Slashdot Mirror
See 4-D Space With 3-D Glasses
purpleant writes: "A hyperplane is a 3-dimensional space that slices through the 4-dimensional space, the same way a 2-dimensional plane can slice through our 3-dimensional space. The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope. The
HyperStar applet displays those finite chunks, one shell at a time. The inner shells are complete -- each shell completely encases the previous shell. The outermost shells have holes in them."
4 dimensional space is relevant to slashdot, why?
In my complex analysis class at University, my professor said it was easy to visualize 4 dimensional functions. He proceeded to draw some kind of squiggle on the chalkboard and said, "There, just don't be close minded". We didn't laugh.
It the worlds first java-based kaladioscope!!
Now all I need s a webbrowser at the end of a tube and I can relive my childhood.
In Soviet Russia you dant have to put up with these crappy jokes
I thought the fourth dimension was time.....
Think of the PORN!
"But the cars are all flashing me, bright lights are passing me, I feel life passing me by" - Stiff Little Fingers
... too bad I don't really have a clue what it means. *sigh* I guess this is why I'm not majoring in Math ;-)
As if trying to visualize the 4th dimension wasn't enough to give you a headache it comes with a 'cross-eyed' setting.
"A language that doesn't affect the way you think about programming, is not worth knowing" - Alan Perlis
FE:So, what's the closest you ever came to experiencing the fourth dimension?
Rucker: Well, there was this one time, we'd been partying all night, and I wanted to get a little higher. We were almost out of drugs, but I did have some acid. So I took it, but then I fell asleep. And when I woke up...
FE: Oh, I've been there. That's the fourth dimension?
so it's 5 am monday morning on the east coast and i decide to check out slashdot before going to bed for 4 hours of shuteye before work tomorrow (don't ask, crazy weekend). i am bleary eyed, brain dead, exhausted.
;-P
and i read "The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope."
dudes! my functional iq right now is about 50! if you are going to post these kind of stories on slashdot, could you PLEASE post them around, say 3pm on a thursday? thanks
i should be awake by then, and i promise i will come back and try to wrap my mind around this story at that time... grumble, grumble
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Step 1: Make cool applet with shapes and colors. .....
Step 2: Explain shapes and colors with big words and things nobody knows anything about ie: hyperplanes, polytopes, and the fourth dimension
Step 3:
Step 4: Profit!!
I'm a minister!
These leaks should perhaps be viewed with 3D glasses, but yet more important - in the light of nVidia's financial turmoil in the stock market... ;)
It's one of those OpenGL Windows 95 screensavers! :) Why didn't you just say so?
"Again the inner chunks are finite, and they are distributed in shells around the core polytope."
uhh yeah, but it all depends on the capacitive current getting to the space modulator
come on, lets do a thorough reporting job. You didnt even mention the fucking space modulator.
Looking directly at four-dimensional stereograms can *really* screw up your eyes. Caution or strong hallucinogenics advised.
I am a Karma Library.
It's already been invented. It's quite simple really. To travel forward in the 4th dimension, simply insert your pr0n tape into the device and hit Fast-Forward. To travel backward in the 4th dimension, hit Rewind.
I'm a minister!
If you set the Stereo mode to "Cross-eyed," you can view the picture in 3-D using the Magic Eye technique.
My Blog Sucks.
...now you go and give me a bastard headache looking at 3D images of a 4D environment on a 2D screen. Yowch.
I don't have a pair of 3d glasses, is there any kind of computer screen filter that has the same effect? Or do one's actual eyes need to be cross-eyed?
This sounds alot like Gene Ray, of Time Cube. Creepy, man.
How exactly do you think they are similar?
This isn't new. There have been real applications and Java applets, too that have been able to do this sort of thing. I've got an old app for the classic Mac OS called "HyperSpace" that does exactly this (draw multiple 3D cross-sections of 4-D hypercubes). It's a really, really old app.
Here
Less pretty but more understandable
BTW: things like the famous Stereoscopic Animated Hypercube have been around for quite some while. There even is a game around to be played.
Thanks to slashdot many people can actually find out about it.
the thing about opening our minds is right. :-)
We have always lived in three dimensions, so visualizing 4 dimensions Per Se is almost impossible coz our nuerons have been hardwired for 3 dimensions. So we can observe 4 dimensions in transit. For example if youwere a 2 dimensional being(thats not possible coz 3 is the minumum number of dimensions to sustain life) and a 3D sphere passed through your space, you will see a point, growing into a circle and then again into a point.
So if a 4D object came it would look like a morphing 3D object.
If mankind were able to create and use 4D's travel would be a whole new frontier. Esp since space-time is curved, Just imagine traveling a million miles instantaniosly
Confused! Go through stephen hawkings works! you will be even more so
My Aurora : http://www.youtube.com/watch?v=o91ZsGwJYyg
FB : https://www.facebook.com/TanveersPhotography
I would assume that if multiple dimensions exist, then we actually live in them already, it's just that we only have the ability to percieve the 4 obvious dimensions to us. While the other Nth dimensions are still existing just not eaqsily percieved by us. (AS in that quarks may in fact exist in the "4th dimension" (or properly termed by us as the 5th dimension.... don't start with the classic rock jokes!!) which would easily explain how some of them can exist in 2 physical "3d" locations at once.. existing in the "4d" space there will be multiple intersections from the "3d" space.... espically if the particle was elongated.
Is this a correct assumption?
Do not look at laser with remaining good eye.
If you think about it, it doesn't really make sense to be able to visualize a four-dimensional object using sight. Why? Because sight is a two-dimensional sense that on a daily basis we use to visualize three-dimensional space. Visualize trying to understand a 3D shape looking at a pinhole view of it (1D to 3D). Can't really be done, certainly not without a ton of staring at it.
Seeing as how it's so difficult to jump two dimensions in visualization, how do we do it? We use the only 3D sense that we've got... touch. Since we can "see" all sides of an object at once using touch, then we are truly experiencing that object in 3D.
So create some kind of device that you hold in your hands and moves around to simulate a hypercube. Simple answer :).
Find me in ~/.sig
Somehow my pride of my country (Netherlands) has been deministed :(
We used to argue this in the computer science lab at college. Can the human mind gain visualization skills in four dimensional geometry? We came up with the following interesting answers:
p rod.html">Crystal Eyes</a>. Now there are liquid crystal on silicon solutions that are much cleaner, if not cheaper.
1. It's hard. We never see four diminsions. The brain would keep wanting to make one dimension some known continuim such as time, a color sequence, tone, or intensity. Only after this intermediate step would you get a true four dimensional geometry in your head.
2. You would need to have a true 3D display. Current rendering of three dimensional pictures flattened onto simple two dimensional screens would never work. Imagine using a laser pointer as a point source, and imagine that you had never seen a three dimensional object; now draw a three dimensional picture of a pick-up truck using the laser pointer. At the time, we were trying to get a simple three dimensional output, like <a href="http://www.stereographics.com/frames/frame-
We were students once, and poor.
I'm looking forward to attending your lecture on the topic. Please remember to give enough examples.
After stareing at this for about 30 mins it made me wonder if God is a 4D being..
It's talking about a shape in 4 spatial dimesions, not 3 spacial dimensions and one time dimension. Also, movies aren't 3d - not even those red-cyan ones. If movies were truly 3d, you'
i finde ur ideers intreeging an wants to sib...sebsri...subscrib to ur news leter!
to learn more read some Kaku - one of the foremost scientist on hyperspace....(fixed link from previous post.
Hyperspace
People who have witty things here blow.
Hey, did anyone tell Tom Banchoff@Brown University
about this? He is the master when it comes to
4-d visualization. I still remember the opening
celebration of the Thomas J. Watson Jr. Center
for Information Technology at Brown when he
put on a music/graphics show projected outdoors
onto these huge screens.
http://www.math.brown.edu/~banchoff/
There was something similar done by a guy called Luke Dahl, only it was for audio.
:-)
It was a Markhov chain extrapolation of the 3d sound as perceived by a 3d being and using a series of normalizations and transforms.
It was called Frobenius Norm, and was a composition of how a 4-d sound would sound to a 5-d being, I think. I just remember it being "spiffy" and very addictive!
It was also featured in Woodstockhausen 2000.
It's full of stars!
Beware: In C++, your friends can see your privates!
A 3D sphere intersecting a 2D plane would create a circle, but you could only see the circle from a 3D view ontop of the plane.
If you were on the plain and had no concept of 3D, but still had depth perception, what you would see would be an arc. You could think its a circle, but without going around to the back and making sure the arc follows itself around the entire 360 degrees, you wouldnt know it was complete from just a single viewpoint on the 2D plane.
Morphing Software
Can the human mind gain visualization skills in four dimensional geometry? ... We never see four diminsions. The brain would keep wanting to make one dimension some known continuim such as time, a color sequence, tone, or intensity. Only after this intermediate step would you get a true four dimensional geometry in your head.
Your actually wrong in the second part. While our senses can't pick up more than 3D Sensory input our brain can very well imagine (and sense) more dimenions. It's simply a matter of training.
Indian Yogis would call that 'meditation'.
The stuff those kind of people talk about like "when time becomes irrelevant" and such isn't some mystical BS (at least not with the honorable ones) - it's actually what you expierience when your brain is trained apropriately. Or forced into such condition by (ab)use of drugs.
You can see "everything happen at once" like one would say. It's interesting that people reaching this kind of 'sense' have a syncronized activity of both halfs of the brain.
Normaly we don't have that. But Yogis and people who have trained meditation can actually achieve such 'brainsyncing' at will. (a tranquil enviroment given)
Tibetian meditation 'training' is known to train the same as modern biofeedback 'brainsyncing', often with a nearly identical setup like: "look at those 2 spots and see them as one".
We suffer more in our imagination than in reality. - Seneca
if a 3d sphere in a 2d perception looks like a circle growing and then shrinking over a long period of time, could time itself be just a approxmiation of objects that have more than just 3 diminsions? /andrew
as in, are we just in a single 3d plane and our perception of time is just things moving through it?
I don't know enough about hyperspace to properly explain this, is this what hyperspace is about though?
I have some GPL'ed 3-D Anaglyphic code here if anyone wants to play with this sort of 3-D rendering. Of course, you could also use jad to decompile that applet if you feel randy.
I thought hyperplanes are just 3D slices of data taken from any number of dimensions. So if you have an m x n matrix and want to visualize it, just take 3 of the columns.
... Until someone makes a videogame using these shapes. Maybe something funky like Frequency Cubed, Dance Dance Dance Revolution, or Duke Nukem 4D?
I'm serious though.
[PowerPoint] is a tool for capitalist presentation
High-dimensional (or multivariate) visualization is nothing new in the world of statistics & exploratory data analysis. Check out the freely available XGobi software or the new GGobi package. For a 100% Java version, see Blue Orca.
Read "And He Built a Crooked House". Heinlein did a bang up job of explaining a hypercube there using toothpicks and clay.
Phoenix
Don't be fooled--this is not a kaleidoscope! : )
hell
"..The bounding hyperplanes can be extended infinitely so that they criss-cross through each other, chopping up hyperspace into many 4-dimensional 'chunks.' Again the inner chunks are finite, and they are distributed in shells around the core polytope."
...must the best BOFH "Plausible Excuse" ever!
I can't even take this writeup right after waking up, never mind the article itself... it sounds way too much like the timecube guy for me...
the coolest club on
If you're into this sort of thing you should pick up Hyperspace by Michio Kaku, it's a very interesting book that does a pretty good job of explaining multiple dimensions in a way that most can understand.
How's my typing? Call 1-800-eta-shut
Hey guys! It is really a full-motion magicEye and if you squint your eyes it will come into focus -- A resume of Bernard Shifman, in an apparent attempt to spam the 4th dimension.
From excellent karma to terible karma with a single +5 funny post...
- Start with your typical 3x3 tic-tac-toe, on a piece of paper.
- Now add two more grids. Visualise each grid on top of the one before. It's not difficult to see how this is played. You can get three in a row on a single grid, just like normal. Or you can get three in a row by getting the middle square of each grid (3 in a row, vertically). And so on. This is basically tic-tac-toe in 3D. 3 sets of 3x3 grids. 3x3x3.
- Now, add another two sets of three grids. So now you've got 3x3 3x3 grids (still with me?). You can still win just like in the 3x3x3 version. But you've got another 3x3 ways in which to do it. The tricky part is, to visualise each possible `3 in a row', you've got to mentally `rotate in' any one (and only one) 3x3x3 cubic plane.
Sorry if that's difficult to follow. If you work it through on paper, you'll see what I mean. This is what being bored in math class will lead you to think of, when plain old tic-tac-toe just doesn't seem challenging anymore.- SMJ - (It's not just a name: it's a bad aftertaste.)
The correct definition of a hyperplane is here.
If you all want to understand hyperspace better you shoud pick up a copy of Michio Kaku's 'Hyperspace'. It covers most of the subject matter of flatland, and goes into more depth on the possibilities of higher dimensional space and unified field theory. It's a really interesting read and speaks on a level that most people can understand. I got alot out of it when I first read the book 6 years ago (I was 14 years old). I didn't get all the mathematics then, but the basic concepts were very well illustrated, and it got me started thinking even then.
-dewhite
Hello flonker,
Could you please post your telephone number? My lawyer would like to talk to you. I'm off to the hospital, cu guys.
"It's too bad that stupidity isn't painful." - Anton LaVey
In calculus, a slice of a higher dimensional shape represented in lower dimesional space is called a level curve. For instance, a level curve of a sphere is a circle. So a sphere is the level curve of a 4th dimensional solid.
I didn't see any source code --
If it is available, please say where!
Just thought I'd mention the interest.
this is all well and good..but a question or two. first of all, isn't it generally agreed that time is the forth dimension? please correct me if i'm wrong, here. therefore, the whole thing about watching the sections transform over the fourth dimension like it's some super fancy function is preposterous! how hard is it to see something change over time? my bottom line is this: it's as easily explained from the second to third dimension as it is from the third to fourth or even seventh to eighth. the author is just relating one dimension to the next dimension up the order. no matter what dimension you stand in, there is going to be one more that you are incapable of seeing higher up. if you treat the fourth dimension like it's something that we have as much control over as the first, second, or third then you will find, eventually, that you are mistaken. finally, your analogy to a 2-d being observing a 3-d object brings up an interesting point. we, as humans, have long realized that while we have control over three dimensions we exist, actually, in many (at least 5, i believe), but are held directly captive by the fourth (which would, in turn, be held captive by the 5th, etc). you say that our brains are hardwired to think in 3 dimensions. is it possible to imagine a purely 2-d existence?
Those who can, do. Those who can't, go into business for themselves.
I recently worked on a project (I am not the author) that modeled 4-D environments on the screen. We made a spaceship that had 4-D elements in it where doors would show or hide based on whether or not the correct hyperplane was in view.
There is a demo of the software that runs on windows and the navigation is very easy to figure out.
LOL... Wilhelm
A few people have posted with a comment about how they consider time to be the fourth dimension.
Sure, that's one way to think of it, but I think what this animation is attempting to describe is a fourth spatial dimension. That is, describing a geometry where 4 lines can be perpendicular to eachother, instead of the 3 that we are used to.
Saying the 4th dimension is time is an easy way out.
The damned thing does not work. I just get a blank grey screen no matter which button or slider I press or change.
Any n-1 dimensional plane cutting through an n dimensional space is a hyperplane. So, the correct wording of the story would have been "A hyper plane is a 3-dimensional space that cuts through a 4-dimensional space, just as a 2-dimensional hyperplane cuts through 3-dimensional space."
Posted from the wireless couch.
Haven't gotten to the M-Theory section yet.
(* If 2D lifeforms did exist (Planiverse suggests they would need zipper-like 2D organ structures) it's quite likely they would have some form of 'depth' perception - along a plane, of course. A sphere intersecting with their world could indeed be recognized as a circle, much like our brains can recognize the depth difference between a ball and a flat disc. *)
If a 4th dimensional biological entity intersected our dimension, it would probably look really really funky, like a bunch of morphing blobs. Imagine sitting there in a chair watching Bay Watch, and suddenly in the middle of the room small blobs of flesh appear, grow in size, but change shape in really really odd, unnatural ways, then disappear.
If that wouldn't make your skin crawl off, I don't know what would. It would even be odder than watching obese porn in reverse (not that I recommend it).
Note that there are some UFO reports of odd blobs appearing, morphing funny, and then just dissappearing. Long shot, I know, but you just never know what may have came our way before.
Table-ized A.I.
I COULD see all angles of the scenes at the same time. Of course, time stopped... Sorry.
CAn'T CompreHend SARcaSm?
Actually, a hyperplane is a subspace of a vector space, with the stipulation that all of the vectors in the subspace have one specific dimension in common (i.e. the same for all of them). A 0D point is a hyperplane of a 1D line, a 1D line is a hyperplane of a 2D plane, ...
E
If I'm understanding it right... It seems that while it is modelling 4D space, it's stil only displaying 3D at any given time. The question is, can you extend the mathematics of displaying 3D on a 2D screen, to displaying 4D on a (not yet available) 3D holigraphical projector?
It looked painful when Beavis blew Butthead from 2 dimensions to 3 dimensions on the Celebrity Deathmatch episode...
If the 4-D glasses are packaged with a fire extinguisher or another compressed air tank with a menacing looking hose (e.g. colonoscopy probe) watch out!
Good luck. I've read the book three times and always get hung up on it.