Editing Duodecimal (section)

=== Transdecimal symbols ===
{{infobox symbol
|mark={{mono|1=<span style="display: inline-block; transform: scale(-1);">2</span>{{NBSP}}<span style="display: inline-block; transform: scale(-1);">3</span>}}
|name = duodecimal&nbsp;{{angbr|1=ten, eleven}}
|unicode={{ubli
| {{unichar|1=218A|2=TURNED DIGIT TWO}}
| {{unichar|1=218B|2=TURNED DIGIT THREE}}
}}
|unicode note=Block [[Number Forms]]
|note={{ubli
|Arabic digits with 180° rotation, by&nbsp;[[Isaac Pitman|Isaac&nbsp;Pitman]]
|In [[LaTeX]], using the TIPA package:<ref name="LATEX">{{cite web |url=https://www.ctan.org/pkg/comprehensive |title=The Comprehensive LATEX Symbol List |year=2021 |edition=14.0 |orig-year=2007 |last=Pakin |first=Scott |website=Comprehensive TEX Archive Network }} {{pb}} {{cite web |url=https://www.ctan.org/pkg/tipa |title=tipa – Fonts and macros for IPA phonetics characters |last=Rei |first=Fukui |year=2004 |orig-year=2002 |website=Comprehensive TEX Archive Network |edition=1.3 }} {{pb}} The turned digits 2 and 3 employed in the TIPA package originated in ''The Principles of the International Phonetic Association'', University College London, 1949.</ref><br/>{{angbr|1={{code|\textturntwo}}, {{code|1=\textturnthree}}}}}}
}}

Several authors have proposed using letters of the alphabet for the transdecimal symbols. Latin letters such as {{angbr|{{mono|1=A, B}}}} (as in [[hexadecimal]]) or {{angbr|{{mono|1=T, E}}}} (initials of ''Ten'' and ''Eleven'') are convenient because they are widely accessible, and for instance can be typed on typewriters. However, when mixed with ordinary prose, they might be confused for letters. As an alternative, Greek letters such as {{angbr|{{mono|1=τ, ε}}}} could be used instead.<ref name="Symbology Overview"/> Frank Emerson Andrews, an early American advocate for duodecimal, suggested and used in his 1935 book ''New Numbers'' {{angbr|{{mono|''X'', ''Ɛ''}}}} (italic capital X from the [[Roman numeral]] for ten and a rounded [[Italic script|italic]] capital E similar to [[Latin epsilon|open E]]), along with italic numerals {{mono|''0''}}–{{mono|''9''}}.<ref name="New Numbers 1935"/>

Edna Kramer in her 1951 book ''The Main Stream of Mathematics'' used a {{angbr|{{mono|1=*, <nowiki>#</nowiki>}}}} ([[Astrological aspect#Sextile|sextile]] or six-pointed asterisk,<ref>Note that the symbol displayed is a standard asterisk; for technical reasons, this page cannot display the sextile inline.</ref> [[Number sign|hash]] or octothorpe).<ref name="Symbology Overview"/> The symbols were chosen because they were available on some typewriters; they are also on [[push-button telephone]]s.<ref name="Symbology Overview"/> This notation was used in publications of the Dozenal Society of America (DSA) from 1974 to 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>

From 2008 to 2015, the DSA used {{angbr|1={{NNBSP}}[[File:Dozenal us 10.svg|8px]], [[File:Dozenal us 11.svg|8px]]{{NNBSP}}}}, the symbols devised by [[William Addison Dwiggins]].<ref name="Symbology Overview"/><ref name="DB01">{{cite journal|title=Mo for Megro|journal=The Duodecimal Bulletin|volume=1|issue=1|date=1945|url=http://www.dozenal.org/drupal/sites_bck/default/files/DuodecimalBulletinIssue011-web.pdf}}</ref>

The Dozenal Society of Great Britain (DSGB) proposed symbols {{angbr|1={{NNBSP}}<span style="display: inline-block; transform: scale(-1);">{{math|2}}</span>, <span style="display: inline-block; transform: scale(-1);">{{math|3}}</span>{{NNBSP}}}}.<ref name="Symbology Overview"/> This notation, derived from Arabic digits by 180° rotation, was introduced by [[Isaac Pitman]] in 1857.<ref name="Symbology Overview"/><ref name="Pitman1857">{{cite news |last=Pitman |first=Isaac |author-link=Isaac Pitman |title=A Reckoning Reform |newspaper=Bedfordshire Independent |date=24 November 1857 }} Reprinted as {{cite journal |last=Pitman |first=Isaac |display-authors=0 |title=Sir Isaac Pitman on the Dozen System: A Reckoning Reform |journal=The Duodecimal Bulletin |volume=3 |issue=2 |pages=1–5 |year=1947 |url=http://www.dozenal.org/drupal/sites_bck/default/files/DuodecimalBulletinIssue032-web_0.pdf }}</ref> In March 2013, a proposal was submitted to include the digit forms for ten and eleven propagated by the Dozenal Societies in the [[Unicode|Unicode Standard]].<ref name="N4399">{{cite web |author=Pentzlin |first=Karl |date=March 30, 2013 |title=Proposal to encode Duodecimal Digit Forms in the UCS |url=https://www.unicode.org/wg2/docs/n4399.pdf  |publisher=ISO/IEC JTC1/SC2/WG2 |access-date=2024-06-25}}</ref> Of these, the British/Pitman forms were accepted for encoding as characters at code points {{unichar|218A|TURNED DIGIT TWO}} and {{unichar|218B|TURNED DIGIT THREE}}. They were included in [[Unicode 8.0]] (2015).<ref name="Unicode8">{{cite web|url=https://www.unicode.org/charts/PDF/Unicode-8.0/U80-2150.pdf|title=The Unicode Standard, Version 8.0: Number Forms|publisher=Unicode Consortium|access-date=2016-05-30}}</ref><ref>{{cite web
  | url        = https://www.unicode.org/charts/PDF/U2150.pdf
  | title      = The Unicode Standard 8.0
  | access-date = 2014-07-18
}}</ref>

After the Pitman digits were added to Unicode, the DSA took a vote and then began publishing PDF content using the Pitman digits instead, but continues to use the letters X and E on its webpage.<ref>{{Cite web |last=The Dozenal Society of America |date=n.d. |title=What should the DSA do about transdecimal characters? |url=https://dozenal.org/drupal/content/what-should-dsa-do-about-transdecimal-characters.html |access-date=January 1, 2018 |website=Dozenal Society of America |publisher=The Dozenal Society of America}}</ref>

{| class="wikitable" id="transdecimal-symbols-table" style="font-size:90%; max-width:50em;"
! colspan=2 | Symbols
! style="width:20em" | Background
! Note
|-
| <big>A</big>
| <big>B</big>
| As in [[hexadecimal]]
| Allows entry on typewriters.
|-
| <big>T</big>
| <big>E</big>
| Initials of ''Ten'' and ''Eleven''
| Used (in lower case) in [[Pitch class|music set theory]]<ref>[[Arnold Whittall]], ''The Cambridge Introduction to Serialism'' (New York: Cambridge University Press, 2008): 276. {{ISBN|978-0-521-68200-8}} (pbk).</ref>
|-
| <big>X</big>
| <big>E</big>
| X from the [[Roman numeral]]; <br> E from ''Eleven''.
|
|-
| <big>X</big>
| <big>Z</big>
| Origin of Z unknown
| Attributed to [[Jean le Rond d'Alembert|D'Alembert]] & [[Georges-Louis Leclerc, Comte de Buffon|Buffon]] by the DSA.<ref name="Symbology Overview" />
|-
| <big>δ</big>
| <big>ε</big>
| Greek [[Delta (letter)|delta]] from {{lang|grc|δέκα}} "ten"; <br> [[epsilon]] from {{lang|grc|ένδεκα}} "eleven"<ref name="Symbology Overview"/>
|
|-
| <big>τ</big>
| <big>ε</big>
| Greek [[tau]], [[epsilon]]<ref name="Symbology Overview"/>
|
|-
| <big>W</big>
| <big>∂</big>
| W from doubling the Roman numeral V; <br> ∂ based on a pendulum
| Silvio Ferrari in ''Calcolo Decidozzinale'' (1854).<ref name="Ferrari 1854">{{cite book|first=Silvio |last=Ferrari|title=Calcolo Decidozzinale|date=1854|page=2}}</ref>
|-
| <big>''X''</big>
| <big>''Ɛ''</big>
| italic ''X'' pronounced "dec"; <br> rounded [[italic script|italic]] ''Ɛ'', pronounced "elf"
| Frank Andrews in ''New Numbers'' (1935), with italic ''0''–''9'' for other duodecimal numerals.<ref name="New Numbers 1935">{{cite book|first=Frank Emerson |last=Andrews |title=New Numbers: How Acceptance of a Duodecimal (12) Base Would Simplify Mathematics |date=1935 |page=52 |publisher=Harcourt, Brace and company |url=https://archive.org/details/newnumbershowacc0000fran/page/52/mode/1up?q=%22quantity+eleven%22 |url-access=limited}}</ref>
|-
| <big>{{mono|1=*}}</big>
| <big>{{mono|1=<nowiki>#</nowiki>}}</big>
| [[Astrological aspect#Sextile|sextile]] or six-pointed asterisk,<br/>[[Number sign|hash]] or octothorpe
| On [[push-button telephone]]s; used by Edna Kramer in ''The Main Stream of Mathematics'' (1951); used by the DSA {{nobr|1974–2008}}<ref name="bellchange">{{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 name="classic">{{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><ref name="Symbology Overview"/>
|-
| <big><span style="display: inline-block; transform: scale(-1);">2</span></big>
| <big><span style="display: inline-block; transform: scale(-1);">3</span></big>
| {{ubli
| Digits 2 and 3 rotated 180°
}} 
| [[Isaac Pitman]] (1857);<ref name="Pitman1857"/> used by the DSGB; used by the DSA since 2015; included in [[Unicode 8.0]] (2015)<ref name="Unicode8">{{cite web|url=https://www.unicode.org/charts/PDF/Unicode-8.0/U80-2150.pdf|title=The Unicode Standard, Version 8.0: Number Forms|publisher=Unicode Consortium|access-date=2016-05-30}}</ref><ref>{{cite web
  | url        = https://www.unicode.org/charts/PDF/U2150.pdf
  | title      = The Unicode Standard 8.0
  | access-date = 2014-07-18 }}</ref>
|-
| <big>[[File:Dozenal us 10.svg|8px]]</big>
| <big>[[File:Dozenal us 11.svg|8px]]</big>
| Pronounced "dek", "el"
| {{ubl
|[[William Addison Dwiggins|William Dwiggins]] (1945/1932?).<ref name="Symbology Overview"/><ref name="DB01">{{cite journal|title=Mo for Megro|journal=The Duodecimal Bulletin|volume=1|issue=1|date=1945|url=http://www.dozenal.org/drupal/sites_bck/default/files/DuodecimalBulletinIssue011-web.pdf}}</ref>
|Used by the DSA 1945&ndash;1974 and 2008&ndash;2015<ref name="bellchange"/><ref name="classic" />}}
|}