Natural Numbers, Natural Language: Architecting the Semantic Web
Robert P. C. de Marrais · 2008
Two disparate themes are brought together, to underwrite Semantic Web architecture. A bit-string-(as opposed to quantity-) based Number Theory gives body to the study of zero-divisors (ZDs) in infinite-dimensional extensions of hypercomplex numbers, via the Cayley-Dickson Process (CDP). Their Cayley-Table-like Emanation Tables (ETs) of ZD products – representable as infinitely extensible spreadsheets – have patterns of empty cells defining fractals … and "fractality" is, per Sir Tim Berners-Lee, the fundamental feature of World Wide Web geometry. But ETs themselves decompose into integral numbers of ZD "atoms" called Box-Kites, octahedral wire-frame figures whose 6 vertices represent planes whose diagonals are saturated with all and only "primitive" ZDs. Their basic circuits and scaffolding provide a "representation theory" unifying two distinct semantic models, derived by Jean Petitot from Singularity Theory mathematics, and applied to the semiotics of literary and mythological structures, of Algirdas Greimas and Claude Lévi-Strauss respectively.