Mathematics – General Mathematics
Scientific paper
2008-04-21
Complex Systems 18:1 (2008) 75-102
Mathematics
General Mathematics
30 pages, 6 figures, 2 tables, 20 references; V1 split into two parts, published separately: this longer will appear in "Compl
Scientific paper
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 (HBKs) in the 2^(N+1)- ions, are "exploded" from (and uniquely linked to) each standard box-kite in the 2^N-ions, N > 3. 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 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 Levi-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 switching focus, from the octahedral box-kite's four triangular "sails," to its trio of square "catamarans" and their box-kite-switching "twist products."
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