The I Ching's Placement Method: Unraveling Ancient Chinese Calendar Secrets

2. The Five Positions Mutually Obtain

The Appended Statements says: "Heavenly number five, earthly number five, the five positions mutually obtain and each has unions." Ancient annotations are confused, none clear. What exactly is "five positions mutually obtain"? It is the body model of the nine-palace calendar algorithm. The Yi's ten numbers form the body, eight and nine for use. The innate eight trigrams' body is the "five positions mutually obtain," namely the "one-two, three-four, five-six, seven-eight, nine-ten" ones. What does it unite with "each has unions"? Obviously, it unites with the "one-six, two-seven, three-eight, four-nine, five-ten" ones, namely the ten-number River Map. These two differ yet work together in numerology. Also, according to the Qing dynasty Jiang's "Fire-Gold Yi Positions" view, the River Luo system shares the same source. Thus, the "five positions mutually obtain" ones also unite with the River Map and Luo Book.

The "five positions mutually obtain," precisely four images generate eight trigrams, the middle palace's "void" as well. If the Yi has no void, it cannot accommodate, nor change. The innate eight trigrams is a dynamic composite model; its secret in application lies in one union one open: union changes to four-image state, middle void, ten numbers use its eight, different structure from River Map; open changes to nine-palace state, heaven nine stands in middle, ten numbers use its nine, different structure from Luo Book. In short, the innate eight trigrams' open-union use, void-real changes, eight-nine never leave ten. If not studying the "five positions mutually obtain" body model, there is no way to grasp the innate eight trigrams' application mechanism and its life-death relation with River Luo.

The Appended Statements says: "Eight trigrams form columns, images reside within and complete." What natural great phenomena does the innate eight trigrams conceal? Sun and moon come and go, day and night alternate, cold and heat succeed, yin and yang sun lacks; all great nature's myriad changes have fixed numbers. Research shows, the River Luo body is precisely the sun-east moon-west "small cosmic cycle" numerical model; the eight trigrams body is the sun-moon union "great cosmic cycle" numerical model. The Zhou Yi's combination numerology of these two great image-number models all derives from the nine-palace algorithm of "participate odd with change, complex its numbers." River Map mainly even numbers, Luo Book mainly odd number tiers, innate eight trigrams also both odd and even. The River Luo model can only solve the full-state structure body of odd squares, while the vanishing state structure body of odd squares is unique to the eight trigrams model. Hence "eight trigrams, River Map ten Luo Book." If deriving all possible solutions of each tier calculation problems according to the eight trigrams model, its elements' "participate odd" changes can all express "balance one vanish one balance" one great cycle movement.

Calendar calculation's research object is the sun-earth-moon system celestial phenomena; they each have relatively independent running cycles with non-integral nature. In ancient times with only grasping "establish winter solstice measurement influence" technology, using "year month day" integral standard units to integrate sun-moon view movement's space relations is no easy task. But our ancestors brilliantly created the "participate odd" algorithm and change method, establishing a nine-palace calendar algorithm, namely the Zhou Yi stalk method, solving the difficulty "placement leap" issue in calendar calculation. Experts believe: the innate eight trigrams nine-palace calculation is the most appropriate numerical form and method to solve natural world non-uniform object body balance state movement systems; the stalk method correctly grasps the approximation object's tier conditions, thus the four-image state eight trigrams (second order) model as fourth-order evolution can precisely calendar patterns. The Appended Statements says: "Extend it and it reaches, touch a class and it grows"; if applying nine-palace state eight trigrams (third order) model, it can correctly measure solar system planets' orbit parameters. This is the scientific principle of the placement method.

3. Pre-Placement: The Great Derivative's Number

The Appended Statements says: "The great derivative's number fifty, its use forty-nine." This is a pre-placement program of the stalk method, must clarify the following two basic issues: first, how does the great derivative number come? What does it represent? Second, why use forty-nine? What does the "not used" one stalk represent? This is another mystery of the Yi placement.

"Fifty" is the base number of the placement method's evolution; how is it derived? There are several theories: one is River Luo theory, two is Taiji theory, three is heaven-earth number theory, four is yarrow stalk theory, five is square garden theory, etc. Zhu Jia's Zhou Yi Original Meaning says: "In the River Map middle position, heaven five times earth ten obtains it." This saying is correct but unexplained. Research shows, River Map has void in middle, but "void" does not mean non-existence; "heaven five earth ten" is a middle parameter, this differs from Luo Book's "middle five" in principle. The difference between the two lies in: Luo Book is a third-order odd square, hence "middle five" is a real fixed number; while River Map is only a second-order model, hence "heaven five earth ten" is a latent parameter. The innate eight trigrams dynamic composite model center is a mysterious void; in application, it unites with River Map and Luo Book's middle positions "each has unions." Placement method now with eight trigrams evolves fourth order, each of the four images one element can form a middle second-order in single unit, its four elements sum fixed namely "34." But the specific four elements of fourth-order middle are variable; how many variable states does it have? Answer: "heaven five times earth ten" fifty variable states. At this time, eight trigrams middle unites with River Map, its "heaven five earth ten" becomes a manifest parameter. Hence the said "great derivative's number fifty," refers to the fourth-order middle composite's fifty change states. Experts in fourth-order odd square all solutions, search four images full-state odd square patterns have thirty-six states, four images vanishing state odd square patterns have forty-eight states, non-repeating count fifty states, can prove the "great derivative number" without error.

The middle is the core of odd squares, one moves and hundred move; hence the middle's change like the nine-palace calculation's key lock. Placement with fourth-order fifty middle evolutions, visible its algorithm's brilliance. The importance of evolving from middle lies in the fourth-order middle being the placement method's precise sun-moon two-body movement cycle "integration" relation positioning coordinate; this means calculating fourth-order related elements in middle second-order in single unit's positioning order number is the key issue of calendar calculation.

Why great derivative number fifty but use forty-nine? This is not the placement method's contrived mystery; the "not used" one stalk regarding calendar means the "re-remainder" part of time within eight heavy hexagrams (fourth order) calendar length. In the four operations main program, four times divide integration, remainder, re-remainder three parts time. The pre-placement pre-raised "re-remainder" time will with hang one "re-remainder" part together in post-stalk processing. Why do these two parts "re-remainder" times need another "first spoil then hang" post-stem program? Because great derivative's number fifty, pre-placement "not used" one stalk, and before four operations insert four first "hang" one stalk; this operation method matches the middle change of forty-eight states of four images vanishing state odd square patterns, so represents the two parts time of "re-remainder," in nine-palace calculation already confirmed as non-"integration," namely no corresponding fourth-order odd square graph exists, while post-stalk "five years leap again" is only a conventional arrangement of calendar method. In short, if pre-placement not first raise this one stalk, fourth-order evolution would be chaotic, and also affect the objective description of sun-moon view movement space changes.

4. Four Operations Main Program

The Appended Statements says: "Divide and as two with image two, hang one with image three, insert it with four with image four times, return odd to spoil with image forty. ... Thus four operations form the Yi, eighteen changes form hexagram, eight hexagrams form small achievement." This is the four operations main program, including "divide two, hang one, insert four, return odd" four operations. Stem method evolution, one change four operations, three changes one turn, eighteen changes form one hexagram. The Placement Branches is very familiar with the operation method of four operations, this article no longer verbose. But Placement Method evolves eight heavy hexagrams, its meaning differs from Placement Branches "divination hexagram" concept, so should focus on deep internal coverage of four operations eighteen changes. (1) Divide two: With middle position (Taiji) change image sign sun-moon (two stems) running's vanishing process, here not the probability issue divination emphasizes. (2) Hang one: This is in divide two's right side pre-raised time "re-remainder" part, to be placed in post-placement this one stalk. (3) Insert four: This is "year month day" four times' integration standard, one over-insert represents one "integration" unit; insert remainder as non-integration's "remainder" time. (4) Return odd: Refers insert remainder's stalk in this program placement.

How to read the four operations main program? In this program, nine-palace calendar's content includes two aspects: first, operate four "integration" parts; second, return odd "image forty" part. Hang one "re-remainder" part in post-placement another read. Reading method can be simple and concise, experts use "four operations seek old young" method read it.

Three changes "four operations" seek old young: old yang 36 stalks, young yin 32 stalks, young yang 28 stalks, old yin 24 stalks. The Say Hexagram says: "Sufferers and holy people's make Yi also, admire praise to divine clarity and born divination, participate heaven two earth and depend numbers, observe change yin yang and establish hexagram." Precisely this saying, two old "depend numbers," namely fixed "participate heaven two earth" great rules; two young "establish hexagram," namely "observe change yin yang" and evolve Yi. Diviners crudely use only two young "divination hexagram" methods. But what is "participate two"? How "depend numbers"? Diviners place two old in disregard, ancient annotations also fall into "divination hexagram" old trap. "Participate two" is two old's "integration" ratio, old yang as "participate heaven," old yin as "two earth," use it as nine-palace calculation great rules. The said "participate heaven two earth and depend numbers," refers system four times "integration" number and "leap remainder" number. Old yang over-insert 36 stalks, insert 19 as nine "integration" units. So sixty-four hexagrams three hundred eighty-four turns calculate 389×9=3456, old yin "two earth" rule it 3456×2=6912 "integration" units, this refers to 6912 fourth-order odd square graphs. Old yang insert remainder 12 stalks (return odd), but its "time" capacity different, over-insert stalks one as one, while return odd stalks with twelve as one, so one turn actually counts one stalk. Sixty-four hexagrams three hundred eighty-four turns return odd "remainder" 384 stalks, insert it with four "integration" place leap 96, corresponding to another exist 96 fourth-order "image forty" odd square graphs.

From this know, stem method total seeks out 7008 fourth-order odd squares (including eight preserve pure images) all possible solutions.

Sixty-four hexagrams placement 96, then calendar time four hundred years. One turn represents one year, sixty-four hexagrams 384 years. But why say sixty-four hexagrams model has four hundred years calendar length? This is because before insert four one turn three changes hang three stalks, plus pre-spoil middle "not used" one stalk, these four stalks "re-remainder" time span sixteen years, so 384+16=400 years, this is the placement method's calendar length.

5. Qian Kun Stalk Numbers

The Appended Statements says: "Qian stalks two hundred eleven thousand six hundred, Kun stalks one hundred forty thousand nine hundred four." Qian Kun's stalks are the placement method's four times "integration" parameters, thus more deeply revealing the intrinsic mechanism of nine-palace calendar. Placement method fourth-order evolution, set middle second-order sub-unit as four times "integration" standard position, thereby establishing a precise coordinate for approximating sun-moon view movement cycles. In this fourth-order calendar coordinate, sixteen elements on sixteen digit positions' positioning opportunities mutually vanish, and in the entire vanishing process must have one element reach the highest balance point, experts call this element the four times "integration" standard quantity. When this standard quantity no element on four standard positions positioning, it certainly will have equal opportunity on other twelve positions positioning, hence represents four times "integration." When this standard quantity element on other twelve positions positioning, and no opportunity on four standard positions positioning, then represents four times "non-integration" leap remainder. This is the placement method's nine-palace calendar mechanism.

Qian 216 stalks, with old yang over-insert 36 stalks times six turns obtain it, experts call it heaven stalks. Fourth-order sixteen elements in positioning vanishing process reach highest balance point that standard quantity element, on sixteen digit positions equal positioning times namely 216 Qian stalks, thus represents earth public rotation and self-rotation cycle's "integration" relation, namely one year is 365 days' integer part. By this calculate: 216 × 16=3456 fourth-order odd squares, this matches old yang nine insert times sixty-four hexagrams three hundred eighty-four turns calculated. This odd square pattern as four images vanishing state structure body (four images vanishing area 1-12), its other fifteen elements on sixteen digit positions' positioning opportunities unequal.

Old yin "two" rule calculate, obtain another 3456 fourth-order odd square patterns, all full-state structure bodies (each image sum value "34"), its sixteen elements on sixteen digit positions equal positioning 216 times, this also is Qian's stalk number. In placement method fourth-order calendar coordinate, this group odd squares represents four times "integration" initial balance point, or say four hundred years calendar length's starting calculation point, at this moment "time" in no gain no loss state.

What number is the standard quantity element? In this part return odd image forty 96 corresponding fourth-order odd squares this standard quantity element again how positioning? This is nine-palace calendar algorithm's key issue. For convenience of deeper analysis, experts put 3456+96=3552 fourth-order four images vanishing state odd square sixteen elements' positioning opportunity list as below:

This table setting: sixteen digit positions divide into "middle, four corners, eight dimensions" three areas, middle four elements' fifty states divide into "parallel, intersect" two big classes (parallel middle 26, intersect middle 24), then by area classify search each element on each digit position's positioning times. According to table shown element positioning data analysis: in parallel middle conditions, each pair corresponding two elements in each area positioning times have symmetry; while in intersect middle conditions then asymmetric positioning. Table with bold line marked "6-11" six elements, match insert times in three changes, visible this is placement method's algorithm interval.

Qian stalks 216 position outside algorithm interval margin, corresponding to "12" and "5" two elements, who is standard quantity element? Element "12" in middle 216 times, four corners 208 times, eight dimensions 232 times, namely in three areas experts on equal opportunity less than 216 Qian stalks, hence "12" not standard quantity element. Element "5" in middle each position positioning 216 times, in four corners and eight dimensions each position positioning 224 times, from this visible element "5" on sixteen digit positions can equal positioning 216 Qian stalks, while other elements cannot reach this highest balance point. Undoubtedly heaven stalks match heaven number, "5" as Qian stalks standard quantity element. Heaven number "5" in four corners and eight dimensions twelve digit positions' each position than middle area more out 224-216=8 times positioning opportunity, calculate 12×8=96 fourth-order four images vanishing state odd squares. Because standard quantity element cannot enter four times "integration" standard position (refer middle), hence represents 96 odd squares are four times "non-integration" leap remainder part.

Kun stalks 144, with old yin over-insert 24 stalks times six turns obtain it, experts call it earth stalks. From table check know, Kun stalks position in placement method algorithm interval within, it represents in entire 3552 fourth-order four images vanishing state odd square group, sixteen elements on experts all reach equal positioning opportunity 144 times, calculate 144×16=2304 odd squares. What special meaning do this part odd squares have? According to structure analysis, they with four images full-state odd square group special exist 2304 odd squares "eight dimensions" change relation, thus Kun stalks reveals fourth-order odd square from four images vanishing to four images full-state's transformation rules. For convenience of examination, experts according to four images structure and its composite nature, display fourth-order odd square all solutions' classification table as below:

Placement method fourth-order evolve eight trigrams, only a counting method, as for fourth-order odd square's structure graph method, can adopt middle structure graph method, or four images structure graph etc., simulate eight trigrams model synthesis.

6. Post-Stalk: Five Years Leap Again

The Appended Statements says: "Five years leap again, hence first spoil and then hang." This is another supplementary algorithm started, experts call it post-spoil. The Stem Branches avoids talking about this, ancient annotations also not clear its algorithm, but this special one change in calendar to crucial importance.

Post-spoil only one change, and change method as "first spoil then hang," this differs greatly from four operations main program. This one change's stalk number source: one is pre-spoil middle "not used" one stalk; two is four operations main program each change "hang one," one turn three changes count three stalks. Combine four stalks, this is placement leap "96" after's "re-remainder" time. How place this other head? Placement method ingeniously change algorithm program, neither divide one, nor hang one, but "first spoil," namely insert it with four "image forty." The said "post-hang," actually already no stalk to hang. Calendar method again how arrange this one leap? Called "five years leap again," this refers to the fourth century year placement leap. Because 396 year is leap year, 400 year also leap year, namely five years two heads have leap, hence last one mouth called "five years leap again." Front three century years all insufficient placement leap. From this know, three changes "hang one" three stalks are front three hundred years' "re-remainder," pre-spoil "not used" one stalk is after one hundred years' "re-remainder," these two parts other head time together in last one century year placement. Placement method every four years place one leap, 384 years 96 leaps, four century years time span sixteen years only place one leap.

Sum up above, placement method in four hundred years calendar length within total set ninety-seven intervals, hence one year is 365(97/400) days, namely 365.2425 days. According to modern calendar data says: one year is 365.2422 days. So, placement method one year average more calculate 0.0003 days, namely 0.108 seconds. According to report: 2000 year new millennium "advance" arrive, this time difference will need design a quite long calendar unit to "integration."

How does nine-palace calculation reflect "leap again" issue? Four operations main program placement 96 is sufficient's, hence have "image forty" 96 fourth-order odd squares exist. While "five years leap again" slightly insufficient, fourth century year placement leap is a calendar conventional arrangement, hence no exist corresponding to this one leap fourth-order odd square graph. Placement method therefore start another supplementary algorithm program's reason cover from this. Post-spoil only incomplete one change, while one turn is three changes, hence "first spoil then hang" not occupy one turn, diviners basically unknow its reason. According to middle search, except "great derivative's number fifty" states, another have two kinds match eight trigrams model "mutual generate mutual become" method's composites, namely "1,2,15,16" and "1,3,14,16." But these two middles yet cannot form fourth-order odd square image, this is "re-remainder" part insufficient "integration" placement's nine-palace calculation expression method.