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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).--[[User:Любослов Езыкин|Lüboslóv Yęzýkin]] ([[User talk:Любослов Езыкин|talk]]) 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 [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/89.100.168.185|89.100.168.185]] ([[User talk:89.100.168.185|talk]]) 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). [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 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.--[[User:Любослов Езыкин|Lüboslóv Yęzýkin]] ([[User talk:Любослов Езыкин|talk]]) 13:35, 30 May 2016 (UTC)
:I would support capital tau and epsilon for these reasons. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 16:20, 26 September 2016 (UTC)

== Compare with music? ==

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 [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/101.15.147.75|101.15.147.75]] ([[User talk:101.15.147.75#top|talk]]) 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. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 13:19, 31 August 2017 (UTC)

== silly divergent series ==

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? [[User:Staecker|Staecker]] ([[User talk:Staecker|talk]]) 00:19, 15 May 2018 (UTC)

:In my opinion, this and similar divergent series have no place in this article. [[User:Dbfirs|<span style="font-family: verdana;"><i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i></span>]] 00:58, 15 May 2018 (UTC)
::I agree with Dbfirs. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 01:05, 15 May 2018 (UTC)
:::As such, I have [[WP:BOLD|boldly]] removed these series. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 01:09, 15 May 2018 (UTC)
::::See the article [[1 + 1 + 1 + 1 + ⋯]], it says that 1 + 1 + 1 + 1 + ⋯ = -1/2, because it is <math>\zeta(0)</math> (see [[Riemann zeta function]])

::::<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 [[1 + 2 + 3 + 4 + ⋯]]. 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)

::::Also see the article [[1 + 2 + 4 + 8 + ⋯]] 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". [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 10:51, 22 May 2018 (UTC)
::::::This list continues to get bigger and bigger with more examples that are ultimately [[WP:OR]]. I have restored the 15 May version. [[User:D4iNa4|D4iNa4]] ([[User talk:D4iNa4|talk]]) 21:03, 5 July 2018 (UTC)
:::::::These things I added are all true. <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/175.97.48.79|175.97.48.79]] ([[User talk:175.97.48.79#top|talk]]) 21:21, 5 July 2018 (UTC)</small> <!--Autosigned by SineBot-->
::::::::[[WP:NOTTRUTH]]. [[User:D4iNa4|D4iNa4]] ([[User talk:D4iNa4|talk]]) 08:10, 6 July 2018 (UTC)

== Some properties ==

I think the entire "some properties" section is junk. Can someone give me a good reason for not reinstating my removal of it? —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 20:55, 22 August 2018 (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 [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/49.215.177.200|49.215.177.200]] ([[User talk:49.215.177.200#top|talk]]) 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 [[WP:OR|original research]]. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 06:45, 23 August 2018 (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 Wikipedia. I support removing it all. [[User:BabelStone|BabelStone]] ([[User talk:BabelStone|talk]]) 09:33, 23 August 2018 (UTC)

::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).[[User:Spitzak|Spitzak]] ([[User talk:Spitzak|talk]]) 18:23, 23 August 2018 (UTC)

:::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. [[User:Purgy Purgatorio|Purgy]] ([[User talk:Purgy Purgatorio|talk]]) 08:29, 24 August 2018 (UTC)

::::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}}).

:::::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. [[User:Skatebiker|S k a t e b i k e r]] ([[User talk:Skatebiker|talk]]) 14:42, 21 October 2018 (UTC)

:::::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. [[User:Skatebiker|S k a t e b i k e r]] ([[User talk:Skatebiker|talk]]) 14:42, 21 October 2018 (UTC)

== Line ==

The link to the wikipedia article for line shows the value offer here, 12^-2, is wrong. --[[User:Backinstadiums|Backinstadiums]] ([[User talk:Backinstadiums|talk]]) 10:05, 5 July 2019 (UTC)

: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. [[User:Dbfirs|<span style="font-family: verdana;"><i style="color: blue;">D</i><i style="color: #0cf;">b</i><i style="color: #4fc;">f</i><i style="color: #6f6;">i</i><i style="color: #4e4;">r</i><i style="color: #4a4">s</i></span>]] 10:36, 5 July 2019 (UTC)

== notability ==

Question on the [//en.wikipedia.org/w/index.php?title=Duodecimal&oldid=895990090 comment here], must we only mention "notable" typefaces? Surely notability is contextual. The fonts removed in this edit may not have their own article (per [[WP:NOTA]]), 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 [[WP:DUE]]. 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;">[[User:ChristTrekker|ChristTrekker]]</span> [[User talk:ChristTrekker|🗣]]</span> 19:35, 24 July 2019 (UTC)
: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 [[WP:OR|original research]]? 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. —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 20:09, 24 July 2019 (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 [[WP:OR]] to look out the window and say the sky is blue without citation, because anybody can provide [[WP:V]] 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;">[[User:ChristTrekker|ChristTrekker]]</span> [[User talk:ChristTrekker|🗣]]</span> 21:50, 25 July 2019 (UTC)
:For the record, I had made a similar removal a while back [https://en.wikipedia.org/w/index.php?title=Duodecimal&diff=864169369&oldid=864167513 here]. &ndash;[[User:Deacon Vorbis|Deacon Vorbis]]&nbsp;([[User Talk:Deacon Vorbis|carbon]]&nbsp;&bull;&nbsp;[[Special:Contributions/Deacon Vorbis|videos]]) 22:12, 25 July 2019 (UTC)

== RfC: Extra digits ==
{{atop|result=Closing per request at [[WP:ANRFC]]. The question is what to use to signify "ten" and "eleven" within the duodecimal numbers given in the article. Possibilities raised include inverted 2 and 3; {{unichar|1614|CANADIAN SYLLABICS CARRIER JU|nlink=Canadian Aboriginal syllabics}} and {{unichar|0190|LATIN CAPITAL LETTER OPEN E|nlink=Latin epsilon}}; A and B; X and E; * and #. Regardless of which is chosen, these should be implemented through the templates [[Template:D2]] and [[Template:D3]] introduced by [[User:Spitzak|Spitzak]], to enable changes to be made in future if necessary. <br> Out of these options, inverted 2 and 3, * and #, and {{unichar|1614|CANADIAN SYLLABICS CARRIER JU|nlink=Canadian Aboriginal syllabics}} and {{unichar|0190|LATIN CAPITAL LETTER OPEN E|nlink=Latin epsilon}} have all received very little or no support, and it therefore seems appropriate to say that there is consensus against these options. The majority of participants are happy with either A and B, or with X and E, which suggests that there is '''consensus in favour of using either A/B or X/E'''. <br> Among the !votes for A/B and X/E, I count three editors who favour A/B, one editor who favours X/E, and two who express no preference between A/B and X/E. This may suggest that A/B is the most generally acceptable solution.
<small>[[Wikipedia:Deletion process#Non-administrators closing discussions|(non-admin closure)]]</small> [[User:Dionysodorus|Dionysodorus]] ([[User talk:Dionysodorus|talk]]) 21:14, 3 October 2019 (UTC)}}
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? –[[User:LaundryPizza03|<b style="color:#77b">Laundry</b><b style="color:#fb0">Pizza</b><b style="color:#b00">03</b>]] ([[User talk:LaundryPizza03|<span style="color:#0d0">d</span>]][[Special:Contribs/LaundryPizza03|<span style="color:#0bf">c̄</span>]]) 22:09, 21 August 2019 (UTC)

:{{re|LaundryPizza03}} Per [[WP:RFCBEFORE]], 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 [[Module:BaseConvert]] &ndash; it uses A and B and automatically puts the <sub>12</sub> subscript after the result.
:
: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;[[User:Deacon Vorbis|Deacon Vorbis]]&nbsp;([[User Talk:Deacon Vorbis|carbon]]&nbsp;&bull;&nbsp;[[Special:Contributions/Deacon Vorbis|videos]]) 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). —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 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.[[User:Spitzak|Spitzak]] ([[User talk:Spitzak|talk]]) 15:17, 22 August 2019 (UTC)
* Everything except &#123;{rotate}} which defeats text processing. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 07:51, 23 August 2019 (UTC)
*: And more… “E” is stupid—at least for Wikipedia—because conflicts with the well-known [[hexadecimal]] 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. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 09:58, 23 August 2019 (UTC)
*I am in agreement with Deacon Vorbis. A and B will be understood as part of standard notation for bases higher than ten; the rotated 2 and 3 (as Unicode characters) are used by both Dozenal Societies (who probably constitute a significant fraction of the actual use and advocacy of base twelve); and X and E will probably be understood as an ASCII fallback used by the Dozenal Society of America itself. Of course, the trouble with the rotated 2 and 3 is that the actual Unicode characters are usually not supported, and using CSS to rotate an actual 2 and 3 will mean that copy-paste doesn't work (as Deacon Vorbis says, it's semantically wrong), so either A/B or X/E seems the way to go. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 13:26, 27 August 2019 (UTC)
*: Where is {{u|Double sharp}}’s proposal? Obviously the bulk of the article should subscribe to one uniform notation, and there are already two templates: {{tl|d2}} and {{tl|d3}}. What ''to do'' (if anything) now? [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 13:39, 27 August 2019 (UTC)
*::As I said at the end: "either A/B or X/E seems the way to go" in my opinion. [[User:Double sharp|Double sharp]] ([[User talk:Double sharp|talk]]) 13:40, 27 August 2019 (UTC)
* '''Whatever''' else, I agree with the opinions that only characters that are compatible with keyboards and scanners should be used, or even considered. As a long-time user of Hexadecimal, I would prefer A and B for 10 and 11(denary) but if the majority prefer X and E, I could live with that. But above all, keep it simple, easy, and readable. [[User:JonRichfield|JonRichfield]] ([[User talk:JonRichfield|talk]]) 11:22, 29 August 2019 (UTC)
*: “Characters compatible with keyboards”? For typing there are &#123;{d2}} and &#123;{d3}}, and how keyboards help an end user to ''read?'' A pack of down-to-ASCII simplifiers pushes for Latin letters and despise (or evade addressing) such options as U+0190. Would “A”, “B”, “X” and “E” be very helpful for people with [[screen reader]]s? It isn’t certain that—when read aloud—this digits+letters mess would result in anything intelligible. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 12:06, 29 August 2019 (UTC)
*'''Do not use rotated characters'''. [[User:Softlavender|Softlavender]] ([[User talk:Softlavender|talk]]) 05:48, 8 September 2019 (UTC)
*'''How about * and #'''. * and # have been mentioned in the article, yet it isn't an option here. These two symbols answer both similarity to Hexadecimal problem and semantics! [[User:Worra Mait Kosit]] ([[User talk:Worra Mait Kosit|talk]]) [[User:Worra Mait Kosit|Worra Mait Kosit]] ([[User talk:Worra Mait Kosit|talk]]) 09:12, 11 September 2019 (UTC)
*: {{re|Worra Mait Kosit}} ''who'' uses these characters for encoding numbers in duodecimal? [[WP:No original research|Wikipedia doesn’t invent]] or [[WP:Advocacy|promote]], Wikipedia mostly compile sources. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 09:52, 11 September 2019 (UTC)
*: {{re|Incnis Mrsi}} From the article, although I understood that this is not a strong argument: Edna Kramer in her 1951 book ''The Main Stream of Mathematics'' used a six-pointed asterisk ([[sextile]]) '''⚹''' and a [[Number sign|hash]] (or octothorpe) '''#'''.<ref name="Symbology Overview"/> The symbols were chosen because they are available in typewriters, they also are on [[push-button telephone]]s.<ref name="Symbology Overview"/> This notation was used in publications of the '''Dozenal Society of America''' ('''DSA''') in the period 1974–2008.<ref>{{cite journal|title=Annual Meeting of 1973 and Meeting of the Board|journal=The Duodecimal Bulletin|volume=25 [29]|issue=1|date=1974|url=http://www.dozenal.org/drupal/sites_bck/default/files/DuodecimalBulletinIssue251-web_0.pdf}}</ref><ref>{{cite journal|last=De Vlieger|first=Michael|title=Going Classic|journal=The Duodecimal Bulletin|volume=49 [57]|issue=2|date=2008|url=http://www.dozenal.org/drupal/sites_bck/default/files/DuodecimalBulletinIssue492_0.pdf}}</ref> [[User:Worra Mait Kosit|Worra Mait Kosit]] ([[User talk:Worra Mait Kosit|talk]]) 17:11, 11 September 2019 (UTC)
*First Choice '''A and B'''. Second choice X and E. A and B are used in hexadecimal, and anyone who knows hexadecimal knows what they are, and anyone who doesn't use hexadecimal either won't use duodecimal or can learn. [[User:Robert McClenon|Robert McClenon]] ([[User talk:Robert McClenon|talk]]) 13:01, 11 September 2019 (UTC)
*'''Absolutely not {{unichar|1614}} and {{unichar|0190}}''' because those characters have different meanings to the Dozenal Society symbols. With the mention of screen readers, I'm inclined to prefer A/B over the rotated 2/3, but I see pros and cons to both choices. — '''[[User:Bilorv|Bilorv]]''' ('''[[User talk:Bilorv|<span style="color:purple">talk</span>]]''') 19:07, 15 September 2019 (UTC)
{{reftalk}}
{{archive bottom}}

=== Why not use A for ten and B for eleven ? ===
In the same Wikipedia, the Base 16 (hexadecimal) article uses A and B for ten resp. eleven. So why not the same in duodecimal / dozenal ? That results in more consistency and the weird epsilon like symbol for eleven is not available in many letter fonts.
[[User:Skatebiker|S k a t e b i k e r]] ([[User talk:Skatebiker|talk]]) 12:04, 16 January 2020 (UTC)
:According to above discussion X and E are more popular. X is the roman numeral for ten, and E stands for "eleven". I am unclear why the epsilon is being used instead of E as that is not really mentioned above.[[User:Spitzak|Spitzak]] ([[User talk:Spitzak|talk]]) 18:44, 16 January 2020 (UTC)
::The closing statement clearly says A/B is more popular among editors, and it looks accurate. I'll change the templates. -- [[User:Beland|Beland]] ([[User talk:Beland|talk]]) 16:59, 31 July 2020 (UTC)

== Pitman’s digits ==

Not only {{diff|Duodecimal|912715013|912149876}} failed to fix markup which was genuinely broken, but pushed a misconception that en.Wikipedian internal symbols {{d2}} and {{d3}} are based on the Isaac Pitman’s turned digits. No, currently ''our'' ten is not turned “2”, and the Wikipedian presentation may [[WP:consensus may change|change together with consensus]], anyway. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 12:40, 27 August 2019 (UTC)

=== They still use the letters X and E in ASCII text ===
By the way, the meaning is rather ambiguous. Does DSGB use X and E ''only'' when technical restrictions force it to ASCII characters? Or they don’t use any non-ASCII code points for digits in principle? [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 13:34, 4 September 2019 (UTC)

== Arabic numbers, or ? ==

With duodecimal, one cannot use the [[Hindu–Arabic numeral system]] (a decimal system) by definition. {{ping|Soumya-8974}} don’t make such edits as {{diff|Duodecimal|913984857|913984372}}.

Moreover, {{diff|Duodecimal|913984273|913545184|removal of explanation text for symbols}} is not acceptable for accessibility reasons. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 13:14, 4 September 2019 (UTC)

: That was my fault. But why you have reverted "As these Unicode symbols are not rendering in many browsers, this article uses {{unichar|2169|ROMAN NUMERAL TEN}} and {{unichar|0190|LATIN CAPITAL LETTER OPEN E}}" to "but here {{nobr|"{{d2}}"}} and {{nobr|"{{d3}}"}} are used instead"? Also, there are many types of Arabic numerals. —Yours sincerely, [[User:Soumya-8974|Soumyabrata]] ([[User talk:Soumya-8974|talk]] • [[Special:PrefixIndex/User:Soumya-8974|subpages]]) 13:33, 4 September 2019 (UTC)
:: {{serif|I}} have no strong opinion about “this article uses…” paragraph and will not quarrel on this specific point. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 13:38, 4 September 2019 (UTC)

== Spacing in multiplication table ==

{{reply|Spitzak}} I just looked at the column widths in Firefox's web inspector, and they are actually all different widths because of the different widths of the different character combinations. The right way to make consistent column widths would probably be to use CSS. But looking at it on a mobile phone, I also noticed that the width of the table is close to the width of my phone screen. I'm sure at slightly lower resolutions or higher zoom levels, the table would force horizontal scrolling, which is quite bad. So on balance I think the best thing to do is make the table as narrow as possible by letting the browser decide how wide each column should be, which is what we do for the vast majority of tables anyway, and simplifies the markup. -- [[User:Beland|Beland]] ([[User talk:Beland|talk]]) 16:51, 31 July 2020 (UTC)
:This is an attempt to make the first column the same widths as the others. I agree that letting the browser choose the widths is best want the same answer for all of them. At least on my system the character given now produces matching widths and I have not seen any examples where it does worse than nbsp.[[User:Spitzak|Spitzak]] ([[User talk:Spitzak|talk]]) 17:50, 31 July 2020 (UTC)
:{{pb}}All columns should now have equal widths. &ndash;[[User:Deacon Vorbis|Deacon Vorbis]]&nbsp;([[User Talk:Deacon Vorbis|carbon]]&nbsp;&bull;&nbsp;[[Special:Contributions/Deacon Vorbis|videos]]) 18:07, 31 July 2020 (UTC)
::Thanks {{u|David Eppstein}}; I forgot to kill the special character in all that. &ndash;[[User:Deacon Vorbis|Deacon Vorbis]]&nbsp;([[User Talk:Deacon Vorbis|carbon]]&nbsp;&bull;&nbsp;[[Special:Contributions/Deacon Vorbis|videos]]) 18:10, 31 July 2020 (UTC)
:::Forcing the widths to all be the same (as opposed to letting the browser choose different widths for each column, which is what I was proposing) has the effect of making the table wider than it needs to be, and thus for horizontal scrolling to start earlier than it needs to. But at least this method makes the columns the same width; there were 1-pixel differences between most of the columns without the "width" CSS. -- [[User:Beland|Beland]] ([[User talk:Beland|talk]]) 18:28, 31 July 2020 (UTC)


== Whitespace characters ==
== Whitespace characters ==
Line 164: Line 32:


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? [[Special:Contributions/23.150.224.60|23.150.224.60]] ([[User talk:23.150.224.60|talk]]) 16:30, 8 September 2022 (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? [[Special:Contributions/23.150.224.60|23.150.224.60]] ([[User talk:23.150.224.60|talk]]) 16:30, 8 September 2022 (UTC)

:It does not "stand for" anything. -- [[User:27 is the best number|27 is my favorite number]]. [[User talk:27 is the best number|You can ask me why here.]] 22:37, 16 September 2022 (UTC)
:it stands for "six" [[User:Brawlio|Brawlio]] ([[User talk:Brawlio|talk]]) 23:33, 25 February 2024 (UTC)


== Divisibility Tests from Duodecimal ==
== Divisibility Tests from Duodecimal ==


{{copied|from=duodecimal|to=senary}} [[User:27 is the best number|27 is my favorite number]]. [[User talk:27 is the best number|You can ask me why here.]] 22:36, 16 September 2022 (UTC)
{{copied|from=duodecimal|to=senary}} [[User:27 is the best number|27 is my favorite number]]. [[User talk:27 is the best 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... [https://m.economictimes.com/news/new-updates/13-full-moons-4-supermoons-and-1-blue-moon-2023-will-be-a-treat-for-night-sky-lovers/articleshow/96785682.cms including this year, 2023. (August gets a 2nd Full Moon, aka "Blue Moon".)] &ndash;&nbsp;[[User:.Raven|<big>'''.'''</big>Raven]]&nbsp;<sup>[[User talk:.Raven|&nbsp;'''''.'''talk'']]</sup> 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. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 22:34, 28 September 2023 (UTC)

== Fractions comparison ==

> ''"... 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.)
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;[[User:.Raven|<big>'''.'''</big>Raven]]&nbsp;<sup>[[User talk:.Raven|&nbsp;'''''.'''talk'']]</sup> 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. [[User:EducatedRedneck|EducatedRedneck]] ([[User talk:EducatedRedneck|talk]]) 10:47, 3 August 2023 (UTC)

== Duodecimal Conversion Table ==

<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:
# 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. [[User:EducatedRedneck|EducatedRedneck]] ([[User talk:EducatedRedneck|talk]]) 00:57, 20 November 2023 (UTC) <ins>[[User:EducatedRedneck|EducatedRedneck]] ([[User talk:EducatedRedneck|talk]]) 00:59, 20 November 2023 (UTC)</ins>

:@[[User:Jacobolus|Jacobolus]] I concur with [[Special:Diff/1199249029|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? [[User:EducatedRedneck|EducatedRedneck]] ([[User talk: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? –[[user:jacobolus|jacobolus]] [[User_talk: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. [[User:EducatedRedneck|EducatedRedneck]] ([[User talk:EducatedRedneck|talk]]) 16:43, 26 January 2024 (UTC)
::::I chopped some columns out. The narrower one seems okay enough to me. –[[user:jacobolus|jacobolus]] [[User_talk: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! [[User:EducatedRedneck|EducatedRedneck]] ([[User talk:EducatedRedneck|talk]]) 16:50, 26 January 2024 (UTC)

Latest revision as of 23:33, 25 February 2024

Whitespace characters[edit]

@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 Wikipedia: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)[reply]

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 Wikipedia: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)[reply]
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)[reply]
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)[reply]
{{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)[reply]
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)[reply]
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)[reply]
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)[reply]
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)[reply]

Notations table[edit]

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)[reply]

Year 2022 in duodecimal[edit]

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)[reply]

It does not "stand for" anything. -- 27 is my favorite number. You can ask me why here. 22:37, 16 September 2022 (UTC)[reply]
it stands for "six" Brawlio (talk) 23:33, 25 February 2024 (UTC)[reply]

Divisibility Tests from Duodecimal[edit]

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

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

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  .talk 20:36, 16 April 2023 (UTC)[reply]

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)[reply]

Fractions comparison[edit]

> "... 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  .talk 21:08, 16 April 2023 (UTC)[reply]

Uncial[edit]

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)[reply]

Duodecimal Conversion Table[edit]

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)[reply]

@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)[reply]
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)[reply]
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)[reply]
I chopped some columns out. The narrower one seems okay enough to me. –jacobolus (t) 16:48, 26 January 2024 (UTC)[reply]
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)[reply]
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