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Space is the boundless
three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Greek wikt:παρά#Ancient Greek, παρά, ''par ...
extent in which objects and events have relative position and
direction Direction may refer to: *Relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy *Cardinal direction Mathematics and science *Direction vector, a unit vector that ...
. In
classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
, physical space is often conceived in three
linear Linearity is the property of a mathematical relationship (''function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out se ...

linear
dimension In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

dimension
s, although modern
physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at leas ...

physicist
s usually consider it, with
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

time
, to be part of a boundless
four-dimensional A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which thre ...
continuum Continuum may refer to: * Continuum (measurement) Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variatio ...
known as
spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three ...
. The concept of space is considered to be of fundamental importance to an understanding of the physical
universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

universe
. However, disagreement continues between
philosophers A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, ...
over whether it is itself an entity, a relationship between entities, or part of a
conceptual framework A conceptual framework is an analytical tool Analytical chemistry studies and uses instruments and methods used to separate, identify, and quantify matter. In practice, separation, identification or quantification may constitute the entire anal ...
. Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the '' Timaeus'' of
Plato Plato ( ; grc-gre, wikt:Πλάτων, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was an Classical Athens, Athenian philosopher during the Classical Greece, Classical period in Ancient Greece, founder of the Platonist school of thoug ...

Plato
, or
Socrates Socrates (; ; –399 BC) was a Greek philosopher from Athens Athens ( ; el, Αθήνα, Athína ; grc, Ἀθῆναι, Athênai (pl.) ) is the capital city, capital and List of cities in Greece, largest city of Greece. Athens domi ...

Socrates
in his reflections on what the Greeks called ''
khôra ''Khôra'' (also ''chora''; grc, χώρα) was the territory of the Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is ...
'' (i.e. "space"), or in the ''
Physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...
'' of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental quest ...

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 Ḥasan Ibn al-Haytham (Latinization of names, Latinized as Alhazen ; full name ; ) was a Muslim Arab Mathematics in medieval Islam, mathematician, Astronomy in the medieval Islamic world, astronomer, and Physics in the medieval Islamic world, ...
. Many of these classical philosophical questions were discussed in the
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in ...

Renaissance
and then reformulated in the 17th century, particularly during the early development of classical mechanics. In
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

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 Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the "#1666–1676, 1666–1676" section. ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist, and diplomat. He is a promin ...
, thought instead that space was in fact a collection of relations between objects, given by their
distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or eve ...

distance
and
direction Direction may refer to: *Relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy *Cardinal direction Mathematics and science *Direction vector, a unit vector that ...
from one another. In the 18th century, the philosopher and theologian
George Berkeley George Berkeley (; 12 March 168514 January 1753) – known as Bishop Berkeley (Bishop of Cloyne The Bishop of Cloyne is an episcopal title that takes its name after the small town of Cloyne in County Cork, Republic of Ireland Irelan ...

George Berkeley
attempted to refute the "visibility of spatial depth" in his ''Essay Towards a New Theory of Vision''. Later, the
metaphysic Metaphysics is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and ...
ian
Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about r ...

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 ''Critique of Pure Reason'' (german: Kritik der reinen Vernunft; 1781; second edition 1787) is a book by the German philosopher Immanuel Kant Immanuel Kant (, ; ; 22 April 1724 – 12 February 1804) was a German Philosophy, philosopher a ...
'' as being a subjective "pure ''
a priori ''A priori'' and ''a posteriori'' ('from the earlier' and 'from the later', respectively) are Latin phrases used in philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaph ...
'' 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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

Albert Einstein
's theory of
general relativity General relativity, also known as the general theory of relativity, is the of published by in 1915 and is the current description of gravitation in . General generalizes and refines , providing a unified description of gravity as a geome ...
, space around
gravitational field In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

gravitational field
s deviates from Euclidean space. Experimental
tests of general relativity Tests of general relativity serve to establish observational evidence for the theory of general relativity General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory o ...
have confirmed that non-Euclidean geometries provide a better model for the shape of space.


Philosophy of space


Galileo

Galilean Generically, a Galilean (; he, גלילי; grc, Γαλιλαίων; la, Galilaeos) is an inhabitant of Galilee, a region of Israel surrounding the Sea of Galilee (Kinneret).The New Testament notes that the Apostle Saint Peter, Peter's accent ...

Galilean
and
Cartesian
Cartesian
theories about space, matter, and motion are at the foundation of the
Scientific Revolution The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in History of mathematics#Mathematics during the Scientific Revolution, mathematics, History of phys ...

Scientific Revolution
, which is understood to have culminated with the publication of
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * Newton (film), ''Newton'' (film), a 2017 Indian fil ...

Newton
's '' Principia'' 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
modern science The history of science covers the development of science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), organizes knowledge in the form of ...
, Galileo revised the established
Aristotelian Aristotelian may refer to: * Aristotle (384–322 BCE), Greek philosopher * Aristotelianism, the philosophical tradition begun by Aristotle * Aristotelian ethics * Aristotelian logic, term logic * Aristotelian physics, the natural sciences * Aristot ...
and Ptolemaic ideas about a
geocentric In , the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a description of the with at the center. Under the geocentric model, the , , s, and all Earth. The geocentric model was the pre ...
cosmos. He backed the
Copernican
Copernican
theory that the universe was
heliocentric Heliocentrism is the astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematics ...
, 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

Descartes
Descartes
set out to replace the Aristotelian worldview with a theory about space and motion as determined by
natural law Natural law ( la, ius naturale, ''lex naturalis'') is a system of law based on a close observation of human nature Human nature is a concept that denotes the fundamental disposition A disposition is a quality of character, a habit A habit (or ...
s. In other words, he sought a
metaphysical Metaphysics is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and ...

metaphysical
foundation or a
mechanical Mechanical may refer to: Machine * Mechanical system A machine is any physical system with ordered structural and functional properties. It may represent human-made or naturally occurring device molecular machine that uses Power (physics), p ...

mechanical
explanation for his theories about matter and motion.
Cartesian spaceCartesian means of or relating to the French philosopher René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French-born philosopher, mathematician A mathematician is someone wh ...
was
Euclidean Euclidean (or, less commonly, Euclidian) is an adjective derived from the name of Euclid, an ancient Greek mathematician. It is the name of: Geometry *Euclidean space, the two-dimensional plane and three-dimensional space of Euclidean geometry a ...
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 rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the
empiricists In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, ...
believe. He posited a clear distinction between the body and mind, which is referred to as the
Cartesian dualismCartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to: Mathematics * Cartesian closed category, a closed category in category theory *Cartesian coordinate system A C ...
.


Leibniz and Newton

Following Galileo and Descartes, during the seventeenth century the
philosophy of space and time Philosophy of space and time is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mi ...
revolved around the ideas of
Gottfried Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the "#1666–1676, 1666–1676" section. ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist, and diplomat. He is a promin ...
, a German philosopher–mathematician, and
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

Isaac Newton
, 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
abstraction Abstraction in its main sense is a conceptual process where general rules Rule or ruling may refer to: Human activity * The exercise of political Politics (from , ) is the set of activities that are associated with Decision-making, mak ...

abstraction
from the relations between individual entities or their possible locations and therefore could not be
continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ga ...
but must be
discrete Discrete in science is the opposite of :wikt:continuous, continuous: something that is separate; distinct; individual. Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory *Discrete device, an electronic c ...

discrete
. 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
identity of indiscernibles The identity of indiscernibles is an ontology, ontological principle that states that there cannot be separate object (philosophy), objects or wikt:entity, entities that have all their property (philosophy), properties in common. That is, entities ' ...
, there would be no real difference between them. According to the
principle of sufficient reasonThe principle of sufficient reason states that everything must have a Reason (argument), reason or a cause. The modern formulation of the principle is usually attributed to early age of enlightenment, Enlightenment philosopher Gottfried Wilhelm Leibn ...
, 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
observation Observation is the active acquisition of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristics. Th ...

observation
and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant
velocity The velocity of an object is the Time derivative, rate of change of its Position (vector), position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction ...

velocity
, and non-inertial 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 non-inertial motion generates
force In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to acce ...

force
s, it must be absolute. He used the example of water in a spinning bucket to demonstrate his argument. Water in a
bucket A bucket is typically a watertight, vertical cylinder A cylinder (from ) has traditionally been a Solid geometry, three-dimensional solid, one of the most basic of curvilinear geometric shapes. Geometrically, it can be considered as a Prism ( ...

bucket
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
Immanuel Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about r ...

Immanuel Kant
developed a theory of
knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to e ...
in which knowledge about space can be both ''a priori'' and ''
syntheticA synthetic is an artificial material produced by organic chemistry, organic chemical synthesis. Synthetic may also refer to: In the sense of both "combination" and "artificial" * Synthetic chemical or synthetic compress, produced by the process ...
''. 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
parallel postulate In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: ' ...

parallel postulate
, has been the subject of debate among mathematicians for many centuries. It states that on any
plane Plane or planes may refer to: * Airplane An airplane or aeroplane (informally plane) is a fixed-wing aircraft A fixed-wing aircraft is a heavier-than-air flying machine Early flying machines include all forms of aircraft studied ...
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 János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the ...
and the Russian
Nikolai Ivanovich Lobachevsky Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russia Russia (russian: link=no, ...
separately published treatises on a type of geometry that does not include the parallel postulate, called
hyperbolic geometry In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no g ...
. In this geometry, an
infinite Infinite may refer to: Mathematics *Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (band), a South Korean boy band *''Infinite'' (EP), debut EP of American musi ...

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 A circle is a shape A shape or figure is the form of an object or its external boundary, outline, or external surface File:Water droplet lying on a damask.jpg, Water droplet lying on a damask. Surface tension is high enough to preven ...

circle
's
circumference In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...
to its
diameter In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space ...

diameter
is greater than . In the 1850s,
Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of ...
developed an equivalent theory of
elliptical geometry Elliptic geometry is an example of a geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is conc ...
, 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 .


Gauss 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.
Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician This is a List of German mathematician A mathematician is someone who uses an extensive knowledge of m ...

Carl Friedrich Gauss
, 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.
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French French (french: français(e), link=no) may refer to: * Something of, from, or related to France France (), officially the French Repu ...
, 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 sphere-world. 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 Convention may refer to: * Convention (norm), a custom or tradition, a standard of presentation or conduct ** Treaty, an agreement in international law * Convention (meeting), meeting of a (usually large) group of individuals and/or companies in a ...
. Since
Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematics , Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's method consists in assuming a sma ...
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,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

Albert Einstein
published his special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as ''
spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three ...
''. In this theory, the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in a
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gree ...

vacuum
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 to be shortened in the direction that they are moving with respect to the observer. Subsequently, Einstein worked on a
general theory of relativity General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern ph ...
, which is a theory of how
gravity Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

gravity
interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself. According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of
binary pulsar A binary pulsar is a pulsar Animation of a rotating pulsar. The sphere in the middle represents the neutron star, the curves indicate the magnetic field lines and the protruding cones represent the emission zones. A pulsar (from ''pulse'' and ' ...
s, confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime.


Mathematics

In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of
manifold The real projective plane is a two-dimensional manifold that cannot be realized in three dimensions without self-intersection, shown here as Boy's surface. In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of su ...

manifold
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,
vector space In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...
s such as
function space In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
s may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and
topological space In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gener ...
s replace the concept of distance with a more abstract idea of nearness.


Physics

Space is one of the few fundamental quantities in
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

physics
, 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
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
), space can be explored via
measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependen ...

measurement
and experiment. Today, our
three-dimensional space Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the ...
is viewed as embedded in a four-dimensional
spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three ...
, called
Minkowski space In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space Euclidean space is the fundamental space of classical geometry. Originally it was the three-dimensional space of Euclid ...
(see
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
). The idea behind space-time is that time is
hyperbolic-orthogonal In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that ...
to each of the three spatial dimensions.


Relativity

Before
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born , widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the , but he also made important contributions to the develo ...

Albert Einstein
'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–
spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three ...
. It turns out that distances in Spacetime#Space-like interval, space or in Spacetime#Time-like interval, time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals 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
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
(where time is sometimes considered an imaginary number, imaginary coordinate) and in
general relativity General relativity, also known as the general theory of relativity, is the of published by in 1915 and is the current description of gravitation in . General generalizes and refines , providing a unified description of gravity as a geome ...
(where different signs are assigned to time and space components of
spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three ...
metric tensor, metric). Furthermore, in Einstein's general theory of relativity, 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 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 at the LIGO and Virgo interferometer, Virgo collaborations. LIGO scientists reported the first observation of gravitational waves, first such direct observation of gravitational waves on 14 September 2015.


Cosmology

Relativity theory leads to the cosmology, 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 Inflation (cosmology), cosmic inflation.


Spatial measurement

The measurement of ''physical space'' has long been important. Although earlier societies had developed measuring systems, the SI, 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 speed of light, 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 The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
plays the role of a fundamental constant of nature.


Geographical space

Geography is the branch of science concerned with identifying and describing places on Earth, utilizing spatial awareness to try to understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics 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 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 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 airspace and of International waters, waters is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the electromagnetic spectrum or to cyberspace. 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 space-related phobias have been identified, including agoraphobia (the fear of open spaces), wikt:astrophobia, astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces). The understanding of three-dimensional space in humans is thought to be learned during infancy using visual perception#Unconscious inference, unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception.


In the social sciences

Space has been studied in the social sciences from the perspectives of Marxism, feminism, postmodernism, postcolonialism, urban theory and critical geography. 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 Henri Lefebvre'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,'' David Harvey describes what he terms the "time-space compression." 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,'' Edward Soja describes space and spatiality as an integral and neglected aspect of what he calls the "trialectics of being," 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. Postcolonialism, Postcolonial theorist Homi K. Bhabha, Homi Bhabha's concept of Third Space Theory, Third Space is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a Binary opposition, binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories, the term Hybridity, hybrid describes new cultural forms that emerge through the interaction between colonizer and colonized.


See also

* Absolute space and time * Aether theories * Cosmology * General relativity * Philosophy of space and time * Proxemics * Shape of the universe * Social space * Space exploration * Spatial analysis * Spatial–temporal reasoning


References


External links

{{Authority control Space, Geometry Spacetime Topology Nature