Exampe: I-Ching Bagua
The I-Ching categorizes future trajectories (essentially a person's fortune, which really is nothing but his/her future) into eight possibilities -- the Bagua system of trigrams.The I-Ching further expands this categorization by doubling up the Bagua trigrams into duplets called the 64 Gua's of hexgrams.
Example: Sun Signs
Western astrology associates a person's inherent personality with his/her sun sign, which is further categorized into 12 possibilities according to the zodiac of the sun's position.It can be seen in a future blog entry that the 12 sun signs are further decomposed into three orthogonal axes -- energy (i.e. extrovert vs introvert), logic vs intuition, outwards vs inwards (self-centered or public-centered).
Example: The Five Elements
In Chinese fortune telling, the Five Elements are used extensively as a categorization of future trajectories (i.e. Fire, Water, Wind/Wood/Air, Metal, Earth).Example: Ziwei Numbers
In the system of Ziwei Numbers, fortune is categorized into 14 stars, which, as will be seen in a future blog entry, can be further decomposed into three othogonal axes -- energy (i.e. extrovert vs introvert), logic vs intuition, outwards vs inwards (self-centered or public-centered).Notice the uncanny similarities between the categorization of personality in the Ziwei Numbers with the corresponding categorization of personality in western astrology.
Purposes of Categorization
One can guess the reasons for such categorizations -- to aid in calculation, especially in an age without calculating instruments (or even writing instruments) and sound knowledge of mathematics.Another rationale beyond categorizations is to simply interpretation. Life is complex, and realities are complex. Any predictive system, to be useful, must use categorizations to aid in forming opinions on possible future outcomes. Think, for instance, the Myers-Briggs Type Indicator.
Conjecture: Fortune Categorization and the Chinese Remainder Theorem
Notice an interesting phenomenon -- Chinese culture appears to favor prime numbers, or sets of prime numbers that are co-prime with each other. For instance, 2 (yin/yang 陰陽), 3 (heaven/earth/man 天地人), 5 (five elements 五行), 7 (seven stars 七星), 8 (bagua 八卦), 9 (nine-squares 九宮).Some Chinese fortune telling systems use several categorizations simultaneously, and in the vast majority of those cases (if not all), the categorizations used are co-prime with each other.
For instance, the Bagua is essentially a categorization based on 2. Feng Sui is based on the Nine Squares matrix. The Four Pillars system uses the Five Elements (5) with two further axes of 10 (天干) and 12 (地支), with 10 being 2x5 and 12 being 2x2x3 -- thus the Four Pillars uses categorizations of 2, 3, and 5 respectively.
This brings one to the mystery of the Chinese Remainder Theorem -- a general result about congruences in number theory and especially to the moduli of pairwise co-primes, laid out in a 1247 book by Qin Jiushao (秦九韶), the Shushu Jiuzhang (數書九章, or Mathematical Treatise in Nine Sections). An earlier form of the theorem was outlined in the third-century book The Mathematical Classic of Sun Tsu (孫子算經).
This theorem, when first revealed, shocked the western mathematics world, as it would take western mathematics centuries later to come up with similar results. There is also no particular reason why such a theorem is practically needed, since the rest of the materials in both publications cited above deal with arithmetic techniques in practical everyday usage. Some have conjectured that the theorem was used in fixing calendars -- but there are holes in this argument: firstly, Chinese calendars have never been extremely accurate, and secondly, western civilizations did not need this theorem to formulate their accurate calendars.
The theorem, however, is essential if one is to formulate and use a mathematical model to calculate fortune and future trajectories. As most fortune telling systems use categorization to indicate results, and if the results from two or more categorizations are available, the theorem is needed to find out the exact value of the result from two or more categories. Since fortune telling has been an important activity throughout ancient Chinese society, the practicality of this theorem can be well explained if put in such context.
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