SPACE

The term space, derived from the Latin spatium. has a variety of meanings both in ordinary language and in philosophical and scientific usage. While corresponding etymologically to the Greek στάδιον, it has a much wider meaning than the latter; thus it can signify distance or length, place, temporal duration or interval, or other types of dimensionality. In the Greek language there is no term corresponding to this broad signification of the Latin and modern term. It is difficult, then, to speak about the historical development of the concept of space. Rather one must speak about various concepts and problems that are more or less connected with the meanings attributed to the word in modern usage. This article proposes to do so by a philosophical analysis of the concept.

Philosophical Analysis. A philosophical analysis of the concept of space distinguishes a threefold aspect or usage of the concept, viz, the psychological, the mathematical, and the physical.

Psychological Aspect. According to the investigations of contemporary psychology, the representation of space is gradually formed in the consciousness of the child through a complex experience that begins from the very early months of his life. The senses principally involved in this experience present a whole field wherein single objects are perceptible; this forms, as it were, a unitary and permanent picture wherein individual objects appear and disappear. The unitary and permanent picture gradually becomes distinct and separate from the individual objects and, notably in the imagination, is established as something independent and existing in itself. Thus, by successive integrations, there is formed visual, tactile, imaginary, etc., space.

By reason of its very origin, the space pertinent to perception and imagination has an essential unity, an absolute center of reference, and privileged directions of up and down, length, width, and depth. With the extension of infantile experience, the space relevant to perception, initially limited to present perception, is progressively broadened and identified first with the space of familiar surroundings, places of travel and play, and the region about the horizon of one's own experience. Finally, by way of information gleaned from stories and schooling, it is identified with terrestrial space, wherein the earth, with its complex of mutually similar objects, constitutes the privileged and absolute platform on which bodies exist and physical phenomena develop and about which the celestial sphere moves with the stars.

This geocentric representation, which has formed the space of humanity for thousands of years, has the same characteristics of absoluteness and independence of individual bodies, together with unity, center, and privileged directions, as the primitive representation in the child. When the Copernican revolution substituted the heliocentric system for the geocentric, it did not make essential modifications in the representation of space. A more decisive and revolutionary step was taken shortly afterward: this resulted from the recognition of the sun's equality with other stars, the recognition of equivalence in inertial systems, and the definitive renunciation of privileged centers and direction—all associated with the beginnings of modern mechanics, especially the work of Galileo galilei. Did these developments imply a renunciation of all systems of extrinsic reference for the position and movement of bodies or of all stable platforms for the description of physical phenomena? In the 17th century an affirmative answer would have demanded an audacity of which a genial poet might possibly have been capable, but not a methodical and reflective scientist such as Isaac Newton. A man of his times, Newton restricted himself to the path that seemed safer and less risky for him. For the egocentric, geocentric, and heliocentric platform, he substituted the notion of absolute space, existing by itself, always conformed to itself, and immobile, infinite, and eternal, without being dependent upon particular terrestrial and heavenly bodies.

From the psychological point of view, Newton's absolute space constitutes the projection of imaginary space into the world of physical reality, while maintaining the same characteristics of unity, absoluteness, and necessity. In fact, although the fantasy can imagine that it is suppressing all existing bodies, it cannot suppress imaginary space. This is a matter however, of psychological necessity deriving from the fact that the imagination is an organic faculty and, therefore essentially spatial. However, as a spiritual faculty, the intellect—which has being as such as its object—can discern (that is, judge, and not merely imagine) that the world and space itself would not exist if matter were totally annihilated. The intellect, then, can recognize that imaginary space is fictitious entity lacking reality in itself, independent of material bodies. This realization opens the door to a more rational consideration of space through the sciences of mathematics and physics.

Mathematical Aspect. Mathemathical space, which is the proper object of classical geometry and its more recent generalizations, can be defined as pure extension. Absolutely considered in its essence, abstracting from all the concrete conditions of its realization, as well as from every relation, either of dependence or of content, to real bodies. As such, it is absolutely possible extension.

Mathematical space received a systematic treatment, admirable for its logical rigor and completeness, in the Elements of Euclid about the year 300 b.c. Transmitted through Arabian culture to medieval Europe, this treatise still constitutes the nucleus of geometric knowledge for the person of ordinary culture. At the basis of this teaching there is a natural, uncritical, and directly realistic conception taking fundamental notions (point, line, surface, etc.) from spontaneous intuition. It proceeds from principles held as evident and necessary truths, and it claims that all its propositions contain absolute truth. Euclidean space is three-dimensional, homogeneous, and isotropic, as well as infinite, or rather, indefinite. In it, parallel straight lines are equi-distant; there is the possibility of similar figures, and the form of geometric things is independent of their position and extension. In short, Euclidean space is straight, having no curvature.

All the properties of Euclidean space can be deduced by introducing a postulate, namely, Euclid's fifth postulate, which states in substance that through a point external to a straight line one and only line can be drawn parallel to that line. The evidence and necessity of this postulate, and equivalent statements that have been substituted for it, have been disputed since the time of Euclid's first commentators. In fact, it constitutes an extrapolation from immediate intuition, lacking logical justification. The critique of Euclidean geometry, through the work of many mathematicians, such as K. F. Gauss, J. Bolyai (1802–60), N. I. Lobachevskĭ, and G. F. B. Riemann, has led to the conclusion that Euclid's postulate does not have an intrinsic and exclusive logical necessity, since it is possible to substitute opposite postulates for it. These lead to concepts of curved, hyperbolic, or elliptical spaces having properties different from those of Euclidean space, yet logically coherent and free from internal contradictions. This development has led to a generalization of the concept of mathematical space, further elaborated by the consideration of nonisotropic and differential spaces, of hyperspaces having more than three dimensions, and of functional spaces having infinite dimensions, etc.

The evolution of geometry, then, has shown the need for distinguishing the question of absolutely possible mathematical spaces from that of a really existing physical space. Rene descartes and classical physicists deemed these questions to be identical.

Physical Aspect. By physical space is meant the first, fundamental, dimensional quantity that, along with time, enables one to describe the emotion of bodies, define velocity as the derivative of space with respect to time, and, consequently, determine the position of the body at the term of its motion. Two questions are posited in reference to physical space: (1) Does physical space haven an existence distinct from the bodies that fill it (or can there be space without matter)? And (2) What are the properties of physical space?

As regards the first question, the Greek atomists, in opposition to parmenides, claimed that the void exists together with the plenum and that this is necessary for the multiplicity and motion of atoms. This teaching was restored by Pierre gassendi during the 17th century, in opposition to Descartes; the latter, identifying the essence of bodies with their extension, denied all possibility of empty space. Aristotle, and scholastic philosophers generally, deny the possibility of an absolute void; as a mere nonentity, this cannot exist in itself. Aristotelians explain the multiplicity and movement of bodies in terms of real divisibility of matter, itself made intelligible by the concept of potency. There would seem to be no validity Isaac Newton's arguments in favor of an absolute space independent of sensible bodies or fixed stars, since the position and movement of bodies can be explained in reference to the complex of sensible bodies or fixed stars, without recourse to a system of uncontrollable and purely imaginary reference. Physical space, then, is identical with the complex of extended bodies constituting the universe—not only directly sensible bodies, that is, solids, liquids, and gases, but also ether and the fields of modern physics.

As regards properties, man has always asked whether physical space is finite or infinite. According to the Ptolemaic conception, it was easy to deem physical space to be finite and limited by the outermost celestial sphere; according to the Copernican conception, however, one was led to think of space as open and infinite. More recently, equilibrium considerations in celestial mechanics and deductions from the theory of general relativity lead scientists to conceive of physical space as finite. In recent times a question has also arisen as to whether physical space is Euclidean or non-Euclidean. There is no absolute answer to this question, since all physical measurements for ascertaining the geometry of space are approximate and imprecise; one can speak only of a greater or lesser approximation to a geometric space. Within the limits of attainable measures and terrestrial experiments, physical space constitutes a good approximation to Euclidean space. Where astronomical distances are involved, however, it is more exact to say (in keeping with the theory of general relativity) that physical space is what Riemann has described it to be—elliptical, curved in its totality, and enclosed within itself, as a spherical hypersurface. Finally, as regards the relations between space and time, the theory of special relativity rejects the absolute separation of these categories and claims the existence of a sole spatial-temporal physical reality, the space-time continuum, wherein spatial and temporal relations among various bodies and events depend upon the state of reciprocal movement.

See Also: continuum; place; time; motion

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