Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

224939

Some constraints on the physical realizability of a mathematical construction

Francisco Hernández-QuirozPablo Padilla

pp. 235-240

Abstract

Mathematical constructions of abstract entities are normally done disregarding their actual physical realizability. The definition and limits of the physical realizability of these constructions are controversial issues at the moment and the subject of intense debate.In this paper, we consider a simple and particular case, namely, the physical realizability of the enumeration of rational numbers by Cantor's diagonalization by means of an Ising system.We contend that uncertainty in determining a particular state in an Ising system renders impossible to have a reliable implementation of Cantor's diagonal method and therefore a stronger physical system is required. We also point out what are the particular limitations of this system from the perspective of physical realizability.

Publication details

Published in:

Dodig Crnkovic Gordana, Dodig-Crnkovic Gordana, Giovagnoli Raffaela (2013) Computing nature: turing centenary perspective. Dordrecht, Springer.

Pages: 235-240

DOI: 10.1007/978-3-642-37225-4_15

Full citation:

Hernández-Quiroz Francisco, Padilla Pablo (2013) „Some constraints on the physical realizability of a mathematical construction“, In: G. Dodig Crnkovic, G. Dodig-Crnkovic & R. Giovagnoli (eds.), Computing nature, Dordrecht, Springer, 235–240.