Retracted: New parallel theory (Q988740)

Editorial comment: The publisher has retracted this article on the basis that ``the authors have falsified mathematical findings and have made unsubstantiated claims regarding Euclid's parallel postulate. This article represents a severe abuse of the scientific publishing system.'' The following review tries to give a hint of the flavour of the paper. ``\textit{It is well known}'', says the abstract of the paper under review, ``\textit{that for a given line, there is only one parallel line through a point in Euclidean space, there are many parallel lines through a point in Lobachevskian space and there are no parallel through a point in spherical space. But in this work, the author has attempted and showed that there is a set of parallel segment spheres.}'' The introduction that follows talks about the history of geometry, and about Newtonian and quantum mechanics. One supposes that the next section, four lines long and entitled ``Construction and result'', clarifies the last sentence of the abstract. It says: ``\textit{In a sphere \(S\), choose two points \(A\) and \(B\) not lying on the poles \(N\) and \(S\) as shown in the spherical Fig. 1. At \(A\) and \(B\) erect two perpendiculars contacting at \(C\) and \(D\) on the opposite side of the perimeter. Einstein geometrically proved that a light source which originates at a point \(O\) will reach back this point \(O\). Einstein used spherical concepts for his proof. The same proof holds here also. So the segments \(AC\) and \(BD\) are parallel.}'' Then the last section discusses various issues. These include Gödel's incompleteness theorems, and then the difference between science, which ``\textit{is based on equations and experiments}'', and spirituality, which ``\textit{relies on beliefs}''. ``\textit{The spirituality}'', the author says, ``\textit{promises that everything in this universe was created in pairs but in opposites, origin and end, man and woman, light and dark, \(\dots\). Similarly, possible and impossible are consistent in mathematics.}'' The thirteen references at the end of the paper are written, either singly or jointly with others, by the same author.