Motivated by such philosophy of loop quantum gravity, recently it has been shown that such conceptions can be realized through some elementary constructions based on the refinement of the first axiom of geometry, namely, the concept of a point by considering Klein's prescription of accounting for the extension of a small spot that represents or demonstrates a point, which was a programmatic call that he called as a fusion of arithmetic and geometry. Klein's program, according to Born, was actually a mathematical route to consider 'natural uncertainty in all observations' while describing 'a physical situation' by means of 'real numbers'.