Four Pillars of Destiny

The Four Pillars of Destiny, as known as "Ba-Zi", which means "eight characters" or "eight words" in Chinese, is a Chinese astrological concept that a person's destiny or fate can be divined by the two sexagenary cycle characters assigned to their birth year, month, day, and hour. This type of astrology is also used in Japan and Korea.
Development.
Four Pillars of Destiny can be dated back to the Han Dynasty, but it was not systematic as it is known today. In the time of Tang dynasty, Lǐ Xūzhōng (Chinese: 李虛中) reorganized this concept, and used the each of the two sexagenary cycle characters assigned to a person's birth year, month and date to predict one's personality and future. This was called the "Three Pillars of Destiny", and after this theory become more and more popular.
During Song Dynasty, "Xú Zi Píng" (Chinese:徐子平), who reformed "Lǐ Xū- Zhōng"'s "Three Pillars of destiny", by adding the "birth time" as the fourth pillar, which means adding another 2 sexagenary cycle characters to the person's fate pillars, from six characters into eight characters, which made the forecast accuracy seem much higher and became more useful. Therefore, people regarded "Xú Zi Píng" as the layer of a solid foundation of Four Pillars of Destiny.
Method.
Days, hours, months, and years are all assigned one of the ten Celestial Stems (Chinese: 十天干) and one of the twelve Terrestrial Branches (Chinese: 十二地支) in the sexagenary cycle. A person's fortune is determined by looking up the branch and stem characters for each of these four parts of their birth time, with relation to the 10-year luck cycle (Chinese: 十年大运).
The Schools.
The schools are the Scholarly School (學院派, "Xué Yuàn Pài") and the Professional School (江湖派, "Jiāng Hú Pài").
The Scholarly School began with "Xú Zi Píng" (徐子平) at the beginning of the Song Dynasty. Xú founded the pure theoretical basis of the system. Representatives of this school and their publications include:
In Japan.
Definitions.
"Shō-Kan" is also the relative pronoun among the "Heavenly Stems". When we have our birthday as "甲子", "甲戌", "甲申", "甲午", "甲辰", "甲寅", in the Chinese calendar, the will belong to the Shō-Kan. When we have the Heavenly Stems as "甲" in our birthday, the "丁" acts as a Shō-Kan factor, as follows:
Example.
The chart is as follows:
The main structure of his chart is "傷官" (Shō-Kan), "格".<br>
The day of 丁 (in the Chinese calendar) meets April, the month of , the month of "戊", so that we get the Shō-Kan. The most important element and worker in his chart is the "甲" or "乙". The Inju is also the worker which controls Shō-Kan. In 1945, in the year of "乙酉", the Inju has no effect. The Heavenly Stem "乙" is in .
Additionally, the "Dai Un" (Japan's own long-term history) is as follows. The beginning of April in the Lunar calendar is the fifth day, so there are 24 days from day 5 to Hirohito's birthday. One month is equivalent to ten years in "Dai Un", and the 24 days are equivalent to eight years. Events in the historical timeline corresponding to his life from age eight to 18 are as follows.
From the age of 8 to the age of 18 : 辛卯 
Advocates of the Shō-Kan system believe that Hirohito's chart somehow explains the defeat of Japan in World War II after the catastrophic atomic bomb explosions at Hiroshima and Nagasaki.
Periodicity of Four Pillars.
The problem of periodicity of four pillars is a problem in calendrical arithmetics but most of fortune tellers are unable to handle the mathematics correctly. Hee for example, proposed that it takes 240 years for a given four-pillar quadruplet to repeat itself. In p. 22, Hee wrote, . . . because of the numerous possible combinations, it takes 60 years for the same set of year pillars to repeat itself (by comparison, as set of month pillars repeats itself after just five years). Therefore, if you have a certain day and time, the set of four pillars will repeat itself in 60 years. However, since the same day may not appear in exactly the same month - and even if it is in the same month, the day may not be found in the same half month - it takes 240 years before the identical four pillars appear again . . .Hee's proposal is incorrect and can be easily refuted by a counterexample. For example, the four-pillar quadruplets for 1984-3-18 and 2044-3-3 are exactly the same (i.e. 甲子-丁卯-辛亥-xx) and they are spaced only by 60 years. But the next iso-quadruplet will reappear only after 360 years (on 2404-4-5). Furthermore, a periodicity of 1800 years is needed to order to match both sexagenary cycle and the Gregorian cycle. For example, 4-3-18, 1980-3-18, and 3964-3-18 share the same four-pillar quadruplet.
The solution to the iso-Gregorian quadruplet is a Diophantine problem. Suppose that the gap, formula_1, between two successive four-pillar quadruplet is irregular and it is given by formula_2 and suppose that formula_3 and formula_4 are two successive rata die numbers with identical Gregorian month and day, then it can be shown that the interval formula_5 is given byformula_6For formula_1 and formula_5 to coincide, we need solve 
formula_9
to which one of the solution is formula_10 Therefore formula_11days or about 1800 Gregorian years. 