The Dozenal Society of America

The Society is a voluntary nonprofit educational corporation, organized for the conduct of research and education of the public in the use of base twelve in calculations, mathematics, weights and measures, and other branches of pure and applied science.

Duodecimal Bulletin:

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“Best Base” Essays

Which is the best number base? Is it hexadecimal, octal, base 6, or decimal? The question is pondered many times.

The Dozenal Society of America has published a half dozen essays that endeavor to determine which number base is optimum for general human computation. These essays often explore topics like divisibility and fractional expansion, which are linked to prime factorization of the number base. The field of eligible number bases are normally constrained to small positive integers, the magnitude of the base often limited by the size of the multiplication table for that base. Fractional expansion, divisibility, and a small multiplication table that maximizes human computational ability are seen as measures of utility. These essays arrive at one conclusion: dozenal is the optimum base for general human computation.

Simply click the thumbnail (the icon) on the left to download the full article in PDF form. Click the Newhall number for articles extracted from the Duodecimal Bulletin or other dozenal publications to download the entire archived original issue. Example: Ralph Beard’s original “Why Change?” article begins in Vol. 4; No. 3 at page ii and has a Newhall number of db043r2.

Visit the Duodecimal Bulletin Digital Archive

DSA-MT

“Dozenal Frequently Asked Questions”
Michael T. De Vlieger, 2011. NEW!
Answers to a dozen frequently asked questions about dozenal, fully illustrated. Two dozen pages explaining why duodecimal is the optimum number base for general human intuitive computation. Answers include benefits of dozenal beyond the often-heard reasons of the large number of divisors and “easy fractions”. Candid responses describing the drawbacks of dozenal and the benefits of decimal.

db4X117

“Some Notes on the History and Desirability of Using Alternate Number Bases in Arithmetic”
Christopher J. Osburn, 2009, db4X117.
Mr. Osburn’s article examines the number theoretical properties of the dozen and other bases, concluding that twelve would be the optimum base for computation.

DSA-MultAnalysis

“Analysis of Multiplication Tables”
Michael T. De Vlieger, 2011.
The optimum number base may be more or less attributable to a number’s prime factorization. The behavior of a number base’s digits, from periodicity in the multiplication table to regularity in fractions, is governed by the number-theoretical relationships of each digit to the base.

Other ”best base“ articles include:
Nina McCLelland’s “An Ideal Numerical Base” (db04101),
Courtney B. Owen’s “Patten’s Law” (db3E212),
Harold M. Country’s “Numbers and Number Systems” (db40108),
Addie Andromeda Evans’ “Numbers: Cheaper by the Dozen?” (db48205 & db49105).
These will be remastered in the future.

Visit the Duodecimal Bulletin Digital Archive. Revisit this page from time to time to read new or remastered ”best base“ articles.

This page revised Wednesday 30 November 2011.