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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."
Here you go. It was Cosmo's take on "flatland":
http://www.youtube.com/watch?v=KIadtFJYWhw
To download any of the videos directly, go here:
http://www.sciencenews.org/pictures/mathtrek/082208/
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.
I find that the animations in the article are not at all four dimensional
Duh. That's because our screens are two dimensional, and you and I are three dimensional. Certainly you can't fault them for this? (Please tell me that I'm somehow misunderstanding this objection..)
In other words, the method that they have used does not actually visualize a fourth dimension in any mathematical or logical sense
That's nonsense. Their videos show the edges of the object (although distorted) as well as the interconnections of each of the vertices. What would qualify to you as a "real" mathematical or logical way of viewing these objects in a 3-D world?
As for your previous post:
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.
Okay, when you get down to it, this is stuff that any programmer knows when working with arrays. (ie- int[][][][][], etc.) Now your task is to *draw* your example for us in 3-D space.
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?
http://bittornado.com/torrents/Dimensions-English.torrent
BitTorrent download for all the (English) movie files on the source website.
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.
Bullshit. Salivia Divinorum is so non-toxic it has no known LD50. All this woo-woo scary crap about souls "not making it back" is about as credible as a summer camp ghost story. As with any hallucinogen, care must be taken to use it in a controlled environment so as to minimize the unpleasantness and potential for accidents (i.e. don't drive, walk tightropes, or handle rattlesnakes while high) but there's no inherent danger to it.
If a job's not worth doing, it's not worth doing right.