A Topological Approach to Infinity in Physics and Biophysics

Physical and biological measurements might display range values extending towards infinite. The occurrence of infinity in equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical and biophysical equations. In this unconventional approach, a continuous monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations. In other words, we may state that Achilles leaves the straight line and overtakes the turtle.
Author(s): Arturo Tozzi [sup.1] , James F. Peters [sup.2] [sup.3] Author Affiliations: (1) grid.266869.5, 0000 0001 1008 957X, Center for Nonlinear Science, Department of Physics, University of North Texas, , [...]