# Talk:Dimension

## Penrose Section

With the thought that someone might be interested in Penrose's singularity theorem, I added a section on it to the article. This was done in spite of the fact that the Wikipedia article on Roger Penrose states that one of the predicates associated with him is that of being a philosopher. It is therefore moot whether he may be considered to be an authority on the subject.Lestrade 13:26, 7 March 2006 (UTC)Lestrade

I have more trouble with the fact that the article about the book doesn't mention the theorem at all, and only says that Penrose was "skeptical" towards string theory. Can you put the info on the theorem into the book description? --Alvestrand 12:16, 24 September 2006 (UTC)
I can't find the theorem in the book, can someone give the page number Agingjb 12:59, 19 August 2007 (UTC)
I move we delete the Penrose section. If it is mentioned anywhere, it could be mentioned on the book page, or in a string theory page, or on Penrose's personal page. It does not contribute to the article in a substantial way. Rybu (talk) 00:30, 2 September 2008 (UTC)

## Tesseracts as the Fourth Dimension??

In this article, the author says that tesseracts represent the fourth dimension of space. But, I have read that a tesseract actually represents time squared, or the fifth dimension. Am I wrong in thinking this? And if so, why?--Princess Janay (talk) 15:01, 12 February 2008 (UTC)

You may be right in thinking you read this, but in that case whoever wrote such a thing was producing gibberish. A tesseract is an abstract mathematical object that by itself does not represent anything other than itself.  --Lambiam 20:42, 8 March 2008 (UTC)
I believe that the illustration of the tesseract represents the three dimensional shadow a tesseract would cast onto three dimensional space. Rsduhamel (talk) 19:58, 13 August 2008 (UTC)

Humans measure space by using three dimensions.Lestrade (talk) 20:09, 13 August 2008 (UTC)Lestrade

Not Humans but it is Modern Mathematics that measure Space in three spatial dimensions only as there can not a dimension representing the negative count on number line,otherwise Human senses are capable of sensing & experiencing upto eighth Dimensions.Alkagl (talk) 07:22, 16 July 2012 (UTC)

Tesseract can not be fourh dimension.The illustration and shadow theory is not correct.However shadow itself is fourth dimension,and always displays itself in an euclidian independent to the euclideans & spates which its the mother solid object's dimensions displays into. [email protected] — Preceding unsigned comment added by 27.97.100.52 (talk) 10:56, 13 January 2012 (UTC)

Hi, The lead section of this article seems to me to be too long and a bit confused/rambling. I propose the following shorter version. Please comment and/or amend and I'll put it up in a few days. Thanks Andeggs (talk) 00:17, 9 March 2008 (UTC)

In physics a dimension is a mode of linear extension of which there are three in space and one in time. Dimensions are equivalent to the axes in a Cartesian co-ordinate system, which in a three-dimensional system run left-right, up-down and forward-backward. A set of three co-ordinates on these axes specifies the position of a particular point. An event’s position in time is specified if four co-ordinates are given.
By comparison, on flat surfaces (such as a plane or the surface of a sphere), a point can be specified using just two numbers; this space is said to be two-dimensional. On a one-dimensional line only one co-ordinate is needed. In mathematics, spaces with more than three dimensions are sometimes used to describe abstract objects and spaces for which no geometric picture is needed. In these n-dimensional spaces a point is located by a set of n co-ordinates {n1, n2, … nn}. Some theories, such as those used in fractal geometry, even make use of a non-integer or negative number of dimensions.
The concept of dimensions and co-ordinate spaces can be generalized to describe abstract parameters in other systems. For example in economics, dimensions are used to model economic parameters, such as demand, supply and price. The position of a point in this model would then refer to a particular set of values of those parameters.

Is this meant to be the whole lead? The way it starts, it is as if dimension is purely a concept of physics, and then one that only concerns aspects of space and time. I don't know what "a mode of linear extension" means. What happened to the mathematical meaning? The statement about the theory of relativity in the current version ([1]) is misleading; time is also a dimension, according to any reasonable definition of dimension, in the Newtonian universe. I agree that the introduction (and in fact the whole article) is a bit rambling and should be tidied up, but I'm afraid your version is not a viable replacement, nor do I see clear potential for it evolving into one.  --Lambiam 21:17, 9 March 2008 (UTC)
Hi Lambian. I've put the latest version of it here. I think it is important to recognise that the most commonly used meaning of dimension in maths is an extension of the physical meaning (3 in space, 1 in time). Only by understanding 3D space can one generalize the concept to higher dimensions. We have to clearly state how many dimensions there are before proceeding.
The problem we have is that dimension can refer to different things: 1) everyday meaning: height, length, mass, size 2) physical meaning (3 in space, 1 in time) and mathematical extension into higher dimensions 3) dimensional analysis 4) dimensions of equations. In my opinion this article should concentrate only on the second meaning.
Finally, I agree "mode of linear extension" sounds odd but it does make sense and is the Oxford definition. I haven't yet seen a better one, although please suggest one if you find one. I hope we can collaborate on this. Thanks Andeggs (talk) 23:22, 9 March 2008 (UTC)
I've put up a new lead now and redrafted some of the 'physical dimension' section to make it read more clearly. Extraneous material was removed - please talk about it here if you feel I have made any mistakes. Thanks Andeggs (talk) 19:44, 10 March 2008 (UTC)
I think you should reach consensus before you make such drastic changes. The new version of the article you created looks like an approach to an article Dimension (mathematics), and in fact having a separate article on the mathematical meanings would be quite reasonable. But even limited to that aspect, valid content has gone missing, and there are other quite serious problems, such as that the so-called Introduction has no clear relation with the rest. An article just named Dimension, if not a disambiguation page, should treat the most common meanings, as given for example here.  --Lambiam 20:24, 10 March 2008 (UTC)
OK, I agree that my edit was not reached by consensus but I hope you will appreciate that it was an honest attempt to be bold rather than an effort in malicious destruction. My main aim was to put the lead on a stronger and clearer footing. Although I will stand by the other changes, I will not die in a ditch pacefor them. Firstly, then, I think we should agree about the definition of dimension. I feel quite strongly that the one given on the page as it stands now is confusing. The two references I gave in the edit (this and this) are unequivocal: the dimension of a manifold is the mimimum number of coordinates needed to specify every point within it. From here all discussions of the physical world and mathematical functions follow. The definition in the current article talks about the 'paramters of a system' but this is just a looser version of the same thing (the parameters are the independent variables in a function). There is no great divide between the 'mathematical' meaning of dimension and any other meaning - so we should not unnecessarily shield the reader from the full concept (without of course plunging into formulae immediately!). Please let me know what you think and whether you agree Andeggs (talk) 00:18, 11 March 2008 (UTC)
Well, I did not like the article before your changes, but I was even more unhappy with your changes. Most readers will have no idea what a manifold is, and to even explain the notion requires a crash course in relatively advanced mathematics. You can't define 0 either by "The number 0 is the additive identity element of the ring of integers." Even though this is true, it has the effect of an obfuscation. There is no excuse for a lead to the article that is not understandable to a large majority of readers.
Also, "not reached by consensus" is a bit of a euphemism; 100% of the reactions to your proposal were not positive. OK, that was only one reaction, but it was rather strong ("your version is not a viable replacement, nor do I see clear potential for it evolving into one"). I'm sorry I can't be more positive, but I think it is best if I am blunt here.  --Lambiam 21:17, 11 March 2008 (UTC)
Sure, but the version I posted contains references whereas the lead as it currently stands is not verifiable! We can make amend the proposed changes so that 'manifold' is better explained (perhaps "a type of abstract mathematical space" is more gentle than "a type of abstract topological space") but it is crucial that the definition is accurate and clear. At the moment the first defintion ('common usage') is misleading and more appropriate for a dictionary than an encyclopedia. The second definition ("dimensions are the parameters required to describe the position of any object within a conceptual space") is misleading and, by the way, uses concepts which are just as difficult to understand as those in the proposed defintion. In my view, we must veer towards the what the sources say. As well as Lambian's response, I would be interested in the reaction of other editors to these arguments. Andeggs (talk) 23:15, 11 March 2008 (UTC)

## Fourth Dimension

The fourth spatial dimension is 'VISION',as it always remain orthogonal at 180 degree at 3D surface, and is ever relegating perpendicular to axis x at 90 degrees in clockwise circulatory motion.It is 2-D disc perpendicular and 3D surface contact.Now,what could be the 5Th spatial Dimension!! Alkagl (talk) 14:08, 1 February 2012 (UTC)1.187.227.235 (talk) 05:03, 1 February 2012 (UTC)

## Higher Dimensions

One does not need a Phd in physics to verify the existence of higher dimensions. Dimensions I might add, that are the exact same size as man's 3-dimensional world. Further reading on the simple field observations that can be performed to verify their existence, can be found at "wikipedia interdimensional hypothesis" and at "wikipedia bigfoot". In the United States at least, we are fortunate to have real life and benevolent beings that can eagerly assist us in getting a handle on the truth surrounding the higher dimensions. Much of the arbitrary hypothesis in print on the higher dimensions, including the tesseract and hypercube, are lacking in even the slightest circumstantial evidence to convince us of their validity. Although I am no physicist, the controlled varying of the vibration of certain quanta string energy loops, (the most basic building block of matter), appears to have infinitely more merit since it seems to be compatible with simple field observations. This type of string theory is described in detail, in a book entitled "X3", by Adrian Dvir.208.100.241.148 (talk) 20:42, 7 April 2008 (UTC)

## Mathematics in the lede

The first sentence of the lede section states that the term "dimension" has various different, although related, meanings

1. in common usage,
2. in mathematics, and
3. in physics.

The lede then further proceeds to give an overview of the meanings in these three areas, in that order, devoting a paragraph to each. The last two are elaborated upon at length in later sections.

Recently another paragraph was added to the lede, starting with: "In mathematics ...". That makes two paragraphs in the lede starting "In mathematics ...". That doesn't make sense. If something essential is missing from the existing mathematics paragraph, or something is essentially wrong with it, that should be fixed by editing that paragraph and not by putting another one next to it.

I did not see anything essential in the parallel paragraph missing from the existing lede. The term "manifold" is mentioned, but in my opinion that is unnecessarily technical for the lede, and best left to the existing subsection Manifolds of the section In mathematics. I removed the new paragraph with edit summary first read the whole lede before insterting (sic) a paragraph. However, this was reverted and the paragraph was re-added.

I'll remove it again, and hope that will be the end of it.  --Lambiam 19:27, 12 April 2008 (UTC)

I reject the idea that 'dimension' has three different meanings. It has two. The first meaning is identical in both mathematics and physics: "the dimension of a manifold (a type of abstract topological space) is roughly defined as the mimimum number of coordinates needed to specify every point within itCurious About AstronomyMathWorld: Dimension].". The meaning in common usage is basically a poorly-understood version of the mathematical/physical meaning and in my opinion is not worth elaborating on. The second meaning is actually about dimensional analysis.
Unfortunately the lead on this page is currently a bit of a muddle, leaving a novice no clearer about what the definitive meaning of the term is, even though there is one. I suggest we 1) remove reference to the "common usage" version, which is confusing 2) tighten the description of the mathematical/physical definition 3) simply signpost towards the page on dimensional analysis rather than discuss it here. I would appreciate it if you could address these suggestions. Please also recognise that the version I added to the lead contains references, whereas no other statement in the current version does. To just remove it because it does not fit with the existing material comes across as unhelpful. Andeggs (talk) 22:56, 12 April 2008 (UTC)
In the context of a vector space, the dimension is the cardinality of a basis of that space. In some cases this may coincide with the dimension in the sense of a manifold, but not all vector spaces are manifolds. and, moreover, even if they are but the vector space is over the field of the complex numbers, the definitions differ by a factor of 2. so they are definitely not equivalent. This is not abstruse mathematics used by only a few mathematicians; it is a quite common meaning of dimension in mathematics. So if you believe the term "dimension" has only one meaning in mathematics, you are definitely mistaken. This should be clear if you take the effort of reading on beyond the lead section. There many different meanings in mathematics are given.  --Lambiam 18:30, 19 April 2008 (UTC)
Yes we certainly could add reference to the dimensions of vector spaces in the lead. How about after "...Generalizations of this concept are possible, and different fields of mathematics use different, specialized definitions." we add something like "For example, the dimension of a vector space V is given by the Hamel dimension, the cardinality of a basis of V." Andeggs (talk) 18:46, 21 April 2008 (UTC)

## Dimensional analysis

I would like to remove references to dimensional analysis from this page since it is a different concept and has its own page dedicated to it. Please say here if you object to me removing this content (which is repeated on the dimensional analysis page) and adding an otheruses template. Thanks Andeggs (talk) 18:32, 21 April 2008 (UTC)

I object. Even though it is a different concept, the treatment of the notion of dimension in physics related to the type of measurement should refer to dimensional analysis.  --Lambiam 18:45, 23 April 2008 (UTC)
Why? As you say it is a different concept. Dimensional analysis is not the "treatment of the notion of dimension to measurement" but rather a completely different tool for understanding variables and their relation to one another. They happen to share a similar title (and nothing more) so the link should be a an 'otheruses' one. Andeggs (talk) 22:30, 23 April 2008 (UTC)
I agree, dimensional analysis is about units, not dimension. At most it deserves a place here to emphasise that dimensional analysis is a misnomer and would be better called unit analysis. This is much like how the current article explains that dimension in common sci-fi usage is also a misnomer. Since dimensional analysis is clearly marked in the disambiguation page it's not really appropriate here. Rybu (talk) 23:28, 1 September 2008 (UTC)

## improve top figure

It would be nice to improve the top figure. The square should be shaded, so it is clear that it is the interior that has dimension 2, not the boundary. For lay people, the term square is as likely to mean the boundary of a square as it is likely to mean the 2 dimensional shape, I believe. Oded (talk) 02:39, 12 May 2008 (UTC)

## Super-Z Theory

This is something that I came up with. Please state any errors I may have made if you find any.

"In mathematics the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it."

And if the concept of multiverse is true then there must be another dimension that should be used to specify an object's position within that continuum of parallel universes. Moreover, a different parallel universe is created for each possible movement of every quantum in existence.

Therefore, out of the numerous quanta, one quantum should be selected to represent the origin of this dimension. It can be absolutely anything. For example, it can even be an elementary particle that is part of my ass.

So, now that a quantum has been selected to represent the origin, this should then be the observer particle for every other quanta in the universe, therefore causing it to be viewed as stationary (even if it IS moving, Einstein's special theory of relativity states that "all uniform motion is relative, and that there is no absolute and well-defined state of rest", which explains how we do not feel the movement of Earth around the Sun nor its spin.

This then can be used to calculate the change in position of every other quanta in the universe, which will allow one to identify which multiverse an object is present in, ergo inevitably compelling this to be a "coordinate needed to specify every point within a space."

Feel free to criticise me. I've read all the arguments going on in this page, and I am expecting at least everyone who read this bullshit to disagree with this. Don't let me down. (But please PLEASE state why my theory is scientifically incorrect and specify what part of it makes it so. Thanks. Looking forward to hearing from you.) Asiant X13 (talk) 07:37, 18 July 2008 (UTC)

Your post is completely irrellevant and has no place here. Rybu (talk) 22:13, 1 September 2008 (UTC)

I understand shadow is the fourth coordinate and is constitutive of seperate spatial euclidian from its mother solid body distributed in space in its three coordinates. alok agrawal — Preceding unsigned comment added by 27.97.100.52 (talk) 12:35, 13 January 2012 (UTC)

This article is a mess. I move that the Penrose singularity theorem section, dimensional analysis and negative dimension sections all be erased or minimized. Penrose's singularity theorem doesn't contribute anything to the article. Moreover, it's vague, and poorly stated. Dimensional analysis is something that should be linked to from units as it is not properly concerned with dimension, and Mandelbrot's negative dimension section is pretty much vacuous as written. IMO the whole Physics section is poorly thought-out. Classical physical theories include *many* very high-dimensional models as anyone who has spent any time using Hamiltonian or Lagrangian mechanics can tell you -- consider the problem of a hanging cable, for example. Classical physics considers that to be an infinite-dimensional problem. Basically, there is no special usage of dimension in physics, no more than in any other science other than the fact that they use the word. So, after a lot of edits I think the article is a bit less random looking and more on-topic. Rybu (talk) 23:37, 1 September 2008 (UTC)

## More revisions needed

I've made quite a few small revisions to the article. Some things need further modification like the first picture in the article, where the caption really is asking for more. Rybu (talk) 03:28, 2 September 2008 (UTC)

## A dimension is not a world

A dimension is a way of measuring space in any one of three directions: height, width, or depth. It can also be a way of measuring time, but this is not a proper use of the word. It is, however, not a world. Therefore, it is incorrect to use the word "dimension" as though it signifies the concept of a universe, cosmos, or world, as in "He came from another dimension."Lestrade (talk) 12:24, 29 September 2008 (UTC)Lestrade

Who decides that? Wikipedia is descriptive, not prescriptive. If the word has been used in that capacity by authors, then it's fair enough to report it. That sense of the word is used frequently in science fiction literature and other genres. One might think it's incorrect to use the word "dimension" in that way, but that doesn't prevent the fact that it has indeed been used as such. Xantharius (talk) 21:19, 29 September 2008 (UTC)
Then the article should inform readers that the original meaning of the word has been extended to contain foreign or alien meanings. If not, then confusion will result from the ambiguity of the word.Lestrade (talk) 23:56, 29 September 2008 (UTC)Lestrade
If you think it makes it the article clearer, go ahead and make the changes. Xantharius (talk) 16:12, 13 October 2008 (UTC)

## Circles are 2-dimensional constructs

The first paragraph of this article is in error. A circle is not a 1-dimensional object that lives in 2-dimensions. (Whatever that might mean) A circle requires two coordinates to define it, not one. In addition to the "polar coordinate angle" one also needs the radius. (In the clock example offered later, one also needs to know the length of that clock hand) Cajarr (talk) 19:04, 14 October 2008 (UTC)

No, that is not the case. You only need radius if you're describing more than one circle. A fixed circle has a fixed radius. That's why points on a fixed circle only need 1 coordinate to describe their position, the polar angle. Please provide references to your assertion that the initial paragraph is in error -- the article refers to several references that back up this point -- flatland for example. Rybu (talk) 06:43, 15 October 2008 (UTC)
Rybu you are misreading your sources. Neither of the citations in the intro para says that a circle is one dimensional or a one dimensional construct "living in" two dimensions. Quite the contrary, both sources state that a circle is a two dimensional construct. Any construct with measurable area is two dimensional. The circumference of a circle, on the other hand, can be a line segment (a one dimensional construct) describing the perimeter of a two dimensional space and requires only one coordinate to describe the location of any point along it. You are confusing two different things. A line describing the circumference of a circle is what the second source calls a "'dragged' version of a zero dimensional space", whereas the circle itself is two dimensional. Your statement that "you only need radius if you're describing more than one circle" is false. A fixed circle does have a fixed radius, but that is not why only one coordinate is required to describe a point on its circumference. Only one coordinate is needed because the circumference can be described by a line, a one dimensional construct that does not exhibit area. The statement that "the circle is 1-dimensional even though it exists in the 2-dimensional plane" is poorly worded and misleading, because it is unclearly describing two different things: a two dimensional area and a one dimensional construct describing its perimeter. The later statement, "Returning to the circle example: a circle can be thought of as being drawn as the end-point on the minute hand of a clock, thus it is 1-dimensional," is also false as a circle is not an end point on a line segment. If you mean to say that you are extending a line from a fixed point, you might be describing the radius of a circle, but you are not describing the circle itself, which has two dimensions. It is true that dragging a 0-dimensional construct can create a 1-dimensional construct, but what you are dragging is a line describing the radius of your unit circle, which is itself another line: both the dragged radius and the unit circle are 1-dimensional spaces, but the circle they jointly describe is 2-dimensional. I challenge you to find any of the listed references (including Flatland, for example) that supports your version of the facts. To be fair, Cajarr erred also: the polar coordinate angle is the intersection of a radial line (or radius) with the circumference; they are essentially the same thing. 12.233.146.130 (talk) 23:09, 4 March 2009 (UTC)

A circle doesn't have an area. You're thinking of the two-dimensional area x^2 + y^2 <= r^2. Strictly speaking, a circle is x^2 + y^2 = r^2, i.e. the one dimension surface that bounds that area.

It doesn't matter how many coordinates you need to define a circle; that will depend on the dimensionality of the space in which the circle is embedded. What matters is how many coordinates you need to specify a point on a given circle. For any given circle you can specify a point on it with a single parameter; therefore a circle is a one-dimensional object.

Hesperian 00:24, 5 March 2009 (UTC)

This had me confused, too, until I realised that correspondents here are talking at cross-purposes. A circle is indeed two dimensional - but only if it is filled (or solid - ●). Otherwise it is a one dimensional object sitting in two dimensional space - basically a line whose two ends have been brought together and the rest of the line arranged so that it forms a smooth curve (○). Such a circle does not have two dimensions because it is to all intents and purposes "empty". The only meaningful measure is its circumference, which is one dimensional. However, in order to be represented it must be embedded in at least two dimensional space - just as a Moebius strip is a two dimensional object but must be represented in three dimensional space.
Think of it this way: a sphere can be either solid (filled, like a billiard ball) or empty (hollow, like a tennis ball). It is sensible to talk about the co-ordinates of a point located somewhere inside a solid sphere, which is three dimensional, but not for an empty or hollow sphere, which consists only of its "skin" - and is therefore two dimensional (it has no volume - although it could be said to enclose a volume). The assumption made here is that the thickness of the skin of such an empty or hollow sphere is to all intents and purposes immeasurably thin.
I don't know whether it would be helpful to distinguish between the different types of object in the article - i.e., emphasize the nature of the one dimensional versus two dimensional circle.
Kudos to Rybu for making me think hard! :) AncientBrit (talk) 17:07, 24 August 2010 (UTC)

All unit types,measuring the angular deviation,essentially are measurements of angular respective positions between two spatial coordintes joining on same axis.Wherefore the moment we talk of measurement in angular degrees,it must be a talk of 2-dimensional display system.Wherefore a circle can not be a one dimensional continuation. — Preceding unsigned comment added by 27.97.100.52 (talk) 13:56, 13 January 2012 (UTC)

Hi there anonymous person at IP address 12.233.146.130. Flatland, Munkres "Topology" text, Dugunji's topology text, any manifolds textbook on the planet (guillemin and pollack, for example), they all support this notion of dimension. It's the standard notion of dimension used throughout most of mathematics. I have reverted your edits. In the future, please log-in -- anonymous edits tend not to be taken very seriously, especially if they completely change the meaning of the article. Rybu (talk) 18:46, 5 March 2009 (UTC)

## Scientific Worldview

Here's an original idea, so sorry I cannot cite any references. If we take the word 'dimension' to mean a fundamental aspect of our reality, where a minimum set of dimensions can fully envelope (or provide a framework) for describing our reality, then I would say that the universe has five dimensions. These are 4-d spacetime currently accepted in the mainstream scientific view, plus a fifth dimension - a non-physical dimension of mind or spirit. The fifth spiritual dimension does not influence the mechanics of the physical universe, however it encapsulates things such as perceptions, emotions, and a sense of right or wrong (just to name a few examples). People with a purely physical view of the universe would say that mind (or spirit) is comprised of the purely physical, ie. just chemical and electrical signals in the brain. People with a bit more imagination might agree that thoughts and feelings, perceptions, memories, dreams, expectations, love for family and friends, concepts of ownership, concepts of tribe or nation, concepts of right and wrong - are more than just chemical and electrical signals in the brain. In other words, if we want a rational scientific view that can encapsulate all aspects of our reality, it needs to include the non-physical (mind/spirit). This theory need not be falsifiable, because at its very roots scientific understanding rests on assumptions based on common sense. String Theory (from theoretical physics) suggests there may be 10 or 11 or so higher dimensions. But if these are just more physical/spatial dimensions at a sub-atomic scale, then wouldn't they be redundant? (ie. overlapping with 4-d spacetime)Crazygrandpa (talk) 11:03, 29 October 2008 (UTC)

Without references and citation this is original research or opinion, and as such doesn't really have a place on Wikipedia. Sorry. Xantharius (talk) 13:23, 29 October 2008 (UTC)

Watch Illusions of Space Dimensions and Time Travel to clarify the definition of Dimension. —Preceding unsigned comment added by StudyLakshan (talkcontribs) 23:04, 4 May 2010 (UTC)

You can if you want to, but it doesn't have anything to do with this article. — Arthur Rubin (talk) 23:12, 4 May 2010 (UTC)

## Other mathematical definitions of dimension

Would anyone be sad if I added a few more topological definitions of dimension? In particular, this article lacks any mention of partition dimension, or discussion of when the different definitions of topological dimensions are equivalent (ie., on separable metric spaces, etc.) Druiffic (talk) 20:12, 6 December 2008 (UTC)Druiffic

Hi there Druiffic. This article functions as more of a front-line non-technical article where at best the main idea is delivered, and lots of hyperlinks are given. IMO it'd be best to farm off any technical bits to their own articles, and link to them from here. There's already a Lebesgue covering dimension article. There's a Hausdorff dimension article, etc. I think wikiproject mathematics tends to want to keep the technical bits to a minimum here since this is a very popular article -- everyone seems to have an opinion on it. Lots of anonymous edits, especially to the first paragraphs. Rybu (talk) 18:52, 5 March 2009 (UTC)

## Only dimensions in space

The way i see it, the first part of the article only concerns dimensions in space. Should the description not go further than that i.e give a more general explenation of the matter? Is it not a narrow description of 'deimensions' to say that it only governs space? —Preceding unsigned comment added by ConferAll (talkcontribs) 18:04, 14 January 2009 (UTC)

What non-spatial aspects of the word "dimension" do you want discussed? The article later brings up the way dimension gets used for things like space-time and Kaluza-Klein type theories. Is there something else you're referring to? A lot of people (me included) tend to think of space-time as just another type of space, in the general topological sense of the word. That's one of the reasons why KK and space-time doesn't enter the front of the article, as it's just a compound concept, built off a primitive concept described in the lead. Rybu (talk) 18:56, 5 March 2009 (UTC)

## Coordinate system diagrams

I have been working on some coordinate system diagrams based on the work of InductiveLoad and I think they might be relevant for this page. If no-one objects I'll add them shortly. Thanks Andeggs (talk) 17:56, 7 August 2009 (UTC)

• Very nice. Some of those diagrams would likely help the article if incorporated well. Rybu (talk) 03:57, 1 October 2009 (UTC)

## Merge proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
The result was keep. -- Jim (talk) 19:45, 1 October 2009 (UTC)

User:Jmath666 has proposed a merger of Dimension with Dimension (vector space).

• Oppose - vector space dimension is a very specific meaning of dimension, but is sufficiently notable and has enough material to deserve an article in its own right. Gandalf61 (talk) 09:55, 30 September 2009 (UTC)
• Oppose. Dimension of vector spaces is a particularly important type of dimension, and deserves its own article. --Zundark (talk) 10:29, 30 September 2009 (UTC)
• Oppose. The whole point of having a separate dimension article from specific notions of dimension is so that this article can be general, and specific articles can dive into particular technical notions. Rybu (talk) 03:55, 1 October 2009 (UTC)
• Oppose. For the reasons given above, though I think that this page could use some more material on dimensions of vector spaces. In any case, since there seems to be a consensus (and since Jmath666 has not provided any reasons for the proposed merger) I am closing the request. Jim (talk) 19:45, 1 October 2009 (UTC)

The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

## Space-filling curve issue

At some point this article should probably address the issue of space-filling curves. Ie:you can find an onto continuous function [0,1]-->[0,1]x[0,1]. So some readers might be concerned that dimension is not well-defined, or that the square is 1-dimensional, etc. IMO this isn't a major issue but maybe it should be worked into the mathematical section, somewhere pretty deep in the article so that it doesn't confuse people early. Rybu (talk) 22:26, 26 October 2009 (UTC)

Does such a curve really exist? I doubt it, at best couldn't you only cover points that have a rational component, but still always miss uncountably many other points? Cesiumfrog (talk) 00:48, 3 May 2011 (UTC)

## Negative dimensions

Since there are positive dimensions (1, 2, 3, 4, ...) and even a zeroeth dimension (0, a point), would it theoretically be possible to have negative dimensions (-1, -2, ...)? Like an imaginary dimension (just like ${\displaystyle {\sqrt {-1}}=i}$ )?

I personally think it wouldn't be possible, but maybe it could be.

Thanks, 80.101.212.102 (talk) 16:03, 16 November 2009 (UTC)

I don't see negative dimensions cropping up much at all. I think the only time I see it crop up is as a description for the empty set. Some people consider the empty set to have any dimension (vacuously), some say it has dimension -1. You also get negative dimensions in certain rather formal boring ways, like as gradings of various algebraic objects like chain complexes, etc. These kinds of negative dimensions have a pretty tenuous hold on the word dimension. Rybu (talk) 19:12, 16 November 2009 (UTC)

## Question

What is the term for the number of dimensions in a coordinate system? Dimensionality?· CUSH · 18:10, 21 April 2010 (UTC)

## General Definition

Dimension is a relative concept used for analysis, where one dimension is mutually exclusive to another dimension.

This definition clarifies controversial areas like: parallel universes, string theory, M-theory, wormhole

Fantasize on parallel dimensions, fold/branch dimensions and tunnels between dimensions contradict with the above definition.

Reference: Illusions of Space Dimensions and Time Travel StudyLakshan (talk) 23:43, 4 May 2010 (UTC)

This should not be in the article unless a reliable source can be found. YouTube videos are hardly ever reliable sources. — Arthur Rubin (talk) 00:08, 5 May 2010 (UTC)

## Removed unsourced nonsense

I have twice removed the following unsourced section added to the article by new user SpikeTD:

"The "three dimensions" is the way that humans (and possibly many other animals) orient themselves to their environment. The human body is imagined to have six planar surfaces: 1), 2), top of head and soles of feet, corresponding to walking on the surface of a sphere; 3), 4) a symmetry of arms and legs, etc., regarded as "left-right" and necessary for efficient locomotion, and, 5),6) a "front" and a "back" surface, the front being that which faces in the direction of vision and locomotion. The three dimensions are six imaginary projections, one from each of these surfaces, and are not an observable part or characteristic of the universe. The concept's lack of universality can be understood by conceiving of a tetrahedral creature, which would orient itself using four imaginary projections rather than six, and would thus employ the most simple and efficient means of orientation possible.
"Time" is a similarly imaginary dimension. While events seemingly occur prior or subsequent to other events, a 'road' upon which these events occur has no observable presence. A clock only counts the number of times it ticks, and the duration of an event can only be measured in terms of multiples of the duration of other, briefer events."

Not only is it unsourced original research, it is also complete nonsense. Clearly earthworms and starfish do not inhabit a universe of different dimensions from us just because they have a different body plan. Gandalf61 (talk) 13:27, 12 May 2010 (UTC)

The point here is that the universe does not really have dimensions. Dimensions are a mental tool -- and only a mental tool -- that an entity might use to determine its orientation to its environment. Whatever form the entity might have, and whatever system of dimensions it uses, doesn't endow those qualities to the universe as a whole beyond being one point of view among an infinite possible. SpikeTD (talk) 14:39, 12 May 2010 (UTC)
At the moment this appears to be just your own opinion. If you want to add this to the article then you need to cite a reliable source that says this. Gandalf61 (talk) 14:45, 12 May 2010 (UTC)

## Psychology

Hello. In psychology the concept of dimensions is prominent (it is a theoretical approach which differs from the criteria-driven approach that is the medical model). I would appreciate it if someone in Wikipedia would start a page on dimensions in psychology, & that that page be referenced on this page (i.e., a link to dimensions in psychology). That would be most helpful.75.220.29.149 (talk) 17:54, 10 October 2010 (UTC)Dean Pappas

I imagine the notion of dimension you're interested in should be linked to the [disambiguation page] rather than this page. Moreover, if you want to make a request you should probably go to the appropriate [wikiproject psychology] chat page where requests can be made. Rybu (talk) 22:36, 11 October 2010 (UTC)

## dimensional analysis of a unit of measure

I think a paragraph should be added to deal with the dimensions of a measurement (units of phisical quantities). —Preceding unsigned comment added by 216.47.144.124 (talk) 14:46, 6 May 2011 (UTC)

That's covered in our artcile on dimensional analysis. Gandalf61 (talk) 14:49, 6 May 2011 (UTC)

## Definition by mathematics

The word dimension, after studying relativity and the way mathematicians and physicists describe the universe in general, means something specific to me that I believe the mathematical definition here should be similar to.

Physics: Space has 3 dimensions. Time has 1.

Math: Numbers are used to describe position along a number-line type concept. The imaginary number i, for instance, is 90 degrees between the negative and positive of a number line, must be plotted in another physical dimension, and therefore its own dimension in its mathematical context. Time, when plotted against position in a space-time diagram, takes up another physical dimension to draw, so therefore should be considered another dimension in its context. Basically, anything which is separate in any situation by a linear counting, should be considered another dimension in its context. A plotting of suicide rates should be considered a dimension against the dimension of time, for example, since it is a counting of something different, but combines with the other dimension to create a 2 dimensional picture. — Preceding unsigned comment added by 180.131.226.31 (talk) 13:16, 13 June 2011 (UTC)

## Mislabeling of lines in drawings

In the section "In physics" subsection "Spatial dimensions" are presented a set of drawings. Both the "Cartesian (2-dimensional)" and "Cartesian (3-dimensional)" drawings have mislabelings. We'll start with the "Cartesian (3-dimensional)" drawing first. The drawing has the x, y, and z axises are labeled correctly, but for the point "P" the lines leading to "P" are mislabeled. The z line is parallel to the z axis, but the x line and the y line are orthoginal to there respective axises. The x line and the y line need to be parallel to the x axis and the y axis. For the "Cartesian (2-dimensional)" drawing the axises are labeled correctly but the lines leading to "P" are mislabeled. Once again the x line and the y line are orthoginal to there respective axises. Katacomb (talk) 02:04, 19 June 2011 (UTC)

By gum, you're right. —Tamfang (talk) 07:34, 19 June 2011 (UTC)
The 3 dimensional Cartesian is correct as I see but your right about the 2D one DARK HUNTER X (talk) 18:06, 15 February 2013 (UTC)

## Should not the dimensions be force energy and matter basically

1st dimension = force same from all sides even tilting the area used to measure makes force from left side come in and from the right most side go out 2nd dimension = goes through matter anywhere but in a single direction 3rd dimension = is full every where and keeps moving as per what we can count due to general theory of relativity with no motion and exact stillness you would have froznen — Preceding unsigned comment added by Khpatil (talkcontribs) 10:10, 6 June 2012 (UTC)

Apparently you make a confusion of the subject of this article with Dimension of a physical quantity. I have added a hatnote in the article to avoid such a confusion. D.Lazard (talk) 10:26, 6 June 2012 (UTC)

## Simple

Under "additional dimensions" this article speaks about space possible having 10, 11 or 24 dimensions. I find this difficult to understand, but the Simple English version doesn't help much either. Can we have some volunteers in the Simple English article please (here)? Pass a Method talk 12:56, 25 September 2012 (UTC)

## Technical drawing

Doesn't "dimensions of an object" have a different meaning than described in this article? There are references to this article form articles like (for example) Production drawing. --Hardi27 (talk) 23:22, 8 November 2012 (UTC)

When you find such a link, consult Dimension (disambiguation) and change it appropriately. —Tamfang (talk) 02:37, 9 November 2012 (UTC)
The meaning of "dimension" you are talking of is explicitly given in the first line of Dimension (disambiguation) --D.Lazard (talk) 10:12, 9 November 2012 (UTC)

## Move of the article

I have moved Dimension to Dimension (mathematics and physics) because its content may not be considered, by most readers, as the main topic (see above section Technical drawing), the primary meaning being "dimension of an object", described in the first line of Dimension (disambiguation). After this move, Dimension (disambiguation) should normally be moved to Dimension. But, before this move, it is better to modify all links to Dimension into links to here. Due of the number of these links, I have asked on Wikipedia talk:WikiProject Disambiguation#Move of dimension to Dimension (mathematics and physics) some help for a robot making these redirects. An editor has commented "That's a pretty verbose qualifier". Here is my answer:

"I agree that it is a verbose qualifier. I have chosen it because the article begin by "In mathematics and physics, ...". Rereading the article, it appears to be about a single topic that is called "dimension of a space" in mathematics, "dimension of the space" in physics, "number of dimensions" (fourth dimension, for example) or "degree of freeness" in other contexts. For the moment, it seems to me that the best title would be "Dimension of a space". I'll start a move discussion on the talk page on the basis of what precedes."

Thus, I starts here a discussion on the best title of this article. IMH, "Dimension" should be avoided because of the ambiguity with the common meaning of the word (dimension of an object), "Dimension (mathematics and physics)" is too long and too restrictive (there is a section "Literature" in the article). I suggest Dimension of a space, but a consensus is needed. D.Lazard (talk) 17:45, 9 November 2012 (UTC)

I would actually suggest "dimension (mathematics)". "Space" is a rather vague term in this context. (Is an algebraic variety a "space"?) In physics, the term can also refer to the dimension of a quantity.TR 22:00, 9 November 2012 (UTC)
Note that mathematics is, more or less, only half of the article, and Dimension of a physical quantity exists. Also, a variety is, without any doubt, a topological space, and its dimension is, at least for a real variety, its spatial dimension. D.Lazard (talk) 22:17, 9 November 2012 (UTC)

## Cartesian coordinate system illustrations

The letters marking the coordinate values in the illustrations for the 2 and 3 dimensional Cartesian coordinate systems appear to be inconsistent.

In the illustration for 3-dimensions the x,y,z values are parallel to the X,Y,Z axes, however in the illustration for 2-dimensions they seem to be reversed. Kelly F Thomas (talk) 16:15, 13 March 2013 (UTC)

You are right: the blue and red x and y in the 2D figure must be exchaanged. However I am not able to edit figures. Can somebody do that? D.Lazard (talk) 16:42, 13 March 2013 (UTC)

## Navbox

"Dimension" has various, strongly related, meanings. Therefore this article is a WP:DABCONCEPT article. However the high number of notions of dimension makes that the dab aspect of the article may be unclear, or, at least, the reader may have difficulties to find the article which contains the notion of dimension that interests him. This dab role is well played by the navbox. Therefore, I have moved it in the lead, although it is not the common usage. (For the other article in which this navbox appears, the right place is, as usual, at the bottom of the article). D.Lazard (talk) 09:15, 18 January 2014 (UTC)

## Requested move

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: moved. Number 57 15:57, 10 October 2014 (UTC)

Dimension (mathematics and physics)Dimension – per WP:BROADCONCEPT, basically. Note that the article was previously moved away from dimension after light discussion above, and dimension still redirects to it. Also, the current parenthetical disambiguation, "mathematics and physics", is erroneous as the article includes sections on literature and philosophy. For those concerned about primary topic status, beyond even the indications of WP:BROADCONCEPT, my cursory examination of page views indicated this article to be more viewed than all other articles combined on Dimension (disambiguation). For those concerned about topical specificity, may I suggest peeling off separate, dedicated (single-word disambiguated) articles as necessary. ENeville (talk) 18:19, 11 September 2014 (UTC)

• Oppose and comment. IMO, the primary topic is the dictionary definition "A dimension of an object is its spatial extent as measured in some relevant direction, such as its length, width, or height.", which does not deserve a WP article ("Wikipedia is not a dictionary"). Above quote is the first line in Dimension. Where should it be placed if the proposed move will be accepted? Therefore, I object to this move. However, I agree that the present title is not convenient. In preceding discussion, it was proposed Dimension of a space. I suggest also Dimension (geometry). Both are less restrictive than the present title, and, I guess that physicists may accept to consider that they are doing some geometry. Nevertheless Dimension (geometry) could need more explanation for the layman. Therefore, finally, I would prefer Dimension of a space or, maybe, Dimension (space). D.Lazard (talk) 20:46, 11 September 2014 (UTC)
IMO the new item of the dab page does not agree with the dab guidelines (I have not checked) and is not useful. However if the move is done, the article must have a hatnote like "For the dimension of an object, such as its length, width, or height, see Measurement. For other uses, ...". With such a hatnote, I does not oppose to the move anymore. D.Lazard (talk) 08:48, 14 September 2014 (UTC)
• Support as general primary topic. Red Slash 19:08, 20 September 2014 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

## high dimensional spaces

would it be worth having a section describing the idea of high-dimensional spaces used in AI (word embeddings 'word2vec' etc). 'higher dimensional spaces appear in... ' — Preceding unsigned comment added by Fmadd (talkcontribs) 01:02, 13 June 2016 (UTC)

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## page titles in sections, directions on top of wikilinks

While I appreciate your reasoning and even your fervor -:) there is a reason for the agreement in WP:MOS to drop page titles in sections, and to not use {{main|this}} and {{main|that}} under every little paragraph where the respective wikilink already exists. Maybe you are not familiar with the reasons?

I do not think that reverting me twice is good faith however, and rather poor communication. Maybe you should get a WP:Third opinion rather than heading towards an WP:editwar ? you dont WP:own this page. --Wuerzele (talk) 10:43, 18 May 2017 (UTC)

"Too time consuming to revert item by item. I'll just add those part of the reverted edit that were correct." as an editsummary is revealing. How much time do you think I spent on clarifying a lot of poor structure and language related nonsense? I edited the lede and you, a non native speaker returned it to its childish form- out of laziness!--Wuerzele (talk) 11:05, 18 May 2017 (UTC)

Please, read WP:BRD: When an editor is reverted, he must not revert the revert, as you did; instead he must open a discussion in the talk page for trying reaching a consensus, which you did not. Also, you should read MOS:HEADING, which asserts "Headings should not refer redundantly to the subject of the article ... unless doing so is ... clearer. Clearly your heading changes make them much less clear. Note also WP:TPYES, which asserts "Comment on content, not on the contributor"; your preceding posts consist essentially of doing the contrary. D.Lazard (talk) 14:10, 18 May 2017 (UTC)
While I agree that repeating page titles in section headings is to generally be avoided, I do think that an exception should be made in this article. Dropping the term "dimension" in these headings leaves a very ambiguous remainder that a reader, not already familiar with the topic, would have a hard time deciphering. --Bill Cherowitzo (talk) 17:59, 18 May 2017 (UTC)

## Template "main" in short sections (third opinion needed)

Wuerzele has removed (or tried to remove) systematically the templates {{main}} of the short subsections of this article. This should be discussed. In fact such a template is not really needed if the main article is linked in the body of the section. However, in the particular case of this article, where several subsections are displayed simultaneously (at least on a laptop), the template allows the reader to know at a single glance that the sections are summaries of other articles. Without the templates, the reader has to read the first sentence of the section for knowing that. Thus, it seem better to restore the templates {{main}} and to remove the corresponding link in the body.

However, there may be different opinions on this. Therefore, I have not restored the removed templates (except in the case where there was a stronger reason for that), and I am waiting for other opinions toward a consensus. D.Lazard (talk) 14:30, 18 May 2017 (UTC)

{{main}}, like other hatnotes, is a directional aid for the reader. In this case the reader is being promised a more fully developed treatment of the topic. A link on the other hand promises no more than a basic definition. These are of course my subjective evaluations as a reader, I am not referring to any kind of policy or definition. Given these perceptions, I think that it is important to keep the {{main}} tags. It is of course true that in some of our articles the section contains more information than the main article does (alas!), but this should not be a reason to not include a {{main}} tag, because we should always hope that the main article gets improved in the future. --Bill Cherowitzo (talk) 17:32, 18 May 2017 (UTC)