八卦数 - The Number of Trigrams

华夏文明中，多以奇数为“阳”，偶数为“阴”。

前面已经提过，八卦对应时空，取洛书九宫，根据卦象而变，

• ☷坤，全阴爻，数值零，九宫无零，取值一；

• ☶艮，第一爻为阳，数值一，九宫取值二；

• ☵坎，第二爻为阳，数值二，九宫取值三；

• ☴巽，第一第二爻为为阳，数值三，九宫取值四；

• ☳震，第三爻为阳，数值四，九宫值五是中宫，不取，取值六；

• ☲离，第一第三爻为阳，数值五，九宫取值七；

• ☱兑，第二第三爻为阳，数值六，九宫取值八；

• ☰乾，全阳爻，数值七，九宫取值九。

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The Chinese civilization often regards odd numbers as "yang" and even numbers as "yin." As previously mentioned, the eight trigrams correspond to time and space, taking the Lo Shu nine palaces as an example, and changing according to the trigram image:

• ☷Kun, all yin lines, numerical value zero, nine palaces without zero, take value one;

• ☶Gen, the first line is yang, numerical value one, nine palaces take value two;

• ☵Kan, the second line is yang, numerical value two, nine palaces take value three;

• ☴Xun, the first and second lines are yang, numerical value three, nine palaces take value four;

• ☳Zhen, the third line is yang, numerical value four, nine palaces value five is central palace, not taken, take value six;

• ☲Li, the first and third lines are yang, numerical value five, nine palaces take value seven;

• ☱Dui, the second and third lines are yang, numerical value six, nine palaces take value eight;

• ☰Qian, all yang lines, numerical value seven, nine palaces take value nine.

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表格助记如下，(Table Mnemonic)

卦名-trigrams	计数（二进制）-binary	十进制（校准助记数）-decimal
坤 - Kun	000	0（一）
艮 - Gen	001	1（二）
坎 - Kan	010	2（三）
巽 - Xun	011	3（四）
-	-	-（五）- 5 as "I"
震 - Zhen	100	4（六）
离 - Li	101	5（七）
兑 - Dui	110	6（八）
乾 - Qian	111	7（九）

八卦分先天八卦和后天八卦，彼此呼应。

• 先天八卦根据洛书而来，表现相对稳定的静态结构；

• 后天八卦根据先天八卦推演而来，表现动态的八卦形态。

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The eight trigrams are divided into Primordial Trigrams and Derived Trigrams, which are mutually responsive.

• The Primordial Trigrams are derived from the Lo Shu and represent relatively stable static structures;

• The Derived Trigrams are derived from the Primordial Trigrams and represent dynamic trigram forms.

The eight trigrams

（先后天八卦对照图，内八卦先天，外八卦后天） (comparison diagram of Primordial Trigrams [inner] and Derived Tragrams [outer])

先天八卦 - The Primordial Trigrams

“先天八卦”由洛书而得，

• 一坤九乾，三坎七离为阳数，对应长宽两维；

• 二艮八兑，四巽六震为阴数，对应高三维及时四维。

• 先天八卦逆推未来，所以时间轴向量需要置换，二八对调。

• 以人测天，所以南北对调。

东坤一东北艮二北坎三西北巽四西乾九西南兑八南离七东南震六。

八兑	九乾（西）	四巽
七离（南）	x（5）	三坎（北）
六震	一坤（东）	二艮

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The "Primordial Trigrams" are derived from the "Lo Shu",

• One (Kun) and Nine (Qian) are yang numbers, corresponding to the length and width dimensions;

• Two (Gen) and Eight (Dui) are yin numbers, corresponding to the height and time dimensions.

• The primordial eight trigrams predict the future by reverse calculation, so the time axis vector needs to be switched, two and eight are exchanged.

• It is measured by humans, so north and south are exchanged.

East (Kun) one, Northeast (Gen) two, North (Kan) three, Northwest (Xun) four, West (Qian) nine, Southwest (Dui) eight, South (Li) seven, Southeast (Zhen) six.

8 Dui	9 Qian (West)	4 Xun
7 Li (South)	x (5)	3 Kan (North)
6 Zhen	1 Kun (East)	2 Gen

后天八卦 - The Derived Trigrams

后天八卦在先天八卦基础上推演而出。

太阳东升西落，所以定义阳进于东，阴进于西。

阳进数取阳数“1”；阴进数取阴数“2”。 我在中央，为“五”。

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The "Derived Tragrams" is derived from the "Primordial Tragrams" based on the dynamic changes of the world.

The sun rises in the east and sets in the west, so the definition is that yang enters the east and yin enters the west.

The yang-in number is "1" and the yin-in number is "2". The self is in the center and is "five".

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后天阳进顺推四卦，

• 阳数（1）变

  • 从5+1=6（震六） 开始；6+1=7（离七），（后天）震占（先天）离位；

  • 7+2=9，离占乾位；

  • 9+3=12，10进制个位为2，乾占艮位；

  • 2+4=6，艮占震位。

后天阴进逆推四卦，

• 阴数（2）变

  • 从 5-2=3开始，3-2=1（3+2=5，不能用，变符号），坎占坤位；

  • 1+3=4，坤占巽位；

  • 4+4=8，巽占兑位；

  • 8+5=13，10进制个位为3，兑占坎位。

上古中古与近古发生的地轴变化，后天八卦回归了左东右西上南下北，所以后天八卦的五行指代和洛书直接推演的先天八卦已经有差别了。

四巽	七离（南）	一坤
六震（东）	5	八兑（西）
二艮	三坎（北）	九乾

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"Derived Yang-In" is a sequence of four Trigrams (Gua),

• The "Yang-In" (1) changes:

  • Starting from 5+1=6 (Zhen 6); 6+1=7 (Li 7), (Derived Trigrams) Zhen occupies (Primordial Trigrams) Li position;

  • 7+2=9, Li occupies Qian position;

  • 9+3=12, the 10th digit is 2, Qian occupies Gen position;

  • 2+4=6, Gen occupies Zhen position.

"Derived Yin-In" is a reverse sequence of four Trigrams (Gua),

• The "Yin-In" (2) changes:

  • Starting from 5-2=3, 3-2=1 (3+2=5, cannot use, change sign), Kan occupies Kun position;

  • 1+3=4, Kun occupies Xun position;

  • 4+4=8, Xun occupies Dui position;

  • 8+5=13, the 10th digit is 3, Dui occupies Kan position.

In ancient and recent times, the earth's axis has changed, the Derived Trigrams has returned to left east and right west, up south and down north. Therefore, the five elements of the Derived Trigrams have differences compared to the Primordial Trigrams derived directly from the Lo Shu.

4 Xun	7 Li (South)	1 Kun
6 Zhen (East)	5	8 Dui (West)
2 Gen	3 Kan (North)	9 Qian