When frequencies never synchronize: the golden mean and the resting EEG

Abstract

The classical frequency bands of the EEG can be described as a geometric series with a ratio (between neighbouring frequencies) of 1.618, which is the golden mean. Here we show that a synchronization of the excitatory phases of two oscillations with frequencies f1 and f2 is impossible (in a mathematical sense) when their ratio equals the golden mean, because their excitatory phases never meet. Thus, in a mathematical sense, the golden mean provides a totally uncoupled ('desynchronized') processing state which most likely reflects a 'resting' brain, which is not involved in selective information processing. However, excitatory phases of the f1- and f2-oscillations occasionally come close enough to coincide in a physiological sense. These coincidences are more frequent, the higher the frequencies f1 and f2. We demonstrate that the pattern of excitatory phase meetings provided by the golden mean as the 'most irrational' number is least frequent and most irregular. Thus, in a physiological sense, the golden mean provides (i) the highest physiologically possible desynchronized state in the resting brain, (ii) the possibility for spontaneous and most irregular (!) coupling and uncoupling between rhythms and (iii) the opportunity for a transition from resting state to activity. These characteristics have already been discussed to lay the ground for a healthy interplay between various physiological processes (Buchmann, 2002).