============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 1, Iss. 8 Official Newsletter 1 October 11E9 ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Donations -Now taking donations via WePay---no login necessary 2. Article: SDN for Word Construction 3. Dozenal News -"Summer Reading: 'New Numbers'" by Charles Petzold -"The case for base-twelve" by Eric L. Dion -"Leclerc sur Douzainisme" by Georges-Louis Leclerc 4. Society Business -Bulletin Publication -Potential Presentation at NCTM 5. Poetical Diversion 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 or WePay. 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 ---------------------------WePay---------------------------- We have accepted donations through PayPal for some time; now we can also accept them via WePay, which allows donations to be made without having an account. We hope that this will make it easier to support the Society. ============================================================ = SDN for Word Construction = ============================================================ We saw, in Issues 01:06 and 01:07, the basics of Systematic Dozenal Nomenclature (SDN). To recap very briefly, here is the chart of SDN words: 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 We also saw that the simplest way to use SDN is to name the highest power in the number, and then to list the digits in order. For example, the current year is 11E9; in SDN, we could pronounce this as: 11E9 = "one triqua one elv nine" However, while SDN makes talking about dozenal numbers as easy (easier!) than talking about decimal ones, it also makes it possible to dozenalize all of our nomenclature without invalidating many of the common words we use every day. For example, consider the words for various types of vehicle, based on the number of wheels they have: Wheels Name --------------------------------------------- 1 Unicycle 2 Bicycle 3 Tricycle 4 Four-wheeler 16; Eighteen-wheeler We can see that our common system of cobbling together anglicized Greek roots breaks down after three; but it will please us to note that the first three are all perfectly regular, orthodox SDN! They're not irregular, just magic syllables which we must memorize to be correct; but they are still the same words that we've grown up using. However, SDN is easily able to go up the chain here, making words for all sorts of vehicle which are clumsy or even impossible in our current systemless system: No. of Wheels Name --------------------------------------------- 1 Unicycle 2 Bicycle 3 Tricycle 4 Quadcycle 5 Pentcycle 6 Hexcycle ... 16 Unhexcycle Our famous "eighteen wheeler," what I grew up calling a "semi" and what is regularly called a "tractor-trailer," is trival to name concisely and simply according to SDN. And we can extend this even further. Consider our names for polygons; that is, enclosed, two- dimensional shapes. While these follow a system, the system is not normal for our language, nor is it well understood by many. Particularly in the simpler shapes, we have many irregular words; some polygons are named by number of sides, some by number of angles; and when we get into higher ranks, they start becoming quite unfamiliar. Below is a chart of our traditional polygon names to demonstrate the confusion and difficulty. Polygon Name Number Word ---------------------------------------------- 3 Triangle Tri 4 Rectangle; Quad Quadrilateral 5 Pentagon Pent 6 Hexagon Hex 7 Septagon Sept 8 Octagon Oct 9 Nonagon Enn X Decagon Dec E Hendecagon Undec 10 Dodecagon Dodec 11 Triskaidecagon, Tridec tridecagon 12 Tetrakaidecagon, Unquad tetradecagon ... 18 Icosagon Vigi, Icosa ... 20 Icosatetragon ? There is a system here, but it's opaque and unfamiliar; indeed, geometers typically start referring to polygons as "n-gons" (e.g., "twelve-gon" or "thirty-four-gon") just to avoid this whole mess. However, SDN makes these all quite simple: Polygon Name Number Word ---------------------------------------------- 3 Triangle, trigon Tri 4 Quadragon; Quad Quadrilateral 5 Pentagon Pent 6 Hexagon Hex 7 Septagon Sept 8 Octagon Oct 9 Ennagon Enn X Decagon Dec E Levagon Lev 10 Unquagon; Unqua; unnil Unniligon 11 Ununigon Unun 12 Unbigon Unbi ... 18 Unoctagon Unoct ... 20 Binaunquagon; Binaunqua; binil biniligon We see here that the names of the polygons *exactly matches* the SDN number root, making it easy to tell at a glance what shape goes with what name and vice-versa. We see a few interesting things here. One is that SDN sometimes provides more than one possible name for a thing. For example, the 10-gon is either "unquagon" or "unniligon"; both of these are correct and regular, easily constructible according to a short and simple set of rules. "Unquagon" is formed from the the root for 1, "un," plus the positive power suffix, "qua"; this forms our regular root for 10^1, "unqua." "Unniligon" is the more direct formulation; it is simply "un" for 1 and "nil" for zero, forming "10" in words rather than digits, plus "i" to make it flow better and "gon" to show that we mean a polygon. The same thing goes for "binaunquagon," which can also be called a "biniligon." The latter is easy: "bi" for 2 and "nil" for zero, writing "20" in words rather than digits. The former is likewise simple, though a bit less so. We start with "unquagon"; but this time, we want "unquagon" multiplied by 2. So we use our root for 2, "bi," and attach it. However, "biunquagon" would look like 10^21, much larger than our intended meaning of "2 x 10^1"; so to ensure clarity of meaning, we add "na" to separate the two. This provides a good segue into the full power of SDN. The table given above is E0 perbiqua (SDN for "per gross") of what any user of SDN needs. However, there is more for when we need it. Specifically, there are the *multiplier forms*: Part. Mult. Pos. Power Neg. Power ------ ------ ----------- ------------ Nil Nili Nilqua Nilcia Un Uni Unqua Uncia Bi Bina Biqua Bicia Tri Trina Triqua Tricia Quad Quadra Quadqua Quadcia Pent Penta Pentqua Pentcia Hex Hexa Hexqua Hexcia Sept Septa Septqua Septcia Oct Octa Octqua Octcia Enn Enna Ennqua Enncia Dec Deca Decqua Deccia Lev Leva Levqua Levcia These multiplier forms, as can be seen, are typically just the root particular plus a vowel, either "a" or "i". However, when the root particle ends in a vowel, an "n" is added, as well; this avoids such ugliness as "biaunqua." Further, "quad" becomes "quadra," in accordance with normal usage. These multiplier forms are used for disambiguation. The example above of binaunquagon (2 x 10^1-gon) and biunquagon (10^21-gon) is an obvious example. Another example might be a 200th anniversary (for more on anniversaries, see below). A town celebrating its 200th anniversary (in SDN, its "two biqua anniversary") might want to put up banners proclaiming this fact, as they often do to proclaim sesquiduplicentennials and other decimal silliness. This is a "binabiquennium," taking care to use "bina," the multiplier form. To leave it out and have a "bibiquennium" would be to proclaim a 10^22 anniversary, which is likely quite a bit longer than this particular town has been around. (Of course, one can avoid this whole issue and simply proclaim a "binilnilennium," writing "200" in words (bi-nil-nil) rather than digits. But the other forms are there when we want them.) Two more prominent examples of SDN simplifying and dozenalizing our nomenclature are base names and anniversaries. Base names, of course, are dear to the heart of every DSA member. However, they are clumsy in our current nomenclature. Let's line them up with SDN and see how much simpler we can make them. Throughout, in SDN, I will use "-ary" as a suffix; however, "-al" could be interchanged in every or any case. Base Traditional SDN ---- ------------ ---------- 2 Binary Binary 3 Ternary Trinary 4 Quadral, Quadrary quaternary 5 Quinary Pentary 6 Senary Hexary 7 Septal Septary 8 Octal Octary 9 Nonary Ennary X Decimal Decimal, decary E Undecimal Levary 10 Duodecimal, Unnilary, unquary dozenal ... 14 Hexadecimal Unquadrary ... 18 Vigesimal Unoctary ... 50 Sexagesimal Pentnilary, pentanunquary Notice that many of these words are the same (e.g., binary, octal), but that the system in SDN tracks the words we use for successive powers of a dozen *exactly*. Furthermore, we can easily predict words for bases even if we don't actually know them. For example, without either previous knowledge of base mathematics (or of the Latin language), hearing "vigesimal" carries no meaning whatsoever. However, with SDN, "unoctary" or "unoctal" *immediately* and *unambiguously* presents the same meaning, base 18;, to anyone who knows how to count; that is, to practically everybody. Anniversaries are another common and greatly simplified area of application for SDN. We in America celebrated our bicentennial only a few dozen years ago; and "bicentennial" is an easy word to figure out. However, many localities celebrate 150.-year anniversaries, or 350.-year anniversaries; and determining what to call such things is not only difficult, but also productive of ridiculous results ("sesquiduplicentennial" and such monstrosities). The dozenal analogs of these anniversaries, of course, are 160 or 260; but even the exact dozenal duplicates of these hard-to-name anniversaries, such as 106 for 150., or 18X for 250., are just as simple. The table below contains a few major anniversaries in both dozenal and decimal, with the SDN name listed. Decimal Dozenal SDN -------- -------- --------------- 5 5 Pentennial 6 6 Hexennial 10 X Decennial 12 10 Unquennial; Unnilennial 15 13 Untriennial 18 16 Unhexennial 20 18 Unoctennial 24 20 Binaunquennial; Binilennial 25 21 Biunennial 30 26 Bihexennial 35 2E Bilevennial 36 30 Trinaunquennial; trinilennial 40 34 Triquadrennial 45 39 Triennennial 48 40 Quadrunquennial; Quadnilennial 50 42 Quadbiennial 100 84 Octquadrennial 125 X5 Decpentennial 144 100 Biquennial; unnilnilennial 150 106 Unnilhexennial 175 127 Unbiseptennial 180 130 Untrinilennial 192 140 Unquadnilennial 200 148 Unquadoctennial 216 160 Unhexnilennial 240 180 Unoctnilennial 250 18X Unoctdecennial 252 190 Unennnilennial 275 1XE Undeclevennial 288 200 Binabiquennial; binilnilennial 360 260 Bihexnilennial We can see here that it is trivial to name anniversaries that are difficult or even impossible in traditional decimal-based English nomenclature. The ability extends well beyond the anniversaries of city-foundings and the like; even wedding anniversaries can benefit. A couple's quadrunquennial (or quadnilennial, if you will) is truly a great accomplishment; but what would you call it without using SDN? Next month: SDN for *fractional* words! ============================================================ = DOZENAL NEWS = ============================================================ ----"Summer Reading: 'New Numbers'" by Charles Petzold----- Charles Petzold, a mathematician and computer scientist, some years ago discovered the work of one of our founders, F. Emerson Andrews, _New Numbers_. http://www.charlespetzold.com/blog/2006/08/250954.html He seems quite taken by the text, and has some interesting comments which may be worth perusing. Thanks to DSA Secretary Jen Seron (#3X2) for pointing out this text. ---------"The case for base twelve" by Eric L. Dion--------- Eric L. Dion, back in June, wrote a delightful two-part blog post on why we should switch to dozenal. Oddly, the posts give no indication that Mr. Dion has ever heard of the DSA: http://dissentofman.blogspot.com/2013/06/the-case-for-base-twelve-part-1.html Using lowercase Greek letters gamma and psi for X and E, Mr. Dion explains the nature of place notation; the advantages of base twelve; and proposes a system of nomenclature. Worth the read. ----"Leclerc sur Douzainisme", by Georges-Louis Leclerc----- In keeping with our last few articles delving into the historic roots of dozenalism, we are proud to announce the publication of an excerpt from Georges-Louis Leclerc, the Count of Buffon, on dozenalism: http://www.dozenal.org/drupal/content/leclerc-sur-douzainisme It is offered here in its original language, along with a facing English translation. ============================================================ = SOCIETY BUSINESS = ============================================================ --------------------Bulletin Publication-------------------- We're proud to repeat our announcement earlier this month that _The Duodecimal Bulletin_ WN X0 was published on 15 September, a day ahead of our previously announced schedule. Our editor put together an excellent and intriguing issue, and we hope that the membership was able to enjoy it. The _Bulletin_ schedule for the immediate future remains the same: 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.). ============================================================ = POETICAL DIVERSION = ============================================================ The below was inspired by William Lauritzen's article in the recent _Bulletin_ on versatile numbers. For generations past, the primes have reigned, the scholars plumbing through their fertile depths, all students drilling them with interest feigned, til later, scholars, they retraced these steps. But primes, so still and dull, so sterile too, with but themselves and one to hold them up, may scholars draw, but practice fail to woo, for practice with variety would sup. But versatiles! what joy you bring the soul! each with more factors than all less than you! O infinite, like primes, no rule can poll! All are twelve's multiples or factors, too! The source of usefulness in numbers all, without you senseful number systems fall! ============================================================ = 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 EACH ONE, TEACH ONE