Fractal Time

Abstract

This work deals with an age-old problem of mankind in a highly modern original way. The geniuses of Aristotle and Mandelbrot are brought together for the first time. Few living scientists are in a position to undertake or venture upon such an attempt. The work is timeless. Even in a 100 years, it will still be characterised as difficult-despite the fact that it is written in an extraordinarily clear manner. One is reminded of Fichte's "Sonnenklarer Bericht", which is still, even today, characterised as obscure despite its transparency. The fundamentalidea of the work is a definition of duration which is based on content and may therefore be described objectively, independent of the momentary experience. Mozart's draft of a complete time contour before its first internal or external hearing was a determining motivation. Husserl's and Bieri's ideas and perceptions have been assimilated. If an experience becomes or may become ever richer with every new contemplation of it, this fact reveals something about the structure of time. The duration of tedium and its opposite become, in principle, formally capable of being grasped. Learning is seeing anew, is work on the past. These are convincing and, within the context of modern theory of the brain, unknown, insights. The may well gain neurobiological relevance.What is most amazing, however, is that Ms Vrobel succeeds in combining her own intuitive approach to the problem of time-an approach which has been shaped by the great history of philosophy-with the wholly new technical concept of self-similarity and self-affinity. Self-similar time series exist, for example, in dendrochronology, but also in music, in each case, across a certain scaling interval. The idea is to, again, turn this fact around, in order to apply it to the structure of the experienced time itself. This new epoché by Ms Vrobel is non-trivial. It may be used to define a machine which, in a recursive way, generates an ever-richer Now. This "Now" machine would-paradoxically-be independent of any embedding into a certain time interval. Ms Vrobel introduces here the novel concept of "condensation", which may be the most important technical concept of her work. There even arises-as she shows in the final paragraph of her work-an "ethical" problem. May we, at this stage, continue to think and build such a machine? It is rare for works of philosophy to be directly convertible into a possibly dangerous technology. The mere possiblity of such a thought says something about the originality of the work in question. We all know that scientific work is difficult and time-consuming, and that very few of the most original ideas survive. In spite of this, science lives off those few original ideas which emerge from such work. The number of original ideas in this work is far above average. The reader has undeniably the feeling of being witness to the emergence of a novel theoretical structure. One is impressed and mentally stretched by the emerging forming power. One is reminded of the originality of another Husserl disc...

Dark Energy and its Cosmic Density from Einstein’s Relativity and Gauge Fields Renormalization Leading to the Possibility of a New 'tHooft Quasi Particle

“…However the reader may find all these points and more adequately covered in Refs. [63][64][65][66][67][68][69][70].…”

A Rindler-KAM Spacetime Geometry and Scaling the Planck Scale Solves Quantum Relativity and Explains Dark Energy

“…We may also note that the theory of quantum sets was extensively developed by D. Finkelstein who also introduced the notion of quantum relativity [69][70][71][72][73][74][75][76][77]. We should add at this point that the KAM Cantorian spacetime theory has wider ramifications than only physics and cosmology and has found applications in brain and consciousness research by M. Persinger, C. Lavalle [78] as well as S. Vrobel's fundamental discourses into time, perception, music and love [79].…”

“…These particles and waves arise naturally from a KAM-like fractal-Cantorian spacetime which is the ultimate source of matter and fields [18,22,61]. Consequently this KAM spacetime picture is far more accurate than the ad hoc conventional picture of fractal spacetime [77][78][79][80][81] because we have only disjointed random sets interwoven together in an intricate manner but leaving only thin and fat Cantor sets to represent particles-zero sets and wave-empty sets respectively to form pre-space, pre-time and pre-matter to emerge from quantum spacetime geometry [10,14,18,22,61]. In other words, quantum mechanical entanglement is what is behind the geometry of spacetime and vice versa [20,21].…”

“…In what follows we would like to make the KAM spacetime picture more specific. As hinted at in the previous section Penrose fractal tiling universe [5,11,24] is the prototype par excellence of a noncommutative geometry reflecting the essence of K-theory [8] as well as E-infinity theory [5,16,18,79] and its bijection formula which gives the Hausdorff dimension as a function of the zero set topological dimension  and the topological dimension n [5,11]. The corresponding dimension function is given by A.…”

“…In other words, the present new derivation of the world's most celebrated formula explains in one stroke the two most puzzling problems of quantum physics and relativistic cosmology, namely the physico-mathematical meaning of the wave function and the nature of dark energy . In essence they are one and the same when looked upon from the view point of quantum-fractal geometry and KAM theorem [2,7,19,[69][70][71][72][73][74][75][76][77][78][79][80][81][82][83].…”