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How To See In Four Dimensions

Posted by timothy on from the wrinkle-in-time-time dept.

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."

4 of 227 comments (clear)

  1. not by Holi · · Score: 5, Insightful

    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.
  2. Just so we are clear... by Anonymous Coward · · Score: 5, Insightful

    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

    1. Re:Just so we are clear... by Drinking+Bleach · · Score: 5, Insightful

      In a way, it's also projected into a 1-dimensional stream of bits.

  3. Re:Easy to see in four dimensions by MrNaz · · Score: 5, Insightful

    After thinking about this some more, I find that the animations in the article are not at all four dimensional, as the so called "fourth" dimension they are representing exists in the same physical space as the third.

    This breaks the dimensional relationship. Imagine, if you will, a single point with no dimensions. Then extrapolate that into a line to get one dimension, imagine that line them extrapolating perpendicular to the line to form a square, and then imagine that square extruding into a cube. So far, no physical overlap has occurred. The fourth dimention as represented in these videos, does nothing but add more "balls and sticks", which is not adding another dimension, it's simply adding detail to the existing dimension.

    Likewise, those 2D imaginings of a 3D object are not visualizations of a 3D object in 2d, they are the visualization of a changing 2D object, with the simulated third dimension being time.

    In other words, the method that they have used does not actually visualize a fourth dimension in any mathematical or logical sense, they are really just optical illusions. Personally, my method of visualization that I described in my previous post is far superior, and more accurate from a logical and mathematical point of view, as it truly does represent a 1:M maping of every dimensional unit in the (n-1) dimensional space.

    P.S., I've always wanted to start a sentence with "Imagine, if you will...".

    --
    I hate printers.