Magic square in China

Magic Square in Lo Shu

"Magic Square occurred in Lo Shu of the ancient China. I think that represents the core of Chinese culture: Constructivism, Combinatorics. But they never become main stream culture in China." Steve Han

The story of 'Lo Shu' is as follows:

In the ancient time of China, there was a huge flood.
The people tried to offer some sacrifice to the 'river god'
of one of the flooding rivers, the 'Lo' river, to calm his
anger. However, every time a turtle came from the river and
walked around the sacrifice. The river god didn't accept
the sacrifice until one time, a child noticed the curious
figure on the turtle shell. Hence they realized the correct
amount of sacrifice to make.

http://mathforum.org/alejandre/magic.square/loshu.html

Legends attribute China prehistoric personality, Hsia Yu () - he who tamed the Yellow River of floods ( ) to be the one who discovered the Lo Shu.
Yu saw some very interesting markings on the shell of a giant tortoise that emerged from the River Lo in Central China. This became Lo Shu.
http://www.hiakz.com/loshu.asp

Lo Shu, "scroll of the river Lo", dating as early as 2800 BC.
In Chinese, the square is known as Luo Shu (Simplified Chinese: 洛书; Traditional Chinese: 洛書; pinyin: luò shū; Literal: Luo (River) Book) or the Nine Halls Diagram (Simplified Chinese: 九宫图; Traditional Chinese: 九宮圖; pinyin: jiǔ gōng tú).
http://en.wikipedia.org/wiki/Lo_Shu_Square


The Metaphor of Lo Shu
by Doctor  Rudolf Kaehr

The Lo Shu Story is very interesting! I think it supports very much my ideas about the relationship of Chinese writing (logograms) and the design of new mathematics, maybe based on Morphogrammatics.

The metaphor of Lo Shu seems to confirm that Chinese math is radically different from Greek math as we know it in Western mathematics.

1. First it is in a written form, thus it has to be read (and not heard), i.e., it has to be deciphered and this knowledge has to be translated into sentences, i.e., into spoken language and then interpreted.

2. This procedure is not happening to a single Genius, like a Eureka insight, happening in the mind and then translated into spoken language and from there to an inscribed and written form. What happens with Lo Shu is a societal, co-operative and negotiating interpretation of the inscription on the back of the turtle which has to be discovered.

2. It is practical. The calculation which happens after the "child", i.e., a member of the population, not a Genius, discovered the signs on the turtle, i.e., the magic square, is practical (and mythical, sacrifice for the river-god) bridging the gap between culture and nature to stop the flooding.

3. Thus, the sign on the turtle is in fact not a sign but a topological logogram (morphogram), a tabular matrix, a mathematical inscription. But there is no need to identify such a tabular inscribtion with the modern mathematical concept of a matrix.

4. The problem inscribed on the turtle is purely combinatorial, and not in any sense logical, or sentence-based. It is in this sense not a riddle. Also not pronounced by an Oracle, offered to the scholars to interpretation.

5. The "truth" of the Square is given by a the reading (collecting) of it from all possible points of view, i.e., from all positions of the counting process, the sum has to be the same, which is 15. This process is generating an invariance principle as the form of truth.

6. The way of the counting, represented by the chain of numbers, is for all positions different. Each point of view has its own history and rationality.

7. The final result, the number 15, is not depending on the view-points, but is invariant of the single approaches. It is producing a collective mediation of the different positions, and at once generating societal collectivity. Also it appears as a final result, 15, the number is complex by the history of its construction. Each position has its own number 15. But a single result wouldn't convince the river-god. The convincing result is the collective number 15 as a result of mediation.

8. To each position, point of view, a singular number system can be attributed. Thus the result can be seen as a mediation, harmony, of different number systems. There is no information involved which would demand a unique number system like the modern linear arithmetic of natural numbers.

9. Also it is connected with numbers, the numbers are placed in a tabular order, square, grid, matrix and not linearly as a singular succession. The numbers are marked as patterns. Despite the strict positionality of the numbers, there is no zero sign involved.

There are many more interesting aspects in the story, like the fact that the turtle-matrix gives access to Nature. Thus, the writing is a bridge between human culture and nature. The turtle is considered as celestial. It is also producing time, societal time of the people involved. It is local, a gift for the specific river-god, but connected with a global cosmic insight. The Lo Shu is mediating local and global thematizations. 

With this grammatological approach, I tried to avoid to map the Magic Square of Lo Shu to Western binary digitalism and arithmetic as it is usual today. Thus, in strict mathematical terms, the Lo Shu is not a Magic Square. Simply because it is not a mathematical matrix based on natural numbers. Such an interpretation of Lo Shu as a Magic Square is denying its specific Ancient concept of Numbers. This may have far reaching consequences in the context of interpretations of I Ching, Trigrams, Feng Shui and Yin&Yang.

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