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III. An Organic, Conducive, Habitable MultiUniVerse

F. Systems Cosmology: Fractal SpaceTimeMatter

Krioukov, Dmitri, et al. Network Cosmology. Nature Scientific Reports. 2/793, November, 2012. On occasion, a paper comes along of such unique, meritous content that it bodes for a significant breakthrough and synthesis. A team of five University of California, San Diego, systems scientists with Marian Boguna, a University of Barcelona physicist, proceed via sophisticated quantifications to discern the same nonlinear dynamics that infuse from proteins to cities within celestial topological networks. Its technical acumen and depth requires several excerpts. For example, Figure 2, “Mapping between the de Sitter universe and complex networks” illustrates many isomorphic affinities. As per Figure 4, “Degree distribution and clustering in complex networks and space time,” Internet, social network, brain anatomy, and hyperbolic spatial lineaments all graph on the same line, indicating common node and link geometries. As the quotes allude, a grand unification of universe, life, cognition, and humankind could be in the offing, a nascent witness of a biological genesis uniVerse.

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology. (Abstract)

Physics explains complex phenomena in nature by reducing them to an interplay of simple fundamental laws. This very successful tradition seems to experience certain difficulties in application to complex systems in general, and to complex networks in particular, where it remains unclear if there exist some unique universal laws explaining a variety of structural and dynamical similarities found in many different real networks. One could potentially remedy this situation by identifying a well-understood physical system whose large-scale dynamics would be asymptotically identical to the dynamics of complex networks. One could then try to use the extensively studied dynamical laws of that physical system to predict and possibly control the dynamics of networks. (1)

We show here that there exists a very simple but completely unexpected connection between networks and cosmology. In cosmology, de Sitter spacetime plays a central role as the exact solution of Einstein’s equations for an empty universe, to which our universe asymptotically converges. Here we show that graphs encoding the large-scale causal structure of de Sitter spacetime and our universe have structure common to many complex networks, and that the large-scale growth dynamics of these causal graphs and complex networks are asymptotically the same. (1)

In short, past light cones of new nodes, shown by green in Fig. 2, are asymptotically equal to the corresponding hyperbolic discs, shown by red. The green light cone bounds the set of nodes to which node P connects as a new causet element. The red hyperbolic disc bounds the set of nodes to which P connects as a new node in the hyperbolic network model that accurately describes the growth of real networks. Since these two sets are asymptotically the same, we conclude that not only the structure, but also the growth dynamics of complex networks and de Sitter causets are asymptotically identical. (5)

Kroger, Helmut, ed. Fractal Geometry in Quantum Physics. Chaos, Solitons & Fractals. 14/6, 2002. A special issue to explore the pervasive self-similarity of nature from sub-atomic to galactic realms.

Landais, Francois, et al. Multifractal Topography of Several Planetary Bodies in the Solar System. arXiv:1805.11249. When this website went online in the early 2000s, observations of a naturally pervasive self-similar geometry were spurious if at all. Here geophysicists Landais and Frederic Schmidt, Universite Paris-Saclay, and Shaun Lovejoy, McGill University evince a self-similar mathematical presence across our home stellar array. See also Universal Multifractal Martian Topography by this team in Nonlinear Processes in Geophysics (22/6, 2015).

Topography is the expression of both internal and external processes of a planetary body. We propose here to use the multifractal approach to describe fields of topography. This theory both encompass height and slopes and other statistical moment of the field, tacking into account the scale invariance. As we commonly observe the juxtapostion of rough and smooth at given scale, the multifractal framework seems to be appropriate for hypsometric studies. Here we analyze the data at global scale of the Earth, Mars, Mercury and the Moon and find that the statistics are in good agreement with the multifractal theory for scale larger than 10km. Surprisingly, the analysis shows that all bodies have the same fractal behavior for scale smaller than 10km. (Abstract excerpts)

Lapidus, Michel. An Overview of Complex Fractal Dimensions. arXiv:1803.10399. The French-American, UC Riverside polymathematician posts a latest intricate, 100+ page, contribution about nature’s intrinsic, structural self-similarities. Visit the author’s website for a lifetime lists of papers and books such as Fractal Geometry, Complex Dimensions and Zeta Functions (Springer 2013). Since our sapient emergence arises from these same geometric codes, when might we see ourselves as their way of reaching conscious recognition, so as we may carry forth to a new creation?

Laskin, Nick. Fractals and Quantum Mechanics. Chaos. 10/4, 2000. A novel hypothesis of a “fractional quantum physics” as an indication of its fundamentally discrete, self-similar character.

Liang, L., et al. Self-Similarities and Power-laws in the Time-resolved Spectra of GRB 190114C, 130427A, 160509A, and 160625B. arXiv:1910.12615. In an entry to appear in Astronomy & Astrophysics, five scientists at the International Center for Relativistic Astrophysics Network, Pescara, Italy report upon the title Gamma Ray Burst (GRB) phenomena as it exemplifies a natural fractal display.

Conclusion: The most far reaching discovery of self-similarities and power-laws are extensively confirmed, thanks also to the conclusions presented in the companion papers, which leads to the existence of a discrete quantized repetitive polarized emission on a timescale as short as 10−14s. These results open new paths in the discovery of fundamental physical laws.

Lima, J. A. S. and R. E. de Souza. Power-law Stellar Distributions. Physica A. 350/303, 2005. Another example of how and where nonlinear self-similarities are being found on interstellar scales.

Liu, Qin. Towards a Fractal Approach to Hadronization. Physica A. 338/1-2, 2004. One more example of the intensifying global discovery of a self-similar universality from quanta to humankind.

Financial markets and those at the subnuclear level of matter are very much the same. (42)

Maeder, Andre. Evolution of the Early Universe in the Scale Invariant Theory. arXiv:1902.10115. The Geneva Observatory astronomer (search) expands his collegial quantification of a universally repetitious self-similarity onto the whole evolutionary cosmos. See also The Growth of the Density Fluctuations in the Scale-Invariant Vacuum Theory by AM and Vesselin Gueorguiev at 1811.03495.

Analytical solutions are obtained for the early cosmological phases in the scale invariant models with curvature k=0. The physical properties in the radiative era are derived from conservation laws and compared to those of current standard models. The critical runs of the temperature and of the expansion rate of the scale invariant models with low densities, are quite similar at the time of nucleosynthesis to those of standard models, leading to the same freezing number ratio of neutrons to protons. These results are consistent with the fact that the scale invariant models appear to not require the presence of dark matter. (Abstract)

Maeder, Andre. The Acceleration Relation in Galaxies and Scale Invariant Dynamics. arXiv:1804.04484. We cite this work by a Geneva Observatory astronomer records in 2018 how a broad and deep cosmic self-similarity, only spurious two decades ago, has now become commonly accepted, Here a collaborative technical presentation explains in extensive detail. See also Self-Similar Behavior in Galaxy Dynamics and Distributions of Dark Matter at 1804.06212.

We show that the scale invariant theory, with the assumption of the scale invariance of the empty space, correctly predicts the observed deviations in the acceleration relation. The large deviations and the flattening of the acceleration relation observed for the dwarf spheroidal galaxies are also well described. The presence of dark matter is no longer necessary in the scale invariant context, which also accounts why dark matter usually appears to dominate in galactic regions with low baryonic gravities. (Abstract excerpt)

Maeder, Andre and Vesselio Gueorguiev. Scale-Invariant Dynamics of Galaxies, MOND, Dark Matter and Dwarf Spheriodals. arXiv:2001.04978. Geneva Observatory and Institute for Advanced Physical Studies, Sofia astrophysicists report further evidence for nature’s pervasive celestial self-similarity. In regard, when we first posted this section in the early 2000s, a detection of any fractal forms in space was spurious and patchy. At this new 2020 decade dawns, their presence in every feature across the spatial raiment and its temporal course are now well proven. By a natural philoSophia, might we contemplate where do these ordained, non-random mathematical regularities come from. Might we wonder and as whatever reality put them there in the first place.

The Scale-Invariant Vacuum (SIV) theory is based on (Herman) Weyl's Integrable Geometry, endowed with a gauge scalar field. The main difference between MOND (Modified Newtonian Dynamics) and the SIV theory is that the first considers a global invariance of space and time, where the scale factor λ is constant, while the second considers λ as a function of time. The SIV theory shows an excellent agreement with observations and with MOND for baryonic gravities. These results support the view that there is no need for dark matter and that the RAR (Radial Acceleration Relation) and dynamical galaxies can be interpreted by a modification of gravitation. (Abstract excerpt)

A Dwarf Spheroidal Galaxy is a term in astronomy applied to small, low-luminosity galaxies with very little dust and an older stellar population. They are found in the Local Group as companions to the Milky Way and to the Andromeda Galaxy. (Wikipedia)

Marcolli, Matilde and Nicolas Tedeschi. Multifractals, Mumford Curves and Eternal Inflation. P-Adic Numbers, Ultrametric Analysis, and Applications. 6/2, 2014. We select this certain paper as an example of the infinite brilliance of an ordained human ability to quantify and comprehend any breadth and depth of natural phenomena. In this new journal described below, Caltech mathematicians contribute to our project as the universe’s way of consciously perceiving how thee and we came into being and becoming. Search Karthnik Siva for more of the lead author’s contributions.

We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes related to quantum statistical mechanical systems on Cuntz-Krieger algebras. We extend the eternal inflation model from the Bruhat-Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras. (Abstract)

This is a new international interdisciplinary journal which contains original articles, short communications, and reviews on progress in various areas of pure and applied mathematics related with p-adic, adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis, number theory, algebraic geometry, non-Archimedean and non-commutative geometry, theory of finite fields and rings, representation theory, functional analysis and graph theory; classical and quantum information, computer science, cryptography, image analysis, cognitive models, neural networks and bioinformatics; complex systems, dynamical systems, stochastic processes, hierarchy structures, modeling, control theory, economics and sociology; mesoscopic and nano systems, disordered and chaotic systems, spin glasses, macromolecules, molecular dynamics, biopolymers, genomics and biology; and other related fields.

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