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Dozenal Society of America

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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.

Collected Works on Reckoning Reform

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Title: Collected Works on Reckoning Reform

Author: Sir Isaac Pitman

Year: 10A8_z (1856_d)

Subject:Collected works of Sir Isaac Pitman on the dozenal base.

Sir Isaac Pitman was one of the earlier consistent proponents of a dozenal system, and this article presents four pieces in which he proposed and defended the system. Better known for his system of shorthand, his work on the “reckoning reform” deserves more attention. One of these works, titled “Reckoning Reform,” marks one of the first uses of the now-common “Pitman” characters for ten and eleven, which as of 11BB_z (2015_d) have been included in the Unicode standard.

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., 2014_d = 11BA_z = 7DE_x.

(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., 0.5_d = 0.6_z = 0.8_x

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

EACH ONE, TEACH ONE.