Dictionary

pathion en · NOUN

Etymology

Blend of path + quaternion. Named after the 32 paths of wisdom of Kabbalah.

Meanings

1. A 32-dimensional hypercomplex number that is a nonassociative extension of a sedenion.
   • There is no theoretical limit to multispace dimensional numbering as there are definitions for octonion (8D), sedenion (16D), pathion (32D), chingon (64D), routon (128D), and voudon (256D) numbered space. 2023, Melanie Swan, Renato P. dos Santos, “Quantum Intelligence: Responsible Human-AI Entities”, in AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA, CEUR Workshop Proceedings, →DOI:
   • According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (#92;mathbbO—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons. 2022, Zlatka Valkova-Jarvis, Vladimir Poulkov, Viktor Stoynov, Dimitriya Mihaylova, Georgi Iliev, “A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks”, in Symmetry, volume 14, number 3, MDPI AG, →DOI, →ISSN:
   • Let’s expand our horizons to the 32-D and 64-D cases and give them names (since they currently don’t have any!). Following the convention adopted by Tony Smith, who has called the 2⁸-ions Voudons after the 256 deities of the Ifa pantheon of Voodoo or Voudon, we’ll call these Pathions (for the “32 Paths” of Kabbalah) and Chingons (for the 64 Hexagrams of the I Ching or Book of Changes). 2002, Robert P. C. de Marrais, “Flying Higher Than a Box-Kite: Kite-Chain Middens, Sand Mandalas, and Zero-Divisor Patterns in the 2ⁿ-ions Beyond the Sedenions”, in arXiv, →DOI, page 7:

Forms

Relateds

voudon · routon · sedenion · octonion · quaternion · chingon

Synonyms

trigintaduonion