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== Whitespace characters ==
==Counting to 12 on fingers==

I am flummoxed by the correct name for this body part, but I know how to count to 144 on my fingers using my thumbs as marker and counter - what do you call the finger-lengths from joint to joint?

Take your hand (R, L, whatever works for you) and touch your thumb to the farthest finger-length on the index finger = 1. then the next length down = 2. the one closest to your palm = 3; then you move your counting to the middle finger (4,5,6), ring finger (7,8,9), little finger (10,11,12). Mark the first length on the OTHER hand with your thumb. Start over = 13-24. Etc. You can tally a gross of whatever you need to count without writing. MOST convenient, and often used as an explanation for the use of duodecimal systems in ancient Mesopotamia - and hence in Astrology, Astronomy, Chronology, etc., since we all adopted their version of that. I learned this at my father's knee, but I think I saw it confirmed in one of Eviatar Zerubavel's books on time. --].

:*The bones are called '']''. There are 14 per hand (the 12 you mention, plus 2 for the thumb). --]
:**Aha! Thank you. Yes, one uses the thumb to touch the phalanges.

:*I post a question on the ] page sometime ago about using the thumb to count the finger joints and finger tips in a hexadecimal system. That may have been mistaken version of the duodecimal system. I think this tallying method should be part of the article.

:I have also come across reference to so using the fingers for hexadecimal. ] (]) 16:31, 17 December 2008 (UTC)

The reference for this is a dead link. So I've searched for and read a few other articles that talk about ancient Egyptians counting to twelve by their fingers. I haven't yet seen a primary source referenced however. Does anyone know of a primary source, ancient papyrus, or even an ancient historian, etc., that describes this? <small><span class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) 01:51, 28 December 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

==Notation==

Isn't the standard base notation for digits in a base greater than 10 is to say 1,2,3,...,8,9,A,B,C...? Instead of the X we have here. Is this notation only for the duodecimal system? ] 12:53, 23 Aug 2003 (UTC)

:*Yes, X is only for the duodecimal system. A,B,C,D,E,F are used for the ] system. There is no standard notation for digits in a base greater than 10, that I know of in use. -- ]

:*Script capital E is possible in Unicode: <big><big>&#8496;</big></big>. You could also use <big><big>&#8455;</big></big> or <big><big>''&#8455;''</big></big>. --] 07:49, Sep 10, 2004 (UTC)
:**There is also <big><big>&#400;</big></big>, LATIN CAPITAL LETTER OPEN E. However, there still seems to be no satisfactory Unicode glyph for the DSGB's suggested "ten" symbol (a rotated 2) . ] 07:57, 10 Sep 2004 (UTC)

:*It would be fun to see a table that shows the character used for ten and eleven according to various stardards, e.g. DSGB, the American guy who used script X and E, etc. That way you can compare at a glance the various ways people have suggested to write ten and eleven, and maybe decide which standard you prefer, or see their similarities and how they differ, etc.--] 08:09, Sep 10, 2004 (UTC)

:* For script x, Unicode character 1D4CD (𝒳) can be used. It's outside the Basic Multilingual Plane, so its usefulness is limited, but Firefox is one browser that displays it by means of substitution (to the normal ASCII x). FF has a substitution file, ./res/entityTables/transliterate.properties, that provides for that. --] (]) 14:36, 10 September 2009 (UTC)
:**Assuming it's the script capitals you want, it's U+1D4B3 for the X and U+2130 for the E. An alternative, especially if you want to use Pitman's "rotated 2" glyph, is the Private Use Area. I suggest U+E03A for base-12 b^1−2 and U+E03B for b^1−1, because that way they look like a continuation of the ASCII codes 30–39 (the digits 0–9). There's even a third alternative, though much less comfortable to handle: use decimal multiple digits as duodecimal digits, as customary for sexagesimal, like 1:2:10 doz = 178 dec. --] (]) 23:35, 6 October 2009 (UTC)

:* The thing about using X and E, or V and E as I do, is that it presupposes decimal numbers still exist. In my case, this is true, because i use base twelfty (120), and V, E are used for teenty and elefty respectively. For those who really want to use a strict duodecimal system, one has to eliminate the underlying decimal substrate, deriving new numbers and runes for 10, 11. Although i use E for writing, the thing is actually a back-to-front nine or large 'e'.

:Were one to push for Unicode digits (rather than just picking out letters from assorted fonts), one would be advised for digits from -1 to 19 or something like this. There are other things to consider. For example, one needs to look at the 'lower case' or hanging form, such as one might see in the font Georgia. One might look at assorted diacritics that might be added (eg writing 17 in base 20 as '7. In my script, V is written as x-height, while E is written with a descender.

:In some cases, there is need for a second series of number (eg roman digits). This allows things like apposition of numbers without conflict, eg 2009ix9. I don't think enough detail has been given to this. --] (]) 07:03, 11 September 2009 (UTC)

::Please move to DozensOnline. PiotrGrochowski - 16:29, 17 July 2014

==Pronunciation?==

How do they intend we pronounce a dozenal number like 14? "A dozen and four"? Would 3E be pronounced "three dozen eleven"? What about higher numbers, in the 3rd column where we normally had hundreds before. Dozenal 100 is decimal 144. Is there already an English word for the decimal number 144?--] 08:14, Sep 10, 2004 (UTC)

:*Oh, there's ] for 12*12 and ] for 12*12*12! How far do such names go? --] 08:15, Sep 10, 2004 (UTC)

:There are a few systems for dozenal pronunciation. I only really know of the Pendlebury system, where X = ten, E = elv and 10 = zen. 14 becomes zen four, and 3E becomes threezen elv. ] (]) 22:01, 16 June 2011 (UTC)

: of counting in dozenal seems reasonable. <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 02:07, 13 March 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

: is generally what I've heard before as far as pronunciation. One, do, gro, mo, do-mo, gro-mo, etc. <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 23:40, 28 December 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

I usually use something like Pitman's scheme, where one to eleven keep their current names, and the multiples of twelve are: onezen, twozen, threezen, fourzen, fivezen, sixzen, sevenzen, eightzen, ninezen, tenzen, elevenzen. Twelve twelves make a gross; twelve grosses make a grand; a grand grands make a zillion (neatly rationalizing the "z" as coming from "dozen"). The multiples of twelve are basically contracted forms of "one dozen", "two dozen", etc.: if communicating in dozenal to someone else, I would use the full forms, and "great gross" instead of "grand". ] (]) 15:12, 12 April 2015 (UTC)

I can't remember where I got it, maybe http://www.dozenal.org/archive/ManualOfTheDozenSystem1174-web.pdf but I like one, two, ... nine, dec, el, do, one do one, one do two, one do three ... one do el, two do, two do one, two do two ... and so on. it's quick and easy to learn and handy enough to use. Then they used Gro for gross and some other stuff from then on

==Polygons==

I find it worth mentioning that there also seems to be a relation to ]:
Regular triangles, squares and hexagons (3,4 and 6) will ]
in the ] with themselves as well as in combination with each other (triangles/squares, triangles/hexagons, triangles/squares/hexagons), whereas regular pentagons (5) will neither tesselate in the plane with themselves nor with other regular polygons.
Twelve regular pentagons may however form a pentagonal ] in three dimensions.

==Names==

About the special names for 11 and 12 in european Languages:

<code>
English: eleven (not one-teen) &nbsp;twelve (not two-teen)<br>
German: &nbsp;elf (not eins-zehn) &nbsp;&nbsp;&nbsp;zw&ouml;lf (not zwei-zehn)<br>
Dutch: &nbsp;&nbsp;elf (not een-tien) &nbsp;&nbsp;&nbsp;&nbsp;twaalf (not twee-tien)
</code>
<br>
--] 14:32, 29 Sep 2004 (UTC)

:*And in french onze (not dix-un), douze (not dix-deux) but also treize (not dix-trois), quatorze (not dix-quatre), quinze (not dix-cinq) and seize (not dix-six). So I don't think french is accurate in the article. ] 14:23, 28 Nov 2004 (UTC)

:*In Finnish we say "yksitoista", "kaksitoista", "kolmetoista" etc. This literally means "one of the second", "two of the second", "three of the second", etc. This can be extended further, for example "yksikolmatta", meaning "one of the third", means 21. This was in very common use for centuries right until the early 20th century, but is now archaic. Nowadays we only use "-toista" for 11 through 19 and then we use the normal form of concatenating the tens and the ones. ] &mdash; <font color="#CC0000">J</font><font color="#00CC00">I</font><font color="#0000CC">P</font> | ] 09:59, 4 Mar 2005 (UTC)

:: All of this suggest base 4. (multiples of 4 are 8, 12, 16, 20). Also 8 in the most ancient form is a dual form (ie being 2×4), and nine and new come from the same root (the new group of four). French also uses scores to count in, as in sixty-seventeen and four-twenty-eightteen (98 = 4×20+8+10). ] (]) 10:46, 9 March 2012 (UTC)

==Time?==

There seems to be a dozenal-inspired system used in time as well. Days have 24 hours (or two sets of 12), hours have 60 minutes (or 12 sets of 5), there are likewise 60 seconds in a minute, and there are 12 months in the year in most calendars, including the Julian, Gregorian, Hebrew, Hindu, Islamic, and Persian (although admittedly there are practical considerations for this, it could be divided another way). I can't say I know anything about the history of the time measurement, but maybe someone who does could include something on the topic? ] 00:39, July 15, 2005 (UTC)

:*The number of months is due primarily to the length of the lunar month. The 60 goes back to the Babylonians, who used a base-60 numerical system.
:Incidentally, in East Asia, the day was traditionally divided into ''12'' units, each, therefore, 2 hours in length, and named after the animals of the ] -- ] 15:06, 15 July 2005 (UTC)

:*The sexagesimal number system, base 60, comes from the Sumerians and is what led to the Babylonian number system. Many Sumerian creations are with us today. 12 hours in a day, 60 seconds per minute, 60 minutes per hour, and even 360 degrees in a circle originate from the first civilization to bring us both mathematics and writing. Base 60 comes from counting to twelve on one hand with your thumb as a pointer and tallying the number of sets of twelve you have counted on your other hand. Five sets of twelve equals 60. <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 14:43, 3 January 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

:: The sumerian day is divided sixty-wise, preserved in India as a day of 60 ghurries, a ghurry of 60 pali, a pali of 60 vipali. The hour is an egyptian decimal day: a day of 10 hours + two twilights + rising of 12 decans at night = 24 hours. The modern time system is a greek composite of egyptian hours divided in the sumerian fashion.

:: The number of signs in the zodiac is pretty much cultural. It places the sun and planets at points of the sky, but the division into 12, 13, 15, 18 (mayan) or 36 (egyptian) is a matter of calendar. Months are quite used, so 12 is common for that reason (alone). Cetus is usually the next constellation to use.

:: Base 60 actually comes from ''three scores'', and then multiples of 10 alternated with divisions of 6. Using twelfts in 60 is like using twentieths in decimal. You soon think in terms of tens and halfs of tenths or sixths and halves of sixths.

:: Twelve in the divisions is a roman process, and used on cultural dependencies of Rome. The dram, for example, was divided into 6 obols, and 100 made the pound (mina). This is pretty much how it would happen when one counts 'drachma' coins. The romans incorporated the unit into a pound, divided into 12 uncia, so the dram is rounded to 1/96 lb, and the obol to 1/576 lb. A scruple of 1/288 lb creeps in elsewhere. It should be noted that the romans only ''divided'' duodecimally, counts are always in decimal.

:: In the north of europe, lies an entirely different metrological tradition based on 120 and its multiples. The pound of king Offa was made by an ounce of 10 dirhems, a pound of 12 ounces. The dirhem yields two silver pennies, which leads to an oz of 20 dwt. Likewise, a hundredweight of 120 lbs is usual in north europe. ] (]) 10:43, 9 March 2012 (UTC)

==Music Notes==

Twelve half-steps are present per octave in music. Counting a scale of 8 notes, with the bottom and top note identical, is the etymology of the word "octave," but that is only counting one key's scale. Counting every half-step, without counting two of the same note, makes a piano, keyboard, or guitar frets useful in counting according to the dozenal system.

A, A#/Bb, B, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab <span style="font-size: smaller;" class="autosigned">— Preceding ] comment added by ] (]) 22:38, 15 April 2014 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

==growth==

This article has grown really well. Can we nominate it for featured article?--] 05:25, 27 January 2006 (UTC)
:Not yet, please. There's still a lot of info I'd like to add before having this article featured, such as about prime number identification, factorials, the patterns in the multiplication table, the relation of twelve to certain elementary angles and geometric shapes, the relevance of twelve in Western music, the system of dozenal fractions used by the Romans, the proposals for filling the gaps in English duodecimal nomenclature and the way some African languages developed a duodecimal nomenclature from a decimal one and viceversa, the existence of a complete proposal for a consistently duodecimal system of measures, the hurdles an eventual dozenalization would have to face, etc. I'm also planning to refurbish the whole article so that the issue is handled in a more structured way. I want this article to describe the duodecimal system in depth, with all its pros and cons, so that readers have all the information to make a fair comparison with the decimal system they are already familiar with, and thus be able make an informed judgement about dozenalism for themselves rather than going with the preconceived idea that decimal is "the natural way for humans to count" and dozenalism merely "a freaky idea no-one should take seriously". ] 04:21, 4 February 2006 (UTC)

== English duodecimal names ==

In the article it says that A^5 (49,A54) would be:
: ''four dozen and nine great gross, ten gross five dozen and four''
and A^6 (402,854):
: ''four gross and two great gross, eight gross five dozen and four''
Are these right? Above it seems to imply that there are no names for 10,000 or 100,000 in duodecimal. And even if there were, wouldn't 49,A54 be something like four great great gross and nine great gross...? --] 21:53, 8 March 2006 (UTC)
: So far there are no standard English names for dozenal 10,000 and 100,000 that I know of (let alone for higher dozenal numbers), save for the straightforward ''a dozen great-gross'' and ''a gross great-gross'' (maybe ''great-great-gross'' and ''great-great-great-gross'' have already been used by some people, but I cannot tell for sure). Note that ''four gross and two great gross'' is not to be read as "four-gross and two-great-gross", but as "four-gross-and-two great-gross", i.e. analogously to "four hundred and two thousand" meaning 402,000 (the same possible ambiguity with the meaning 400+2000 exists in decimal). There have been a number of proposals to expand and standardize English nomenclature for the big dozenal numbers, though. In the , some dozenists have suggested to substitute a simpler, more manageable name (like ''grand'') for great-gross. Others have proposed naming schemes that would generate a unique name for every dozenal power. I myself have suggested the name ''zyriad'' (from ''do<U>z</U>enal m<U>yriad</U>'') for 10^4 = 10,000 = 1,0000, as well as similar ''z-'' names like ''zillion'' for 10^6 = 10^(3+3) = 1,000,000 = 100,0000, ''zyrion'' for 10^8 = 10^(4+4) = 100,000,000 = 1,0000,0000, ''zilliard'' for 10^9 = 10^(3+3+3) = 1,000,000,000 = 10,0000,0000, and the merely tentative name ''doogol'' (based on ]) for 10^10 = 10^(3+3+3+3) = 10^(4+4+4) = 1,000,000,000,000 = 1,0000,0000,0000). But so far, all of these are mere suggestions. ] 16:31, 22 April 2006 (UTC)

There is this scheme http://www.dozenal.org/archive/ManualOfTheDozenSystem1174-web.pdf do = 10 gro = 100 mo = 1000 do mo = 10,000 gro mo = 100,000

::It would be even funnier in German, "vier gross-gross-Grosse und neun gross-Grosse"... ;) ] 15:08, 18 November 2006 (UTC)
:::The names above seem to be as transparent and "standard English" as you'll ever get for high dozenal numbers. ] (]) 15:14, 12 April 2015 (UTC)

== Question on societies ==

Why isn't there a separate article on the Duodecimal Society of America? ] 23:02, 24 October 2006 (UTC)
:Well, :-), because it seems no one has cared to create it so far. I've found that in general the articles dealing with topics related to other number bases than decimal and the ones commonly used in computing are still poor and lack info on many important points (for example, until I added it the other day, the article on ] didn't mention anything about using it to represent rational numbers like the basic fraction 1/2, and I had to correct the still-stubby article on ] where it said that Babylonian sexagesimal was mixed radix just because they represented their ''digits'' using a sub-base of ten&mdash;which is analogous to how the Maya represented their digits using a sub-base of five and doesn't mean they used mixed radix because of that, although the Maya actually used mixed radix of twenty and eighteen when computing dates). This very article on dozenal still lacks tons of info, without which it is not possible to make a fair judgement about the case for dozenal over decimal that the DSA and DSGB promote. But I myself am already working on expanding it. I'm currently finishing two comparative charts, one showing the effect of decimal, dozenal and hexadecimal in the perception and choice of numbers (which numbers look "rounder" than others in that base; e.g., people using decimal tend to prefer numbers such as 10, 25 and 50 over 12, 24 and 60, even though the latter are inherently more well-suited for many purposes), and the other chart showing how the choice of base affects the representation of rationals and thus the everyday choice of certain fractions and proportions over others according to their ease of representation in that base. Here's an almost finished version of the first one: http://img214.imageshack.us/img214/4301/tabla8oo.png ] 18:37, 1 November 2006 (UTC)

== Easier to memorize? ==

The article states:

"As can be seen, it is easier to memorize the first nine digits of pi in base twelve than in base ten, while the opposite happens with the first ten digits of the number e."

How can one prove that this is the case? Unless there is a pattern <s>(which dose not appear to be the case)</s>, what might be easier for you to remember, might not be easier for me.

Unless some can give a cite for this, I think it should be removed.
—] <sup>(])</sup> 10:26, 14 December 2006 (UTC)

:Sorry - I just noticed the "1828" repartition in decimal e. Still, how is it easier to remember dozenal pi as apposed to decimal pi? —] <sup>(])</sup> 10:31, 14 December 2006 (UTC)

Can't you really see the patterns?
''doz pi dec pi dec e doz e''
''vs vs''
3. 3. 2.7 2.7
18 48 14 15 18 28 87 52
09 49 92 65 18 28 36 06
They should be pretty obvious if you just care to look at the numbers for a while: one-eight, four-eight, then oh-nine, four-nine (patterns: 1_4_ / 0_4_ and _8_8 / _9_9); that's a more regular pattern than one-four, one-five, then nine-two, six-five (patterns: 14 / 15 and ___5 / ___5). ] 00:01, 18 December 2006 (UTC)

:I see the patterns, but as far as I'm concerned that's original research. And I'm also not at all sure what the point is, because it doesn't have anything intrinsic to do with decimal or duodecimal bases. Essentially irrational numbers produce different random sequences when expressed in different bases, and some random sequences are easier to perceive patterns in than others.

:I don't see the point... and even if I did, it is not a description of anything that is a well-known or well-established characteristic of duodecimal numbers. If it were, you would be able to cite a source for it. It's just your own personal observation. It's not even clear whether everyone perceives these patterns the same way. ] ] 01:12, 18 December 2006 (UTC)

::So if the article mentions that 1/35 or the Euler-Mascheroni constant in base twelve equal (blah blah) and those particular numbers happen to not be explicitly published somewhere (I haven't cared to check), but those are simply the digit sequences one gets by doing the well-known base conversion algorithm (which any calculator with a base conversion function can do), then doing those straighforward mathematical conversions to include them in the illustrative charts would be original research too? Would someone place a "citation needed" tag until someone provides some reference asserting explicitly that 1/35 in base twelve is indeed (blah blah)? If in the ] article someone puts an illustrative chart that highlights the objective digit patterns in the tables (e.g. the patterns in the table of 7, which are there, one just has to look at the numbers for a moment to find them) and then mentions "without a source" that the patterns in the table of 5 (5-10-15-20-25-30-35...) make it easier to remember this table in decimal as opposed to the table of 5 in e.g. dozenal (5-A-13-18-21-26-2B...), will you ask them for a "citation" to back up such a straightforward fact saying that "It is not clear that everyone perceives those patterns the same way"? The article is just mentioning that the patterns are there in dozenal 3.18480949... and decimal 2.718281828..., which is an objetive, uncontroversial fact about those digit sequences (it is ''not'' a matter of personal perception that 1_4_-0_4_, or _8_8-_9_9, or 18-28-18-28, or 5-10-15-20-25, create patterns, the patterns are there objectively, and they are not at all particularly difficult to see). And the point is, patterns serve as a ] (e.g. telephone numbers: a patterned number like 1-800-234-5656 is easier to memorize than some random number like 1-475-823-9465 &mdash; would you challenge the assertion of this common-sense fact asking for a citation to back it up?), and the ] is relevant given that this number is very frequently used. So the more regular patterns in the first dozenal digits of pi (3 - 18 48 - 09 49) as compared to the patterns observable in its first decimal digits (3 - 14 15 - 92 65) make the dozenal representation of pi easier to memorize than the decimal equivalent at least up to the ninth digit (in decimal it is straightforward to memorize up to the fifth digit: 3.1415... or the rounding 3.1416, which are fairly good approximations for everyday purposes but not as good as the 9-digit approximation which you can get in dozenal with about the same memorization effort), and this is a relative practical advantage of dozenal over decimal; while, to balance the matter, decimal allows easier memorization than dozenal for the first ten digits of e, another very frequently used number, and that is a relative practical advantage of decimal over dozenal. I don't see why this simple statement of fact about mathematically objective digit sequences should be any controversial at all. In any case, given that it seems that even simple statements about straightforward mathematical facts need to be "sourced", I will ask the DSGB/DSA people in the DozensOnline forum for "citations" that explicitly mention it (some of the people there like to discover ''really'' arcane dozenal patterns, so probably someone will laugh at me when I ask them for a reference about the in-your-face-simple pi thing). I'm sure there must be some explicit reference somewhere, since there are entire books devoted to the many patterns observable in dozenal numbers, and the one in the first digits of pi is one of the most straightforward to see and is of practical use for remembering this everyday number, although it is a "trivial" one in that it is not a consequence of the divisibility properties of twelve the way e.g. the patterns in the multiplication tables are. ] 03:43, 18 December 2006 (UTC)

:: Of pi, e, etc. Use provides a rapid way of recalling these numbers. A four-function calculator does wonders to learning the irrationals to any number of places. These are usually limited by the places of the calculator, so eg 1/2(sqrt(2)+sqrt(6)) is 1.93185165259, and sqrt(2.5+sqrt(1.25) = 1.90211303259, are numbers learnt on a 12-place calculator, while the chords of the heptagon 1.801937736 and 2.2469796037 date from a period when i had a 10-place calculator.

:: The fraction for e is best thought as 2721/1001. The number is 2.718 281 828, add 718+281=999, so it's 2 719/1001. In duodecimal, we get 2.8 7 5 2 3 6 0 6 9 for e and 2.8 7 5 2 3 5 8 7 5 2 3 5 for 2721/1001. It's much easier to calculate this fraction in any given base.

:: For pi, the easiest to find is 3 16/113, or say 3 17/120 -1/113. However, another approximation exists as 7^7/8^6, in octal, we have pi = 3.110 375 524 cf 7^7 = 3.110 367, corresponding to a difference of 6 in the sixth octal. In base 56, we get eg that pi is 3.7 52 1 52 21 32, 1/pi = 0. 17 46 12 17 16, while 3 7 51 53 26 20 7 × 17 46 12 42 35 33 8 gives 56^13, the numbers are the 13th powers of 7 and 8 respectively.

:: Of course, if you want ease of remembering pi, base 22 is hard to go by. pi = 3. 3 2 11 14, 22/7 is 3. 3 3 3 3, and 3.3 3 is 1.17 squared, while sqrt(pi) is 1.16 21 19 1 20 (a difference of 3 in the third place). pi^2 is 9.19 2 19 12, while 227/23 is 9.19 2 19 2 19 .. pi^3 is 1 9.0 3 0 8, pi^4 is 4 9.9 0 0 0 0 14 3. 1/pi is 0.7 0 1 8 , etc. --] (]) 11:04, 25 December 2010 (UTC)

i see the pattern . π 10 : 3.14159265 , π 12 : 3.w5x6y5z6 ] (]) 09:18, 28 July 2013 (UTC)

==Conversion from decimal==
Is there any known system for quick conversions from decimal to dozenal? ] 21:47, 2 February 2007 (UTC)

:What do you mean by "quick conversions"? The fastest way is usually to simply use a calculator that supports that function (there is one available from the DSGB site, although it has some minor bugs). The other two methods are: to use the general base-conversion algorithm (which can be a bit tedious), or to memorize or look up the tables of digit conversions (this method is easier for dozenal-to-decimal conversions, unless you also learn to do simple dozenal arithmetic, because it works by adding the corresponding values in the target base for each digit in the source base, e.g. dozenal 123=100+20+3 corresponds to decimal 144+24+3=171, which is an easy sum to do because we all are already trained to do sums with decimal numbers, but to convert decimal 123 into dozenal one needs to know how to sum the dozenal numbers 84+18+3, which is not really difficult at all but requires that you learn to "switch" from decimal arithmetic thinking to dozenal arithmetic thinking, because in dozenal 4+8+3 equals 13 and not 15 as would be expected in decimal, and then 8+1+1 adds to A and not to 10, so the result of 84+18+3 is A3 in dozenal and not 105 as one would have obtained doing the sum in decimal, and thus decimal 123 corresponds to dozenal A3 (as a side note, in this particular example it would be easier if one just remembers that decimal 120, i.e. twelve tens, equals dozenal A0, i.e. ten dozens). Alternatively, if what you're looking for is merely an estimate of "how large" the number is, rather than its accurate converted value, then it's useful to memorize some easy to remember "landmarks" (e.g., doz 90 = dec 108, doz 300 = dec 432, doz 600 = dec 864, doz 700 = doz 1008, doz 2000 = dec 3456). For your reference, the following are the digit conversion tables in both directions, up to fifth digits:

DOZENAL TO DECIMAL
Doz Dec Doz Dec Doz Dec Doz Dec Doz Dec
1 1 10 12 100 144 1000 1728 10000 20736
2 2 20 24 200 288 2000 3456 20000 41472
3 3 30 36 300 432 3000 5184 30000 62208
4 4 40 48 400 576 4000 6912 40000 82944
5 5 50 60 500 720 5000 8640 50000 103680
6 6 60 72 600 864 6000 10368 60000 124416
7 7 70 84 700 1008 7000 12096 70000 145152
8 8 80 96 800 1152 8000 13824 80000 165888
9 9 90 108 900 1296 9000 15552 90000 186624
A 10 A0 120 A00 1440 A000 17280 A0000 207360
B 11 B0 132 B00 1584 B000 19008 B0000 228096
DECIMAL TO DOZENAL
Dec Doz Dec Doz Dec Doz Dec Doz Dec Doz
1 1 10 A 100 84 1000 6B4 10000 5954
2 2 20 18 200 148 2000 11A8 20000 B6A8
3 3 30 26 300 210 3000 18A0 30000 15440
4 4 40 34 400 294 4000 2394 40000 1B194
5 5 50 42 500 358 5000 2A88 50000 24B28
6 6 60 50 600 420 6000 3580 60000 2A880
7 7 70 5A 700 4A4 7000 4074 70000 34614
8 8 80 68 800 568 8000 4768 80000 3A368
9 9 90 76 900 630 9000 5260 90000 44100

This tables should be added to the article eventually. ] 14:37, 5 February 2007 (UTC)

You could use my number converter that has been on the web since 1995 at http://www.footrule.com/1/conversn/convjvsc.htm?sr=homepage&ac=1&jt=1.1.1 . This allows conversions between all bases up to 36 (the limit of decimal digits plus 26 alphabetic characters). This also allows fractional values. There are some limitations due to the inability of javascript handling that may produce a close approximation which can usually be recognized and rounded yourself.
] (]) 22:17, 14 June 2016 (UTC)

== Dozenal Doesn't? come again? ==

"They use the word dozenal instead of "duodecimal" because the latter comes from Latin roots that express twelve in base-ten terminology."

And how does dos + zehn not? Is it just something about the Latin that the Gallic is more acceptable? <small>—Preceding ] comment added by ] (] • ]) {{{2|}}}</small><!-- Template:Unsigned -->

:Uh? What do you mean by that strange mix of Spanish/Latin + German, "dos + zehn"? That's by no means the origin of the word "dozen". The point is, "duodecimal" is clearly analyzable as a compound of the Latinate prefix ''duo-'' meaning "two" + the Latinate root ''dec-'' meaning "ten" + the Latinate adjectival ending ''-imal'', all of which are identifiable elements to be found in many other English words (''duo, duo-poly, duo-logue, duo-dec-illion, dec-illion, dec-imal, dec-imal-ize, tri-dec-imal, hexa-dec-imal, hex-imal, viges-imal, sexages-imal,'' etc.). That is, '''in English''', the term "duodecimal" is obviously a ten-based way of naming this numeral system, implying the decimal point of view of "twelve = ten + two" (twelve is no more "ten + two" than it is "nine + three" or "eleven + one" or "seven + five" or just "twelve"; viewing it as "ten + two" is a decimal-minded construct). In contrast, "dozen" is an unanalyzable term, not a compound, referring to a group of "::::::" elements directly without implying the decimal-based way of looking at it as ":::::" plus ":". Sure the source of the word "dozen" goes back to the Latin compound ''duodecim'' (which in old French became ''douze'' and then entered English through the derived word ''douzaine''); that is, ultimately it has the same etymological origin as "duodecimal". However, that decimal-based origin '''in a different language''' does not apply to the English language, where "dozen" entered as a single unanalyzable root referring directly to twelve without implying "ten + two". You cannot break up the English word "dozen" into *''do-'' + *''-zen'' the way you can break up "duodecimal" into ''duo-dec-imal'' implying "two + ten". English "dozen" is an unbreakable, unanalyzable single morpheme referring to a "group of ::::::" just like "score" means "group of ::::::::::" without the ten-based analysis as "::::: + :" and "::::: + :::::". "Dozen" refers to the number twelve as a counting unit, as an underived quantity, which is precisely the point of view of the dozenal numeral system (in dozenal you count by the dozen, so the name is very well-fitted), unlike "duodecimal" which implies the decimal perspective of "ten" as the counting unit and of "twelve" as a derived quantity composed of "one ten, plus two units" (in dozenal, twelve is "10" not "12"). "Hundred" and "thousand" are two other examples of words which in their remote etymological origin were breakable, analyzable compounds (both ultimately based on the Proto-Indoeuropean root *''dekm'' for "ten") but which by the time English came into existence had become single unanalyzable morphemes. ] 17:52, 26 May 2007 (UTC)

I concurr with Uaxuctum that the word 'dozen' is derived from the French word 'douzaine', and it is also true that the French word was derived from the Latin duodecima and is therefore still a reference to the 'two-ten' origin. If it is desirous to provide a word for a 12 base number system, it would be far more acceptable to use a root that is completely disconnected from the base ten system using the Latin basis of 'decima' for the 'decimal' system. Therefore why not use the same form of root as used for the decimal system but based on 12, and there is such a perfectly good basis. I discovered this when researching Roman mathematics and the Roman hand abacus, which led to the Roman names for fractions, which were themselves overwhelmingly 12 based. The Roman word for a tenth was the decima, but the Roman word for a twelfth was 'uncia'. What better word for a base 12 root than the base 12 analogue of the base 10 word? Thus the 'Uncial' or even 'Uncimal' system! Note that although I have suggested such a name for a base 12 number system, I was later to find that it had been suggested many years earlier by Pvt. William S. Crosby in a letter to the DSA and published in the Vol.1 No.2 edition of The Duodecimal Bulletin of June 1945 under the title of "Uncial Jottings of a Harried Infantryman". I quote directly from that article.

:"On Nomenclature, Notation, and Numeration: Maybe I am a factionlist, but here are some of the prejudices I stick by.

:'''Duodecimal''', (two more than ten) is a derived concept as well as a clumsy word. What is needed is a word expressing "counting by the scale of twelve", but as far as possible not depending on any other concept. "Uncial" is a suitable word to replace "decimal" in naming point-form fractions, and I myself use the word for the whole field of counting by dozens. Its chief drawback is that only a specialized meaning (in the field of paleography) is given in most dictionaries. "Dozenal I consider beneath contempt."

The entire article can be found beginning on page 9 of .

It seems good ideas will always re-occur!

] (]) 20:35, 22 December 2010 (UTC)

: If I may pick an etymological nit or two: the classical Latin words for 'ten, twelve' are ''decem, duodecim''; the corresponding ordinal adjectives are ''decim–um, duodecim–um'' (''–us, –a'', etc). The French word ''douzaine'' is ''douze'' (from a Vulgar Latin form that probably resembled Italian ''dodici'') with a French suffix ''–aine'' that forms other "group of N" words (e.g. ''quarant-aine'' for a set of 40 days); this suffix is unique to French as far as I know. Nor is ''–imal'' a morpheme as Uaxuctum would have it. —] (]) 21:41, 22 December 2010 (UTC)

== Fractions ==

Hi everyone!

I have tried to work some fractions out using duodecimal though I am very stuck!

Can someone explain in a very easy way to me (since I am very dumb!) how the duodecimal works and how to get those fractions the article showed?

Thanks a lot!! <small><span class="autosigned">—Preceding ] comment added by ] (] • ]) 13:59, 9 November 2008 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

:Calculations in base 12 are done by carrying or borrowing in multiples of 12. For example, the example that 1/9 = 0.14, goes like this:

9 goes into 1 0 times remainder 1 : units = 0 carry remainder 1 as 12 twelfths
9 goes into 12 1 times remainder 3: digit = 1 carry remainder 3 as 36
9 goes into 36 4 times remainder 0: digit = 4 carry remainder 0 as 0

So we have 9 goes into 1 as 0.14

cf dec
9 goes into 1 0 remainder 1 write 0, carry 1 as 1*10 tenths
9 goes into 10 1 remainder 1 write 1, carry 1 as 1*10
repeat
1/9 = 0.11111111111 decimal

Books on arithmetic give this calculation as a means of dealing with products of feet, inches and twelfths, where the output is given as cu ft, 144 cu in, 12 cu in, cu in, etc.

--] (]) 12:53, 27 August 2009 (UTC)

== Germanic and Twelve / Twelfty ==

There are some commnets about germanic languages and twelve that need fixing.

Indo-European is a decimal system that went as far as 100, but not 1000. The words for 100 are easily seen to be related, but the words for 1000 are later inventions (eg mill vs thousand).

The change from eleven/twelve to thirteen etc, is a base 4 feature, not a base 12 one. Nine and new are etymologically related in all IE languages, nine being the new one in the third four. Also, Finnish changes from names to decimal relatives at 9 (nine = one-removed). French changes from two-lif to -teen forms at 16 to 17 (dix-sept, dix-huit).

There is no germanic tradition of dodecimal multiple or division. The hundred is always 120, divided into twelve tens. The thousand is always 1200. Germanic languages have words for writing numbers in 'long' and 'short' forms, or twelftywise, teentywise.

Latin weights and measures show decimal multiples (eg mile = 5000 paces), while the divisions are largely duodecimal, with factors of 2 and 3 only. Germanic number systems tend to have relatively equal numbers of 3 and 5 on each side (eg cwt = 120 lb, lb = 7680 gr).

The six score hundred was typically used of things with heads (eg people, nails), while the new five-score hundred has elsewere use.

One notes that E Gordon 1956 "Introduction to old norse" gives in section 107 (page 292), as numerals, 100 tiu tigir (teenty), 110 ellifu tigir (elefty), 120 hundrað (hundred), 200 hundrað ok atta tigir (hundred and eighty), 240 twau hundrað (two hundred), 1200 þusand (thousand), all given without comment.

The system of dozens, grosses, and great grosses form a system of super-divisions, ie larger units that are intended to be divided. A grocer is one who deals in grosses, dividing these into dozens for sale, and the buyer divides the dozen to units. Dozens and grosses are only used of things that are itself cheap and undivided: fruit, eggs, etc: the undivided nature suggests that 1 is a division, the cheap-price suggests that one might want to make larger units to divide into smaller ones.

--] (]) 12:40, 27 August 2009 (UTC)
:Firstly, Finnish does not change naming pattern from 9 (''yhdeksän''), but from 8 (''kahdeksan''); the second member of the compounds in both ''kahdeksan'' and ''yhdeksän'' is an Indo-European loan meaning ‘ten’. All the Uralic languages have invented new words for both 8 and 9; no common denominator can be found or reconstructed—in fact, only 1–5 can be reconstructed for Uralic with any certainty. The rest are later innovations or borrowings in individual branches.

:Secondly, I don’t see how Germanic ‘hundred’, being always 120 and divided into twelve equal units, is not a tradition of duodecimal division. To me, that’s exactly what it is: a tradition of mixed decimal and duodecimal division.

:Thirdly, while ‘nine’ and ‘new’ are etymologically related, there doesn’t seem to be any evidence that they were transparently connected as such by Germanic times (when the ‘one-left’ and ‘two-left’ terms were coined). Common Germanic forms like ''*newjaz'' and ''*niwun'' are not that parallel. And any association between ‘eight’ and ‘sharp’ was definitely completely gone by Germanic times (and probably only vaguely relevant even in Proto-Indo-European).

:There’s little doubt that ''*neu̯n̥'' is ‘the new one’; but that only points to vestiges of a base-4 system in Indo-European itself. It doesn’t support any theory that new terms coined (to replace the inherited, purely decimal ones) in a much later stage of a daughter language, are base-4 in nature. Nor do terms naming added or removed items from a decimal base lend much credence to claims that they are in fact base-4.

:] (]) 12:49, 16 October 2012 (UTC)

== Unwarranted Emphasis on English Weights & Measures for Duodecimal Usage ==

The ultimate sentence in the section titled "Origin" attributes the usage of 12 as a major basis for several units of measure and a monetary system mainly to the English system of measures and coinage. Although there is a reference to ] which does provide a more complete description of the origin of these systems, the emphasis in this section on the 'English' origin gives a skewed impression by ignoring the details in the referenced entry for Charlemagne that clearly explains that the mixed 20/12 based monetary system originated with Charlemagne, was adopted by King Offa in Britain, but was widespread throughout central and western Europe. It was probably the introduction of the metric system (not the S.I.) that mainly involved the adoption of decimal monetary systems. For example, the French system of money used the livre of 20 sous and the sou of 12 deniers up until the adoption of the metric system. Likewise, the monetary systems of many European counties used the same mixed base monetary system, and it was only the fact that the United Kingdom was the last country to abandon that system that made it the "English" system in common experience.

Again the entry for Charlemagne does note the origin of the duodecimal use of fractions by the Romans, and it was this that resulted in the base 12 portion of these monetary systems. It also notes that the English words 'inch' and 'ounce' are both derived from the Roman word for <sup>1</sup>/<sub>12</sub> or an 'uncia'. This use of a base of 12 was also widespread across Europe for the use of length measures as exemplified by the words for 'inch' in several European languages. Whereas England (Britain) used the word inch, the main practice in continental Europe was to use a word derived from the Roman usage for that measure which was a 'thumb inch', such that the words for inch and thumb in many languages are the same or closely related. Examples are shown below.

{| class="wikitable"
|-
! Language !! Inch !! Thumb
|-
| Catalan || polzad || polze
|-
| Danish || tomme || tommel
|-
| Dutch || inch(1) || duim
|-
| French || pouce || pouce
|-
| Finnish || tuuma || peukalo
|-
| Galician || polgada || polgar
|-
| Icelandic || þumlungur || þumall
|-
| Irish || orlach || ordóg
|-
| Italian || pollice || pollice
|-
| Portuguese || polegada || polegar
|-
| Spanish || pulgada || pulgar
|-
| Swedish || tum || tumme
|}
(1)
* duim als lengtemaat
* Engelse duim

I think it would be appropriate to modify this section to broaden the origin of the mixed base monetary system and to give a better understanding of the wider European usage of a base of 12 in many units of measure, not limiting this to the English, but acknowledging the true origins that began with Charlemagne and earlier with the Romans.

] (]) 00:45, 1 October 2010 (UTC)

:The Romans used a weight-fraction system, where an 'as' is a unit (foot, pound, grain, coin-measure), which was then divided into lesser units by weight (uncia, drachma, scrupule, obolus, calculus, etc). These typically consistent with the duodecimal fractions, and Roman and Greek money traditions. (drachma = 6 obolus, in copper was a handful of 6 spear-coins). Every foot and pound the Romans inherited was divided in the same manner.

:For weights, the usual weights were in ounces, the pound becoming an ever larger number of ounces. The divisions of the ounce are still preserved.

:Of length, the pre-roman tradition (Greece, Egypt), was to divide the foot into 16 digits. The division into 16 is a clavis (claw, clove, digit, (finger)nail), which becomes a 16th of any other measure. We see dutch nagel of weight, being 1/16 of a larger unit. Likewise, english digit, nail, clove divide the foot, yard and cwt into 16, are all etymologically related to 16 fingernails to the foot.

:Most of Europe inherited the Roman tradition, and even though the uncia becomes the thumb (and this divided duodecimally to lines and points), still retain the Roman twelfth divisions, rather than other divisions. When decimalisation came to europe pre-metrically, the same sequence of names (foot, inch, line, point) are applied to various duodecimal/decimal divisions. The duodecimal units in common use (Eng foot, inch; French inch, foot, line), retained their values, and decimals applied elsewhere. A tradition in Germany has decimalisation on the rood (12 ft), foot, inch as the Kette-mass, Geometric and miners units.

:A similar process occurs today with 1000 vs. 1024 for powers of kilo. A 1.44 MB diskette, is actually 1.44 × 1000 × 1024.

--] (]) 10:26, 25 December 2010 (UTC)

== Usage section ==
Would it be applicable to have a section about practical usage of the system in speaking, writing and such? There is already a section on symbology (which takes up most of the advocacy section), but the article lacks mention of any nomenclature. This is likely to leave the reader confused with saying things like "aye-ty bee", which sounds like "eighty three" (the digit 'A' especially so). Of nomenclatures to suggest, I know about the classic "ten, eleven, dozen, gross", TGM's "ten, elv, zen, duna" and Schoolhouse Rock!'s "dek, el, doh, " (as said in this article).

It would be useful if this section was early on, so that readers know about it before trying to use it.

M1n1f1g on Dozensonline, ] (]) 16:21, 28 August 2011 (UTC)

: Old English had words that become teenty and elefty in ME for the decades after 90. These avoid clashes between tenty/twenty and eleventy/seventy, because there is some word-space between teenty/twenty and elefty/seventy. Most of the duodecimal words i have seen have been based on decimal ten / eleven, which mean 'two hands' and 'one left'.

: For a hundred of six-score (which is what OE, old norse etc used), it does not really matter, because there is a decimal step, and teenty, elefty are perfectly appropriate. For a pure twelfty base, one should take cognance that PIE used a four-based system, and that 'nine' is the /new/ one of the third tetrad. One might suppose, 'med' and 'alt' might form the etymological roots for 10 and 11 digits in a pure twelve-system, and higher numbers in the manner of new-welsh, eg one ty six (for 18). This allows one to use simpler numbers for the 144's etc, as one decides whether one should use 144-based or 1728-based steps (cf 100, 1000 based commas).

: Much of what is written in 12 is mainly how to calculate in the duodecimal divisions. Older German units had names for 12*cube and 144*cube, along with 12*sq, which allows duodecimal names for something like 144*foot³. See, eg Muret-Sanders English/German Dictionary 1902, in particular the extensive table of weights and measures.

--] (]) 08:17, 29 August 2011 (UTC)

== is ''base-30'' the smallest system that has three different prime factors? ==

Article says: "''] is the smallest system that has three different prime factors (all of the three smallest primes: 2, 3 and 5) and it has eight factors in total (1, 2, 3, 5, 6, 10, 15, and 30)''". IMHO it's not true. ] is the smallest system that has three different prime factors — 2, 3, 5 (and has five divisors — 1, 2, 3, 5, 15). <br/> ] (]) 20:37, 9 February 2012 (UTC)
: Base 15 does not have 2. ] (]) 13:03, 10 February 2012 (UTC)

== Dozenal... ==

...is the most optimal radix, am I not correct? '''''<font color="#ff8000">]</font>''''' 05:36, 18 May 2012 (UTC)
:No, twelfty (six-score) is. ] (]) 07:00, 18 May 2012 (UTC).
::Well, if society can memorize 7T34<sub>doz</sub> multiplication problems and able to remember T0<sub>doz</sub> different symbols, base T0<sub>doz</sub> is the most optimal base.

::: 13572 = E3.12? i don't understand. I use 144 = 1.24. 120 symbols? I use 12. Still, i did a fairly extensive survey of number systems and assorted tools, including bases, to determine the most suited method for hand calculations. 120 won hands down. You just need a more advanced notion of bases to handle it. I've been using it as the normal base for a number of calculations (such as symmetries). I will often do calculations in an assortment of other bases, such as 12 and 18 and 30, but the only ones that don't need annotations are 10 and 120, since these were designed to be concurrent. ] (]) 06:59, 19 May 2012 (UTC)
::::Yes but if I was to pick a new number base for society, it would be 10<sub>doz</sub>. '''''<font color="#ff0080">]</font>''''' 15:08, 19 May 2012 (UTC)

:: twelfty has historical usage. twelve doesn't. so þere ye go. ] (]) 10:27, 21 May 2012 (UTC)

10 is not as bad as many 12-ists seem to think: while 10 does not support 3 completely, the fact that 9 (adjacent to 10) is a multiple of 3 does partially alleviate this issue. 12 does not have similar solutions for 5. (6, 14, and 15 are also not bad.) I'm aware you can test for 5 in base 12 based on the fact that 12<sup>2</sup> ≡ −1 (mod 5), but this is not really on the order of ease of finding the digital root. Nevertheless the advantages of 12 are not inconsiderable. ] (]) 11:19, 5 April 2013 (UTC)

I've kinda thought about a little more. I'm not really a fan of 12. The solutions for 5 are only partial, and while its treatment of its divisors is awesome, its treatment of 5 leaves much to be desired. And I feel 5 is important. (DeVlieger explains perfectly why.) I'm beginning to think that sixty might be the optimal radix. (No, I do not want to be teleported to ancient Babylon. I just want to have their arithmetic back. IMO we should have stayed with sixty.) It solves the problem of 5, has a half-maximal expansion for 1/7 (0.08;34;17;08;34;17...), and anything higher is not really necessary. And the 1/7 expansion is quite recognizable. I can estimate it pretty well as 0.08;30, by just feeding of twelfty's (0.17;17;17...) 120 solves that problem, but I think it is really too large to handle, while sixty isn't quite there yet IMO. (Sexagesimalist here.) 120 has a lower totient ratio, but has twice the digits, utterly removing the benefits and making it about 50% (30 per sixty) more complicated. ] (]) 15:41, 10 November 2013 (UTC)

Now that I have thought about it a bit more, I now think 12 is actually the best human-scale base, with 10 very close behind, though if 60 were considered human scale I think it might actually win. ] (]) 13:36, 15 November 2013 (UTC)

== Merge with Base 13 ==

While this has been historically labeled as "duodecimal", this article technically describes a base-13 number system, not base-12. This article and ] should be merged and a new page accurately describing a base-12 number system should be created.

Explanation:<br />
'''Base-2:''' 0 1<br />
'''Base-3:''' 0 1 2<br />
'''Base-4:''' 0 1 2 3<br />
'''Base-5:''' 0 1 2 3 4<br />
'''Base-6:''' 0 1 2 3 4 5<br />
'''Base-7:''' 0 1 2 3 4 5 6<br />
'''Base-8:''' 0 1 2 3 4 5 6 7<br />
'''Base-9:''' 0 1 2 3 4 5 6 7 8<br />
'''Base-10:''' 0 1 2 3 4 5 6 7 8 9<br />
'''Base-11:''' 0 1 2 3 4 5 6 7 8 9 "10"<br />

'''Base-12''' should be: 0 1 2 3 4 5 6 7 8 9 "10" "11" yet it's described here as what should logically be a base-13 system...<br />
'''Base-13:''' 0 1 2 3 4 5 6 7 8 9 "10" "11" "12" <br />

] (]) 22:03, 17 July 2013 (UTC)

:You're wrong. — ] ] 00:10, 18 July 2013 (UTC)
:Duodecimal / Dozenal uses 12 "digits"; whether they are 0 1 2 3 4 5 6 7 8 9 10/Z/T/A 11/E/B or 1 2 3 4 5 6 7 8 9 "10" "11" "12", there are 12 digits. — ] ] 00:20, 18 July 2013 (UTC)
:I have reverted the addition of the merge tags as they are based on completely bogus reasoning. As for counting systems that use digits 1...base instead of 0...base–1, see ]. —] (]) 00:39, 18 July 2013 (UTC)
::Then I recommend the wording of this article be a bit more clear in that regard (perhaps in including more direct examples of the system) and that the inaccurate multiplication table included in this page be corrected, re-labeled, or removed. — ] (]) 01:07, 18 July 2013 (UTC)
:::I don't see anything wrong the multiplication table. — ] ] 01:27, 18 July 2013 (UTC)
::::The table is base-13! Also, in reading the article as it is currently, I should also point out that its ] describes the number system as including characters for both zero and twelve as well.

::::{{Quotation|In a duodecimal place system, ten can be written as A, eleven can be written as B, and twelve is written as 10.}}

::::If twelve can be written as "10" and the multiplication table includes a character for both zero and twelve, then (at least at first glance) what is being described here is a base-13 system. — ] (]) 01:54, 18 July 2013 (UTC)
{{od}}If you think that "10" is a single digit, in base 12 or any other base, then you have no business editing or discussing articles on number bases. It is two digits. And the multiplication table is fine; it includes 13 columns, but that is no different than a decimal multiplication table that includes multiplication by ten (with eleven columns, zero through ten). —] (]) 01:58, 18 July 2013 (UTC)
:::::Sorry. I just counted columns, apparently. I didn't realize I was making a complete fool of myself until after I typed that. — ] (]) 02:11, 18 July 2013 (UTC)
::::::Oh, well, no harm done I think except maybe to some dignity. I'm sorry if my language earlier came off as a bit harsh. —] (]) 04:59, 18 July 2013 (UTC)

== Fractions ==

How do you convert fractions from base 10 to base 12? <small><span class="autosigned">— Preceding ] comment added by ] (] • ]) 21:10, 26 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

Fractions like decimals and dozenals, actally are continued numerators, so 0.538 = 5.38/10, eg 5 dm and then 0.38 is 3.8/10 (cm), and so forth. The conversion is to replace these 10's to 12's. 0.538 * 12/12 = 6.456/12, so the first digit is 6. 0.456 * 12/12 gives 5.472/12, this is the second place, and 12*0.472/12 gives 5.664, gives 5 as the third place. So 0.538 decimal = 0.6558 dozenal.

The same method can be used of changing numerators, so 0,538 * 6/6 = 3.228, 0.228*10/10 = 2.28/10; .28*6/6 gives 1.68/6, and 0.68 *10/10 gives 6.8/10, so this gives 0.538 hours = 0.3217 (sixtywise) hours = 32' 17''.

Likewies, you can use it of units: 0.538 acres * 4/4 = 2.152 roods, 0.152 * 40/40 gives 6.08 perches, so 0.538 acres = 2 roods, 6 perches. ] (]) 10:36, 27 September 2013 (UTC)

(I am aware that this section is nearly a month old.)<br>
There is another way to convert dozenal fractions to decimal, though you have to be proficient with dozenal arithmetic since that is used instead of decimal. For example, I'll convert decimal 0.375 to dozenal. (ᘔ is 10 in decimal form.) Take the least significant digit, 5, and divide it by ᘔ, yielding 0.6. Take that result and add it by the next least significant digit, 7, to get 7.6. Divide that by ᘔ to get 0.9. Take that and add by the next least significant digit, 3, to get 3.9. Divide that by ᘔ to arrive at 0.46. ] 21:36, 26 October 2013 (UTC)

Thanks to both of you, and I know how to so dozenal math. <small><span class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) 02:58, 6 November 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->


you can also do this. for example if you want to make 0.375 decimal to dozenal all you do is convert 375 into dozenal and 1000 into dozenal and divide them <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) 04:28, 22 November 2018 (UTC)</small> <!--Autosigned by SineBot-->

== Article Title ==

Has it been discussed yet whether this article should be titled "Dozenal" rather than "Duodecimal"? There are Dozenal Societies of America and Great Britain, not Duodecimal Societies. Most people I hear speaking of the topic use "dozenal" and avoid "duodecimal." Thank you, <span style="background-color:#bbcc99;">] (])</span> 02:11, 18 January 2014 (UTC)
:I support changing the article's title to "Dozenal". It's been getting more and more attention in recent years and I almost never see people refer to it as "duodecimal". ] 01:10, 21 January 2014 (UTC)
::Oppose. Duodecimal is the logical word and title in line with decimal. --] (]) 13:54, 21 January 2014 (UTC)
:::Please elaborate. ] 06:52, 26 January 2014 (UTC)
:::Yes, please elaborate a little more on what makes it logical, why being in line with decimal is preferable. Thank you, <span style="background-color:#bbcc99;">] (])</span> 19:27, 26 January 2014 (UTC)
::::"Duodecimal" is derived from Latin ''duodecem'' analogous to "decimal" from Latin ''decem''. Dozenal, however, is derived from ''English'' "dozen" + "-al". --] (]) 07:38, 27 January 2014 (UTC)
:::::You still haven't given a real reason why the rename shouldn't occur. Base twelve has been getting famous in recent years (partially due to numberphile's video ''Base 12'') and it's better known as ''Dozenal'' than ''Duodecimal''. I'm seeing more and more people on the net treat it as ''Dozenal'' rather than ''Duodecimal''. As the OP said, there's no "Duodecimal" society of America or Britian, but dozenal. Imo I feel that base twelve and the term ''dozenal'' has gained enough prominence to rename the article to ''Dozenal''. ] 20:20, 2 February 2014 (UTC)
::::::Haven't I? It apparently just isn't anything you deem good enough (from what I can tell, only strict "most common usage" matters to you). --] (]) 08:12, 3 February 2014 (UTC)
:::::::From what I read above, the only argument presented in favor of keeping the title "duodecimal" is that it more closely correlates to the word "decimal." But why would that matter—shouldn't this article title be most relevant to the numbering system it discusses, rather than being named in contrast or comparison to another system? I believe most-common-usage would better guide here.<span style="background-color:#bbcc99;">] (])</span> 18:02, 3 February 2014 (UTC)
::::::::Not just decimal, though, but all base-number articles. Decimal is just the best-known one. Other examples can be found in the box on the right in this article's lead. Note especially ], among several similar ones. --] (]) 18:22, 3 February 2014 (UTC)
:::::::::There is little consistency between the articles, and there are many exceptions. Of course ], ], and all other bases below ten have no "&#8209;decimal" in their names. Many articles are named simply "Base&#8209;X" (], ]). And there are others above base ten without "&#8209;decimal" (] and ], from the Latin ''vigesimus'' for "twenty"). <span style="background-color:#bbcc99;">] (])</span> 20:43, 4 February 2014 (UTC)
::::::::::"Vigesimal" and the others are actually consistent. The only ones that are not consistent are the "Base XX" titles, and even their inconsistency is quite distinct from that of "dozenal". --] (]) 21:13, 4 February 2014 (UTC)
:::::::::::But note that base-36 has been called both "hexatridecimal" (six-and-three-tens) and "sexatrigesimal" (six-twenties). Numbering systems are commonly named in relation to base-10 ("-decimal") when used in reference to base-10, but sometimes they are named after other bases—such as base-20 ("-esimal")—when that base is more relevant or primal. <span style="background-color:#bbcc99;">] (])</span> 18:59, 5 February 2014 (UTC)
:{{od}}So people have tried to come up with a term based on Latin roots, but have come up with different terms for various reasons. It seems to me that that is why the article is located at ]. Here, however, it is not about competing terms that are both based on Latin, but one that is and one that is based on an English word to make it seem like it were based on Latin roots. --] (]) 08:22, 6 February 2014 (UTC)
::::::::::::The word "dozen" is derived from Middle English, from Old French, from Latin, from Indo-European. The suffix "-al" is applied to words based in Latin (such as "infernal"), Greek (e.g. "comical"), and English ("tidal"). How is the etymology relevant and inhibitory? <span style="background-color:#bbcc99;">] (])</span> 00:40, 8 February 2014 (UTC)
:::::::::::::I know that. The difference is that that word changed a lot in the process, so that "dozen" cannot be considered Latin in origin, only etymologically traceable to a different Latin word. Moving this article to "dozenal" breaks the symmetry with those related articles located at proper titles (thus excluding "Base XXX" articles. --] (]) 11:09, 9 February 2014 (UTC)

#Why should the article title be kept how it is just because other bases' articles are X-decimal?
#What's wrong with going by "most common usage"?
:] 21:54, 8 February 2014 (UTC)
::Most common usage breaks consistency and introduces unnecessary irregularities. A redirect here is appropriate and exists, so anyone searching for 'dozenal' will find what they are looking for. --] (]) 11:09, 9 February 2014 (UTC)
:::I don't see where in ] that consistency trumps common name. And we don't have consistency anyway (viz. the Base-XX articles). <span style="background-color:#bbcc99;">] (])</span> 01:11, 13 February 2014 (UTC)

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== A problem in base 12 ==

The problem of {{oeis|id=A088622}} and {{oeis|id=A088623}} in base 12:

Form: n (written in base 12), f(n)=(smallest k>0 such that concatenation of n^k and 1 (in base 12) is prime, or 0 if no such number exists,written in base 12),g(n)=(smallest k>0 such that concatenation of 1 and n^k is prime, or 0 if no such number exists,written in base 12)

n,f(n),g(n)

if n mod 13=1 (n>1) or n mod 143=142, then f(n)=0.

if n is divisible by 2 or 3, then g(n)=0.

1,1,1
2,3,0
3,1,0
4,2,0
5,1,1
6,1,0
7,4,1
8,1,0
9,1,0
ᘔ,2,0
Ɛ,2,1
10,(]),0
11,1,1
12,0,0
13,1,0
14,1,0
15,2,2
16,2,0
17,1,1
18,1,0
19,ᘔ,0
1ᘔ,4,0
1Ɛ,1,1
20,36,0
21,9,4
22,1,0
23,0,0
24,1,0
25,1,1
26,713,0
27,1,2
28,2,0
29,1,0
2ᘔ,1,0
2Ɛ,1,1
30,1,0
31,3,1
32,1,0
33,2,0
34,0,0
35,2,7
36,2,0
37,2,6
38,3,0
39,1,0
3ᘔ,6,0
3Ɛ,3,1
40,1,0
41,2,1
42,1,0
43,1,0
44,3,0
45,0,1
46,4,0
47,1,1
48,1,0
49,3,0
4ᘔ,4,0
4Ɛ,1,3
50,2,0
51,1,92
52,23,0
53,1,0
54,1,0
55,490,14
56,0,0
57,Ɛ3,1
58,(>100000),0
59,1,0
5ᘔ,7,0
5Ɛ,1,4
60,24,0
61,1,13
62,2,0
63,49,0
64,2,0
65,3,(?)
66,1,0
67,0,1
68,2,0
69,42,0
6ᘔ,8Ɛ,0
6Ɛ,1,1
70,1,0
71,1,1
72,1,0
73,852,0
74,9,0
75,1,1
76,3,0
77,1,2
78,0,0
79,1,0
7ᘔ,1,0
7Ɛ,2,1
80,1,0
81,2,1
82,2,0
83,26,0
84,1,0
85,1,2
86,1703,0
87,1,11
88,1,0
89,0,0
8ᘔ,Ɛ6,0
8Ɛ,4,1
90,1,0
91,2,4
92,1,0
93,2,0
94,ᘔ,0
95,4,1
96,13,0
97,1,2
98,3Ɛ,0
99,6,0
9ᘔ,0,0
9Ɛ,1,1
ᘔ0,2,0
ᘔ1,1,81
ᘔ2,2,0
ᘔ3,2,0
ᘔ4,1,0
ᘔ5,6,1
ᘔ6,5,0
ᘔ7,2,1
ᘔ8,4,0
ᘔ9,1,0
ᘔᘔ,6,0
ᘔƐ,0,2
Ɛ0,2,0
Ɛ1,1,1
Ɛ2,1,0
Ɛ3,1,0
Ɛ4,2,0
Ɛ5,3,1
Ɛ6,1,0
Ɛ7,1,1
Ɛ8,3,0
Ɛ9,1,0
Ɛᘔ,0,0
ƐƐ,2,(?)
100,0,0
101,1,1
102,1,0
103,2,0
104,1,0
105,1,1
106,1,0
107,2,1
108,4,0
109,2,0
10ᘔ,2,0
10Ɛ,1,3
110,1,0
111,0,(?)
112,2,0
113,ᘔ1,0
114,2,0
115,1,1
116,18,0
117,(>46000),4
118,1776,0
119,2,0
11ᘔ,1,0
11Ɛ,27,2
120,1,0
121,1,14
122,0,0
123,1,0
124,2,0
125,4,1
126,1,0
127,2,(?)
128,1,0
...

Is there a prime of these forms?

(58^n)1, 1(65^n), 1(ƐƐ^n), 1(111^n), (117^n)1, 1(127^n), ...
<small><span class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) </span></small><!-- Template:Unsigned -->

:This is a talk page for the '''article''' "duodecimal". If you are proposing including this in the article, I say "why?" If you asking for information, Misplaced Pages is not the place. — ] ] 15:17, 17 August 2015 (UTC)

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== Multiplication table ==

I consider the 30<sub>12</sub>×30<sub>12</sub> multiplication table excessively wide for a Misplaced Pages article. — ] ] 08:28, 5 September 2015 (UTC)
:And I agree. What does it show that the 12×12 one doesn't? You only need a 12×12 table to multiply two arbitrary numbers in duodecimal, after all. ] (]) 17:25, 10 September 2015 (UTC)

== Ordinals ==

How should one use ordinal suffixes for duodecimal in English? For now I am using superscript ordinal º for prime factors and ª for everything else. <small><span class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) 13:39, 9 December 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

== Dozenal digits ==

Pardon me if this isn't the correct place to post this, but my computer (albeit going through many updates) still doesn't have the digits for ten and eleven. How can I get these digits? ] 09:27, 12 December 2015 (UTC)
:Download a font with them? Try . ] (]) 05:28, 13 December 2015 (UTC)

== Irrational Numbers not having a pattern? ==

The article says "Moreover, the infinite series of digits of an irrational number does not exhibit a pattern of repetition; instead, the different digits succeed in a seemingly random fashion." This doesn't seem right to me - that no irrational numbers exhibit a pattern of repetition. For example, the decimal number 0.121121112111121111121111112... exhibits a pattern, and is irrational, right? ] (]) 10:20, 16 December 2015 (UTC)

: Presumably the article is referring to the fact that a number is rational if and only if the sequence of its digits (in any non-mixing radix) is eventually periodic. ] (]) 04:52, 18 December 2015 (UTC)

::174.102.27.76 - your number certainly exhibits a pattern, but not a pattern of repetition, as its decimal expansion never repeats itself ''exactly''. ] (]) 07:39, 18 December 2015 (UTC)

::: As far as I know, the definition of being rational is whether the number can be represented by the division of two integers (in any base). I do not believe that any pattern being present is addressed. It just so happens that rational numbers either terminate or repeat at some point. ] (]) 22:51, 3 June 2016 (UTC)Alan B

:::: I've adjusted the wording to cover your concerns (I hope), with a link to ] for anyone who is not clear about the meaning. Please adjust the sentence further if you think it is still ambiguous. ] 11:15, 4 June 2016 (UTC)

== Base identification subscripts (dec and duod) ==

In the section ], there are formulas such as {{!xt|1=1/(2<sup>2</sup>) = 0.25 <sub>dec</sub> = 0.3 <sub>duod</sub>}}; shouldn't a more standard notation be used, such as {{xt|1=1/(2<sup>2</sup>) = 0.25 <sub>10</sub> = 0.3 <sub>12</sub>}}? — ] ] 10:42, 19 January 2016 (UTC)Ī
:... or {{xt|1=1/(2<sup>2</sup>) = 0.25 <sub>ten</sub> = 0.3 <sub>twelve</sub>}}? — ] ] 17:19, 20 January 2016 (UTC)
:: I think that 0.25 <sub>ten</sub> = 0.3 <sub>twelve</sub> is better, since the former favors the decimal numerical system. ] (]) 05:31, 21 January 2016 (UTC)
:::Well, that may not be a bad thing. Outside the context of these articles about bases, and the few places where you would directly work with binary, octal, or hexadecimal, don't we all interpret all numbers as decimal? Still, I suppose the "ten/twelve" subscripts do save on unnecessary confusion. ] (]) 13:41, 4 June 2016 (UTC)

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== Notation problems ==

There are some problems with the notation:

1) The "open E" U+0190 and the Canadian syllabary U+1614 may look like a turned two and a turned three, but such a usage is definitely wrong. Moreover, the latter symbol is present only in some specialized fonts.

2) The proper symbols have been added to Unicode only a year ago, but as well there are only a few fonts with them. There is a big chance that it will not be seen by an average reader.

3) The info about notation is split between three chapters, and the main chapter about it is definitely one-sided. There is no authority which would require the usage of exactly turned two and three.

So I suggest: a) some other symbols; b) the merger of three chapters into one (with three sub-chapters if needed).--] (]) 11:55, 30 May 2016 (UTC)

4) While a less mathematical problem, the new symbols X wouldn't be able to clearly appear on a seven-segment-display. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 23:35, 29 June 2016 (UTC)</small> <!--Autosigned by SineBot-->
:Not really; turned 3 is obvious, and turned 2 can be represented by removing the top segment from a standard 2 (just turn the result about 45° counterclockwise mentally). ] (]) 07:39, 27 March 2019 (UTC)

I've made the merger, however we are left to decide what exact symbols to use. I suggest T and E as the most intuitive, though it would be better to actually employ the Greek capital letters tau and epsilon to avoid confusion and for an easy find-replace.--] (]) 13:35, 30 May 2016 (UTC)
:I would support capital tau and epsilon for these reasons. ] (]) 16:20, 26 September 2016 (UTC)

== 10 and 11==
Why use those names, when you can recycle 10 for X and 11 for E, then you can call 10 "onety". ] (]) 18:06, 12 July 2016 (UTC)

== Requested move 4 January 2017 ==

<div class="boilerplate" style="background-color: #efe; margin: 2em 0 0 0; padding: 0 10px 0 10px; border: 1px dotted #aaa;"><!-- Template:RM top -->
:''The following is a closed discussion of a ]. <span style="color:red">'''Please do not modify it.'''</span> Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a ]. No further edits should be made to this section. ''

The result of the move request was: '''not moved''' per ]. This RM is clearly not going to pass. <small>(])</small> ] (], ]) 18:51, 5 January 2017 (UTC)
----

] → {{no redirect|Dozenal}} – more direct/clear and probably more common (dozenal societies etc.)&nbsp;] (]) 17:13, 4 January 2017 (UTC)
:<small>This is a contested technical request (]). ] (]) 17:49, 4 January 2017 (UTC)</small>
*'''Oppose''' - A reputable mathematics source (Wolfram) titles it as duodecimal, and duodecimal is the version that i have encountered in all (UK) textbooks. <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (] • ]) </small>
*'''Oppose'''. Google Books, while not the only useful metric of course, overwhelmingly supports "Duodecimal", and many of the hits for "Dozenal" pertain to the Dozenal Society of America. ] (]) 17:53, 4 January 2017 (UTC)
*'''Support''' per St.nerol. ]] 23:16, 4 January 2017 (UTC)
**The problem, {{U|PlantStar}} (I can barely read your name--please see ]), is that the nominator presents no solid evidence at all, and so "per nom" isn't very strong. ] (]) 04:45, 5 January 2017 (UTC)
*'''Oppose''' — ''Dozenal'' is not even a word in British English (per OED, though we apparently do have a dozenal society). No evidence has been presented that it is used anywhere. ] 09:50, 5 January 2017 (UTC)
*'''Oppose'''. ''Duodecimal'' is the standard term. The only reason why ''dozenal'' is ever used is to dissociate twelve from the decimal concept of it being two more than ten, which makes sense for organisations like the Dozenal Societies (which advocate a change to base twelve numeration), but not for a reference work like Misplaced Pages (which should use the common term and not advocate anything). (Besides, ''dozenal'' is still decimally constructed, if a bit less clearly. How would one apply such logic to hexadecimal?) ] (]) 13:00, 5 January 2017 (UTC)
----
:''The above discussion is preserved as an archive of a ]. <span style="color:red">'''Please do not modify it.'''</span> Subsequent comments should be made in a new section on this talk page or in a ]. No further edits should be made to this section.''</div><!-- Template:RM bottom -->


{{reply|Spitzak}} Hello, again! Regarding : Best I can tell, the ensp characters are not needed because the text in question is aligned-right. Looking at ], thinsp characters are not used for spaces in HTML equations. I generally convert both types of whitespace to regular spaces to make the markup easier to read, per the "keep markup simple" guideline at ]. -- ] (]) 20:08, 9 April 2022 (UTC)
== Compare with music? ==
:Variation in spacing is definitely part of proper mathematical typography, as would be obtained by using LaTeX-style markup. It is normally provided automatically as part of the system that formats the mathematics. I see no guidance in ] about avoiding variation in spacing for HTML-formatted mathematics. All I can see is some guidance to avoid using explicit spacing commands as a trick to force LaTeX formulas to be displayed as images. It doesn't even say not to use explicit spacing in LaTeX, only not to use them for that one weird purpose. —] (]) 20:19, 9 April 2022 (UTC)
::The note re ensp is correct: right-alighed so useless (also, in general and here too margins, padding &tc in table cells preferable not done by space characters). -] (]) 14:07, 10 April 2022 (UTC)
::] gives one clue for proper rendering in HTML: use {{tl|math}}. And doing so stimulates having same formatting throughout, so no blanket reason to adjust whitespace case by case. I note that it is not a good idea trying to emulate exact Latex formatting. -] (]) 14:24, 10 April 2022 (UTC)
:::{{tl|math}} is not proper mathematics rendering. It is a hack that sort of looks like LaTeX but is not as good. That does not mean that we have to make it even worse by sticking with uniform spacing when better spacing options are available. —] (]) 05:27, 28 April 2022 (UTC)
::::As always, you are ] to point out the "not proper" and propose improvements for those unspecified "worse" effects. Until that effectuates, {{tlf|math}} a good inline one to use. -] (]) 09:17, 28 April 2022 (UTC)
:For me removal of the nbsp from the table results in the left column being centered, not right-justified. That was why I reverted the edit. I don't have any opinion on putting thinsp in the math expressions, except I have rarely seen this in other articles.] (]) 14:34, 11 April 2022 (UTC)
::Ah, the ! directive apparently overrides the table-wide align-right CSS. I fixed that by adding align-right to the needed cells and it should be behaving now. Sorry for not catching that the first time. -- ] (]) 23:09, 27 April 2022 (UTC)
:::Great catch, ]! (the table is in {{slink|Duodecimal|Comparison to other number systems |nopage=yes}}). The "!" is the ] marker for "row/column header" (giving those styling effects, together with semantics). -] (]) 04:55, 28 April 2022 (UTC)


== Notations table ==
Has anyone thought the base 12 number can be correspond with musical scale? 0=C, 1=C#, 2=D, 3=Eb, 4=E, ..., 10=Bb, 11=B. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 13:16, 31 August 2017 (UTC)</small> <!--Autosigned by SineBot-->
:Music is more like mod 12 than base 12, since octave displacements, while not irrelevant, can be considered to be equivalent. ] (]) 13:19, 31 August 2017 (UTC)


I have added the notation options in table form (by characters, by base indicators); {{slink|Duodecimal|Notations and pronunciations|nopage=yes}}. They are derived from the existing text. We could reduce the overlap, but I am not sure about removing (redundant) text boldly. -] (]) 07:48, 17 April 2022 (UTC)
== silly divergent series ==


== Year 2022 in duodecimal ==
The list of divergent series seems silly to me. I see 1 + 1 + 1 + 1 + 1 + 1 + ... = −0.6, which seems so weird that it looks like this is some kind of special property of duodecimal notation. But of course 1+1+1+... diverges whether we're doing decimal or duodecimal, and all we're saying is that 0.6 duodecimal is 1/2 in decimal. Is there any point to these series in this article? ] (]) 00:19, 15 May 2018 (UTC)


The current year represented in duodecimal (base 12) notation is written as 1206. Can anyone guess what the '6' at the end of the duodecimal representation of the current year stands for? ] (]) 16:30, 8 September 2022 (UTC)
:In my opinion, this and similar divergent series have no place in this article. ] 00:58, 15 May 2018 (UTC)
::I agree with Dbfirs. ] (]) 01:05, 15 May 2018 (UTC)
:::As such, I have ] removed these series. ] (]) 01:09, 15 May 2018 (UTC)
::::See the article ], it says that 1 + 1 + 1 + 1 + ⋯ = -1/2, because it is <math>\zeta(0)</math> (see ])


:It does not "stand for" anything. -- ]. ] 22:37, 16 September 2022 (UTC)
::::<math>\zeta(x)=\sum_{n=1}^{\infin}\frac{1}{n^x}</math>, and when n=0, this sequence become 1 + 1 + 1 + 1 + ⋯, when n=-1, this sequence become ]. Besides, we know that <math>\zeta(0)=-\frac{1}{2}=-0.6</math> and <math>\zeta(-1)=-\frac{1}{10}=-0.1</math> (all numbers are written with duodecimal)
:it stands for "six" ] (]) 23:33, 25 February 2024 (UTC)
::… which is the remainder of 2022/12. ] (]) 01:48, 14 June 2024 (UTC)


== Divisibility Tests from Duodecimal ==
::::Also see the article ] for the reason that 1 + 2 + 4 + 8 + ⋯ = -1
:::::Those are not the sums of those divergent series, except under some generalisations of the word "sum". ] (]) 10:51, 22 May 2018 (UTC)
::::::This list continues to get bigger and bigger with more examples that are ultimately ]. I have restored the 15 May version. ] (]) 21:03, 5 July 2018 (UTC)
:::::::These things I added are all true. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 21:21, 5 July 2018 (UTC)</small> <!--Autosigned by SineBot-->
::::::::]. ] (]) 08:10, 6 July 2018 (UTC)


{{copied|from=duodecimal|to=senary}} ]. ] 22:36, 16 September 2022 (UTC)
== Some properties ==


== "The importance of 12 has been attributed to the number of lunar cycles in a year..." ==
I think the entire "some properties" section is junk. Can someone give me a good reason for not reinstating my removal of it? —] (]) 20:55, 22 August 2018 (UTC)


Ironically, 12 lunar cycles at 29.5 days apiece total only 354 days, just a '''dozen''' days short of a Leap Year. This is why we occasionally get 13 Full Moons in a year... &ndash;&nbsp;]&nbsp;<sup>]</sup> 20:36, 16 April 2023 (UTC)
:Why remove? Some of them are specific to this base (duodecimal), e.g. 12 (twelve) is the largest base such that both “all squares end with square digits” and “all primes end with prime digits or 1” are true. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding ] comment added by ] (]) 06:35, 23 August 2018 (UTC)</small> <!--Autosigned by SineBot-->
::Repeating another junk property is not a reason to keep. And why remove: because it's primarily ]. —] (]) 06:45, 23 August 2018 (UTC)


:However, splitting the ] into 12 equal parts (the signs of the ]) is a basic part of ancient Mesopotamian astronomy (cf. ]), which was then incorporated into Greek astronomy and persists today. –] ] 22:34, 28 September 2023 (UTC)
:This article has been taken over by duodecimal hobbyists. The "some properties" section belongs on someone's personal web page or blog, but not on Misplaced Pages. I support removing it all. ] (]) 09:33, 23 August 2018 (UTC)


== Fractions comparison ==
::Interesting facts that are ''unique'' to duodecimal, or where duodecimal is either the largest or smallest base to have that property, are perhaps interesting. But many pages of stuff about palidromes, especially with no indication whatsoever whether any of this is true or false or different in other bases, is a waste of time. So your one sentence about 12 (twelve) is the largest base such that both “all squares end with square digits” and “all primes end with prime digits or 1” are true is interesting (in fact I am wondering if it is the *only* base where this is true, except for 4 but that is only because all the non-zero digits are prime).] (]) 18:23, 23 August 2018 (UTC)


> ''"... in the duodecimal system, {{sfrac|8}} is exact; {{sfrac|20}} and {{sfrac|500}} recur because they include 5 as a factor...."''<br>However, this comparison loads the dice, because 20<sub>d</sub> and 500<sub>d</sub> end in zeroes ''only in decimal''. (In duodecimal, they are respectively 18<sub>z</sub> and 358<sub>z</sub>, not exactly obvious breakpoints.)
:::Personally, I can't help but finding some properties worth being reported here. The wholesale removal appears to me as excessive, even when I agree with it to an overwhelming part (primes in certain intervals!). Maybe, from an economic view, it should be the task of the Dozenal Society's fans to suggest selective, noteworthy content for re-enclosing it with the article (no wholesale revert!). I also cannot help but comparing this content with other "junk" in WP. I know I am not allowed to derive anything here from this. ] (]) 08:29, 24 August 2018 (UTC)
Conversely, 20<sub>z</sub> and 500<sub>z</sub> are 24<sub>d</sub> and 720<sub>d</sub>. Decimal {{sfrac|24}} and {{sfrac|720}} are recurring numbers: respectively 0.041{{Overline|666}}... recurring (rounded to 0.0417), and 0.0013{{Overline|888}}... recurring (rounded to 0.00139). That's a wash between systems, if fairly measured. &ndash;&nbsp;]&nbsp;<sup>]</sup> 21:08, 16 April 2023 (UTC)


== Uncial ==
::::To Spitzak: The bases which both “all squares end with square digits” and “all primes end with prime digits or 1” are true are 2, 3, 4, 8 and 12, and 12 is the largest of them. The former is true for bases 2, 3, 4, 5, 8, 12 and 16 (and possible no more, see {{oeis|A254328}}), and the latter is true for bases 2, 3, 4, 6, 8, 12, 18, 24 and 30 (and possible no more, see {{oeis|A048597}}).


I've removed the references to "Uncial" (one mention in the lede, and a single sentence in 'Advocacy and "dozenalism"') with the following justification:
:::::Well, why is this section, removed on 2018 Aug 22 considered as junk ? It is a more extended description of several arithmetic facts like primes, recurrent fractions, palindromes, but particularly in Base 12, rather than Base 10, which is decribed in the pages on the subject. ] (]) 14:42, 21 October 2018 (UTC)
* "Uncial" seems to chiefly refer to a script system, or else relations to an ounce.
* Other than the single listed source, I wasn't able to find a single source using "Uncial" to mean "duodecimal"
* The listed source is highly dated (from 1945) and furthermore, the part that discusses the word "Uncial" is submitted not by an expert, but by an infantryman. One layperson using a word once 80 years ago in a letter to a niche publication does not a current ] make.
If others disagree with this change, feel free to discuss and revert, but this seemed to me to be an oversight. ] (]) 10:47, 3 August 2023 (UTC)


== Duodecimal Conversion Table ==
:::::Another issue, why are you using these weird characters for the numerals ten and eleven ? No keyboard kan enter these digits, and the convention for base 16 is using the letters A and B for ten and eleven, so why not in Base 12 ? Only in the (very unlikely) case that mankind switches to base 12, these nonletter digits make sense. ] (]) 14:42, 21 October 2018 (UTC)


<s>I've reverted</s><ins>I had intended to revert</ins> an edit adding in a list of the numbers one through one hundred in base 12 and base 10<ins>, but someone seems to have beat me to it</ins>. I've done this for three reasons:
== Line ==
# Having duodecimal notation in a section prefaced by saying it's all in decimal notation is confusing. Note that this also means we may want to move the duodecimal addition and multiplication tables to a different section.
# It's of limited utility. There are many free calculators, apps, and sites which can convert arbitrary numbers between decimal and duodecimal. A table dealing only with the first hundred integers doesn't add much.
# It's redundant. In the very next section there are two tables that convert integers of several orders of magnitude, and also details how to convert from one system to the other.
{{pb}}I figured I'd open the discussion here so if anyone disagrees, we can hash it out and keep improving the article. ] (]) 00:57, 20 November 2023 (UTC) <ins>] (]) 00:59, 20 November 2023 (UTC)</ins>


:@] I concur with ] re: the tables being too wide. Do you think there's any value in keeping them at all? Given the abundance of conversion apps, is a table informative? The only thing it adds, in my opinion, is an at-a-glance notion of scale. (E.g., "Oh, so 100,000 base 10 is 49,A54 base 12.") I'm not sure that's worth the extensive real estate it takes up on the page. Thoughts? ] (]) 15:57, 26 January 2024 (UTC)
The link to the wikipedia article for line shows the value offer here, 12^-2, is wrong. --] (]) 10:05, 5 July 2019 (UTC)
:: I think they could be removed or radically shrunk, but I don't care enough to do it myself. Maybe skim back through the history to figure out who added them, and that person can explain their reasoning? –] ] 16:18, 26 January 2024 (UTC)
:::Whoops, sorry about the misaimed ping. And a quick dig shows that they've been around since at least 2013, and was worked on by a bunch of folks. I'll try boldly removing it, and if anyone objects, they can revert and discuss here. ] (]) 16:43, 26 January 2024 (UTC)
::::I chopped some columns out. The narrower one seems okay enough to me. –] ] 16:48, 26 January 2024 (UTC)
:::::Whoops! I managed to edit conflict and destroy your work. I've self-reverted; agreed that the new tables are better. I still don't see much point in having them, but that doesn't mean no other readers will find a use. Thanks for your work! ] (]) 16:50, 26 January 2024 (UTC)


== Changing examples of Germanic 11 and 12 words ==
:I suppose the logic is that a line is a twelfth of an inch which is itself a twelfth of a foot, hence the denominator of 144. ] 10:36, 5 July 2019 (UTC)


There has been a slight edit war on whether the example language used for special Germanic 11 and 12 words should be English (eleven, twelve) or German (elf, zwölf). How could we possibly resolve this? ] (]) 16:05, 13 June 2024 (UTC)
== notability ==


:Well, the first step is what you already did; go to the talk page. Thank you! My first thought is to use both, such as the following:
Question on the , must we only mention "notable" typefaces? Surely notability is contextual. The fonts removed in this edit may not have their own article (per ]), but given how few typefaces support the new dozenal digits, aren't they notable enough for that to be included here? I don't think that violates ]. Would like to hear {{reply to|David Eppstein|p=}}'s thoughts. <span style="font-size-adjust:0.54;">🖖 <span style="font-family:Ovidius,'Horizon BT',Horta,Roddenberry,Charcoal,Virtue,Krungthep;">]</span> ]</span> 19:35, 24 July 2019 (UTC)
:...such as {{lang|de|elf}} (eleven) and {{lang|de|zwölf}} (twelve)...
:Do you have a published reliable source, by people not associated with these fonts, for their support of duodecimal, or is this all hypothetical and ]? Because when I removed them from the article the listing of supporting fonts was (and still is) completely unsourced. And the LaTeX source for the next sentence is extremely minimal (two lines in a table showing those names for the characters, with no text supporting their use in duodecimal, out of a 164-page document). I think more should be removed unless it can be supported by better sources. —] (]) 20:09, 24 July 2019 (UTC)
:Also note the <nowiki>{{lang}}</nowiki> template to show it's a foreign language. Is there a way to apply that to the Proto-Germanic as well? If possible, it'd be good to comply with ]. ] (]) ] (]) 16:40, 13 June 2024 (UTC)
::Do you know how extremely unlikely it is that there will ever be anything written about obscure typefaces that support obscure characters? However, it is abundantly self-evident to anyone who bothers to look. Is it really ] to look out the window and say the sky is blue without citation, because anybody can provide ] by doing the same. Nobody is challenging the fact, nor do I see it as likely that anyone would. The usefulness of this encyclopedia is diminished by overly narrow interpretations of policies. <span style="font-size-adjust:0.54;">🖖 <span style="font-family:Ovidius,'Horizon BT',Horta,Roddenberry,Charcoal,Virtue,Krungthep;">]</span> ]</span> 21:50, 25 July 2019 (UTC)
:I don't understand the goal of the change. This is an English encyclopedia and readers are going to be familiar with the English words "eleven" and "twelve", which makes it accessible and interesting for them to see how they relate to original Proto-Germanic words. By comparison, most will not be familiar with the German equivalents. In my opinion switching English to German makes this passage less relevant, harder to read, and less memorable. –] ] 16:41, 13 June 2024 (UTC)
:For the record, I had made a similar removal a while back . &ndash;]&nbsp;(]&nbsp;&bull;&nbsp;]) 22:12, 25 July 2019 (UTC)
::Well, why not use both English and German? ] (]) 18:55, 13 June 2024 (UTC)
:::@] I think that, given that we're talking about another language, it is prudent to include it. After all, the words we're discussing are "elf" and "zwolf", not "eleven" and "twelve". If we use the English words, I could see some readers being confused about whether it's German or English which has ties with duodecimal. Put another way, Without the German words, we're asserting the existence but not providing any supporting data for non German speakers to verify. (I do not have the sources on that sentence, but they seem to be associated with the old German, not modern German.)
:::IP, I appreciate the attempt to add English as well. I'm not thrilled with that exact construction; while a reasonable reader would infer the association, a particularly slow (or, more likely, tired) reader might not. I'd be more comfortable if we added "respectively" (so it reads: ...English equivalents ''eleven'' and ''twelve'', respectively ). I'd still prefer the parenthetical to save space, but we can hash out the details if we establish a consensus for inclusion at all. :)
:::Also, thank you both for having this discussion; I've seen enough bad editing that it makes me happy when editors show up and talk things out, like colleagues over tea. ] (]) 19:54, 13 June 2024 (UTC)
::::We're talking about "Germanic languages", of which the most obvious and familiar example for an English encyclopedia is.... English (] starts with "English is a West Germanic language ..."). The English examples also have the advantage that (a) they are a bit closer to their proto-Germanic origins, and (b) they can be more obviously related to "one left" and "two left" mentioned in the article. Throwing in the German words just seems like gratuitous and largely irrelevant trivia here. If we insist on including German, why not also Dutch, Afrikaans, Yiddish, Swedish, Norwegian, or Faroese? I don't think there is a consensus (or any good reason) for adding the German words, and I intend to take them back out when I get a chance. –] ] 02:24, 14 June 2024 (UTC)
:::::Huh. I always thought of English as a bastard language. I've learned something today. You make good points; I now support using English only. ] (]) 10:51, 14 June 2024 (UTC)
::::::I would support using German only, however. ] (]) 00:34, 19 June 2024 (UTC)
::::::The words we use most, including counting-numbers (and about half the words of this sentence), are nearly all Germanic; since 1066 we have added a big load of words from French and Latin – not counting the trickle of loanwords that every language gets. ] (]) 02:49, 20 June 2024 (UTC)
:::::I like the German examples better because:
:::::# I don’t like using English as an example of a particular thing at all.
:::::# I like examples in foreign languages better.
:::::Can we change the examples to be German only and keep it at that? ] (]) 00:36, 19 June 2024 (UTC)
:::::English first, others in a footnote. The English words show the roots most transparently, and the roots are the relevant thing in context. ] (]) 02:45, 20 June 2024 (UTC)
::::::The article currently uses German first and puts others (including English) in a footnote. ] (]) 19:51, 20 June 2024 (UTC)
:::::::I reverted back to the English version. I'm not sure how to footnote, so have not risked breaking things by trying. Good catch, IP! ] (]) 20:03, 20 June 2024 (UTC)
::::::::I honestly think it's quite dumb to use the Misplaced Pages language as an example for any given topic, and I think we need to emphasize other languages with the examples, which is why I keep reverting to the German version. ] (]) 14:50, 21 June 2024 (UTC)
:::::::::Could you give us a hint of why you think it dumb? Does “language” imply “foreign language”? ] (]) 06:08, 22 June 2024 (UTC)
:::::::Stop trying to replace the English words with German. It is worse for readers and you haven't given a good reason, let alone established consensus, for the change. –] ] 21:48, 20 June 2024 (UTC)
::::::::Tell this persistent editor to read ]. They seem to be confusing that term with ]. ] (]) 23:00, 20 June 2024 (UTC)
::::::::How about we compromise and just use no examples at all? ] (]) 14:46, 21 June 2024 (UTC)
:::::::::I'm hesitate to accept this, just because an example clears up what we mean by "special words". Without an example, it sounds like they have special meaning, but the example illustrates that it's just a different ''form'' for the word. ] (]) 15:32, 21 June 2024 (UTC)
:::::::::Using no examples also seems worse to me. The point here is to connect something readers know (the English words "eleven" and "twelve") with something they didn't know (these are Germanic-origin words which come from "one left" and "two left"), in the service of briefly giving an example of language(s) that have non-standard words for 11 and 12. {{pb}} Your insistence against using English as an example in the English language Misplaced Pages seems arbitrary and unreasonable to me. –] ] 19:42, 21 June 2024 (UTC)
::::::::::Let's try to stick with using the German examples only. Sounds good? ] (]) 16:04, 23 June 2024 (UTC)
:::::::::::No, it doesn't. Let's stick with English examples only. Please don't make that change again until and unless you get consensus for it. ] (]) 16:20, 23 June 2024 (UTC)
::::::::::::How would you think about compromising and using both? ] (]) 16:27, 23 June 2024 (UTC)
:::::::::::::I would be against it. See the discussion in this section for reasoning. Why do you insist on including German? ] (]) 16:29, 23 June 2024 (UTC)
::::::::::::::Because I think we need to pay more attention to foreign languages with the examples. ] (]) 16:43, 23 June 2024 (UTC)
:::::::::::::::Okay. Per ] and ], it's up to you to demonstrate and convince other editors that, 1) English alone is insufficient, and 2) that attention to a foreign language (as opposed to merely a Germanic language) is appropriate. ] (]) 16:48, 23 June 2024 (UTC)
:::::::::::::::In many Misplaced Pages articles, I agree it would be helpful to aim for a more international and cross-cultural set of examples and topics.
:::::::::::::::But in any specific case, you have to think about the ''purpose'' of the example in context, and how it connects readers to the topic. You haven't yet given any reason why a German example would do a better job illuminating ] number systems than an English example, nor have you addressed the several reasons why other editors claim it would do a worse job. You haven't explained why having multiple examples or no examples (your supposed "compromise" solutions) would be an improvement.
:::::::::::::::If you want to make meaningful contributions to this or other Misplaced Pages articles I would urge you to give up on this dispute and go do some book research. –] ] 17:34, 23 June 2024 (UTC)
:::::::::::::::This is not exactly a language article. ] (]) 23:37, 23 June 2024 (UTC)
:::::::::::You have already been told no on that. ] (]) 23:37, 23 June 2024 (UTC)
:::::::::By the way, if you have an ever-changing IP address, you may find it helpful to create an account. (See ]) –] ] 19:46, 21 June 2024 (UTC)
:I have now changed the examples into a table, as well as adding Dutch and Swedish. ] (]) 00:42, 19 June 2024 (UTC)
::This is unhelpful and distracting to readers. We're not here to give a detailed analysis of number words or an exhaustive cross-linguistic comparison. We're talking about the mathematics of duodecimal number system(s) here, and mentioning Germanic languages merits no more than a brief aside. –] ] 01:07, 19 June 2024 (UTC)
:::As a compromise, I think it's unhelpful but I won't complain if you put a couple of other examples in a footnote. Skip the table though. –] ] 01:15, 19 June 2024 (UTC)
::If you want you can write a new article called ] or similar, where a suitably expanded version of this table would be appropriate. –] ] 01:09, 19 June 2024 (UTC)
:::I imagine that such an article would be absorbed into ], either as a table or in a format like that of ''Buck's Synonyms''. ] (]) 02:51, 20 June 2024 (UTC)
:I have now added a page with a larger version of the table, as a subpage of my user page: ] ] (]) 01:36, 19 June 2024 (UTC)


== RfC: Extra digits == == Symbols for Ten and Eleven ==


@] recently replaced the transformation template with the unicode version. @] reverted, citing that the characters don't display. I feel that, because the infobox references the unicode, the unicode should be used. Copying and pasting the rotated 2 or 3 only yields the standard 2 or 3, which could cause some confusion. I also see Jacobolus' point that it may not display properly. (It displays fine on my desktop, but not on my mobile.) If we do keep the unicode versions, it may be worth adding the same warning as on ] that it uses uncommon unicode. If consensus is instead to stick to the transformation template, I suggest we remove the displayed unicode in the infobox. ] (]) 17:24, 10 August 2024 (UTC)
{{rfc|sci|tech|rfcid=494CB42}}
Should this article use <code><nowiki>{{rotate|180|2}}</nowiki></code> and <code><nowiki>{{rotate|180|3}}</nowiki></code> ({{rotate text|180|2}} and {{rotate text|180|3}}) with markup or the special characters {{unichar|1614|CANADIAN SYLLABICS CARRIER JU|nlink=Canadian Aboriginal syllabics}} and {{unichar|0190|LATIN CAPITAL LETTER OPEN E|nlink=Latin epsilon}} for the digits ten and eleven, like other articles? Or should we use something else entirely, like X and E? –] (]]) 22:09, 21 August 2019 (UTC)


:The unicode is directly included in the infobox (and again separately in the article body!), as "U+218A ↊ TURNED DIGIT TWO" etc., which is fine. What we ''shouldn't'' do is put giant missing glyph symbols in the middle of our pages, since the goal is to communicate the appearance of these symbols to readers. If the infobox isn't going to have legible symbols it should be removed altogether. –] ] 17:25, 10 August 2024 (UTC)
:{{re|LaundryPizza03}} Per ], why start an RfC on this before there's been any discussion? This seems like something that could be figured out without a big show. But anyway, this is also right after {{u|Spitzak}} converted all uses to {{tlx|d2}} and {{tlx|d3}}. Presumably, everything should use those (and while I appreciate the need for a short name, I wonder if d2 and d3 are maybe too short and likely to clash with something), and then any decisions could easily be implemented wiki-wide. There's also {{tlx|duodecimal}}, which is used by number articles (and maybe other stuff?), which is really just a wrapper for ] &ndash; it uses A and B and automatically puts the <sub>12</sub> subscript after the result.
::Ah, I'd missed that. I could see that; Leave the unicode in the body (in the description you cited), and have the rotated version at the top to ensure it displays. It's a shame <nowiki><math></nowiki> doesn't seem to recognize these symbols; that would be an easier and more standardized solution. ] (]) 17:41, 10 August 2024 (UTC)
:
:::Aside: 1/3 is not a "precomposed fraction". ] is talking about Unicode symbols such as ⅓, which are discouraged whenever on a page also involving a wider variety of fractions because these will look inconsistent. (Even though they are better looking and more appropriately sized than the results of the {{t|frac}} or {{t|sfrac}} templates, {{frac|1|3}}, {{sfrac|1|3}}, consistency was considered more important than good typography.) The MOS has no problem with inline fractions using full-height numerals and an ordinary / separator. –] ] 02:31, 11 August 2024 (UTC)
:Anyway, there are two main considerations here: rendering support and semantic correctness. A/B and X/E have both (probably). <span style="display:inline-block; {{transform|rotate(180deg)}}">2</span> and <span style="display:inline-block; {{transform|rotate(180deg)}}">3</span> will likely render fine just about everywhere, but lack semantic correctness, and likely won't work correctly with screen readers. The actual unicode points mentioned in the article are semantically most meaningful, but apparently lack support. Other things that just look close (like the ju syllabics thing) fail all tests and have no business being used at all. &ndash;]&nbsp;(]&nbsp;&bull;&nbsp;]) 23:32, 21 August 2019 (UTC)
*'''X and E'''. The rotated characters are clever but cleverness is not always a virtue. They make sense as modified versions of the digits 2 and 3 only if one is coming at this from the point of view of octal (where the numbers they represent are the base + 2 or 3), unlikely for readers of this article. The Canadian and Latin special characters are just wrong (have unrelated meanings to the ones here). And for purposes of both general audience readers not getting confused by special characters, and ease of editing, X and E are much better. (A and B would also both be acceptable but are more decimal-centric than X and E). —] (]) 23:35, 21 August 2019 (UTC)
*The template names were chosen because they were not already taken (t2 and t3 were taken, that is what I tried first). I don't have any problem changing them to produce X and E or A and B or whatever. However the few uses where they *should* be the rotated digits should be converted back. I think leaving them as templates is a good idea as this will allow further changes when this subject comes up again.] (]) 15:17, 22 August 2019 (UTC)
* Everything except &#123;{rotate}} which defeats text processing. ] (]) 07:51, 23 August 2019 (UTC)
*: And more… “E” is stupid—at least for Misplaced Pages—because conflicts with the well-known ] notation. Seemingly “Ɛ” is the best for eleven. No strong opinion on character for the digit “ten”, although “X” is already used in Roman numerals and hence would not look unreasonable in this context. ] (]) 09:58, 23 August 2019 (UTC)

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Whitespace characters

@Spitzak: Hello, again! Regarding this revert: Best I can tell, the ensp characters are not needed because the text in question is aligned-right. Looking at Misplaced Pages:Manual of Style/Mathematics, thinsp characters are not used for spaces in HTML equations. I generally convert both types of whitespace to regular spaces to make the markup easier to read, per the "keep markup simple" guideline at MOS:MARKUP. -- Beland (talk) 20:08, 9 April 2022 (UTC)

Variation in spacing is definitely part of proper mathematical typography, as would be obtained by using LaTeX-style markup. It is normally provided automatically as part of the system that formats the mathematics. I see no guidance in Misplaced Pages:Manual of Style/Mathematics about avoiding variation in spacing for HTML-formatted mathematics. All I can see is some guidance to avoid using explicit spacing commands as a trick to force LaTeX formulas to be displayed as images. It doesn't even say not to use explicit spacing in LaTeX, only not to use them for that one weird purpose. —David Eppstein (talk) 20:19, 9 April 2022 (UTC)
The note re ensp is correct: right-alighed so useless (also, in general and here too margins, padding &tc in table cells preferable not done by space characters). -DePiep (talk) 14:07, 10 April 2022 (UTC)
MOS:MATH gives one clue for proper rendering in HTML: use {{math}}. And doing so stimulates having same formatting throughout, so no blanket reason to adjust whitespace case by case. I note that it is not a good idea trying to emulate exact Latex formatting. -DePiep (talk) 14:24, 10 April 2022 (UTC)
{{math}} is not proper mathematics rendering. It is a hack that sort of looks like LaTeX but is not as good. That does not mean that we have to make it even worse by sticking with uniform spacing when better spacing options are available. —David Eppstein (talk) 05:27, 28 April 2022 (UTC)
As always, you are invited to point out the "not proper" and propose improvements for those unspecified "worse" effects. Until that effectuates, {{math}} a good inline one to use. -DePiep (talk) 09:17, 28 April 2022 (UTC)
For me removal of the nbsp from the table results in the left column being centered, not right-justified. That was why I reverted the edit. I don't have any opinion on putting thinsp in the math expressions, except I have rarely seen this in other articles.Spitzak (talk) 14:34, 11 April 2022 (UTC)
Ah, the ! directive apparently overrides the table-wide align-right CSS. I fixed that by adding align-right to the needed cells and it should be behaving now. Sorry for not catching that the first time. -- Beland (talk) 23:09, 27 April 2022 (UTC)
Great catch, Beland! (the table is in § Comparison to other number systems). The "!" is the wikitable marker for "row/column header" (giving those styling effects, together with semantics). -DePiep (talk) 04:55, 28 April 2022 (UTC)

Notations table

I have added the notation options in table form (by characters, by base indicators); § Notations and pronunciations. They are derived from the existing text. We could reduce the overlap, but I am not sure about removing (redundant) text boldly. -DePiep (talk) 07:48, 17 April 2022 (UTC)

Year 2022 in duodecimal

The current year represented in duodecimal (base 12) notation is written as 1206. Can anyone guess what the '6' at the end of the duodecimal representation of the current year stands for? 23.150.224.60 (talk) 16:30, 8 September 2022 (UTC)

It does not "stand for" anything. -- 27 is my favorite number. You can ask me why here. 22:37, 16 September 2022 (UTC)
it stands for "six" Brawlio (talk) 23:33, 25 February 2024 (UTC)
… which is the remainder of 2022/12. —Tamfang (talk) 01:48, 14 June 2024 (UTC)

Divisibility Tests from Duodecimal

Text and/or other creative content from duodecimal was copied or moved into senary. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists.

27 is my favorite number. You can ask me why here. 22:36, 16 September 2022 (UTC)

"The importance of 12 has been attributed to the number of lunar cycles in a year..."

Ironically, 12 lunar cycles at 29.5 days apiece total only 354 days, just a dozen days short of a Leap Year. This is why we occasionally get 13 Full Moons in a year... including this year, 2023. (August gets a 2nd Full Moon, aka "Blue Moon".) – .Raven  20:36, 16 April 2023 (UTC)

However, splitting the ecliptic into 12 equal parts (the signs of the zodiac) is a basic part of ancient Mesopotamian astronomy (cf. MUL.APIN), which was then incorporated into Greek astronomy and persists today. –jacobolus (t) 22:34, 28 September 2023 (UTC)

Fractions comparison

> "... in the duodecimal system, ⁠1/8⁠ is exact; ⁠1/20⁠ and ⁠1/500⁠ recur because they include 5 as a factor...."
However, this comparison loads the dice, because 20d and 500d end in zeroes only in decimal. (In duodecimal, they are respectively 18z and 358z, not exactly obvious breakpoints.) Conversely, 20z and 500z are 24d and 720d. Decimal ⁠1/24⁠ and ⁠1/720⁠ are recurring numbers: respectively 0.041666... recurring (rounded to 0.0417), and 0.0013888... recurring (rounded to 0.00139). That's a wash between systems, if fairly measured. – .Raven  21:08, 16 April 2023 (UTC)

Uncial

I've removed the references to "Uncial" (one mention in the lede, and a single sentence in 'Advocacy and "dozenalism"') with the following justification:

  • "Uncial" seems to chiefly refer to a script system, or else relations to an ounce.
  • Other than the single listed source, I wasn't able to find a single source using "Uncial" to mean "duodecimal"
  • The listed source is highly dated (from 1945) and furthermore, the part that discusses the word "Uncial" is submitted not by an expert, but by an infantryman. One layperson using a word once 80 years ago in a letter to a niche publication does not a current WP:RS make.

If others disagree with this change, feel free to discuss and revert, but this seemed to me to be an oversight. EducatedRedneck (talk) 10:47, 3 August 2023 (UTC)

Duodecimal Conversion Table

I've revertedI had intended to revert an edit adding in a list of the numbers one through one hundred in base 12 and base 10, but someone seems to have beat me to it. I've done this for three reasons:

  1. Having duodecimal notation in a section prefaced by saying it's all in decimal notation is confusing. Note that this also means we may want to move the duodecimal addition and multiplication tables to a different section.
  2. It's of limited utility. There are many free calculators, apps, and sites which can convert arbitrary numbers between decimal and duodecimal. A table dealing only with the first hundred integers doesn't add much.
  3. It's redundant. In the very next section there are two tables that convert integers of several orders of magnitude, and also details how to convert from one system to the other.

I figured I'd open the discussion here so if anyone disagrees, we can hash it out and keep improving the article. EducatedRedneck (talk) 00:57, 20 November 2023 (UTC) EducatedRedneck (talk) 00:59, 20 November 2023 (UTC)

@Jacobolus I concur with your edit summary re: the tables being too wide. Do you think there's any value in keeping them at all? Given the abundance of conversion apps, is a table informative? The only thing it adds, in my opinion, is an at-a-glance notion of scale. (E.g., "Oh, so 100,000 base 10 is 49,A54 base 12.") I'm not sure that's worth the extensive real estate it takes up on the page. Thoughts? EducatedRedneck (talk) 15:57, 26 January 2024 (UTC)
I think they could be removed or radically shrunk, but I don't care enough to do it myself. Maybe skim back through the history to figure out who added them, and that person can explain their reasoning? –jacobolus (t) 16:18, 26 January 2024 (UTC)
Whoops, sorry about the misaimed ping. And a quick dig shows that they've been around since at least 2013, and was worked on by a bunch of folks. I'll try boldly removing it, and if anyone objects, they can revert and discuss here. EducatedRedneck (talk) 16:43, 26 January 2024 (UTC)
I chopped some columns out. The narrower one seems okay enough to me. –jacobolus (t) 16:48, 26 January 2024 (UTC)
Whoops! I managed to edit conflict and destroy your work. I've self-reverted; agreed that the new tables are better. I still don't see much point in having them, but that doesn't mean no other readers will find a use. Thanks for your work! EducatedRedneck (talk) 16:50, 26 January 2024 (UTC)

Changing examples of Germanic 11 and 12 words

There has been a slight edit war on whether the example language used for special Germanic 11 and 12 words should be English (eleven, twelve) or German (elf, zwölf). How could we possibly resolve this? 2601:C6:D200:E9B0:CC47:CFD0:245D:7739 (talk) 16:05, 13 June 2024 (UTC)

Well, the first step is what you already did; go to the talk page. Thank you! My first thought is to use both, such as the following:
...such as elf (eleven) and zwölf (twelve)...
Also note the {{lang}} template to show it's a foreign language. Is there a way to apply that to the Proto-Germanic as well? If possible, it'd be good to comply with WP:!EN. EducatedRedneck (talk) EducatedRedneck (talk) 16:40, 13 June 2024 (UTC)
I don't understand the goal of the change. This is an English encyclopedia and readers are going to be familiar with the English words "eleven" and "twelve", which makes it accessible and interesting for them to see how they relate to original Proto-Germanic words. By comparison, most will not be familiar with the German equivalents. In my opinion switching English to German makes this passage less relevant, harder to read, and less memorable. –jacobolus (t) 16:41, 13 June 2024 (UTC)
Well, why not use both English and German? 2601:C6:D200:E9B0:D1E2:5217:CBA8:FB34 (talk) 18:55, 13 June 2024 (UTC)
@Jacobolus I think that, given that we're talking about another language, it is prudent to include it. After all, the words we're discussing are "elf" and "zwolf", not "eleven" and "twelve". If we use the English words, I could see some readers being confused about whether it's German or English which has ties with duodecimal. Put another way, Without the German words, we're asserting the existence but not providing any supporting data for non German speakers to verify. (I do not have the sources on that sentence, but they seem to be associated with the old German, not modern German.)
IP, I appreciate the attempt to add English as well. I'm not thrilled with that exact construction; while a reasonable reader would infer the association, a particularly slow (or, more likely, tired) reader might not. I'd be more comfortable if we added "respectively" (so it reads: ...English equivalents eleven and twelve, respectively ). I'd still prefer the parenthetical to save space, but we can hash out the details if we establish a consensus for inclusion at all. :)
Also, thank you both for having this discussion; I've seen enough bad editing that it makes me happy when editors show up and talk things out, like colleagues over tea. EducatedRedneck (talk) 19:54, 13 June 2024 (UTC)
We're talking about "Germanic languages", of which the most obvious and familiar example for an English encyclopedia is.... English (English language starts with "English is a West Germanic language ..."). The English examples also have the advantage that (a) they are a bit closer to their proto-Germanic origins, and (b) they can be more obviously related to "one left" and "two left" mentioned in the article. Throwing in the German words just seems like gratuitous and largely irrelevant trivia here. If we insist on including German, why not also Dutch, Afrikaans, Yiddish, Swedish, Norwegian, or Faroese? I don't think there is a consensus (or any good reason) for adding the German words, and I intend to take them back out when I get a chance. –jacobolus (t) 02:24, 14 June 2024 (UTC)
Huh. I always thought of English as a bastard language. I've learned something today. You make good points; I now support using English only. EducatedRedneck (talk) 10:51, 14 June 2024 (UTC)
I would support using German only, however. 2601:C6:D200:E9B0:99AF:66D1:66A8:2912 (talk) 00:34, 19 June 2024 (UTC)
The words we use most, including counting-numbers (and about half the words of this sentence), are nearly all Germanic; since 1066 we have added a big load of words from French and Latin – not counting the trickle of loanwords that every language gets. —Tamfang (talk) 02:49, 20 June 2024 (UTC)
I like the German examples better because:
  1. I don’t like using English as an example of a particular thing at all.
  2. I like examples in foreign languages better.
Can we change the examples to be German only and keep it at that? 2601:C6:D200:E9B0:99AF:66D1:66A8:2912 (talk) 00:36, 19 June 2024 (UTC)
English first, others in a footnote. The English words show the roots most transparently, and the roots are the relevant thing in context. —Tamfang (talk) 02:45, 20 June 2024 (UTC)
The article currently uses German first and puts others (including English) in a footnote. 2601:C6:D200:E9B0:8083:AAB1:FA58:1588 (talk) 19:51, 20 June 2024 (UTC)
I reverted back to the English version. I'm not sure how to footnote, so have not risked breaking things by trying. Good catch, IP! EducatedRedneck (talk) 20:03, 20 June 2024 (UTC)
I honestly think it's quite dumb to use the Misplaced Pages language as an example for any given topic, and I think we need to emphasize other languages with the examples, which is why I keep reverting to the German version. 2601:C6:D200:E9B0:A4ED:D8FB:CD17:1710 (talk) 14:50, 21 June 2024 (UTC)
Could you give us a hint of why you think it dumb? Does “language” imply “foreign language”? —Tamfang (talk) 06:08, 22 June 2024 (UTC)
Stop trying to replace the English words with German. It is worse for readers and you haven't given a good reason, let alone established consensus, for the change. –jacobolus (t) 21:48, 20 June 2024 (UTC)
Tell this persistent editor to read Germanic languages. They seem to be confusing that term with German language. Spitzak (talk) 23:00, 20 June 2024 (UTC)
How about we compromise and just use no examples at all? 2601:C6:D200:E9B0:A4ED:D8FB:CD17:1710 (talk) 14:46, 21 June 2024 (UTC)
I'm hesitate to accept this, just because an example clears up what we mean by "special words". Without an example, it sounds like they have special meaning, but the example illustrates that it's just a different form for the word. EducatedRedneck (talk) 15:32, 21 June 2024 (UTC)
Using no examples also seems worse to me. The point here is to connect something readers know (the English words "eleven" and "twelve") with something they didn't know (these are Germanic-origin words which come from "one left" and "two left"), in the service of briefly giving an example of language(s) that have non-standard words for 11 and 12. Your insistence against using English as an example in the English language Misplaced Pages seems arbitrary and unreasonable to me. –jacobolus (t) 19:42, 21 June 2024 (UTC)
Let's try to stick with using the German examples only. Sounds good? 2601:C6:D200:E9B0:C0CC:BB36:D4CA:9991 (talk) 16:04, 23 June 2024 (UTC)
No, it doesn't. Let's stick with English examples only. Please don't make that change again until and unless you get consensus for it. EducatedRedneck (talk) 16:20, 23 June 2024 (UTC)
How would you think about compromising and using both? 2601:C6:D200:E9B0:C0CC:BB36:D4CA:9991 (talk) 16:27, 23 June 2024 (UTC)
I would be against it. See the discussion in this section for reasoning. Why do you insist on including German? EducatedRedneck (talk) 16:29, 23 June 2024 (UTC)
Because I think we need to pay more attention to foreign languages with the examples. 2601:C6:D200:E9B0:C0CC:BB36:D4CA:9991 (talk) 16:43, 23 June 2024 (UTC)
Okay. Per WP:BRD and WP:ONUS, it's up to you to demonstrate and convince other editors that, 1) English alone is insufficient, and 2) that attention to a foreign language (as opposed to merely a Germanic language) is appropriate. EducatedRedneck (talk) 16:48, 23 June 2024 (UTC)
In many Misplaced Pages articles, I agree it would be helpful to aim for a more international and cross-cultural set of examples and topics.
But in any specific case, you have to think about the purpose of the example in context, and how it connects readers to the topic. You haven't yet given any reason why a German example would do a better job illuminating duodecimal number systems than an English example, nor have you addressed the several reasons why other editors claim it would do a worse job. You haven't explained why having multiple examples or no examples (your supposed "compromise" solutions) would be an improvement.
If you want to make meaningful contributions to this or other Misplaced Pages articles I would urge you to give up on this dispute and go do some book research. –jacobolus (t) 17:34, 23 June 2024 (UTC)
This is not exactly a language article. —Tamfang (talk) 23:37, 23 June 2024 (UTC)
You have already been told no on that. —Tamfang (talk) 23:37, 23 June 2024 (UTC)
By the way, if you have an ever-changing IP address, you may find it helpful to create an account. (See Misplaced Pages:Why create an account?) –jacobolus (t) 19:46, 21 June 2024 (UTC)
I have now changed the examples into a table, as well as adding Dutch and Swedish. 2601:C6:D200:E9B0:99AF:66D1:66A8:2912 (talk) 00:42, 19 June 2024 (UTC)
This is unhelpful and distracting to readers. We're not here to give a detailed analysis of number words or an exhaustive cross-linguistic comparison. We're talking about the mathematics of duodecimal number system(s) here, and mentioning Germanic languages merits no more than a brief aside. –jacobolus (t) 01:07, 19 June 2024 (UTC)
As a compromise, I think it's unhelpful but I won't complain if you put a couple of other examples in a footnote. Skip the table though. –jacobolus (t) 01:15, 19 June 2024 (UTC)
If you want you can write a new article called Germanic number words or similar, where a suitably expanded version of this table would be appropriate. –jacobolus (t) 01:09, 19 June 2024 (UTC)
I imagine that such an article would be absorbed into Indo-European number words, either as a table or in a format like that of Buck's Synonyms. —Tamfang (talk) 02:51, 20 June 2024 (UTC)
I have now added a page with a larger version of the table, as a subpage of my user page: Germanic duodecimal number words TheCool1Z (talk) 01:36, 19 June 2024 (UTC)

Symbols for Ten and Eleven

@Kwamikagami recently replaced the transformation template with the unicode version. @Jacobolus reverted, citing that the characters don't display. I feel that, because the infobox references the unicode, the unicode should be used. Copying and pasting the rotated 2 or 3 only yields the standard 2 or 3, which could cause some confusion. I also see Jacobolus' point that it may not display properly. (It displays fine on my desktop, but not on my mobile.) If we do keep the unicode versions, it may be worth adding the same warning as on List of numeral systems that it uses uncommon unicode. If consensus is instead to stick to the transformation template, I suggest we remove the displayed unicode in the infobox. EducatedRedneck (talk) 17:24, 10 August 2024 (UTC)

The unicode is directly included in the infobox (and again separately in the article body!), as "U+218A ↊ TURNED DIGIT TWO" etc., which is fine. What we shouldn't do is put giant missing glyph symbols in the middle of our pages, since the goal is to communicate the appearance of these symbols to readers. If the infobox isn't going to have legible symbols it should be removed altogether. –jacobolus (t) 17:25, 10 August 2024 (UTC)
Ah, I'd missed that. I could see that; Leave the unicode in the body (in the description you cited), and have the rotated version at the top to ensure it displays. It's a shame <math> doesn't seem to recognize these symbols; that would be an easier and more standardized solution. EducatedRedneck (talk) 17:41, 10 August 2024 (UTC)
Aside: 1/3 is not a "precomposed fraction". MOS:FRAC is talking about Unicode symbols such as ⅓, which are discouraged whenever on a page also involving a wider variety of fractions because these will look inconsistent. (Even though they are better looking and more appropriately sized than the results of the {{frac}} or {{sfrac}} templates, 1⁄3, ⁠1/3⁠, consistency was considered more important than good typography.) The MOS has no problem with inline fractions using full-height numerals and an ordinary / separator. –jacobolus (t) 02:31, 11 August 2024 (UTC)
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