Complex Systems

Effecting Semantic Network Bricolage via Infinite-Dimensional Zero-Divisor Ensembles Download PDF

Robert P. C. de Marrais
Thothic Technology Partners
P.O. Box 3083, Plymouth, MA 02361
rdemarrais@alum.mit.edu

Abstract

Continuing arguments presented [1] or announced [2, 3] here, zero-divisor (ZD) foundations for scale-free networks (evinced, in particular, in the "fractality" of the Internet) are decentralized. Spandrels, quartets of ZD-free or "hidden" box-kite-like structures (HBKs) in the 2(N+1)-ions, are "exploded" from (and uniquely linked to) each standard box-kite in the 2N-ions, N ≥ 4. Any HBK houses, in a cowbird's nest, exactly one copy of the (ZD-free) octonions, the recursive basis for all ZD ensembles. Each is a potential way-station for alien-ensemble infiltration in the large, or metaphor-like jumps, in the small. Cowbirding models what evolutionary biologists [4], and structural mythologist Claude Lévi-Strauss before them [5], term bricolage: the opportunistic co-opting of objects designed for one purpose to serve others unrelated to it. Such arguments entail a switch of focus, from the octahedral box-kite's four triangular sails, to its trio of square catamarans and their box-kite-switching twist products.