Hypercube

Yeah i'm a real big nerd + fanatic about higher dimensions? (particularly the 4th). uh this isn't an opinion post about it (although you say whatever you want about it) but mainly a request. Would it be possible for me to ask one of the designers here to create a really cool wallpaper of a Hypercube? (the cube within a cube perspective) and like, use all ur cool..effects to make it look good and illusionegetic etc..? yeah, cool. thanks. seeya.
13,135 views 62 replies
Reply #1 Top
Hahaha... I don't even know what it looks like let alone make it as a WP.



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Reply #2 Top
Guess I better do a Google search...



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Reply #3 Top
Actually, you might want to poke around the wallpaper section for some of the older walls. I believe someone actually *did* do a hyper cube.



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Reply #4 Top

Well, there's no way to represent a 3 dimensional object in one dimension, other than as a line which would imply 0 extent for one dimension of the three making it therefore only a two dimensional object represented in one dimension.

So, how in thunderation is one going to represent a FOUR dimensional object in the only TWO dimensional medium these artists work in ????

Coooome ooon, gimme a break !

Your Pal,

John Stossel

P.S. I think I did see this "picture" of a hypercube or something 4 dimensional in a Scientific American, or the like, sometime in the last several months. Couldn't make heads or tails of it.
[Message Edited]
Reply #5 Top
I understand, but I really think that someone tried one.



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Reply #6 Top
Yup, your jest a leettle ahead of me there wolfie !
(if I may call you that without offense )

I would certainly encourage any attempts, regardless.

P.S. What I mean above is that I was composing my tongue-in-cheek tirade as citizen werewolf was making his suggestion. My longer post was NOT a response to his.
[Message Edited]
Reply #7 Top

 

The hypercube theory:

Reply #8 Top
whoa...a hypercube is a sunken square cutout with a raised square inside of that with a red x inside of that. My god, it's so simple. I totally get it now. Man, I can't believe I never saw that before.





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Reply #9 Top
Tesseract: is what you are actually looking for.
The Tesseract (or Hypercube)
A guided demonstration
http://www.geom.uiuc.edu/docs/outreach/4-cube/

The Tesseract
A look into 4-dimensional space
http://pw1.netcom.com/~hjsmith/WireFrame4/tesseract.html

Tesseract Facts
http://mathworld.wolfram.com/Tesseract.html
Reply #10 Top

OK, another try.

Here is the hypercube theory explained with an animation:

Reply #11 Top
Simple, Elegant and Very Nice, paxx.
Reply #12 Top
I liked the movie Cube 2: Hyper Cube on the Sci-fi channel... It was cool...
Reply #13 Top

Oh Cygnus, it's not from me. I grabbed it from a web site. 

http://www.geocities.com/CapeCanaveral/7997/

All I did is turn the Flash into an animated GIF. :)

Reply #14 Top
That's good Paxx, thanks for digging that up.

Although I was tongue-in-cheek earlier, I had quite forgotten the technique of using another attribute, color being one of the most convenient, to represent an extra dimension. I should have known better, being and engineer and always having to cram mult-dimensional data onto 2 & 3-D charts.


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[Message Edited]
Reply #15 Top
That is a Hypercube? So its a cube squared? I think that is cool. so how do you make such an opject in a 3 dimentional world?



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Reply #16 Top
Don't you have to ask for permission to use that animation? I was actually gonna use it myself but I didn't wanna play phlagerism. I've been interested in higher dimensions for years. The hypercube isn't a Tesseract by the way a tesseract is an unfolded hypercube (like the Net is an unfolded cube). Remember that the hypercube only looks like a cube within a cube from one four dimensional angle. Rotate around the hypercube 3 dimensionally and the cube will always have another smaller cube inside it connected to the vercities. Rotating 4 dimensionally is different. when you do so, you'll notice that the interior of the hypercube becomes the exterior. that's the 4th direction by the way

Up/down 1D
left/right 2D
forward/backward 3D
upsilon/delta 4D

In the 4th dimension, there is no exterior or interior. If you are contained inside a hypercube and you try and go out one side of the hypercube, you'll appear at the other side (the train station in the 3rd Matrix installation is a 4 dimensional realm, When neo exist one side, he enters at the other in essence, there is no such thing as Entrance or Exit in the 4th dimension.) I am digressing here now, sorry.

Anyways, visualising a hypercube in our 3rd dimension is practically impossible (a 2D person [[eg a shadow]] cannot see a cube, only one side) so we can only perceive 'one' side of the hypercube (the cube within a cube perspective) the other perspectives are fortified angles, they are 'slices' of a 4D cube.

If you're going to try and design it, don't bother think about how it will look, because it will only be a wallpaper right? which means its only appropriate you worry about making the cube-within-a-cube look cool since you can only really 'see' a 4D cube when it's in motion, preferably 4D motion (upsilon and delta).

If anyone's interested in the 4th dimension such as I am, and you wish to try and understand/visualise 4D space, try and put it into perspective of a 2D person transitioning into the 3rd dimension, he would grow proportion.

Edwin Abbott wrote the book Flatland, describing how a 2D person saw a sphere enter his world (obviously it entered in slices since the 3rd dimensional aspect of the sphere is cross-sectioned through the surface of Flatland)

http://roark.ry4an.org/flatland/

and here's a fictional interview conducted by a human, with a hyperbeing (4 Dimensional person)

http://web.mit.edu/maiki/www/stories/hexa.html

Thanks.
Reply #17 Top
Oh and here's what happens when a hypercube moves 'through' our 3 dimensional world. (imagine a sphere plunging through flatland, the flatlanders would only see cross-sections of the sphere, meaning they would only see a circle suddenly appear growing larger until it dissappears)

http://cips02.physik.uni-bonn.de/ScienceSite/hypercubus/animator/main.html
Reply #18 Top
gizzimo is Channeling Carl Sagan again.
Reply #19 Top
(imagine a sphere plunging through flatland, the flatlanders would only see cross-sections of the sphere, meaning they would only see a circle suddenly appear growing larger until it dissappears)


Ooohh... be careful!! It would only look circular from the 3rd dimension (which flatlanders cannot move into)...

The following is from "Of the Nature of Flatland - Edwin A. Abbott (1838-1926)"

"Place a penny on the middle of one of your tables in Space
and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower
your eye (thus bringing yourself more and more into the condition of
the inhabitants of Flatland), and you will find the penny becoming
more and more oval to your view, and at last when you have placed
your eye exactly on the edge of the table (so that you are,
as it were, actually a Flatlander) the penny will then have ceased
to appear oval at all, and will have become, so far as you can see,
a straight line."




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Reply #20 Top
Hang on...the flat landers would see it as a line from one side, but if they looked around it (or had "stereo scopic vision", they'd see it as rounded. Just as we see a sphere as a "sphere" even though when projected into 2d from one point of view it would appear as a flat circle. So, if we look as a sphere with just one eye and from one point in space then it looks like a circle, but we see it from 2 points at the same time with paralax, and can move to look around it too, so we perceive it as a 3d solid.

Thus, the flat liners would see a sphere passing through their plan as a curved "surface" getting bigger and then smaller again....but it wouldn't appear as a line if the could percieve "depth" from them to the "surface" as we do.

....I think
Reply #21 Top
...I suspect that Edwin A. Abbott when staring at his coin on a table was doing so with just one eye and squinting
Reply #22 Top
WOW, this stuff is cool to me!



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Reply #23 Top
Yeah it is very cool. That's why I've been fascinated by it for years. Check it out though, (I know it sounds pathetic and weird,) I can understand and visualise the 4th dimension so well that I actually feel confined by the 3 dimensions I exist in now. Whew.

Stereo-scopic (or binocular) vision does indeed serve the purpose of visual depth. However there is more to it than that.

Binocular vision is a representational dimension. We have representational dimensions (colour, time, vision etc) and physical dimensions (Length, Height, Depth, katath)

Physical dimensions are dimensiones of our universe indicated by movement, and proportion (each of those words have a slightly altered definition in other dimensional worlds).

Representational dimensions is what allows us to indicate dimensions by vision (and in some cases, sound, but that is easily betrayed because when you go to the cinema, you're already hearing 4 Dimensional sound). Colour and Stereo vision are both representational dimensions.

Colour was longly labelled as a dimension, such as how time was labelled a dimension. these are not spatial dimensions though, they cannot allow organisms to exist by themselves.

Stereoscopic vision is basically where two eyes are both facing the same direction, being 2 1/2 inches away from each other. without stereo vision, you can still see depth, but it is only fixated. the product of stereoscopic vision is "Emphasis" (or Focal Point). you can never tell the effects of stereo vision because it is always working in the background. Hold a penny infront of your vision and focus on it. Here, stereo vision isn't distinguishable, but if you notice in the background of that image, (say for instance you're doing this experiment at your pc right now) your monitor has split into two separate unfocused images. simalarly when you focus on your monitor, the penny will follow the same result.

It is representational dimensions that allow us to tell whether a shape has depth, without it, a sphere may aswell be a circle.

Here's something intersting that whoever may wish to design the wallpaper may want to know, in our 3 dimensional world, there are 56 million colours. there are no more colours than that. In Flatland, only primary colours exist. This is because depth adds in the extra millions of colours that can be filtered through light. Imagine that you are in a hall-like room with various shapes scattered throughout. Also imagine that the only source of light in the room is coming from you (so you're... the light, the sun as it where) you'll notice that all the shapes that have sides facing you, are in primary colour (yellow fo instance) and the sides of the same shapes that are 'not' facing you are in...i don't know..cream. sorry i'm not good with colour, but what i'm trying to say is that the sides not facing you will never emit a primary colour (when the source of the light is coming from your direction).

So in our dimension there are 56 million colours, representing depth. A sphere will obviously utilise many colours (shadings of it's colour I mean). Without representational dimensions, we wouldn't be able to tell it's a sphere unless we use physical dimensions to 'feel' around the shape (which is what A. Square did in the book Flatland).

It's interesting to know that in the 4th dimension, the limit of colours will extend from 56 million, to 224 million colours. that's right, new colours, or..shadings should I say.

It's sometimes quite difficult to explain to someone about the 4th dimension..especially when they're opinionated. Man it turns into an argument everytime I try and do so. But sometimes I can't win, mainly because i'm useless with words and...evidentially, the 4th dimension remains to be a theory, even though it is mathemathically proven. I mean I haven't been there have I? so how the *@%# am I supposed to know?
For instance, I was *trying* to explain to a friend of mine what it would be like in Flatland. Remember that in Flatland, depth isn't removed (as most people think) Height is removed. And he argued that you could not live in a world without height, you couldn't even exist. Well you could, but you'd only have one layer of height. Remember that to have upward depth is simply to have more than ONE layer. one layer of height isn't really height at all. Dimensions have to have a measurement so if you live in Flatland, your will have the same upward depth as your world, and your fellow inhabitants. Meaning that height is indistinguishable. He then argued that Flatland MUST have one some small measurement of a 3rd dimension - no, one slice of a dimension isn't a dimension at all. if you put it like that, then we also have one slice of the 4th dimension. we have one section of 'Upsilon' - but that doesn't mean we live in the 4th dimension, it means that the 3rd dimension is 'contained' in the 4th dimension, just as Flatland is 'contained' in the 3rd dimension.
So there you go ADAM PRESCOTT!

...

Sorry for making this..so long. I'd really appreciate if one of the talented designers on wincustomize rendered a really cool hypercube wallpaper. there isn't really a wallpaper image out there on google. Please. I'd deeply appreciate it and would offer anything in return.

Thanks!
Reply #24 Top
#23 by gizzimo - 4/2/2004 4:10:15 PM Yeah it is very cool. That's why I've been fascinated by it for years. Check it out though, (I know it sounds pathetic and weird,) I can understand and visualise the 4th dimension so well that I actually feel confined by the 3 dimensions I exist in now. Whew.




I don't know about that one buddy!
Reply #25 Top
Oh - My - God! looka this.

Adam says:
and i still disagree with you lol
/\/\att: The 4th Dimensi۞n says:
really?
Adam says:
yup
/\/\att: The 4th Dimensi۞n says:
not as intelligent then.. Cos the people who argued that you couldn’t live without height understood what I meant, and now agree with me.
Adam says:
so you're basically sayin that im less intelligent than you for not fully agreeing with your side of the argument?
Adam says:
even though i've said to you that i know what you mean?
/\/\att: The 4th Dimensi۞n says:
no.. i'm saying that you may not have the correct height of intelligence to acknowledge that height is only a dimension when there are two or more components put ontop of each other. One slice of height is a layer that EVERY dimension has. cos one slice can be built sideways, forwards, whichever.
/\/\att: The 4th Dimensi۞n says:
you can't seem to see it. which just means that you do not have as good imagination and interlect.
/\/\att: The 4th Dimensi۞n says:
it's not an insult.
Adam says:
well thanks
/\/\att: The 4th Dimensi۞n says:
changing your opinion is like changing...you - i'd never do the sort of thing! i'd only change your opinion with a fact, and if you do not agree, then thats as far as i will go. i refuse to MAKE someone agree with me
/\/\att: The 4th Dimensi۞n says:
by force.
/\/\att: The 4th Dimensi۞n says:
thats not right
Adam says:
just then you've called me unimaginatively stupid.
/\/\att: The 4th Dimensi۞n says:
no, stupid is a negative definition. Stupid is below the average threshold, i said that you do not have the equivelant imagintion and interlect as me on that particular topic. this is not malice. I could by implying that i have 5+ intelligence, and you have lower (eg 3+ intelligence) in which case stupid would be a negative degree (-1 or -50) you being lower than me is not you being lower than the
/\/\att: The 4th Dimensi۞n says:
threshold. hence, you are not stupid.
/\/\att: The 4th Dimensi۞n says:
this is an allegation. nothing more.
Adam says:
but saying you have, on a scale of some sort, an intellect of +5 and i have an intellect of less than +5, by resetting your intelligence to 0, you're saying that i don't meet up to the standards, which makes me stupid compared to you
Adam says:
stupidity is relative
/\/\att: The 4th Dimensi۞n says:
no. that example was an individual analogy. the word standard cannot be used in an individual illustration. no where did i say that you are stupid, meaning that you are either making the matter worse than it actually is, or misinterpreting what i meant (which isn't my behalf of the problem). the 4th dimension is a topic that requires an open-mind, high understanding and imagination.
/\/\att: The 4th Dimensi۞n says:
You cannot put that comparison at a standard level, or a reset 0 mark, because a standard level would be something that everyone is capable of. You must research into this, and acquire the knowledge at your own approval. I said you are not as intellect (‘as me’ – part of sentence removed for obvious English emphasis) “me” is individual,
/\/\att: The 4th Dimensi۞n says:
I am NOT standard, no one is. I am not calling you stupid nor am I implying it. You are simply at a lower degree of intelligence than me on THAT specific topic. Like I said, I’ve acquired the knowledge on that and researched for years, you haven’t. And the people that can/have understand/understood me are those who are willing to
/\/\att: The 4th Dimensi۞n says:
blindly acknowledge this fact based on the 2nd hand information I have conveyed to them. You do not wish to accept my information because you, just as I, are also an individual.
Adam says:
not once have i said that i do not wish to accept your information
Adam says:
and i thought the word open-minded would come up somewhere
Adam says:
you seem to think im a close-minded freak
Adam says:
or somethin im sure of it
/\/\att: The 4th Dimensi۞n says:
not close-minded, just narrow-minded.
Adam says:
no-one said i didnt WANT to accept your information as factual evidence
Adam says:
the meaning is practically the same
/\/\att: The 4th Dimensi۞n says:
no it's not. close-minded is where you do not accept anyone's opinion. narrow-minded means you have trouble accepting someone's opinion.
Adam says:
the opposite of close-minded is open-minded, opposite of narrow-minded is broad-minded the meaning's have become crossed
Adam says:
thats besides the point
Adam says:
im not being either narrow-minded OR close-minded
/\/\att: The 4th Dimensi۞n says:
you say that you accept the evidence - why?
Adam says:
no
Adam says:
i dont accept the evidence
Adam says:
i can see what you're saying
Adam says:
and i understand it
Adam says:
but i dont agree with it
Adam says:
which is not to say
Adam says:
in any way
/\/\att: The 4th Dimensi۞n says:
how is that different to what you agree with?
Adam says:
that i dont want to accept it
/\/\att: The 4th Dimensi۞n says:
Tell me why you don't agree with it. Try and use actual evidence to back up your side, as i have, so that this can become a test of justice. If you don't have any evidence, and you just don't..feel its correct what i have said, then this will prove that you are narrow-minded. i honestly don't believe that you accept what i say if you do not have any information regarding your side of the argument.
Adam says:
i have all of the maths ive been taught to use as evidence
Adam says:
flatland, does it have a height?
/\/\att: The 4th Dimensi۞n says:
by all means illustrate them to me.
It does not have height, correct. note that height is upward depth, depth (from the dictionary i have infront of me) The extent, measurement, or dimension that has more than one layer distant from it’s origin.
Adam says:
distant from its origin
Adam says:
which is positive or negative
Adam says:
in the physical world
Adam says:
there is no such thing as a negative measurement
Adam says:
height = depth
Adam says:
there's no difference
/\/\att: The 4th Dimensi۞n says:
there is no measurement difference. but they are perpendicular.
Adam says:
and what exactly do you mean by perpendicular
Adam says:
you're saying that height is perpendicular to depth?
/\/\att: The 4th Dimensi۞n says:
perpendicular ... That means that any of the directions is its own and not combined of any of the other directions
Adam says:
|
|
|-
Adam says:
those two lines are perpendicular
/\/\att: The 4th Dimensi۞n says:
Yes.
Adam says:
you cant have height and depth being perpendicular
Adam says:
when they're the same axis
Adam says:
Z
/\/\att: The 4th Dimensi۞n says:
Of course you can. upwards is not the same as sidewards. You can walk forward and not utilise the other 2 dimensions (left/right/updown)
Adam says:
in which case you'd be one dimensional, in your case at least.
Adam says:
does flatland have a height/depth?
Adam says:
yes or no
/\/\att: The 4th Dimensi۞n says:
flatland has length (going left or right) and also has depth (going forward or backward) they cannot rise up or fall down from the surface they are on.

See what I mean?! Can someone please help me, since i am bad with words, try and explain that you do not need height to exist. Those of you who know what I mean, help me please.