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The golden mean as clock cycle of brain waves
Excerpt:
The golden mean as clock cycle of brain waves
- Harald Weiss, Volkmar Weiss
Cite: https://doi.org/10.1016/S0960-0779(03)00026-2
Abstract
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.
Introduction
“It bothers me that, according to the laws as we understand them today, it takes … an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what a tiny piece of space–time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities,” wrote Feynman in 1965 (cited from [1], p. 638). Wolfram [2], too, believes that there are quite simple mechanisms that underlie human reasoning. He asserts that the use of memory is what in fact underlies almost every aspect of human thinking. Capabilities like generalization, analogy and intuition immediately seem very closely related to the ability to retrieve data from memory on the basis of similarity.
Already in 1966, Kac [3] had put forward the question: Can one hear the shape of a drum? In order to find an answer, Kac asks for the energy in the frequency interval df. To this end, he calculates the number of harmonics which lie between the frequencies f and df and multiplies this number by the energy which belongs to the frequency f, and which according to the theory of quantum mechanics is the same for all frequencies. By solving the eigenvalue problem of the wave equation, Kac is able to state that one can not only hear the area of a reflecting surface, its volume and circumference, but also the connectivity of paths of an irregular shaped network. If the brain waves had the possibility to measure and hence to know the eigenvalues of a spatially distributed information amount, they would have nearly perfect access to information and––in terms of communication theory––perform nearly perfect bandlimited processing. As we know, the eigenvalues are proportional to the squares (i.e. variances) of resonant frequencies [4].
The question whether brain waves reflect underlying information processing is as old as EEG research itself. Therefore, relationships between well-confirmed psychometric and psychophysiological empirical facts [5] and EEG spectral density are very interesting.