Rewrite Science - The Universal Semantic Calculus and Grammatical Cosmos
Symposium 10A - CASYS 07

Elementary Particle Spectroscopy in Regular Solid Rewrite (one of the two CASYS 07 symposium 10 best paper awards)
Erik Trell - Symposium invited speaker
Professor Emeritus, University of Linköping, Strandviksvägen 47, SE-65590 Karlstad, Sweden.
Tel +46 (0)705970727.

Abstract

The Nilpotent Universal Computer Rewrite System (NUCRS) has traced back the lingering ontological question: “What, then, determined the vacuum state for our observable Universe?” to its ground dilemma of Nothing - at All - versus the equally singular offset counterpart to this of Anything - at All. Since nothing is not even a void, but total Absence, its substantial twin of bare Presence is just as amorphous and radical, a diametral state that is everything there is and therefore indefinitely infinite: a mirror-inflated nilpotent vacuum as such.

The great accomplishment of NUCRS is to track down the recursive syntax and common computational principles of the dichotomous situation itself and hence governing all its sui generis modalities, leading to fulfilment of their individual terms and compass when the respective choice sequence operations are brought to closure. Focussing on the general grammar, NUCRS by pure logic and its algebraic notations thus bootstraps Quantum Mechanics, aware that it “is the likely keystone of a fundamental computational foundation” also for e.g. physics, molecular biology and neuroscience.

The present work deals with classical geometry where morphology is the modality, and ventures that the ancient regular solids are its specific universal rewrite system, in effect extensively applicable to the elementary particle spectroscopy, and further to essential structures at large both over the inorganic and organic realms. The geodetic antipode to Nothing is extension, with natural eigenvector the endless straight line. This in turn generates three-dimensionality as clearest expressed by Ptolemy, who in his book ‘On Distance' (150 AC) prescribed: “Draw three mutually perpendicular lines. Try to draw another line perpendicular to all of these lines. It is impossible. The fourth perpendicular line is entirely without measure”. The axis lines can maximally be drawn from all over the three directions, and when infinitesimally tight enclose the so inflated space’s eigen- element, which is a cube, or cubicle, too, whose sides are so close that they touch, rendering it a solid.

This is the ground plan of the whole family; the infinitesimal line bit is in the second dimension expansion folded to a plane, i.e. equilateral triangle, square, pentagon, hexagon etc. of which only those which can be iteratively convoluted to a volume form the then closed three-dimensional regular bodies. They are the triangle (tetrahedron, octahedron and icosahedron), square (cube) and pentagon (dodecahedron) whereas the hexagons and larger stay flat. Aristotle then introduced dynamics in the arrangement, stating that “everything that comes to be comes into being from its contrary” and found “contrary to circular, a straight line”. Hence he envisioned an all- pervading dynamical phase transition system of primary structure, corresponding to the “new class of geometrical transformations” disclosed by Marius Sophus Lie in 1871.

From non-being’s very simplest antipodal ground materialization, existence’s infinitely extended and infinitesimally partitioned straight line, a coherent functioning Universe is unfolded under perpetual attraction by the Idea of the alternative, spherically harmonic form of absolute endlessness. The cubical eigen- space and eigen-elements are the parental state and frame, and the other solids are a range of transition matrix elements and portions adapting to the spherical root vector symmetries and so exactly and extensively reproducing the elementary particle spectroscopy, including a modular, truncated octahedron nano-composition of the electron which piecemeal enters into molecular structures or compressed to each other fuse into atomic honeycombs of periodic table signature.