气者天地之气候，数者天地之定数。天地之道，一阴一阳而尽之，升降有期而气候行，
阴阳有数而次第立。次第既立，则先后因之而定；气候既行，则节序由之而成。节序之所
以分者，由寒暑之再更；寒暑之所以更者，由日行之度异。每岁之气，阳生于子而极于午，
阴生于午而极于子，阳之进者阴之退，阳之退者阴之生，一往一来，以成一岁。朱子曰∶
冬至前四十五日属今年，后四十五日属明年。子时前四刻属今日，后四刻属明日。邵子
曰∶冬至子之半，天心无改移。是俱言一岁之气，终始皆在于子半，而冬至之日，正当斗柄
建于子中，是为一岁之首尾也。岁有三百六十五日二十五刻者，以周天之度，凡三百六
十五度四分度之一也。天之行速，故于一昼一夜，行尽一周而过日一度。日行稍迟，每
日少天一度，凡行三百六十五日二十五刻，少天一周，复至旧处而与天会，是为一岁。故
岁之日数，由天之度数而定；天之度数，实由于日之行数而见也。岁有十二月者，以月之
行天，又迟于日，每日少天十三度十九分度之七，（又曰∶百分度之三十七。）积二十九日九百
四十分日之四百九十九，与日合朔而为一月。岁有十二会，故为十二月。斗有十二建，故为
十二辰。斗之所建地上辰，辰之所会天上次，斗与辰合而月建昭然矣。故十一月建在子，
一阳卦复；十二月建在丑，二阳卦临；正月建在寅，三阳卦泰；二月建在卯，四阳卦大壮；三
月建在辰，五阳卦 ；四月建在巳，六阳卦干；五月建在午，一阴卦 ；六月建在未，二阴
卦遁；七月建在申，三阴卦否；八月建在酉，四阴卦观；九月建在戌，五阴卦剥；十月建在亥，
六阴卦坤，是为一岁之气而统言其月日也。月日既定，时序乃分，四而分之，是为四季，曰
春、曰夏、曰秋、曰冬。春为阳始，阳始则温，故曰少阳，少阳数七，阴中阳也，其气木，自东
而西，其令生，自下而上，春者蠢也，言万物之蠢动也。夏为阳极，阳极则热，故曰老阳，老
阳数九，阳中阳也，其气火，自南而北，其令长，自长而茂，夏者大也，言万物之盛大也。秋
为阴始，阴始则凉，故曰少阴，少阴数八，阳中阴也，其气金，自西而东，其令收，自上而下，
秋者收也，言万物之收敛也。冬为阴极，阴极则寒，故曰老阴，老阴数六，阴中阴也，其气
水，自北而南，其令藏，自下而闭，冬者终也，言万物之尽藏也。土为充气，其位象君，故不
主时，分王四季，各一十八日。以五分而分四季，每分各得七十二日，以成一岁之数。然而
一岁之气始于子，四季之春始于寅者何也？盖以建子之月，阳气虽始于黄钟，然犹潜伏地
下，未见发生之功，及其历丑转寅，三阳始备，于是和风至而万物生，萌芽动而蛰藏振，遍满
寰区，无非生意，故阳虽始于子，而春必起于寅。是以寅卯辰为春，巳午未为夏，申酉戌为
秋，亥子丑为冬，而各分其孟仲季焉。由四季而分为八节，则春秋有立而有分，夏冬有立而
有至。四季何以言立？立者建也，谓一季之气，创建于此也。春秋何以言分？分者半也，
谓阴阳气数，中分于此也。故以刻数之多寡言，则此时昼夜各得五十刻，是为昼夜百刻之
中分。以阴阳之寒暄言，则春分前寒而后热，秋分前热而后寒，是为阴阳寒热之中分。以
日行之度数言，则春分后，日就赤道之北，（赤道者，天之平线，居两极之中，各去九十一度三分
度之一，横络
天腹，以纪经纬之度数也。日行之路，谓之黄道。月行之路，谓之白道。）秋分后，日就赤道之南，
是为日行南北之中分。故春分曰阳中，秋分曰阴中也。夏冬何以言至？至者极也，言阴阳气数，消长
之极也。故以刻数之多寡言，则夏至昼长五十九刻，夜长四十一刻，冬至昼长四十一刻，夜
长五十九刻，是为昼夜长短之至极。以阴阳之寒暄言，则冬至阴极而阳生，夏至阳极而阴
生，是为阴阳寒热之至极。以日行之度数言，则冬至日南极而北返，夏至日北极而南返，是
为日行南北之至极。故冬至曰阳始，夏至曰阴始也。至真要大论曰，气分谓之分，气至谓
之至，至则气同，分则气异者是也。由四季而分为二十四气，则每季各得六气。如立春、雨
水、惊蛰、春分、清明、谷雨，为春之六气，而四季各六也。由二十四气而分为七十二候，则
每气各得三候，如礼记。月令及吕氏春秋云，立春节，初五日东风解冻为初候，次五日蛰虫
始振为二候，后五日鱼陟负冰为三候也。候之所以五日者，天数五以竟五行之气也。六节
藏象论曰，五日谓之候，三候谓之气，六气谓之时，四时谓之岁也。然而一岁之中，复又有
大六气以统之者，曰风热暑湿燥寒，分司天在泉，左右间气，以行客主之令。斯天地之气，
如环无端，周而复始，而亿万斯年，营运不息矣。
然而既有其气，亦必有其数，数非气不行，气非数不立，故易传曰，天地之数，所以成变
化而行鬼神者。然太极未动，气未见也，数何有焉？及自动而生阳，便有一数，自动而静，
便是二数，静极复动，便是三数，动极复静，便是四数。朱子曰∶两仪者，始为一面以分阴
阳；四象者，次为二面以分太少也。是数之所起，亦惟阴阳而已。（老子曰∶一生二，二生三，三生万
物。夫一者太极也，二者阴阳也，三者阴阳之交也，阴阳交而万物生矣。）阳数奇而属天，阴数偶而属地。天
圆径一而围三，三各一奇，故曰参天，三三而九，阳数从此而流行；地方径一而围四，四为
二偶，故曰两地，二四合六，阴数从此而凝定。三二相合，是为五数，故图书之数，皆以五居
中也。河图以天一生水，一得五而六，故地以六成之而居北；地二生火，二得五而七，故天
以七成之而居南；天三生木，三得五而八，故地以八成之而居东；地四生金，四得五而九，故
天以九成之而居西；天以五生土，五得五为十，故地以十成之而居中。生数为主而居内，成
数为配而居外，此则河图之定数也。若以阴阳之次第老少参之，则老阳位一而数九，少阴
位二而数八，少阳位三而数七，老阴位四而数六。阳主进，故由少阳之七，逾八至九而其进
已极，故曰老阳；阴主退，故由少阴之八，逾七至六而其退已极，故曰老阴。阳数长，故少
阳之七长于六，老阳之九长于八；阴数消，故少阴之八消于九，老阴之六消于七。此阴阳
老少，消长进退之理也。故河图以老阳之位一而配老阴之数六，少阴之位二而配少阳之数
七，少阳之位三而配少阴之数八，老阴之位四而配老阳之数九，是又河图阴阳互藏之妙也。
故伏羲则之以画八卦，孔子推之而为大衍，而三百八十四爻，一万一千五百二十策，而乾坤
万物之数备矣。洛书之数，则阳为君而阴为臣，君居正而臣居侧。故戴九履一，左三右七，
二四为肩，六八为足，五居于中，而纵横之数皆十五。一居正北，得中为六，而合南方之九
为十五；三居正东，得中为八，而合西方之七为十五；二居西南，得中为七，而合东北之八为
十五；四居东南，得中为九，而合西北之六为十五。故大禹则之以叙九畴∶一曰五行，二曰
五事，三曰八政，四曰五纪，五曰皇极，六曰三德，七曰稽疑，八曰庶征，九曰福德。皇极居
中，而八者环列于外。河图之数，分生成而言其全，以生数为主而以成数合之，故河图之位
十，而数凡五十五；洛书之数，分奇偶而言其变，以四正之阳而统四隅之阴，故洛书之位九，
而数凡四十五。合河洛二数，共成一百，乃为天地自然之全数。然二数虽有异同，而理则
相为迭用，是以天地之数，始于一而全于十。天数五，一三五七九是也；地数五，二四六八
十是也。天数二十五，五其五也；地数三十，六其五也。小衍为十，两其五也；大衍五十，十
其五也。故又曰五为数祖。邵子曰∶天地之本起于中。夫数之中者，五与六也。五居一三
七九之中，故曰五居天中，为生数之主；六居二四八十之中，故曰六居地中，为成数之主。
天元纪大论曰∶天以六为节，地以五为制。是以万候之数，总不离于五与六也。而五六之
用，其变见于昭着者，尤有显证。如初春之桃五其瓣，天之所生也；深冬之雪六其出，地之
所成也。造化之妙，夫岂偶然？故以五而言，则天有五星，地有五岳，人有五常，以至五色、
五味、五谷、五畜之类，无非五也。而十根于一，百根于十，小之而厘毫尘秒，大之而亿兆无
量，总属五之所化，而皆统于天之五中也。以六而言，则天有六合，岁有六气，卦有六爻，以
至六律、六吕、六甲、六艺之类，无非六也。而老阳之数三十六，老阴之数二十四，合之而为
六十；少阳之数二十八，少阴之数三十二，合之亦为六十。总属六之所化，而皆统于地之六
中也。总之五为阳也，而五实统乎阴之六；六为阴也，而六实节于阳之五。天元纪大论曰∶
所以欲知天地之阴阳者，应天之气，动而不息，故五岁而右迁；应地之气，静而守位，故六期
而环会。五六相合，而七百二十气为一纪。得非天地之气，总皆五六之所生成者欤？试举
一岁之气及干支之数而言，从天用干，则五日一候，五阴五阳而天之所以有十干，甲戊以阳
变，己癸以阴变，五之变也；从地用支，则六日一变，六刚六柔而地之所以有十二支，子巳以
阳变，午亥以阴变，六之变也。十干以应日，十二支以应月。故一年之月两其六，一月之日
六其五，一年之气四其六，一气之候三其五。总计一年之数，三十六甲而周以天之五，三
十子而周以地之六。故为十二月、（以二因六，得此。）二十四气、（以十五日，归三百六十，得此。）七十二
候、（以五日，归三百六十，得此。）三百六十日、（以三十日，因十二月，得此。）四千三百二十辰、
（以十二辰，因三百六十日，得此。）十二万九千六百分，（以三百六十日，因三百六十分，得此。）
何非五六之所化？一岁之数如此，而元会运世之数亦如此。如一岁之统十二月，一月之统三十日，一
日之统十二时，
一时之统三十分；故一元之统十二会，一会之统三十运，一运之统十二世，一世之统三十
年，而天地气运之道，概乎此矣。惟是数之为学，圆通万变，大则弥纶宇宙，小则纤悉秋毫。
若夫拆一为二，拆二为四，拆四为八，拆八而十六，拆之到底，何有穷已。譬之因根而干，因
干而枝，愈多则愈细，愈细则愈繁，固茫然莫可测其徼，而实则各得其一耳。故凡象之在天
下，形之在地上，鬼神居幽冥之间，无不丽乎数。而先王所以察河洛之图书，垂奇偶之名
目，数天以度，数地以里，数神鬼以阴阳，数气候以律吕，轻重者数以权衡，方圆者数以规
矩，长短者数之以度，浅深者数之以量，归除可以数消，因乘可以数长。然则仰而观，俯而
察，上而苍天，下而黄泉，大含元气，细入无伦，亦有能逃于数之外者否乎？故以天地而观
人，则人实太仓之一粟；以数而观天地，则天地特数中之一物耳。数之为学，岂易言哉！苟
能通之，则幽显高下，无不会通，而天地之大，象数之多，可因一而推矣。明乎此者，自列圣
而下，惟康节先生一人哉。
气，是天地间的自然气候现象；数，是天地间确定的规律定数。天地的运行法则，归结为一阴一阳的变化，升降有固定的时期从而形成气候，阴阳有确定的数量从而确立次序。次序一旦确立，先后顺序便由此确定；气候一旦运行，季节节令便由此形成。季节节令之所以划分，是因为寒暑的交替更迭；寒暑之所以更迭，是因为太阳运行的度数不同。每年的气运，阳气在子月（十一月）开始生发而在午月（五月）达到极盛，阴气在午月开始生发而在子月达到极盛，阳气的进长意味着阴气的退却，阳气的退却意味着阴气的生发，一进一出，构成了一年。朱熹说：冬至前四十五天属于今年，后四十五天属于明年。子时前四刻属于今日，后四刻属于明日。邵雍说：冬至日的子时半刻，天心（宇宙本体/规律）没有改变移动。这都是说一年的气运，始终都在于子时的半刻，而冬至这一天，正当北斗斗柄指向子位正中，这是一年岁首和岁尾的交汇点。一年有三百六十五日二十五刻，这是因为周天度数总共是三百六十五度又四分之一度。天体运行速度快，所以在一个昼夜之间，运行完一周天并超过太阳一度。太阳运行稍慢，每天比天少行一度，总共运行三百六十五日二十五刻，比天少行一周天，重新回到原来的位置并与天体会合，这就是一年。所以一年的日数，由天体的度数决定；天体的度数，实际上是通过太阳的运行度数体现出来的。一年有十二个月，是因为月亮绕天运行，比太阳更慢，每天比天少行十三度又十九分之七（又说：百分度之三十七），累计二十九日九百四十分之四百九十九，与太阳相合朔望，成为一个朔望月。一年有十二个节气会合，所以分为十二月。北斗有十二个方位建立，所以对应十二辰。北斗所建立的地上辰位，辰位所会合的天上星次，北斗与辰位相合，月建就清晰可见了。所以十一月建在子，对应一阳复卦；十二月建在丑，对应二阳临卦；正月建在寅，对应三阳泰卦；二月建在卯，对应四阳大壮卦；三月建在辰，对应五阳卦（夬卦）；四月建在巳，对应六阳乾卦；五月建在午，对应一阴姤卦；六月建在未，对应二阴遁卦；七月建在申，对应三阴否卦；八月建在酉，对应四阴观卦；九月建在戌，对应五阴剥卦；十月建在亥，对应六阴坤卦，这是对一年之气按月日进行的总体论述。月日既定，时序才分明，将其分为四份，就是四季，称为春、夏、秋、冬。春季是阳气的开始，阳气初生则温和，所以称为少阳，少阳数为七，属于阴中之阳，其气属木，自东向西，其令主生发，自下而上，春即蠢动之意，指万物蠢动生长。夏季是阳气的极盛，阳极则炎热，所以称为老阳，老阳数为九，属于阳中之阳，其气属火，自南向北，其令主生长，从生长到茂盛，夏即盛大之意，指万物盛大成长。秋季是阴气的开始，阴气初生则凉爽，所以称为少阴，少阴数为八，属于阳中之阴，其气属金，自西向东，其令主收敛，自上而下，秋即收敛之意，指万物收敛闭藏。冬季是阴气的极盛，阴极则寒冷，所以称为老阴，老阴数为六，属于阴中之阴，其气属水，自北向南，其令主闭藏，自下而闭，冬即终结之意，指万物尽行闭藏。土气为充盛之气，其位象喻君主，所以不单独主宰一个季节，而是分旺于四季，每季各十八天。将一年五分以分配四季，每部分得七十二天，以构成一年的总数。然而，一年的气运始于子月，而四季中的春季始于寅月，为什么呢？大概因为建子之月，阳气虽然开始在黄钟律管中萌动，但仍然潜伏在地底下，未见发生生长的功效，等到经历丑月转向寅月，三阳之气始备，于是和风到来而万物生长，萌芽萌动而蛰伏之物振奋，遍满寰宇，无非生机，所以阳气虽然始于子月，但春季必定起于寅月。因此寅、卯、辰月为春，巳、午、未月为夏，申、酉、戌月为秋，亥、子、丑月为冬，并且各自分为孟、仲、季三个阶段。由四季再分为八个节气，则春秋有立春和春分，夏冬有立夏和夏至（及立秋、秋分、立冬、冬至）。为什么四季要说“立”？立就是建立的意思，指一季的气运在此创建。为什么春秋要说“分”？分就是一半的意思，指阴阳气数在此平分。所以从刻数多少来说，此时昼夜各得五十刻，是一百刻的中分。从阴阳寒热来说，春分前寒而后热，秋分前热而后寒，这是阴阳寒热的中分。从太阳运行的度数来说，春分后，太阳行至赤道以北（赤道是天球的平线，位于两极中间，距离各九十一度又三分之一，横贯天腹，用来记录经纬度数。太阳运行的路线，称为黄道。月亮运行的路线，称为白道），秋分后，太阳行至赤道以南，这是太阳运行南北的中分。所以春分称为阳中，秋分称为阴中。为什么夏冬要说“至”？至极的意思，指阴阳气数消长的极点。所以从刻数多少来说，夏至昼长五十九刻，夜长四十一刻，冬至昼长四十一刻，夜长五十九刻，这是昼夜长短的至极。从阴阳寒热来说，冬至阴极而阳气生，夏至阳极而阴气生，这是阴阳寒热的至极。从太阳运行的度数来说，冬至日行至南极而向北返回，夏至日行至北极而向南返回，这是太阳运行南北的至极。所以冬至称为阳始，夏至称为阴始。《素问·天元纪大论》说，气分称为分，气至称为至，至则气同，分则气异，说的就是这个道理。由四季再分为二十四节气，则每季各有六个气。如立春、雨水、惊蛰、春分、清明、谷雨，是春季的六个气，四季各六个。由二十四节气再分为七十二候，则每个气各有三个候，如《礼记·月令》及《吕氏春秋》所说，立春节，前五日东风解冻为初候，次五日蛰虫始振为二候，后五日鱼陟负冰为三候。候之所以定为五日，是因为天数五以穷尽五行之气。《素问·六节藏象论》说，五日称为候，三候称为气，六气称为时，四时称为岁。然而一年之中，又有大六气来统摄它，称为风、热、暑、湿、燥、寒，分别司掌司天、在泉及左右间气，以行使客主加临的命令。这天地之气，如环无端，周而复始，亿万年来，营运不息。
既然有了气，也必然有其数，数不能离开气而运行，气不能离开数而确立，所以《易传》说，天地的数，是用来成就变化并推行鬼神作用的。然而太极尚未发动时，气尚未显现，数又从何而来呢？等到自动而生阳，便有一个数，自动而静，便是两个数，静极复动，便是三个数，动极复静，便是四个数。朱熹说：两仪，开始时是一面以分阴阳；四象，其次是两面以分太少。所以数的起源，也只在于阴阳罢了。（老子说：一生二，二生三，三生万物。一就是太极，二就是阴阳，三是阴阳的交合，阴阳交合而万物产生。）阳数为奇数而属天，天圆径一而围三，三都是奇数，所以叫参天，三三得九，阳数从此流行；地方径一而围四，四是两个偶数，所以叫两地，二四合六，阴数从此凝定。三和二相合，就是五数，所以河图洛书之数，都以五居中央。河图中天一生水，一加五得六，所以地以六成之而居北方；地二生火，二加五得七，所以天以七成之而居南方；天三生木，三加五得八，所以地以八成之而居东方；地四生金，四加五得九，所以天以九成之而居西方；天五生土，五加五得十，所以地以十成之而居中央。生数为主居于内，成数为配居于外，这就是河图的定数。如果以阴阳的次第老少参看，则老阳位居一而数九，少阴位居二而数八，少阳位居三而数七，老阴位居四而数六。阳主进长，所以由少阳之七，经过八到九而其进长已到极点，所以叫老阳；阴主消退，所以由少阴之八，经过七到六而其消退已到极点，所以叫老阴。阳数长，所以少阳之七长于六，老阳之九长于八；阴数消，所以少阴之八消于九，老阴之六消于七。这是阴阳老少消长进退的道理。所以河图中老阳之位一配老阴之数六，少阴之位二配少阳之数七，少阳之位三配少阴之数八，老阴之位四配老阳之数九，这又是河图阴阳互藏的奥妙。所以伏羲效法它画八卦，孔子推演它为大衍筮法，而三百八十四爻，一万一千五百二十策，乾坤万物的数就完备了。洛书的数，则是阳为君而阴为臣，君居正位而臣居侧位。所以戴九履一，左三右七，二四为肩，六八为足，五居于中，纵横之数皆十五。一居正北，加上中间的数六，合南方之九为十五；三居正东，加上中间的数八，合西方之七为十五；二居西南，加上中间的数七，合东北之八为十五；四居东南，加上中间的数九，合西北之六为十五。所以大禹效法它来叙述九畴：一是五行，二是五事，三是八政，四是五纪，五是皇极，六是三德，七是稽疑，八是庶征，九是福德。皇极居中，其他八项环绕排列在外。河图的数，分生成而言其全貌，以生数为主而以成数配合，所以河图有位十，数共五十五；洛书的数，分奇偶而言其变化，以四正的阳数统摄四隅的阴数，所以洛书有位九，数共四十五。合并河洛二数，共成一百，才是天地自然的完整之数。然而二数虽有异同，但理则相互迭代使用，所以天地的数，始于一而终于十。天数五，是一三五七九；地数五，是二四六八十。天数总和二十五，是五乘以五；地数总和三十，是六乘以五。小衍为十，是两倍的五；大衍为五十，是十倍的五。所以又说五是数的祖先。邵雍说：天地的根本起源于中。中的数，就是五和六。五居于一三五七九之中，所以叫五居天中，为生数之主；六居于二四六八十之中，所以叫六居地中，为成数之主。《素问·天元纪大论》说：天以六为节，地以五为制。所以万候之数，总离不开五和六。而五六的运用，其变化见于显著者，更有明显的证据。如初春的桃花五瓣，是天所生的；深冬的雪六角形，是地所成的。造化的奇妙，难道是偶然的吗？所以以五来说，天有五星，地有五岳，人有五常，以至五色、五味、五谷、五畜之类，无非五。而十根源于一，百根源于十，小到厘毫尘秒，大到亿兆无量，总属于五所化生，且都统摄于天的五中。以六来说，天有六合，岁有六气，卦有六爻，以至六律、六吕、六甲、六艺之类，无非六。而老阳之数三十六，老阴之数二十四，合起来为六十；少阳之数二十八，少阴之数三十二，合起来也为六十。总属于六所化生，且都统摄于地的六中。总之五是阳，但五实际统摄阴之六；六是阴，但六实际节制阳之五。《素问·天元纪大论》说：想要了解天地的阴阳，应天之气动而不息，所以五年向右迁移；应地之气静而守位，所以六年周期循环会合。五六相合，七百二十气为一纪。难道不是天地之气，总都是由五六所生成吗？试举一年的气及干支之数来说，从天用天干，则五日一候，五阴五阳，所以天有十天干，甲戊以阳变，己癸以阴变，这是五的变化；从地用地支，则六日一变，六刚六柔，所以地有十二地支，子巳以阳变，午亥以阴变，这是六的变化。十天干对应日，十二地支对应月。所以一年的月数是二的六倍，一个月的日数是六的五倍，一年的气数是四的六倍，一个气的候数是三的 five 倍。总计一年的数，三十六甲循环以天之五，三十子循环以地之六。所以有十二月（以二乘六，得此），二十四节气（以十五日归三百六十，得此），七十二候（以五日归三百六十，得此），三百六十日（以三十日乘十二月，得此），四千三百二十辰（以十二辰乘三百六十日，得此），十二万九千六百分（以三百六十日乘三百六十分，得此），哪一项不是五六所化生？一年的数如此，元会运世的数也是如此。如一年统十二月，一月统三十日，一日统十二时，一时统三十分；所以一元统十二会，一会统三十运，一运统十二世，一世统三十年，天地气运的道理，概略于此。只是数作为学问，圆通万变，大的涵盖宇宙，小的细致入微。如果拆一为二，拆二为四，拆四为八，拆八为十六，一直拆下去，哪有穷尽之时。譬如因根而有干，因干而有枝，越多越细，越细则越繁，固然茫然不可测其边际，但实际上各得其一分而已。所以凡是形象存在于天下，形体存在于地上，鬼神居于幽冥之间，无不依附于数。先王所以考察河洛图书，垂示奇偶名目，数天以度，数地以里，数神鬼以阴阳，数气候以律吕，轻重者数以权衡，方圆者数以规矩，长短者数以度量，浅深者数以量器，归除可以用数消除，因乘可以用数增长。那么仰而观察，俯而察识，上至苍天，下至黄泉，大含元气，细入无伦，也有能逃脱于数之外的吗？所以以天地来看人，人实在是太仓中的一粒粟米；以数来看天地，天地不过是数中的一个物体罢了。数这门学问，岂是容易言说的！如果能通晓它，则幽显高下，没有不会通的，天地之大，象数之多，可以因一而推知了。明白这个道理的人，自历代圣王以下，只有康节先生（邵雍）一人啊。
Qi (Vital Energy) refers to the climatic phenomena of Heaven and Earth; Shu (Number/Law) refers to the fixed laws of Heaven and Earth. The way of Heaven and Earth is exhausted by one Yin and one Yang; with rising and falling having their appointed times, climate moves forward; with Yin and Yang having their numbers, sequence is established. Once sequence is established, priority and posteriority are determined thereby; once climate moves forward, seasonal order is formed thereby. The reason for dividing seasonal order lies in the alternation of cold and heat; the reason for the alternation of cold and heat lies in the varying degrees of the Sun's movement. In each year, Qi begins to generate at Zi (November) and reaches its peak at Wu (May); Yin begins to generate at Wu and reaches its peak at Zi. Advancement of Yang implies retreat of Yin; retreat of Yang implies generation of Yin. One goes and one comes, forming one year. Zhu Xi said: Forty-five days before Winter Solstice belong to the current year, and forty-five days after belong to the next year. Four quarters before the hour of Zi belong to today, and four quarters after belong to tomorrow. Shao Yong said: At the halfway point of the hour of Zi on Winter Solstice, the Heavenly Heart (Cosmic Principle) does not shift or move. All these statements indicate that the beginning and end of a year's Qi lie in the halfway point of Zi, and on the day of Winter Solstice, the handle of the Big Dipper points exactly to the center of Zi, marking the head and tail of the year. A year has 365 days and 25 ke (quarter-hours), based on the degree of the celestial sphere, which totals 365 and 1/4 degrees. Heaven moves quickly, thus completing one revolution of the celestial sphere within one day and night, surpassing the Sun by one degree. The Sun moves slightly slower, moving one degree less than Heaven each day. After traveling 365 days and 25 ke, it falls short of Heaven by one full revolution, returning to its original position to meet Heaven again, thus constituting one year. Therefore, the number of days in a year is determined by the degrees of Heaven; the degrees of Heaven are actually manifested through the movement of the Sun. There are twelve months in a year because the Moon's movement around Heaven is slower than the Sun's, moving 13 and 7/19 degrees less than Heaven each day (also stated as 37/100 degrees). Accumulating 29 days and 499/940 days results in a conjunction with the Sun (New Moon), forming one lunar month. Since there are twelve meetings of Qi in a year, there are twelve months. The Big Dipper establishes twelve positions, corresponding to the Twelve Earthly Branches (Shichen). The earthly branches established by the Dipper correspond to the celestial stations met by the branches. When the Dipper and branches align, the Monthly Branch (Yuejian) becomes clear. Thus, the eleventh month builds at Zi, corresponding to the Fu Hexagram (One Yang); the twelfth month builds at Chou, corresponding to the Lin Hexagram (Two Yangs); the first month builds at Yin, corresponding to the Tai Hexagram (Three Yangs); the second month builds at Mao, corresponding to the Da Zhuang Hexagram (Four Yangs); the third month builds at Chen, corresponding to the Guai Hexagram (Five Yangs); the fourth month builds at Si, corresponding to the Qian Hexagram (Six Yangs); the fifth month builds at Wu, corresponding to the Gou Hexagram (One Yin); the sixth month builds at Wei, corresponding to the Dun Hexagram (Two Yins); the seventh month builds at Shen, corresponding to the Pi Hexagram (Three Yins); the eighth month builds at You, corresponding to the Guan Hexagram (Four Yins); the ninth month builds at Xu, corresponding to the Bo Hexagram (Five Yins); the tenth month builds at Hai, corresponding to the Kun Hexagram (Six Yins). This summarizes the Qi of the year by month and day. With months and days fixed, the temporal sequence divides. Dividing into four parts yields the Four Seasons: Spring, Summer, Autumn, and Winter. Spring is the beginning of Yang; when Yang begins, it is warm, hence called Shaoyang (Lesser Yang). Shaoyang's number is seven, representing Yang within Yin. Its Qi is Wood, moving from East to West, its command is Generation, moving from bottom to top. "Spring" means stirring/moving, indicating all things stir and grow. Summer is the peak of Yang; when Yang peaks, it is hot, hence called Laoyang (Old Yang). Laoyang's number is nine, representing Yang within Yang. Its Qi is Fire, moving from South to North, its command is Growth, growing from growth to flourishing. "Summer" means great/profound, indicating all things grow grandly. Autumn is the beginning of Yin; when Yin begins, it is cool, hence called Shaoyin (Lesser Yin). Shaoyin's number is eight, representing Yin within Yang. Its Qi is Metal, moving from West to East, its command is Harvest/Gathering, moving from top to bottom. "Autumn" means gathering, indicating all things gather and store. Winter is the peak of Yin; when Yin peaks, it is cold, hence called Laoyin (Old Yin). Laoyin's number is six, representing Yin within Yin. Its Qi is Water, moving from North to South, its command is Storage/Closing, closing from bottom to top. "Winter" means end, indicating all things are completely stored. Earth Qi is abundant Qi; its position resembles the Sovereign, so it does not govern a specific season but rules over the Four Seasons, eighteen days each. Dividing the year into five parts allocates seventy-two days to each part to complete the year's count. However, why does the year's Qi begin at Zi, while Spring begins at Yin? Although Yang Qi begins to stir in the Huangzhong pitch-pipe during the Zi month, it remains latent underground, showing no effect of generation. Only when passing through Chou to Yin, when Three Yangs are prepared, do gentle winds arrive and all things grow, buds sprout and hibernating creatures awaken, filling the universe with vitality. Thus, although Yang begins at Zi, Spring must rise from Yin. Therefore, Yin, Mao, Chen constitute Spring; Si, Wu, Wei constitute Summer; Shen, You, Xu constitute Autumn; Hai, Zi, Chou constitute Winter, each divided into Meng (Beginning), Zhong (Middle), and Ji (End). From the Four Seasons, we divide into Eight Solar Terms: Spring and Autumn have Li (Establishment) and Fen (Equinox); Summer and Winter have Li and Zhi (Solstice). Why speak of "Li" for seasons? Li means establishment, implying the Qi of a season is established here. Why speak of "Fen" for Spring and Autumn? Fen means half, implying Yin and Yang Qi and numbers are equally divided here. Thus, in terms of ke counts, day and night each get fifty ke, the midpoint of one hundred ke. In terms of Yin/Yang cold/warmth, before Spring Equinox it is cold then warm; before Autumn Equinox it is warm then cold, the midpoint of Yin/Yang cold/warmth. In terms of Sun's degrees, after Spring Equinox, the Sun moves north of the Celestial Equator (the equator is the sky's horizontal line, midway between poles, ninety-one and 1/3 degrees from each, crossing the sky's belly to record latitude/longitude. The Sun's path is the Ecliptic/Huangdao; the Moon's path is the White Path/Baidao). After Autumn Equinox, the Sun moves south of the Celestial Equator, the midpoint of the Sun's north-south movement. Hence Spring Equinox is called Yang Middle, Autumn Equinox Yin Middle. Why speak of "Zhi" for Summer and Winter? Zhi means extreme, implying the extreme of Yin/Yang Qi waxing and waning. In terms of ke counts, Summer Solstice day is 59 ke long, night 41 ke; Winter Solstice day is 41 ke long, night 59 ke, the extreme of day/night length. In terms of Yin/Yang cold/warmth, Winter Solstice Yin peaks and Yang generates; Summer Solstice Yang peaks and Yin generates, the extreme of Yin/Yang cold/warmth. In terms of Sun's degrees, at Winter Solstice the Sun reaches its southernmost point and returns north; at Summer Solstice it reaches its northernmost point and returns south, the extreme of the Sun's north-south movement. Hence Winter Solstice is called Yang Beginning, Summer Solstice Yin Beginning. *Suwen: Tian Yuan Ji Da Lun* states: Qi division is called Fen; Qi arrival is called Zhi. At Zhi, Qi is same; at Fen, Qi is different. From Four Seasons, we divide into Twenty-Four Solar Terms, six per season. E.g., Lichun, Yushui, Jingzhe, Chunfen, Qingming, Guyu are the six Qi of Spring, and similarly for other seasons. From Twenty-Four Solar Terms, we divide into Seventy-Two Pentads (Hou), three per term, as stated in *Liji: Yue Ling* and *Lüshi Chunqiu*: At Lichun, first pentad (5 days) wind thaws ice; second pentad insects stir; third pentad fish ascend carrying ice. Hou is five days because the number Five exhausts the Qi of the Five Elements. *Suwen: Liu Jie Cang Xiang Lun* states: Five days is Hou; three Hou is Qi; six Qi is Shi (Season); four Shi is Sui (Year). However, within a year, Great Six Qi govern it: Wind, Heat, Summer-Heat, Dampness, Dryness, Cold, governing Sitian (Heavenly Qi), Zaiquan (Earthly Qi), and Left/Right Intercalary Qi, executing Guest-Master commands. This Heaven-Earth Qi is like a ring without end, cycling endlessly, operating ceaselessly for billions of years.
Since there is Qi, there must be Shu (Number); Shu cannot move without Qi, Qi cannot stand without Shu. Thus, *Yi Zhuan* says: The numbers of Heaven and Earth are what accomplish changes and operate spiritual influences. Before Taiji moves, Qi is unseen, so where is Shu? When it moves to generate Yang, there is one number; when it moves to stillness, there are two numbers; when stillness極ly moves, there are three numbers; when movement極ly stills, there are four numbers. Zhu Xi said: Liangyi (Two Modes) starts as one face to divide Yin/Yang; Sixiang (Four Images) next as two faces to divide Shao/Lao (Lesser/Older). Thus, the origin of numbers lies only in Yin and Yang. (Laozi said: One generates Two, Two generates Three, Three generates Ten Thousand Things. One is Taiji; Two is Yin/Yang; Three is the intersection of Yin/Yang. Yin/Yang intersect and Ten Thousand Things are born.) Yang numbers are odd and belong to Heaven; Heaven is round, diameter one, circumference three. Three is odd, hence Can Tian (Par Heaven). Three times three is nine, Yang numbers flow from here. Earth is square, diameter one, circumference four. Four is even, hence Diang Di (Pair Earth). Two times four is six, Yin numbers condense from here. Three and two combine to form Five, hence the numbers in Hetu and Luoshu all center on Five. In Hetu, Heaven One generates Water; One plus Five is Six, so Earth completes it at Six in the North. Earth Two generates Fire; Two plus Five is Seven, so Heaven completes it at Seven in the South. Heaven Three generates Wood; Three plus Five is Eight, so Earth completes it at Eight in the East. Earth Four generates Metal; Four plus Five is Nine, so Heaven completes it at Nine in the West. Heaven Five generates Earth; Five plus Five is Ten, so Earth completes it at Ten in the Center. Generating numbers (Shengshu) are primary and inner; Completing numbers (Chengshu) are auxiliary and outer. This is the fixed number of Hetu. Considering the sequence and age of Yin/Yang: Lao Yang occupies Position One and Number Nine; Shao Yin occupies Position Two and Number Eight; Shao Yang occupies Position Three and Number Seven; Lao Yin occupies Position Four and Number Six. Yang advances, so from Shao Yang's Seven, passing Eight to Nine, advancement is extreme, hence Lao Yang. Yin retreats, so from Shao Yin's Eight, passing Seven to Six, retreat is extreme, hence Lao Yin. Yang numbers grow, so Shao Yang's Seven grows longer than Six, Lao Yang's Nine longer than Eight. Yin numbers diminish, so Shao Yin's Eight diminishes below Nine, Lao Yin's Six diminishes below Seven. This is the principle of Yin/Yang age, waxing/waning, advancing/retreating. Thus, in Hetu, Lao Yang's Position One pairs with Lao Yin's Number Six; Shao Yin's Position Two pairs with Shao Yang's Number Seven; Shao Yang's Position Three pairs with Shao Yin's Number Eight; Lao Yin's Position Four pairs with Lao Yang's Number Nine. This is the mystery of Yin/Yang mutual containment in Hetu. Fuxi modeled this to draw the Eight Trigrams; Confucius deduced it for Dayan (Great Expansion) divination, completing the numbers of Qian, Kun, and all things with 384 lines and 11,520 straws. In Luoshu, Yang is Sovereign, Yin is Minister; Sovereign is central, Minister is lateral. Hence, Wear Nine, Tread One, Left Three, Right Seven, Two/Four Shoulders, Six/Eight Feet, Five in Center. Vertical/horizontal sums are fifteen. One in North, plus Center Six, plus South Nine equals fifteen. Three in East, plus Center Eight, plus West Seven equals fifteen. Two in Southwest, plus Center Seven, plus Northeast Eight equals fifteen. Four in Southeast, plus Center Nine, plus Northwest Six equals fifteen. Yu the Great modeled this to arrange the Nine Categories: One Five Elements, Two Five Affairs, Three Eight Administrations, Four Five Chronologies, Five Imperial Norm, Six Three Virtues, Seven Divination Doubts, Eight Various Omens, Nine Fortune/Virtue. Imperial Norm is central, others surround. Hetu numbers discuss completeness via Generation/Completion, prioritizing Generation, totaling 55. Luoshu numbers discuss variation via Odd/Even, prioritizing Four Cardinals' Yang, totaling 45. Combining Hetu and Luoshu makes 100, the complete natural number of Heaven and Earth. Though differing, their principles alternate, so Heaven/Earth numbers start at One and complete at Ten. Heaven Numbers are Five: 1, 3, 5, 7, 9. Earth Numbers are Five: 2, 4, 6, 8, 10. Heaven Sum is 25 (5x5); Earth Sum is 30 (6x5). Small Yan is 10 (2x5); Great Yan is 50 (10x5). Hence Five is the Ancestor of Numbers. Shao Yong said: Heaven/Earth root in the Center. The Center numbers are Five and Six. Five is among 1,3,7,9, hence Five is Heavenly Center, Master of Generating Numbers. Six is among 2,4,8,10, hence Six is Earthly Center, Master of Completing Numbers. *Tian Yuan Ji Da Lun* states: Heaven uses Six as rhythm, Earth uses Five as system. Thus, all pentad numbers rely on Five and Six. Their variations are evident: Early spring peach blossoms have five petals (Heaven's generation); deep winter snowflakes have six arms (Earth's completion). Is creation's wonder accidental? Regarding Five: Heaven has Five Stars, Earth has Five Mountains, Humans have Five Constants, plus Five Colors, Flavors, Grains, Animals—all are Five. Ten roots in One, Hundred in Ten, down to tiny units, up to infinite billions, all transform from Five and unify under Heaven's Five Center. Regarding Six: Heaven has Six Directions, Year has Six Qi, Hexagrams have Six Lines, plus Six Pitchpipes, Six Stems, Six Arts—all are Six. Lao Yang number 36, Lao Yin 24, sum 60. Shao Yang 28, Shao Yin 32, sum 60. All transform from Six and unify under Earth's Six Center. Ultimately, Five is Yang but unifies Yin's Six; Six is Yin but regulates Yang's Five. *Tian Yuan Ji Da Lun* states: To know Heaven/Earth Yin/Yang, Heaven's Qi moves incessantly, shifting right every five years; Earth's Qi stays static, circling every six periods. Five/Six combine, 720 Qi make one Ji (Cycle). Are not Heaven/Earth Qi generated by Five/Six? Consider one year's Qi and Gan-Zhi: Using Heavenly Stems, five days per pentad, five Yin/five Yang, hence Ten Stems. Jia/Wu change by Yang, Ji/Gui by Yin, variation of Five. Using Earthly Branches, six days per change, six Gang/Rou, hence Twelve Branches. Zi/Si change by Yang, Wu/Hai by Yin, variation of Six. Ten Stems correspond to Days; Twelve Branches to Months. So monthly count is 2x6=12; daily count in a month is 6x5=30; annual Qi count is 4x6=24; pentad count per Qi is 3x5=3. Total year: 36 Jia cycles with Heaven's Five; 30 Zi cycles with Earth's Six. Hence 12 Months (2x6), 24 Solar Terms (15 days x 24 = 360), 72 Pentads (5 days x 72 = 360), 360 Days (30 days x 12), 4320 Chen (12 Chen x 360 days), 129,600 Fen (360 days x 360 fen). None is not transformed by Five/Six. One year's number is so; Yuan/Hui/Yun/Shi numbers are also so. One year governs 12 months; one month 30 days; one day 12 hours; one hour 30 fen. Thus, One Yuan governs 12 Hui; one Hui 30 Yun; one Yun 12 Shi; one Shi 30 years. The Dao of Heaven/Earth Qi and Luck is summarized here. Number studies are versatile, covering the universe broadly and hairs finely. Splitting One to Two, Two to Four, Four to Eight... endless. Like root to trunk to branch, more becomes finer, finer becomes complex, boundless yet each holds a part. All images on earth, forms on ground, spirits in darkness adhere to Number. Ancient Kings examined Hetu/Luoshu, named Odd/Even, measured Heaven by degrees, Earth by li, Spirits by Yin/Yang, Climate by Pitchpipes, Weight by Balance, Shape by Compass/Square, Length by Measure, Depth by Vessel, Division/Multiplication by Number. Looking up/down, high/low, heaven/earth, vast Qi/tiny atoms, can any escape Number? Viewing humans from Heaven/Earth, humans are one grain in a granary; viewing Heaven/Earth from Number, they are one object in Number. Is Number easy to discuss? If understood, hidden/clear, high/low connect; Heaven/Earth vastness, Image/Number multitude, can be deduced from One. Those who understand this, since sages, only Kangjie Xiansheng (Shao Yong).