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THE DSA NEWSCAST
http://www.dozenal.org
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The Dozenal Society of America Vol. 1, Iss. X
Official Newsletter 1 December 11E9
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= CONTENTS =
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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
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= REFLECTIONS ON OUR FIRST YEAR =
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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.
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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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= NUMERICAL ABBREVIATIONS FOR FUN AND PROFIT =
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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.
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= DOZENAL NEWS =
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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
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= SOCIETY BUSINESS =
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--------------------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.).
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= POETICAL DIVERSION =
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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.)
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= BACKMATTER =
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