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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 18z (20d) | Vol. 9 No. 1 | Year 1169z (1953d) ▶️



Click to view PDF

Editor: George Terry

Contents:

  • Why Change? (page iiid)
  • The Annual Meeting (page 1z)
    • Officers and Committees, 1169z (1953d) (page 2z)
  • How We Began | F. Emerson Andrews (page 3z)
  • Citation of F. Emerson Andrews on the Occasion of His Receiving the Degree of Doctor of Humane Letters at the 165thd Annual Commencement of Frankling and Marshall College, Lancaster, Pennsylvania, June 6th, 1952d (1168z) (page 8z)
  • Do-Metric Thermal Units (page 8z)
  • The Uncial System | Paul Van Buskirk (page Bz)
    • Evolution of Our Measures from Roman Uncial Fractions (page 11z)
    • Table of Decimal Equivalents (page 12z)
  • Scales of Notation | D. W. Mynett (page 13z)
  • Hand Base Changing by Summation | H. F. Stevens (page 15z)
    • Six Place Table for Dec. to Doz. Conversion by 102z Summation (page 16z)
    • Conversion Tables, by (late) F. Howard Seely, for comparison (page 17z)
  • The Reciprocal of 3937d | Ralph H. Beard (page 19z)
  • Dozenal Compass Rose (page 18z)
  • I'm A Dozener | Eugene J. Zirkel (page 1Bz)
  • Diurnal Clock, with Time Expressed as a Duodecimal of the Day (page 22z)
  • A Note of Conversion Multiples | George S. Terry (page 22z)
  • A Mathematical Recreation (page 24z)
  • Science Fiction and Duodecimal | F. H. Ames, Jr. (page 25z)
  • Excerpt from “Our Money Words” | Webb B. Garrison (page 26z)
  • The Curate & The Girls | Lewis Carl Seelbach (page 27z)
  • Counting in Dozens (page 28z)
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.