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Duodecimalbulletinissue521.Pdf The Duodecimal Bulletin THETHE DuodecimalDuodecimal BulletinBulletin Vol. 52z (62d), No. 1 • July 11EEz (2015d) • Volume 52 z (62 d ), Number 1 • Whole Number X 2 z (122 d ) • July 11 Base Annotation Schemes Whole Number EE z (2015 X d ) z (122 ) ISSN 0046-0826d 2d X ETY Volume Five Dozen Two (52z) Number 1 Whole Number Ten Dozen Two ( 2z) CI O The Dozenal Society of America • • O F is a voluntary, nonprofit corporation, organized to S E 0 1 A L conduct research and educate the public in the use X 2 M The DuodecimalDuodecimal A of base twelve in calculations, mathematics, weights DuodecimalDuodecimalDuodecimal 9 3 E N R and measures, and other branches of pure and ap- E 8 4 I Bulletin Z BulletinBulletin C BulletinBulletin 7 5 plied science. BulletinBulletinBulletinBulletin A O 6 D Volume Sixty Two (62 ) Number 1 Whole No. One Hundred Twenty Two (122 ) d • • d S Basic membership is free, but as a nonprofit we de- pend upon the generosity of our members to continue operating. An annual subscription of US$18.00d B Table of Contents C The Duodecimal Bulletin (US$16.00z) entitles the member to delivery of pa- is an official publication of: per copies of The Duodecimal Bulletin. President’s Message by Donald Goodman ....................................................2z Officers The Dozenal Society Editorial: Radically Conventional ..................................3z Board Chair Jay Schiffman of America, Inc. New Members ...........................................................7z 13510 Photo Drive President Donald Goodman Accuracy of Common Roundings Vice President Graham Steele Woodbridge, VA 22193 by Donald Goodman ....................................................8z Secretary Jen Seron Base Annotation Schemes Treasurer Jay Schiffman Founded: 1160z (1944d) by John Volan.........................................................10z Patterns and Palatable Morsels in Duodecimal Official Website: Board of Directors by Prof. Jay L. Schiffman .............................................22 EE z www.dozenal.org Class of 11 z (2015d) From the Archives: Uncial Jottings of a Harried Infantryman Jay Schiffman philadelphia, pa by Pvt. William S. Crosby .............................................29z Email us at: Dan Simon new york, ny Systematic Dozenal Nomenclature Summary ......................31z [email protected] Timothy Travis fayetteville, nc Dozens in the Media ..................................................32z Patricia Zirkel boynton beach, fl Follow us on Twitter: Class of 1200z (2016d) @dozenal John Earnest baldwin, ny Editor: John Volan John Impagliazzo long island, ny [email protected] Graham Steele framingham, ma Gene Zirkel boynton beach, fl The Dozenal Society Class of 1201z (2017d) of Great Britain: Michael De Vlieger st. louis, mo www.dozenalsociety.org.uk Donald Goodman woodbridge, va Jen Seron new york, ny John Volan belmont, ma The DSA does not endorse particular symbols for digits in alternate bases. Authors are free to propose their own symbols. However, unless otherwise specified, this publication defaults to the Pitman numerals for the digits ten (X) and eleven (E). The DSA does not endorse any particular scheme for disambiguating the base of a number. Authors are free to propose their own notations. However, this publication will annotate the base of any number containing more than one digit, and as a default will do so using a single- letter subscript: d for Decimal, z for doZenal, x for heXadecimal, o for Octal, b for Binary, etc. By default, numbers are annotated individually, although whole numeric expressions in parentheses may be given a single annotation applying to all of their components. A tabular display may omit annotations, as long as the base used by the entire display is indicated. The Duodecimal Bulletin, Volume Five Dozen Two, Number One, Whole Number Ten Dozen Two. Copyright © 11EEz (2015d), The Dozenal Society of America. July 11EEz (2015d) Page One 1z President’s from the Message Editor’s Desk reetings to our membership; we hope this long-awaited issue of our Bulletin Radically finds you well. A great deal has come and gone since our last issue, and we ConventionalConventionalConventional are excited to have this issue in our hands, ready to reveal to us new aspects G If you’re a long-time member of the Dozenal Society of America, some changes you see of the dozenal base. This issue brings us change, and with that change growth; the in this issue of the Duodecimal Bulletin may take you aback. First, you’ll have noticed DSA is continuing its march into the future at the dawning of the 1200 ’s. z that the Dwiggins ten digit (X) has been replaced with the Pitman ten (X). Second, First, we must regretfully bid farewell to the past editor of the Bulletin, Michael something seems to have happened to all the usual Humphrey points (semicolons De Vlieger (Member 37E ). Since his first issue, in 11E4 (2008 ), Mike has continually z z d acting as “duodecimal” points, in contrast to periods acting as “decimal” points). In pushed the DSA forward, and it is with great sorrow that the Board accepted his their stead there seem to be a lot of “z” and “d” subscripts. Gentle Readers, I beg resignation earlier this year. Unfortunately, the press of business was simply too great your indulgence, as I address both of these developments in turn. for him to continue his duties, and we wish him the best of luck in the future. Mike’s first issue was a lot of firsts: the first digitally-produced Bulletin; the first full-color Bulletin; the first Bulletin in many years to return to our original Dwiggins Pitman versus Dwiggins numerals. But fittingly, it also was headlined by a history of the DSA, uniting both As long anticipated, the glyphs for the Pitman characters have achieved official our long and distinguished past with our journey into the future. recognition by a mainstream, international standards body: the Unicode Consortium. We continue that journey with this issue. Our new editor, John Volan (Mem- 1 As of June 15thz, 11EEz (June 17thd, 2015d), version 8.0.0 of the Unicode standard ber 418 ) has endeavored to keep the same look-and-feel of Mike’s original and beautiful z has been released, including the following two code-points of dozenal interest:2 design; he has succeeded brilliantly, despite using different software. John has con- tributed to the Bulletin in the past, notably an extensive article on Systematic Dozenal U+218Ax X TURNED DIGIT TWO Nomenclature; he submits an article in this issue on “Base Annotation Schemes” which digit for 10d in some duodecimal systems E • will surely provoke an equal amount of thought and discussion. Like Mike’s initial U+218Bx TURNED DIGIT THREE digit for 11 in some duodecimal systems issue, this article hearkens back to the very beginnings of our Society, with a “new/old” • d proposed solution to a problem inherent in proposing a change of base. Kudos to our Israeli friend “Treisaran” for alerting the DozensOnline Forum about E Readers will be delighted to see Prof. Jay Schiffman (Member 2 8z) returning to this.3 Also, someone has already updated the “Duodecimal” article on Wikipedia.4. our pages once again, providing us great food for thought on integer sequences and Of course, it will be some time before operating system fonts catch up with the new why dozens are so powerful a tool in that field. standard, so that we can actually see these glyphs rendering on our web browsers. But We also explore some recent contributions to mass media which highlight our the significance of this milestone for the DSA, as well as for its sister organization, the favorite number. Online videos expositing not only the utility of base twelve, but also Dozenal Society of Great Britain, cannot be overstated. The time has come for this its beauty, are just some of the joys that we will look at in these pages. publication to begin using the Pitman characters as its default convention. Our membership has been exploding; our Internet presence has been doing an This is feasible, thanks to the efforts of our current president, Don Goodman incredible job spreading knowledge of and interest in the Society. In the past two years (Member 398z), who some time ago developed a package for typesetting these characters alone, we have gained over 90 new members; this is significantly more than the several 5 z in LATEX . Not to mention the brilliant work of our previous editor, and past president, years prior to our expanded website and the ability to join online. This membership Mike De Vlieger (Member 37Ez), using Adobe Illustrator to render these, and numerous surge is just another sign of encouragement as we move forward into the future. other alternate characters. Our Bulletin, thanks to Mike De Vlieger, has already entered the Twenty-First The official position of the DSA has long been, and continues to be, not to endorse 1 Century; join us as we usher it into the One Dozen Third Biquennium . The future is particular characters, but rather uphold the freedom of individual dozenalists to full of possibilities, and the DSA intends to be fully a part of it. experiment with characters they prefer. This publication has always been a friendly 1 Donald P. Goodman III, current President of the DSA, also publishes a monthly email http://www.unicode.org/versions/Unicode8.0.0/ 2http://www.unicode.org/charts/PDF/Unicode-8.0/U80-2150.pdf newsletter, The DSA Newscast. It’s free to all DSA members—so be sure to join! 3http://z13.invisionfree.com/DozensOnline/index.php?showtopic=1324 4https://en.wikipedia.org/wiki/Duodecimal 1 5 See page 31z. http://www.ctan.org/tex-archive/fonts/dozenal 2z Page Two The Duodecimal Bulletin July 11EEz (2015d) Page Three 3z place for members to field their symbology suggestions, and that will not change.6 • familiar—one that requires as little deviation as possible from what everyday Nevertheless, the DSA has also long recognized the importance of settling upon folks are used to (“Principle of Least Change”).
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