david wrote:But I still don’t understand why the images of those hexagrams were chosen as they were, not otherwise. They were seemingly chosen arbitrary. As many hexagrams are symmetric, their images can be switched without altering the system at all.
You have hit the key point. The symmetry and symmetry breaking are the two key points of modern physics and modern mathematics. If a system is completely symmetric, then the image assignment can be switched without altering the system at all. However, if a largely symmetric system has a small symmetry breaking, the image switching scheme will not work.
The ancients did know some symmetric properties about the hexagram system. Two of them are well-known.
1. “錯”(exchange operation), the lines (yao) of a trigram (or hexagram) become its opposite. The new trigram (or hexagram) is called a 錯 卦 of the original one, such as,
(乾) vs
(坤)
坎 vs
離
Every hexagram has one and only one 錯 hexagram. That is, for the “錯”(exchange) symmetry, it is a perfect symmetry, no symmetry breaking. Thus, a selected way of image swapping will not change the system.
Note: it will be a good exercise for the reader to find the 錯 卦 of each hexagram.
2. “綜” (flip over operation), two “different” trigrams (or hexagrams) are related by turned upside down of each other, such as,
震 vs
艮
巽 vs
兌
The 綜 (flip over) operation for
乾 becomes itself, not a different trigram. Thus,
has no 綜 partner.
You can see that 離, 坎 have the 錯 symmetry but not the 綜 symmetry. For hexagrams, there are only 28 pairs of 綜 symmetry. Thus, the 綜 is not a perfect symmetry. An image swapping operation will change this symmetry, that is, change the system.
Note: if Chinese language is your mother tongue, you have read and used the phrase 錯 綜 複 雜 zillion times. Now, you know where this phrase comes from and what it truly means.
Therefore, the image assignment to each hexagram cannot be completely arbitrary. Then, the question is, “Was King Wen’s assignment making sense and valid?” If a different choice of assignment was made, there will be a different Yijing. Indeed, it will. That is, even without changing the hexagram system, there can be many different versions of Yijing. This was, in fact, the case. As far as we know, there were three Yijing while the first two were no longer in existence.
a. 「 連 山 」 為 「 夏 」 易 --- the Yijing of Xia dynasty (around 21st century BC).
b. 「 歸 藏 」 為 「 殷 」 易 --- the Yijing of Yin dynasty (between 夏 and 周).
c. 「 周 易 」 是 「 周 易 」 --- the Yijing of Chou dynasty (around 11st century BC).
Again, was King Wen’s choice making sense?
In the book “Linguistics Manifesto (ISBN 978-3-8383-9722-1, available at amazon and Barnes & Noble)”, it states a "Spider Web Principle" --- The whereabouts to build a spider web is completely arbitrary (total freedom or total symmetry). However, as soon as the first spider thread is casted, that total symmetry is broken, total freedom no more. For spider web, the first thread decides its location, here, not there. The second thread decides the center of the web. After these two threads, the scope of the web is very much determined. In fact, this "Spider Web Principle" applies on all systems. The first choice of any system can be arbitrary, defining what this system is all about, a language, a machine or the whatnots. And, the second choice fixes the scope of the system.
So, what was King Wen’s first choice on the hexagram system?
He chose the Yang yao (
) has the image and virtue of “moving forward, aggressive” and Ying yao (
) has the image and virtue of “moving inward, receptive.” Thus,
becomes Father, and
Mother. From here, the other six trigrams are constructed, as a family.
震, the eldest son from 坤, is thunder, the arousing.
坎, the second son from 坤, is water, the abysmal.
艮, the youngest son from 坤, is mountain, the still, stay put.
巽, the eldest daughter from 乾, the wind, the gentle, all permeating.
離, the second daughter from 乾, the fire, the clinging.
兌, , the youngest daughter from 乾, water lake, the joyous.
In fact, the image (corresponding to a corporeal object) and the virtue of each trigram were assigned by King Wen somewhat arbitrary, trying to encompass the known nature phenomena. However, as soon as those choices were made, the images and virtues of hexagrams become derivative of those early choices by following an inheritance law. The image and the virtue of each symbol are inherited by a descendent symbol.
After knowing these principles, the reader can actually derive the image and the virtue of each hexagram yourself. Then, you can compare your findings to King Wen’s writing. That is, there is no abstruseness or incomprehensibleness at all about King Wen’s language.
However, were King Wen’s choices the best choices? This is a major issue and will be discussed in the future.