The golden mean, scale free extension of real number system, fuzzy sets and \(1/f\) spectrum in physics and biology. (English) Zbl 1032.26502

Summary: We show that the generic \(1/f\) spectrum problem acquires a natural explanation in a class of scale-free solutions to the ordinary differential equations. We prove the existence and uniqueness of this class of solutions and show how this leads to a nonstandard, fuzzy extension of the ordinary framework of calculus, and hence, that of the classical dynamics and quantum mechanics. The exceptional role of the golden mean irrational number is also explained.


26E50 Fuzzy real analysis
00A79 Physics
26E35 Nonstandard analysis
34A99 General theory for ordinary differential equations
81P05 General and philosophical questions in quantum theory
92B99 Mathematical biology in general
Full Text: DOI arXiv


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