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How to Depict a Four-Dimensional Object

The universe occupied by humans is defined by three spatial dimensions. As a result, it is impossible to experience a four-dimensional object directly. However, it is possible to represent a four-dimensional object with three-dimensional sculpture in the same way that it is possible to represent a three-dimensional landscape with two-dimensional painting. By meditating on the manner in which a painting represents a three-dimensional object, you can infer how a sculpture could serve as a representation of a four-dimensional object.

Things You'll Need

  • Flashlight
  • Small, irregularly shaped object (wristwatch, scissors, or fork)
  • Blank piece of paper
  • Dark room
  • Three dimensional medium of your choice (clay, metal, LEGO bricks)
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Instructions

    • 1

      Take your flashlight, small object and blank piece of paper into a darkened room. Hold the object between the flashlight and paper. With the flashlight on, rotate the object. Notice how the image that forms on the paper represents an outline of the object. Spend a length of time you long feel appropriate meditating on how the projection of the object produces a representation of the object by "flattening" or "collapsing" one of its dimensions onto the two-dimensional plane of the paper.

    • 2

      Begin rotating the object as you shine the flashlight on it. Notice how the two-dimensional projection of the object's shape changes as the object is rotated. Consider what it would be like to try to guess the shape of the object having only seen two-dimensional projections of it from a variety of angles. Or, if possible, have a friend rotate a mystery object in the flashlight beam while you try to guess the three-dimensional shape of the mystery object from the different two-dimensional projections it produces.

    • 3

      Meditate on how a three-dimensional projection could serve as a representation for one perspective of a four-dimensional object in the same way that a two-dimensional projection can serve as a representation for one perspective of a three-dimensional object. Continually remind yourself that the true shape of the three-dimensional object could only be inferred from viewing multiple two-dimensional projections from different perspectives. Thus, the "true shape" of a four-dimensional object would require multiple three-dimensional projections from different perspectives to represent it.

    • 4

      Once you feel mentally prepared, use a three-dimensional medium of your choice to construct a series of three-dimensional sculptures. Have each sculpture represent a three-dimensional projection of a single-four dimensional object from a particular perspective. These sculptures, taken collectively, will depict that four-dimensional object.

Sculpture

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