14. Space as all-inclusive category
A lot of mathematical and physical proof found in the ancient time and at present bears witness to the three-dimensionality of the continued space. Aristotle gave the clearest statement of the space three-dimensionality. He asserted that a line has one dimension. If we add one more dimension to the line, we can get a plane. If we add one more dimension to the plane, we can get a volume. This volume will possess a length, a width and a height, i.e. three dimensions.
This conclusion is corroborated by the following obvious within Euclidean geometry definitions. The position of a point on a strait line is determined by one number - by one coordinate. To define the position of the point on a plane you will need two coordinates, in space (volume) - three numbers or three coordinates. The other conclusion corroborating the space three-dimensionality and also resulting from Euclidean geometry: space has three dimensions since one can draw three and only three mutually perpendicular lines at one point.
Assuming three-dimensionality of the space, we thereby recognize that the position of any point in the space can be determined by three coordinates. However, the coordinates of any system (Cartesian, polar, elliptic, curvilinear etc.) are peculiar kinds of "scaffolding" and are of a subjective nature. They are introduced for analysis of the geometric or physical continuum. If the continuum has no breaks, the position of the point can always be determined within the Cartesian or other coordinate system.
Recent investigations showed that the physical state cannot be sufficiently described using four spatial coordinates that have a dimension of length. In this case the causality principles would be violated. For the four-dimensional (as well as for the 4+1-dimensional) space, the Huygence principle, providing the basis for optics, would be broken .
Using the results of physical observations the philosopher Immanuel Kant concluded that the three-dimensionality of space is proved by the fact that the acting force is inversely proportional to the distance squared from the point source in the space. As is well known, within gravitational and electric fields the acting forces decrease proportionally to the distance squared. Elliptical orbits of planets that circle the Sun are stable only because the physical space is three-dimensional.
The visible space of the universe is filled with the ether medium. Due to the influence of the astronomic masses (black holes, Galaxies, stars, planets, dark substance etc.) and powerful magnetic and electrical fields, the ether medium including that in the interstellar space is deformed. Gravitation of physical (astronomic) bodies is a consequence of the ether medium deformity. Great deformations of this medium near very massive bodies cause a formation of the so-called gravitational lenses. Rays of light would not propagate along a strait line in the deformed ether medium. This has been proved many times, for instance, during the earth observations of the passing of the far stars' rays near the solar disk [60, 70].
To analyse the universe geometry astronomers can use only the objects radiating light and take observations on the trajectories of electromagnetic and light waves. The observations on the so-called gravitational lenses gave rise to the notion that space is subject to the geometry of Riman or Lobachevsky. However the geometry of space is Euclidean. At the same time the ether medium in which electromagnetic radiation (including visible light) propagates can possess geometry that differs from the Euclidean one.
S.A. Tochelnikova-Murri suggested the following definition of the visible (within the attainability of observations taken by astronomical instruments) space : "Since the distances to farther objects defined by other methods depend on the values of trigonometric parallaxes of stars, one may state that the universe space is Euclidean, but it would be more precise (from the gnoseology point of view) to put it in other words: the Euclidean geometry, elaborated on the basis of the movement studies in the terrestrial conditions and in the near-earth space, serves as a theoretical foundation during determining distances in the universe".
Riman's or Lobachevsky's geometry can under certain conditions be applied only to the ether medium filling the space.