Search Results Fail to Link Babylonian Regular Numbers to Z³, A₃, or Tetrahedral Symmetry — E8 Intelligence Research

FINDING: Search results are predominantly low-quality video tutorials on Babylonian base-60 numeration; no source in this set establishes a connection between Babylonian regular numbers, the lattice Z³, root system A₃, or tetrahedral symmetry. | MATH: Babylonian system: positional sexagesimal, base b=60=2²·3·5. Regular numbers (S-regular, 60-regular) = {2^a·3^b·5^c : a,b,c ∈ ℤ}. These form a multiplicative monoid isomorphic to the additive lattice ℤ³ via (a,b,c) ↦ 2^a3^b5^c. Reciprocals terminate in base 60 iff the number is 60-regular. | CONNECTION: The ℤ³ structure of 60-regular numbers is real and well-documented (Neugebauer, Friberg, Robson). However, ℤ³ here is the exponent lattice of the prime factorization, NOT the A₃ root lattice. A₃ root system lives in the hyperplane {x₁+x₂+x₃+x₄=0} ⊂ ℝ⁴, has 12 roots, Weyl group S₄ of order 24, and its weight lattice is the FCC lattice (A₃ ≅ D₃). The claim "Babylonian regular numbers lattice Z³ = A₃" is not supported: Z³ is the root lattice Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-27
DOI
https://doi.org/10.5281/zenodo.23690841
Primary Topic
History and Theory of Mathematics
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
preprint

Search Results Fail to Link Babylonian Regular Numbers to Z³, A₃, or Tetrahedral Symmetry — E8 Intelligence Research

Andrew Stewart Caldin
10 links
Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
preprint

Search Results Fail to Link Babylonian Regular Numbers to Z³, A₃, or Tetrahedral Symmetry — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search results are predominantly low-quality video tutorials on Babylonian base-60 numeration; no source in this set establishes a connection between Babylonian regular numbers, the lattice Z³, root system A₃, or tetrahedral symmetry. | MATH: Babylonian system: positional sexagesimal, base b=60=2²·3·5. Regular numbers (S-regular, 60-regular) = {2^a·3^b·5^c : a,b,c ∈ ℤ}. These form a multiplicative monoid isomorphic to the additive lattice ℤ³ via (a,b,c) ↦ 2^a3^b5^c. Reciprocals terminate in base 60 iff the number is 60-regular. | CONNECTION: The ℤ³ structure of 60-regular numbers is real and well-documented (Neugebauer, Friberg, Robson). However, ℤ³ here is the exponent lattice of the prime factorization, NOT the A₃ root lattice. A₃ root system lives in the hyperplane {x₁+x₂+x₃+x₄=0} ⊂ ℝ⁴, has 12 roots, Weyl group S₄ of order 24, and its weight lattice is the FCC lattice (A₃ ≅ D₃). The claim "Babylonian regular numbers lattice Z³ = A₃" is not supported: Z³ is the root lattice Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
History and Theory of Mathematics
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon