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Anticipating Real-Form Periodical System by Self-Templating Expansion of Platonic and Archimedean Solids in Original Digital Universe

p. 176-202

Abstract

When, collage-style quoted, a recent authoritative "scientific data mining for conserved quantities and meaningful and nontrivial invariants that underlie physical phenomena in nature, discovered Hamiltonians, Lagrangians and other concise analytical expressions", such "distilled conservation equations" are still analogue since functions of the respective "system's partial derivatives". These, in tum, are of course all equal and the real nontrivial conserved quantity at the ground in any e.g. curve, intercept or identity/spin matrix therefore reduces to a sole infinitesimal straight line bit so that at smallest scale the world is digital - like in modem informatics and computing, the only sufficient letter and number and structural element alike is the binary unit, I, which then forms the reality it may by the canvas and lacework of its own. Showing that the current "digital revolution" is in fact the digital Renaissance, this is the profound meaning of the ancient regular solids, too, opening up long forgotten corridors also to the original Diophantine equations and onwards, e.g. to Keplerian Cosmography, Renaissance Arithmetic, and Fermat's Last Theorem and its offspring Beal's Conjecture. In fact, at the then available level of resolution, the anticipation of the possibly underlying common alphabet of the physical systems and processes around came down to the same ground invariant at hand, namely, anew, the straight line bit, I, from which a complete Universe could be filled by the elements outlined by the infinitesimal digit distributed via first-degree straight and square or diagonal wave sequences and second-degree self-closing equilateral quadrate, triangle and pentagon planes to the maximally three-dimensional, in all but five feasible regular solid expansions. As reported in the CASYS '07 meeting, a transfer to modem elemental counterparts yields exact and exhaustive, both channel, angular and electromagnetic quantum number, mass, and quark inclination reproduction of the meson symmetries by the (assigned to) fire tetrahedron, baryons by the air octahedron, and electrons/positrons by the only spacefilling, truncated octahedron distribution of the continuous 2-tetrahedrons/ I-octahedron lattice complex of their unit root vectors. In principle, there is no difference between an orbital and an axially twisting truncated octahedron distribution of the stepwise path of the extra-nuclear electron domain, but the interesting advantage of the latter is its direct root vector constitution with concomitantly defined lattice segment shape, enabling further nanotechnological self-templating reduplication of its motif into serially enlarged atomic and onwards modules. However, there are problems with this solution as well, and other feasible alternatives are sought for a complete and faithful continuous replication of the periodical system.

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References

Bibliographical reference

Erik Trell, « Anticipating Real-Form Periodical System by Self-Templating Expansion of Platonic and Archimedean Solids in Original Digital Universe », CASYS, 25 | 2010, 176-202.

Electronic reference

Erik Trell, « Anticipating Real-Form Periodical System by Self-Templating Expansion of Platonic and Archimedean Solids in Original Digital Universe », CASYS [Online], 25 | 2010, Online since 12 September 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=3222

Author

Erik Trell

Faculty of Health Sciences, University of Linköping, Se-581 83 Linkoping, Sweden

Copyright

CC BY-SA 4.0 Deed