SPACE is the boundless threedimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions , although modern physicists usually consider it, with time , to be part of a boundless fourdimensional continuum known as spacetime . The concept of space is considered to be of fundamental importance to an understanding of the physical universe . However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework . Debates concerning the nature, essence and the mode of existence of
space date back to antiquity; namely, to treatises like the _Timaeus _
of
Plato
In the 19th and 20th centuries mathematicians began to examine
geometries that are nonEuclidean , in which space is conceived as
_curved_, rather than _flat_. According to
Albert Einstein
CONTENTS * 1 Philosophy of space * 1.1 Leibniz and Newton
* 1.2 Kant
* 1.3
NonEuclidean geometry
* 1.4 Gauss and Poincaré
* 1.5
Einstein
* 2 Mathematics * 3
Physics
* 3.1
Classical mechanics
* 3.2 Relativity
* 3.3
Cosmology
* 4 Spatial measurement * 5 Geographical space * 6 In psychology * 7 See also * 8 References * 9 External links PHILOSOPHY OF SPACE LEIBNIZ AND NEWTON In the seventeenth century, the philosophy of space and time emerged
as a central issue in epistemology and metaphysics . At its heart,
Gottfried Leibniz , the German philosophermathematician, and Isaac
Newton , the English physicistmathematician, set out two opposing
theories of what space is. Rather than being an entity that
independently exists over and above other matter, Leibniz held that
space is no more than the collection of spatial relations between
objects in the world: "space is that which results from places taken
together". Unoccupied regions are those that _could_ have objects in
them, and thus spatial relations with other places. For Leibniz, then,
space was an idealised abstraction from the relations between
individual entities or their possible locations and therefore could
not be continuous but must be discrete .
Space
Newton took space to be more than relations between material objects
and based his position on observation and experimentation . For a
relationist there can be no real difference between inertial motion ,
in which the object travels with constant velocity , and noninertial
motion , in which the velocity changes with time, since all spatial
measurements are relative to other objects and their motions. But
Newton argued that since noninertial motion generates forces , it
must be absolute. He used the example of water in a spinning bucket
to demonstrate his argument.
Water
KANT In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both _a priori_ and _synthetic _. According to Kant, knowledge about space is _synthetic_, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but imposed by us as part of a framework for organizing experience. NONEUCLIDEAN GEOMETRY Main article: NonEuclidean geometry Spherical geometry is similar to elliptical geometry . On a sphere (the surface of a ball ) there are no parallel lines . Euclid's _Elements_ contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate , has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line _L1_ and a point _P_ not on _L1_, there is exactly one straight line _L2_ on the plane that passes through the point _P_ and is parallel to the straight line _L1_. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms. Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry . In this geometry, an infinite number of parallel lines pass through the point _P_. Consequently, the sum of angles in a triangle is less than 180° and the ratio of a circle 's circumference to its diameter is greater than pi . In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry , in which no parallel lines pass through _P_. In this geometry, triangles have more than 180° and circles have a ratio of circumferencetodiameter that is less than pi . TYPE OF GEOMETRY NUMBER OF PARALLELS SUM OF ANGLES IN A TRIANGLE RATIO OF CIRCUMFERENCE TO DIAMETER OF CIRCLE MEASURE OF CURVATURE HYPERBOLIC Infinite < 180° > π < 0 EUCLIDEAN 1 180° π 0 ELLIPTICAL 0 > 180° < π > 0 GAUSS AND POINCARé
Carl Friedrich Gauss
Although there was a prevailing Kantian consensus at the time, once
nonEuclidean geometries had been formalised, some began to wonder
whether or not physical space is curved.
Carl Friedrich Gauss
Henri Poincaré , a French mathematician and physicist of the late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment. He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphereworld . In this world, the temperature is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface. In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of convention . Since Euclidean geometry is simpler than nonEuclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world. EINSTEIN
Albert Einstein
In 1905,
Albert Einstein
Subsequently,
Einstein
MATHEMATICS Main article: Threedimensional space Not to be confused with Space (mathematics) . In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds , which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness. PHYSICS Many of the laws of physics, such as the various inverse square laws , depend on dimension three. In physics, our threedimensional space is viewed as embedded in fourdimensional spacetime , called Minkowski space (see special relativity ). The idea behind spacetime is that time is hyperbolicorthogonal to each of the three spatial dimensions. CLASSICAL MECHANICS Main article: Classical mechanics CLASSICAL MECHANICS F = m a {displaystyle {vec {F}}=m{vec {a}}} Second law of motion * History * Timeline Branches * Applied
* Celestial
* Continuum
* Dynamics
*
Kinematics
Fundamentals *
Acceleration
* kinetic * potential *
Force
* Mechanical power * Mechanical work *
Moment *
Momentum
* Space
*
Speed
Formulations * NEWTON\\'S LAWS OF MOTION * ANALYTICAL MECHANICS * Lagrangian mechanics * Hamiltonian mechanics * Routhian mechanics * Hamilton–Jacobi equation * Appell\'s equation of motion * Udwadia–Kalaba equation * Koopman–von Neumann mechanics Core topics *
Damping (ratio )
* Displacement
*
Equations of motion
* Inertial / Noninertial reference frame * Mechanics of planar particle motion * Motion (linear ) * Newton\'s law of universal gravitation * Newton\'s laws of motion * Relative velocity * dynamics * Euler\'s equations *
Simple harmonic motion
*
Vibration
Rotation * Circular motion * Rotating reference frame * Centripetal force * reactive * Coriolis force * Pendulum * Tangential speed * Rotational speed * Angular acceleration / displacement / frequency / velocity Scientists * Galileo * Newton * Kepler * Horrocks * Halley * Euler * d\'Alembert * Clairaut * Lagrange * Laplace * Hamilton * Poisson * Daniel Bernoulli * Johann Bernoulli * Cauchy * v * t * e
Space
RELATIVITY Main article:
Theory of relativity
Before
Einstein
In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski spacetime. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric ). Furthermore, in Einstein\'s general theory of relativity , it is postulated that spacetime is geometrically distorted _curved_ near to gravitationally significant masses. One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of spacetime, called gravitational waves . While indirect evidence for these waves has been found (in the motions of the Hulse–Taylor binary system, for example) experiments attempting to directly measure these waves are ongoing. COSMOLOGY Main article: Shape of the universe Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang , 13.8 billion years ago and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the cosmic inflation . SPATIAL MEASUREMENT Main article:
Measurement
The measurement of _physical space_ has long been important. Although earlier societies had developed measuring systems, the International System of Units , (SI), is now the most common system of units used in the measuring of space, and is almost universally used. Currently, the standard space interval, called a standard meter or simply meter , is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature. GEOGRAPHICAL SPACE See also: Spatial analysis
Geography
Geographical space is often considered as land, and can have a
relation to ownership usage (in which space is seen as property or
territory). While some cultures assert the rights of the individual in
terms of ownership, other cultures will identify with a communal
approach to land ownership, while still other cultures such as
Australian Aboriginals , rather than asserting ownership rights to
land, invert the relationship and consider that they are in fact owned
by the land.
Spatial planning is a method of regulating the use of
space at landlevel, with decisions made at regional, national and
international levels.
Space
Ownership
Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all, while private property is the land culturally owned by an individual or company, for their own use and pleasure. Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain. IN PSYCHOLOGY Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of psychology . Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived, see, for example, visual space . Other, more specialized topics studied include amodal perception and object permanence . The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space . Several spacerelated phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces). The understanding of threedimensional space in humans is thought to be learned during infancy using unconscious inference , and is closely related to handeye coordination . The visual ability to perceive the world in three dimensions is called depth perception . SEE ALSO *
Physics
* Book:
Space
*
Absolute space and time
*
Aether theories
*
Cosmology
REFERENCES * ^ "space  physics and metaphysics". _Encyclopædia Britannica_.
* ^ Refer to Plato's _Timaeus_ in the Loeb Classical Library,
Harvard University
