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Mathematical aesthetic principles and nonintegrable systems

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This article is an outline of the talks given by Muraskin and is a summary of his book “Mathematical Aesthetic Principles/Nonintegrable Systems” published by World Scientific Press in 1995, as well as many articles published by him, and also includes some additional observations. The discussion presents a study of a set of mathematical principles that can be classified as “aesthetic” and shows that these principles can be cast into a set of nonlinear equations. The system of equations is nonintegrable in general. New techniques to handle the nonintegrability feature are discussed. We then illustrate how this system of equations leads to sinusoidal solutions, sine within sine solutions, the phenomenon known as beats, random type oscillations, two and three-dimensional lattices, as well as multiwave packet systems. The sinusoidal solutions occur when the arbitrary data associated with the equations cause the equations to be linearized. The sinusoidal behavior totally disappears once the integrability equations are satisfied, illustrating how important the nonintegrability concept is to the development.
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Keywords: Mathematical Aesthetics; Mathematical Model Universes; Nonintegrable Systems; Nonlinear Equations

Document Type: Research Article

Publication date: September 6, 2015

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  • Physics Essays has been established as an international journal dedicated to theoretical and experimental aspects of fundamental problems in Physics and, generally, to the advancement of basic knowledge of Physics. The Journal's mandate is to publish rigorous and methodological examinations of past, current, and advanced concepts, methods and results in physics research. Physics Essays dedicates itself to the publication of stimulating exploratory, and original papers in a variety of physics disciplines, such as spectroscopy, quantum mechanics, particle physics, electromagnetic theory, astrophysics, space physics, mathematical methods in physics, plasma physics, philosophical aspects of physics, chemical physics, and relativity.
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