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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Unpredictability of Coin Tossing in the Most Sensitive Regions of the Phase Space

Discontinuity, Nonlinearity, and Complexity 4(1) (2016) 79--89 | DOI:10.5890/DNC.2016.03.006

Zengyuan Yue

Institute of Training Science and Sport Informatics, German Sport University Cologne, 50933 Cologne, Germany

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Abstract

Detailed calculations reveal that the sensitivity of the dependence of the result of coin toss (head or tail) on the initial state in the phase space is not only very inhomogeneous but also fractal. In the most sensitive regions, the number of turns of the coin is still fluctuating as the initial height changes within the atomic scale. Thus, the predictability of the toss of a real coin fails in these regions. The portion of such unpredictable regions with sub-atomic sensitivity becomes dominant in the phase space with the improvement of the elasticity of the surface. This offers one unique example in the macroscopic physics that macroscopic determinism fails due to the extreme sensitivity. This also helps to understand why the long-time accurate weather report is not possible.

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