Talk:Fourth dimension
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There should be a mention that the fourth dimension is also commonly used to refer to time. 86.135.161.60 16:57, 15 December 2005 (UTC)
The disambiguation page has a link to Spacetime, which is the correct name for what you are referring to. Saying that the fourth dimension is time is misleading. This is because we know that there are at least three spacial dimensions and one temporal. If there was actually four spacial dimensions then that would make time the fifth dimension. Having said that, people do call it the fourth, so if someone puts a comment about that can they include that it is a misleading way of naming it? Thanks. --Aceizace 18:27, 19 February 2006 (UTC)
Time is the way we percive distance in the fourth dimension. Time is not a dimension of space, so time by itself is not a dimension. Time multiplied by the speed of light is the distance through which the observer has moved in the fourth dimension. There is no mention of a fifth dimension in relativity, so references to it ought to be removed.FVP 07:43, 10 September 2006 (UTC)
- This article is not talking about 4-dimensional space-time as defined in relativity. It is talking about 4-dimensional Euclidean space. Time, if one wishes to consider it in this context, could be regarded as a "fifth dimension". This has nothing to do with whether such a thing exists in Einstein's theory.—Tetracube 15:05, 19 October 2006 (UTC)
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[edit] SPOILER!
I feel The Star Ocean reference should be removed as it is a spoiler and the basis for a BIG plot twist in the game. —The preceding unsigned comment was added by 80.213.106.141 (talk • contribs) 13:06, 16 January 2006 UTC.
[edit] Reality and the fourth dimension
I think this section needs cleaning up. There are style issues such as the need to enter the mathematical forumlae with the wikipedia provided function, but also the way it is written is very hard to follow. I am unsure whether the author is trying to prove the existance of the fourth dimension, or say there can only be four (ie no fifth or higher spacial dimensions). --Aceizace 18:27, 19 February 2006 (UTC)
Although I am not good enough at mathematics/physics to say for certain whether the following is right or not, it sounds to me very suspicous. It seems to be either original research, or nonsense, or if its neither its not explained very well. In particular, the idea that you can prove a physical property of our universe based on mathematical theorems? Talk about a leap from the a priori to the a posteriori!
- The fact that our universe can only be described by four dimensions is clear from the Pythagoras theorem and vector multiplication. The proof is as follows: The rule for multiplying two vectors is to multiply their magnitudes and add their angles. [1] Pythagoras' theorem for a triangle with one 90 degree angle is h^2=x^2+y^2 where h is the magnitude of the hypotenuse (opposite the right angle) and x and y are the magnetudes of the other two sides.
- But y can be expressed as a length in the x direction multiplied by 'j' where 'j' is unit length in the x direction with the 90 degree angle that rotates the x direction into the y direction. But h^2=(x1)^2+(jx2)^2 is not correct as j^2=-1 so we must consider that both the x and the y directions have been rotated from the z direction. Now h^2=(iz1)^2+(jz2)^2 =-(z1^2+z2^2) so the squares of the two vectors add. But the Pythagoras theorem works in three dimensions so a fourth dimension must be present which is at right angles to the x and y and z directions.
I will remove this. If someone with a maths/physics background confirms there is truth in this, they can re-add it (and please clarify it at the same time.) --SJK 12:03, 23 February 2006 (UTC)
This article is the result of original research carried out by the author. It forms the basis for understanding the how the Universe works. What mass is and how mass inevitably generates gravitational, inertial and electromagnetic interactions and many more. As these insight have not been recognised what is said must be different and therefor strange. Please bear with me, am doing my best to make it clear, many of the concepts are strange and have taken me many years to appreciate.
I have just found the Editing Talk pages and am greatful for the feed back that helps me to understand what problems that have been encountered with what I have written. I did not know about wikipedia mathematical functions. As a result of your comment I have found that they exist and where they are. Thank you for telling me..
This artical proves the nature of the fourth dimension as follows.
All four orthogonal dimensions are identical. The Universe exists as a mathematical surface made of nothing expanding at the speed of light away from its point of origin. The fourth dimension is the direction or dimension that the observer is moving. The Pythagoras theorem proof resolves the logical contradiction between vector multiplication and the Pythagoras theorem and proves that there must be an invisible fourth dimension of space. The Lorentz equation shows that the fourth dimension is a surface moving at the speed of light, which explains why we can not see the fourth dimension with light. Relative velocity means that the observer and the observed object are moving at the speed of light in different directions.
Higher dimensions do not form part of this artical on the fourth dimension. The possibility of higher dimensions is not ruled out but I have not found any reason to postulate their existence as every physical observation that I have considered is explicable to me with the four dimensions that are considered here.
Regarding a leap from a priori to a posteriori I am not sure what is meant here.
A priori means proceeding from from causes to effects, or logically independent of experience or not submitted to critical investigation. Well I agree that the fourth dimension must be inferred from the experience and logical deduction from the other three dimensions we are therefor proceding from the effects to infer the cause so that is not a priori. The fourth dimension is not logically independant of experience, so that is not 'a priori'. The fact that I am presenting this to the world is submitting it to your critical investigation so that is not 'a priori'. However I will grant you that it has not been subject to critical acceptance by the world as, apart from giving some lectures and discussing it with friends, I have not found a way to publish it.
A posteriori means inductive, empirical, moving from effects to causes , prior knowledge being used to deduce what comes after. This seems to me to be what I am doing here. FVP 00:29, 27 February 2006 (UTC)
I see that despite my editing efforts this entry has been deleted and rewritten by someone introducing the dreaded word space-time. Interestingly enough the artical does not mention time in connection with space time. However the connection between Pythagoras and the Lorentz equation has been preserved even if its derivation has been removed. Great chaps lets just say it works no need to have all that tedious derivation logic who bothers with derivation anyway.
I'm also very skeptical about proving existence of fourth dimension through maths. For example some real-life engineering problems can only be solved using i (the square root of minus 1) yet nothing measuring i cm will ever be found to exist in reality. I didn't have enough maths to understand the vector proof but it seems possible that all that is being proved is the need for a 'mathematical' fourth dimension as opposed to a real one. Also, don't really understand dimensional analogy. For example if you shine a light on a 3D object you get a 2D image. If you shone a light at a 4D object surely you wouldn't get a 3D object? MikeyMike
- If you shone (4D) light at a 4D object, you will get a 3D shadow, just like how shining (3D) light on a 3D object makes a 2D shadow. That's what the dimensional analogy section is driving at. Of course, this will take a while to grasp; understanding 4D is not simple.—Tetracube 17:56, 31 August 2006 (UTC)
I hope this new entry is acceptable. I need to show that the fourth dimension is a reality rather than a mathematical abstraction. 'Spacetime' is of course only space. The fourth dimension of space is measured in metres defined by seconds multiplied by the speed of light.
[edit] Shadows of Ourselves
This might have been mentioned before, but I read that 3d objects cast 2d shadows. So, what if our mind where we think and compute our thoughts is indeed 4d so the bodies that are cast are our 3d forms. Even more so, the prospect of ghosts could be defined as a 5d figure with a 4d shadow, which shadow is 3d. Only something to wonder about.--Dige 00:43, 22 June 2006 (UTC)
[edit] Directions
The directions up and down are based on gravity; north, south, east, and west are based on the orientation of the Earth; and foward, backward, left, and right are based on our own bodies. What are these other directions like ana and kata based on? —Keenan Pepper 05:52, 4 September 2006 (UTC)
- A (hypothetical) 4-dimensional being's body. Or the orientation of a 4-dimensional planet, as the case may be. The idea is that ana and kata are simultaneously perpendicular to all of north, south, east, west, up, and down. Of course, this is only possible in 4-dimensional space. Note that there is no established consensus whether ana and kata are absolute terms (based on 4-dimensional planetary orientation) or relative terms (based on the orientation of a 4-dimensional being's body). Some authors use it one way, others use it another way. Also, some authors use up and down as horizontal directions when in 4D (i.e., perpendicular to 4D gravity), and ana and kata as the 4D equivalents of up and down (colinear with 4D gravity). The common factor is simply that ana and kata refers to the extra pair of directions available when in 4D space.—Tetracube 16:40, 4 September 2006 (UTC)
[edit] Writing style
I'm sorry, but this reads like a textbook, especially when words like "we" are used. Is there any way of cleaning it up (or simplifying it to make it more readable) without losing important information? SKS2K6 09:21, 19 October 2006 (UTC)
- Go ahead and fix the "we" references. That should give us a start. As for the accessibility of the article itself, I think it is in need of a major reorg, but I'm not sure how to go about it.—Tetracube 15:07, 19 October 2006 (UTC)
[edit] My head hurts!
Is a 2D representation of a 4D object even possible? It seems too far removed in dimensions. Then, can a 4D object be efficently depicted using 3D paper? Also, how come the 4D cubes are only cubes joined on their sides, not their top and bottom faces? Is it just a coincidence that the net of a tesseract is composed of 6 cubes just as the net of a cube is composed of 6 square? The net of a square is composed of only 4 lines, and the net of a line is an infinite number of points, no? Aaadddaaammm 09:09, 20 October 2006 (UTC) PS. No idea what I'm talking about.
- The net of a tesseract has 8 cubes. --WikiSlasher 09:32, 23 October 2006 (UTC)
- Well, a 2D representation of a 4D object is of course possible, and so is a 2D representation of an object of any larger dimension. A better question would be, is a 2D representation of a 4D object sufficient to convey the geometry of the 4D object? As you note, too much information is lost in going from 4D to 2D, which is why many Java applets you see out there trying to draw 4D objects with lines end up showing an incomprehensible tangle of lines which is very hard to understand.
- As for whether a 4D object can be adequately represented on "3D paper", the answer is yes!, because our own eyes only see in 2D, but we have no problem perceiving 3D depth from the images. A hypothetical 4D being with eyes similar to ours would have a 3D retina, and thereby perceive 4D objects from 3D images. Therefore, projecting 4D objects to 3D is a good way to visualize them.
- However, to fully appreciate such projections, we'd need to be able to see every point of a 3D volume simultaneously, which is impossible for us because our eyes only see in 2D. Therefore, some simplification is needed. Usually, this is done by drawing only the faces or edges of the 4D object, leaving plenty of blank spaces for our 2D eyes to be able to see the internal structure of the 3D projection image (we are really projecting from 4D to 3D, and then from 3D to 2D). The animation of the 4D hypercube recently added to this article is a good example of this: it "fattens" the vertices and edges of the projected image so that when rendered on the 2D screen, we properly perceive the 3D depth of the image. (Otherwise, our eyes will get very confused by optical illusions caused by ambiguity in 3D depth.)
- Of course, to understand what we're looking at is another matter altogether. For this we need to use dimensional analogy, which is briefly discussed in the section with that heading.
- And yes, don't be surprised that your head hurts trying to grasp this. :-) Nobody said visualizing 4D was easy. In fact, many mathematicians still have trouble with the concept, even if they can mathematically manipulate these objects.—Tetracube 00:21, 2 November 2006 (UTC)
[edit] Simpler?
Can this article be made to be understandable by us less-smart people who are just curious? Or is the concept of the fourth dimension just an incredibly complex topic? Dylanga 01:52, 15 December 2006 (UTC)
I also want a simpler explanation :S--71.62.178.53 05:43, 7 January 2007 (UTC)
- I think it's difficult to avoid the complexity. It's a simple concept, just a natural extension of the sequence (1, 2, 3... ) of dimensions. But it is very difficult for us three dimensional creatures to visualise. You can use mathematics but it is hardly easy, and there are some additional complexities in four (and higher) dimensional mathematics that don't help.
- If anything this article is less technical than it could be, with no formulae or mathematical discussions, except for the volume of the hypersphere.
JohnBlackburne 16:18, 20 January 2007 (UTC)
[edit] Incorrect caption for the animation
The animation in the article is actually a two dimensional projection of a three dimensional projection of a fourth dimensional object (http://upload.wikimedia.org/wikipedia/en/5/55/Tesseract.gif), not a three dimensional projection as the caption (3D projection of a rotating tesseract) states. A computer screen cannot create a three dimensional projection. —The preceding unsigned comment was added by 24.187.17.94 (talk) 00:04, 2 January 2007 (UTC).
- Every image is 2D. So an image of a 3D object, real or virtual, is a 2D projection. Because it is always true it does not need to be stated and hardly ever is. JohnBlackburne 22:43, 23 January 2007 (UTC)
[edit] Do we live in four-spatial dimensions space?
General relativity says that Universe is a curved space.Scientists proved the that massive objects such as SUN bend the light coming from the stars.
The question is
Does that also mean that this Universe a four spatial dimensions universe since it is a close/ curved space universe?.
86.147.252.83 12:59, 15 January 2007 (UTC)
General Relativity says that four dimensional spacetime is curved, i.e. non-Euclidean. Some people like to imagine it as embedded in a fifth dimensional space, as this space can be Euclidian. This space is also used by some science fiction writers for faster than light travel. There is no mathematical justification for it though.
JohnBlackburne 23:29, 16 January 2007 (UTC)
[edit] Physics???
This article is about 4-dimensional Euclidean space, not about 4-dimensional Minskowskian space-time. I. e., it is an article about geometry and not about physics, even though there is a tenuous mathematical connection. I don't think this article is relevenat to WikiProject Physics.—Tetracube
My brain, it BURNS! Seriously, that animated gif blows my mind.--Daniel Berwick 23:50, 9 April 2007 (UTC)
