Yin yang and mathematics
of ba zhai
by Jayashree Bose
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These calculations are based on the Greater and Lesser yin/yang transformation of the Taiji and it uses the early heaven numbers. Kua number is also equivalent to later heaven number.
What does it mean when we use the term early heaven and later heaven?
Early heaven formation is preordained and not much can be done on the human level to change the outcome or quicken the process. It can be said that Early Heaven basically means, that when the heavens rule and one can enjoy the fruits of heaven if one has the patience.
The early heaven arrangement or the early heaven ba gua was formulated by Fu Hsi (approximate 29th century BC). It is the perfect balance of yin and yang and the representation of the perfect universe. Early heaven is fixed.
Later heaven is human induced, we as human beings have the control and the reins are in our hands. The later heaven formation was formulated by King Wan (born BC1231) and his son, Duke of Kau after they studied the principles of the Early heaven formation and the He Tu. It is the representation of the ever changing universe and is dynamic.
The mystery of Fu Hsi -
Fu Hsi who designed the Hetu was the first of the five Ti's (emperor's), in the Shu King (Book of historical documents containing historical documents of various kinds from BC 2357 - 627), there is documented evidence of Ti Yao who was the fourth in the succession of the five emperors. These documents are not chronologically given, they profess to be compilations of older documents, it was only during the Han dynasty that an attempt was made to construct a chronological scheme of the history of the chinese nation. The scholars employed a sexagenarian cycle for this purpose.
In the works of Mencius (Chinese philosopher) he says "from Yao and Shun to Thang (a period including all of Hsia Dynasty) there were 500 years and more; from Thang to King Wan (the period of Shang Dynasty) 500 years and more; and from King Wan to Confucius, 500 years and more." Therefore knowing that Confucius was born in 551 BC if we add 1500 years "and more" given by Menecius, we have an approximate of 2100BC when Yao was ruling over China. Vague words from Menecius does not give any conclusive time frame, the only other way to determine the length of Chinese history is to base it on astronomical calculations.
In the Shu King - Canon of Yao, Yao gives instruction to his astronomers on how to determine the equinoxes and solstices. "He separately commanded the second brother ..in what was called the Bright valley ...The day (said he), "is of medium length and the star is in Niao; you may thus determine mid-spring.""
Astronomers who studied the patterns in the sky (stars) put the date of Yao's accession in BC.2357 (Approximate 24th century B.C.). Now, we have to remember that Fu Hsi, the founder of the Chinese nation, was the first of the Five Ti's (Yao being the fourth). Approximate deduction would put Fu Hsi in twenty ninth century B.C. Thus it could be said that the first step towards development of feng shui began around the twenty ninth century B.C.
It is quite debatable as to why a person in pre historic Chinese era designed a beautiful yet complicated mathematical structure to explain the workings of the heaven. Not much can be found on Fu Hsi and the debate continues.
The birth of the trigrams
Explantion of the image - From Wu Ji (nothingness) was born Tai Ji (the union of yin and yang) - Yin(broken line(yao)) and Yang(unbroken line(yao)) further divided to Greater/Old Yin, Lesser/Young Yang, Lesser/Young Yin and Greater/Old Yang. From these four further divisions took place and the eight trigrams were born. From greater/old yang we have Qian and Dui, from greater/young yin comes Kun and Gen, from lesser/young yang comes Kan and Xun, from lesser/young yin comes Li and Zhen. The numbers in the early heaven sequence differ from the numbers in the later heaven sequence and it is also not to be confused with the lo shu numbers.
The numbers are as follows :-
Greater Yang
Qian - 1
Dui - 2
Lesser Yin
Li - 3
Zhen - 4
Lesser Yang
Xun - 5
Kan - 6
Greater Yin
Gen - 7
Kun - 8
I use the term brother or friend for the ones belonging or have taken birth from the same parent. For eg. Qian and Dui are friends as they are both born of greater yang. Hence Qian and Dui share the same root.
Kua Numbers and its directions
Everyone knows how to derive the kua number, or one can use the kua calculator available in the site to do so.
It is from the kua numbers that ones personal directions can be found. Below is the chart of the auspicious or good directions/locations, along with the name of the trigram, early heaven numbers and the root they were born from (greater yang, lesser yang, greater yin and lesser yin).
The visible pattern
It is seen that Sheng Qi and Tien Yi always add up to number 9, also the Yen nien and Fu wei adds up to 9.
When kua number belongs to Greater Yin (or any of the other three greater yang, lesser yang, lesser yin) then the Sheng Qi trigram also belongs to Greater Yin (the brother/friend trigram), Tien yi would then automatically take Greater Yang followed by Yen Nien that takes on the other trigram of greater yang followed by Fu wei taking the trigram of the kua number itself.
To explain it further, it can be said that the Kua number determines the yin or yang of all the directions. If the Kua number happens to belong to Greater Yang then Sheng qi, Tein yi, Yen Nien and Fu wei would all belong to Greater yin or yang. Simply said greater to greater and lesser to lesser.
Lets take an example of Kua Number 2 (Kun - Greater Yin - 8)
Sheng Qi - Gen - North East - Greater yin - 7
Tien Yi - Dui - West - Greater Yang - 2
Yen Nien - Qian - North West - Greater Yang - 1
Fu Wei - Kun - South West - Greater Yin - 8
Here Sheng Qi (7) + Tien Yi (2) = 9
Yen Nien (1) + Fu Wei (8) = 9
The East Group kua numbers viz. 1,3,4,9 all belong to Lesser Yin/Yang and the West Group kua numbers viz. 2,6,7 and 8 all belong to Greater Yin/Yang.
Futher more the early heaven numbers of the East Group auspicious directions are always 3,4,5,6 and for the inauspicious directions 1,2,7,8. The vice versa is applicable for the West group kua numbers.
Below is the chart for inauspicious directions/locations.
For the inauspicious directions/locations the same rule is followed. Cheuh ming and Lui Sha always add to form 9. Similarly, Ho hai and Wu Gwei also add up to form 9. Further more it can be said that Chueh Ming always takes the opposite qi (greater/lesser) and opposite polarity(yin/yang) of the kua number.
Again taking the example of Kua Number 2 (Kun - Greater Yin - 8)
Chueh Ming - Kan - North - Lesser Yang - 6
Lui Sha - Li - South - Lesser Yin - 3
Ho Hai - Zhen - East - Lesser Yin - 4
Wu Gwei - Xun - South East - Lesser Yang - 5
Here again, Chueh Ming (6) + Lui Sha (3) = 9
Ho Hai (4) + Wu Gwei (5) = 9
Ba zhai is perfect in terms of mathematical calculations and has a logical pattern behind the formula. It is not the only formula in feng shui that is mathematically and logically perfect. Many other formuas can be deduced mathematically.
It has been written that the ancient masters studied the patterns in the sky (stars) to reach the conclusions for the formulas. Could it be possible that they used mathematics and logic for the same purpose? Nothing can be said conclusively, at least not until all the ancient texts have been restored and carefully studied.
Many believe that feng shui is an abstract art while others say it is a logical science. If the formulas can be deduced mathematically then it does make feng shui a logical science but it is while the formula is applied or used that we require the abstract or creative thinking. In my opinion feng shui is a blend of logic and creativity, for one cannot exist without the other.
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