pathion

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

pathion (plural pathions)

1. (mathematics) A 32-dimensional hypercomplex number that is a nonassociative extension of a sedenion.
   • 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:

     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).

   • 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:

     According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (${\displaystyle \mathbb {O} }$—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons.

   • 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:

     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.

• trigintaduonion

• (mathematics):
  • quaternion
  • octonion
  • sedenion
  • chingon
  • routon
  • voudon