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The Dozenal Society of America
The DSA is a voluntary, nonprofit education corporation, organized for the conduct of research and education of the public in the use of dozenal (also called duodecimal or base-twelve) in calculations, mathematics, weights and measures, and other branches of pure and applied science.

The Duodecimal Bulletin

◀️ Issue: Whole Number A2z (122d) | Vol. 52z (62d) No. 1 | Year 11BBz (2015d) ▶️



Click to view PDF

Editor: John Volan

Cover Title: Base Annotation Schemes

Contents:

  • President’s Message | Donald Goodman III
  • Editorial: Radically Conventional | John Volan
    • Pitman versus Dwiggins
    • Humphrey-Free Zone
  • New Members
  • Accuracy of Common Roundings | Donald Goodman III
  • Base Annotation Schemes | John Volan
    • The Problem
    • An Early Expedient: Stylistic Marking
    • Humphrey's Radical Radix-Point
    • Modularity in Design .. and Its Lack
    • Honourable (?) Mentions
    • The Mainstream Solution
    • Approaches from Programming Languages
    • A New/Old Solution
    • “Nominal” and “Digital” Annotations
    • To Subscript or Not Subscript
    • International Neutrality
    • “Why Change?”
  • Patterns and Palatable Morsels in Duodecimal | Prof. Jay L. Schiffman
    • Rationale
    • Morsel #1: Twin Primes
    • Morsel #2: Pythagorean Triples
    • Morsel #3: Pisano Periods
    • Morsel #4: Lucas Sequences
    • Morsel #5: Fibonacci-Pythagorean Connection
    • Morsel #6: Square Numbers
    • Morsel #7: Triangular Numbers
    • Conclusion
  • Reprint: Uncial Jottings of a Harried Infantryman | Pvt. William S. Crosby
  • Systematic Dozenal Nomenclature Summary
  • Dozens in the Media
    • The Ancient Melodies | Jim Zamerski
    • Numberphile: Base 12 | Brady Haran & Dr. James Grime
    • Multiplication Tables in Various Bases | Michael Thomas DeVlieger
  • Preview of the Next Issue
  • The Annual Meeting of 11BBz (2015d)
  • Application Form
Copyright © 11B9–120Az (2013–2026d). The Dozenal Society of America. Contact Us.
Creative Commons License
This site and the documents on it are licensed under a Creative Commons Attribution 4.0 International License.

This site expresses numbers in alternative bases, particularly dozenal (also called duodecimal, or base twelve).
The DSA does not endorse any particular notation or pronunciation scheme for alternative bases.
However this site defaults to the following to ensure online readability across all platforms:
“Computerese” uppercase letters represent transdecimal digits: A = ten, B = eleven, C = twelve, etc.
Single-character subscripts annotate bases: d = decimal, z = dozenal, x = hexadecimal, etc., e.g., 2014d = 11BAz = 7DEx.

(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ...)d
(0 1 2 3 4 5 6 7 8 9  A  B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 21 22 23 24 25 26 27 28 29 2A 2B 30 ...)z
(0 1 2 3 4 5 6 7 8 9  A  B  C  D  E  F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 ...)x

PDF documents on this site reflect changing practices among dozenalists over the years:
Various symbols have been used to represent digits ten and eleven:
Dwiggins 𝒳 and Ɛ (often rendered X and E); Bell Telephone * and #; Pitman turned 2 and 3 (↊ and ↋); etc.
Italics were once used to distinguish dozenal numbers from decimal: e.g. 0.5 = 0.6.
Later, semicolon became a separate‑identity “dozenal point”, versus period as “decimal point”: e.g., 0.5 = 0;6.
However, subscript base annotations provide a more versatile solution that is least‑change: e.g., 0.5d = 0.6z = 0.8x

Dozenal offers superior divisibility over decimal, which can make everyday arithmetic easier to learn:
⅙ = 0.2z | ¼ = 0.3z | ⅓ = 0.4z | ½ = 0.6z | ⅔ = 0.8z | ¾ = 0.9z | ⅚ = 0.Az
⅙ = 0.1666…d | ¼ = 0.25d | ⅓ = 0.333…d | ½ = 0.5d | ⅔ = 0.666…d | ¾ = 0.75d | ⅚ = 0.8333…d

EACH ONE, TEACH ONE.