Arturo Tozzi (corresponding Author),
Center for Nonlinear Science, University of North Texas
1155 Union Circle, #311427 Denton, TX 76203-5017 USA
James F. Peters
2 Department of Electrical and Computer Engineering, University of Manitoba
75A Chancellor’s Circle Winnipeg, MB R3T 5V6 CANADA and
Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
The first definition (prior to the well-known five postulates) of Euclides describes the point as “that of which there is no part”. Here we show how Euclides’ account of manifolds is untenable in our physical realm and that the concepts of points, lines, surfaces, volumes need to be revisited, in order to allow us to be able to describe the real world. Here we show that the basic object in a physical context is a traversal of spacetime via tiny subregions of spatial regions, rather than the Euclidean point. We also elucidate the psychological issues that lead our mind to think to points and lines are really existing in our surrounding environment.