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Dozenal Society of America
Promoting base twelve and alternative base mathematics
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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 35z (41d) | Vol. 1Az (22d) No. 1 | Year 117Bz (1967d) ▶️



Click to view PDF

Editor: Jamison “Jux” Handy, Jr.

Contents:

  • Annual Meeting
  • First U.S. Dek-Cent Postage Stamp 1847 | U.S. Post Office
  • Julian Period Moments | Gower Neal Euston
  • Replacing Knots | John Jarndyce
  • Dit Acronym for (;) | Thomas Pendlebury
  • Worldwide Zip Code | H. C. Churchman
    • Zip Angles
    • London and Chelmsford Zip Code Symbols
  • American Mistakes of the Past | Lawrence Boythorn
  • Base Twelve Military Weapons and E-Z Locator | Lt. Col. Grosvenor Bond, FA-Res.
  • Simpler Sums (Abstracted From) | J. Halcro Johnston
    • A Change to Decimals
    • Why so Unpopular?
    • Small Factor
    • Decimal Shortcomings
    • The Choice of a Better System
    • Twelve Arithmetic
    • What Benefits Would Result
    • Multiplication
    • Shortcuts
    • Compound Sums
    • Why Was It Not Thought Out Before?
  • Renaissance in Arithmetic | Henry C. Churchman
  • Case Against Decimalisation, Part III | A. C. Aitken
    • Recapitulation
    • Monetary and Metrical Units
    • General Arithmetic
  • Base-Ten — A Double Prime | Egbert Pardiggle
  • Telephone and Social Security Numbers | Westbourn Grove
    • Double Our Population?
    • Social Security Unique Groupings
    • Numbers and Symbols
    • Other Uses
  • (T. Jefferson's) Poplar Forest Retreat, Lynchburg, Virginia | H. C. Churchman
  • Counting in Dozens
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.