Higher dimensions are dimensions beyond the familiar three spatial dimensions of which we are aware in every day life. Intense speculation, both scientific and fictional, has naturally been directed toward the possibility of a fourth dimension. One way to think of points in four-dimensional space is as ordered sets of four numbers (see quaternion). Clearly, this algebraic representation can be extended to arbitrary many dimensions: n-dimensional space is defined as the set of the set of points (a₁, a₂, ... , a_n) where a₁ to a_n can take any real number value.

 

There has been much conjecture that the universe in which we live contains many more than three spatial dimensions. This speculation began with the Kaluza-Klein theory but is now firmly embedded in modern string theory.

 

References

1. Banchoff, Thomas F. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. New York: W. H. Freeman, 1990.
2. Burger, Dionys. Sphereland: A Fantasy About Curved Spaces and an Expanding Universe. New York: Barnes & Noble, 1983.
3. Dewdney, A. K., The Planiverse: Computer Contact with a Two-dimensional World. New York: Simon & Schuster, 1984.