Foundational Questions Institute: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) Support materials for the submission from Bruce Camber in April 2020.
|Background: FQXi’s challenge helped us to focus on the role of simple geometries. In the sciences and in mathematics, we learned that everything starts simply such that the active demonstration of cubic-close packing of equal sphere became an awakening. We suspect it may be others. First, we see how the universe is tiled and tessellated with this configuration, then we see emergence, expansion, and more.
 Triangulations. Spheres, sphere stacking and then cubic-close packing of equal spheres hold the foundations of triangulation, and a tetrahedral-octahedral couplet. With that couplet we know that the universe is tiled and tessellated and therefore profoundly integrated. We also recognize that just five tetrahedrons create a geometric gap, one that Aristotle’s failed to recognize (and threw scholarship off for 1800 years) as all those who followed with intellectual authority simply regurgitated that mistake (since dubbed, Aristotle’s deviated saeptus*). It even held today’s scholars back until the physics of quasicrystals emerged. Not quite fully appreciated, we believe this emergence will be carried into the periodic table as further explorations go deeper and deeper.
*We’ll consult with Jeffrey C. Lagarias and Chuanming Zong and others like them to come up with the best possible descriptive name for Aristotle’s mistake. Aristotle’s deviated saeptus is admittedly rather oblique.
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