Voyage by Catamaran: Effecting Semantic Network Bricolage via Infinite-Dimensional Zero-Divisor Ensembles

Continuing arguments presented [1] or announced [2][3] in Complex Systems, 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 (HBK’s) in the 2N+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, and each a potential waystation 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. 1 From Box-Kites to Brocades via Catamaran Twists This work had its beginnings in [6], where an abstract result of Guillermo Moreno [7] was employed to explicitly delineate the ZD structure of the 16-D Sedenions. These hypercomplex numbers are reached via the Cayley-Dickson Process ∗Email address: [email protected]