The golden mean, scale free extension of real number system, fuzzy sets and 1/f spectrum in physics and biology

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. (C) 2003 Elsevier Science Ltd. All rights reserved.