Hetu 河圖 as more plausibly an abacus to arrive to the 25,920-year Great Year, the
129,600-year Shao Yung cycle, with perhaps a surprisingly different outcome for the
Galactic Year than a usually estimated 225 million years. Set aside Hetu 5 and 10
to multiply-divide Hetu numbers; do the same for Luoshu and Kanagi Guruma.
360 : 5 = 72 x 360 = 25,920
360 : 10 = 36 x 360 = 12,960 x 10 = 129,600
Canonical – not intended for application in
9 Ki Divination event forecasting
Nine Star Ki Astrology
Flying Star Feng Shui
Hold on to your chair
It’s not improbable that you will here gain new esteem for Hetu Yellow River Map 河圖[1].
This time as it was truly intended, although this may go against what perhaps we had seen before on the subject in literature or studies.
With the difference that this time – the ancients no backward folk – you can check the accuracy with your desk calculator.
It is how you can imagine now that indeed it would have – somewhere 1996 – paid off to sit with pen and beer mat on just some lost weekday Sunday, as now as a first it unfolds a systematic Hetu methodology in ways not acknowledged quite like now.
We may finally uncover the – as would only seem so intended – direct link between Hetu Yellow River Map and then Galactic Cycles, which will become an adventure, as now in new ways Hetu will become a turbine, using Hetu numbers and Hetu pairings for timing of the Great Year, the Great Shao Yung Cycle and the Galactic – Cosmic – year.
Gradually over time, Hetu has become obscured with ‘finger pointing to the moon’-style correlations, which could only distract from its essence, much of that deliberate.
As already master Céng Gōng Ān – 曾公安 – had us forewarned: if the
emperor ordered his scholar to change the actual astronomy to come up
with a Red Herring only to ‘create a state of confusion’ (dian dao 顛倒) for
‘foreigners’ 外國’, we may care to quit wanting to play such foreigner.
Or, as only recently one Chinese master had it on the equally
faulty Ming Gua 命卦 system as devised by monk Yi Xing 一行 (to
change 9 Star Ki birth Stars for females born in the same year
as males) and Bazhai Feng Shui 八宅風水:
‘Yes, we know that it is in fact a false system, but let’s just say that,
if still 60% of it works, why not continue to teach it’.
That should make one stop and think.
To put everything into perspective and to lay bare Hetu’s core relevance, let’s bear in mind that, at the end of the day, what really matters in Oriental metaphysics and in our varying systems of application:
The Great Year of 25,920 years.
Earth’s axial precession.
The Great Cycle (Yuán 元) of 129,600 years[2].
The Galactic Year of ± 225 million years.
Solar system orbit around the center of the Milky Way Galaxy.
All this, from the get-go, lies firmly ingrained within Hetu Yellow River map, now that its numbers 5 and 10 serve as its factors, until Hetu comes as an abacus – suànpán 算盤 -, to get to these cosmic cycles, which may not be in line with the widespread assumption as if the numbers in Hetu were 9 Stars, just as the 9 Stars in Luoshu would be persistently considered numbers, while:
Hetu 9 numbers are not as so presumed Luoshu 9 Stars
Luoshu 9 Stars are not as so presumed Hetu numbers
Which is for reason now that as it is:
Luoshu once for purpose of 9 Stars is magic square in nothing
Magic square once for purpose of numerology is Luoshu in nothing
Yet, such Hetu pairings as between 1-6; 2-7; 3-8 and 4-9 would be widely taken for 9 Star combinations, until no matter in Nine Star Ki or Flying Star Feng Shui, it would be assigned these number combinations energetic significance if they appeared in an annual- and monthly Luoshu for purpose of 9 Ki Divination 九星占卜 (9 Stars and Luoshu event forecasting), or in our Flying Star chart for purpose of house divination in Fei Xing Feng Shui, while each time more faithfully in Hetu, the difference would be a mere arithmetic value of 5.
That’s quantity mistaken for quality (Qi 氣) and quality (九星) for quantity.
Even though the most commonly cited duration for the Great Year may vary (25,800-25,920 years), mere Hetu calculations will finally show the intended range as 25,920 years.
To make such time cycles more manageable in our application of for example 9 Stars and Luoshu event forecasting, for purpose of 9 Ki we can reduce them to smaller portions until we arrive at 81 year cycles and 9 year cycles (these not to be confused with the San Yuan Jiu Yun 三元九運 calendar and time reckoning in use for purpose of Fei Xing Feng Shui 飛星風水, which lets 9 Stars abide by 9 portions of 20 year Periods and fails to arrive at 9 or 9 x 9 = 81).
81 year cycle 9 year cycle
Star 3 1712-1792 Star 2 2018-2026
Star 2 1793-1873 Star 1 2027-2035
Star 1 1874-1954 Star 9 2036-2044
Star 9 1955-2035 Star 8 2045-2053
Star 8 2036-2116 Star 7 2054-2062
Let’s no longer delay and immediately get to the calculations.
While as an aside and for the betterment of students, clients and our industry, teachers and professional consultants are warmly invited to reconsider whether Hetu would have provided for a) compass directions or b) Wuxing significance, as the list of other such correlations goes on indefinitely.
It’s just that, once you got started with this, your head will spin with such a barrage of variables, each time relative to how we may alternately divide 360 by 5, 10, 72, 144, or using 12, 24, 30, the zodiacal month of 216[3], or the 24 Solar Terms or 28 Lunar Mansions. You will also find 2,160 for the zodiacal age, then as the pivot 1,008 years, where a period reaches its peak before it starts to decrease.
Further down we will see the significance of 1,728 and 8,640, which may however soon alter how we came to see the duration of the ‘225 million’ years to the Galactic Year.
The sum of the outer Hetu numbers is 40:
1 + 6 + 2 + 7 + 3 + 8 + 4 + 9 = 40.
129,600 : 40 = 3,240[4], a key divisor in ancient calendars.
Hetu center 5 and 10 added give 15.
25,920 : 15 = 1,728 (key factor in metrology).
Pending method of division we can arrive to 25,920 or 129,600 base-9, base-12.
12 x 12 = 144 x 9 = 1,296
25,920 : 216 = 120
25,920 : 144 = 180
We nonetheless first convert the square representation of Hetu into a circle to denote 360 years.
We then multiply or divide Hetu numbers and Hetu Pairings by 5 or 10.
For example as in 360 : 5 = 72 years, then that multiplied by Hetu numbers and other such values.
As seen from the earth’s wobble due to axial rotation, the stars and constellations move westward by 1 degree every 72 years.
Well, 72 years x again 360 years will then give 25,920 years for the Precession Cycle, or Great Year – aka Platonic Year -, while we can also take 10:
Precession calendar
Using Hetu 5 as our calculation factor:
360 : 5 = 72 x 360 = 25,920.
360 : 5 = 72 x 360 = 25,920 x 5 = 129,600.
360 : 5 = 72 x 4 x 9 x 10 = 25,920.
Using Hetu 10 (2 x 5 implied) as our calculation factor:
360 : 10 = 36 x 360 = 12,960 x 2 (one round Yin, one round Yang) = 25,920.
360 : 10 = 36 x 360 = 12,960 x 10 = 129,600.
360 : 10 = 36 x 4 x 9 x 10 = 129,600.
Note that, if then we did 12,960 x Hetu 10 we get to the Great Cycle, i.e. 129,600 years as attributed to Shao Yun 邵雍[5] or same difference, as we may divide 129,600 years by 12 to get to the 12 epochs (Hui 會) of 10,800 years.
On the whole, Hetu is a mathematical structure seemingly designed to map the Solar cycle and Lunar cycle to come to the Great Year Precession cycle [25,920 years] and eventually the Great Yuan cycle [129,600 years].
The approach therefore can be one time into the Solar cycle, the other time into the Lunar cycle along values as 1008 or 3600, which were not even considering 64 Hexagrams in light of cosmic time cycles.
All values after multiplication here and henceforth are a round and a double round – dual cycle – i.e., values can be further multiplied to eventually give either 25,920 years for the Great Year or 129,600 years for the Shao Yong Yuan 元.
Zodiacal calendar
Using Hetu 5 as our multiplication factor to arrive to the 3,600 years:
360 x 5 = 1800 x 2 (Yin and Yang cycle) = 3600 for the Zodiacal Epoch, or using Hetu 10 as a multiplication factor right away: 360 x 10 = 3600.
Everything with zodiacal significance:
Hetu at the ‘Water’ domain
The Hetu ‘Water’ domain handles number 1 and 6 that can be read as a factor multiplied by either Hetu 10 or 5, then x 1 x 6 = 216 which is the cubic seed of the 2160 year age. We’ll first see how we arrive at 216, which is known as Great Month 大月, i.e. 12 x 2160 = 25,920.
360 : 10 = 36 x 1 x 6 = 216.
216 x 10 = 2,160 years.
216 x 5 = 1,080 years.
216 x 120 (15 x 8 Luoshu Palaces) = 25,920 years.
Hetu at the ‘Metal’ domain
The Hetu ‘Metal’ domain handles number 4 and number 9, which can be read as a certain factor then multiplied by Hetu 10 x 4 x 9 = 144. We’ll first see how we arrive at 144.
360 : 10 = 36 x 4 = 144. 144 x 9 = 1,296.
360 : 10 = 36 x 4 x 9 = 1,296.
1,296 x 10 = 12,960 x 2 = 25,920.
1,296 x 5 = 6,480 years (x 2 = 12,960).
12,960 x 10 = 129,600.
144 x 5 x 4 x 9 = 25,920.
Hetu at the ‘Wood’ domain
The Hetu ‘Wood’ domain handles number 3 and number 8 that can be read as a certain factor then multiplied by Hetu 5 x 3 x 8 = 120.
360 : 10 = 36 x 3 = 108. 108 x 9 = 972. 10,800 years is one Hui 會 (epoch) x 12 (named after the Twelve Earthly Branches dìzhī 地支) = 129,600.
360 : 10 = 36 x 3 x 8 = 864 x 30 = 25,920 years.
108 x 10 = 1,080.
1,080 x 5 = 5,400 years (x 2 = 10,800 – Hui 會 sub-cycle of Great Year).
1,080 x 3 x 8 = 25,920.
144 x 5 x 3 = 2,160.
Hetu at the ‘Fire’ domain
The Hetu ‘Fire’ domain handles number 2 and number 7, while here we use sum instead of product, as in 2 + 7 = 9, such as 144 x 9 (coming from 2 + 7 = 9) = 1,296.
1,296 x 5 = 6,480 years (x 2 = 12,960).
12,960 x 10 = 129,600.
360 : 10 = 36 x 2 x 7 = 504 x 2 = 1,008.
360 : 5 = 72 x 2 x 7 = 1,008
36 x 360 = 12,960 x 2 = 25,920.
All this would hardly introduce the invention of a new model, as rather more we may appreciate how Hetu would have been waiting all along to unveil its message for everyone to see.
It then took little more than our receptive, all-expectant approach as if it were the first time, so that we stepped aside to let Hetu ‘do the talking’, which then – just as Luoshu would – it will do, probably only now that this time we gave it space to do so, only this time showing the true face of Hetu numbers 5 and 10, then the Hetu pairings, not so much as local remedies, unfounded correlations or decoys, but indeed Hetu as a deliberate mathematical panoramic calculation model, intended so that finally we could marvel at the inherently embedded 25,920-year Great Year for the Precession Cycle, Shao Yung’s 129,600 years and the ‘so-many millions of years’ (see below) Galactic Year.
How about Luoshu 洛書
We will, for the occasion, move from Luoshu for 9 Stars to magic square for numbers.
We say that ‘5 generates; 10 completes the process.’
All opposite numbers in Luoshu add to 10, while the sum of every row, column and diagonal in Luoshu is 15.
Number 5 aside, all outer numbers in Luoshu add to 40:
4 + 9 + 2 + 7 + 6 + 1 + 8 + 3 = 40.
We recognize clusters in Luoshu between 1-4-7, 2-5-8 and 3-6-9.
1-4-7 added give 12 360 : 12 = 30
2-5-8 added give 15 360 : 15 = 24
3-6-9 added give 18 360 : 18 = 20
Luoshu by its moving magic constant 15, bridges Hetu, by squaring Luoshu 15 and the power of 10, to arrive at 225 million years for the Galactic Year.
To get to the Galactic Year, we may do 152 x 106 = 225,000,000.
In Luoshu the 9 Stars are ‘walking’ in nines, while it fits in cycles of 12, such as for the Chinese zodiac, where every solar year 3 months repeat with the same 9 Star.
It’s where 9 Stars and the Chinese Zodiac (animals) meet, as we will appreciate, now that certain zodiac signs will be 1-4-7, 2-5-8 and 3-6-9 in terms of 9 Ki years, months and days always.
360 : 5 = 72 x 3 = 216 x 6 = 1,296 x 10 = 12,960 x 2 = 25,920.
360 : 5 = 72 x 2 = 144 x 5 = 720 x 36 = 25,920.
72 x 24 = 1,728 : 12 = 144 x 9 = 1,296 x 10 = 12,960 x 2 = 25,920.
How about Kanagi Guruma
Kanagi Guruma may be considered the world’s oldest calendar, while it will get us to 225 million years.
To complete Kanagi Guruma, sketch Luoshu of 5 Yellow as if it unfolded into 9 subsquares, while take one digit Luoshu numbers to the ‘Water’ sections of each subsquare.
Proceed from the usual ‘Luoshu pattern’, adding 9 each time to complete each subsquare (numbers cannot exceed 81).
My pal Andy Nicola and I were always busy calculating Galactic cycles using 9 Stars and Luoshu, then Kanagi Guruma, while this once-in-a-lifetime-only expert would devise not only your 9 x 9 = 81 Kanagi Guruma destiny chart, but a 9 x 9 x 9 = 729 destiny chart, until no wall in his house could accommodate his 6,561 units chart:
Luoshu 9 units used for annual Stars.
9 x 9 = 81 units used for annual- and monthly Stars.
9 x 9 x 9 = 729 units annual-, monthly- and daily Stars.
81 x 81 = 6,561 units annual-, monthly-, daily- and hourly Stars.
Here – just as earlier we dismissed central 5 from Luoshu -, use Kanagi Guruma Magic Number 81 minus central unit = 80.
129,600 : 80 = 1,620 x 5 = 25,920.
80 x 9 = 720 x 1 x 6 = 4,320 : 2 = 2,160 x 12 = 25,920.
80 x 9 = 720 x 2 x 7 = 10,080.
80 x 9 = 720 x 3 x 8 = 17,280 (Satya Yuga) : 80 = 216.
80 x 9 = 720 x 4 x 9 = 25,920.
All central units vertically, horizontally and diagonally add to 123:
40 + 41 + 42 = 123.
45 + 41 + 37 = 123.
38 + 41 + 80 = 123.
39 + 41 + 44 = 123.
This is what made number 369 significant as ‘number of days’ to a year in ancient lunar-solar calendric timing, as years were varyingly 12 or 13 months in length, while so as to arrive back to 365 days, we take away ‘1’ each time as we horizontally, vertically or diagonally pass through the center.
Marking seasons
Numbers ending in 1 in Kanagi Guruma – indicated by larger black dots – bode yet special significance concerning time, as they may be taken to mark the beginning of seasons, the Equinoxes and Solstices. Smaller dots are to mark the position of number 5.
Going clockwise from bottom number 1:
# Direction Northern Hemisphere Southern Hemisphere
1 North December Solstice December Solstice
71 Northeast Beginning of Spring Beginning of Autumn
21 East March Equinox March Equinox
31 Southeast Beginning of Summer Beginning of Winter
81 South June Solstice June Solstice
11 Southwest Beginning of Autumn Beginning of Spring
61 West September Equinox September Equinox
51 Northwest Beginning of Winter Beginning of Summer
1 + 11 + 21 + 31 + 51 + 61 + 71 + 81 + central Number 41 = 369.
That may be everything here my own estimate, while as it is -, at least if based in Hetu, Luoshu and Kanagi Guruma related arithmetics -, an otherwise approximated 225 million years for Galactic year, would seem to come to – give or take uncertainty margin – a plausible 223.948,800 years.
On closer examination
Galactic Year 223.948.800 years – inevitably!
In conclusion, and even though Hetu calculations would suggest much more accurate outcomes, the values we used so far do not seem to directly provide for the Galactic year of – an estimated – 225 million years, while we might still not feel satisfied with such an estimate.
Several of my calculations then weirdly started showing differently as a rather more exact 223,948,800 years, while to achieve this, we still use Hetu, this time over the numbers 1.728 and 8,640 – our Harmonic Ideals.
Until building this article, I was not familiar with these numbers, while in astronomy and mathematics 1.728 and 8,640 are highly esteemed as fundamental constants, the transition from linear to cubic harmony in sacred geometry.
I will spill examples, keeping in mind of course always the uncertainty factor, if due only to the mass of the Milky Way, the distribution of dark matter, or the fact that the Milky Way itself changes.
The numbers 1,728 and 8,640 are significant harmonic constants that bridge the gap between human timekeeping, such as for seconds and days, and cosmic cycles such as for the Great Year.
If we keep to Hetu calculations however, number 223,948,800 acts as a macro-octave of the Shao Yung cycle, where number 216 becomes critical, as goes for 1,729 and 8,640.
Number 216 (63) is the cubic root of the Precession Cycle, as it gives 2,160 years for each zodiac sign:
1 x 6 x 6 = 216.
1 x 6 x 4 x 9 = 216.
216 x 10 = 2,160.
2,160 x 12 = 25,920.
If then we go by 1,728 – which is 8 x 216 and the cube of 12 x 12 x 12 – we may appreciate the transition from the Shao Yung cycle to the Galactic year, while now 223,948,800 becomes a necessity:
129,600 x 1,728 = 223,948,800.
1,728 x 10 : 2 = 8,640.
25,920 x 8,640 = 223,948,800
We can now fall back on Hetu Pairings.
First again is 1,728, where 144 is the gross and 1,728 is the great gross, as in 12 x 12 x 12 = 1,728 (also compare Satya Yuga).
Hetu 1-6
1 x 6 (number of faces on a cube) x 1 x 6 x 1 x 6 x 8 = 1,728.
1 x 6 x 144 = 864 x 10 = 8,640.
8.640 : 2 x 1 x 6 = 25,920.
360 x 1 x 6 = 2,160.
2,160 x 4 = 8,640.
8,640 x 2 x 3 x 5 = 259,200 : 10 = 25,920.
129,600 x 1,728 = 223,948,800.
129,600 : 25,920 x 1,728 = 8,640 x 25,920 = 223,948,800.
Hetu 2-7
360 : 5 = 72 x 2 x 7 = 1,008.
360 x 2 x 7 x 2 = 10,080.
360 : 5 = 72 x 2 x 7 = 1,008.
Hetu 3-8
8,640 is at the heartbeat of Solar geometry, as there are 24 x 60 x 60 = 86,400 seconds in a day, until also the Sun’s diameter is seen as 8,640 x 100 = 864,000 miles.
3 x 8 = 24.
360 x 24 = 8.640
24 x 24 x 15 = 8,640.
8,640 x 3 = 25,920.
8,640 x 15 = 129,600.
8,640 x 25,920 = 223,948,800.
Hetu 4-9
4 x 9 = 36 years (360 : Hetu 10).
36 x 4 x 12 = 1,728.
1,728 x Luoshu 15 = 25,920.
129,600 x 1,728 = 223,948,800.
It becomes hard to imagine how the founding fathers would have come up with Hetu with a purpose for letting us ‘see’ colors, Wuxing, compass directions or to persist in all this symbolism, as it becomes unthinkable that they would not have figured out all these calculations to arrive at the Great Year and Galactic Year.
If not in 1972 I thought Hetu ‘beautiful’, it becomes movingly stunning, while I now see this contented scholar on the edge of the lake playing with stones as a pastime, everything if only as a mental note, while the moon winks to light up his grin.
“Devoted To Your Destiny In One Peaceful World”
