Dimension
 From left to right, the square has two dimensions, the cube has three and the tesseract has four. In mathematics the dimension of a space is roughly defined as the mimimum number of coordinates needed to specify every point within it[1][2]. Dimensions can be thought of as the axes in a Cartesian coordinate system, which in a three-dimensional system run left-right, up-down and forward-backward. A set of three co-ordinates on these axes, or any other three-dimensional coordinate system, specifies the position of a particular point in space[3]. In the physical world, according to the theory of relativity the fourth dimension is time, which runs before-after. An event’s position in space and time is therefore specified if four co-ordinates are given.
On surfaces such as a plane or the surface of a sphere, a point can be specified using just two numbers and so this space is said to be two-dimensional. Similarly a line is one-dimensional because only one co-ordinate is needed, whereas a point has no dimensions. In mathematics, spaces with more than three dimensions are used to describe other manifolds. In these n-dimensional spaces a point is located by n co-ordinates (x1, x2, … xn). Some theories, such as those used in fractal geometry, make use of non-integer and negative dimensions.
Another meaning of the term "dimension" in physics relates to the nature of a measurable quantity. In general, physical measurements that must be expressed in units of measurement, and quantities obtained by such measurements are dimensionful. An example of a dimension is length, abbreviated L, which is the dimension for measurements expressed in units of length, be they meters, nautical miles, or lightyears. Another example is time, abbreviated T, whether the measurement is expressed in seconds or in hours. Speed, which is the distance (length) travelled in a certain amount of time, is a dimensionful quantity that has the dimension LT −1 (meaning L/T). Acceleration, the change in speed per time unit, has dimension LT −2.
[edit] Science fiction
Science fiction texts often mention the concept of dimension, when really referring to parallel universes, alternate universes, or other planes of existence. This usage is derived from the idea that in order to travel to parallel/alternate universes/planes of existence one must travel in a spatial direction/dimension besides the standard ones. In effect, the other universes/planes are just a small distance away from our own, but the distance is in a fourth (or higher) spatial dimension, not the standard ones.
One of the most heralded science fiction novellas regarding true geometric dimensionality, and often recommended as a starting point for those just starting to investigate such matters, is the 1884 novel Flatland by Edwin A. Abbott. Isaac Asimov, in his foreword to the Signet Classics 1984 edition, described Flatland as "The best introduction one can find into the manner of perceiving dimensions."
[edit] More dimensions
[edit] See also
[edit] By number of dimensions
- Zero dimensions:
- One dimension:
- Two dimensions:
- Three dimensions
- Four dimensions:
- Five dimensions:
- Ten, eleven or twenty-six dimensions:
- Infinitely many dimensions:
[edit] Further reading
- Thomas Banchoff, (1996) Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions, Second Edition, Freeman.
- Clifford A. Pickover, (1999) Surfing through Hyperspace: Understanding Higher Universes in Six Easy Lessons, Oxford University Press.
- Rudy Rucker, (1984) The Fourth Dimension, Houghton-Mifflin.
- Edwin A. Abbott, (1884) Flatland: A Romance of Many Dimensions, Public Domain. Online version with ASCII approximation of illustrations at Project Gutenberg.
[edit] References
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