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Abstract The principle of information coding by the brain seems to be based on the golden mean. Since decades psychologists have claimed memory span to be the missing link between psychometric intelligence and cognition. By applying Bose-Einstein-statistics to learning experiments, Pascual-Leone obtained a fit between predicted and tested span. Multiplying span by mental speed (bits processed per unit time) and using the entropy formula for bosons, we obtain the same result. If we understand span as the quantum number n of a harmonic oscillator, we obtain this result from the EEG. The metric of brain waves can always be understood as a superposition of n harmonics times 2 F, where half of the fundamental is the golden mean F (= 1.618) as the point of resonance. Such wave packets scaled in powers of the golden mean have to be understood as numbers with directions, where bifurcations occur at the edge of chaos, i.e. 2 F = 3+ f3. Similarities with El Naschie’s theory for high energy particle’s physics are also discussed.
At the most basic level, if different frequencies are generated by entirely different local networks it is reasonable to suggest that the purpose is to keep activity coded in each frequency band separate – i.e. to minimise cross-frequency interference. But how best to achieve this? The pattern of neuronal connectivity within a single cortical column is extremely rich (Binzegger et al., 2004; Thomson et al., 2002), making it likely that even local networks in completely different laminae may readily interact. A solution to the interference problem can be found if the ratio of frequencies is ‘irrational’ . In this situation the two rhythms never fully synchronise and the phase relationship between frequencies constantly changes. Coexistent gamma and beta2 rhythms in association cortex provide an example of this method from minimising interference. The two rhythms are generated in different cortical laminae and survive physical separation of these laminae. The ratio of modal peak frequencies is approximately phi, resulting in a periodic pattern of change in low-level synchrony between laminae with period equal to the sum of the two periods of oscillation present. This phenomenon can occur, to some extent, with any pair of co-expressed frequencies. However, in using phi as a common ratio between adjacent frequencies in the EEG spectrum , the neocortex appears to have found a way to pack as many, minimally interfering frequency bands as possible into the available frequency space.