The golden mean as a clock cycle for brainwaves

In the publication Chaos, Solitons & Fractals 18 (2003), Harald Weiss and Wolkmar Weiss published the most interesting scientific paper I ever read. I confess I didn’t understand all of it, it’s too interdisciplinary for me, but the proposition is most interesting. The abstract reads:

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 (= 1.61 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.

They used statistical mechanics used in quantum effects to model the distribution of learning and found staggering similarities with the results of other scientists. This paper suggests that short term memory span is related to intelligence, brain processing speed and age (more short term memory span is indicator of greater intelligence and processing speed). No only related, but as the driving quantum measure for the shape of brainwaves. Mapping the variance of this memory span as an oscillator, the fundamental harmonic was found to be 2Phi (Phi being 1.6180339…)

Incredibly this has been gaining strenght with other experiments:

“The distribution of the time elapsed between two consecutives spikes in the firing response of visual cortex neurons has been studied in cat [40] and macaque [41]. The distribution of time intervals clearly follows a power law over several orders of magnitude. In both experiments the exponent of the time separating two firings was roughly equal to 1.60 ( » F).”

[40] Koch C. Computation and the single neuron. Nature, 1997; 385:207-210

[41] Papa ARR, Da Silva L. Earthquakes in the brain. Theory in Biosciences, 1997, 116: 321-327

The brainwaves having a fundamental harmonic of 2Phi, implies that all other harmonics are infinitesimals or multiples of Phi, including the resonant frequencies which are powers of 2Phi/2. Even more, the brain can use powers of the golden section or the infinite Fibonacci word for its coding.

This paper also refers the idea that universe is a Cantorian space-time (a certain type of fractal), developed by El Naschie. Fractals have fractional dimensions called Hausdorff dimension (not 1, 2 or 3, but for example 1.5138…) and this specific Cantor space-time proposed by El Naschie, barely touches full chaos, it is stable on the route to chaos, and has an Hausdorff dimension of a certain power of the golden mean which is (1 + f)³

(f being 0.6180339…)

I do really believe that the golden mean is as important in the universe as it seems to be and that this universe is a simple dynamic fractal. It is at these moments that I hit myself for not paying any attention to math and physics classes =)

~ by Anima Within on Monday, 19 November 2007.