robot describes their spaceship by saying: "The craft is surrounded by a force field in the fifth dimension, which is... mathematically... impossible."
 * In 1966, The Byrds released an album titled Fifth Dimension, using the fifth dimension as a metaphor for unexplored and unknown aspects of the universe and oneself.
 * The 5th Dimension is the name of an American vocal music group popular in the late 1960s and early 1970s.
 * In Hindu philosophy, the fifth dimension of love of the Divine is termed by the Gaudiya Vaisnavas as turyatita, the dimension of the soul's Soul. The original Doctor Who episode hints at the 5th dimension being key to the abilities of the TARDIS.
 * Other uses of the "fifth dimension" are closer to its mathematical meaning. For example, the novel The Boy Who Reversed Himself features 4-dimensional and 5-dimensional spaces, using the mathematical fact that a 3-dimensional object can be turned into its mirror image if additional spatial dimensions were available for it to rotate through. The characters in Madeleine L'Engle's novel A Wrinkle In Time use the fifth dimension as a "dimensional shortcut" to travel through space. A similar concept appears in the Powerpuff Girls episode Bring Back Jojo, where a creature able to see higher dimensions takes a dimensional shortcut through a fifth dimension to travel through time. The Red Dwarf episode "Parallel Universe" refers to the fifth dimension as the space in which multiple four-dimensional spaces exist.
 * Not all references to the "fifth dimension" in the mathematical sense involve time travel or space travel; Douglas Adams' book Mostly Harmless advances the idea of the fifth dimension being probability.
 * In Mikhail Bulgakov's The Master and Margarita, valet Koroviev in an explanation to Margarita attributes the expansion of a small apartment into the size of a large auditorium to the fifth dimension.
 * In the "original" or "boxed" version of the Dungeons & Dragons role-playing game rulebooks (discontinued in 2000), consisting of the Basic set, and then the Expert, Companion, Master, and Immortals expansion sets, a five-dimensional model was proposed in the Masters set where characters from the ordinary plane had the first, second, and third dimensions as their three-dimensional home, but other-dimensional beings called the third, fourth, and fifth dimensions home. Upon perceiving each other, each thought the other kind to be horribly deformed "demons".
 * In Family Guy, Mayor Adam West sends Alex Trebek, host of Jeopardy, to the fifth dimension by making him say his name backwards, commenting: "Only saying his name backwards can send him back to the fifth dimension where he belongs." This is a parody of Mr. Mxyzptlk's weakness in the Superman comics.
 * In a well-received 2010 CBS commercial for How I Met Your Mother, Accidentally on Purpose, Two and a Half Men, The Big Bang Theory, and the Late Show with David Letterman, an announcer states that "Everyone has 3-D, but only CBS has comedy in 5-D." This was a reference to the growing popularity of 4-D film in the later half of 2009, suggesting that certain programs on CBS feature 5-dimensional effects. By the end of the commercial, however, it is revealed that the letter D in 5-D does not stand for "Dimension," but stands for "Delightful, Delicious, Daring, Demented, and Dave."


 * Yes, masses of unsourced trivia and trivial uses. It probably could all be sourced to first party sources, to the relevant works of fiction etc. but it would still be trivia and excessive. If anyone can find any coverage in reliable secondary sources then it could be restored based on them but I don't hold out much hope, I certainly don't know of any sources or where to start.-- JohnBlackburne wordsdeeds 23:08, 4 December 2014 (UTC)


 * See also above; the reply I think makes another important point. Even when "the fifth dimension" comes up in popular culture it's very often nothing to do with this topic. It's often just shorthand for a mystical thing outside our space, and is utterly meaningless - it might as well be "hyperspace", "limbo". "the fifth dimension" sounds more formal and fits nicely after the four dimensions of space and time. There are exceptions in the above list but I suspect even they are largely using it as a buzz-word, not really considering a five-dimensional space. I doubt e.g. the the Powerpuff Girls episode Bring Back Jojo is a good example of a near mathematical use. But that's why we need reliable sources other than the works of fiction, TV programmes etc..-- JohnBlackburne wordsdeeds 02:32, 5 December 2014 (UTC)
 * Agree that some of it is trivia or relates to a concept of the fifth dimension that is not accurate, but a label for a deus ex machina. However, some of the references seem to relate to the concept in physics. A Wrinkle in Time in particular stands out. Regardless, agree that it needs to be referenced by non primary sources. Plumpy Humperdinkle (talk) 00:42, 13 September 2015 (UTC)

Gerard 't Hooft
The section on Hooft needs expansion with references. Searching peer reviewed literature has not resulted in much substantiation. Requesting help modifying/referencing this section. Plumpy Humperdinkle (talk) 17:16, 12 September 2015 (UTC)

Need help with article on the Four dimensional shape, the Cubinder.
Hello fellow Wikipedian. I am in the process of creating an article about the 4D shape, the “cubinder”. It was previously red linked on other articles (including the one you created) and I was surprised to see it was not already an item listed for creation by Wiki Projects Mathematics, as the duocylinder and spheriender are already articles. I require help to improve the draft, as I require more formulae, sources, and additional information to create this article. You can access this page at User:Darnburn98/Cubinder, please come on over and help improve this article to get into the main space! Darnburn98 (talk) 23:33, 20 January 2017 (UTC)

axes (to grind?)

 * Fifth dimensional geometry is generally represented using 5 coordinate values (x,y,z,w,v), where moving along the v axis involves moving between different hyper-volumes. [ref omitted]

This strikes me as redundant and, in part, too narrow; moving along any line involves moving between different hyper-volumes. Your thoughts? —Tamfang (talk) 01:18, 30 April 2024 (UTC)
 * In general the article focuses way too much on a particular coordinate system. It should be re-written from a more coordinate-free perspective.  (Also the link redirects to Lebesgue measure, which has no immediate connection to the sentence.) --Trovatore (talk) 01:53, 30 April 2024 (UTC)