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A Topological Approach to Infinity in Physics and Biophysics

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Abstract

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.

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Modified from: CFD Moduule. https://www.technic.com.au/products/cfd/ (Retrieved 2018). c One of the feasible modifications of the Alexander horned sphere. Here two opposite logistic plots are inserted into the branched section of the horned torus

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Authors and Affiliations

  1. Center for Nonlinear Science, Department of Physics, University of North Texas, 1155 Union Circle, #311427, Denton, TX, 76203-5017, USA

    Arturo Tozzi

  2. Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg, MB, R3T 5V6, Canada

    James F. Peters

  3. Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040, Adıyaman, Turkey

    James F. Peters

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  1. Arturo Tozzi
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Correspondence to Arturo Tozzi.

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Tozzi, A., Peters, J.F. A Topological Approach to Infinity in Physics and Biophysics. Found Sci 26, 245–255 (2021). https://doi.org/10.1007/s10699-020-09674-0

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