1 the magnitude of something in a particular direction (especially length or width or height)
2 a construct whereby objects or individuals can be distinguished; "self-confidence is not an endearing property" [syn: property, attribute]
3 one of three cartesian coordinates that determine a position in space
4 magnitude or extent; "a building of vast proportions" [syn: proportion]
1 indicate the dimensions on; "These techniques permit us to dimension the human heart"
2 shape or form to required dimensions
- A single aspect of a given thing.
- A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.
- A construct whereby objects or individuals can be distinguished.
- Any of the independent coordinates used to specify uniquely the location of a point in a space.
- The number of elements of any basis of a vector space.
- One of the physical
property regarded as a
fundamental measure of a physical quantity,
such as mass, length and time.
- The dimensions of velocity are length divided by time.
- Any of the independent ranges of indices in a multidimensional array.
- An alternative universe or plane of existence.
- correlation dimension
- dimensional analysis
- exterior dimension
- fourth dimension
- fractal dimension
- Hamel dimension
- Hausdorff dimension
- information dimension
- isoperimetric dimension
- Kaplan-Yorke dimension
- Krull dimension
- Lebesgue covering dimension
- Lyapunov dimension
- pointwise dimension
- poset dimension
- third dimension
measure of spatial extent
construct whereby objects or individuals can be distinguished
- Swedish: dimension
in science fiction
to mark, cut or shape something to specified dimensions
- SAMPA: /di.mA~.sjO~/
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.)
TimeTime 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 dimensionsTheories 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 theoremIn 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 quantitiesIn 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 fictionScience 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."
- 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:
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:
- 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.
dimension in Catalan: Dimensió
dimension in Danish: Dimension
dimension in German: Dimension (Mathematik)
dimension in Estonian: Mõõde
dimension in Spanish: Dimensión
dimension in Esperanto: Dimensio
dimension in Persian: بعد
dimension in French: Dimension
dimension in Galician: Dimensión
dimension in Korean: 차원
dimension in Ido: Dimensiono
dimension in Indonesian: Dimensi
dimension in Italian: Dimensione
dimension in Hebrew: ממד (מתמטיקה)
dimension in Latvian: Dimensija
dimension in Hungarian: Dimenzió
dimension in Marathi: मिती
dimension in Dutch: Dimensie
dimension in Japanese: 次元
dimension in Norwegian: Dimensjon
dimension in Norwegian Nynorsk: Dimensjon
dimension in Polish: Wymiar (matematyka)
dimension in Portuguese: Dimensão (matemática)
dimension in Romanian: Dimensiune
dimension in Russian: Размерность пространства
dimension in Albanian: Përmasa
dimension in Simple English: Dimension
dimension in Slovak: Rozmer
dimension in Slovenian: Razsežnost
dimension in Serbian: Димензија
dimension in Finnish: Ulottuvuus
dimension in Swedish: Dimension
dimension in Thai: มิติ
dimension in Urdu: بُعد (لکیری الجبرا)
dimension in Yiddish: דימענסיע
dimension in Chinese: 維度
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