â—SPACEâ—
Space is a three-dimensional continuum
-containing positions and directions.In classical physics, physical space is often conceived
in three linear dimensions. Modern physicists usually consider it, with time, to be part of
a boundless four-dimensional 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, or Socrates in his reflections on what the
Greeks called khôra (i.e. “space”), or in the Physics of Aristotle (Book IV, Delta) in the definition
of topos (i.e. place), or in the later “geometrical conception of place” as “space qua extension”
in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath Alhazen. Many
of these classical philosophical questions were discussed in the Renaissance and then
reformulated in the 17th century, particularly during the early development of classical
mechanics. In Isaac Newton’s view, space was absolute—in the sense that it existed permanently
and independently of whether there was any matter in the space. Other natural philosophers,
notably Gottfried Leibniz, thought instead that space was in fact a collection of relations
between objects, given by their distance and direction from one another. In the 18th century, the
philosopher and theologian George Berkeley attempted to refute the “visibility of spatial depth”
in his Essay Towards a New Theory of Vision. Later,
-the metaphysician Immanuel Kant said that the concepts of space and time are not empirical
ones derived from experiences of the outside world—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 his Critique of Pure Reason as being a subjective “pure a
priori form of intuition”.
In the 19th and 20th centuries mathematicians began to examine geometries that
are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert
Einstein’s theory of general relativity, space around gravitational fields deviates from Euclidean
space.Experimental tests of general relativity have confirmed that non-Euclidean geometries
provide a better model for the shape of space.
â—Mathematicsâ—
-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 mathema
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