Space is the boundless extent in which and events have relative and . In , physical space is often conceived in three s, although modern s usually consider it, with , to be part of a boundless known as . The concept of space is considered to be of fundamental importance to an understanding of the physical . However, disagreement continues between over whether it is itself an entity, a relationship between entities, or part of a .
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the ' of , or in his reflections on what the Greeks called ' (i.e. "space"), or in the ' of (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 . Many of these classical philosophical questions were discussed in the and then reformulated in the 17th century, particularly during the early development of . In 's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other s, notably , thought instead that space was in fact a collection of relations between objects, given by their and from one another. In the 18th century, the philosopher and theologian attempted to refute the "visibility of spatial depth" in his ''Essay Towards a New Theory of Vision''. Later, the ian 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 ' as being a subjective "pure ' form of intuition".
In the 19th and 20th centuries mathematicians began to examine geometries that are , in which space is conceived as ''curved'', rather than ''flat''. According to 's theory of , space around s deviates from Euclidean space. Experimental have confirmed that non-Euclidean geometries provide a better model for the shape of space.

_{1}'' and a point ''P'' not on ''L_{1}'', there is exactly one straight line ''L_{2}'' on the plane that passes through the point ''P'' and is parallel to the straight line ''L_{1}''. 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 and the Russian separately published treatises on a type of geometry that does not include the parallel postulate, called . In this geometry, an 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 's to its is greater than . In the 1850s, developed an equivalent theory of , in which no parallel lines pass through ''P''. In this geometry, triangles have more than 180° and circles have a ratio of circumference-to-diameter that is less than .

Philosophy of space

Galileo

and theories about space, matter, and motion are at the foundation of the , which is understood to have culminated with the publication of 's ' in 1687. Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in Physics, it emerged from his predecessors' ideas about the same. As one of the pioneers of , Galileo revised the established and ideas about a cosmos. He backed the theory that the universe was , with a stationary sun at the center and the planets—including the Earth—revolving around the sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galileo wanted to prove instead that the sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galileo, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging.René Descartes

set out to replace the Aristotelian worldview with a theory about space and motion as determined by s. In other words, he sought a foundation or a explanation for his theories about matter and motion. was in structure—infinite, uniform and flat. It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space. The Cartesian notion of space is closely linked to his theories about the nature of the body, mind and matter. He is famously known for his "cogito ergo sum" (I think therefore I am), or the idea that we can only be certain of the fact that we can doubt, and therefore think and therefore exist. His theories belong to the tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the believe. He posited a clear distinction between the body and mind, which is referred to as the .Leibniz and Newton

Following Galileo and Descartes, during the seventeenth century the revolved around the ideas of , a German philosopher–mathematician, and , who 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 from the relations between individual entities or their possible locations and therefore could not be but must be . Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the , there would be no real difference between them. According to the , any theory of space that implied that there could be these two possible universes must therefore be wrong. Newton took space to be more than relations between material objects and based his position on and experimentation. For a there can be no real difference between , in which the object travels with constant , and , in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates s, it must be absolute. He used the example of to demonstrate his argument. Water in a is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water. Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter.Kant

In the eighteenth century the German philosopher developed a theory of in which knowledge about space can be both ''a priori'' and '. 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.Non-Euclidean geometry

Euclid's ''Elements'' contained five postulates that form the basis for Euclidean geometry. One of these, the , has been the subject of debate among mathematicians for many centuries. It states that on any on which there is a straight line ''LGauss and Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved. , a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by mountain tops in Germany. , 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 . 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 . Since is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.Einstein

In 1905, published his , which led to the concept that space and time can be viewed as a single construct known as '. In this theory, the in a is the same for all observers—which has that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to than one that is stationary with respect to them; and objects are measured in the direction that they are moving with respect to the observer. Subsequently, Einstein worked on a , which is a theory of how interacts with spacetime. Instead of viewing gravity as a acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself. According to the general theory, time at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of s, confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime.Mathematics

In modern mathematics are defined as with some added structure. They are frequently described as different types of s, 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, s such as s may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and s replace the concept of distance with a more abstract idea of nearness.Physics

Space is one of the few in , meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and ), space can be explored via and experiment. Today, our is viewed as embedded in a four-dimensional , called (see ). The idea behind space-time is that time is to each of the three spatial dimensions.Relativity

Before 's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object–. It turns out that distances in or in separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along s are—which justifies the name. In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in (where time is sometimes considered an coordinate) and in (where different signs are assigned to time and space components of ). Furthermore, in , it is postulated that space-time 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 space-time, called s. While indirect evidence for these waves has been found (in the motions of the system, for example) experiments attempting to directly measure these waves are ongoing at the and collaborations. LIGO scientists reported the on 14 September 2015.Cosmology

Relativity theory leads to the question of what shape the universe is, and where space came from. It appears that space was created in the , 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 .Spatial measurement

The measurement of ''physical space'' has long been important. Although earlier societies had developed measuring systems, the , (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 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 in which the plays the role of a fundamental constant of nature.Geographical space

is the branch of science concerned with identifying and describing places on , utilizing spatial awareness to try to understand why things exist in specific locations. is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. apply statistical concepts to collected spatial data of Earth to create an estimate for unobserved phenomena. Geographical space is often considered as land, and can have a relation to usage (in which space is seen as 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 , rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming. Ownership of space is not restricted to land. Ownership of and of is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the or to . 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 is the land culturally owned by an individual or company, for their own use and pleasure. is a term used in to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit 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 . 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, . Other, more specialized topics studied include and . The of surroundings is important due to its necessary relevance to survival, especially with regards to and as well as simply one's idea of . Several space-related s have been identified, including (the fear of open spaces), (the fear of celestial space) and (the fear of enclosed spaces). The understanding of three-dimensional space in humans is thought to be learned during infancy using , and is closely related to . The visual ability to perceive the world in three dimensions is called .In the social sciences

Space has been studied in the social sciences from the perspectives of , , , , and . These theories account for the effect of the history of colonialism, transatlantic slavery and globalization on our understanding and experience of space and place. The topic has garnered attention since the 1980s, after the publication of 's ''The Production of Space .'' In this book, Lefebvre applies Marxist ideas about the production of commodities and accumulation of capital to discuss space as a social product. His focus is on the multiple and overlapping social processes that produce space. In his book ''The Condition of Postmodernity,'' describes what he terms the "." This is the effect of technological advances and capitalism on our perception of time, space and distance. Changes in the modes of production and consumption of capital affect and are affected by developments in transportation and technology. These advances create relationships across time and space, new markets and groups of wealthy elites in urban centers, all of which annihilate distances and affect our perception of linearity and distance. In his book ''Thirdspace,'' describes space and spatiality as an integral and neglected aspect of what he calls the "," the three modes that determine how we inhabit, experience and understand the world. He argues that critical theories in the Humanities and Social Sciences study the historical and social dimensions of our lived experience, neglecting the spatial dimension. He builds on Henri Lefebvre's work to address the dualistic way in which humans understand space—as either material/physical or as represented/imagined. Lefebvre's "lived space" and Soja's "thridspace" are terms that account for the complex ways in which humans understand and navigate place, which "firstspace" and "Secondspace" (Soja's terms for material and imagined spaces respectively) do not fully encompass. theorist 's concept of is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories, the term describes new cultural forms that emerge through the interaction between colonizer and colonized.See also

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