â—SPACEâ—

SpaceÂ is aÂ three-dimensionalÂ continuum

-containingÂ positionsÂ andÂ directions.InÂ classical physics, physical space is often conceived

in threeÂ linearÂ dimensions.Â Modern physicistsÂ usually consider it, withÂ time, to be part of

a boundlessÂ four-dimensionalÂ continuumÂ known asÂ spacetime. The concept of space is

considered to be of fundamental importance to an understanding of the physicalÂ universe.

However, disagreement continues betweenÂ philosophersÂ over whether it is itself an entity, a

relationship between entities, or part of aÂ conceptual framework.

Debates concerning the nature, essence and the mode of existence of space date back to

antiquity; namely, to treatises like theÂ TimaeusÂ ofÂ Plato, orÂ SocratesÂ in his reflections on what the

Greeks calledÂ khÃ´raÂ (i.e. “space”), or in theÂ PhysicsÂ ofÂ AristotleÂ (Book IV, Delta) in the definition

ofÂ toposÂ (i.e. place), or in the later “geometrical conception of place” as “spaceÂ quaÂ extension”

in theÂ Discourse on PlaceÂ (Qawl fi al-Makan) of the 11th-century ArabÂ polymathÂ Alhazen.Â Many

of these classical philosophical questions were discussed in theÂ RenaissanceÂ and then

reformulated in the 17th century, particularly during the early development ofÂ classical

mechanics. InÂ Isaac Newton’s view, space was absoluteâ€”in the sense that it existed permanently

and independently of whether there was any matter in the space.Â OtherÂ natural philosophers,

notablyÂ Gottfried Leibniz, thought instead that space was in fact a collection of relations

between objects, given by theirÂ distanceÂ andÂ directionÂ from one another. In the 18th century, the

philosopher and theologianÂ George BerkeleyÂ attempted to refute the “visibility of spatial depth”

in hisÂ Essay Towards a New Theory of Vision. Later,

-theÂ metaphysicianÂ Immanuel KantÂ said that the concepts of space and time are not empirical

ones derived from experiences of the outside worldâ€”they are elements of an already given

systematic framework that humans possess and use to structure all experiences. Kant

referred to the experience of “space” in hisÂ Critique of Pure ReasonÂ as being a subjective “pureÂ a

prioriÂ form of intuition”.

In the 19th and 20th centuries mathematicians began to examine geometries that

areÂ non-Euclidean, in which space is conceived asÂ curved, rather thanÂ flat. According toÂ Albert

Einstein’s theory ofÂ general relativity, space aroundÂ gravitational fieldsÂ deviates from Euclidean

space.ExperimentalÂ tests of general relativityÂ have confirmed that non-Euclidean geometries

provide a better model for the shape of space.

â—Mathematicsâ—

-In modern mathematicsÂ spacesÂ are defined asÂ setsÂ with some added structure. They are

frequently described as different types ofÂ 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 mathema

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