Talk:Dimension

From Wikipedia, the free encyclopedia

WikiProject Mathematics
Mathematics Portal
This article is within the scope of WikiProject Mathematics, which collaborates on articles related to mathematics.
Mathematics rating: B Class Top Priority  Field: Geometry
One of the 500 most frequently viewed mathematics articles.
Socrates
Philosophy Portal
This article is within the scope of the WikiProject Philosophy, which collaborates on articles related to philosophy. To participate, you can edit this article or visit the project page for more details.
??? This article has not yet received a rating on the quality scale.
??? This article has not yet received an importance rating on the importance scale.


Contents

[edit] Number of parameters

What is the "number of parameters or measurements" needed to describe an object? Since when do angles used to describe orientation count as "dimensions"? I have reverted the introduction. Brian Jason Drake 06:34, 20 November 2005 (UTC)

See "Electron spin" above. The spin is a parameter/measurement, but it is not a dimension. [signature added just after submitting comment Brian Jason Drake 06:44, 20 November 2005 (UTC)]

[edit] Euclidean vs spherical geometry

I had to reword the last couple of sentences of this paragraph, since east-west and north-south movements are only applicable to spherical geometry, and spatial dimensions are based on Euclidean geometry. NickBush24 06:49, 5 October 2005 (UTC)

[edit] Infinity?

I'm moving this paragraph to talk, because as far as I can tell it's either hogwash, or at least not properly sourced:

Infinity is the 5th dimension because it cannot be defined using the other four dimensions. We know of it's existence because no matter how large you can always add one more unit of measurement to almost any distance/time/number. However since we can engineer everything from the wheel to a moon-landing using just the first four dimensions there been no practical need to recognize infinity as being the 5th dimension, although it will be necessary in describing the Theory of everything.

--Delirium 17:53, 17 October 2005 (UTC)

Infinity is not a dimension. It is the continual expansion of the current 4 finite dimensions at light speed. Also, it is impossible to have a one dimensional object/entity. The smallest dimensions allowed for an object/entity are two dimensions. Only the motion of an object and the direction of forces are allowed to have one dimension. ( Francie. Scientific Ambassador of the universe. 25 May 2007)

The pages "infinity" and "theory of everything" don't appear to support that paragraph. Brian Jason Drake 07:07, 22 October 2005 (UTC)
The fifth dimension is not infinity; see Hilbert space. Fredil Yupigo 00:26, 26 October 2006 (UTC)

[edit] Physics

[edit] Movement

"We can move up-or-down, north-or-south, or east-or-west, and movement in any other direction can be expressed in terms of just these three."

Can you really speak of movement in terms of just the three spatial dimensions? Doesn't the very concept of movement depend on the time dimension? Without time all you have is position and no movement. Right?

yeah, that's right - BriEnBest 10:36, 31 March 2007 (UTC)
Movement is change of location. One moment a thing is here, and another it's there. Moving is not necessarily related with time. --Inyuki 12:09, 2 Dec 2004 (UTC)
yeah but moments are, i challenge you to define "movement" without using a word that is somehow related (directly) to time. - BriEnBest 10:36, 31 March 2007 (UTC)
How would a change of location occur except through or in time? Hyacinth 00:15, 3 Dec 2004 (UTC)
You can argue that time is the same as the three spatial dimensions, so "location" includes all 4 dimensions as well as any others that may exist, and movement is still defined as "change of location", so there is nothing special about time when it comes to movement. Brian Jason Drake 06:38, 20 November 2005 (UTC)
It doesn't matter how movement is discribed. Time has no relevence to where an object is. Therefore time is not another dimention. If time was another dimention, it would not speed up or slow down as it states in Einstein's theory of relitivity.
3 dimensions could describe the universe AT ONE MOMENT IN TIME, but no more than that. If you want to describe movement (motion, kinetics, which are a part of our world), then you need time. Time is the 4th dimension, because energy can be converted from matter, and it is the "stuff" inside of time, just like matter is the stuff inside of the 3 dimensions of space. - BriEnBest 10:36, 31 March 2007 (UTC)

[edit] Spacetime

What's the difference between space and time? Haven't we treated them as one thing ("spacetime") since Einstein? Brianjd | Why restrict HTML? | 02:26, 2 October 2005 (UTC)

In most usages, no we haven't: people continue to perceive them as 3-space and 1-time. And if you want to be picky the strong people like 11-d (10-d?) space anyway. The "physical" section seems to handle this OK; the intro is a bit odd, though it says "a space" not "space". William M. Connolley 09:31, 2 October 2005 (UTC).
It says "a space", which is correct. In mathematics we can have 3 dimensions or 4 dimensions - they can't be the same space, so there is more than one space, and in the intro we are not referring to any particular space. Brian Jason Drake 08:36, 17 November 2005 (UTC)

[edit] Space origin

Why (how come?) our space have three dimensions of space and one of time? How did the space originate? --Inyuki 12:09, 2 Dec 2004 (UTC)

Many Some scientists believe that space originated from particales slaming together at hype-speed, thus, creating the Big Bang, but there is also an unknown factor, where did the the particals come from, and what made them accelerate so fast, so it might point to a God, or a great force, existing before and possibly after the Big Bang.:No,1 kg corresponds to 25,000,000,000 kWh of energy,the "Fight" between matter and anti-matter is simular to the rebellion against Heavean strangely,here :No,1 kg corresponds to 25,000,000,000 kWh of energy, here, http://livefromcern.web.cern.ch/livefromcern/antimatter/academy/AM-travel01.html--Dansanman 06:37, 3 February 2006 (UTC)}

[edit] Electron spin

Electrons can move in 3 dimensions in space, move through time, can spin, and don't appear to have an internal structure. How can all this be accomplished if there are only 4 dimensions? Brianjd | Why restrict HTML? | 12:00, 2005 May 8 (UTC)

An electron's position in spacetime can be described with four coordinates. An electron's _state_ takes more degrees of freedom. It's spacetime that has four dimensions. State of a system that evolves over time is often expressed in terms of Hilbert spaces with an infinite number of degrees of freedom. Different things being talked about.--Christopher Thomas 21:32, 20 Jun 2005 (UTC)
Physics is confusing... Brianjd | Why restrict HTML? | 08:40, 2005 Jun 21 (UTC)

[edit] Multiple Dimensions

Can't multiple dimensions exist in a way that allows a particle to be in two places at once. If so, our whole universe could be a single particle (entity) that can be veiwed from an astronomical number of locations.

Huh? Brianjd | Why restrict HTML? | 09:49, 28 August 2005 (UTC)

My theory (and i think it happens to coincide with the accepted theories lol) is that the universe is a big 4 dimensional sphere that we are on the surface of...kind of like the earth is a 3 dimensional sphere and the things living on the surface of it basically can only move in 2 dimensions...
so yeah, if you were a 4 dimensional (spacial) guy or girl floating around "above" our universe then yeah you could see it from different angles (at different times) (or if you were 5 dimensional then you could see it from different angles at once :p .... but... about being in two places at once? wtf? - BriEnBest 10:42, 31 March 2007 (UTC)

[edit] Reality

"Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward."

Is there anything in physics to justify the "up/down", "left/right" and "forward/backward" labels or are these arbitary directions that humans have decided to label and consider special? Brian Jason Drake 08:08, 20 November 2005 (UTC)

IMO, i think physics is a description OF those directions and the different applications of "moving" in different directions (and stuff...) - BriEnBest 10:23, 23 March 2007 (UTC)

[edit] Science fiction

"Also, in science fiction, a "dimension" can also refer to a separate world or plane of existence, though this meaning is not discussed in this article.)"

What article would this concept be addressed in? parallel universe? i am sure several articles aim here for that concept. - Omegatron 02:44, Apr 25, 2005 (UTC)
It is discussed in "parallel universe", which is under a proposal to merge into Multiverse. Brian Jason Drake 08:43, 17 November 2005 (UTC)
This proposal seems to be gone from both articles and Talk:Multiverse. Brian Jason Drake 08:05, 20 November 2005 (UTC)

[edit] String theory?

String theory certainly should be somewhere other than the science fiction section, for it has been proposed as a real theory, but it might belong in science fiction as well. Brianjd | Why restrict HTML? | 06:16, 4 September 2005 (UTC)

string theory can dip its balls in lava for all i care - BriEnBest 10:26, 23 March 2007 (UTC)
I am thinking of this edit, where someone seems to have assumed that string theory does not appear in science fiction. Brian Jason Drake 08:54, 17 November 2005 (UTC)

[edit] Lead

Well I have rewritten the lead and my change has been reverted. I think however the lead should not make a too strong distinction between common sense, mathematics and physics. The mathematical definition is simply an extension (abstraction) of the common sense concept. The difference with physics is not really true. Adding a unit to a dimension is not really something that important. Not only physicist are using multi dimensional spaces with units. Economists, chemists, physicians, etc... Moreover an simple example should belong to the lead just as in manifold or in eigenvalue. This is also recommended in the mathematics project. Vb12:25, 21 November 2005 (UTC)

I prefer your version to the one with bullet points, which reads more like a disambiguation page. Charles Matthews 12:47, 21 November 2005 (UTC)
I prefer the bulletted version (otherwise I would have modified it after seeing the change myself). The point of an introduction is to be introductory. As long as all interpretations of "dimension" are mentioned, and have sections discussing them, I think that smaller is better. --Christopher Thomas 20:43, 21 November 2005 (UTC)
Bulletted sections are systematically criticized as list-like when it comes to featured article candidates. List-like paragraph are frown upon in wikipedia. Prose should always be the first choice. Introductory means often understandable for the layman. From this point of view, introduction to math articles usually have to show a simple example. Opposing the common usage to mathematics or physics usage is in this case a bad idea because the mathematics concept is clearly a generalization or abstraction of the common usage. I think the present version of the lead does not present an interpretation. If you believe so, then could you expand a bit your criticism so that we can find a compromise. Vb 08:35, 22 November 2005 (UTC)
If you feel strongly that it should be prose, fine - make it half the length, and briefly touch on uses in physics and other uses in mathematics besides degrees of freedom. At present, it doesn't mention these and it goes into an in-depth discussion of dimension as used to mean degrees of freedom, which is a) disproportionate to the amount of space used to describe other uses in the introduction, and b) already covered in the appropriate subsection. I find your statement that it "does not present an interpretation" to be puzzling - it's _supposed_ to give an overview of _all_ interpretations, and does so (with the exceptions noted above). The key word here is overview. An introduction is the first thing that a reader will see. The first decision they make is whether to bother reading it. The second decision they make, after reading it, is whether to read any of the rest of the article. If the introduction is overly-long, it won't get read, and the user will either skim at random or move on to another article. If it does not reflect the contents of the article (or in this case, strongly emphasizes some parts at the expense of others), the reader will make the decision to read or not read based on incomplete information. This is why the goal of an introduction is to provide a concise overview of an article's content, which I do not feel is being adequately done here. I'd modify it myself, but you appear to feel strongly about what it should look like. --Christopher Thomas 17:30, 22 November 2005 (UTC)
I have rewritten the lede simply because it needed to be done. The previous version was just too poorly entangled with the airplane concept and needed to be abstracted. Someone qualified might want to try writing an article on the concept of position - currently there is only a disambig. -MagnaMopus 22:08, 16 January 2006 (UTC)

[edit] 3D-Film

Some of the information added in this section was incorrect. The relevant info belongs to the 3-D film article. The Simpsons mention would also be better served elsewhere. Correct me if I'm wrong.--Metron4 23:25, 24 January 2006 (UTC)

[edit] Philosophical calculations - huh?

I wasn't able to make any sense out of this:

But looking at the four dimensions starting from 1 up to 4, we can see through philosophical calculation that there might be a small question mark at the 3rd an 4th dimension. If we consider that the 3 rd dimension (depth which allows radiation).
But we need time through which space is created in the calculative world where time involves any material action or development. If an object wants to radiate energy then that energize needs time and space to travel toward our eyes. So the 3rd dimension can only do its job when the 4th dimension is created first to allow that specific energy (radiation-3rd dim) to travel through space (4th dim) in and (with) a certain time sequence.

So I deleted it. --Alvestrand 21:36, 25 January 2006 (UTC)

[edit] Christopher Thomas's Reversion

Lestrade's deleted comments

"...a maximum of three lines can intersect a point at right angles... according to Kant... is the reason that space has three dimensions". Shouldn't that be the other way around? That space having 3 dimensions is the reason why no more than 3 lines can intersect a point at right angles? Of course, that still leaves unanswered the reason as to why space only has (or seems to have) the 3 dimensions. Answer that one -- in a way that everyone here can agree to -- and we'll let you put anything you want on this page. Deal? Ewlyahoocom 16:36, 2 March 2006 (UTC)
Lestrade's deleted comments
I interpreted the sentence you added as trying to make a claim that any space must have three dimensions, because of a property observed in (and unique to) our three-dimensional universe. If this is not what you meant, or what Kant meant, then by all means propose an alternate phrasing here. If it was instead intended a means of _measuring_ the number of dimensions in the universe we inhabit, then I'd again suggest altering the phrasing to make this clear, though that material is already covered in the preceding paragraphs (the number of degrees of freedom, or (alternatively) the number of non-degenerate basis vectors, required to uniquely define a location in a space is the dimensionality of that space, for spaces with integer dimensionality). --Christopher Thomas 20:14, 2 March 2006 (UTC)

Why would we be using Kant as an authority on this anyway? He is a philosopher. I very much doubt he originated the idea anyway William M. Connolley 20:16, 2 March 2006 (UTC)

Lestrade's deleted comments
You miss the point. I don't think the idea is original to Kant. what makes you think it is? Did he ever claim it was? William M. Connolley 14:04, 3 March 2006 (UTC)

Lestrade's deleted comments

[edit] Anaglyph

this section needs its tone revised

any reason to not just delete it? it's covered adequately elsewhere, and doesn't seem to add to the subject of this article. --Alvestrand 05:51, 5 September 2006 (UTC)

[edit] 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)

[edit] Dimension and exponentiation

There is a discussion at the ref desk about whether raising to a different power expresses a different dimension. If you want to contribute, be quick, because these discussions die out in a few days. DirkvdM 08:58, 4 September 2006 (UTC)

[edit] Vandalism

If you look at sections 4, 4.2, and 4.4.1 there seems to be some vandalism there. 24.185.25.78 02:49, 23 October 2006 (UTC)

[edit] Innacuracy in diagram

This diagram is extremely innacurate for the 0th and 1st dimension. Even the slightest thickness of a 0 dimensional object would make it one dimensional. An actual one dimensional shape should be an infinitely small point. Any thickness of a one dimensional line would make it two dimensional. An actual one dimensional shape should be an infinitely thin line. Fredil Yupigo 00:25, 26 October 2006 (UTC)

[edit] Removed "Imagining the Tenth Dimension" link

My reasons:

1. It's primarily designed to sell a book on the subject,
2. It's pseudoscientific, and unaccepted by the majority of the scientific community, and,
3. It's not mentioned elsewhere in the article. illspirit|talk 04:54, 10 November 2006 (UTC)

I very much agree with your reasons and have just removed the link. It hurts Wikipedia's credibility to have these kinds of links. Mdmkolbe 04:10, 4 January 2007 (UTC)

I would have liked to have had that link personally - BriEnBest 08:59, 24 March 2007 (UTC)

[edit] Narcissism?

I've been removing this poorly-written, (apparently) ideologically driven section. It needs the following to reappear: coherent style, sources, and NPOV. 129.171.233.29 18:09, 12 January 2007 (UTC)

I will not replace this section. It contains a very basic (even if unorthodox) observation, so it would be hard to find a citation that would make it conform to NOR. It was, however, entirely coherent, and was no more ideological than any other contribution. SemblaceII 20:27, 12 January 2007 (UTC)

Sadly, people can actually look at the history page and read it, so your claim of its coherence is pretty much refutable by a few seconds of reading. But ok then. 72.144.103.202 22:03, 12 January 2007 (UTC)

[edit] Showing a new reality


I am somewhat new to the whole more than three dimensions. done some research and found the tesseract and torus. however, it is real hard to visualize what it would look like being a 4 dimensional being. how about starting a project about what the world would look like if we could see it in the 4th dimension? THE WORLD IN 4D 5D and so forth. —The preceding unsigned comment was added by Paintedrealms (talk • contribs) 18:04, 18 February 2007 (UTC).

So, what the world would look like if we were entirely different creatures. Hard sell, man. 72.144.60.229 09:36, 25 February 2007 (UTC)


I'm not wikismart at ALL but I'm fascinated by theoretical dimensions despite the fact that I can very loosely understand even the 4th dimension...anyway I don't want to mess up the main page so I thought I'd leave this here for someone else to do...[1] thats a link to a very good example of what a spider web would look like in 4D, i thought it might be a useful thing to have on the page... --71.117.1.116 07:35, 20 March 2007 (UTC)

[edit] Mistake in 1.3 - Additional Dimensions

&QUOTE "Theories such as string theory and m theory predict that the space we live in has in fact 10 or 11 dimensions, respectively, but that the universe measured along these additional dimensions is subatomic in size. As a result, we perceive only the three spatial dimensions that have macroscopic size. We as humans can only perceive up to the third dimension while we have knowledge of our travel through the fourth. We, however can not perceive anything past the fourth."

the universe is NOT smaller than an atom - i'm sorry - not even string theory could say anything that contradictory - must be a mistake. BriEnBest 10:34, 23 March 2007 (UTC)
Have you read Flatland by Edwin A Abbott? If not, you should, before you comment on the thickness or lack thereof of imperceivable dimensions. Stannered 13:18, 23 March 2007 (UTC)
Lol, Stannered, the universe is STILL not smaller than an atom. This is like saying THE house someone lives in is smaller than an apple.
it's just some sort of error is all...i know that the author was not trying to make it sound like that.
I will look for the book though, soon. and thanks for turning me on to that as i am very interested in impercievable dimensions and the like... - BriEnBest 08:06, 24 March 2007 (UTC)

for reference, here is the next sentence: " As a result, we perceive only the three spatial dimensions that have macroscopic size" - this does not make sense because the sentence before it says that our universe (and more importantly, the dimensions we perceieve) are all MICROSCOPIC in size, then it says they're macroscopic...

let me try again, "...predict that the space we live in has in fact 10 or 11 dimensions, respectively, but that the size of these dimensions compared to the universe as a whole are subatomic in size."

how's that? can someone verify that for me, please? BriEnBest 08:38, 24 March 2007 (UTC)

No, the current version makes more sense. the universe measured along these additional dimensions is subatomic in size means that if you could put a nano-ruler along the imperceivable axes, then the distance measured would be less than 10-10 metres. The universe measured along the three conventional dimensions (which aren't "additional") is much larger than this. We are specifically not saying that the house is smaller than the apple. Stannered
well that should be explained better. what does that mean - that the universe is hella small along some dimensions.......ugh......maybe that whole part should just be taken out - or explained in just a tad more depth... - BriEnBest 09:09, 24 March 2007 (UTC)
on second thought - the two statements mean the exact same thing, in terms of relativeness: the universe is small when measured along the certain imperceivable dimensions and "the dimensions are small, compared to the universe as we perceive it"

Insertformulahere

Nope, yours doesn't say "additional". With "additional" included, they would mean pretty much almost the same thing, but the "compared to the universe" is unnecessary and confusing IMO. Stannered 17:51, 24 March 2007 (UTC)
so "predict that the space we live in has in fact 10 or 11 dimensions, respectively, but that the size of these additional is subatomic in size." is this better than what is there now, do you think? ie. clearer and easier to understand than "the universe measured along these additional dimensions is subatomic in size? - BriEnBest 05:08, 25 March 2007 (UTC)
Now I see the simplified version, it's still not necessarily accurate IMO - theoretically, the dimensions themselves could extend beyond the Universe. I think. Draw some co-ordinate axes, and draw a blob centered about the origin to represent the Universe. The size of the Universe measured along either of the co-ordinate axes is finite, but the length of the axes themselves is obviously infinite (or at least longer than the measured width of the Universe along that axis). Stannered 22:41, 25 March 2007 (UTC)
ummm, i think the term "dimension" is something that is applied to something in particular, therefor the "dimension" when applied to the "perpendicular parts" of OUR universe that are subatomic in size (if that is true.... although i see as probably necessary to the 2 small forces). well the dimensions are subatomic in size.... but the universe is DEFINATELY NOT subatomic...lol. sorry .
about the coordinate axes, think of a sphere...think of yourself on the surface of that sphere... which would be somewhat of a plane, right? so if you draw the coordinate axes on the ground, then they have a finite circumferance. it depends on the shape of the universe, but i think the dominant theory (i could be wrong) is that the universe is somewhat of a 4 dimensional sphere or something like that, which would mean that the three spacial dimensions are in fact finite. - BriEnBest 10:51, 31 March 2007 (UTC)

[edit] Additional Dimensions

how exactly do string theory and m theory predict that *just one* additional spatial dimension? what evidence do they base this on, or is it just theoretical math? if so, what is the math based on and where does it start? - BriEnBest 09:23, 24 March 2007 (UTC)

Try having a read of [2]. Stannered 17:56, 24 March 2007 (UTC)
k, i really don't see anywhere on that page where they point out how they predict extra dimensions? - BriEnBest 06:06, 25 March 2007 (UTC)
No, but if you don't understand that far, then I doubt you'll stand a chance of getting as far as the point where you're able to understand the derivation of a multi-dimensional universe. You could do worse than trying reading the rest of the site. Or doing an undergraduate degree in Physics (if you have not already done so). Stannered 13:09, 25 March 2007 (UTC)

it seems that this page assumes that
a) certain particles are made up of, or in fact are strings
b) when these strings are applied to the laws of harmonics, there is some type of mathematical need for 26 dimensions?

that is basically where i'm at right now... i would like to see the "proofs" of the equations they start with on that page, or maybe be told where they came from. i research that page off and on and the rather esoteric physics vocabulary they use. they also do things to the equations like change an x to a t. and add things without adding the same to both sides... it has a pretty reputable address, but seems a bit, unfinished. i do believe there is reason to why they do those things, but i do not understand them... - BriEnBest 10:28, 3 April 2007 (UTC)

- BriEnBest 07:47, 28 March 2007 (UTC)

[edit] mistake

"Adding the three Euler angles, for a total 6 dimensions, allows the current degrees of freedom —orientation and trajectory —of the aircraft to be known."

Preceeding this sentence, which is in the second paragraph of the article, is discussion saying that to pinpoint an aircraft you need three dimensions, and then comes a sentence stating that time can be a dimension, making the total count so far - four. Then comes this sentence which says that if you add three more "Euler angle" dimensions the total count is 6. Either this means that: 6 should be 7; or, they should say that "without the dimension of time," or something like that. - BriEnBest 08:02, 24 March 2007 (UTC)

6 is correct, and it shouldn't include time. It used to make sense, but has been messed up by careless edits. I'll attempt to fix it. --Zundark 08:32, 24 March 2007 (UTC)
nice edit - BriEnBest 08:45, 24 March 2007 (UTC)

[edit] This Quantum Theory is highly illogical

Mmmmmm, Donuts. —The preceding unsigned comment was added by 76.26.1.99 (talk) 23:58, 11 May 2007 (UTC).

It might be illogical but it's still a theory. ♥ Fredil 02:59, 25 November 2007 (UTC)

Larn to splel (Deliberate -_-) Gamesftw (talk) 12:49, 7 March 2008 (UTC)

[edit] Overkill

With regards to: "The equations used in physics to model reality often do not treat time in the same way that humans perceive it. In particular, the equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy)."

While this is very true and very interesting and very impressive sounding, I'm not sure it has found it's home in Dimension -> Time. Dhatfield 15:04, 27 July 2007 (UTC)

[edit] Disbelief

I'm no rocket scientist, but if there are dimensions in space, then the simple act of moving backward would be moving backward in time. The article gives misleading hints that the fourth dimension is time, but a tesseract is seen to be a hypercube and all dimensions have time. So, if it is proved that there is one dimension, there is one dimension in time, et ceterae (not et cetera) and therefore you may see that a for every unit in space, there is a unit of time. Even from a simple notion of force, one would find squared time. If so then there must be another set dimensions for time that match each and every superposition or "world" of space. —Preceding unsigned comment added by 69.122.10.103 (talk) 23:51, 4 October 2007 (UTC)

[edit] To Add to the Disbelief Article

Note to the author of this article:

I recommend not watching sci-fi movies deep in the night an writing an article some may be unfortunate as to cite.


Note to those who think the quantum theory and its applications are highly illogical:

Please explain why light can be polarized. —Preceding unsigned comment added by 69.122.10.103 (talk) 23:58, 4 October 2007 (UTC)

[edit] books

I am doing a research paper and i was wondering, what books should I read to get a better understanding about different dimensions? My topic is how understanding dimensions can be beneficial to our society. if there is any book or website to help me with my topic i would like to know what they are, but i am mainly focused on understanding the demensions first.i would like some differing opinions as well, so i can interprit what i think

Maybe the novella Flatland: A Romance of Many Dimensions? By the way, this page is for discussing improvements to this article. A better spot for such questions is Wikipedia:Reference desk/Mathematics. But then, of course, once you understand the concept of dimensions really well, you can help improve this article, which will be beneficial to Wikipedia specifically and thereby to our society in general.  --Lambiam 08:32, 16 November 2007 (UTC)
could i have a copy of your report lol, i'll help you understand what physical dimensions are - i don't know how understanding them can benefit but that is why i want to read your report - to learn that. BuT THIS PERSON DID NOT SIGN so it's kind of hard to communicate with him/her -BriEnBest (talk) 12:09, 22 November 2007 (UTC)

[edit] 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)

[edit] new lead

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.

the latest version of this lead is here Andeggs (talk) 13:45, 9 March 2008 (UTC)
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 ([3]) 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)

[edit] Fourth Dimension

For at least a brief period of time in the spring of 1975, both educators and scientists at U.C. Berkeley, made it be known that they had reassigned the fourth dimension and booted TIME out of that position. The new purpose of the fourth dimension was then to explain the ability of certain unproven lifeforms, that were briefly held in captivity at Lawrence Livermore National Labs in the 60's, to make themselves invisible to man. Participating in this decision were high profile educators at U.C. Berkeley, the son of Albert Enstein (also at U.C. Berkeley), and Stephen Hawking (who was on sabatical at Caltech at the time). Apparently some governmental pressure was later applied to this group to disregard their decision, due to the nature of that large interdimensional lifeform and the secrecy of the report surrounding it's captivity study.208.100.240.151 (talk) 17:42, 7 April 2008 (UTC)

[edit] 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)

[edit] 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 it[1][2].". 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)

[edit] 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)

[edit] 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)