The love of mathematics does not imply the ability to solve real life’s mysteries. Nevertheless, logical thinking alone, could more than enough, provides ample means of understanding physical reality. To become enchanted with the power of mathematics is to uphold its continued utility regardless of its illogical misunderstanding. A state of mathematical abstraction disenchantment (MAD) could gradually becoming more and more obvious when a mathematical structure under study and discussion becoming more and more abstract, alienating from a metric structure in addition to separating from an affine structure becoming the sojourn or rest area of pure abstraction appearing as a differentiable manifold. Its sole definable property is the derivative, existing in a domain rules by a theory of limit and an axiom of choice.
However, a differentiable manifold could not respond to questions regarding non-metrical or topological properties, whether the fact that its space and time domain “go on forever” or “have boundaries” or whether there are “holes” in them or not. It is for these reasons that a differentiable manifold is useless for a full description of all points of quantum spacetime which is necessarily compact, multiply-connected, and nonorientable in singular dimension.


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