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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boolos, G.S., Burgess, J.P., Jeffrey, R.C.: Computability and Logic. Cambridge Univ. Press, New York (2007)
Cantor, G.: Contributions to the Founding of the Theory of Transfinite Number. Dover, New York (1915)
Chalmers, D.: On Implementing a Computation. Mind and Machines 4, 391–402 (1994)
Kintchin, A.: Mathematical Foundations of Information Theory. Dover, London (1963)
Parisi, G.: Statistical Field Theory. In: Frontiers in Physics. Addison-Wesley Publishing Company (1988)
Rosen, R.: Church’s thesis and its relation to the concept of realizability in biology and physics. Bulletin of Mathematical Biology 24, 375–393 (1962)
Petersen, I., Shaiju, A.: A Frequency Domain Condition for the Physical Realizability of Linear Quantum Systems. IEEE Transactions on Automatic Control (9) (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hernández-Quiroz, F., Padilla, P. (2013). Some Constraints on the Physical Realizability of a Mathematical Construction. In: Dodig-Crnkovic, G., Giovagnoli, R. (eds) Computing Nature. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37225-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-37225-4_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37224-7
Online ISBN: 978-3-642-37225-4
eBook Packages: EngineeringEngineering (R0)