Abstract
Do you believe that science is based on contradictions? Let me consider the common experience of seeing a dot of the pencil on a paper. If I call the dot ``zero length dimension'' or ``zero extension'', then certainly I have seen `nothing'. But, if I have seen `nothing', I wonder how I can refer to `nothing', let alone naming `nothing' as ``a point''. Therefore, the expression ``zero length dimension'' is a contradiction. Mathematical science, as of now, is based on this contradiction that results from the attitude of exactness, because exact ``zero'' is non-referable and inexpressible. Such attitude leads to incomplete statements like ``infinitesimal quantities'' which never mention ``with respect to'' what. Consequently, as I find, science becomes fraught with singularity and the definition of `field' seems either circular or incomplete in reasoning. I avoid this contradiction, by accepting my inability to do exact science. Therefore, I consider the dot as of ``negligible length dimension''. It is a practical statement rather than a sacrosanct axiom. The practicality serves the purpose of drawing geometry, that becomes impossible if I decide or choose to look at the dot through a magnifying glass. It then answers a different practical question, namely, what the dot is made up of. Certainly, reality of the dot depends on how I choose or decide to observe it. This is the essence of ``relational existence''. On the contrary, modern mathematical science is founded upon belief of ``independent existence''(invariant). My belief in inexact mathematical science and relational existence needs the introduction of an undecidable length unit to do arithmetic and leads to non-singular gravity. Further, the quest for justification of my choice or decision leads to my incompleteness -- ``I''-- the undecidable premise beyond science, the expression of which is a (useful) contradiction in itself as ``I'' is inexpressible.
Abhishek Majhi