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)

Contents

[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)
It helps a lot if you draw out a few different perspectives of a hypercube by manipulating the perspectives of the individual cubes forming it's sides. Thats how I got my first glipse of a hypercube.--Scorpion451 04:17, 15 July 2007 (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)

Hmmm... while I agree this article could be a lot more complex with the formulas and what not, perhaps we should have an article which serves as an intro to higher dimensions. Actually, that gives me an idea. I will add a section to the talk page about it. Jaimeastorga2000 13:56, 9 August 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)
I think the caption is correct as it stands, as the person above said, there is no need to call a picture of a three dimentional apple a 2-dimentional projection of an apple--Scorpion451 04:20, 15 July 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)

Physics and mathematics are basically the same in reguards to geometry. One mathematicians deirivative is another physicists velocity.--Scorpion451 04:23, 15 July 2007 (UTC)

I think it is important to cover all the aspects of the topic.Southafrica6 (talk) 00:15, 29 April 2008 (UTC)

[edit] Scientists???

Can somebody make a list with all the scientists involved with the study? Izaak 08:44, 15 April 2007 (UTC)

[edit] Image mistake

The uppermost image on the page seems to be missing an arrow (the ones that point perpendicularly into the 4th dimension). There are only 7 arrows, but 8 vertices on the cube. The front upper right vertex is missing an arrow. Leon math 21:32, 20 April 2007 (UTC)

[edit] Pictures

I know the rotating 3D tesseracts are pretty and all, but is it really necessary to have 2 of them? If nobody raises an objection I'm going to delete the second one because it doesn't look as good as the first one. RageGarden 23:34, 28 April 2007 (UTC)

The first is of a rotating (4D) tesseract, the second is of a rotating 24-cell. Not only are they different but the second one is the only 24-cell pictured. I think a rotating version of it works well, as it gives it some depth - a 2D picture of a 24-Cell is a lot less interesting. JohnBlackburne 12:10, 17 May 2007 (UTC)
There used to be another 4D tesseract, but I deleted it already. The one I was talking about was Image:Changingcube.gif RageGarden 04:22, 18 May 2007 (UTC)
I think rotating tesseracts are entirely unnecessary. They make me want to throw up, and they aren't any better at explaining the concept than a stationary 2D tesseract. PyroGamer 20:18, 24 June 2007 (UTC)
I agree, or at least I think they're pretty, but not helpful here. Tom Ruen 21:07, 24 June 2007 (UTC)
Personally, in my experience it's the only way to get a good idea of what they look like, even if it is only a zoetrope view. And of course it will make some people sick to your stomach, Its something the brain isn't hardwired to handle.--Scorpion451 04:30, 15 July 2007 (UTC)

[edit] Should this clarification be added?

I propose we add the following clarification to the header:

This article refers to a fourth proposed spatial dimension. For the einsteinian concept of time playing the role of a fourth dimension, see spacetime.

PyroGamer 20:16, 24 June 2007 (UTC)

This would be helpful, yes. I second this.—Tetracube 01:30, 5 October 2007 (UTC)
You can add this yourself if you think it would be helpful. Be bold! Pi is 3.14159 | Talk 01:40, 5 October 2007 (UTC)

Good idea!Italic textSouthafrica6 (talk) 00:24, 29 April 2008 (UTC)

[edit] New Introductory Level Article?

Well, after reading http://en.wikipedia.org/wiki/Talk:Fourth_dimension#My_head_hurts.21 , I thought that maybe an introductory level article to higher dimensions (or indeed, the 4th dimension only, as I doubt anybody who is trying to understand higher dimensions wishes to go any higher) would be appropriate. After all, we have seen introductory level articles to complex subjects before, such as http://en.wikipedia.org/wiki/Introduction_to_general_relativity or http://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics . Therefore, by http://en.wikipedia.org/wiki/Wikipedia:Make_technical_articles_accessible , an article which would make this one more accessible is desirable. I suggest we use the already written section of dimensional analogies as a base or as a guide, because of two reasons:

-I fully believe dimensional analogies are the best method of introduction and the beginning of true understanding of the 4th dimension.
-As http://en.wikipedia.org/wiki/Wikipedia:Make_technical_articles_accessible states:
Use analogies to describe a subject in everyday terms. The best analogies can make all the difference between incomprehension and full understanding. As an example, the Brownian motion article contains a singularly useful entry entitled Intuitive Metaphor:
Consider a large balloon of 10 meters in diameter. Imagine this large balloon in a football stadium or any widely crowded area. The balloon is so large that it lies on top of many members of the crowd. Because they are excited, these fans hit the balloon at different times and in different directions with the motions being completely random. In the end, the balloon is pushed in random directions, so it should not move on average. Consider now the force exerted at a certain time. We might have 20 supporters pushing right, and 21 other supporters pushing left, where each supporter is exerting equivalent amounts of force. In this case, the forces exerted from the left side and the right side are imbalanced in favor of the left side; the balloon will move slightly to the left. This imbalance exists at all times, and it causes random motion. If we look at this situation from above, so that we cannot see the supporters, we see the large balloon as a small object animated by erratic movement.
Now return to Brown’s pollen particle swimming randomly in water. A water molecule is about 1 nm, where the pollen particle is roughly 1 µm in diameter, 1000 times larger than a water molecule. So, the pollen particle can be considered as a very large balloon constantly being pushed by water molecules. The Brownian motion of particles in a liquid is due to the instantaneous imbalance in the force exerted by the small liquid molecules on the particle.

What do you think? Jaimeastorga2000 14:31, 9 August 2007 (UTC)

I fully second this idea. I also believe that dimensional analogy is the best way to develop an intuitive feel of 4D space. This is not to discount most mathematicians' preferred approach, which is with algebra and hard equations. Rather, an intuitive grasp of 4D space can complement and enhance one's facility with algebraic manipulation. Dimensional analogy is best because it relates unfamiliar things in 4D with similar things in the 3D space we're familiar with. I would say that dimensional analogy of perspective/parallel projections is probably one of the best tools for visualizing 4D objects. Many regular and Archimedean polytopes may be re-discovered by simple application of this method, once one is familiar with how 4D works. (Of course, such results have to be verified mathematically, but the fact that one can arrive at them using just dimensional analogy speaks of its usefulness as a visualization method.)—Tetracube 01:30, 5 October 2007 (UTC)

It would be good to create a jumping of point that deals with our everyday objects instead of the more advanced stuff.Southafrica6 (talk) 00:23, 29 April 2008 (UTC)

[edit] TIME was kicked out of the 4th Dimension Spot in 1975

At U.C. Berkeley in 1975, University staff quietly decided to reallocate the 4th dimension for purposes of explaining Bigfoot invisibility. The son of Albert Einstein was on staff at that time, and gave his approval. Scientist Stephen Hawking was on sabatical at Berkeley for the the year 1974-75, and apparently gave his approval. They had access to the poorly kept, top secret Bigfoot captivity report of two live Bigfoot subjects, that took place at Lawrence Livermore National Labs in the 60's. Both Bigfoot outwitted their captors and escaped from their holding cells. Bigfoot, as are dozens of other little nature people, interdimensional. This was common knowledge at Berkeley, starting in 1975. The 4th dimension and higher are NOT spacial dimensions. They are dimensions based on modifying the vibrational frequency of free quanta loops, similar to super-string theory of quantum physics, as explained in the book entitled X3, by Adrian Dvir. —Preceding unsigned comment added by 216.239.166.251 (talk) 18:33, 24 September 2007 (UTC)

[edit] The weight of the Tardis

Rephrasing my question to this context: if the Tardis can be treated as a tesseract of a given weight, how would one calculate the weight in each variant visible in three dimensions (ie how much would the police box in the series, rather than the Tardis-complete) weigh?

A suitable website redirect would suffice. Jackiespeel 15:30, 5 October 2007 (UTC)

[edit] Time OR Spacetime

This article, and a lot of the rhetoric I've found on the fourth dimension, does not seem to discuss a difference between Einstein's concept of spacetime and the generally understood construction of "time." Is this article saying that the fourth dimension is the union of space and time that Einstein called spacetime OR is it simply time by itself? Most people, I would think, would agree that time can be defined by change -- in video, for example, the change between frame 1 and frame 2 being a measure of time -- and that this traditional flavor of "time" can exist on all dimensional levels. Whether I'm a dot, a square, or a cube, if I'm late to a meeting, the meeting is no longer at the same x,y, and/or z coordinate at a particular time t and I will have to get the meeting's minutes at a later time t + n. This situation seems to change when I'm a hypercube.

What I believe the article is arguing is that the fourth dimension is spacetime, and whenever the article mentions the word "time" it is really talking about "spacetime." Since I am not a physicist, I do not know if this is accurate, but if it is, we should by no means make the assumption that everyone who reads this article will understand that "time" and "spacetime" are the same, even if they actually are.

If my assumptions are correct, we should clarify a couple things. The solutions I can think of off the top of my head would be: either make a note in the introduction about time and spacetime being the same, OR replace all instances of "time" with "spacetime" where appropriate. // Montag 05:20, 10 October 2007 (UTC)

I think making a distinction between "fourth spatial dimension" and "spacetime/temporal dimension" (or similar term) would resolve the unclarity - being the way most people would divide them. Jackiespeel 13:38, 11 October 2007 (UTC)

I believe the article was originally intended to discuss 4-dimensional Euclidean space, rather than Einsteinian space-time. Contrary to popular understanding, these are two very different things. Einstein's concept of space-time is not Euclidean, but Minkowskian. The fourth dimension in Euclidean 4-space has absolutely nothing to do with time, just as the 3rd dimension in 3-space has nothing to do with 2D time! Einstein's concept of space time may be regarded as 3+1 dimensions, where the extra dimension is different from the other 3 in the sense that it is temporal, and behaves differently from the spatial dimensions. Even mathematically, the time dimension in relativity does not behave like the other dimensions: it has a negative sign whereas the other dimensions have positive sign. Another major difference is that you cannot arbitrarily interchange the time dimension with the other spatial dimensions, the way you can interchange the spatial dimensions via rotation.
The 4th dimension this article is discussing is Euclidean rather than Minkowskian, which means that all four dimensions behave exactly the same way, and are freely interchangeable with each other via rotations. They are spatial and not temporal. Only in this context, geometry makes any sense: geometry by definition deals with shapes and angles, etc., in an absolute sense. Geometry doesn't apply to temporal dimensions (although this is often attempted, esp. when discussing relativity, because it appeals to people's imagination), at least, not in a sensible way like it does to spatial dimensions. For example, 4-dimensional polytopes, which are geometric objects, do not make very much sense in Einstein's space-time, where they represent mutating shapes over time. (And I'm not even sure if this is a valid interpretation, as they probably violate fundamental laws of Einsteinian space-time, such as the fact that the rate of shape change cannot possibly exceed light-speed, which severely limits the allowed angles between facets lying across the time dimension.) Most of their beauty and symmetry is lost because space-time does not allow you to rotate these polytopes the way you can rotate them in Euclidean 4-space. The common attempt to understand them as "snapshots" of shapes in space-time is misguided, and does not really explain their true geometry.
Anyway, Einstein's theory is already discussed adequately in spacetime. The focus of this article is really to discuss Euclidean 4-space. (Unfortunately, that last paragraph in the intro about considering a 4th spatial dimension as the "5th dimension" only serves to confuse this issue more.)—Tetracube 01:56, 16 October 2007 (UTC)

[edit] The methaphysics of the fourth dimensional space

According to my knowledge, whatever corresponds to the fourth-dimensional space in physics and maths is a spiritual image of a higher world, the world of perfect ideas in Plato, the Kingdom in Christian thought, etc. Anyone? —Preceding unsigned comment added by 202.80.43.11 (talk) 02:00, 13 October 2007 (UTC)

[edit] Variants of the "hypercube"

"During studies, dimensions relate by multiplying itself by itself (squaring it), then multiply it by it's next dimension. This will give you the amount of "drawn lines" within the next dimension.

I.E.(1) 1st Dimension, multiplied by itself, Gives you 1. Multiply 1 by the next dimension (2), and you receive the answer of 2, which is how many lines represent the 2nd dimension. (Right Angle)

I.E (2) 2nd Dimension, multiplied by itself, gives you 4. Multiply 4 by the next dimension (3), and you receive the answer of 12, which is how many lines represent the 3rd dimension. (Cube)

I.E (3) 3rd Dimension, multiplied by itself, gives you 9. Multiply 9 by the next dimension (4), and you receive the answer of 36, which is how many lines represent the 4th dimension."


Would it be more practical make a study of the required vertices (corners) involved in these shapes? Such a equation would be far easier to explain with:

2D = V

Where d is the dimension count (0, 1st, 2nd, 3rd etc) and V is the required amount of vertices.

For example a dot in the 0 dimension has one point. A line has 2, a square has four, a cube with 8 and the cube within cube design has 16. This would require consensus that a cube-within-cube design is a valid tesseract of course. Lagginwagon (talk) 08:16, 23 November 2007 (UTC)

[edit] Something to ponder

Thinking on fromwhat was touched upon in the section above 'Shadows of ourselves'.
Doesn't the 4d concept ever strike you as an explantion for paranormal activity? I'm kinda thinking of ghosts or Mothmen - the idea of just having random apparitions appearing (as a 3d cross-section of a 4d being passing through the plain of our deminsion) and being able to comunicate without being see and also know the contents of a sealed container (like us seeing the contents of a 2d container).
Anyways I quite liked the idea and thought it might be worth sharing, if not the plot to a cheap movie(!). ArdClose (talk) 18:38, 20 December 2007 (UTC)

Coming to a theater near you... GhostCube! J-ſtanContribsUser page 18:44, 20 December 2007 (UTC)

[edit] Where to find out about the eccentricities in higher dimensions?

I know there are many properties of higher dimensions that can't be discovered by simple Dimensional analogy, as described in this article, because the third dimension is, in some sense, a special case. An example I've heard (just heard, from someone who has about 90% reliability) is that a knot can't exist in higher dimensions. Another one I found from a tesseract form of the Rubik's cube (computer simulation). In the tutorial, if I remember correctly, was something about a 'turn' being different in the 4th dimension; it said that our version of a turn, a rotation around an axis, is a quirk of the third dimension (or something like that).

Where can I find out about that and other strange properties of higher dimensions (within the realms of a high-school education)? --70.124.85.24 (talk) 15:19, 7 January 2008 (UTC)

Thanks for your help. Much appreciated. </sarcasm> --70.124.85.24 (talk) 22:28, 19 January 2008 (UTC)
Knots do exist in 4D. Just that 1D objects (ropes, strings, vines, etc.) can't knot; you need a 2D sheet to knot in 4D. This gives rise to such objects as the Klein bottle, the real projective plane, and other interesting objects. Also, rotations in general should be thought of as motion in a 2D plane, rather than around some axis. You're quite right that rotational axes only exist in 3D: even in 2D space, there is no such thing as an axis of rotation (because the axis we like to imagine lies outside of the 2D space!). There is only a central point everything else revolves around. Similarly, in 4D, you rotate around a plane, not an axis. 4D also has compound rotations (sometimes called "Clifford rotations"), in which there are two independent rates of rotations. Such rotations happen about a point. Hope this helps. (P.S., no need to be sarcastic, sometimes it just takes a while for people to notice your question.)—Tetracube (talk) 13:48, 5 April 2008 (UTC)
Here's another tidbit for you: In 2D there is an infinite family of regular polygons; in 3D there are nine regular polyhedra (five convex and four stars); in 4D there are sixteen regular polychora (six convex and ten stars); and in each higher space there are only three regular figures (all convex). —Tamfang (talk) 07:29, 21 May 2008 (UTC)

I thought that objects such as ropes and vines were 3 dimensional, as they have height length and width. If this is right, shouldn't 4th dimensional knots have to be created by 4th dimensional objects?Southafrica6 (talk) 21:37, 12 May 2008 (UTC)

Physical ropes have three dimensions, but the objects considered in knot theory are made of abstract strings with zero thickness. —Tamfang (talk) 07:25, 21 May 2008 (UTC)

[edit] Field Study of 4th Dimension People (and higher)

WARNING! If you are potentially living in denial of a weak mind and/or are emotionally insecure in regard to the thought of millions of either large or small hairy and benevolent interdimensional people inhabiting this planet, STOP right here and instead go read those vanilla coated fairy tale stories that you read to your children. Otherwise, read on at your own risk of suffering either unjustified anger, temporary or permanent mental illness, hallucinations and/or nightmares. Remember the First Amendment to the U.S. Constitution, in regard to Free Speech. You did not even have to come here to read this. Nor is anyone forcing you to read the following: In an attempt to get the reader immediately up to speed on the subject matter, I offer this summary of scientifically verifiable field observations that could be considered as highly useful for those with an open mind. First of all, Bigfoot for instance, are just one species of an entire family of interdimensional people that inhabit this planet. Interdimensional means that they can both exist in the higher dimensions, as well as in Man's dimension by changing their apparent dimension at will. When they are existing in a higher dimension, they are normally invisible to Man, but we can hear their noises. Bigfoot are normally polite, benevolent and just want to get along, so the fact that they are invisible in a higher dimension, does not automatically spell trouble for Man. Quite the opposite. They appear to prefer to constantly "cut Mankind slack" in view of Man's perpetual disrespect for them. At least half a dozen Bigfoot appear to have followed me home and hung around and inside my house. There was never any indication of hostility. So no worries mate. They are audio detectable in at least 3 higher dimensions. The higher dimensions appear to be sub-dimensions of Man's 3 dimensional world. Although the number of higher dimensions may well be infinite, the Bigfoot appear to emit noises that tends to indicate that they have some favorite higher dimensions that they exist in. Physicists will be absolutely NO HELP on the subject matter, since many are still falsely claiming that the higher dimensions are "very small". Of course, with the pressure from Right Wing Extremists to bury this truth, it is no small wonder that the Physicists are not interested in being publicly candid in regard to this subject matter. The higher dimensions appear to be sub-dimensions of Man's dimension because the Bigfoot's footsteps still contact our 3 dimensional ground and make some noise in the first favorite two removed dimensions from Man's. (There appears to be both audio and physical "overlap" between nearby dimensions. Think of the bell curve as somewhat indicative of what level of interaction that occurs in not only the primary favorite dimension, but the other nearby dimensions.) The further out in primary dimensions that they go, the less gravity effects them as does the solidity of our 3 dimensional objects such as trees. So they can walk through our trees in the further out dimensions because our trees have virtually no physical presence in those higher dimensions. Bigfoot can howl, throw both solid and invisible objects, make footprints, make snorting or heavy breathing sounds, etc., all while completely invisible in at least the primary dimension once removed from ours. In the dimension twice removed from Man's, their footstep force on the ground is no more than a few ounces. They often tiptoe through camp at night, in this dimension. Bigfoot often understand the local language and are highly telepathic. They have appeared to perform telepathic eavesdropping from at much as 300 yards away. Consequently they can and do like to eavesdrop on our dreams. They also like to communicate with us and they especially like to establish a friendship. Some will demonstrate their telepathic ability with a simple camping game, but only if they like you. In that harmless game, they position themselves perhaps a hundred yards away from your tent or camper. The instant that you change your level of waking consciousness (just prior to either moving or even opening your eyes) in the early morning or even in the middle of the night, they will break a small branch as a "good morning" greeting. They will wait up all night to do this so they apparently like to play this game of amazement. Most of the games that they play with us, are games of amazement that even our best magicians would be envious. Their attempts at communication is evident by branch breaks, wood knocks, foot scuffing, electronic clicks, electronic beeps, howls, etc. They have special skills to imitate extraordinary sounds. If they don't like what you are just thinking, they may demolish the local area with a large branch, or slap the side of your house or trailer. In very rare circumstances, Bigfoot have been witnessed transforming into a visible Orb. They likely travel as an invisible Orb during daylight hours, and perform reconnaissance of our campsites within a few moments of our arrival, as an Orb. If you are a good listener, you can hear the invisible Bigfoot Orb briefly buzz your campsite or your living room, but you will naturally see nothing with your naked eye. Night vision with IR assist can see them. The audio detection requires complete silence by all. Their faint electronic buzzing sound can be heard at air temperatures well below the temps that bees can fly at. Orbs can instantaneously accelerate to extremely high speed and stop on a dime. So the Bigfoot can follow you home as an invisible Orb, or find you at a later date by following perhaps your aura, or your stink. So be nice to the Bigfoot at all times. When they change back to a 3-D being, we can sometimes hear either two footsteps hit the ground or a single foot push off in loose gravel, for instance. Bigfoot can consume the higher dimensional presence of food that you leave, and leave the rest for you. Early decay spots on fruit, may indicate that a 4th dimensional bite was taken out of it. So they can and do enter houses at night and eat perhaps the 4th dimensional presence (the dimension once removed from Man's) of the food, and then they just leave without so much as a thank you note. You would never know that they were there unless perhaps a dog gets upset. They especially like Christmas because of the cookies that you leave around the tree. Listen next year from an adjoining room, for very light electronic clicks, footsteps, foot scuffing sounds or even package wrapper crinkling, from around the tree. The fabled Santa's Elves would likely be just one of the many types of little interdimensional people, some of whom actually wear tailored clothing. The Bigfoot appear to like to celebrate our holidays with us. Please leave some fresh fruit behind when you visit the forest next time. Also leave fresh fruit out in your kitchen or on your dining room table, if you live near a forest. Both the big and the little interdimensional people will find it, and hold kind thoughts about you. Which never hurts considering that they are supernatural for all practical purposes, and appear to possess many of the characteristics that we assign to either Santa Claus and/or God. The possibility exists that the conglomerate of Bigfoot people may even act together as a unit to essentially be God, for what little we know as a result of research being stifled by society. So the Right Wing Extremist's apparent goal to seek complete societal ignorance in regard to the subject matter, does not appear to be particularly well thought out. Bigfoot can easily become emotionally attached to us, but that does not mean that they will make themselves visible to us. They do not wish to scare people that they like so they remain invisible to be polite. If they do not like either you or what you may stand for, they are more likely to make themselves visible in order to scare you away. Right Wing Extremists would be a likely candidate for a brief visual display. To the more intellectually astute, this display can be perhaps a way of demonstrating God's will by disciplining those that sorely need it. Did I mention that they are fairly intelligent yet? Try getting a picture of one if you haven't figured that out yet. This should suffice as a good basic primer to get thousands of the curious onto the same page. Or they can continue to live in either denial or ignorance for the rest of their lives. Tricks, camera traps, guns, intent to do harm, intent to be friends, etc, can all be easily detected by the Bigfoot. So pursuit type tactics of obtaining proof of their existence, are normally a complete waste of time. Bigfoot will find you, if you let them know that you truly wish to be friends with them.208.100.241.68 (talk) 15:00, 21 May 2008 (UTC)