English

Noun

dimensions

1. Plural of dimension

Verb

dimensions

1. third-person singular of dimension

French

Noun

f|p

1. Plural of dimension

Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative amount. Moving diagonally upward and forward is just as the name of the direction implies; i.e., moving in a linear combination of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See Space and Cartesian coordinate system.)

Time

Time is often referred to as the "fourth dimension". It is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, that movement in time occurs at the fixed rate of one second per second, and that we cannot move freely in time but subjectively move in one direction.

The equations used in physics to model reality do not treat time in the same way that humans perceive it. The equations of classical mechanics are symmetric with respect to time, and equations of quantum mechanics are typically symmetric if both time and other quantities (such as charge and parity) are reversed. In these models, the perception of time flowing in one direction is an artifact of the laws of thermodynamics (we perceive time as flowing in the direction of increasing entropy).

The best-known treatment of time as a dimension is Poincaré and Einstein's special relativity (and extended to general relativity), which treats perceived space and time as components of a four-dimensional manifold, known as spacetime, and in the special, flat case as Minkowski space.

Additional dimensions

Theories such as string theory and M-theory predict that physical space in general has in fact 10 and 11 dimensions, respectively. The extra dimensions are spacelike. We perceive only three spatial dimensions, and no physical experiments have confirmed the reality of additional dimensions. A possible explanation that has been suggested is that space is as it were "curled up" in the extra dimensions on a very small, subatomic scale, possibly at the quark/string level of scale or below.

Penrose's singularity theorem

In his book The Road to Reality: A Complete Guide to the Laws of the Universe, scientist Sir Roger Penrose explained his singularity theorem. It asserts that all theories that attribute more than three spatial dimensions and one temporal dimension to the world of experience are unstable. The instabilities that exist in systems of such extra dimensions would result in their rapid collapse into a singularity. For that reason, Penrose wrote, the unification of gravitation with other forces through extra dimensions cannot occur.

Dimensionful quantities

In the physical sciences and in engineering, the dimension of a physical quantity is the expression of the class of physical unit that such a quantity is measured against. The dimension of speed, for example, is LT−1, that is, length divided by time. The units in which the quantity is expressed, such as ms−1 (meters per second) or mph (miles per hour), has to conform to the dimension.

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."

More dimensions

• Dimension of an algebraic variety
• Lebesgue covering dimension
• Isoperimetric dimension
• Poset dimension
• Metric dimension
• Pointwise dimension
• Lyapunov dimension
• Kaplan-Yorke dimension
• Exterior dimension
• Hurst exponent
• q-dimension; especially:
  • Information dimension (corresponding to q = 1)
  • Correlation dimension (corresponding to q = 2)

See also

By number of dimensions

• Zero dimensions:
  • Point
  • Zero-dimensional space
• One dimension:
  • Line
• Two dimensions:
  • 2D geometric models
  • 2D computer graphics
• Three dimensions
  • 3D computer graphics
  • 3-D films and video
  • Stereoscopy (3-D imaging)
• Four dimensions:
  • Time (4th dimension)
  • Fourth spatial dimension
  • Tesseract (four dimensional shapes)
• Five dimensions:
  • Kaluza-Klein theory
  • Fifth dimension
  • Seventh dimension
• Ten, eleven or twenty-six dimensions:
  • String theory
  • M-theory
  • Calabi-Yau spaces
• Infinitely many dimensions:
  • Hilbert space

Other

• Degrees of freedom
• Dimension (data warehouse) and dimension tables
• Hyperspace (disambiguation page)

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.

References