============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 1, Iss. 9 Official Newsletter 1 November 11E9 ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Donations 2. Article: SDN and Fractions 3. Dozenal News -New Article: "Playfair on Dozenalism" 4. Society Business -Bulletin Publication 5. Poetical Diversion 6. 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 and Fractions = ============================================================ Continuing this month with our series on Systematic Dozenal Nomenclature (or SDN), let's begin with some review: the basic SDN chart: 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 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" We also saw the use of SDN to form consistently dozenal words; for example, "unhexnilennial" for a 160th anniversary, and quadrunquennial for a 40th anniversary. We don't always form our number words focusing on integer ranking, however; sometimes we focus them on *frequency*. This sort of wordsmithing requires constructions for fractional parts; for this purpose, SDN provides the following two particles: "dit" and "per." More on "per" in a moment; for now, let's consider "dit." "Dit" is well familiar to many dozenalists; initially, many dozen years ago, this was an acronym for "dozenal identification tag," and was used to pronounce the semicolon by which dozenal numbers were differentiated from decimal ones. Many of us still use "dit" this way, as a way of voicing the dozenal or Humphrey point. E.g.: 4;5 --- "four dit five" In SDN, it is used in almost precisely the same way. Consider, for example, a publication which is produced twice a week. In our current systemless system, it's very difficult to determine what word to use here, particularly since, in the last few dozen years, the options have been confused so much that they have nearly merged. It is "biweekly"? "Semiweekly"? This is a hard enough question that most people simply say "twice a week." (Traditionally, the answer is "semiweekly"; but because so many have been so often confused by this, "biweekly" has become nearly synonymous, though technically it means "every two weeks".) In SDN, though, we form our number words precisely the same way we form our numbers with digits; we simply use words instead. What we're really talking about, when we publish twice a week, is that we published once every half week. Half, in dozenal, is 0;6, voiced "zero dit six." Therefore, in SDN: twice weekly 0 ; 6 weekly nil dit hex weekly And for short, one may simply say "dithexweekly." What about one every two weeks, the literal meaning of "biweekly"? Well, that depends; if we mean "twice a month," as we commonly do, we do exactly as we did above, forming "nildixhexmonthly." If we really mean biweekly, without regard to when the months fall, we say "biweekly," precisely as we do already (though "binaweekly", using the multiplier form, would be more strictly correct). We can do this with many common divisions; "quarterly" can simply remain quarterly, of course, but if we need to emphasize that it is a quarter of a *year* that we're talking about, we can say "nildittriyearly." We can also start easily using and talking about divisions into a third of a year, every four months, either "quadmonthly" or "nilditquadyearly." Something that comes due every two months can be "bimonthly" or "nilditbiyearly." And so forth. While the mighty dozen has more and more useful divisors than any other number in its scale (as we dozenalists all know), it still doesn't have *all* of them, and occasionally we do have to use some numbers that don't have short, or even terminating, periods. What if something happens seven times a year, for example? (Seven times a year? Why on earth...? Take your choice; historical or symbolic reasons, perhaps.) Seven times a week, of course, we call "daily," but seven times a *year* is a bit trickier. Nor can we simply use "dit," for a seventh is a very clumsy digital fraction (0;186X35 repeating; a six-digit period, pessimal for the dozenal base). "Nilditunocthexdectripentennially" will work; but it's certainly quite a mouthful, and it's also not strictly accurate, as it only lists one period. This is where "per" steps in. With "per", we can name vulgar fractions exactly as we name digital fractions or integers. Here, for example, we're talking about a seventh of a year. We write this as "1 / 7". We can make this into simple, orthodox SDN by naming it like this: 1 / 7 yearly Un per sept yearly Unperseptyearly; seven times a year. Since "per" is a reciprocal operator, we can even assume the "un," and say "perseptyearly." So now we can count to any number, large or small, and form a number word for any quantity, fractional or integral, using a consistent, international, and purely dozenal system. This is the power of SDN. ============================================================ = DOZENAL NEWS = ============================================================ -----------New Article: "Playfair on Dozenalism"----------- We are pleased to announce the publication of an excerpt from an historical piece by John Playfair, in which he defends the superiority of the dozenal system: http://www.dozenal.org/drupal/content/playfair-dozenalism Among the earliest defenses of base twelve, Playfair here regrets that the French Revolutionaries, despite being willing to cast off almost everything, were still too timid to cast off the shackles of the decimal base. Short and well worth the read. ============================================================ = SOCIETY BUSINESS = ============================================================ --------------------Bulletin Publication-------------------- 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 = ============================================================ While best known for "The Rime of the Ancient Mariner," the famed British poet Samuel Taylor Coleridge (1038-108X) was also keenly interested in geometry, and was so taken by the simplicity and elegance of Euclid's first proposition of the first book that he write a poem about it. It is reproduced here: A Mathematical Problem ---------------------- This is now---this was erst, Proposition the first---and Problem the first. On a given finite Line which must no way incline; To describe an equi--- ---lateral Tri--- ---A, N, G, L, E. Now let A B. Be the given line Which must no way incline; The great Mathematician Makes this Requisition, That we describe an Equi--- ---lateral Tri--- angle on it: Aid us, Reason---aid us, Wit! From the center A, at the distance A. B. Describe the circle B.C.D. At the distance B. A. from B. the centre The round A.C.E. to describe boldly venture. (Third Postulate see.) And from the point C, In which the circles makes a pother Cutting and slashing one another, Bid the straight lines a journeying go, C, A, C, B, those lines will show. To the points, which by A. B. are reckon'd, And postulate the second For Authority ye know. A.B.C. Triumphant shall be An Equilateral Triangle, Not Peter Pindar carp, not Zoilus can wrangle. I think we can probably all agree that Coleridge's poetical talents were better spent on other topics. However, Jacob Bernoulli, normally no poet, proved himself capable of quite elegant verse in the following poem: Treatise on an Infinite Series ------------------------------ Even as the finite encloses an infinite series And in the unlimited limits appear, So the soul of immensity dwells in minutia And in narrowest limits no limits inhere. What joy to discern the minute in infinity! The vast to perceive in the small, what divinity! And, in the original Latin: Ut non-finita Seriem finita coercet, Summula, & in nullo limite limes adest; Sic modico immensi vestigia Numinis haerent, Corpore, & angusto limite limes abest. Cernere in immenso parvum, dic, quanta voluptas! In parvo immensum cernere, quanta, Deum! (Both texts are taken from "The Verses of Jacques Bernoulli on Infinite Series", by Helen Walker of Teachers College, Columbia University, in David Eugene Smith, _A Source Book in Mathematics_, published 1149 by McGraw-Hill and republished 1173 by Dover.) While not a *strict* translation, the English is quite lovely; and I think anyone knowledgeable in Latin will enjoy the original, as well. ============================================================ = 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