Kurzweil Rays

Robert de Marrais

Thothic Technology Partners, LLC
Cambridge MA

Abstract

Inventor/futurist Ray Kurzweil famously predicted the Internet, and stages the long-range development of product launches, using a methodology based on the ubiquity of “Moore’s Law”-style period-doubling, in most or all component parts of processes being anticipated. Its description in The Singularity Is Near can itself be modeled by a bare-bones, bitstring-based number-theoretic approach, developed in the abstract in our prior “Complex Systems” monographs.  

Networks of zero-divisors (ZD-Nets) are deployed to simulate threads of historical unfoldings—“Kurzweil rays”—whose nodes can be interpreted semiotically via local dynamics (Catastrophe Theory), while global behavior displays the implicit “fractality” (also displayed, per Sir Tim Berners-Lee, by the Internet) of ZD-Nets’ indefinite dimension-doubling algorithm.  The flexible linkage of local to global is most clearly modeled in “explosions” of the Double Cusp catastrophe, abstractly used to analyze the interconnectedness of mythological systems by Petitot’s reading of Lévi-Strauss.

Exploiting inherent topological features of this complicated object by a heuristic first suggested by Poston and Stewart in their treatment of the instability of square oil-rig platforms being towed into the Gulf (with a finite truncation of the theoretical infinities deployed in later work of string-theorists), we situate it within the highly generalized framework of the “A, D, E Classification” of Arnol’d (as realized via the so-called “MacKay correspondence” between SU2 geometry and Plato’s Timaeus!).  

We conclude by indicating key features of ongoing work to integrate a Mathematica “front end” of the just-limned mathematics, to “back end” database-building via Quinn Jackson’s adaptive parsing engine, written in C++.