============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 2, Iss. 1 Official Newsletter 1 January 11EX ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Goals for our Second Volume 2. Donations 3. For sale: Dozenal Calendars 4. Erratum: Mathematical Abbreviations 5. Mathematical Abbreviations, by Imre Ipolyi (#411) 6. Dozenal, Paper, and TGM 7. Dozenal News 8. Society Business 9. Poetical Diversion X. Backmatter ============================================================ = Goals for our Second Volume = ============================================================ As we plunge out into our second volume of this newsletter, it seems appropriate to outline a few of our goals. Beginning in this first issue of 11EX, we hope to accomplish two things: 1.) Encourage the participation of more of our membership with the Newscast. For example, we have an Erratum published below that resulted from the input of a member on the article published in Issue 01:0X; this corrects a real problem with the ASCII version of one of the notations we spelled out in that article. But more participation would be even greater. 2.) Assist our membership in the practical application of dozenals in our daily lives. Dozenal is an interesting abstract pursuit, to be sure; but it is also a way to make the real application of mathematics and arithmetic easier. We hope to publish articles this year which will help, in small and daily ways, encourage us to really use dozenals in our daily lives. We are very excited about these goals, and hope that our membership will find this both useful and worthy of their assistance. ============================================================ = 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: DOZENAL CALENDARS = ============================================================ It has often been difficult for those attached to the dozenal base to actually use that base in their daily lives. Now, we can buy dozenal calendars to help begin, in a small way, to change that. These items are all presented entirely in dozenal: Wall Calendar for 11EX, stapled binding ($11.60): http://www.lulu.com/shop/donald-goodman/dsa-wall-calendar-11ex-stapled/paperback/product-21221299.html Wall Calendar for 11EX, coiled binding ($16.70): http://www.lulu.com/shop/donald-goodman/dsa-wall-calendar-11ex-coiled/paperback/product-21223106.html These are "wall calendars," intended for hanging open on the wall or laying out on a desk; facing each calendar page is some dozenal-related image with some salutary dozenal fact or quotation accompanying it. An ideal conversation piece, if nothing else; hang them on the office wall and respond to comments. Also, of course, useful for keeping appointments and dates. These are in full color; hence the price. There is also a weekly planner available: Weekly Calendar for 11EX ($11.29): http://www.lulu.com/shop/donald-goodman/weekly-calendar-11ex/paperback/product-21242155.html This calendar has yearly, monthly, and weekly planning sections; the weekly sections are broken up by hour, allowing appointments, dates, and scheduling. All of these items are sold at cost, in the hopes that they will assist in the DSA's mission. They can all also be previewed on their respective pages, so you can determine whether they would be useful to you. So, to sum up: Monthly Calendar (stapled) $11.60 Monthly Calendar (coiled) $16.70 Weekly Planning Calendar $11.29 Dozenal is meant to be *used*, not just considered; these items will hopefully help that become a reality. ============================================================ = ERRATUM: MATHEMATICAL ABBREVIATIONS = ============================================================ Our last issue proposed an abbreviation for lengthy numbers that consisted of superscripting the order of magnitude in front of the relevant number; e.g.: 3^3;6 = 3600 One of our members pointed out, though, that this notation is ambiguous: it could just as easily mean three to the 3;6 power as 3;6 to the third order of magnitude. Unfortunately, we ran across the limits of ASCII text here; while the typeset notation is *not* ambiguous (the three should be superscripted, the 3;6 inline), it is impossible to represent this in ASCII ("plain text") in an unambiguous way. In ASCII, perhaps we should stick to the alphabetical abbreviations, rather than the numerical ones: t^3;6 = ^t3;6 = 3600 Which, as long as we are not using "t" as a variable name, should be reasonably clear. ============================================================ = MATHEMATICAL ABBREVIATIONS, BY IMRE IPOLYI (#411) = ============================================================ As for my contribution, I think I should write it to the newscast address. It's about the notation of subscript and superscript when no graphical text representation is possible by raising or lowering the characters. Computer code is always simple text, so 2^3 only can mean 8 not 300, and we also use variables, so a variable name "a" with an index "b", which is noted "a_b", should not be confused with 0;0b. I know, is would be highly unusual to use a number for "a" in a name for a variable. Nevertheless, there has to be a clearly different notation for raised and lowered prefix than for raised and lowered suffix, to avoid confusions in program codes and messages that don't allow spa[t]ial positioning of the characters (sms, simple email editors, social media). Example for the raised suf[f]ix: 2^'3 or '^2'3 or (^2)3 or (2^)3 or 2^!32 and lowered suffix: 2_'3 or '_2'3 or (_2)3 or (2_)3 or 2_!3 Probably the best of these 5 options would be the last with !, maybe with some other easily accessible character instead of !. Maybe not the ' sign as in the first example. That may be used to mark 'bulks of texts' at beginning and end similarly to (xyz) or "xyz". I would suggest 2^!3 and 2_!3. ============================================================ = DOZENAL, PAPER, AND TGM = ============================================================ Paper is such a mundane topic that we rarely consider it, but it's worth a little thought on occasion. Specifically, paper by necessity has a *shape*; and given that paper is practically two-dimensional, it by necessity has a *polygonal* shape. We occasionally see sheets of paper in all sorts of interesting shapes; but most commonly it is quadrangular, and then most commonly rectangular. This brings into question the ratio of the shorter to the longer sides. By tradition, the "perfect" shape for paper has been the Golden Ratio, 1;74EE6772... However, rather close to the Golden Ratio is 1:sqrt(2), which has the additional benefit that, when folded in half, it produces a new sheet with sides of the same ratio. This is a useful property which makes 1:sqrt(2) the ideal ratio for this purpose; particularly considering that it's at least in the same ballpark as the Golden Ratio. Traditional paper sizes came in all sorts of interesting ratios, which we mostly know by their common names. Still familiar to Americans are (all sizes in the customary decimal) "letter," 8.5x11 inches; "legal," 8.5x14 inches; and "ledger," 11x17 inches. All sorts of other sizes have formerly been common, here and abroad, such as "executive," "foolscap," and so on, but most have fallen into disuse. Metric paper sizes are (unusually for metric) considerably more rational. They are divided into two series, the much more common A-series and the B-series. Both of these series have a ratio of 1:sqrt(2) from their short to long sides. The A-series is *area-based*; it starts with the A0, a sheet of paper with an area of one square meter with the required ratio to its sides. This gets folded in half repeatedly, with each halving incrementing its number, until we get the A4, which is reasonably close to American letter. This continues at least to A-X (decimal A10), only 26;x37; millimeters, for which it is hard to imagine any practical use. The B-series is *length-based*, starting with the B0, a sheet of paper one meter long on the short side with the required ratio to its long side. This continued on until B-X (decimal B10), only 31;x44; millimeters, again difficult to imagine actually using. TGM, a consistently dozenal and coherent metric system developed originally by Tom Pendlebury, wisely adopts the same ratio for its paper sizes as metric did (rounding sqrt(2) to 1;5, which is extremely close to the true value, and which makes these calculations *much* easier). It also wisely introduces two series: a Grafut series (length-based, the Grafut being TGM's unit of length) and a Surf series (area-based, the Surf being a square Grafut). These sizes are abbreviated with the standard TGM abbreviations, Gf and Sf, with the number of folds suffixed to it. So if we want a very large sheet of paper, we might take the Sf+3, which is a page the area of one Surf (the Sf+0) doubled in size three times, each time preserving the 1:sqrt(2) ratio. Or if we want a rather small sheet, we might take the Gf-5, which is the initial page the width of one Grafut (Gf+0) halved five times, each time preserving the 1:sqrt(2) ratio. Remarkably, this system produces paper sizes extremely close to the current standard metric sizes; in fact, as it turns out, an A4 sheet on the long side is a remarkably good Grafut ruler. The Grafut-series corresponds very closely to the A-series, while the Surf-series corresponds very closely to the B-series. The standard "normal" sheet of paper over much of the world, A4, comes within less than a millimeter and a half of the Gf-1; and even the A0 is only 4x6 millimeters larger than the Gf+3. The Surf series has a similarly close correspondence to the B-series. This system of numbering makes more logical sense, as well. It allows for the possibility of larger and larger sizes of paper (it's not at all clear how a sheet larger than A0 would be named in metric; in TGM, it's just Gf+4). It further follows the intuitive rule that smaller numbers mean smaller paper, while larger numbers mean larger, with the 0 as the basic size; in metric's naming scheme, increasing numbers mean decreasing size. Finally, each number *up* indicates a doubling in size, while each number *down* indicates a halving, which makes more sense than having each number *up* mean a halving. These sizes are so close that, in a world in which TGM has taken over from metric, the differences between the A- and B-series and the Gf and Sf series can simply be classed as manufacturing error, without any change to the equipment at all. For more on TGM, see: http://www.dozenal.org/drupal/content/tgm-coherent-dozenal-metrology ============================================================ = DOZENAL NEWS = ============================================================ We noted in our last issue the interest generated by the fascinating shape of the stellated dodecahedron. Now, we can easily make many of these shapes by printing out and assembling simple patterns: http://www.korthalsaltes.com/model.php?name_en=small stellated dodecahedron While I was quite taken by the small stellated dodecahedron, a great variety of other polyhedra are available there, including a dodecahedron, a great stellated dodecahedron, a great dodecahedron, and others. Thanks to Gils Korthals Altes for making these available. Incidentally, in SDN we can refer to the "dodecahedron" as an "unquahedron" or a "unnilihedron," and the "dodecagon" as an "unquagon" or "unniligon." Dr. Andy Kass, a geophysicist for the U.S. Geological Survey, gave us an explanation and defense of dozenalism a little over a year ago: http://faradaysheadache.wordpress.com/2012/12/13/the-dozenal-system/ By way of explaining that dozenalism will never catch on, Dr. Kass states, "We can't even go metric in the United States." What a failure to adopt a poorly designed decimal metric system has to do with adopting a well-designed dozenal mathematical base, I'm not sure; but the article is worth perusing all the same. Our own Dr. Paul Rapoport (#230) was interviewed back in January of last year on the CBC's "As it Happens", with Carol Off and Jeff Douglas. You can listen here: http://www.cbc.ca/asithappens/features/2013/01/07/dozenal-society-man/ Dr. Rapoport focused pretty strongly on his clock, but he also discusses the ease of converting to dozenal, his membership in the DSA, and other matters. It's a short interview, but quite interesting, and with a receptive host. ============================================================ = SOCIETY BUSINESS = ============================================================ --------------------Bulletin Publication-------------------- As you all heard yesterday, our esteemed Editor, Michael de Vlieger, has produced another issue of our flagship publication, _The Duodecimal Bulletin_. This issue, Vol. 51 Iss. 1 (WN X1), focuses on dozenal nomenclature, and presents a full-length exposition of the Systematic Dozenal Nomenclature that we've reviewed over several months in this Newscast. We hope the issue proves as enlightening and enjoyable to our members as it was for us. Our next issue will be published in March of 11EX; this will have us caught up to the current year, and future issues published in 11EX (after WN X2) will be for the year 11EX (2014.). ============================================================ = POETICAL DIVERSION = ============================================================ A short one this month, which I hope is suitable for the change of year. As we think about time, we can think about the way we measure it; and so the old "Thirty days hath September" rhyme could use some updating to be dozenal. Dozen-six hath September, April, June, and November; The others count the same again, but one more day, a dozen-se'en; But February's dozen-four, in leap years count just one day more. ============================================================ = 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