The Golden mean, scale free extension of Real number system, fuzzy sets and $1/f$ spectrum in Physics and Biology.

link: http://arxiv.org/abs/1001.1688
Abstract

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.