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{{Short description|Traditional arrangement of I Ching hexagrams}}
The '''King Wen sequence''' (文王卦序) of the '']'' (易經) is a series of sixty-four binary figures (]s), each composed of 6 lines, either solid (] 陽) or broken (] 陰).
'''The King Wen sequence''' ({{zh|c=文王卦序}}) is an arrangement of the sixty-four divination figures in the '']'' (often translated as the ''Book of Changes''). They are called '']'' in English because each figure is composed of six 爻 yáo—broken or unbroken lines, that represent ] respectively.


The King Wen sequence, also known as the ''classical hexagram sequence'', is sometimes considered the second&ndash;oldest formal arrangement of the hexagrams, preceded only by the ] (伏羲) arrangement, though the ] arrangement is most often associated with the Song Dynasty scholar ] (邵雍). The historical legend is that ] (周文王) designed this sequence in the ] while imprisoned by the ] King Zhou of Shang; King Wen is said to have died in 1050 BC, by one interpretation of the evidence (Shaughnessy). The King Wen sequence is also known as the "received" or "classical" sequence because it is the oldest surviving arrangement of the hexagrams. Its true age and authorship are unknown. Traditionally, it is said that ] arranged the hexagrams in this sequence while imprisoned by ] in the 12th century&nbsp;BC. A different arrangement, the "binary sequence" named in honor of the mythic ] ], originated in the ]. It is believed to be the work of scholar ] (1011–1077&nbsp;AD). As mirrored by the ] and ] arrangements of the eight trigrams, or ], it was customary to attribute authorship to these legendary figures. Of the two hexagram arrangements, the King Wen sequence is, however, of much greater antiquity than the Fu Xi sequence.<ref name=biroco>Marshall, Steve </ref>


== Notable characteristics == == Structure of the sequence ==
The 64 hexagrams are grouped into 32 pairs. For 28 of the pairs, the second hexagram is created by turning the first upside down (i.e. 180° rotation). The exception to this rule is for the 8 symmetrical hexagrams that are the same after rotation (1 & 2, 27 & 28, 29 & 30, 61 & 62). Partners for these are given by inverting each line: solid becomes broken and broken becomes solid. These are indicated with icons in the table below.


Given the mathematical constraints of these simple rules, the number of lines that change within pair partners will always be even (either 2, 4, or 6). Whereas the number of lines that change between pairs depends on how the pairs are arranged, and the King Wen sequence has notable characteristics in this regard. Of the 64 transitions, exactly 48 of them are even changes (32 within-pairs plus 16 between-pairs) and 16 are odd changes (all between-pairs). This is a precise 3 to 1 ratio of even to odd transitions. Of the odd transitions, 14 are changes of three lines and 2 are changes of one line. Changes of five are absent. Each transition within a pair appears to be the correlating opposite of the other transition within the pair.
The 64 hexagrams are grouped into 32 pairs. The second partner in each pair is created by inverting the first. In four of these pairs inversion (i.e. 180° rotation) of either hexagram effects no change (in which case all six lines will change). The number of lines that change between pair partners is always even (either 2, 4, or 6).


{| border="0" cellpadding="3" style="font-size:80%; text-align:center; width: 100%; "
The number of possible different arrangements of the 32 partner pairs is 32! = 2.63 * 10^35.
|+
|-
| title="U+4DC0 (䷀), U+4DC1 (䷁)" | ]{{nbsp}}]
| title="U+4DC2 (䷂), U+4DC3 (䷃)" | ]{{nbsp}}]
| title="U+4DC4 (䷄), U+4DC5 (䷅)" | ]{{nbsp}}]
| title="U+4DC6 (䷆), U+4DC7 (䷇)" | ]{{nbsp}}]
| title="U+4DC8 (䷈), U+4DC9 (䷉)" | ]{{nbsp}}]
| title="U+4DCA (䷊), U+4DCB (䷋)" | ]{{nbsp}}]
| title="U+4DCC (䷌), U+4DCD (䷍)" | ]{{nbsp}}]
| title="U+4DCE (䷎), U+4DCF (䷏)" | ]{{nbsp}}]
|-
| ''''']&nbsp;&nbsp;↕&nbsp;&nbsp;]'''''
| ]&nbsp;&nbsp;~&nbsp;&nbsp;]
| ]&nbsp;&nbsp;~&nbsp;&nbsp;]
| ]&nbsp;&nbsp;~&nbsp;&nbsp;]
| ]&nbsp;&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
|-
| colspan="4" style="height:0.3em;" |
|-
| title="U+4DD0 (䷐), U+4DD1 (䷑)" | ]{{nbsp}}]
| title="U+4DD2 (䷒), U+4DD3 (䷓)" | ]{{nbsp}}]
| title="U+4DD4 (䷔), U+4DD5 (䷕)" | ]{{nbsp}}]
| title="U+4DD6 (䷖), U+4DD7 (䷗)" | ]{{nbsp}}]
| title="U+4DD8 (䷘), U+4DD9 (䷙)" | ]{{nbsp}}]
| title="U+4DDA (䷚), U+4DDB (䷛)" | ]{{nbsp}}]
| title="U+4DDC (䷜), U+4DDD (䷝)" | ]{{nbsp}}]
| title="U+4DDE (䷞), U+4DDF (䷟)" | ]{{nbsp}}]
|-
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ''''']&nbsp;↕&nbsp;]'''''
| ''''']&nbsp;↕&nbsp;]'''''
| ]&nbsp;~&nbsp;]
|-
| colspan="4" style="height:0.3em;" |
|-
| title="U+4DE0 (䷠), U+4DE1 (䷡)" | ]{{nbsp}}]
| title="U+4DE2 (䷢), U+4DE3 (䷣)" | ]{{nbsp}}]
| title="U+4DE4 (䷤), U+4DE5 (䷥)" | ]{{nbsp}}]
| title="U+4DE6 (䷦), U+4DE7 (䷧)" | ]{{nbsp}}]
| title="U+4DE8 (䷨), U+4DE9 (䷩)" | ]{{nbsp}}]
| title="U+4DEA (䷪), U+4DEB (䷫)" | ]{{nbsp}}]
| title="U+4DEC (䷬), U+4DED (䷭)" | ]{{nbsp}}]
| title="U+4DEE (䷮), U+4DEF (䷯)" | ]{{nbsp}}]
|-
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
|-
| colspan="4" style="height:0.3em;" |
|-
| title="U+4DF0 (䷰), U+4DF1 (䷱)" | ]{{nbsp}}]
| title="U+4DF2 (䷲), U+4DF3 (䷳)" | ]{{nbsp}}]
| title="U+4DF4 (䷴), U+4DF5 (䷵)" | ]{{nbsp}}]
| title="U+4DF6 (䷶), U+4DF7 (䷷)" | ]{{nbsp}}]
| title="U+4DF8 (䷸), U+4DF9 (䷹)" | ]{{nbsp}}]
| title="U+4DFA (䷺), U+4DFB (䷻)" | ]{{nbsp}}]
| title="U+4DFC (䷼), U+4DFD (䷽)" | ]{{nbsp}}]
| title="U+4DFE (䷾), U+4DFF (䷿)" | ]{{nbsp}}]
|-
| ]&nbsp;~&nbsp;]
| ''']&nbsp;~&nbsp;]'''
| ]&nbsp;~&nbsp;]
| ]&nbsp;~&nbsp;]
| ''']&nbsp;~&nbsp;]'''
| ]&nbsp;~&nbsp;]
| ''''']&nbsp;↕&nbsp;]'''''
| ]&nbsp;~&nbsp;]
|}


=== Dual hexagrams ===
In moving from one hexagram to the next a minimum of one line must change. There are no instances in which exactly five lines change.
The I Ching book was traditionally split up in two parts with the first part covering the first 30 hexagrams of the King Wen sequence and the second part with the remaining 34.<ref name="HackerMoore2003">{{cite journal |last1=Hacker |first1=Edward A. |last2=Moore |first2=Steve |date= 6 May 2003 |title=A brief note on the two–part division of the received order of the hexagrams in the ''Zhouyi'' |journal=Journal of Chinese Philosophy |volume=30 |issue=2 |pages=219–221 |doi=10.1111/1540-6253.00115 |url=http://www.biroco.com/yijing/Hacker_Moore_Note_on_two_part_division.pdf |accessdate=31 May 2010 }}</ref><ref name="Nielsen2003">{{cite book|author=Bent Nielsen|title=A companion to Yi jing numerology and cosmology: Chinese studies of images and numbers from Han (202 BCE-220 CE) to Song (960-1279 CE)|url=https://books.google.com/books?id=mQ4im_ICmbYC&pg=PA83|accessdate=31 May 2010|year=2003|publisher=Routledge|isbn=978-0-7007-1608-1|page=83}}</ref> The reason for this was not mentioned in the classic commentaries but was explained in later ] commentaries: 8 hexagrams are the same when turned upside down and the other 56 present a different hexagram if inverted. This allows the hexagrams to be displayed succinctly in two equal columns or rows of 18 unique hexagrams each; half of the 56 invertible hexagrams plus the 8 non-invertible.<ref name=cook/><ref name=dual>{{cite web|url=http://www.biroco.com/yijing/scan.htm |title=Yijing Dao - Archive of Yijing-related scans from Chinese and other sources |date=20 February 2010 |accessdate=19 May 2010}}</ref>


{| style="width:47em; float:left;line-height:1.75em;"
The ratio of even to odd numbers of line changes between the hexagrams is exactly 3:1.
|-
| style="width:20em;" | ䷀&nbsp;&nbsp;乾 ''qián''<br /><small>]</small>
| style="width:3em;" | &nbsp;1&nbsp;→&nbsp;
| style="width:1em;font-size:300%;" | {{Nowrap|1=<nowiki>||||||</nowiki>}}
| style="width:3em;" | || style="width:20em;" |
|-
| ䷁&nbsp;&nbsp;坤 ''kūn''<br /><small>]</small>
| &nbsp;2&nbsp;→&nbsp; || style="font-size:300%;" | {{nowrap|¦¦¦¦¦¦}}
|-
| ䷂&nbsp;&nbsp;&nbsp;屯 ''chún''<br /><small>]</small>
| &nbsp;3&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦¦|¦</nowiki>}}
| &nbsp;&nbsp;←&nbsp;4&nbsp;
| ䷃&nbsp;&nbsp;蒙 ''méng''<br /><small>]</small>
|-
| ䷄&nbsp;&nbsp;需 ''xū''<br /><small>]</small>
| &nbsp;5&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|||¦|¦</nowiki>}}
| &nbsp;&nbsp;←&nbsp;6&nbsp;
| ䷅&nbsp;&nbsp;訟 ''sòng''<br /><small>]</small>
|-
| ䷆&nbsp;&nbsp;師 ''shī''<br /><small>]</small>
| &nbsp;7&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦|¦¦¦¦</nowiki>}}
| &nbsp;&nbsp;←&nbsp;8&nbsp;
| ䷇&nbsp;&nbsp;比 ''bǐ''<br /><small>]</small>
|-
| ䷈&nbsp;&nbsp;小畜 ''xiǎo chù''<br /><small>]</small>
| &nbsp;9&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|||¦||</nowiki>}}
| &nbsp;←&nbsp;10&nbsp;
| ䷉&nbsp;&nbsp;履 ''lǚ''<br /><small>]</small>
|-
| ䷊&nbsp;&nbsp;泰 ''tài''<br /><small>]</small>
| 11&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|||¦¦¦</nowiki>}}
| &nbsp;←&nbsp;12&nbsp;
| ䷋&nbsp;&nbsp;否 ''pǐ''<br /><small>]</small>
|-
| ䷌&nbsp;&nbsp;同人 ''tóng rén''<br /><small>]</small>
| 13&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦||||</nowiki>}}
| &nbsp;←&nbsp;14&nbsp;
| ䷍&nbsp;&nbsp;大有 ''dà yǒu''<br /><small>]</small>
|-
| ䷎&nbsp;&nbsp;謙 ''qiān''<br /><small>]</small>
| 15&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦|¦¦¦</nowiki>}}
| &nbsp;←&nbsp;16&nbsp;
| ䷏&nbsp;&nbsp;豫 ''yù''<br /><small>]</small>
|-
| ䷐&nbsp;&nbsp;隨 ''suí''<br /><small>]</small>
| 17&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦||¦</nowiki>}}
| &nbsp;←&nbsp;18&nbsp;
| ䷑&nbsp;&nbsp;蠱 ''gŭ''<br /><small>]</small>
|-
| ䷒&nbsp;&nbsp;臨 ''lín''<br /><small>]</small>
| 19&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>||¦¦¦¦</nowiki>}}
| &nbsp;←&nbsp;20&nbsp;
| ䷓&nbsp;&nbsp;觀 ''guān''<br /><small>]</small>
|-
| ䷔&nbsp;&nbsp;噬嗑 ''shì kè''<br /><small>]</small>
| 21&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦|¦|</nowiki>}}
| &nbsp;←&nbsp;22&nbsp;
| ䷕&nbsp;&nbsp;賁 ''bì''<br /><small>]</small>
|-
| ䷖&nbsp;&nbsp;剝 ''bō''<br /><small>]</small>
| 23&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦¦¦¦|</nowiki>}}
| &nbsp;←&nbsp;24&nbsp;
| ䷗&nbsp;&nbsp;復 ''fù''<br /><small>]</small>
|-
| ䷘&nbsp;&nbsp;無妄 ''wú wàng''<br /><small>]</small>
| 25&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦|||</nowiki>}}
| &nbsp;←&nbsp;26&nbsp;
| ䷙&nbsp;&nbsp;大畜 ''dà chù''<br /><small>]</small>
|-
| ䷚&nbsp;&nbsp;頤 ''yí''<br /><small style="white-space:nowrap;">]</small>
| 27&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦¦¦|</nowiki>}}
|
|
|-
| ䷛&nbsp;&nbsp;大過 ''dà guò''<br /><small>]</small>
| 28&nbsp;→&nbsp; || style="font-size:300%;" |{{Nowrap|1=<nowiki> ¦||||¦</nowiki>}}
|-
| ䷜&nbsp;&nbsp;坎 ''kǎn''<br /><small>]</small>
| 29&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦|¦¦|¦</nowiki>}}
|
|
|-
| ䷝&nbsp;&nbsp;離 ''lí''<br /><small>]</small>
| 30&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦||¦|</nowiki>}}
|}


{| style="width:41em;line-height:1.75em;"
64 hexagrams &times; the 6 lines of a single hexagram = 384, the same number of days as found in ancient annual lunar calendars (that were based on 13 'months' of ]).
|-

| style="width:17em;" | ䷞&nbsp;&nbsp;咸 ''xián''<br /><small>]</small>
== Chessboard presentation ==
| style="width:3em;" | 31&nbsp;→

| style="width:1em;font-size:300%;" | {{Nowrap|1=<nowiki>¦¦|||¦</nowiki>}}
<table border="0" cellpadding="3">
| style="width:3em;" | ←&nbsp;32
<caption></caption>
| style="width:17em;" | ䷟&nbsp;&nbsp;恆 ''héng''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷠&nbsp;&nbsp;遯 ''dùn''<br /><small>]</small>
<td>]</td>
| 33&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦||||</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;34&nbsp;
<td>]</td>
| ䷡&nbsp;&nbsp;大壯 ''dà zhuàng''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷢&nbsp;&nbsp;晉 ''jìn''<br /><small>]</small>
<td>]</td><tr>
| 35&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦¦|¦|</nowiki>}}
<td align=center>1</td><td align=center>2</td><td align=center>3</td><td align=center>4</td><td align=center>5</td><td align=center>6</td><td align=center>7</td><td align=center>8</td></tr>
| &nbsp;←&nbsp;36&nbsp;
<td>]</td>
| ䷣&nbsp;&nbsp;明夷 ''míng yí''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷤&nbsp;&nbsp;家人 ''jiā rén''<br /><small>]</small>
<td>]</td>
| 37&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦|¦||</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;38&nbsp;
<td>]</td>
| ䷥&nbsp;&nbsp;睽 ''kuí''<br /><small>]</small>
<td>]</td>
|-
<td>]</td><tr>
| ䷦&nbsp;&nbsp;蹇 ''jiǎn''<br /><small>]</small>
<td align=center>9</td><td align=center>10</td><td align=center>11</td><td align=center>12</td><td align=center>13</td><td align=center>14</td><td align=center>15</td><td align=center>16</td></tr>
| 39&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦|¦|¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;40&nbsp;
<td>]</td>
| ䷧&nbsp;&nbsp;解 ''xiè''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷨&nbsp;&nbsp;損 ''sǔn''<br /><small>]</small>
<td>]</td>
| 41&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>||¦¦¦|</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;42&nbsp;
<td>]</td>
| ䷩&nbsp;&nbsp;益 ''yì''<br /><small>]</small>
<td>]</td><tr>
|-
<td align=center>17</td><td align=center>18</td><td align=center>19</td><td align=center>20</td><td align=center>21</td><td align=center>22</td><td align=center>23</td><td align=center>24</td></tr>
| ䷪&nbsp;&nbsp;夬 ''guài''<br /><small>]</small>
<td>]</td>
| 43&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|||||¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;44&nbsp;
<td>]</td>
| ䷫&nbsp;&nbsp;姤 ''gòu''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷬&nbsp;&nbsp;萃 ''cuì''<br /><small>]</small>
<td>]</td>
| 45&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦¦||¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;46&nbsp;
<td>]</td><tr>
| ䷭&nbsp;&nbsp;升 ''shēng''<br /><small>]</small>
<td align=center>25</td><td align=center>26</td><td align=center>27</td><td align=center>28</td><td align=center>29</td><td align=center>30</td><td align=center>31</td><td align=center>32</td></tr>
|-
<td>]</td>
| ䷮&nbsp;&nbsp;困 ''kùn''<br /><small>]</small>
<td>]</td>
| 47&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦|¦||¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;48&nbsp;
<td>]</td>
| ䷯&nbsp;&nbsp;井 ''jǐng''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷰&nbsp;&nbsp;革 ''gé''<br /><small>]</small>
<td>]</td>
| 49&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦|||¦</nowiki>}}
<td>]</td><tr>
| &nbsp;←&nbsp;50&nbsp;
<td align=center>33</td><td align=center>34</td><td align=center>35</td><td align=center>36</td><td align=center>37</td><td align=center>38</td><td align=center>39</td><td align=center>40</td></tr>
| ䷱&nbsp;&nbsp;鼎 ''dǐng''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷲&nbsp;&nbsp;震 ''zhèn''<br /><small>]</small>
<td>]</td>
| 51&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦¦|¦¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;52&nbsp;
<td>]</td>
| ䷳&nbsp;&nbsp;艮 ''gèn''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷴&nbsp;&nbsp;漸 ''jiàn''<br /><small>]</small>
<td>]</td><tr>
| 53&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦|¦||</nowiki>}}
<td align=center>41</td><td align=center>42</td><td align=center>43</td><td align=center>44</td><td align=center>45</td><td align=center>46</td><td align=center>47</td><td align=center>48</td></tr>
| &nbsp;←&nbsp;54&nbsp;
<td>]</td>
| ䷵&nbsp;&nbsp;歸妹 ''guī mèi''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷶&nbsp;&nbsp;豐 ''fēng''<br /><small>]</small>
<td>]</td>
| 55&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦||¦¦</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;56&nbsp;
<td>]</td>
| ䷷&nbsp;&nbsp;旅 ''lǚ''<br /><small>]</small>
<td>]</td>
|-
<td>]</td><tr>
| ䷸&nbsp;&nbsp;巽 ''xùn''<br /><small>]</small>
<td align=center>49</td><td align=center>50</td><td align=center>51</td><td align=center>52</td><td align=center>53</td><td align=center>54</td><td align=center>55</td><td align=center>56</td></tr>
| 57&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦||¦||</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;58&nbsp;
<td>]</td>
| ䷹&nbsp;&nbsp;兌 ''duì''<br /><small>]</small>
<td>]</td>
|-
<td>]</td>
| ䷺&nbsp;&nbsp;渙 ''huàn''<br /><small>]</small>
<td>]</td>
| 59&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦|¦¦||</nowiki>}}
<td>]</td>
| &nbsp;←&nbsp;60&nbsp;
<td>]</td>
| ䷻&nbsp;&nbsp;節 ''jié''<br /><small>]</small>
<td>]</td></tr>
|-
<td align=center>57</td><td align=center>58</td><td align=center>59</td><td align=center>60</td><td align=center>61</td><td align=center>62</td><td align=center>63</td><td align=center>64</td></tr></table>
| ䷼&nbsp;&nbsp;中孚 ''zhōng fú''<br /><small>]</small>
| 61&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>||¦¦||</nowiki>}}
|
|
|-
| ䷽&nbsp;&nbsp;小過 ''xiǎo guò''<br /><small>]</small>
| 62&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>¦¦||¦¦</nowiki>}}
|-
| ䷾&nbsp;&nbsp;既濟 ''jì jì''<br /><small>]</small>
| 63&nbsp;→&nbsp; || style="font-size:300%;" | {{Nowrap|1=<nowiki>|¦|¦|¦</nowiki>}}
| &nbsp;←&nbsp;64&nbsp;
| ䷿&nbsp;&nbsp;未濟 ''wèi jì''<br /><small>]</small>
|}
{{clear left}}


== Explanation == == Explanation ==
Over the centuries there were many attempts to explain this sequence. Some basic elements are obvious: each symbol is paired with an "upside-down" neighbor, except for 1, 27, 29, and 61 which are "vertically" symmetrical and paired with "inversed" neighbors.


There have been recent attempts to apply ] in explaining the logic behind the King Wen sequence, for example Richard S. Cook's proposal.<ref name=cook>{{cite web|url=http://www.biroco.com/yijing/images/kwscook.jpg |author=Cook, Richard S. |title=《周易》卦序詮解 (Zhou yi guaxu quanjie)|format=JPEG Image, 1024x793 |year=2006 |accessdate=22 May 2010 }} STEDT Monograph 5: '': Derivation of the Book of Changes Hexagram Sequence.'' 660 pages. {{ISBN|0-944613-44-6}}. OCLC 77009740.</ref>
Over the centuries there were many attempts to explain this sequence.


== Other hexagram sequences ==
Its true ] basis was reportedly explained for the first time in 2006.<ref>《周易》卦序詮解 , Cook</ref>
*], also known as ] sequence or ] sequence
*] sequence<ref name=biroco />
*] sequence (attributed to ]).


== See also ==
There is evidence for a mathematical structure in the sequence.<br /> Several clusters of ]s point to a careful arrangement rather than a ]. <ref>, by D.H. Van den Berghe</ref>.<br />


* ]
== Other Hexagram Sequences ==
* ]


== References ==
], also known as ] sequence or ] sequence.<br />
] sequence.<ref> Animations of all the main Yijing sequences, by Steve Marshall</ref><br />
Eight Palaces sequence (attributed to ]).

==Notes==
<references/> <references/>

== See also ==

* '']''
* ] Terence McKenna based his 'Timewave Zero' theory on the King Wen sequence.


== External links == == External links ==
* {{OEIS el|sequencenumber=A102241|name=Hexagrams of the Yi Jing interpreted in base 10|formalname=Hexagrams of the Yi Jing interpreted in base 10, with the top line = 2^5 (most significant bit) and the bottom line as 2^0 (least significant bit)}}
*
* -()
*
*
*
* by C.J.Lofting
* -()


{{DEFAULTSORT:King Wen Sequence}}
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Latest revision as of 06:39, 1 October 2024

Traditional arrangement of I Ching hexagrams

The King Wen sequence (Chinese: 文王卦序) is an arrangement of the sixty-four divination figures in the I Ching (often translated as the Book of Changes). They are called hexagrams in English because each figure is composed of six 爻 yáo—broken or unbroken lines, that represent yin or yang respectively.

The King Wen sequence is also known as the "received" or "classical" sequence because it is the oldest surviving arrangement of the hexagrams. Its true age and authorship are unknown. Traditionally, it is said that King Wen of Zhou arranged the hexagrams in this sequence while imprisoned by King Zhou of Shang in the 12th century BC. A different arrangement, the "binary sequence" named in honor of the mythic culture hero Fu Xi, originated in the Song dynasty. It is believed to be the work of scholar Shao Yong (1011–1077 AD). As mirrored by the 先天 Earlier Heaven and 後天 Later Heaven arrangements of the eight trigrams, or ba gua, it was customary to attribute authorship to these legendary figures. Of the two hexagram arrangements, the King Wen sequence is, however, of much greater antiquity than the Fu Xi sequence.

Structure of the sequence

The 64 hexagrams are grouped into 32 pairs. For 28 of the pairs, the second hexagram is created by turning the first upside down (i.e. 180° rotation). The exception to this rule is for the 8 symmetrical hexagrams that are the same after rotation (1 & 2, 27 & 28, 29 & 30, 61 & 62). Partners for these are given by inverting each line: solid becomes broken and broken becomes solid. These are indicated with icons in the table below.

Given the mathematical constraints of these simple rules, the number of lines that change within pair partners will always be even (either 2, 4, or 6). Whereas the number of lines that change between pairs depends on how the pairs are arranged, and the King Wen sequence has notable characteristics in this regard. Of the 64 transitions, exactly 48 of them are even changes (32 within-pairs plus 16 between-pairs) and 16 are odd changes (all between-pairs). This is a precise 3 to 1 ratio of even to odd transitions. Of the odd transitions, 14 are changes of three lines and 2 are changes of one line. Changes of five are absent. Each transition within a pair appears to be the correlating opposite of the other transition within the pair.

               
1  ↕  2 3  ~  4 5  ~  6 7  ~  8 9  ~ 10 11 ~ 12 13 ~ 14 15 ~ 16
               
17 ~ 18 19 ~ 20 21 ~ 22 23 ~ 24 25 ~ 26 27 ↕ 28 29 ↕ 30 31 ~ 32
               
33 ~ 34 35 ~ 36 37 ~ 38 39 ~ 40 41 ~ 42 43 ~ 44 45 ~ 46 47 ~ 48
               
49 ~ 50 51 ~ 52 53 ~ 54 55 ~ 56 57 ~ 58 59 ~ 60 61 ↕ 62 63 ~ 64

Dual hexagrams

The I Ching book was traditionally split up in two parts with the first part covering the first 30 hexagrams of the King Wen sequence and the second part with the remaining 34. The reason for this was not mentioned in the classic commentaries but was explained in later Yuan dynasty commentaries: 8 hexagrams are the same when turned upside down and the other 56 present a different hexagram if inverted. This allows the hexagrams to be displayed succinctly in two equal columns or rows of 18 unique hexagrams each; half of the 56 invertible hexagrams plus the 8 non-invertible.

䷀  乾 qián
The Creative, Heaven
 1 →  ||||||
䷁  坤 kūn
The Receptive, Earth
 2 →  ¦¦¦¦¦¦
䷂   屯 chún
Difficulty At The Beginning
 3 →  |¦¦¦|¦   ← 4  ䷃  蒙 méng
Youthful Folly
䷄  需
Waiting
 5 →  |||¦|¦   ← 6  ䷅  訟 sòng
Conflict
䷆  師 shī
The Army
 7 →  ¦|¦¦¦¦   ← 8  ䷇  比
Holding Together
䷈  小畜 xiǎo chù
The Taming Power of the Small
 9 →  |||¦||  ← 10  ䷉  履
Treading (Conduct)
䷊  泰 tài
Peace
11 →  |||¦¦¦  ← 12  ䷋  否
Standstill (Stagnation)
䷌  同人 tóng rén
Fellowship with Men
13 →  |¦||||  ← 14  ䷍  大有 dà yǒu
Possession in Great Measure
䷎  謙 qiān
Modesty
15 →  ¦¦|¦¦¦  ← 16  ䷏  豫
Enthusiasm
䷐  隨 suí
Following
17 →  |¦¦||¦  ← 18  ䷑  蠱
Work On What Has Been Spoiled (Decay)
䷒  臨 lín
Approach
19 →  ||¦¦¦¦  ← 20  ䷓  觀 guān
Contemplation (View)
䷔  噬嗑 shì kè
Biting Through
21 →  |¦¦|¦|  ← 22  ䷕  賁
Grace
䷖  剝
Splitting Apart
23 →  ¦¦¦¦¦|  ← 24  ䷗  復
Return (The Turning Point)
䷘  無妄 wú wàng
Innocence (The Unexpected)
25 →  |¦¦|||  ← 26  ䷙  大畜 dà chù
The Taming Power of the Great
䷚  頤
The Corners of the Mouth (Providing Nourishment)
27 →  |¦¦¦¦|
䷛  大過 dà guò
Preponderance Of The Great
28 →  ¦||||¦
䷜  坎 kǎn
The Abysmal (Water)
29 →  ¦|¦¦|¦
䷝  離
The Clinging, Fire
30 →  |¦||¦|
䷞  咸 xián
Influence (Wooing)
31 → ¦¦|||¦ ← 32 ䷟  恆 héng
Duration
䷠  遯 dùn
Retreat
33 →  ¦¦||||  ← 34  ䷡  大壯 dà zhuàng
The Power of the Great
䷢  晉 jìn
Progress
35 →  ¦¦¦|¦|  ← 36  ䷣  明夷 míng yí
Brilliance Injured
䷤  家人 jiā rén
The Family (The Clan)
37 →  |¦|¦||  ← 38  ䷥  睽 kuí
Opposition
䷦  蹇 jiǎn
Obstruction
39 →  ¦¦|¦|¦  ← 40  ䷧  解 xiè
Deliverance
䷨  損 sǔn
Decrease
41 →  ||¦¦¦|  ← 42  ䷩  益
Increase
䷪  夬 guài
Break-Through (Resoluteness)
43 →  |||||¦  ← 44  ䷫  姤 gòu
Coming To Meet
䷬  萃 cuì
Gathering Together (Massing)
45 →  ¦¦¦||¦  ← 46  ䷭  升 shēng
Pushing Upward
䷮  困 kùn
Oppression (Exhaustion)
47 →  ¦|¦||¦  ← 48  ䷯  井 jǐng
The Well
䷰  革
Revolution (Molting)
49 →  |¦|||¦  ← 50  ䷱  鼎 dǐng
The Cauldron
䷲  震 zhèn
The Arousing (Shock, Thunder)
51 →  |¦¦|¦¦  ← 52  ䷳  艮 gèn
Keeping Still, Mountain
䷴  漸 jiàn
Development (Gradual Progress)
53 →  ¦¦|¦||  ← 54  ䷵  歸妹 guī mèi
The Marrying Maiden
䷶  豐 fēng
Abundance
55 →  |¦||¦¦  ← 56  ䷷  旅
The Wanderer
䷸  巽 xùn
The Gentle (The Penetrating, Wind)
57 →  ¦||¦||  ← 58  ䷹  兌 duì
The Joyous, Lake
䷺  渙 huàn
Dispersion (Dissolution)
59 →  ¦|¦¦||  ← 60  ䷻  節 jié
Limitation
䷼  中孚 zhōng fú
Inner Truth
61 →  ||¦¦||
䷽  小過 xiǎo guò
Preponderance of the Small
62 →  ¦¦||¦¦
䷾  既濟 jì jì
After Completion
63 →  |¦|¦|¦  ← 64  ䷿  未濟 wèi jì
Before Completion

Explanation

Over the centuries there were many attempts to explain this sequence. Some basic elements are obvious: each symbol is paired with an "upside-down" neighbor, except for 1, 27, 29, and 61 which are "vertically" symmetrical and paired with "inversed" neighbors.

There have been recent attempts to apply mathematical combinatorics in explaining the logic behind the King Wen sequence, for example Richard S. Cook's proposal.

Other hexagram sequences

See also

References

  1. ^ Marshall, Steve Yijing hexagram sequences
  2. Hacker, Edward A.; Moore, Steve (6 May 2003). "A brief note on the two–part division of the received order of the hexagrams in the Zhouyi" (PDF). Journal of Chinese Philosophy. 30 (2): 219–221. doi:10.1111/1540-6253.00115. Retrieved 31 May 2010.
  3. Bent Nielsen (2003). A companion to Yi jing numerology and cosmology: Chinese studies of images and numbers from Han (202 BCE-220 CE) to Song (960-1279 CE). Routledge. p. 83. ISBN 978-0-7007-1608-1. Retrieved 31 May 2010.
  4. ^ Cook, Richard S. (2006). "《周易》卦序詮解 (Zhou yi guaxu quanjie)" (JPEG Image, 1024x793). Retrieved 22 May 2010. STEDT Monograph 5: Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram Sequence. 660 pages. ISBN 0-944613-44-6. OCLC 77009740.
  5. "Yijing Dao - Archive of Yijing-related scans from Chinese and other sources". 20 February 2010. Retrieved 19 May 2010.

External links

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