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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."
Why is the story tagged scientology?
http://shambala.net/3d/tess3d1.gif
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
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.
Buddhabrot in 4D (in 3D, in 2D). The Mandelbrot fractal never looked so good.
Murphey's fighting Occam, and we're in the stands.
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".
I hate printers.
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.
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.
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
I'd argue that it's encoded onto a 1-dimensional stream of bits. The main difference being that an encoding can be used to reconstruct the original, whereas a projection by definition loses information.