Talk:Duodecimal
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[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.
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- 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.
- The bones are called phalanges. There are 14 per hand (the 12 you mention, plus 2 for the thumb). --Zundark
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- 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)
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- 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
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- Script capital E is possible in Unicode: ℰ. You could also use ℇ or ℇ. --Sonjaaa 07:49, Sep 10, 2004 (UTC)
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- 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)
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- 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 tessellate 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)
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- 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)
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- 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)
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- 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 [<link removed - in blacklist> 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)
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). Uaxuctum 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. Dpbsmith (talk) 01:12, 18 December 2006 (UTC)
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- 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 multiplication table 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 mnemonic technique (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 — would you challenge the assertion of this common-sense fact asking for a citation to back it up?), and the memorization of pi's digits 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. Uaxuctum 03:43, 18 December 2006 (UTC)
[edit] Conversion from decimal
Is there any known system for quick conversions from decimal to dozenal? Oberiko 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. Uaxuctum 14:37, 5 February 2007 (UTC)
[edit] 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? —Preceding unsigned comment added by 75.28.41.130 (talk • contribs)
- 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. Uaxuctum 17:52, 26 May 2007 (UTC)
