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NEWSCIENCENEWSCIENCENEWSCIENCE Natural Standard Measures: The Key to Global Scaling clusters) arise on the logarithmic number Natural Standard Measures: The Key chain systems. In 1982, Miiller showed that line, there it is that matter concentrates on to Global Scaling the distribution of matter in logarithmic the logarithmic line of measures. This isn't Exact knowledge of the harmonic struc- _ space also has a continued fraction structure. magic; it is simply a consequence of the fact ture of logarithmic space is the gateway to This structure provides that the concentra- that scales are logarithms, i.e., "just" global scaling. In order to open the gate, one __ tion of matter increases hyperbolically in the numbers. needs the key: natural standard measures _ proximity of node points. So the logarithmic line of scales is (see table 1 on opening page). In first approximation, the distribution of nothing else but the logarithmic number Natural standard measures are themselves _ matter in the logarithmic space of scales has line. And because the standing pressure values of node points. In the node point ofa _ the fractal dimension of Cantor dust, but is wave is a property of the logarithmic _ standing wave, vibrations do not occur; there being deformed hyperbolically in the prox- number line, it determines the frequency of is stillness. This is why natural standard imity of a node point (see illustration). distribution of matter on all physically | measures have a high degree of stability. The mathematical aspect is to be found in calibrated logarithmic lines—the line of | The rest mass of the proton remains stable _ the realisation that not only is it possible to ratios of size, that of masses, of frequencies, over a minimum of 10” years. For the same represent every number as a continued frac- temperatures, velocities, etc. tion, but the distribution of numbers on Now, in order to find a node point on the logarithmic number line altogether the logarithmic line, one only needs the Exact knowledge of the can be represented as such. number line (that everybody knows) and harmonic structure of : This mathematical aspect has jm andr eco wit whch | fagarithmic space is the nmetits nossa The wavelength of the standing density gateway to global scaling. in the natural sciences, sociology or wave on the logarithmic number line is economy—one will encounter the known. The distance between adjacent In order to open the gate, phenomenon that there are certain node points is three units of the natural . attractor values that all systems, totall logarithm. Thus it is easy to calculate one needs the key: independent of their character, prefer, and all nodal values Xn by the simple natural standard measures. that the distribution of these attractor formula Xn = Y x exp(n) (Y being a values along the logarithmic number line natural standard measure, n = 0, + -3, + follows a (fractal) continued fraction rule. -6,+-9, ...). reason also, the speed of light in a vacuum This continued fraction rule "contains" Frequency values of node points are, for constitutes a rather obstinate value. The physics, chemistry, biology and sociology example, 5 Hz (n=-54), 101 Hz (n=-51), _ existence of stable natural standard measures _ insofar as these disciplines work with scales 2032 Hz (n=48), 40.8 kHz (n=-45), 820 _ is the physical basis of a natural metrology (real numbers), i.e., insofar as measurements kHz (n=-42), 16.5 MHz (n=-39), 330.6 on which Global Scaling Theory rests. are made. Many results of complicated MHz (n=-36), etc. The frequency ranges large-scale measurings therefore can be rela- around 5 Hz, 100 Hz, 2 kHz, etc. are predes- Continued Fractions as a "World tively easily pre-calculated within the frame tined for energy transmission in finite media. Formula" of Global Scaling Theory; for example, the This is also where the carrier frequencies In 1950, Gantmacher and Krein proved _ temperature of the cosmic microwave back- for information transmission in logarithmic _ that the spatial distribution of free-moving ground radiation, whose value cannot be space are located. Frequencies that occur _ particles in linear oscillating chain systems _ larger than Tp x exp(—29) = 2.7696 K; the near a node point are not just very common can be described by a continued fraction rest mass of the neutron m, = Mp x in nature but are also used in technological (see below). Terskich (1955) was able to exp(1/726) = 939.5652 MeV, as well as the applications. prove the same for non-linear oscillating _ rest masses of other elementary particles. Exact knowledge of the harmonic structure of has logarithmic space is the gateway to global scaling. In order to open the gate, one needs the key: natural standard measures. Continued Fractions as a "World Formula" In 1950, Gantmacher and Krein proved that the spatial distribution of free-moving particles in linear oscillating chain systems can be described by a continued fraction (see below). Terskich (1955) was able to prove the same for non-linear oscillating Creation's Melody In the context of Global Scaling Theory, the hypothesis of the Big Bang appears in a new light. A propagating shock wave (pres- sure wave) in linear space (the echo of the hypothetical primeval explosion) is not the cause of cosmic microwave background radiation, but a standing pressure wave in logarithmic space is. It is also responsible for the fractal and logarithmic scale-invari- ant distribution of matter in the entire uni- verse. It created the universe as we know it, and recreates it continually. It is the cause of all physical interactions and forces— gravitation, electromagnetism, nuclear = LO180939R875 = 27182818. 52 = NEXUS Continued on page 82 www.nexusmagazine.com AUGUST - SEPTEMBER 2004