Numerical Uncertainty and Its Implications

António F. Rodrigues; Nuno O. Martins

doi:10.4236/jamp.2014.23004

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Numerical Uncertainty and Its Implications ()

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DOI: 10.4236/jamp.2014.23004 4,505 Downloads 7,360 Views Citations

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António F. Rodrigues, Nuno O. Martins

Affiliation(s)

Campus de Angra do Heroísmo, University of the Azores, Angra do Heroísmo, Portugal.

ABSTRACT

A scrutiny of the contributions of key mathematicians and scientists shows that there has been much controversy (throughout the development of mathematics and science) concerning the use of mathematics and the nature of mathematics too. In this work, we try to show that arithmetical operations of approximation lead to the existence of a numerical uncertainty, which is quantic, path dependent and also dependent on the number system used, with mathematical and physical implications. When we explore the algebraic equations for the fine structure constant, the conditions exposed in this work generate paradoxical physical conditions, where the solution to the paradox may be in the fact that the fine-structure constant is calculated through different ways in order to obtain the same value, but there is no relationship between the fundamental physical processes which underlie the calculations, since we are merely dealing with algebraic relations, despite the expressions having the same physical dimensions.

KEYWORDS

Geometry; Algebra; Numerical Uncertainty; Fine Structure Constant and Physical Uncertainty

Cite this paper

Rodrigues, A. and Martins, N. (2014) Numerical Uncertainty and Its Implications. Journal of Applied Mathematics and Physics, 2, 33-44. doi: 10.4236/jamp.2014.23004.

Conflicts of Interest

The authors declare no conflicts of interest.

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