============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 1, Iss. 6 Official Newsletter 1 August 11E9 ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Donations 2. Article: Systematic Dozenal Nomenclature, in Brief 3. Dozenal News -Livin' la Vida Dozenal!, by James Hobbs -60: Behind Every Second, Millenniums of History, by Roni Jacobson -RAENBO Dozenals, by Timothy Travis 4. Society Business -Bulletin Publication -Potential Presentation at NCTM 5. Poetical Diversion 6. Dozenal Thoght of the Month 7. Backmatter ============================================================ = DONATIONS = ============================================================ Members, please remember that while dues are no longer required for membership, we still rely on the generosity of members to keep the DSA going. Donations of any amount, large or small, are welcome and needed. A donation of $10; ($12.) will procure Subscription membership, and entitles the payer to receive both a digital and a paper copy of the _Bulletin_ if requested. Other members will receive only a digital copy. To invoke this privilege, please notify the Editor of the Bulletin, Mike deVlieger, at mdevlieger@dozenal.org As members know, we are a volunteer organization which pays no salaries. As such, every penny you donate goes toward furthering the DSA's goals. It may be worth considering a monthly donation; say, $3, or $6, or whatever seems reasonable to you. This can be set up quite easily with Paypal. Of course, if you prefer to donate by check, you may send them to our worthy Treasurer, Jay Schiffman, payable to the Dozenal Society of America, at: Jay Schiffman 604-36 South Washington Square, #815 Philadelphia, PA 19106-4115 ----------------------Member Benefits----------------------- Chief among the benefits of membership, aside from the knowledge of supporting the DSA's mission, is receipt of _The Duodecimal Bulletin_. In addition, however, members also receive (digitally) a membership card containing their vital member information and a monthly calendar with dozenal numbers, containing suitable and educational dozenal quotations and graphics, laid out for wall display. To receive these, please notify us that you'd like to receive them: Contact@dozenal.org ============================================================ = SYSTEMATIC DOZENAL NOMENCLATURE, IN BRIEF = ============================================================ (Note that this article contains tables which are formatted for plain text. These tables will not not appear properly if you are not using a monospaced font. If you're not sure what this means, try opening this newsletter in Notepad, or setting your email to "Text only" or "Plain text," and see if that helps. Also, this newsletter is posted in the members section of the DSA website, and will appear properly there.) Dozenalists have long argued about the proper way to speak when using dozenals. Is it "ten" or "dek?" Is it "eleven," "el," "elv," "elf," or something else entirely? Do we say "twelve," "dozen," or what? And just what do we call a dozen gross, anyway? Traditional English has a system for talking about dozenals, simple enough, which goes like this: Number (doz.) Word ------------- ----------- 10 dozen 100 gross 1000 great gross And we can extrapolate from these three; for example, the number "743 2X9" is "seven gross four dozen three great gross, two gross ten dozen nine." This works, in the sense that it is functional; and this is usually the very best way to inroduce dozenals to someone who's not familiar with them. However, it is clunky, verbose, and (worst of all) ugly. Something better is needed if we are to make dozenals mainstream. For many years, the DSA used the "do-gro-mo" nomenclature, which is essentially a shorthand for the above "plain English" system. "Dozen" became "do," "gross" became "gro," and "great gross" became "mo," forming the following system well-known to anyone who has perused the older issues of our _Bulletin_: 10 Do 0.1 Edo 100 Gro 0.01 Egro 1000 Mo 0.001 Emo 1 0000 Do-mo 0.0001 Edo-mo 10 0000 Gro-mo 0.0000 1 Egro-mo 100 0000 Bi-mo 0.0000 01 Ebi-mo 1000 0000 Tri-mo 0.0000 001 Etri-mo And so forth, just as far as one cares to take it. This is a much more robust system that the "plain English" method, and served us well for many years. Some of us continue to use it. However, even this system has a flaw: it's too provincial. That is, it fits in pretty well with English (though the fractional names do sound a bit funny), but it fits in poorly or not at all in other languages. Dozenal isn't meant to be limited to the Anglosphere, and never was; it's *mathematically*, not *culturally*, the superior base. So as well as this system has worked, something better is still needed. Enter Systematic Dozenal Nomenclature (SDN). A group of dozenalists on the DozensOnline forum, ably led by John Kodegadulo, has put together a system which is comprehensive; systematic; simple; and international. The system manages all these traits at once by adopting our elder, Ralph Beard's, Principle of Least Change: it uses things which are familiar to all of us, changes them as little as possible to accomplish our goals, and then runs with them. The familiar basis for SDN is the set of numerical particles used by the International Union for Pure and Applied Chemistry (IUPAC). IUPAC takes very familiar Latin and Greek roots, most of which we already know, to form the names of new chemical elements until they can be given their "official" names; SDN adds two new particles for ten and eleven, and then applies them in preditable, easy ways. These particles, 0-9 already international standards, are: Num. Part. ----- ------ 0 Nil 1 Un 2 Bi 3 Tri 4 Quad 5 Pent 6 Hex 7 Sept 8 Oct 9 Enn X Dec E Lev Further particles can be formed using the familiar principles of place notation; e.g., "25" is simply "bipent," the number particles being put together just as the number digits are. There's one more thing to add, though. To really press these convenient little particles into dozenal service, we need something to indicate exponentiation. So we add to these the suffix "qua" if the power is positive, and "cia" if the power is negative, like so: Num. Part. Pos. Power Neg. Power ----- ------ ----------- ------------ 0 Nil Nilqua Nilcia 1 Un Unqua Uncia 2 Bi Biqua Bicia 3 Tri Triqua Tricia 4 Quad Quadqua Quadcia 5 Pent Pentqua Pentcia 6 Hex Hexqua Hexcia 7 Sept Septqua Septcia 8 Oct Octqua Octcia 9 Enn Ennqua Enncia X Dec Decqua Deccia E Lev Levqua Levcia So "10" is now "unqua" (10^1); 100 is "biqua" (10^2); 1000 is "triqua" (10^3); 1 0000 is "quadqua" (10^4); and so on. We literally simply count the digits after the first, use the corresponding word, and call it a day. For example: 7 82E4 XE45 In the "plain English" system, this number is borderline impossible to speak; that is, it could probably be done, but the result would be so unwieldy that speaking it would communicate practically nothing to the listener. In the "do gro mo" system, we get the rather manageable: Seven gro bi-mo eight two el four dek el four five But to speak this, we must recall that "bi-mo" means "10^6," we must count out the digits, we must see that we've got seven gro of bi-mo, and then voice the number accordingly. Doable, certainly; but excessively complex as well as too provincial in its roots. In SDN, we simply count the digits after the first (eight), select the corresponding and very familiar numerical particle (oct), add "qua" to it (since it's clearly a large number rather than a small one), and we've got the answer: Seven octqua eight two el four ten elv four five SDN is at once simpler, more comprehensive, and more international than other systems. Expect a full exposition of SDN in an upcoming _Bulletin_; until then, you can learn more at the DozensOnline forum, and at http://gorpub.freeshell.org/dozenal/blosxom.cgi/dozapp.html#sdn ============================================================ = DOZENAL NEWS = ============================================================ ------------------Livin' la Vida Dozenal!------------------- James Hobbs, an engineering graduate student studying carbon fiber and other composite materials at the University of Utah, has written an excellent little article on our favorite number base, "Livin' la Vida Dozenal!" http://mathematicianscientistengineer.blogspot.com/2013/04/livin-la-vida-dozenal.html Mr. Hobbs not only knows and prefers dozenal, but uses it in his daily life, as does his family. He uses TGM's Tim for his time (essentially, dozenalized hours with dozenal divisions rather than sexagesimal) and notes the use of a dozenal ruler, though he doesn't say what units are on it. Describes very briefly the TGM system and notes a couple of its benefits. Definitely worth a read. ------60: Behind Every Second, Millenniums of History------ This month, the DSA got a mention in none other than the New York Times! The Gray Lady published a brief note with the above title by Roni Jacobson on 8 July 11E9, which notes that ten "is actually an inefficient number on which to build a numeral system." The article, which primarily discusses base five dozen (sixty), mentions the DSA toward the end. http://www.nytimes.com/2013/07/09/science/60-behind-every-second-millenniums-of-history.html The article was originally published on page D2 with the headline "Take a Number." Not exactly above the fold, but still a little bit of good publicity. Thanks to Professor Gene Zirkel, former president and long- time stalwart of the Society, for pointing out this piece. ----------------------Raenbo Dozenals----------------------- Timothy Travis (#342), Society board member, has contributed an article with some lovely graphics and very interesting thoughts on a dozenal system, which he terms the Raenbo system: http://www.dozenal.org/drupal/content/raenbo-dozenals In addition to having some beautiful graphics, Mr. Travis presents a few interesting thoughts, some new symbols, and a truly beautiful geometric design for the backs of playing cards. Which demands the inquiry: playing cards are a fundamentally numerical pursuit. Any ideas for dozen-centric games? Send them in! ============================================================ = SOCIETY BUSINESS = ============================================================ --------------------Bulletin Publication-------------------- Many of you have undoubtedly noticed that our Bulletin has not been published since 11E6 (2010.). After some conversation with our esteemed Editor, Michael deVlieger, we have established a publication schedule for the near future. Sep 16: _The Duodecimal Bulletin_ WN X0, for 11E7 (2011.) Dec 10: _The Duodecimal Bulletin_ WN X1, for 11E8 (2012.) Mar 01: _The Duodecimal Bulletin_ WN X2, for 11E9 (2013.) This will have us caught up to the current year, and future issues published in 11EX (after WN X2) will be for that year (11EX, or 2014.). ---------------Potential Presentation at NCTM--------------- At our annual meeting, due to the successful ASEE presentation discussed in our last issue, the DSA suggested research into a similar practice next year. That is, we wished to investigate the possibilities of setting our annual meeting close in time to some mathematical conference and submit a presentation on dozenals and alternative bases to that presentation. This year, we are considering setting the meeting to coincide with the National Conference of Teachers of Mathematics. There are two regional conferences of the NCTM next year, in October and November, in Indianapolis, IN and Richmond, VA. We are in need of people to help with such a presentation. If you are interested in doing so in any capacity, plese write us at: Contact@dozenal.org This could be great publicity for dozenal and the Society, so please, write if you're able to help. ============================================================ = POETICAL DIVERSION = ============================================================ We noted last issue (Newscast 01:05) that the English tongue has a great variety of rhymes, songs, and games suitable for (and actually used for) teaching numbers and counting to small children. We presented one, which included not only counting but also some more advanced concepts, in that issue, as well. This issue, we intend to adapt many of our current counting songs for dozenal, so that they can be used for teaching our favorite number base. Most of these are quite well-known, or at least exist in quite well-known variations, so we will only be presenting the new verses. This policy saves the reader's patience, as well as limits the length of this newsletter. Some of these, such as "One, Two; Buckle My Shoe," go beyond the decimal base; they are also modified to conform to dozenal. In such cases, however, every effort has been made to ensure they conformity with the original spirit of the rhymes, as far as possible. It is certain that these are not the best that can be done; please, send in your ideas for improvements! ONE, TWO; BUCKLE MY SHOE ------------------------ Eleven, twelve; dig and delve. Twelve-one, twelve-two; court the maids do; Twelve-three, twelve-four; maids at the store; Twelve-five, twelve-six; whip up the mix; Twelve-se'en, twelve-eight; maids now must wait; Twelve-nine, twelve-ten; plates empty again; Twelve-eleven, twelve-twelve; go to the shelf. OVER IN THE MEADOW ------------------ Over in the meadow, snuggled up in their den, lived an old mother fox and her foxes 'leven. "Bark!" said the mother; "We bark!" said the 'leven; and they barked and they snuggled in their cozy small den. Over in the meadow, huddled deep in her delve, lived an old mother gophers and her little gophers twelve. "Dig!" said the mother; "We dig!" said the twelve; and they dug and they played in their mother's deep delve. THE ANTS GO MARCHING ONE BY ONE ------------------------------- The ants go marching ten by ten, hurrah! hurrah! The ants go marching ten by ten, hurrah! hurrah! The ants go marching ten by ten, The little one says it's not the end, And they all go marching down, to the ground, to get out of the rain! The ants go marching 'le'en by 'le'en, hurrah! hurrah! The ants go marching 'le'en by 'le'en, hurrah! hurrah! The ants go marching 'le'en by 'le'en, The little one stops to grab his pen, And they all go marching down, to the ground, to get out of the rain! The ants go marching twelve by twelve, hurrah! hurrah! The ants go marching twelve by twelve, hurrah! hurrah! The ants go marching twelve by twelve, The little one stops to start to delve, And they all go marching down, to the ground, to get out of the rain! TWELVE LITTLE AEROPLANES ------------------------ (Modified from the traditional "Ten Little Indians," due to the latter often being offensive.) One little, two little, three little aeroplanes; four little, five little, six little aeroplanes; seven little, eight little, nine little aeroplanes; ten, eleven, twelve flying high! Twelve little, eleven little, ten little aeroplanes; nine little, eight little, seven little aeroplanes; six little, five little, four little aeroplanes; three, two, one flying high! CONCLUSION ---------- Other songs can be easily modified simply by adding verses. E.g., "Five green and speckled frogs" and can be made into "Six green and speckled frogs"; "There were ten in the bed" and "Ten silly monkeys" can be made into twelve each. But having any of these, either simply extended or actually changed, in our repertoire may prove useful in explaining dozens to others, particularly to the young. ============================================================ = DOZENAL THOUGHT OF THE MONTH = ============================================================ EACH ONE, TEACH ONE ============================================================ = BACKMATTER = ============================================================ _The DSA Newscast_ is a production of the Dozenal Society of America. If you have received this publication in error, or otherwise do not wish to receive it anymore, please unsubscribe by mailing a message containing the string "UNSUBSCRIBE DSA NEWSCAST", exactly as typed, in its body, to the Reply-To address of this message. For questions, comments, submissions, or other communication with the _Newscast_, please write to: newscast@dozenal.org