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CONTENTS

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 * (Top)
 * 1 Philosophy of space
   Toggle Philosophy of space subsection
   * 1.1 Galileo
   * 1.2 René Descartes
   * 1.3 Leibniz and Newton
   * 1.4 Kant
   * 1.5 Non-Euclidean geometry
   * 1.6 Gauss and Poincaré
   * 1.7 Einstein
 * 2 Mathematics
 * 3 Physics
   Toggle Physics subsection
   * 3.1 Relativity
   * 3.2 Cosmology
 * 4 Spatial measurement
 * 5 Geographical space
 * 6 In psychology
 * 7 In the social sciences
 * 8 See also
 * 9 References
 * 10 External links

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SPACE

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From Wikipedia, the free encyclopedia

Framework of distances and directions
This article is about the general framework of distance and direction. For the
space beyond Earth's atmosphere, see Outer space. For the writing separator, see
Space (punctuation). For other uses, see Space (disambiguation).



A right-handed three-dimensional Cartesian coordinate system used to indicate
positions in space

Space is a three-dimensional continuum containing positions and directions.[1]
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.[2] 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.

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, as
in the Euclidean space. According to Albert Einstein's theory of general
relativity, space around gravitational fields deviates from Euclidean space.[3]
Experimental tests of general relativity have confirmed that non-Euclidean
geometries provide a better model for the shape of space.


PHILOSOPHY OF SPACE

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.[4] 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.

Isaac Newton viewed space as absolute, existing permanently and independently of
whether there was any matter in the.[5] In contrast, other natural philosophers,
notably Gottfried Leibniz, thought 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".


GALILEO

Galilean and Cartesian theories about space, matter, and motion are at the
foundation of the Scientific Revolution, which is understood to have culminated
with the publication of Newton's Principia Mathematica in 1687.[6] 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.[7]

As one of the pioneers of modern science, Galileo revised the established
Aristotelian and Ptolemaic ideas about a geocentric cosmos. He backed the
Copernican theory that the universe was heliocentric, 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.[8]


RENÉ DESCARTES

Descartes set out to replace the Aristotelian worldview with a theory about
space and motion as determined by natural laws. In other words, he sought a
metaphysical foundation or a mechanical explanation for his theories about
matter and motion. Cartesian space was Euclidean in structure—infinite, uniform
and flat.[9] 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.[6]

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 believe.[10]
He posited a clear distinction between the body and mind, which is referred to
as the Cartesian dualism.


LEIBNIZ AND NEWTON

Gottfried Leibniz

Following Galileo and Descartes, during the seventeenth century the philosophy
of space and time revolved around the ideas of Gottfried Leibniz, a German
philosopher–mathematician, and 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".[11] 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.[12] 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.[13] 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, there would be no real difference between them.
According to the principle of sufficient reason, any theory of space that
implied that there could be these two possible universes must therefore be
wrong.[14]

Isaac Newton

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 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 forces, it
must be absolute.[15] He used the example of water in a spinning bucket to
demonstrate his argument. Water in a 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.[16] 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

Immanuel Kant

In the eighteenth century the German philosopher Immanuel Kant published his
theory of space as "a property of our mind" by which "we represent to ourselves
objects as outside us, and all as in space" in the Critique of Pure Reason[17]
On his view the nature of spatial predicates are "relations that only attach to
the form of intuition alone, and thus to the subjective constitution of our
mind, without which these predicates could not be attached to anything at
all."[18] This develops his theory of knowledge in which knowledge about space
itself can be both a priori and synthetic.[19] According to Kant, knowledge
about space is synthetic because any proposition about space cannot be true
merely in virtue of the meaning of the terms contained in the proposition. In
the counter-example, the proposition "all unmarried men are bachelors" is true
by virtue of each term's meaning. Further, space is a priori because it is the
form of our receptive abilities to receive information about the external world.
For example, someone without sight can still perceive spatial attributes via
touch, hearing, and smell. Knowledge of space itself is a priori because it
belongs to the subjective constitution of our mind as the form or manner of our
intuition of external objects.


NON-EUCLIDEAN GEOMETRY

Main article: Non-Euclidean 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.[20] 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 circumference-to-diameter 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 Henri 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, 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 triangulating mountain tops in Germany.[21]

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.[22] 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.[23] 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.[24] Since
Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former
would always be used to describe the 'true' geometry of the world.[25]


EINSTEIN

Albert Einstein

In 1905, 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 this theory, the speed of light in vacuum is the same for all
observers—which has the result 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 tick more slowly 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, which is a
theory of how 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.[26] 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 pulsars, confirming the predictions of Einstein's theories,
and non-Euclidean geometry is usually used to describe spacetime.


MATHEMATICS

Main article: Three-dimensional space
For broader coverage of this topic, see Space (mathematics).

In modern mathematics spaces are defined as sets with some added structure. They
are typically topological spaces, in which a concept of neighbourhood is
defined, frequently by means of a distance (metric spaces). The elements of a
space are often called points, but they can have other names such as vectors in
vector spaces and functions in function spaces.


PHYSICS

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This section needs additional citations for verification. Please help improve
this article by adding citations to reliable sources in this section. Unsourced
material may be challenged and removed.
Find sources: "Space" – news · newspapers · books · scholar · JSTOR (April 2020)
(Learn how and when to remove this message)

Space is one of the few fundamental quantities in 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),
space can be explored via measurement and experiment.

Today, our three-dimensional space is viewed as embedded in a four-dimensional
spacetime, called Minkowski space (see special relativity). The idea behind
spacetime is that time is hyperbolic-orthogonal to each of the three spatial
dimensions.


RELATIVITY

Main article: Theory of relativity
This section needs additional citations for verification. Please help improve
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material may be challenged and removed.
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Before 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. It turns out that distances in space or in time separately are
not invariant with respect to Lorentz coordinate transformations, but distances
in Minkowski space along spacetime intervals are—which justifies the name.

In addition, time and space dimensions should not be viewed as exactly
equivalent in Minkowski space. 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.[27]

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 at the LIGO and Virgo
collaborations. LIGO scientists reported the first such direct observation of
gravitational waves on 14 September 2015.[28][29]


COSMOLOGY

Main article: Shape of the universe
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this article by adding citations to reliable sources in this section. Unsourced
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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[30] 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
This section needs additional citations for verification. Please help improve
this article by adding citations to reliable sources in this section. Unsourced
material may be challenged and removed.
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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 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
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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
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

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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), 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 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.[31]

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.[32] 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.[33]

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.[34] 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"[35] and Soja's "thirdspace" 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.

Postcolonial theorist Homi Bhabha's concept of Third Space is different from
Soja's Thirdspace, even though both terms offer a way to think outside the terms
of a binary logic. Bhabha's Third Space is the space in which hybrid cultural
forms and identities exist. In his theories, the term hybrid describes new
cultural forms that emerge through the interaction between colonizer and
colonized.[36]


SEE ALSO

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


REFERENCES

 1.  ^ "Space – Physics and Metaphysics". Encyclopædia Britannica. Archived from
     the original on 6 May 2008. Retrieved 28 April 2008.
 2.  ^ Bunyadzade, Konul (15 March 2018). "Thoughts of Time" (PDF). Metafizika
     Journal (in Azerbaijani). 1. AcademyGate Publishing: 8–29.
     doi:10.33864/MTFZK.2019.0. Archived (PDF) from the original on 5 April
     2019. Retrieved 15 March 2018.
 3.  ^ Carnap, R. (1995). An Introduction to the Philosophy of Science. New
     York: Dove. (Original edition: Philosophical Foundations of Physics. New
     York: Basic books, 1966).
 4.  ^ Refer to Plato's Timaeus in the Loeb Classical Library, Harvard
     University, and to his reflections on khora. See also Aristotle's Physics,
     Book IV, Chapter 5, on the definition of topos. Concerning Ibn al-Haytham's
     11th century conception of "geometrical place" as "spatial extension",
     which is akin to Descartes' and Leibniz's 17th century notions of extensio
     and analysis situs, and his own mathematical refutation of Aristotle's
     definition of topos in natural philosophy, refer to: Nader El-Bizri, "In
     Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn
     al-Haytham's Geometrisation of Place", Arabic Sciences and Philosophy
     (Cambridge University Press), Vol. 17 (2007), pp. 57–80.
 5.  ^ French, A.J.; Ebison, M.G. (1986). Introduction to Classical Mechanics.
     Dordrecht: Springer, p. 1.
 6.  ^ Jump up to: a b Huggett, Nick, ed. (1999). Space from Zeno to Einstein:
     classic readings with a contemporary commentary. Cambridge, MA: MIT Press.
     Bibcode:1999sze..book.....H. ISBN 978-0-585-05570-1. OCLC 42855123.
 7.  ^ Janiak, Andrew (2015). "Space and Motion in Nature and Scripture:
     Galileo, Descartes, Newton". Studies in History and Philosophy of Science.
     51: 89–99. Bibcode:2015SHPSA..51...89J. doi:10.1016/j.shpsa.2015.02.004.
     PMID 26227236.
 8.  ^ Dainton, Barry (2001). Time and space. Montreal: McGill-Queen's
     University Press. ISBN 978-0-7735-2302-9. OCLC 47691120.
 9.  ^ Dainton, Barry (2014). Time and Space. McGill-Queen's University Press.
     p. 164.
 10. ^ Tom., Sorell (2000). Descartes: a very short introduction. Oxford: Oxford
     University Press. ISBN 978-0-19-154036-3. OCLC 428970574.
 11. ^ Leibniz, Fifth letter to Samuel Clarke. By H.G. Alexander (1956). The
     Leibniz-Clarke Correspondence. Manchester: Manchester University Press, pp.
     55–96.
 12. ^ Vailati, E. (1997). Leibniz & Clarke: A Study of Their Correspondence.
     New York: Oxford University Press, p. 115.
 13. ^ Sklar, L. (1992). Philosophy of Physics. Boulder: Westview Press, p. 20.
 14. ^ Sklar, L. Philosophy of Physics. p. 21.
 15. ^ Sklar, L. Philosophy of Physics. p. 22.
 16. ^ "Newton's bucket". st-and.ac.uk. Archived from the original on 17 March
     2008. Retrieved 20 July 2008.
 17. ^ Allison, Henry E. (2004). Kant's Transcendental Idealism: An
     Interpretation and Defense; Revised and Enlarged Edition. Yale University
     Press. p. 97-132. ISBN 978-0300102666.
 18. ^ Kant, Immanuel (1999). Critique of Pure Reason (The Cambridge Edition of
     the Works of Immanuel Kant). Cambridge University Press. p. A3/B37-38.
     ISBN 978-0-5216-5729-7.
 19. ^ Carnap, R. An Introduction to the Philosophy of Science. pp. 177–178.
 20. ^ Carnap, R. An Introduction to the Philosophy of Science. p. 126.
 21. ^ Carnap, R. An Introduction to the Philosophy of Science. pp. 134–136.
 22. ^ Jammer, Max (1954). Concepts of Space. The History of Theories of Space
     in Physics. Cambridge: Harvard University Press, p. 165.
 23. ^ A medium with a variable index of refraction could also be used to bend
     the path of light and again deceive the scientists if they attempt to use
     light to map out their geometry.
 24. ^ Carnap, R. An Introduction to the Philosophy of Science. p. 148.
 25. ^ Sklar, L. Philosophy of Physics. p. 57.
 26. ^ Sklar, L. Philosophy of Physics. p. 43.
 27. ^ Wheeler, John A. A Journey into Gravity and Spacetime. Chapters 8 and 9,
     Scientific American, ISBN 0-7167-6034-7
 28. ^ Castelvecchi, Davide; Witze, Alexandra (11 February 2016). "Einstein's
     gravitational waves found at last". Nature News. Archived from the original
     on 16 February 2016. Retrieved 12 January 2018.
 29. ^ Abbott, Benjamin P.; et al. (LIGO Scientific Collaboration and Virgo
     Collaboration) (2016). "Observation of Gravitational Waves from a Binary
     Black Hole Merger". Phys. Rev. Lett. 116 (6): 061102. arXiv:1602.03837.
     Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102.
     PMID 26918975. S2CID 124959784.
      * "Observation of Gravitational Waves from a Binary Black Hole Merger"
        (PDF). LIGO Scientific Collaboration.

 30. ^ "Cosmic Detectives". The European Space Agency (ESA). 2 April 2013.
     Archived from the original on 5 April 2013. Retrieved 26 April 2013.
 31. ^ Stanek, Lukasz (2011). Henri Lefebvre on Space: Architecture, Urban
     Research, and the Production of Theory. Univ of Minnesota Press. pp. ix.
 32. ^ "Time-Space Compression – Geography – Oxford Bibliographies – obo".
     Archived from the original on 20 September 2018. Retrieved 28 August 2018.
 33. ^ Harvey, David (2001). Spaces of Capital: Towards a Critical Geography.
     Edinburgh University Press. pp. 244–246.
 34. ^ W., Soja, Edward (1996). Thirdspace: journeys to Los Angeles and other
     real-and-imagined places. Cambridge, Mass.: Blackwell.
     ISBN 978-1-55786-674-5. OCLC 33863376.{{cite book}}: CS1 maint: multiple
     names: authors list (link)
 35. ^ Lefebvre, Henri (1991). The production of space. Oxford, OX, UK:
     Blackwell. ISBN 978-0-631-14048-1. OCLC 22624721.
 36. ^ Ashcroft Bill; Griffiths, Gareth; Tiffin, Helen (2013). Postcolonial
     studies: the key concepts (Third ed.). London. ISBN 978-0-415-66190-4.
     OCLC 824119565.{{cite book}}: CS1 maint: location missing publisher (link)


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