The majority of theoretical misconceptions and the most significant misunderstandings in modern astronomy, cosmology and physics are caused by a purely mathematical approach and ignoring philosophical comprehension of physical reality and, as a result, by not deep enough understanding of the essence of certain physical phenomena and objects. Foremost, it's all about phenomena and objects that are under consideration by Special and General Relativity.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not co-moving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in Weyl FR, when it has hollow topological form in the space of Weyl FR and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed.