The principle of information coding by the brain seems to be based on the golden mean. For 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 2Φ, where half of the fundamental is the golden mean Φ (=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. 2Φ=3+φ3. Similarities with El Naschie’s theory for high energy particle’s physics are also discussed.