============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 2, Iss. 2 Official Newsletter 1 February 11EX ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Donations 2. For Sale 3. Comment on Mathematical Abbreviations 4. Cooking with Dozens 5. Dozenal News 6. Society Business 7. Poetical Diversion 8. 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, both of which are available at our web site. 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 ============================================================ = FOR SALE = ============================================================ The DSA is pleased to offer the following for sale. These are all either at cost, or the proceeds go to the Society. Wall Calendar for 11EX (stapled binding) $11.60 Wall Calendar for 11EX, coiled binding $16.70 Weekly Planner for 11EX $11.29 TGM: A Coherent Dozenal Metrology $8.00 Prices are, unfortunately but by necessity, in decimal. To find these works, simply go to: http://www.lulu.com/shop/shop.ep and enter the appropriate terms. E.g., searching for "11EX" will turn up these calendars and the planner; searching for "TGM dozenal" will turn up the TGM book. We hope to offer other titles, and even some other items (such as dozenal clocks and the like), in the near future. ============================================================ = COMMENT ON MATHEMATICAL ABBREVIATIONS = ============================================================ Gene Zirkel (#67) says regarding our recent discussions on this topic: "In t^3;6, I was confused by the 'abbreviation', t. What was it an abbreviation for 2? 3? ????" Here, "t" was an abbreviation of "triqua", from SDN; so in this case, it is equivalent to "3;6x10^3". "And Imre's contributions seem much more complicated than 3x10^12." Perhaps. The limitations of ASCII text are often tyrannical. When limited in this way, it is likely better to simply use the letter abbreviations, as long as they don't conflict with variable names. If they do, ordinary scientific notation seems a better choice. With proper mathematical typesetting, all these issues go away, and we can use whatever format that we find most clear. ============================================================ = COOKING WITH DOZENS = ============================================================ As part of our agenda in this volume of *using* as well as simply *knowing* dozenals, let's examine one of the most mundane and universal of human tasks in light of them: preparing the food that we eat. In the United States, at least, we still commonly use customary measures for cooking. These consist of a variety of almost whimsically-named units, primarily the teaspoon, the tablespoon, and the cup. It goes without saying that teaspoons are not used for tea, and tablespoons almost never see a table; these are traditional names, eyeball values applied haphazardly to precise units. Most of us are at least dimly aware of the relationships of these units to one another; nevertheless, a review will probably be helpful, particularly for those of us who don't cook terribly often: Unit Abbrev. Quantity Metric ------ --------- ---------- -------- Teaspoon tsp 1/3 dram ~5 mL Tablespoon tbs 3 tsp ~13 mL Cup cp 14 tbs ~180 mL Pint pt 2 cp ~340 mL Quart qt 2 pt ~680 mL (~1 L) Gallon gal 4 qt ~2280 mL (~3;95 L) Drams are seldom used today, and it is listed here merely for informative purposes. Importantly, we can note that a tablespoon is almost exactly 13 mL (fifteen milliliters), allowing easy conversion to metric volumes, as well. We should note, though, that by the time we get to the cup level, the milliliter conversions listed here are becoming increasingly inaccurate, and a liter is in fact more than 5 centiliters larger than a quart. Still, for practical work, these conversions are normally sufficient. The thing to notice about these conversions are that they involve both 2 and 3, numbers that (of course) dozenal handles much better than decimal. The other factor involved is 14, which is also handled better by dozenal than by decimal (all fractions of 14 can be expressed in only two dozenal digits, as opposed to *four* for decimal). So as one would expect, these units provide significant playing room for dozenals; let's see how we can leverage that. First, this gives a great means of practicing with the unqua-fourths. In decimal, sixteenths are lengthy and difficult, so most people don't bother learning them; there is no reason to so ignore them in dozenal. 1/14 is simply 0;09; the remainder of the unqua-fourths are just 9 multiplied by the numerator. So, for example: 3/16 9 * 3 = 23 0;23 4/16 9 * 4 = 30 0;30 5/16 9 * 5 = 39 0;39 And so forth. So when counting up tablespoons, why not count up fractions of cups? "Zero dit zero nine cups; zero dit one six cups; zero dit two three cups; zero dit three cups." This is an easy way to work on learning a very useful (because a binary) fraction while doing something you'd likely be doing anyway. Of course, a teaspoon is 0;4 tablespoons, since a tablespoon is three teaspoons; so another useful habit might be to add in many teaspoons rather than few tablespoons, to work on your thirds. This is particularly helpful when the recipe calls for, say, half a tablespoon, because this is 1;6 teaspoons. When your recipe demands two and a half tablespoons of salt, for example, it could be helpful to do the following: 2;6 tablespoons 6 tsp + 1;6 tsp 7;6 tsp Of course, these are merely mathematical exercises, helpful for learning and retaining dozenal arithmetic but not really helpful for your actual cooking. How can dozenal help? In one dozenal metric system, TGM, we find some very interesting correspondences in this field. For example, your normal kitchen teaspoon quite accurately dispenses 4 quadciaVolm ("Volm" is the TGM unit of volume, "quadcia" the SDN prefix indicating 10^-4) (and also quite nearly 5 mL). That means, naturally, that your tablespoon quite accurately dispenses one triciaVolm (4 * 3 = 10). Let's see this lined up a little more orderly: TGM Trad. SI Metric ----- ------- ----------- 4 qVm 1.0117 tsp 4.9865 mL 1 tVm 1.0117 tbp 14.9597 mL 14 tVm 1.0117 cp 239.3551 mL 28 tVm 1.0117 pt 0.4787 L 54 tVm 1.0117 qt 0.9574 L 19;4 bVm 1.0117 gal 3.8297 L ("Vm" is the TGM abbreviation for "Volm"; "q" is for "quadcia" or 10^-4, "t" is for "tricia" or 10^-3, and "b" is for "bicia" or 10^-2.) What does this mean, other than that you don't need to buy new measuring spoons and cups? It means that you can quite easily convert your recipes into dozenal, and cook directly in dozenal. The arithmetic will be a bit tricky if you cook in gallons---you may want to write the dozenal amounts down in that case---but otherwise it is quite straightforward. There is no need to pencil these amounts into your recipe books or onto your recipe cards, unless you'd like to; the conversions are so straightforward that you can easily do it in your head, until dozenal has gained enough ground that cookbooks are printed with it. So happy cooking; and perhaps this routine, even mundane, task will improve our arithmetic and help put dozenal into real practice. ============================================================ = DOZENAL NEWS = ============================================================ --------------Systematic Dozenal Nomenclature--------------- The article on Systematic Dozenal Nomenclature in our last issue of _The Duodecimal Bulletin_ has been a big hit. Due to this, we are pleased to be able to offer a standalone version of the article for download. While the content of this article is the same, its formatting and some wording has been updated by the author, and it offered in that updated form here. http://www.dozenal.org/drupal/content/systematic-dozenal-nomenclature Many in the dozenal community are very excited about SDN, and we are hopeful that our membership finds the system as interesting and useful as we do. -------------------New Calendar Proposals------------------- Those interested in non-Gregorian calendars have had an interesting few months. Dr. Paul Rapoport (#230) and DSA board member Timothy Travis (#342) have both published dozenal calendar. Dr. Rapoport says about his calendar: Rather than simply converting what we know to dozenal (10 months per year, 7 days per week, irregular number of weeks and days per month, year 11EX about to start on January 1, etc.), this calendar starts only with the assumption that there are 265/266 days per year, questioning all other principles, but wishing to maintain astronomical sense, e.g. not having any years misaligned with the solstices. The calendar starts every year on the winter solstice, with notable consequences for leap years, which I realize many people won't like. Each of the 10 months has 26 days, giving a total of 260 (nothing new there). What happens to the remaining 5 or 6 days is, I think, rather interesting. The unique solution here keeps both the winter and the summer solstice in the same location in every year's calendar. There's even a separate solution for the southern hemisphere. The calendar uses a 6-day week. I'm well aware of the problem with that. As for adoption of a calendar, imagining more than a few dozenalists using a new one is for me a non-starter, because a calendar reflects the civilization that uses it. Likewise, common questions such as trying to figure out what a work week or set of holidays in the Western world may look like only lead to keeping pretty much what we have now, with its notable peculiarities (charms or flaws?). Even ignoring practical matters, obviously no calendar can be completely regular, unless one doesn't care about the earth's orbit. Even though agreement over a calendar is as likely as one over symbols, I think the fun comes from the discussions and disagreements. There are five years of this calendar uploaded, with a short explanation of how it works and the rationale behind its construction: www.dozenal.ae-web.ca which is where my dozenal clock has been running for about a year now. Comments are welcome. I'm curious whether anyone else has actually *used* a new calendar, one that doesn't merely take the current calendar and count its years and days in dozens. Mr. Travis's says about his proposal: For the Raenbo Calendar I have taken another approach. To get a consistent, regular calendar every year, my compromise was to put the celebrations of the equinoxes and solstices between three month segments, making them the start of the next season. On the Raenbo Calendar, the solstice and equinox holidays are preceded by the last day of the preceding month, which is always a Saturday and followed by the first day of the next month which is always a Sunday. So, these two extra days make for long solstice and equinox holiday weekends. On the Raenbo Calendar the Winter Solstice Holidays are celebrated on the Old Calendar dates of 21 and 22 December. On Old Calendar Leap Years, they fall on 22 and 23 December. In both cases, we have a four day holiday weekend, starting the winter season. The Spring Equinox is celebrated on the Old Calendar date of 21 March and starts the spring season. Of course, the actual Spring Equinox usually falls on the 20th of March. Whenever the actual equinox occurs, it would be noted and when it occurred the day before, on a Saturday, it would still be during the holiday weekend. The Summer Solstice is celebrated on the Old Calendar date of 22 June and when it is a Leap Year, the Leap Year Holiday is added and celebrated on the 23rd. So during a regular year we have a three day holiday weekend, when its a Leap Year, a four day holiday weekend. -Starting the summer season. The Autumn Equinox Holiday falls on the Old Calendar date of 21 September (22 September if its a Leap Year), a three day weekend, starting the Fall season. ============================================================ = SOCIETY BUSINESS = ============================================================ ----------------------Website Numbers----------------------- Given that our new website is nearly a year old, it seems appropriate to review its progress. Our average visit time seems to be going up significantly, being over four minutes at this point. Our "bounce rate" (those who hit the site, figure out what it is, and leave immediately) is still high, but less than half of all visitors bounce off. For a site of such rarefied interest as our own, this doesn't seem unreasonable. Looking over the year, from 1 Mar 11E9 until 1E January 11EX, we've seen a lot of fluctuation in our exposure. There have been huge spikes in interest at certain periods, where our visitorship doubled (early April) or even tripled (9 July); mostly, however, we have remained steady, with a very slight trend upward over time. People seem to be finding us in mostly the same ways; the majority of our visitors find our sites through links on other sites, with slightly fewer typing in the URL directly. More and more, however, are finding our site through search engines (nearly one in five), which is a big improvement. The top keyword in search engines that brings users to our site are, predictably, "dozenal" (paired with "society", "system", and so forth). Historically, we've been oddly low in the results for "duodecimal", "base 12", and similar searches, and we've endeavored to fix that, with some success. "duodecimal" is now the number 6 search term for our website, with "base 12" being number 7. Of course, the search engine most users come to us from, by far, is Google in its various national incarnations. We're also, hower, ranking respectably with Bing and Yahoo. The most popular of our pages, aside from our main page and our "articles and books" page, are the general mainstays. First is "Fundamental Operations in the Duodecimal System", along with "A Brief Introduction to Dozenal Counting" and, of course, our _Bulletin_ archive. The educational materials prepared by secretary Jen Seron for our presentation at the ASEE conference last year are also quite popular, being viewed 1112 times. "Eggsactly a Dozen" remains popular, and our new multiplication practice utility is also seeing increasing traffic. All in all, the website remains a great success. --------------------Bulletin Publication-------------------- The heroic efforts of our Editor, Michael deVlieger, have given us two splendid issues of _The Duodecimal Bulletin_ in the span of only three months. Since taking up the editorship, he's provided us with visually spectacular full-color issues densely packed with informative content, graphics, and artwork, and we are very appreciative of his exertion in this regard. However, this exertion has not come without its toll, and is after all entirely voluntary in nature. For this reason, we have decided to alter the schedule for the release of subsequent issues of the _Bulletin_. To allow our Editor to apply himself to these tasks when he is most free to dedicate his attention to them, there will be no date certain on which to expect an issue's release. Instead, we have simply committed to at least two issues this year, to be released when the Editor's schedule permits. In this way we can assure ourselves of continuing to receive high-quality releases of the _Bulletin_ without abusing the volunteer labor of our Editor. ============================================================ = POETICAL DIVERSION = ============================================================ Originally published in our _Bulletin_, WN 58, this was penned by one of the great patriarchs of the dozenal system. Where does Cinderella go, Everytime the clock strikes Do? Count the chimes in groups of three, Listen to the One-Two-Three; Four-Five-Six; oh, what a fix, For someone near is timing; Seven-Eight-Nine; will she be mine? Then Dek-El-Do is chiming. But--- Where does Cinderella go, Every time the clock strikes Do? What the heck when it strikes Dek, That is nothing round her neck; Still the belle, let it strike El, While dancing through the music; As you know, then midnight Do, Finds Cinderella homesick. But--- Where does Cinderella go, Everytime the clock strikes Do? Listen and I'll tell you now, Tell you why, exactly how When the clock strikes midnight Do, Cinderella has to go To another dancing spot, Food, Champagne, and music hot. With thanks to H. C. Churchman. ============================================================ = 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