Are Borders Inside or Outside?
- PDF / 1,208,899 Bytes
- 17 Pages / 439.37 x 666.142 pts Page_size
- 0 Downloads / 217 Views
Are Borders Inside or Outside? Arturo Tozzi1 Accepted: 27 September 2020 © Springer Nature B.V. 2020
Abstract When a boat disappears over the horizon, does a distant observer detect the last moment in which the boat is visible, or the first moment in which the boat is not visible? This apparently ludicrous way of reasoning, heritage of long-lasting medieval debates on decision limit problems, paves the way to sophisticated contemporary debates concerning the methodological core of mathematics, physics and biology. These ancient, logicallyframed conundrums throw us into the realm of bounded objects with fuzzy edges, where our mind fails to provide responses to plain questions such as: given a closed curve with a boundary (say, a cellular membrane) how do you recognize what is internal and what is external? We show how the choice of an alternative instead of another is not arbitrary, rather points towards entirely different ontological, philosophical and physical commitments. This paves the way to novel interpretations and operational approaches to challenging issues such as black hole singularities, continuous time in quantum dynamics, chaotic nonlinear paths, logarithmic plots, demarcation of living beings. In the sceptical reign where judgements seem to be suspended forever, the contemporary scientist stands for a sort of God equipped with infinite power who is utterly free to dictate the rules of the experimental settings. Keywords Infinity · Boundary · Jordan curve theorem · Bradwardine · Nicholas of autrecourt Take an object with a border separating the internal from the external. We might ask: is the boundary inside or outside the object? At the very edge of the closed curve, does the last point of the internal occur, or the first point of the external? Medieval scholars confronted diverse types of these challenges that are currently termed “limit decision problems”. The ancient theologians/philosophers/scientists used the weapons available to them, i.e., Aristotelian analytic arguments and thought experiments, to appraise the limits and degrees of “powers” such as time, length, weight, distance, and so on (Offredus 1478; Nielsen 1982). Here I examine the subtleties of limit decision problems going through apparently silly questions such as: “the present time stands for: the current instant, or the last instant * Arturo Tozzi [email protected]; [email protected] 1
Department of Physics, Center for Nonlinear Science, University of North Texas, 1155 Union Circle #311427, Denton, TX 76203‑5017, USA
13
Vol.:(0123456789)
A. Tozzi
of the past, or the first instant of the future?” It is straightforward to claim that this intricate way of reasoning is perplexing for the baffled modern-day readers. Who cares about weird medieval enterprises such as the search for “incipit” and “desinit” (i.e., the “beginning” and the “end”)? What is the practical gist of absurd questions such as: “when we look at a boat disappearing over the horizon, does exist the last instant in which we see the boat, or the first
Data Loading...
