Space is the boundless three-dimensional extent in which objects and events have relative position and direction.
In physics, a physical body or physical object is an identifiable collection of matter, which may be more or less constrained by an identifiable boundary, to move together by translation or rotation, in 3-dimensional space.
Direction is the information contained in the relative position of one point with respect to another point without the distance information.
Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime.
Linearity is the property of a mathematical relationship or function which means that it can be graphically represented as a straight line, that is, that one quantity is simply proportional to another.
In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it.
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
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.
A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside of either theological dogma or science.
A conceptual framework is an analytical tool with several variations and contexts.
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, or in the Physics of Aristotle in the definition of topos, or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place of the 11th-century Arab polymath Alhazen.
In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors v and w at a point of a surface and produces a real number scalar g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.
Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham, also known by the Latinization Alhazen or Alhacen, was an Arab Muslim scientist, mathematician, astronomer, and philosopher.
Plato was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.
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.
The Renaissance is a period in Europe, from the 14th to the 17th century, regarded as the cultural bridge between the Middle Ages and modern history.
In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics.
In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space.
Sir Isaac Newton FRS was an English physicist and mathematician who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution.
Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another.
Gottfried Wilhelm Leibniz was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton.
Natural philosophy or philosophy of nature was the philosophical study of nature and the physical universe that was dominant before the development of modern science.
Distance is a numerical description of how far apart objects are.
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.
George Berkeley — known as Bishop Berkeley — was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism".
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.
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world that encompasses it.
The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159.
Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".
The Latin phrases a priori and a posteriori are philosophical terms of art popularized by Immanuel Kant's Critique of Pure Reason, one of the most influential works in the history of philosophy.
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.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.
In physics, a gravitational field is a model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body.
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.
At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation.