Lin Xiaogong, hailing from Jingzhao Prefecture, was well-versed in astronomy and mathematics. The Emperor held him in high regard. His predictions of disasters and auspicious events were always accurate, so the Emperor put him in charge of studying the Yin-Yang calendar. He later became an official of the highest rank of Yitong. He wrote three volumes titled "Yi Qi Tu," one volume titled "Di Dong Tong Yi Jing," one volume titled "Jiu Gong Wu Mu," ten volumes titled "Dun Jia Yue Ling," ten volumes titled "Yuan Chen Jing," one hundred and nine volumes titled "Yuan Chen E," eighteen volumes titled "Bai Guai Shu," twenty volumes titled "Lu Ming Shu," one hundred and ten volumes titled "Jiu Gong Gui Jing," thirty volumes titled "Tai Yi Shi Jing," and one volume titled "Kong Zi Ma Tou Yi Bu Shu," all of which have been preserved through the ages.
Liu You, hailing from Xingyang, became a Grand General during the Sui Dynasty. He was bestowed the title of Duke of Suolu County. His predictions were consistently accurate, and the Emperor was very fond of him. He initially worked with Zhang Bin, Liu Hui, and Ma Xian to develop the calendar. Later, he was ordered to compile a military book called "Jin Tao," which comprised ten volumes and was highly favored by the Emperor. He also wrote twenty volumes titled "Yin Ce," six volumes titled "Guan Tai Fei Hou," five volumes titled "Xuan Xiang Yao Ji," one volume titled "Lv Li Shu Wen," three volumes titled "Hun Yin Zhi," two volumes titled "Chan Ru Zhi," four volumes titled "Shi Jing," one volume titled "Si Shi Li Cheng Fa," twelve volumes titled "An Li Zhi," and ten volumes titled "Gui Zheng Yi," all of which have also been preserved through the ages.
Zhang Zhouxuan was a native of Zhou County, Bohai. He was knowledgeable and especially proficient in divination and numerology. The Governor of Jizhou, Zhao Jiong, recommended him, and the Emperor summoned him, appointing him as a Cloud Rider Officer and allowing him to work in the Bureau of Astronomy to participate in the formulation of the calendar. Many people at that time were not as skilled as he was, so Chief Astronomer Liu Hui and his associates were envious of him. However, Liu Hui's predictions were often inaccurate, while Zhang Zhouxuan's astronomical calendar calculations were very precise, and the Emperor greatly admired him. The Emperor had Yang Su and some other experts in divination discuss 61 questions, which were long-standing issues in previous calendars that were difficult to solve, allowing Liu Hui and Zhang Zhouxuan to debate. Liu Hui struggled to answer any of the questions, while Zhang Zhouxuan answered 54 questions. As a result, Zhang Zhouxuan was promoted to Assistant Cavalry Attendant and concurrently appointed as the Chief Astronomer, awarded a thousand bolts of cloth, while Liu Hui and his eight associates were all dismissed. Zhang Zhouxuan then formulated a new calendar, stating that the previous calendar was consistently off by a day. The Palace Historian Yan Minchu submitted a report, saying, "During the Han Dynasty, Emperor Hong revised the Zhuanxu Calendar and established the Taichu Calendar, predicting that it would be off by one day in the future. Eight hundred years later, a sage would come to correct it. It has now been seven hundred and ten years, and the astrologers have all calculated this number accurately, claiming it was the work of the sage. Could it be today?" The Emperor was delighted and increasingly trusted and relied on Zhang Zhouxuan. Zhang Zhouxuan's calendar differed from ancient calendars in three key ways.
Zu Chongzhi of the Song Dynasty invented a calculation method called the "method of differences" towards the end of the year. He found that the winter solstice point was gradually shifting each year, unlike in the past when it had been fixed. Every forty-six years, the winter solstice point would shift by one degree. Later, when Yu Xi of the Liang Dynasty formulated a calendar, he believed Zu Chongzhi's calculations contained significant errors, so he changed it to one hundred and eighty-six years for the winter solstice point to move one degree. Zhou Xuan referred to both Zu Chongzhi and Yu Xi's methods and found that the time spans of the two methods differed significantly. By tracing ancient records, he found that the discrepancies were considerable. Therefore, he synthesized the strengths of both methods to develop a new measurement system. He stipulated that the winter solstice point would move one degree every eighty-three years, which not only aligned with the records of the era of Emperor Yao regarding the length of days and constellations but also conformed to the records of the Han Dynasty's calendar regarding the positions of the constellations. The comparisons before and after were very accurate. Ma Xian of the Zhou Dynasty created the "Bingyin Yuanli," which included methods for converting between the lunar calendar and the solar calendar, as well as calculations for adding and subtracting intervals, as well as predicting progress and regressions to forecast solar eclipses. This represented a groundbreaking advancement in numerical calculation methods. At that time, many astronomers struggled to grasp it. Zhang Bin later used this method but could not fully comprehend it either. Zhou Xuan argued that Ma Xian's method was theoretically flawed regarding the addition of time. He believed that this was due to the varying speeds of the sun's movement: when the sun moves slowly, the moon's speed in catching up with the sun is fast, resulting in an earlier new moon; when the sun moves fast, the moon's speed in catching up with the sun is slow, leading to a delayed new moon. He analyzed instances of the new moon occurring early or late in earlier calendar systems to ascertain the ratio of discrepancies. He found that from the autumn equinox to the spring equinox, the sun moves fast, traversing one hundred and eighty-two days for one hundred and eighty degrees; from the spring equinox to the autumn equinox, the sun moves slowly, traversing one hundred and eighty-two days for one hundred and seventy-six degrees. Each solar term adheres to this ratio.
In ancient times, when calculating the conjunctions and oppositions, as long as the eclipse limit was reached, it was considered that a solar eclipse would occur, regardless of internal and external limits. Zhang Bin's calendar introduced the concept of external limits. In some cases, even though the eclipse limit was reached, a solar eclipse did not occur, which remains unexplained. Zhaouxuan believed that the sun travels along the ecliptic, completing one revolution per year; the moon travels along the lunar path, completing approximately thirteen cycles in about twenty-seven days. When the lunar path intersects with the ecliptic, the moon will move from inside the ecliptic to outside after around thirteen days, and then back inside after another thirteen days, repeating this cycle. The point where the moon crosses the ecliptic is called the node. If the opposition occurs within fifteen degrees before or after the node, a solar eclipse will occur. If the moon is traveling inside the ecliptic, to the north of the ecliptic, it is easier to observe a solar eclipse; if the moon is traveling outside the ecliptic, to the south of the ecliptic, even if it encounters the node, it is difficult to observe the solar eclipse phenomenon because the moon is unable to block the sun. Therefore, based on the methods of his predecessors, he established the eclipse limit, calculated the errors based on the proximity of the node, adjusted the degree of the solar eclipse, clarifying everything.
There are seven extraordinary things that are different from ancient times: The first point is that the ancient calendar viewed the movement patterns of the five planets, that is, the time of their appearance and disappearance, to be fixed. However, the actual observations did not follow a precise pattern. Zu Chongzhi discovered the true movement pattern of the stars through long-term observations, and the results he calculated were significantly different from those of ancient calendars, with some discrepancies exceeding thirty days! For example, if Mars appears during the Rain Water solar term, it needs to be calculated as twenty-nine days more than the ancient calendar; if it appears during the Minor Snow solar term, it needs to be calculated as twenty-five days less. Although he calculated the precise appearance time by adjusting for the average appearance duration, other stars also have similar situations, with different numbers of days of difference. Although the accumulated experience of ancient times could predict some phenomena, it is now difficult for modern people to understand the meanings behind them.
In the second paragraph, people once believed that Mercury only appeared once during each orbit around the sun, as indicated by all ancient calendars. If Mercury did not appear when expected, no one could explain its absence. Through long-term observations, Zu Chongzhi discovered that Mercury can appear more than once in a single cycle and is also influenced by other celestial bodies, appearing simultaneously. For example, if Mercury is supposed to be visible during the Rain Water season in the morning, it may not actually be visible; but if it appears in the morning of the Awakening of Insects season, between 18 and 36 degrees away from the sun, and is accompanied by Jupiter, Mars, Saturn, or Venus, Mercury can be observed.
In the third paragraph, ancient calendars calculated the movement of planets based on fixed speeds and trajectories, predicting their next appearance based on these fixed speeds without considering variations in their speeds. Zu Chongzhi's long-term observations revealed that the speeds, stops, and retrograde times of the five planets differed significantly from the results calculated by ancient calendars, with discrepancies of over eighty days and eighty degrees in their trajectories. For example, if Mars first appears at the beginning of Winter Solstice, it will travel 177 degrees in 250 days; but if it appears at the beginning of Summer Solstice, it will only travel 92 degrees in 170 days. He corrected calculation methods based on actual observations, resulting in highly accurate calculations in both modern and ancient times.
In the fourth paragraph, ancient calendars calculated the size of solar eclipses using average calculations, often resulting in significant discrepancies from reality. Zu Chongzhi's long-term observations revealed that the speed of the moon's movement is influenced by Jupiter, Mars, Saturn, and Venus—moving faster when in proximity to these planets and slower when farther away. Only when the moon is more than fifteen degrees away does it move at its original speed. Therefore, he adjusted his calculations of solar eclipse sizes according to the relative positions of the moon and these four planets.
Paragraph five, the ancient calendar calculated the dates of the new moon and full moon in the lunar calendar in the same way. Zu Chongzhi discovered through long-term observations that the location and timing of solar eclipses would change with different observation points, as well as the extent, timing, and characteristics of solar eclipses. He corrected the calculation method based on these actual conditions to make the results closer to the actual celestial phenomena.
Paragraph six, the ancient calendar calculated the degree of solar eclipses based on the distance between the sun and the moon at conjunction. Fourteen degrees from the conjunction point was classified as one part; thirteen degrees as two parts; ten degrees as three parts. The degree of eclipse increased by one part for each degree closer to the conjunction point, reaching the maximum degree at the conjunction point. Sometimes the actual situation of a solar eclipse was contrary to the calculated results, and sometimes the calculated results were less than the actual situation. Zu Chongzhi concluded from long-term observations that near the conjunction point, the moon did not completely block the sun, resulting in a smaller degree of eclipse. When the moon was completely inside the sun approximately five or six degrees from the conjunction point, the eclipse reached its maximum degree. After that, the degree of eclipse decreased as the distance increased. This was the case around the winter solstice. However, the situation was different near the summer solstice. His classification standard for solar eclipses was very detailed and precise.
Paragraph seven, the ancient calendar believed that day and night were of equal length during the spring equinox and autumn equinox. Zu Chongzhi found through long-term observations that in reality, there was a difference. During the spring equinox and autumn equinox, the daytime was fifteen minutes longer than the nighttime, due to variations in the sun's apparent motion.
These were all conclusions that Zu Chongzhi diligently researched and summarized. Everyone admired the precision of his calendar calculations. He passed away during the Deyi era of Emperor Yang of the Sui Dynasty.
Xu Zhicang was from Gaoyang. His ancestor, Xu Daoyou, learned medicine when his mother fell ill and later became a renowned doctor. He advised his sons, "As sons, if you don't even ask about your parents' diet and medications, and don't know anything about medicine, how can you be considered filial?" Therefore, his medical skills were passed down through generations in the family. He served in the Liang Dynasty and rose to the rank of Assistant to the Imperial Physician. His father, Xu Jing, served as an advisor to the Prince of Wuling. Xu Zhicang became famous for his medical skills at a young age and served as an Assistant to the Imperial Physician in the Chen Dynasty. After the fall of the Chen Dynasty, Emperor Yang of Sui appointed him as Assistant to the Imperial Physician and sent him to Yangzhou. By coincidence, Prince Juns of Qin fell ill, so the emperor called him back. Prince Juns dreamed that his deceased wife, Cui, appeared and cried, saying, "I was supposed to come to meet you, but I heard that Xu Zhicang is coming. If he comes, he will make you suffer. What should we do?" The next night, Prince Juns dreamed again, and Cui said, "I have figured out a way. I will hide in the underworld." After Xu Zhicang arrived, he diagnosed Prince Juns and said, "The disease has penetrated deep into the bone marrow; he's going to die soon; there's nothing that can be done." Sure enough, Prince Juns passed away a few days later. The emperor was impressed by his medical skills and rewarded him with a hundred bolts of cloth. By the time Emperor Yang of Sui took the throne, Xu Zhicang had already retired to his home. Whenever the emperor got sick, eunuchs were sent to ask for his advice, or he was brought to the palace and helped onto the royal bed. Xu Zhicang's prescriptions were consistently effective. He passed away peacefully at home at the age of eighty.
Speaking of Xu Cheng's family, he has a remarkable lineage. His father, Xu Shi, was very skilled in medicine. His father held prestigious positions, including Minister of Ceremonies and Chief Military Officer during the Liang Dynasty. Later, he followed Liu Zhongli to Chang'an and gained a reputation that rivaled Yao Sengyuan. Eventually, he even became the Minister of the Right of the Imperial Secretariat, which was truly impressive.
Xu Cheng himself inherited his father's talents, excelling in both knowledge and medicine. He later became the Imperial Pharmacist and a Grand Councillor, and was granted the title of Count of Hechuan. The father and son were both exceptional, renowned for their exceptional medical skills throughout the Zhou and Sui Dynasties. Unfortunately, there are few records of them in official history, so I can only briefly mention them here.
As for Wan Baochang, his identity remains largely unknown. His father, Datong, surrendered to the Qi Dynasty with the general Wang Lin of the Liang Dynasty. Later, he tried to sneak back to Jiangnan but was caught and killed. Wan Baochang was subsequently compelled to become a musician, which gave him a profound understanding of music theory and mastery of various instruments. He even crafted a set of jade chimes to present to the Emperor of the Qi Dynasty.
One time, during a meal with others, they discussed musical tones. Since there were no musical instruments available, Wan Baochang picked up bowls, chopsticks, and various items in front of him, using chopsticks to tap them and imitate different pitches. He covered all the tones of the ancient Chinese music scale, sounding just as harmonious as real silk and bamboo instruments. People of the time greatly admired his talent. However, throughout the Zhou and Sui Dynasties, he never gained significant recognition.
During the reign of Emperor Wen of the Sui Dynasty, Duke Zheng Yi and his colleagues were responsible for establishing new music regulations, initially established as the Huangzhong scale. Although Wan Baochang was just a musician, Zheng Yi and his colleagues often consulted him for discussions, but most of his suggestions went unheeded. Later, after Zheng Yi and his colleagues completed the music regulations and presented them to the emperor, the emperor summoned Wan Baochang to ask for his opinion. Wan Baochang said, "This is the music of a doomed country; how could I let Your Majesty hear it!" The emperor was very displeased. Wan Baochang then explained in detail that the music was mournful and unrestrained, not the orthodox elegant music, and requested to use a standard pitch to correct the instruments. The emperor agreed.
Wan Baochang was ordered to make various musical instruments, and his music was two notes lower than Zheng Yi's. He also wrote 64 volumes of "Music Scores," detailing how the eight tones create the palace mode and the techniques of changing strings and pillars. He established 84 modes, 144 notes, resulting in a total of 1,800 sound combinations. People at that time thought that the principle of "rotating palace" mentioned in the "Rites of Zhou" had been understood, but since the Han and Wei Dynasties, musicians could not grasp it. When they saw Wan Baochang's innovation, they found it laughable.
By this time, when asked to perform, he could play music immediately without hesitation, surprising everyone who saw it. He continued to improve and modify instruments, countless in number. His music was elegant and unpretentious, yet it failed to win over the people of his time, as the musicians at the Ministry of Rites rejected him. The Prince's Equerry, Su Kui, prided himself on his musical knowledge, especially envying Wan Baochang. Su Kui's father, Su Wei, was in power at the time, and everyone discussing music aligned with Su Wei, belittling Wan Baochang.
Wan Bao often visited the court ministers to voice his grievances. Su Wei questioned Wan Bao, "Who did you learn these things from?" A monk advised Wan Bao, "The emperor likes auspicious signs. As long as someone mentions good omens, the emperor will be pleased. You should say you learned it from Hu Sang and that it is the musical principles handed down by the Bodhisattva. The emperor will definitely be pleased. You can implement what you have done." Wan Bao followed this advice and answered Su Wei according to the monk's instructions. Su Wei angrily said, "The music passed down by Hu Sang is from the Western Regions and not something we should perform in China!" This matter ultimately went unresolved.
Wan Bao once heard music being played at the Tai Chang Temple and started crying. When asked the reason, Wan Bao replied, "The music is licentious and mournful. The world will soon be engulfed in mutual slaughter and face its doom." At that time, the world was in a time of peace and prosperity, so those who heard him thought he was wrong. However, during the reign of the Sui Dynasty, his words were eventually proven true.
Wan Bao was very poor and had no children. When his wife saw him fall ill, she secretly took all his belongings and ran away, leaving him hungry and cold with no one to care for him. He ultimately succumbed to starvation. Before he died, he burned the books he had written, saying, "What use are these things?" A few of his books were salvaged from the fire and later circulated, and people felt great pity for him.
During the Kaihuang period, Zheng Yi, He Tuo, Lu Ben, Su Kui, and Xiao Ji studied classics together and compiled music books that were widely circulated and used at the time. However, in terms of natural musical talent, they were no match for Wan Bao. An Maju, Cao Miaoda, Wang Changtong, and Guo Lingyue were skilled composers and top musicians at the time. They also studied Zheng Sheng, but Wan Bao's musical works were considered part of the refined music tradition. Although these people did not openly agree with Wan Bao, they secretly admired him and regarded him as an extraordinary figure.
At that time, there was a musician named Wang Lingyan, who was also well-versed in music theory. During the reign of Emperor Yang of the Sui Dynasty, he planned to visit Jiangdu for leisure, and Wang Lingyan's son followed him. He played the huqin outside the door, performing a variation of a piece called "An Gongzi Qu." Wang Lingyan was inside at the time and was taken aback when he heard it, suddenly standing up and saying, "Oh no, oh no!" He quickly asked his son, "When did this tune become popular?" His son replied, "It only became popular recently." Wang Lingyan started to cry and said to his son, "You must not go with him; the Emperor will definitely not return." When his son asked why, Wang Lingyan said, "The tonality of this tune signifies an irreversible fate; the tonality represents the monarch, that's why I said that." Later, Emperor Yang of Sui was indeed killed in Jiangdu.
Historical texts state: matters of divination and fortune telling, even the sages have offered guidance on them, although they cannot be completely believed or completely denied. If a person can promote the right path, they can benefit society, but if their actions are not in line with morality, they will face the consequences of their actions. That's why the ancient sages advised against reckless actions. Now, the analysis of bone structure and appearance by Wei and Lai, the calculations of Yu and Zhang, even people like Luo Xia, Gaotang, Xu Fu, and Zhu Jian, pale in comparison to them. Bo Chou's tortoise shell divination can divine the thoughts of spirits and deities; Geng Xu's astrolabe can precisely measure celestial bodies; Bao Chang's musical theory can accurately grasp the harmony of the tonal system. Although they cannot compare to the great masters of ancient times, they are all outstanding in their own right. Xu's acupuncture techniques are well-documented in historical texts; Xiao Ji's discussion of yin and yang, however, may be somewhat overstated.
