The Duodecimal Bulletin

is an official publication of The Dozenal Society of America, Inc.
Editorial Office:
5106 Hampton Avenue
Suite 205
Saint Louis, MO 63109-3115

Michael De Vlieger, Editor

Index Links:

About the Bulletin

Archive Index

Pictorial Synopses:
011-00 to 043-0E
051-10 to 0E2-1E
101-20 to 152-2E
161-30 to 230-3E
240-40 to 293-4E
2X1-50 to 313-5E
314-60 to 352-6E
361-70 to 3E2-7E
401-80 to 452-8E
461-90 to 4E2-9E
501-X0 to 552-XE

About the Archive

The Duodecimal Bulletin

Click here for the Archive Index or the Pictorial Synopses Index.

Presenting a series of brief overviews of the DSA and its Bulletin across each “duodecade” or set of dozen issues. These overviews are strictly those written by the present Editor, one who didn’t have the pleasure of knowing the Founders nor the preeminent players of the “classic” Society. In this regard, the following overview is somewhat “non-canonical”: for a history of the DSA seen through someone who knew the early Members and Founders, read Prof. Gene Zirkel’s history. To get an inside look at the foundation of the Society, check out F. Emerson Andrews’ article “How We Began”, focusing on the pre-establishment years, at Vol. 9 pages 3-9.

The relatively recent membership of the present Editor offers a more detached viewpoint that may be of some use and interest. What follows is a synopsis of the development of the DSA as seen from a newly-joined Member (11XE;). This is a viewpoint of someone born when the DSA was two dozen two years old, familiar with the early Society mainly through its Bulletin, having scanned, processed, and read its 2058; pages and roughly one third of the 960; pages of the British publications to make this Digital Archive in the summer of 11E6;. Enjoy the story and write in with comments.

Note: This presentation of the history of the DSA through its Bulletin is dedicated to the memory of our dear friend and longtime Member Alice Berridge, who passed away on the very Saturday of the 2011. DSA Annual Meeting. See Alice’s smiling face on the covers of 331-64 and 3E2-7E, and in the history written by Prof. Zirkel.

011-00 to 043-0E | Foundation and the First Generation of the DSA
051-10 to 0E2-1E | Brave New Era Ahead
101-20 to 152-2E | Going International; Things are Really Humming
161-30 to 230-3E | The Struggle Against Decimalization
240-40 to 251-41 | The Aging and Floundering of a Beautiful Idea & The Hiatus
261-42 to 293-4E | A Second Generation: the DSA Renaissance
2X1-50 to 313-5E | Serene Explorations
314-60 to 352-6E | Questioning with a Smile as the World Wakes up from History
361-70 to 3E2-7E | Exquisite Analysis & Dear Friends Lost
401-80 to 491-96 | Culture Wars within and without
492-97 to Today | A Third Generation: The Digital Bulletin

Foundation and the First Generation of the DSA

The Duodecimal Society of America, established in 1944, begins publishing the Duodecimal Bulletin the next year, opening with hearty greetings and salutations. In this first dozen issues, Editor Ralph Beard establishes the “classical” numerals for digits ten and eleven (the “transdecimal” numerals), and basic dozenal facts are explored. Mathematical constants, new measurement systems, cheerful correspondence from the World War II front lines roll into the Bulletin. Expertly drafted figures in “Kin of The Golden Mean” seem to detail the exacting love some felt for the new cause. Dozenalists revel with enthusiasm in their new organization. Some folks like Messrs. Elbrow and Robertson submit all-encompassing dozenal systems of thought. Others like Mary Lloyd pose teasers, games, even poetry and song about the dozen. It seems, near the end of this first duodecade, that the “first generation” of DSA Members are in on the ground floor of a new, practical, and amazing mathematical tool: the dozen!

(View Duodecimal Bulletin issues from this era.)

Brave New Era Ahead

The founding generation of American organized dozenalists continues to flex their muscles across this duodecade of Duodecimal Bulletin issues. With the War coming to a close, the Allies victorious, the stage is set for the reconstruction of what seems to be the rest of the world. The United Nations is forming; interest in international standards, particularly regarding systems of measurement and currency, is a major concern to the DSA Membership. The decimal metric system (to become le Système Internationale d’Unités) is burgeoning. Time is of the essence if dozenalists want to propose a scalable dozenal system of measurement, striking while the iron was hot, in order to prevent the further entrainment of an inefficient decimal system across the world. The Do-Metric system of measurement is introduced by the DSA’s committee on such. Excitement over new technology, exhibited by the celebration of ENIAC computing power, buzzes in the Bulletin. Tables of mathematical functions often appear as reference material for a new dozenal world. Some like Grover Cleveland Perry believe dozenal can improve the way the USA uses and teaches mathematics. Men like Nystrom and Adams exhibit their thoughts on dozenal in general, and the reform of measurement systems in particular. Indices of dozenal thought are assembled and published, as the Membership taps into the past, to dozenalists in Europe of old. Certain Members like Mr. Gode extrapolate dozenal to the constructed language Interlingua in an attempt to efficiently cast the seed of thought into all Western realms. It is an exciting time to be an American dozenalist. From the standpoint of this particular time, there seems a chance the world might yet go dozenal, and rather soon.

(View Duodecimal Bulletin issues from this era.)

Going International; Things are Really Humming

This third dozen-issue sweep sees the internationalization of the “dozenal movement”, first in France through Jean Essig and his book Douze, Notre Dix Futur, then in England with the formation our sister society, the Duodecimal Society of Great Britain. American dozenalists revel in the newfound overseas kinship, in the apparent emergence of a system of interlinked dozenal foundations. Essig’s book and thoughts are cheered, a celebration reverberating in England. The DSA embraces Esperanto and other constructed languages of unity in order to efficiently reach out to international thinkers. Churchman continues to develop his “doremic” system of measure, as others explore Roman “Dumerals”, the abacus, and dozenal mathematical properties. Through the publications of Mr. F. Emerson Andrews and the general novelty of dozenal thought, some press attention visits the DSA. Materials are developed and published that aid in the teaching of duodecimal concepts to children and neophytes, including the Manual of the Dozen System in 1960. Meanwhile, the world is standardizing; decimal is gaining ground through the adoption of the Système Internationale and decimal currency. British bretheren in twelve begin to worry that their £sd. system will fall to the power of base ten. The economic boom is on and things are humming; increasingly the governments of the world are decimalizing.

(View Duodecimal Bulletin issues from this era.)

Struggling with the Compounding Entrainment of Decimal,
Dreaming It Isn’t So

This set of dozen issues trends toward attempting to build consensus over measurement systems, resisting an increasing societal tendency toward decimalization, and examining real-world applications for dozenal concepts. The world has moved on from the postwar era, many nations are adopting metric and decimalizing currency. New standards are being set in place, and the dozen seems locked out of consideration. Tom Linton and others explore the application of dozenal dimensioning, while Henry Churchman builds on his “dometric” system of weights and measure. Kothe writes a three-part essay exploring the development of musical notation, proposing a dozenal approach in the third part. Some members begin to show strain and lose hope over the decimalization of world standards. The “Winchester Declarations” in Vol. 22; and the “Boulder Concepts” on page 6 of the next issue attempt to rally the Membership in the face of an increasingly decimal world. Wishful diagrams like that in Mr. Churchman’s “Quo Vadis” at Vol. 21; Page 18; still project dozenal victory in the world, while the copy of the article rails against the march of decimal metric. The import for submission to standards authorities of a scalable duodecimal measurement system continues in Mr. Churchman’s “Elusive Peace and Base Twelve” in the same issue. The Duodecimal Bulletin begins to publish only once per year near the end of this duodecade of issues. The next few years will see the Duodecimal Bulletin nearly flicker out, leaving the Society struggling.

(View Duodecimal Bulletin issues from this era.)

The Aging and Floundering of a Beautiful Idea

The last issue of the “classic” phase of the Duodecimal Bulletin, edited by Henry Clarence Churchman, is published in 1974. It replaces the “classical” transdecimal numerals crafted by William Addison Dwiggins with the “Bell” numerals inspired by the touch tone telephone characters * and #.

(View Duodecimal Bulletin issues from this era.)

The Hiatus

The Duodecimal Bulletin enters a six year unplanned hiatus wherein two of the Founders (Messrs. Beard and F. Emerson Andrews) and an active President Tom Linton pass away. At one point, mentioned in Vol. 26; No. 1 Page 4, the DSA considered scrapping its Bulletin and combining dozenal publication with the Dozenal Society of Great Britain.

A Second Generation: the DSA Renaissance

Editor Dr. Patricia Zirkel’s Volume 26; No. 1 represents the relaunching of the Duodecimal Bulletin under a “new generation” of American organized dozenalists. Over the next dozen issues, the proceedings of the Society during the hiatus years are recapped. This “second generation” of Society leaders, more academic than their predecessors, breathes new life and vigor in the organization and its Bulletin. In nothing short of a renaissance, the Society forges connections with mathematics journals and organizations. The Bulletin becomes a peer-reviewed journal. The Society finds a new home at Nassau Community College, complete with a Duodecimal Library dedicated to F. Emerson Andrews, a founder of the DSA. Reporter Irene Virag visits the 1982 Annual Meeting, her report appears in print across the nation, in the Toronto Star and others, and on Los Angeles radio, the publicity netting new Members. Prof. Jay Schiffman pens number theoretical essays revolving around the special number twelve. Prof. Gene Zirkel explores symbology, how we write dozenal numbers. Some articles yet press against the SI-metric system, but the focus of the new generation lies somewhat more serenely on the qualities and mathematics of the dozen. The Society explores its own Members in the “Who We Are” series. All caught up, the DSA returns to a vibrancy it last saw long before the hiatus, and the Duodecimal Bulletin begins more than two dozen years of strong and steady publication heretofore unseen.

(View Duodecimal Bulletin issues from this era.)

Serene Explorations

This sixth duodecade of issues continues a serene exploration of the mathematics of base twelve. The Society’s Members interact continuously with the DSA through the “Dozenal Jottings” department. The Annual Meeting minutes in many issues seem to reveal a tight knit group of folks having a good time under the banner of twelves, and at banquets after the meetings. New puzzles and musings abound in nearly every issue. The Bulletin bravely publishes a debate regarding our Egyptian ancestors’ possible dozenal tendencies at Vol. 31; No. 1, a view flatly rejected in the next issue by Messrs. Whillock and Singmaster. Practical tools like the Fortran conversion scripts and Dr. Rapoport’s dozenal clock appear in the Bulletin. Charles Trigg explores mathematical series in dozenal, Prof. Schiffman covers fundamental dozenal operations, Prof. Zirkel touches on symbology and other topics. A reprise of sorts regarding SI-metric: the idea, even to this day, hasn’t quite breached the American public’s affiliation with the US Customary measurement system. Articles at Vol. 2X; No. 2 and the book review at Vol. 30; No. 2 page E; (#) seem to show metrication is not inevitable and its foreign adoption is usually the effect of government force. The Society seems solid and strong throughout this stretch, and the questing, delightful vigor continues into the next duodecade.

(View Duodecimal Bulletin issues from this era.)

Questioning with a Smile as the World Wakes up from History

As the Berlin Wall comes down and the Cold War world melts away, the Dozenal Society of America continues in its peaceful examination and exposition of the qualities of base twelve. Dr. Impagliazzo explores music and the dozen, a topic John D. Hansen, Jr. returns to later. The long hundred, conveyed twice by Jens Ulff-Møller, PhD., fascinates those gathered at Nassau Community College in 1991 and 1992. Gene Zirkel’s “Binary Coded Digits”, describing Bill Schumacher’s seven-segment digits, thrills Don Hammond across the pond, and like-minded dozenalist fans of the LCD display-style numerals. Mr. Charles Trigg passes away, yet leaves a legacy of articles published postmortem which celebrate dozenal recreational mathematics. Mr. Churchman’s 1975 summation of his “metronic” system of weights and measure finally appears in Vol. 34; No. 3. The Society continues to meet annually, and Dozenal Jottings continue to pour in. The sustained dozenal “peace”, the eager questioning with a smile, continues into the nineties.

(View Duodecimal Bulletin issues from this era.)

Exquisite Analysis, and Dear Friends Lost

This dozen-issue set sees Prof. Jay Schiffman take the Editorship, and continue the exquisite analysis of the mathematical properties of base twelve. He and others explore the Fibonacci sequence, modular checking of arithmetic, factorials and significant digits, perfect numbers, properties of dozenal digits, and number-theoretical properties of integers less than one gross. Anti-metric discussion is minimal but not forgotten. William Lauritzen and Timothy Travis write books involving the dozen and are reviewed. It seems more often than not, an obituary to a mainstay of the Society both here or in Britain appears in the Bulletin. Notables like Don Hammond, British editor; Fred Newhall, bibliographer; Henry Churchman, editor; Charles Bagley, longtime board member; James Malone, author, treasurer, board chair; Dudley George, early enthusiast, longtime member and fellow; Jamison “Jux” Handy, Editor and early Member, all pass on. On 18 July 1995, Prof. Gene Zirkel was interviewed on National Public Radio’s “All Things Considered” on the merits of duodecimal numeration.

(View Duodecimal Bulletin issues from this era.)

Culture Wars within and without

The DSA enters the age of 9/11 still producing exploratory articles. Editor Jay Schiffman pens rigorous mathematical studies of hexadecimal divisibility tests, and illustrates how Wolfram Mathematica is an asset to conversion among the number bases. A strong draft of anti-metrication sentiment materializes in Volumes 41; through 43;. It seems the culture wars of the age have found their way into the perceptions of Euro-government’s drive to decimalize all nations. Often couched in the guise of “Big Brother” style “fascism”, government-mandated compliance with SI-metric units begins to be seen as an affront to private liberties in Britain. There is a ‘Metric Martyr’, letters howling against forced abandonment of traditional measure, questioning whether Europe really is truly ‘metric’. The Duodecimal Bulletin considers other number bases “ecumenically” in articles about Mayan near-vigesimal, Prof. Schiffman’s hexadecimal, and sexagesimal errors in Sumerian dynastic lists. A couple articles look back on the founding of the Society. Some favorite articles are reprinted, such as Prof. Malone’s “Eggsactly a Dozen” (A Simple Approach to Dozenal Counting) and J. Halcro Johnston’s “The Reverse Notation”.

(View Duodecimal Bulletin issues from the eighth duodecade.)

The ninth Duodecimal Bulletin duodecade continues the trends of the previous dozen issues, minus the anti-metric sentiment. Some reprints grace the early pages, like Nina McClellan’s dozenal essay and two of the four Aspirant’s tests. Prof. Schiffman celebrates “The Most Appealing Integer Twelve”. Scott Proctor’s essay discusses various historical number systems, while Ms. Addie Evans pens an eloquent dozenal essay, originally on the hunt for a rational expression for transcendental numbers through alternative bases. Prof. Gene Zirkel extends the much-heralded seven-segment Schumacher binary-coded hexadecimal digit system to cover base five dozen four. In August 2005, DSGB member Bryan Parry started the DozensOnline web forum. In many ways, the excited chats on this forum resemble the ruminations of our Founders, sending letters to one another in New England and California five dozen plus years earlier.

(View Duodecimal Bulletin issues from the ninth duodecade.)

A Third Generation: The Digital Bulletin

In mid 2008, the Duodecimal Bulletin enters a new era in digital full color. Through the power of contemporary software, vintage color photographs of some early Members animate the histories of the DSA and DSGB in Vols. 49; and 4X;. Dozenal numerals are analyzed and celebrated in a two-part symbology theme, the software overcoming the long-mentioned difficulties with newly-devised numeral symbols. Wolfram Mathematica output can be folded into text seamlessly. Vol. 4X; No. 2 is the first issue to be distributed digitally as well as in print. Prof. Schiffman examines home primes in the last issue of the duodecade. In the closing issues of this duodecade, the Duodecimal Bulletin will be linked more often to material on the website. The future of the Bulletin is in your hands! Join us in our dozenal debate...send in your thoughts and ideas.

Join and help us craft the next duodecade of Duodecimal Bulletin issues! We’re starting with celebrating the “great hundred”, examining dozenal systems of measure, and examining music and the dozen.

(View Duodecimal Bulletin issues from the ninth and the current duodecade.)

This page created Saturday 3 September 2011.