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NEWSCIENCENEWSCIENCENEWSCIENCE distance from each other; nor could he fig- ure out why only certain sizes would be advantageous for the survival of a species and what these advantages actually are. Cislenko's work caused the German scien- tist Dr Hartmut Miiller to search for other scale-invariant distributions in physics, as the phenomenon of scaling was well known in high-energy physics. In 1982, he was able to prove that there exist statistically identical frequency distributions with loga- rithmic, periodically recurrent maximums for the masses of atoms and atomic radii as well as the rest masses and life-spans of ele- mentary particles. Miiller found similar frequency distributions along the logarithmic line of the sizes, orbits, masses and revolution periods of the planets, moons and asteroids. Being a mathematician and physicist, he did not fail to recognise the cause of this phenomenon in the existence of a standing pressure wave in the logarithmic space of the scales/measures. Say we have measured 12 cm, 33cmand_ that most natural systems will avoid. 90 cm. Choosing as the standard measure Growing crystals, organisms or populations (etalon) 1 cm, we will get the number that reach the limits of such sections on the sequence 12...33...90 (without measure- _ logarithmic line either will grow no more or ment unit or, as the physicist would say, will begin to disintegrate, or else will with unit 1). The distances between these accelerate growth so as to overcome these numbers on the number line are 33 - 12 = __ sections as quickly as possible. 21 and 90 — 33 = 57. If we were to choose The Institute for Space Energy Research another measuring unit such as the ell, with in memory of Leonard Euler (Institut fiir 49.5 cm, the number sequence will be Raum-Energie-Forschung, IREF) was also 0.24...0.67...1.82. The distance between able to prove the same phenomenon in the numbers has changed. It is now 0.67- demographics (stochastic of worldwide 0.24 = 0.42, and 1.82 — 0.67 = 1.16. Onthe urban populations), in economics (stochastic logarithmic line, the distance will not — of national product, imports and exports change; no matter what measuring unit we — worldwide) and in business economics (sto- choose, it remains constant. In our example, _ chastic of sales volume of large industrial this distance amounts to one unit of the nat- and middle-range enterprises, stochastic of ural logarithm (In) (with radix e = worldwide stock exchange values). 2.71828...): In 33 - In 12 = In 90 - In 33 = The borders of "attractive" and In 0.67 — In 0.24 = In 1.82 - In 0.67 = 1. "repulsive" segments on the logarithmic line Physical values of measurement therefore _ of scales are easy to find because they recur own the remarkable feature of logarithmic regularly with a distance of three natural invariance (scaling). So, in reality, any scale logarithmic units. This distance also defines is a logarithm. the wavelength of the standing pressure It is interesting that natural systems are —_ wave: it is six units of the natural logarithm. not distributed evenly along the logarithmic By its anti-nodes, the global standing line of the scales. There are "attractive" pressure wave replaces matter on the loga- sections which are occupied by a great __ rithmic line of scales and concentrates mat- number of completely different natural ter in the node points. Thus in the transit systems; and there are "repulsive" sections from wave peak (anti-node) to wave node, there occurs a tendency of fusion; while at the transition from node point to anti-node, disintegration tendencies arise. This process causes a logarithmic periodical change of structure. Packed and unpacked systems alternately dominate on the logarithmic line of measures at distances of 3k, i.e., 3, 9, 27, .? a 81 and 243 units of the natural logarithm. The Logarithmic World of Scales What actually is scale? Scale is what physics can measure. The result of a physi- cal measurement is always a number with a measuring unit, a physical quantity. The distribution of matter in the logarithmic space of scales (above) in first approximation has the fractal dimension of Cantor dust (below left), but is deformed hyperbolically in the proximity of a node point (below right) Sound Waves in Logarithmic Space as Cause of Gravitation The existence of a standing density wave in logarithmic space explains, for the first time in the history of physics, the origin of gravitation. The global flow of matter in the direction of the node points of the standing density wave is the reason for the physical phenomenon of gravitational attraction. Thus particles, atoms, molecules, celestia bodies, etcetera—the scales/measures of which stabilise in the node points of the standing pressure wave—become gravitational attractors. In physical reality, therefore, the standing density wave in the logarithmic space of scales also manifests as a global standing gravitational wave. In consequence, the exact identity of value for inert and gravita- tional masses of physical bodies (as it is claimed by physics today), independent of The continued fractional structure of the distribution of matter in logarithmic space ensures that the concentration of matter in the proximity of the node point increases hyperbolically. 50 + NEXUS www.nexusmagazine.com AUGUST — SEPTEMBER 2004