Talk:Duodecimal

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Contents 1 Counting to 12 on fingers 2 Notation 3 Pronunciation? 4 Polygons 5 Names 6 Time? 7 growth 8 English duodecimal names 9 Question on societies 10 Easier to memorize?

[edit] 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. --MichaelTinkler.

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

• I post a question on the talk:Decimal 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.

[edit] 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? Dysprosia 12:53, 23 Aug 2003 (UTC)

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

• Script capital E is possible in Unicode: ℰ. You could also use ℇ or ℇ. --Sonjaaa 07:49, Sep 10, 2004 (UTC)
  • There is also Ɛ, 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) [1]. Livajo 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.--Sonjaaa 08:09, Sep 10, 2004 (UTC)

[edit] 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?--Sonjaaa 08:14, Sep 10, 2004 (UTC)

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

[edit] Polygons

I find it worth mentioning that there also seems to be a relation to polygons: Regular triangles, squares and hexagons (3,4 and 6) will tesselate in the plane 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 dodecahedron in three dimensions. Article on Polygons from DSGB (Adobe PDF)

[edit] Names

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

English: eleven (not one-teen)  twelve (not two-teen)
German:  elf (not eins-zehn)    zwölf (not zwei-zehn)
Dutch:   elf (not men-tien)     twaalf (not twee-tien)
--InsectAttack 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. 82.224.88.105 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. — JIP | Talk 09:59, 4 Mar 2005 (UTC)

[edit] 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? Sarge Baldy 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 Chinese zodiac -- Nik42 15:06, 15 July 2005 (UTC)

[edit] growth

This article has grown really well. Can we nominate it for featured article?--Sonjaaa 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". Uaxuctum 04:21, 4 February 2006 (UTC)

[edit] 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...? --Aceizace 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 DozensOnline forum, 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 dozenal myriad) 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 googol) 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. Uaxuctum 16:31, 22 April 2006 (UTC)

It would be even funnier in German, "vier gross-gross-Grosse und neun gross-Grosse"... ;) 惑乱 分からん 15:08, 18 November 2006 (UTC)

[edit] Question on societies

Why isn't there a separate article on the Duodecimal Society of America? PrimeFan 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 ternary 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 sexagesimal where it said that Babylonian sexagesimal was mixed radix just because they represented their digits using a sub-base of ten—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 Uaxuctum 18:37, 1 November 2006 (UTC)

[edit] 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 (which dose not appear to be the case), 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. —Gary van der Merwe ^(Talk) 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? —Gary van der Merwe ^(Talk) 10:31, 14 December 2006 (UTC)