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THE DSA NEWSCAST
http://www.dozenal.org
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The Dozenal Society of America Vol. 2, Iss. 1
Official Newsletter 1 January 11EX
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= CONTENTS =
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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
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= Goals for our Second Volume =
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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.
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= DONATIONS =
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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
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= FOR SALE: DOZENAL CALENDARS =
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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.
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= ERRATUM: MATHEMATICAL ABBREVIATIONS =
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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.
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= MATHEMATICAL ABBREVIATIONS, BY IMRE IPOLYI (#411) =
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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.
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= DOZENAL, PAPER, AND TGM =
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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
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= DOZENAL NEWS =
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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.
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= SOCIETY BUSINESS =
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--------------------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.).
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= POETICAL DIVERSION =
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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.
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= BACKMATTER =
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EACH ONE, TEACH ONE