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THE DSA NEWSCAST
http://www.dozenal.org
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The Dozenal Society of America Vol. 1, Iss. 9
Official Newsletter 1 November 11E9
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= CONTENTS =
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1. Donations
2. Article: SDN and Fractions
3. Dozenal News
-New Article: "Playfair on Dozenalism"
4. Society Business
-Bulletin Publication
5. Poetical Diversion
6. Backmatter
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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.
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
---------------------------WePay----------------------------
We have accepted donations through PayPal for some time; now
we can also accept them via WePay, which allows donations to
be made without having an account. We hope that this will
make it easier to support the Society.
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= SDN and Fractions =
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Continuing this month with our series on Systematic Dozenal
Nomenclature (or SDN), let's begin with some review: the
basic SDN chart:
Num. Part. Pos. Power Neg. Power
----- ------ ----------- ------------
0 Nil Nilqua Nilcia
1 Un Unqua Uncia
2 Bi Biqua Bicia
3 Tri Triqua Tricia
4 Quad Quadqua Quadcia
5 Pent Pentqua Pentcia
6 Hex Hexqua Hexcia
7 Sept Septqua Septcia
8 Oct Octqua Octcia
9 Enn Ennqua Enncia
X Dec Decqua Deccia
E Lev Levqua Levcia
The simplest way to use SDN is to name the highest power in
the number, and then to list the digits in order. For
example, the current year is 11E9; in SDN, we could
pronounce this as:
11E9 = "one triqua one elv nine"
We also saw the use of SDN to form consistently
dozenal words; for example, "unhexnilennial" for a 160th
anniversary, and quadrunquennial for a 40th anniversary.
We don't always form our number words focusing on integer
ranking, however; sometimes we focus them on *frequency*.
This sort of wordsmithing requires constructions for
fractional parts; for this purpose, SDN provides the
following two particles: "dit" and "per." More on "per" in a
moment; for now, let's consider "dit."
"Dit" is well familiar to many dozenalists; initially,
many dozen years ago, this was an acronym for "dozenal
identification tag," and was used to pronounce the semicolon
by which dozenal numbers were differentiated from decimal
ones. Many of us still use "dit" this way, as a way of
voicing the dozenal or Humphrey point. E.g.:
4;5 --- "four dit five"
In SDN, it is used in almost precisely the same way.
Consider, for example, a publication which is produced
twice a week. In our current systemless system, it's very
difficult to determine what word to use here, particularly
since, in the last few dozen years, the options have been
confused so much that they have nearly merged. It is
"biweekly"? "Semiweekly"? This is a hard enough question
that most people simply say "twice a week." (Traditionally,
the answer is "semiweekly"; but because so many have been
so often confused by this, "biweekly" has become nearly
synonymous, though technically it means "every two weeks".)
In SDN, though, we form our number words precisely the same
way we form our numbers with digits; we simply use words
instead. What we're really talking about, when we publish
twice a week, is that we published once every half week.
Half, in dozenal, is 0;6, voiced "zero dit six." Therefore,
in SDN:
twice weekly
0 ; 6 weekly
nil dit hex weekly
And for short, one may simply say "dithexweekly."
What about one every two weeks, the literal meaning of
"biweekly"? Well, that depends; if we mean "twice a month,"
as we commonly do, we do exactly as we did above, forming
"nildixhexmonthly." If we really mean biweekly, without
regard to when the months fall, we say "biweekly," precisely
as we do already (though "binaweekly", using the multiplier
form, would be more strictly correct).
We can do this with many common divisions; "quarterly" can
simply remain quarterly, of course, but if we need to
emphasize that it is a quarter of a *year* that we're
talking about, we can say "nildittriyearly." We can also
start easily using and talking about divisions into a third
of a year, every four months, either "quadmonthly" or
"nilditquadyearly." Something that comes due every two
months can be "bimonthly" or "nilditbiyearly." And so forth.
While the mighty dozen has more and more useful divisors
than any other number in its scale (as we dozenalists all
know), it still doesn't have *all* of them, and occasionally
we do have to use some numbers that don't have short, or
even terminating, periods. What if something happens seven
times a year, for example?
(Seven times a year? Why on earth...? Take your choice;
historical or symbolic reasons, perhaps.)
Seven times a week, of course, we call "daily," but seven
times a *year* is a bit trickier. Nor can we simply use
"dit," for a seventh is a very clumsy digital fraction
(0;186X35 repeating; a six-digit period, pessimal for the
dozenal base). "Nilditunocthexdectripentennially" will work;
but it's certainly quite a mouthful, and it's also not
strictly accurate, as it only lists one period. This is
where "per" steps in.
With "per", we can name vulgar fractions exactly as we name
digital fractions or integers. Here, for example, we're
talking about a seventh of a year. We write this as "1 / 7".
We can make this into simple, orthodox SDN by naming it like
this:
1 / 7 yearly
Un per sept yearly
Unperseptyearly; seven times a year. Since "per" is a
reciprocal operator, we can even assume the "un," and say
"perseptyearly."
So now we can count to any number, large or small,
and form a number word for any quantity, fractional or
integral, using a consistent, international, and purely
dozenal system. This is the power of SDN.
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= DOZENAL NEWS =
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-----------New Article: "Playfair on Dozenalism"-----------
We are pleased to announce the publication of an excerpt
from an historical piece by John Playfair, in which he
defends the superiority of the dozenal system:
http://www.dozenal.org/drupal/content/playfair-dozenalism
Among the earliest defenses of base twelve, Playfair here
regrets that the French Revolutionaries, despite being
willing to cast off almost everything, were still too timid
to cast off the shackles of the decimal base. Short and well
worth the read.
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= SOCIETY BUSINESS =
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--------------------Bulletin Publication--------------------
The _Bulletin_ schedule for the immediate future remains the
same:
Dec 10: _The Duodecimal Bulletin_ WN X1, for 11E8 (2012.)
Mar 01: _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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While best known for "The Rime of the Ancient Mariner," the
famed British poet Samuel Taylor Coleridge (1038-108X) was
also keenly interested in geometry, and was so taken by the
simplicity and elegance of Euclid's first proposition of the
first book that he write a poem about it. It is reproduced
here:
A Mathematical Problem
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This is now---this was erst,
Proposition the first---and Problem the first.
On a given finite Line
which must no way incline;
To describe an equi---
---lateral Tri---
---A, N, G, L, E.
Now let A B.
Be the given line
Which must no way incline;
The great Mathematician
Makes this Requisition,
That we describe an Equi---
---lateral Tri---
angle on it:
Aid us, Reason---aid us, Wit!
From the center A, at the distance A. B.
Describe the circle B.C.D.
At the distance B. A. from B. the centre
The round A.C.E. to describe boldly venture.
(Third Postulate see.)
And from the point C,
In which the circles makes a pother
Cutting and slashing one another,
Bid the straight lines a journeying go,
C, A, C, B, those lines will show.
To the points, which by A. B. are reckon'd,
And postulate the second
For Authority ye know.
A.B.C.
Triumphant shall be
An Equilateral Triangle,
Not Peter Pindar carp, not Zoilus can wrangle.
I think we can probably all agree that Coleridge's poetical
talents were better spent on other topics. However, Jacob
Bernoulli, normally no poet, proved himself capable of quite
elegant verse in the following poem:
Treatise on an Infinite Series
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Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
And, in the original Latin:
Ut non-finita Seriem finita coercet,
Summula, & in nullo limite limes adest;
Sic modico immensi vestigia Numinis haerent,
Corpore, & angusto limite limes abest.
Cernere in immenso parvum, dic, quanta voluptas!
In parvo immensum cernere, quanta, Deum!
(Both texts are taken from "The Verses of Jacques Bernoulli
on Infinite Series", by Helen Walker of Teachers College,
Columbia University, in David Eugene Smith, _A Source
Book in Mathematics_, published 1149 by McGraw-Hill
and republished 1173 by Dover.) While not a *strict*
translation, the English is quite lovely; and I think anyone
knowledgeable in Latin will enjoy the original, as well.
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= BACKMATTER =
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