Liu You was from Xingyang. During the early period of Emperor Wen of the Sui Dynasty's Kaihuang reign, he became a general and was given the title Duke of Suolu. His predictions were very accurate, as if they were prophetic, so Emperor Wen was very fond of him. Initially, he worked on astronomy and calendar calculations with Zhang Bin, Liu Hui, and Ma Xian. Later, he was commissioned to write a military treatise in ten volumes, called "Jin Tao," which the emperor was very fond of. He also wrote several works, including "Yin Ce" in twenty volumes, "Guan Tai Fei Hou" in six volumes, "Xuan Xiang Yao Ji" in five volumes, "Lu Li Shu Wen" in one volume, "Hun Yin Zhi" in three volumes, "Chan Ru Zhi" in two volumes, "Shi Jing" in four volumes, "Si Shi Li Cheng Fa" in one volume, "An Li Zhi" in twelve volumes, and "Gui Zheng Yi" in ten volumes, all of which were circulated at that time.
Zhang Zhou Xuan hailed from Piao County in Bohai. He was knowledgeable and especially skilled in astronomy and calendar calculations. The provincial governor of Jizhou, Zhao Jiong, recommended him, and Emperor Wen summoned him, appointing him as a Cloud Cavalry Officer to work in the Bureau of Astronomy and participate in the formulation of the calendar. At that time, many people were not as good as him, so the Chief Astrologer Liu Hui and his peers were quite envious of him. However, many of the things Liu Hui said were wrong, while Zhang Zhou Xuan's astronomical calculations were very accurate, which the emperor appreciated. The emperor asked Yang Su and some experts in astronomy and calendar calculations to discuss 61 issues, which were old problems that had not been solved for a long time, and let Liu Hui and Zhang Zhou Xuan debate them. Liu Hui was left speechless, but Zhang Zhou Xuan answered 54 of them. As a result, Zhang Zhou Xuan was promoted to be an external cavalier attendant and concurrently the Chief Astrologer, awarded a thousand bolts of silk, while Liu Hui and his eight associates were all driven away.
Zhang Zhou Xuan revised the calendar, noting that the previous calendar was off by a day each year. Interior Minister Yan Minchu submitted a memorial stating, "During the Han Dynasty, Liu Hong rectified the 'Zhuan Xu Calendar' and established the 'Tai Chu Calendar,' indicating that it would be off by a day in the future. Eight hundred years later, a sage would come to correct it. Now, it has been seven hundred and ten years since the Han Dynasty, and someone has done it. Isn't this person a sage?" The emperor was very pleased and began to place greater value on Zhang Zhou Xuan, often seeking his advice.
The calendar system established by Zhang Zhouxuan differs from ancient calendars in three key ways: first, during the calculation of the precession of the equinoxes, Zu Chongzhi of the Song Dynasty created a differential method, stating that the winter solstice point moves one degree every 46 years. When the calendar system was established by Yu Xi of the Liang Dynasty, he found that Zu Chongzhi's algorithm was too inaccurate and changed it to one degree every 186 years. Zhang Zhouxuan referenced the methods of these two scholars and, after discovering discrepancies in ancient texts, synthesized the strengths of both to create his own measurement system. The constellation associated with the winter solstice moves slowly each year, moving one degree every 83 years, which aligns with records of daylight duration and star positions from the era of Emperor Yao, as well as the records of star positions in the Han Dynasty calendar. He carefully compared the previous calendar systems and found them to be very accurate.
In the "Bingyin Yuanli" written by Zhou Maxian, there is a method for converting between yin and yang, as well as calculations for additions, subtractions, advancements, and delays, used to calculate dates, which was a groundbreaking innovation at the time. Many contemporary astronomers struggled to grasp this algorithm. Although Zhang Bin used this calendar system, he also could not fully understand it. Zhouxuan felt that it was inconsistent in terms of time additions, the intervals between the solar terms were inconsistent, and it was calculated based on months, which lacked theoretical soundness. Therefore, based on the twenty-four solar terms, he analyzed the variations in the sun and moon's phases, discovering that the different speeds of the sun's movement caused this: when the sun moves fast, the moon easily catches up with the sun, resulting in an earlier new moon phase; when the sun moves slowly, the moon lags behind, causing the new moon to be delayed. He meticulously examined the instances of early and late new moons in previous calendar systems and formulated a systematic rule for adjustments. The sun moves fast from the autumnal equinox to the vernal equinox, covering 180 degrees in 182 days; from the vernal equinox to the autumnal equinox, it moves slowly, covering only 176 degrees in 182 days. This rule applies consistently across all solar terms.
Since ancient times, various calendars have considered a solar eclipse to occur as long as it enters the eclipse limit when calculating the new moon and solar eclipse, regardless of the positions of the sun and moon. Zhang Bin created the concept of the "Outer Limit" when formulating a calendar. In some cases, although the conditions for an eclipse limit are met, a solar eclipse did not actually occur, and he was unable to fully explain the reasons for this. Zhou Xuan believed that the sun travels along the ecliptic, completing one circle in a year, while the moon travels along its orbit, completing a circle in a little over twenty-seven days. When the moon's orbit intersects with the ecliptic, the moon will move from inside the ecliptic to outside every thirteen days and back inside after another thirteen days, repeating this cycle. When the moon crosses the ecliptic, it is called an "eclipse," and a solar eclipse will occur if the new moon happens within fifteen degrees before or after the eclipse point. If the moon travels on the inner side of the ecliptic, namely the northern side, a solar eclipse is more likely to occur; if the moon travels on the outer side of the ecliptic, namely the southern side, even if it is precisely at the eclipse point, a solar eclipse is unlikely to occur due to the moon and sun not being able to block each other. Therefore, based on previous methods, Zhou Xuan established a new eclipse limit, correcting each solar term according to the proximity of the eclipse point and adjusting the degree of solar eclipse, resulting in more accurate calculation results.
Zhou Xuan's calendar was particularly advanced in seven aspects: first, in ancient calendars, the speeds of the five planets' movements were assumed to be constant, and there was no accurate calculation method for their appearances, disappearances, and waxing and waning. Zhou Xuan calculated the speeds of the five planets' movements and obtained their true speeds, which were different from the data in ancient calendars, with some celestial bodies varying by more than thirty days! For example, if Mars appears in the Rain Water solar term, it requires an additional twenty-nine days; if it appears in the Minor Snow solar term, it requires subtracting twenty-five days. Although the average value was adjusted, the observed data was still used as the basis. Other celestial bodies also have similar changes in waxing and waning, with only different differences. However, people of that era could not grasp the significance of this accumulated observational data.
Secondly, according to the old almanacs, the reappearance of the Morning Star (Mercury) is often said to occur at similar times, but whether it can actually be seen is uncertain. Through long-term observations, Zhou Xuan discovered that the visibility of the Morning Star varies throughout a cycle, sometimes visible and sometimes not, due to the gravitational interactions with other stars, leading to their simultaneous appearance. For example, if Mercury appears in the morning of the Rain Water solar term (the second solar term after the beginning of spring), theoretically it should be visible, but in reality, it might not be visible; however, if it appears in the morning of the Awakening of Insects solar term (the third solar term after the beginning of spring), between 18 to 36 degrees in daily motion, and at the same time another star from Jupiter, Mars, Saturn, or Venus appears, then it can be seen together.
Thirdly, in the past, the calculation of celestial body movements in calendars was based on fixed rules, which makes it challenging to accurately determine when stars will appear or disappear. Zhou Xuan discovered through long-term observations that the speeds, stationary periods, and retrograde motions of the five planets (Jupiter, Mars, Mercury, Venus, and Saturn) are different from previous algorithms, with errors sometimes reaching over 80 days and positional errors exceeding 80 degrees. For example, when Mars first appears, if it is early in the solar term of the Beginning of Winter, it traverses 177 degrees over 250 days; but if it is early in the solar term of the Summer Solstice, it only traverses 92 degrees over 170 days. Through repeated verification, he found that his calculations were highly consistent with actual observations, surpassing the accuracy of ancient and modern calendars.
Fourthly, in the past, the calculation of solar eclipse sizes in calendars often failed to align with actual occurrences when applying standard formulas. Zhou Xuan found through long-term observations that the moon's speed is affected by Jupiter, Mars, Saturn, and Venus, moving faster when closer to these four planets and slower when further away, only following the original rules when beyond 15 degrees. Therefore, he recalculated the sizes of solar eclipses based on this rule, resulting in more accurate calculations.
Fifth, the methods used in earlier calendars to calculate the new moon and full moon (the first and fifteenth days of each lunar month) were consistent. Zhou Xuan discovered through long-term observations that the position, time, and size of solar eclipses vary in different locations, which is connected to the relative positions of the sun, moon, and Earth during a solar eclipse. The depth and speed of solar eclipses also vary, so using fixed time to calculate solar eclipses will definitely result in errors. He corrected the time based on celestial phenomena to be more accurate.
Sixth, in the past calendars, it was believed that the size of a solar eclipse was related to the angular distance between the sun and moon, with one fraction for every 14 degrees apart, two fractions for 13 degrees apart, three fractions for 10 degrees apart, and so on. However, the reality is often the opposite, where larger fractions can sometimes result in smaller eclipses and smaller fractions can lead to larger ones. Zhou Xuan discovered through long-term observations that when the sun and moon are perfectly aligned, the moon cannot completely block the sun, resulting in a smaller eclipse; when the sun and moon are about five to six degrees apart, the moon completely blocks the sun, resulting in a maximum eclipse; and as the distance increases, the eclipse becomes smaller. This is the case around the winter solstice, and the pattern changes as one approaches the summer solstice. His classification system for solar eclipses is very detailed and accurate.
Seventh, in the past calendars, it was believed that during the spring and autumn equinoxes, day and night were of equal length. Zhou Xuan discovered through long-term observations that in reality, there is a discrepancy, with daytime being about fifteen minutes longer than nighttime during the spring and autumn equinoxes, due to the varying speed of the sun's movement.
In conclusion, Zhou Xuan's unique insights were meticulously calculated and verified, and people hold great admiration for the precision of his calculations. Sadly, he passed away during the Daye period.
Xu Zhicang is from Gaoyang. His grandfather taught him from a young age. When his mother fell ill, he began studying medical books, and the more he learned, the more skilled he became. Eventually, everyone called him a renowned physician. He advised his sons, "As sons, if you cannot grasp the basics of food, medicine, or medical skills, how can you truly be considered filial?" So, this medical knowledge was passed down through the generations. He later served as an official in the Liang Dynasty, achieving the rank of Assistant Cavalry Commandant. His father, Xu Jing, was a consulting military officer for the Prince of Wuling. Xu Zhicang became famous for his medical skills at a young age, serving as an Assistant Cavalry Commandant in the Chen Dynasty. After the fall of the Chen Dynasty, Emperor Gaozu of the Sui Dynasty appointed him as an Assistant Cavalry Commandant and sent him to Yangzhou.
Coincidentally, when Prince Xiao of Qin fell ill, the emperor quickly summoned him. Prince Xiao of Qin dreamed one night that his deceased concubine Cui cried and said, "I was originally here to welcome him, but I heard that Xu Zhicang is coming. If he comes, it will make me very miserable. What should I do?" The following night, Prince Xiao of Qin dreamed again, and Cui said, "I have come up with a plan. I will go hide in the underworld." After Xu Zhicang arrived, he examined Prince Xiao of Qin's pulse and said, "The illness has penetrated deep into the bone marrow; he will soon die; there is no cure." As expected, Prince Xiao of Qin died a few days later. The emperor was astonished by his medical skills and rewarded him with a hundred bolts of cloth. After Emperor Yang of Sui became emperor, Xu Zhicang had already retired at home. Whenever the emperor felt unwell, he would send eunuchs to seek his counsel, sometimes even bringing him into the palace and assisting him onto the imperial bed. Xu Zhicang's prescriptions were remarkably effective. He passed away at the age of eighty at home.
Xu Cheng, a member of Xu Zhicang's clan, was renowned for his medical expertise. His father, Xu Shi, held the positions of Tai Chang Cheng and Chief Military Officer of the Central Army during the Liang Dynasty. He followed Liu Zhongli to Chang'an, where he was celebrated alongside Yao Sengyuan and was appointed as the Supervisor of the Right Division of the Ministry of Rites. Xu Cheng was very knowledgeable and inherited his father's legacy, excelling in the field of medicine. He served as the Imperial Pharmacist and the Grand Councillor, and was titled Earl of Hechuan County. Both father and son were renowned for their superb medical skills during the Zhou and Sui Dynasties. Historical records provide only a brief account of this matter, so some additional information is provided here.
Wan Baochang, of unknown origin, was the son of Wan Datong, who had surrendered to the Qi Dynasty along with the Liang Dynasty general Wang Lin. Later, Wan Baochang attempted to secretly return to Jiangnan, but his plan was exposed and he was killed. As a result, Wan Baochang was assigned to the music ensemble, and he became highly skilled in music theory and adept at playing various instruments. He crafted jade chimes to present to the Emperor of the Qi Dynasty. On another occasion, during a meal with others, they discussed musical tones. In the absence of musical instruments, Wan Baochang used utensils and miscellaneous items in front of him, tapping with chopsticks to imitate various pitches, covering all the five notes of the pentatonic scale. It resonated as harmoniously as silk and bamboo ensembles, and everyone present greatly appreciated it.
However, from the Zhou Dynasty to the Sui Dynasty, Wan Baochang never received significant recognition. During the Kaihuang era of the Sui Dynasty, Duke of Pei Zheng Yi and others established new musical scales, initially set as the Huangzhong mode. Although he was a musician, Wan Baochang was frequently consulted by Zheng Yi and others, but many of his suggestions went unheeded. Later, after Zheng Yi completed the musical scales and presented them to the Emperor, the Emperor called upon Wan Baochang to seek his opinion. Wan Baochang responded, "This is the music of a defeated realm, how can Your Majesty listen to this!" The Emperor was displeased. Wan Baochang vehemently argued that the music sounded mournful and decadent, not aligned with the traditional court music, and requested the use of a standard measure to determine the musical scales and adjust the instruments. The Emperor agreed.
Wan Bao was often tasked with creating various musical instruments, and his musical scale was two notes lower than that of Zheng Yi. He also wrote 64 volumes of "Music Scores," detailing how the eight tones cycle to form palace tones, as well as the changes in strings and pillars. He established 84 tones, 144 scales, and the final combinations resulted in a total of 1,800 distinct sounds. At that time, people believed that there was a record of "rotating palace" in the "Zhou Li," but since the Han and Wei dynasties, no one who understood music theory could grasp it. Seeing Wan Bao's unique creation, they all found him laughable. However, when he actually performed, he could instantly compose music without a moment's hesitation, astonishing all who witnessed it.
He improved and increased the number of musical instruments to the point that their number was countless. His music was refined yet understated, yet it was not favored by the people of his time. Those in the Tai Chang Temple who excelled in music theory ostracized him. Even the Crown Prince's Groom, Su Kui, who claimed to be proficient in music theory, harbored particular jealousy towards Wan Bao. Su Kui's father, Su Wei, was in power at the time, and everyone discussing music theory was aligned with Su Wei and spoke ill of Wan Bao. Wan Bao repeatedly complained to the officials, and Su Wei interrogated him, asking where he learned his music theory. A monk advised Wan Bao, suggesting, "The Emperor likes auspicious signs. As long as you claim it has good omens, the Emperor will be pleased. You should say that you learned it from a barbarian monk, and that it is the music theory passed down by the Buddhas and Bodhisattvas. The Emperor will definitely be pleased. What you have accomplished can be put into practice." Wan Bao followed the monk's advice and answered Su Wei accordingly. Su Wei angrily said, "The music theory passed down by barbarian monks is the music of the foreign tribes, not what China should adopt!" Ultimately, this matter led nowhere.
Wan Bao once listened to the music played in the Tai Chang Temple and couldn't help but cry. When asked why, Wan Bao said, "The music feels both lascivious and mournful, and the world is on the brink of mutual slaughter, approaching its demise." At that time, the world was in a peaceful and prosperous era, and those who heard him thought it was unthinkable. By the end of the Dae Yeong era of the Sui Dynasty, his words ultimately proved true.
Bao Chang was a very poor man with no children. When his wife saw him fall ill, she secretly took his money and belongings and ran away. Bao Chang was left cold and hungry, with no one to care for him, and he eventually starved to death. Before he died, he burned all the books he had written, saying, "What use are these things?" Some of his books were salvaged from the fire and circulated, leaving people feeling great pity for him. During the Kaihuang era, Zheng Yi, He Tuo, Lu Ben, Su Kui, and Xiao Ji studied classics together, creating music books that were widely used at the time. However, when it came to innate musical talent, they were no match for Bao Chang. An Maju, Cao Miaoda, Wang Changtong, and Guo Lingle were all accomplished composers of the time, and they also studied the Zheng style, but Bao Chang's musical compositions belonged to the category of elegant music. Though they didn't openly praise Bao Chang, they all held deep respect for him, considering him almost a godlike figure. At that time, there was a musician named Wang Lingyan who was also very knowledgeable in music theory. During Emperor Yang of Sui's reign, when the emperor was about to go to Jiangdu, Wang Lingyan's son went with him and played a revamped version of "An Gongzi Qu" on the pipa outside. When Wang Lingyan heard the music in his bedroom, he was taken aback and jumped to his feet, saying, "Oh no, oh no!" He quickly asked his son, "When did this tune start to become popular?" His son replied, "It only started recently." Wang Lingyan started to cry and told his son, "You must not go with them; the emperor will surely not return." When his son asked why, Wang Lingyan explained, "The key of this tune is lost forever, and the key represents the monarch, that's why I said that." Later, Emperor Yang of Sui was indeed assassinated in Jiangdu.
In historical records, it is said that even the sages have teachings on the matters of yin and yang, divination, and other related practices. While they may not be entirely trustworthy, they shouldn't be dismissed outright either. If one can uphold the heavenly principles, they can benefit the people. If their actions do not align with righteousness, they will face the consequences of their actions. That is why the ancient gentlemen warned against recklessness. Today, the bone and facial features of Wei and Lai, the fortune-telling of Yu and Zhang, even when compared to figures like Luo Xia, Gao Tang, Xu Fu, and Zhu Jian, cannot surpass them. Bo Chou's turtle oracle can discern the thoughts of the deities; Geng Xun's celestial globe can precisely calculate the movements of celestial bodies; Bao Chang's music theory can accurately grasp the harmony of the five notes, though not as renowned as the ancient masters, they were still considered experts in their own right. The Xu family's acupuncture techniques, as noted in historical texts, are highly regarded; whereas Xiao Ji's interpretations of yin and yang tend to be somewhat exaggerated.
