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How To See In Four Dimensions
An anonymous reader writes "Think it's impossible to see four-dimensional objects? These videos will show you otherwise. Some mathematicians work with four-dimensional objects all the time, and they've developed some clever tricks to get a feeling for what they're like. The techniques begin by imagining how two-dimensional creatures, like those in Edwin Abbot's 'Flatland,' could get a feeling for three-dimensional objects. When those techniques are transferred up a dimension, the results are gorgeous."
AnaKata
If you can read this... 01110101 01110010 00100000 01100001 00100000 01100111 01100101 01100101 01101011
I'm looking at my monitor in three dimensions ... wait one second ... okay, I just saw it in four :)
If you can read this... 01110101 01110010 00100000 01100001 00100000 01100111 01100101 01100101 01101011
Take LSD and sure you'll see 4th dimension.
Why is the story tagged scientology?
then set N = 4....
Sorry it's on my screen, so it's a 2 dimensional representation of a 4 dimensional idea in 3 dimensional space.
Sorry, teleporters just kill you and then make a copy. A perfect, soul-less copy.
I guess that's already way past my abilities.
http://shambala.net/3d/tess3d1.gif
Learned to do this on Tralfamadore.
Just imagine how incredible the true nature of the universe must be if current theories hold true that 10, 11, or even possibly 26 dimensions exist in our universe.
To think about it is mind bending, awe-inspiring, and dream provoking.
Just go to any Burning Man concert and eat the multi colored Brownies.
Does anyone remember in how a good way Carl Sagan explained the problem if there are more or less than 3 dimensions exist?
I remember he was explaining the imaginary 2d creatures not being able to see 3d creatures and so on. It was on a TV documentary. Sorry if I remember it all wrong. I was like 13 ;)
It must be an episode of "Cosmos" http://www.imdb.com/name/nm0755981/filmoseries#tt0081846
A 4D object is mathematically projected to a 3D representation, that is then projected into a 2D representation for display on the monitor, that is then transformed by my brain back into a 3D representation, and then further needs to be transformed into a 4D object... /looks for his linear algebra textbook //begins drinking
I played around with this applet a few months ago. After some practice, getting out & hitting the ball becomes easy. Getting back in is only slightly harder & I still can't hit the point reliably.
Awesome. However, mathematicians and physicist usually don't try to "see" or "get a feeling" of higher (or infinite) dimensional objects.
They familiarize themselves with mathematic properties of two and three-dimensional objects and space and what they mean, and then just use these properties in higher dimensional spaces.
Trying to see these spaces or getting a feeling on how these objects would look like most likely confuses for calculations (our brain wasn't really made for this).
Nice and interesting videos though!
NB: The message above might reflect my opinion right now, but not necessarily tomorrow or next year.
Four? Trivial! I can visualize 11 dimensions...but 8 of them are very very small.
6 dimensions more than in TFA:
http://tenthdimension.com/medialinks.php
Always run = ON
Buddhabrot in 4D (in 3D, in 2D). The Mandelbrot fractal never looked so good.
Murphey's fighting Occam, and we're in the stands.
Shapes with gas. I wonder what he ate to inspire that?
Table-ized A.I.
Perhaps obscure, but perhaps also obligatory: what about using the Resonator to see these dimensions? Humans are such easy prey...
Here is a one dimensional projection of a 5 billion dimensional sphere: _
That completely depends on the mathematicians, and the kind of mathematics they do. For proofs that rely only on calculations, you do not need even to understand the low dimension case, just do the computations right.
But proofs with computations are rarely elegant. Some mathematicians prefer a more geometric approach, and for that, they need to see, un to a certain level, the objects in higher dimensions.
Furthermore, the 2D or 3D spaces we have direct access to are really limited. There are lots of phenomenas that only happen starting with dimension 4 or 5. For example, think of this 2D property: "two lines perpendicular to a common third line are parallel"; if you try to take it as is in higher dimensions, you get something false; fortunately, you can think in 3D and see that it is false. There are similar examples in higher dimensions. Curvature, for example: curvature of 2D surfaces in 3D spaces is misleadingly simple, compared to curvature of higher dimensional spaces.
Sometimes, there just is not space enough to build the objects you need in 3D space. For example, if you want to study circles drawn on a sphere, the object you need to make the properties apparent is a 3D hyperboloid in a 4D space. If you settle for a 2D hyperboloid in a 3D space, you end up studying pairs of points on a circle, which is rather boring.
Take, for example, a hypercube. Imagine a regular 3D cube, hollow, but the outside surfaces are one color and the inside surfaces are another. The fourth dimension is the spectrum of colors in between. If you were to rotate the hypercube in four dimensions, any or all of the three physical dimensions could expand or contract (so the cube could grow or shrink or change into a rectangular block) as the fourth dimension rotated into the other three, while at the same time the inside and outside colors would also change (with a larger or smaller spectral width) as the three physical dimensions rotated into the fourth. At the "reddest" end of the spectrum is the moment of the big bang.
Definitely enjoyable stuff. Of course, you could just play Portal. Oh, sorry, that's just an ordinary 3D space which happens to be multiply disconnected and topologically unsettling. For more (Euclidian!) 4D visualization tools, here are a couple nice (but old) clips of rotating cubes and tesseracts through higher dimensions. For example, it gives you the (x,y,z) view of a cube then a simultaneous projection of that object in the (w,x) plane where w is a 4th orthogonal direction. It then proceeds to rotate the (w,x) projection in a circle to see what the 3D "shadow" in (x,y,z) space is doing. Rather than getting bigger and smaller (simulating perspective) as it moves back and forth in the 4th direction, the faces are color coded (I personally think this makes it easier to visualize). Run the simulation back and forth slowly a couple times and your brain locks in pretty well.
i\hbar\dot{\psi}=\hat{H}\psi
Seeing a forth dimension doesn't have to mean actually seeing it visually or pictorially. Since this is /. how about imagining a multi-dimensional array, with 3 indexes (x, y, & z) and then adding another (4th), Presto.
Another way physical space could be defined is by relationships.
When playing blind chess I don't actually see a board in my head, I just remember how all the pieces relate to each other.
Pff. Real mathematicians just picture N dimensions, then set N = 4.
Slashdot: news for Apple. Stuff that Apple.
Is it just me, or are there more people that take issue with the way these new popups appear as overlays within the page? I usually ctrl-click on a link to see the target (image, flash) in a new page, and return to the original page when I want to.
This is for me a reason to start using greasemonkey. Anyone knows if there is a script or other plugin for FF that kills these misfeatures?
To begin, consider that a 2d picture can either be a picture (things can fall), or a map (things don't fall). Since the corresponding 3d thing is a picture/map of four dimensions, we can build objects like houses, furniture, etc from plan and views.
Not all seems to be aimple. A knife cuts: literally, it makes a surface by motion, and is therefore tipped by a space of N-2 dimensions. Rivers can be either "latrous" (1d) or "hedrous" (2d). A fault lake is 2d (since faults are a break of surface).
Holes come in two types, although these are topologically the same. One can have a "bridge" or "tunnel" kind of hole: in 3d, these are the same, in 4d they are different.
The planet rotates on clifford motion. This makes every point of the 4-sphere go around the centre. One sees this by equality of energy in modes of rotation.
None the same, there can be seasons. If the sun does not follow in the year-circle any of the circles of the earth rotating, then there will be seasons. You don't just have hemispheres in summer vs winter, but season-zones to match the time-zones. That is, for example, Christmas (normally in summer), can fall in early spring, or late winter.
The poles are replaced by circles of extreme climate. One has a "equator circle", and a "polar" circle. At the tropics (a singular torus-shape thing), the sun becomes to the zenith once a year. At the artic torus, the sun hugs the horizon for the equate of the shortest day.
Because the sun is relatively still in the sky, there is no variation in the number of hours. What makes the seasons is that the the sun is lower in the horizon, even at midday.
See, eg my site http://www.geocities.com/os2fan2/gloss/index.html
OS/2 - because choice is a terrible thing to waste.
Three dimensions are not a barrier but a consequence of measurement. This is just silly.
For the same reasons you can't visualize a 3D object on a 1D space you can't visualize a 4D object on a 2D space.
You cannot go up 2 dimensions.
Just as we can visualize a 3D object on a 2D space we can visualize a 4D object on a 3D space.
Thus we need something like this:
http://dogfeathers.com/java/hyprcube.html
*Click the Stereo button 2 times to switch it to cross-eyed view for no glasses. Simply cross your eyes to bring both shapes together in the center and it should become clear.
I can imagine a dimension not only of sight and sound but of mind.
The 2nd explanation for projection of 3D objects onto a plane so as to allow the 2d lizards to perceive the objects is simply ridiculous as it requires them to have an external view point defeating the purpose altogether. The 1st example was ok, but its nearly 100 years old, something new/unique/novel would have been more interesting to watch, also the presentation drags on for too long, it should be sped up.
Arash Partow's Philosophy: Be a person who knows what they don't know, and not a person who doesn't know.
>> Sorry it's on my screen, so it's a 2 dimensional
>> representation of a 4 dimensional idea in 3
>> dimensional space
They do not try to display 4D images on a 2D screen. They show how 3D images that you can see in 3D space are related to a 4D object.
Then you should have no trouble creating a 3D image from a 2D screen (http://en.wikipedia.org/wiki/Engineering_drawing).
Three dimensions ought be enough for anybody!
Of course, we can't really see in 3 dimensions, otherwise, we'd be able to see through stuff. The image projected onto our eyes is a 2D image, and we have 2 eyes, so it's (x*y)+(x*y), not (x*y*z). The third dimension is a cheat and is represented as 'stuff getting smaller'.
If we really could see in 3D, we can use the 'getting smaller' trick to visualize 4 dimensions much more easily.
Anyone know of some images or videos on the net using reverse perspective, where things behind get bigger instead of smaller?
Why OpalCalc is the best Windows calc
I got a screen saver that does this.
But my existence is in two dimensions you inclod sensitive !
But I can guess how it works. A sphere passing through a plane would look at first like a dot, then a gradually wider line, then a dot. I remember flatland saying something about brightness at ends of the line.
So, a hyperball passing through a 3-space would look like a dot, gradually expanding to a sphere, and gradually shrinking to a dot.
These 2D videos show 2D diagrams of what a 4D projection into 3D would look like if it were flat. Entirely unsatisfying.
Want a 4D-in-3D demo? Take a small balloon, blow it up then let it go flat. That's what a 4D sphere projecting into 3D would look like.
You can imagine in 4D fairly easily if you decide to ignore your senses and decide that the smaller faces on the internal cube in a tesseract are indeed the same size (an in fact coincide with) the larger, outer faces, and so the outer pseudo-cubes are in fact cubes with all 90 degree corners. You see perpective with fake apparent angles, you can use the same trick your mind uses to see more.
By the way, we do not see in 3 dimensions. We see in 2.5. We can't see the backs of things. We can feel in 3 dimensions if we can get our hands all the way around it.
We do NOT see in 2 dimensions (as a previous comment stated) unless we have no depth perception. Stereoscopic vision gives us much more than flat projection, and stereointegration in the visual cortex gives us even more. In fact, a one-eyed being with stereointegration need only moves its head around and collect visual images from different angles in order to create a successfully adequate 3D concept.
And ask the previous commenter asked, yes we do have examples of reverse perspective where things behind get bigger. Gravitational lensing of galaxies passing behind smaller, intense gravity fields (theoretically black holes or neutron stars). Can't point to any I've seen on the web offhand, but I've seen them there as well as on some astronomy shows on TV.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
To download any of the videos directly, go here:
http://www.sciencenews.org/pictures/mathtrek/082208/
"Think it's impossible to see four-dimensional objects? These videos will show you otherwise."
No they won't. Submitter needs to learn math.
One of the most common sensations (along with the sense of absolute terror at being ripped into a void in space/time) is the feeling of moving through between more than 3 dimensions of space. In my travels I usually feel like I'm spinning and being folded in about 7 different dimensions before my visions start to settle.
To anyone who decides to take me seriously, make sure you have a sober sitter :)
Nick
So it goes ...
My dungeon master used to bring those 4D tetrahedrons out when he felt especially mean. I still hate him for it.
A physicist, and engineer, and a mathematician are sleeping in a hotel when fires break out in all their rooms. The physicist get up, does some quick calculations, and then gets the exact amount of water required to put the fire out, not a drop wasted. The engineer also does some calculations to work out the amount needed, then proceeds to flood most of the floor, to ensure that there is a sufficient tolerance for error. The mathematician wakes up, and does some extremely complex calculations but does them much quicker than the other two. He then exclaims "I have proven I can put the fire out!" and goes back to bed.
This has nothing to do with string theory, so let's all do a !stringtheory up on the tagline. There is nothing about cosmology in this; it's about methods used for years by mathematicians to visualize 4D abstract objects as they move through 3D space.
It's not even new.
Anybody interested in visualizing hyperspace should learn about Alicia Boole Stott and her amazing story. She was the daughter of George Boole (of boolean algebra fame) who developed a mind-boggling series of paper cutout models of four dimensional objects that won her an honorary math doctorate in 1914. Check out these extensive photos of her work.
Jamie Zawinski's xcreensaver has a hack that does this. It's been in the package since the late 90s, at least. This is news how?
Isn't time the 4th dimension?
"keberT xelA"
Please help, Slashdot seems to be totaly fucked since yesterday. New comments format is not working, I can't change the comments level, dropdown box is gone, just a number is there.
Also, I can't go to my preferences, it all comes up as a big empy box, so no way to change, or even see, anything. I hope somebody is aware of this.
This is on IE7. Also, there will be no way for me to see any replies to this. geez.
Slashdotters still cant see in more than 1.
The link in the ScienceNews page that leads to the actual good stuff is broken; it links to .or, not to .org.
StoneCypher is Full of BS
Actually, we do see in 3D... Sort of. As you note, we have two eyes. This means that we can see in 3D. Consider the following scenario: you have a cylinder. With one eye you can only see 180 degrees. But with two eyes you can see more, depending on how close it is to your eyes.
Additionally, our minds unconsciously do trigonometry using our eyes to calculate the distance to an object...
Your retinas are, even together, a 2 dimensional array. You never "saw" anything but what your brain constructed from 2 dimensional arrays. Turns out your brain is very, very good at visualizing a 3d object based on this input. Would you say you can't visualize an actor's physical body because the screen is 2 dimensional?
Very carefully.
If you click through the sciencenews.org article, you can get to the actual website of the people who made these videos. From there you'll find that these videos are Creative Commons licensed, and available for download as high res MOVs. I tried the torrents, but they all stalled, so I just used wget to grab them from the US mirror.
Give me Classic Slashdot or give me death!
Actually I followed the link hoping for something from Seinfeld...
...not Edwin Abbot.
Slashdot's first reaction to VMware
I bet the server has just gone from a 3-Dimensional object to a 2-Dimensional puddle of ooze. Videos do not fair well on slashdot unless they are from youtube
What really opened up my mind to really thinking about different dimensions and infinity was nitrous oxide, preferably mixed with other substances like marijuana or opiates. The fourth dimension? Many nitrous users report experiencing an infinite number of dimensions, which you then feel as being equivalent to zero dimensional space, or a space that defines itself over and over. It's almost impossible to explain with words, but if you can get to that point, it's quite beautiful and freaky. After my extensive experiences with nitrous, I converted from Christianity (which felt quite childish, at that point) to philosophical Taoism. The first passage in the Tao Te Ching explains what one might experience on nitrous oxide far better than I could possibly:
The Tao that can be told is not the eternal Tao
The name that can be named is not the eternal name
'Nothingness' is the beginning of heaven and earth.
'Oneness' is the mother of everythings.
Ever desireless, one can see the mystery.
Ever desiring, one can see the manifestations.
These two spring from the same source but differ in name; this appears as darkness.
Darkness within darkness.
The gate to all mystery.
Edwin Abbot Abbot wrote Flatland, not Edwin Abbot, who was Edwin Abbot Abbot's father.
objects all the time. Functional analysis, anyone?
Anyone interested in the fourth dimension should definintely check out http://tetraspace.alkaline.org/ It may be kinda old, but it's still sure as hell interesting.
Here I am, excited about seeing something four-dimensional, and when I click the link, I get the message "Error: You are unable to view this section". I guess that settles it.
I started 4-D visualization in 1983 with this book:
http://www.amazon.com/Experiments-Four-Dimensions-David-Heiserman/dp/0830601414
It is kind of basic, so it only gets you through the geometric fundamentals in 500 pages - it is not a "dense" read, I found it a little slow-paced.
We grow up in a 3 dimensional world, or 4 dimensional if you want to count time, but I would say our experience of time is different enough from our experience of the other 3 dimensions not to count. We grok 3 dimensions.
There is a famous logical argument about how vision is not simply a projection of what our eyes see into the brain. The brain has to construct (perhaps computationally?) a virtual world based upon input from the senses. The visual part is done in the visual cortex it seems, one of the largest segments of the brain, just as in whales, the big part of the brain is supposed to be devoted to processing sonar.
Suppose though, that in the future, via some neural interface, a 4 dimensional quality could be projected into the brain. Would it train itself to deal with that? Would it eventually 'grok' it? Or has our capacity been so honed by evolution that that could not happen. We have evolved to detect things in the horizontal plane especially well for example, which is supposed to be why the moon looks bigger when it is close to the horizon. I would say that's a pretty compelling example of the hard-wiring that evolution has done on our perceptions. On the other hand, there's also a lot of compelling evidence for our brain's ability to re-wire itself to adapt to new circumstances. So it would be a kind of tug of war between adaptability and innate hard wiring.
In theory, theory and practice are the same; in practice they're different. (Yogi Berra & A. Einstein)
Got to find a way to duplicate myself several times and then stitch myselves back together in a 4-D arrangement. Then I can truly be a 4th dimensional being.
Tsukasa: All I really want, is to be left alone...
Fry: Wow, you even look beautiful in 2-D!
Colleen: I do? But from your perspective I'm just a line segment.
Fry: A really hot line segment.
It's not even 3D, it's 2D because it's displayed on a monitor which displays things in 2D.
If you want to learn to see in 4d, play with this 4d rubik for a while. Its a great app and it's written in Java so it should run on every OS.
http://www.superliminal.com/cube/cube.htm
There have been techniques around for a long time for visualizing 4-dimensional objects in 3-space, since the 1880's at least. See the wikipedia entry on Schlegel diagrams.
http://en.wikipedia.org/wiki/Schlegel_diagram
Calm down and educate rather than this idiotic fearmongering, please. A small dose of knowledge may just save your life and a large dose will keep your mind at ease. Fear is stupid.
Ahem.
With any mind-altering substance from caffeine to alcohol to marijuana to LSD to DMT to mescaline to crack cocaine to salvia and beyond:
1. Know the source: know the purity of the substance and that it is safe to ingest, inhale, inject, etc.
2. Know the drug: read the common histories and medical/scientific research of these substances. If they are natural substances, pay particular attention to the ways that native peoples used them.
3. Know your setting: Take pains to be free of encumbrances when you will be intoxicated. Make sure you have a plan in place in the event you are in mental or physical distress. Make sure there are at least a few sober people on hand to corroborate the details of your experience later. Make sure you will be in a safe place and will not have to leave that place for the duration.
4. Start with a small dose: it does not make you a pussy to be cautious. Start off slow. You can always take more next time. With certain drugs (I'm looking at you, cocaine, crack, and heroin) if you can get them in their raw forms and try those first you will gain a greater appreciation for them. The profitability of raw opium and raw coca leaves in the black market is not great so in many places your only access to these substances in in highly concentrated form. In this case there is all the more reason for a cautious beginning.
5. Take a break: so you had a fun time with recreational use of a drug. Now go do something else for awhile and later you can always try it again under safe conditions. Using too often and too much are half of the reason for drugs being demonized by society. The other half is the massive profits that can be generated by limiting access to the medicine chest (and then letting some quantities of contraband through in the black market).
"You are unable to view this section" - apparently I really *cant* view in 4 dimensions ...
Way too late in life I realised it would be handy if I could at least start to visualise in higher dimensions, so I knocked up a pair of scripts to explore the sphere packing problem in higher dimensions stochastically, basically by moving as far away as possible from the centres of close-packed n-dimensional spheres.
(While six circles pack tightly in two dimensions, there is some wiggle room even in three where 12 spheres can touch another sphere of equal radius, with a rhombahedral grid being the most symmetric solution though not the only.)
It has long been well known that following the most symmetric grid path to eight dimensions you reach a point where the gaps are big enough to fit an identical second set of 8-spheres, doubling the packing density, but still interesting to follow via numeric data in a terminal window. (In mid 2002 I chose to run it remotely on hosted Linux rather than push the then boundaries of OS X.)
The n-dimensional sphere packing problem has long been interesting to communications theory, error detection and correction.
-- Our systemic servants do not good masters make.
Here's a simple visualization of a 7 dimensional space: a movie!
Dimensions List:
x \
y +-- the obvious 3 dimensions
z /
w - time
r \
g +-- each point is encoded as a 8-bit RGB value
b /
usually movies dont change RGB values that often though, but its still trivial.
Isn't this way to old, even for /. standards?
I remember the first SuSE with a GUI I installed (can't remember the version) back in 98, came with a screensaver of a 4D cube...or more precisely, the 2D shadow of a 4D cube...just like the article says.
Slashdot. Unreadable news to annoy nerds. - wonkey_monkey
Isn't color a dimension? don't we actually see 6 dimensions with ?
There is no way to add dimensions.
Here is why, on a strictly logical reference.
What is dimension or distance? The distance separing things. Since we know that distances ask sometime to be ran, time and distances are completely impossible to separate. Therefore, there is only one dimension, called time-distance or distance-time. Nevertheless, and to be able to create or perceive objects, that dimension is considered as L=l=H=Time.
The dissociative, hallucinogenic, and other interesting effects of Salvia d. are very useful in their own right, in that they bring your mind quickly to a "selfless" state (which otherwise may take years of meditation practice) but the experience is extremely disconcerting, to say the least.
That initial bit where you feel like you're merging with your surroundings as they spiral into the vortical carnivorous plant of eternity can be a little frightening.
The "old hag" part of the experience, where you sense the presence of one or more dark figures just over your left shoulder is also rather eerie. I console myself with the thought that it's merely the watchful "familiars" of the plant keeping their vigil, and no doubt an archetypal reflection of some deeper element of the psyche.
Nice thing is, if you get weirded out at this point you can actually shake off the effects of the salvia, go have a piece of fruit, and reassert your conventional existence. Try that with LSD!
The part where you forget completely who you are, where you are, and that you have a body is just dandy, maybe the best part. That's when the really interesting things can happen, such as deep insights and inter-dimensional adventures. As often occurs with DMT people can have some pretty radical "experiences." My sense of this phase is that the brain is just doing its best to derive a narrative, context, and meaning from a completely dissociative state, and much of what people describe as being their "experience" at the time is actually formulated retrospectively, taking the form of sensory associations.
That final part where you remember who you are can be rather sobering after you've been the entire universe - or a shag carpet - for a few minutes. Little by little you remember you're Joe Smith from Topeka and you're in your house, and you have bills to pay and a job to work and a wife who expects you to pick up eggs... it can be a minor letdown.
But then the real fun begins. After all that jarring existential crisis is over you're left with a feeling of greater possibility and a sense of well-being. This general feeling of well-being can last for a day or two, or even longer.
Although the smoked enhanced leaf is fabulous for all the cool things it does - as recounted above - rebooting your brain is not always the most desirable or enjoyable way to promote a general sense of well-being. Fortunately the concentrated extract of Salvia d. is much milder in its effects and acts simply as a mood enhancer, no merging with the infinite required. It can be taken daily in tiny doses as an anti-depressant and it seems to have no undesirable side-effects whatsoever. The only downside is that keeping the alcohol-based extract in your mouth tends to hurt after a few minutes, and Salvia is rather bitter and some find the taste unpleasant.
I encourage - no urge - all SlashDotters interested in self-nature to order some Salvia and give it a try today!
-- thinkyhead software and media
...but Burning Man never showed up to play. What a gyp!
-- thinkyhead software and media
look at a clock- that displays all four dimensions....
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