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For other uses, see space (disambiguation).

Space has been an occupation for philosophers and scientists for much of human history, and hence it is difficult to provide an uncontroversial and clear definition outside of specific defined contexts. (See Space in philosophy.) The term is also used somewhat differently in different fields of study.

1 Mathematical spaces
- 1.1 Physics and space
  - 1.1.1 Astronomical space
- 1.2 Spatial measurement
  - 1.2.1 Geographical space
2 Space in philosophy
- 2.1 Spaces in psychology
3 References
4 See also

Mathematical spaces

In mathematics, a space is a set, with some particular properties and usually some additional structure. It is not a formally defined concept as such, but a generic name for a number of similar concepts, most of which generalize some abstract properties of the physical concept of space.

In particular, a vector space and specifically a Euclidean space can be seen as generalizations of the concept of a Euclidean coordinate system. Important varieties of vector spaces with more imposed structure include Banach space and Hilbert space. Distance measurement is abstracted as the concept of metric space and volume measurement leads to the concept of measure space.

As far as the concept of dimension is defined, although three-dimensional space is the most commonly thought of dimensional space, the number of dimensions for a space to exist need not be 3: it can also be 0 (a point), 1 (a line), 2 (a plane), more than 3, and with some definitions, a non-integer value. Mathematicians often study general structures that hold regardless of the number of dimensions.

Kinds of mathematical spaces include:

Banach space
Euclidean space
Hilbert space
Metric space
Probability space
Projective space
Topological space
Vector space

Physics and space

Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because there is nothing more fundamental known at present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined via measurement. Currently, the standard space interval, called a standard meter or simply meter, is defined as the distance traveled by light in a vacuum during a time interval of 1/299792458 of a second (exact). This definition coupled with present definition of time makes our space-time to be Minkowski space and makes special relativity theory to be absolutely correct by definition.

In classical physics, space is a three-dimensional Euclidean space where any position can be described using three coordinates. Relativistic physics examines spacetime rather than space; spacetime is modeled as a four-dimensional manifold, and currently, there are theories that can support up to eleven-dimensional spaces.

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's work unified the two into spacetime. In spacetime, measurements of space and time are held to be relative to velocity.

Astronomical space

Main article: Outer space

In astronomy, space refers collectively to the relatively empty parts of the universe. Any area outside the atmospheres of any celestial body can be considered 'space'. Although space is certainly spacious, it is now known to be far from empty, and filled with a tenuous plasma. In particular, the boundary between space and Earth's atmosphere is conventionally set at the Karman line.

Spatial measurement

Main article: Measurement

The measurement of physical space has long been important. Geometry, the name given to the branch of mathematics which measures spatial relations, was popularised by the ancient Greeks, 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 within science.

Geography is the branch of science concerned with identifying and describing the Earth, utilising spatial awareness to try and understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualisation purposes and to act as a locational device. Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

Geographical space

Geographical space is called land, and has a relation to ownership (in which space is seen as property). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership. 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 behaviour, 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. Public space is a term used to define areas of land which are open to all, whilst private property is that area of land owned by an individual or company, for their own use and pleasure.

Space in philosophy

Main article: Philosophy of space and time

Space has a range of definitions.

One view of space is that it is part of the fundamental structure of the universe, a set of dimensions in which objects are separated and located, have size and shape, and through which they can move.

A contrasting view is that space is part of a fundamental abstract mathematical conceptual framework (together with time and number) within which we compare and quantify the distance between objects, their sizes, their shapes, and their speeds. In this view space does not refer to any kind of entity that is a "container" that objects "move through".

These opposing views are relevant also to definitions of time. Space is typically described as having three dimensions, and that three numbers are needed to specify the size of any object and/or its location with respect to another location. Modern physics does not treat space and time as independent dimensions, but treats both as features of spacetime – a conception that challenges intuitive notions of distance and time.

An issue of philosophical debate is whether space is an ontological entity itself, or simply a conceptual framework we need to think (and talk) about the world. Another way to frame this is to ask, "Can space itself be measured, or is space part of the measurement system?" The same debate applies also to time, and an important formulation in both areas was given by Immanuel Kant.

In his Critique of Pure Reason, Kant described space as an a priori notion that (together with other a priori notions such as time) allows us to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic framework we use to structure our experience. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur.

Schopenhauer, in the preface to his On the Will in Nature, stated that "space is the condition of the possibility of juxtaposition." This is in accordance with Kant's understanding of space as a form in the mind of an observing subject.

Similar philosophical questions concerning space include: Is space absolute or purely relational? Does space have one correct geometry, or is the geometry of space just a convention? Historical positions in these debates have been taken by Isaac Newton (space is absolute), Gottfried Leibniz (space is relational), and Henri Poincaré (spatial geometry is a convention). Two important thought-experiments connected with these questions are: Newton's bucket argument and Poincaré's sphere-world.

Spaces in psychology

The way in which space is perceived is an area which psychologists first began to study in the middle of the 19th century, and it is now thought by those concerned with such studies to be a distinct branch within psychology. Psychologists analysing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived.

Other, more specialised 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.

Astrophobia is the fear of celestial space,
Kenophobia is the fear of empty spaces

References

Space perception. Encyclopædia Britannica from Encyclopædia Britannica Online. Accessed June 12, 2005.