============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 1, Iss. X Official Newsletter 1 December 11E9 ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Reflections on Our First Year 2. Donations 3. Article: Numerical Abbreviations for Fun and Profit 4. Dozenal News 5. Society Business -Bulletin Publication 6. Poetical Diversion 7. Backmatter ============================================================ = REFLECTIONS ON OUR FIRST YEAR = ============================================================ Here we are at the end of our first year of _The DSA Newscast_. We had only X issues this year, because our first was in March, but overall the idea of a monthly newsletter, to provide our members with more frequent information on the progress and work of the DSA than our _Bulletin_ can provide, seems to have been a great success. We have had some feedback, and all of it has been positive. The goals of the Newscast when we started out were modest: Our purpose is similarly simple: to provide a more regular and more down-to-earth publication for the world of dozenals than is currently available. The Newscast is *not* intended as a substitute or replacement for _The Duodecimal Bulletin_; the purposes of the two publications are quite different. ... This little newsletter is for minor things, things too small or brief or inconsequential for the _Bulletin_; or, conversely, things too time-sensitive or urgent to wait for the next _Bulletin_. And so it has been. For the new year, we urge our membership to make further use of the Newscast. Have a little thought about dozenals you'd like to share, but don't want to write up a formal article? Read an article relevant to dozenals? Write to newscast@dozenal.org and share it; if it interested you, it would likely interest other members, as well. In closing, thanks for making the Newscast a success; have a wonderful year's end, and we will meet again next month. ============================================================ = 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 ============================================================ = NUMERICAL ABBREVIATIONS FOR FUN AND PROFIT = ============================================================ According to the common understanding of the term, this little article's title has a bit of false advertising to it, I'm afraid; there'll be precious little monetary profit to any of what we're preparing to discuss. Of mathematical profit, though, there will be plenty; so in a more expansive sense of the term, we will see a great deal of remuneration for our brief time together today. So, without further ado, let us proceed to the topic of abbreviating numbers. In current mathematics, we typically abbreviate numbers by using what is often euphemistically called "scientific notation," and which is more accurately called "exponential notation." Suppressing our repugnance and working in decimal for the moment (that is, where "10" equals "ten"), this notation takes advantage of the ease of multiplying and dividing by the base of the system to shorten long strings of digits while retaining ease in the perception of scale. For example: 3.6 x 10^6 Printed above we have a relatively innocuous little number (innocuous, that is, other than its unfortunate expression in an inferior base) which, when written out in full, is simply: 3,600,000 We expand the number by multiplying by the exponent of the base attached to it; here, by 10^6. Since this is multiplication by the base itself, the operation is nothing more than moving the decimal point. This method is quite frequently used, especially in physics, where significant figures of the answer often limit the number of digits that one can reasonably list out anyway, making this an excellent way to write only the significant figures and avoid writing out a long string of meaningless digits. Because this notation consists simply of multiplying by the base, it works just as well in dozenal as in decimal (or, indeed, in any other base), and sometimes it will doubtless be the most convenient method to employ. However, it's still rather bulky, filled with characters which are already understood (namely, " x 10^"), thus requiring more characters than are really necessary. Inspired by that divine species of sloth which fosters so much improvement in our methods, let us consider whether there might not be better ways to accomplish this task. We've noted that there are unnecessary characters in the notation we reviewed above; we not try a system where we simply get rid of them, retaining only the characters that we really need? That is, the exponents? 3;6^3 Ah, because this is ambiguous; do we mean 3;6^3 (3;6 to the third power, or 36;X6), or do we mean 3;6 x 10^3? Well, what if we simply reverse the order; put the power of twelve in the front, to avoid the confusion? 3^3;6 This can mean only one thing; it is at once more concise and yet equally clear as the exponential notation we discussed above. We can list negative powers either by putting them superscripted in the negative, as we would an exponent, or by putting them subscripted in the positive, like so: 3_3;6 Because this system was originally pioneered by DSGB member Tom Pendlebury, it is often called Pendlebury notation. This system combines quite well with SDN, because each prefix of SDN corresponds quite directly with an integer exponential value. For example, in SDN we refer to the third power of twelve as *triqua*: 3^3;6 = "three dit six triqua" Or, of course, in the negative, replacing "qua" with "cia": 3_3;6 = "three dit six tricia" And the system really begins to shine with the unit names of metric systems. As an example, we will take TGM's Tim. In TGM, all units have a standard abbreviation; for the Tim, it is "Tm". We can easily combine SDN with the Tim (and any other units in any metric system, really) by referring to unciaTim (one Tim multiplied by the negative-first power of 10) or quadquaTim (one Tim multiplied by the fourth power of 10). We can further abbreviate in writing, though, by combining SDN with Pendlebury notation, like so: biquaTim = 2^Tm = Tim x 10^2 pentciaTim = 5_Tm = Tim x 10^-5 hexquaTim = 6^Tm = Tim x 10^6 The concision and clarity of expression here is remarkable. SDN also offers a few other options, though, similar to this Pendlebury notation. The astute reader will have noticed that each of SDN's roots begins with a different letter of the alphabet. We can easily, then, use simply that initial letter as an abbreviation, without needing a number. We can do this by either superscripting or subscripting the letter, as we did with the numbers above; or by using capital letters for positive and lowercase for negative. For example: biquaTim = 2^Tm = BTm = b^Tm biciaTim = 2_Tm = bTm = b_Tm pentquaTim = 5^Tm = PTm = p^Tm pentciaTim = 5_Tm = pTm = p_Tm hexquaTim = 6^Tm = HTm = h^Tm hexciaTim = 6_Tm = hTm = h_Tm Typically, though, when applying powers to unit names the simple number is preferable, it being more easily distinguished from the text of the unit name. Letters tend to be more useful when applying to digits: 6^3;6 = h^3;6 = H3;6 6_3;6 = h_3;6 = h3;6 So we have a great variety of options for concisely and clearly abbreviating our numbers while simultaneously improving our ability to quickly perceive the order of magnitude of those numbers. We also have the same ability with units of measurement systems, which makes these methods particularly powerful. ============================================================ = DOZENAL NEWS = ============================================================ Back in February, Steve Lovelace published a very short and rather pessimistic exposition concerning dozenals, "An Intro to Dozenal Numerals": http://www.steve-lovelace.com/an-intro-to-dozenal-numerals Mr. Lovelace identifies the more critical failing of the decimal system --- its dearth of even factors --- and links to the Society's website. While he doesn't believe dozenal numerals would catch on --- the cost, he says, is too high --- he clearly recognizes their superiority. Robert Lindner at the Journal of Unsolved Questions, back in March, briefly addressed why we use the decimal rather than the duodecimal system, coming up with no good answer beyond finger-counting: http://junq.info?p=1686 An unsigned article (that is, signed only by an Internet pseudonym, "paradigmsearch") gives a little tutorial on dozenalism, worth a read for the curious: http://paradigmsearch.hubpages.com/hub/duodecimal-base-12-dozenal Ethan D. Bolker, of the Dep't of Mathematics and Computer Science at the University of Massachusetts at Boston, has transcribed an apparent classroom session developing a dozenal number system: http://www.cs.umb.edu/~eb/sam/duodecimal/ssegm.pdf Professor Bolker also has an interesting site containing some images of that great perfect polyhedron, the stellated dodecahedron: http://www.cs.umb.edu/~eb/stellateddodecahedron/ Templates for building your own are promised, so that we can all build our own and "wish upon a stellated dodecahedron". Professor Bolker's image displaying pi in dozenal is also worth a look: http://www.cs.umb.edu/~eb/stellateddodecahedron/images/48pt.png ============================================================ = SOCIETY BUSINESS = ============================================================ --------------------Bulletin Publication-------------------- The _Bulletin_ schedule for the next few months is slightly changed. Rather than having deadlines on a specific date, you can expect publication of the _Bulletin_ in the following months: December: _The Duodecimal Bulletin_ WN X1, for 11E8 (2012.) March: _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 = ============================================================ Ode of a Young Decimalist on Discovering the Dozen But soft! what light through yonder window breaks? It is the east; the dozen is the sun. Arise, fair sun, and kill the envious ten, Who is already sick and pale with grief, That thou, ignored by many, lost to none, art so much her superior and lord. Her vestal livery, adorned so poor, with two green moons and five pathetic stars, is worn by none but fools; I cast it off for thee, the dozen, lord of bases all! Your robes adorned with two bright suns of gold, with three bright moons, with four more glor'ous stars, and with six comets, bright to top them all, with tow'ring crown upon your brow so fair, thou leav'st all lesser numbers in the dust! So much men talk of ten; yet, like the moon, she hath no light but what the sun doth lend; so thou, O mighty twelve, giv'st what dim light the night of ten might cast upon the earth while saving still illumination great for when thou shin'st directly on us all, to teach what number is, what numbers are, the personalities of smaller primes, geometry and physics; mighty twelve, without thee math might just as well be Greek, but with thee we can understand and love now recognizing in the light of day what once was dim and weak in ten's sad light, what little it reflected of thine own, a long, dark night; but now filled with thy light! O mighty twelve, cease not to shed thy light, thou queen of numbers, giving flight to night. (With many apologies, even more profuse than usual, to Act II Scene II of the great Bard's romance.) ============================================================ = 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