Abstract. Our STEM tool is becoming a working model. It has a simple logic, geometry and algebra based on spheres, tetrahedrons, octahedrons and doublings. It begins with natural units; it is driven by pi (π). And, its 202 predictive, base-2 notations readily absorb big bang cosmology. This mathematically-integrated view of the Universe addresses key issues that big bang cosmology cannot. Five examples follow.
I. Smoothness. The James Webb Space Telescope images have raised anxieties that the early universe is too smooth for our working understanding of the dynamics of big bang cosmology. The transition from smooth to lumpy is not a problem within the 202 base-2 notations. In this model geometric gaps do not become systemic until later in the unfolding of the universe. The earliest notations begin perfectly smooth because it starts with the most simple geometries that tile and tessellate this universe perfectly.
II. The first minute, the first second, and the first zeptosecond. The first minute of the universe is within Notations 149-150. The first second is between Notation 143-and-144. Zeptoseconds (1×10-21) are between Notations 65-and-67. Eminent scholars, Sean Carroll of John Hopkins and James Peebles of Princeton (Nobel laureate, 2019, and a pioneer of cosmic microwave background radiation research) acknowledge the importance of articulating the first minute of the universe. In June 2020 over twenty scholars focused on the emergence. Their publication was “The First Three Seconds: A Review of Possible Expansion Histories of the Early Universe” (arXiv:2006.16182 [astro-ph.co]); they were unable to define the first minutes. The zeptosecond is on the cusp of quantum fluctuations. The first notations begin with the natural units that were defined by Max Planck in 1899 and George Johnstone Stoney in 1874. It is a natural grid. As each notation builds on the prior notations, geometries, numbers and relations necessarily refine the nature of time. Those first 64 notations have been unwittingly defined by hundreds of scholars within Langlands programs, string theory, and like disciplines … all while big bang cosmology hides any access to those first notations.
III. Quantum fluctuations and quantum physics. The study of a geometry of quantum fluctuations over the years is most limited. A most-simple place to start is to recognize the tetrahedral gap that Aristotle did not see. That gap is real. Plus, there are others that are ignored. Add to it our octahedral gap and then the icosahedral gaps. Here are possibilities for fluctuations. Big bang cosmology has no simple geometry and certainly no geometry for chaos and indeterminacy. Our mathematically-integrated view of the Universe begins with the inherent geometries of doublings that perfectly tile and tessellate and it has a geometry for fluctuations that is inherently indeterminant. One of our primary studies is to grasp the varieties of gaps and the probabilities for each manifestation within a given notation.
IV. A natural inflation and dark energy and dark matter. Dark matter and dark energy are below all possible thresholds of direct measurement. The indirect effects have been well-regarded since the work of Lord Kelvin (1884), Jacobus Kapteyn (1922), Jan Oort (1932) and Fritz Zwicky (1933). The mystery prevails. Big bang cosmology blocks the view of both the geometries of perfection and of imperfection. Initially there are no gaps as spacetime is dynamically created. Within this mathematically-integrated view of the Universe, a natural inflation starts with the most simple infinitesimal sphere, sphere stacking, and cubic-close packing of equal spheres. Tetrahedrons and octahedrons are generated and naturally tile and tessellate the early universe.
If taken as a given that one infinitesimal sphere is generated per unit of length and time, the rate would range from 539-to-4609 tredecillion spheres per second. Of course, that range is established by Planck Time and Stoney Time.
V. Finite-infinite, quantitative-qualitative. Big bang cosmology has no finite-infinite relation and makes no distinction between the quantitative and the qualitative. It does not posit the smallest physical unit of spacetime. It makes no statements about pi (π), nor recognizes the essential faces of pi (π): continuity (ordering), symmetry (relating) and harmony (making dynamic). Naturally, the ubiquitous dimensionless constant that generates the natural units for Planck and Stoney is pi (π). We hypothesize that these three faces of pi (π) define the qualitative and the infinite. Within big bang cosmology the Planck Epoch and a singularity are the baseline whereas within our mathematically-integrated view of the Universe, it is the simple perfections of the infinitesimal sphere and the simple perfections and imperfections-or-gaps within tetrahedrons and octahedrons.
Thank you. -BEC
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• The headline for this article: Reason to believe.
• First byline: Anything that comes “after the big bang” is conceptually damaged.
• Second byline: Smoothness, the first minute, fluctuations, dark energy-matter, finite-infinite….