How To See In Four Dimensions 227
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."
Scientology? (Score:5, Interesting)
Why is the story tagged scientology?
did this years ago... (Score:5, Interesting)
http://shambala.net/3d/tess3d1.gif [shambala.net]
Re:Scientology? (Score:5, Interesting)
I see a flash scientology , rather very big ad at bottom of article and in "videos", there are Google Adsense ads mentioning scientology youtube channel.
It could be related to people who sees those ads (must be scientific terms used triggering them) and think the site is Scientology supported. It could be possible but it could be the adsense only too.
BTW Google Adsense advertising Scientology Youtube channel is not really a good, pretty sight. What next? Doubleclick ads too?
Carl Sagan (Score:4, Interesting)
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 [imdb.com]
Interacting is the easiest way to learn (Score:5, Interesting)
Awesome. (Score:2, Interesting)
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!
Buddhabrot (Score:4, Interesting)
Depends on the mathematicians (Score:2, Interesting)
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.
rotating tesseracts (Score:3, Interesting)
Re:did this years ago... (Score:4, Interesting)
Re:Easy to see in four dimensions (Score:5, Interesting)
I "visualize" four dimensions and more often, when programming and setting up multi-dimensional arrays of more than three dimensions.
All one has to do is acknowledge that adding a dimension simply adds a range of points that map to every single point in the (n-1) dimensional range. So, the easiest way to visualize a four dimensional cube is to simply imagine multiple identical cubes, side by side, for as many as the range has been specified. Five dimensions is a flat square arrangement, six is a cube arranged array of cubes, and so on. This way, an infinite number of dimensions can be visualized. Perhaps the term "mental addressing" is more appropriate a name for this mental method.
The limit is, of course, this only works directly for finite and discrete arrays. I find it can be extrapolated to use non-discrete spectra, but describing the way that works in my head will not be possible using this clumsy tool we call "language".
Re:Just so we are clear... (Score:1, Interesting)
You need another dimension to visualize the 4th. (Score:3, Interesting)
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.
Re:Easy to see in four dimensions (Score:5, Interesting)
Yeah I've had arrays with double digit dimensions.
I think my record is 16 or so.
I dont know why but I work with them incredibly easily.
Without them its like programming with a hand tied behind your back.
Cant visualize them at all, I can work with them though.
Try Salvia (Score:4, Interesting)
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 :)
Re:Just so we are clear... (Score:5, Interesting)
Re:Try Salvia (Score:0, Interesting)
You should not even remotely be recommending this "drug". I take it that you are referring to Salvia Divinorium. It is dangerous, and that is the under-fucking-statement of the millennium.
It was used by the Mayans and plenty of shamans after it. However, they way that they use it is far different and is a guarded secret. Their trips last for days, not minutes.
A lot of people, especially those more connected with nature and "hip" seem to think that anything natural and organic cannot hurt you or be bad for you. This is not like weed, it has serious consequences.
The reason why you need a "sitter" as you call it, is that the vast majority of people completely disconnect with "our" reality and seemingly have no judgment or inhibitions regarding their own physical bodies. It is as if they have no control.
Your biggest risk is actually that of a spiritual nature. I don't mean anything Christian like damnation, or moral, or anything like that. Shamans used this as a method to access the underworld, which is part of their belief systems and where they perform most of their actions and receive their insights.
Personally, I believe this is one of the mythical Mayan plants they used for their rituals. You play with fire you get burned. From what I understand, from direct accounts, is that taking the right amount of this is like literally shifting your consciousness to someplace else in existence. What people have tried to relate about their experiences afterwards often has no frame of reference to our realities at all. I actually do believe this can allow you to temporarily exchange your "point" in existence with that of another. What that implies about your own body here, remains to be debated.
YES THERE ARE ACCOUNTS OF PEOPLE NOT MAKING IT BACK. Some have died, but many others never make it back whole again. Part of their minds, their soul maybe, never reintegrate with our reality here.
I realize that this may be a bit heavy for people here and sound weird, but for FUCK'S SAKE do not take it as lightly as the poster here is portraying it.
If Weed and Shrooms are like a 1-2, and LSD could say be a 10, then this shit is a MILLION. If your dead set on doing it, then at least get informed by somebody else that actually knows about this plant. If you want the real experience with someone that might be able to help you if you get into trouble, then you will need a shaman. Period.
Re:Buddhabrot (Score:4, Interesting)
Re:Easy to see in four dimensions (Score:3, Interesting)
Personally, I visualize the fourth dimension in a figure as a kind of color, and the fifth as a variation (say, blinking) of that color; but I rarely need to go that high. This is weird stuff.