Geng Xu, style name Dunxin, was from Danyang. He was especially good at telling jokes, was an excellent speaker, and had outstanding skills that no one could match. When the last emperor of the Chen Dynasty was in power, he went with the Governor of Donghengzhou, Wang Yong, to Lingnan as a guest. After Wang Yong died, Geng Xu did not return but instead became friends with local ethnic leaders, who all liked him.

Later, the local people rebelled and chose Geng Xu as their leader. General Wang Shiji led troops to suppress the rebellion, captured Geng Xu, and sentenced him to death under the law. Geng Xu claimed to have some clever ideas, so Wang Shiji spared his life and made him a domestic servant. After a long time, Geng Xu met his old friend Gao Zhibao, who was working as an official in the Bureau of Astronomy, responsible for astronomical observations. Geng Xu then began studying astronomy and mathematics with Gao Zhibao.

Geng Xu was very creative and made an armillary sphere that was water-powered and didn't require manual operation. Set up in a dark room, Gao Zhibao observed celestial phenomena from outside, and the predicted celestial phenomena matched the actual situation completely. When Shiji learned of this, he reported it to the emperor, and the founding emperor appointed Geng Xu as a court official and sent him to work in the Bureau of Astronomy. Later, the emperor rewarded Geng Xu to Prince Yang Xiu of Shu, who had great trust in him. When Yang Xiu was deposed, Geng Xu faced the threat of execution again. At this time, He Chou said to the founding emperor, "Geng Xu's talent is truly remarkable, and I feel sorry for the court!" The emperor then pardoned him. Geng Xu also made an ingenious water clock known as a clepsydra, which people at the time said was very ingenious.

After Emperor Yang of Sui ascended the throne, Geng Xun presented a kind of tilting vessel (an ancient instrument for measuring liquids), which the emperor liked very much, so he granted Geng Xun the status of a free man. More than a year later, Geng Xun was appointed as the Supervisor of the Right Imperial Household Bureau. Seven years later, Emperor Yang of Sui wanted to send troops to conquer Liaodong, and Geng Xun wrote a memorial saying, "Liaodong is not easy to conquer; this battle is bound to be a failure." Upon hearing this, Emperor Yang flew into a rage and ordered Geng Xun's execution, but only the pleading of He Chou saved Geng Xun's life. Later, after the catastrophic defeat in the Liaodong campaign, Emperor Yang came to understand that Geng Xun had been correct, so he appointed Geng Xun as the Chief Historiographer.

After Yuwen Huaji rebelled and killed Emperor Yang, Geng Xun followed Yuwen Huaji to Liyang. He said to his wife, "I have carefully observed the situation and studied astronomy; Yuwen Huaji will definitely fail, Li Shi will become king, I know what to do." Geng Xun wanted to leave Yuwen Huaji, but he was ultimately killed by Yuwen Huaji. Geng Xun's work "Bird Love Divination" has been handed down through generations.

Wei Ding, styled Chaosheng, hailed from Duling in Chang'an. His grandfather Wei Xuan resided in Shangshan before eventually returning to the Song Dynasty. His great-grandfather Wei Rui was the Minister of War and Equalization of the Left in the Liang Dynasty, which is akin to a senior official. His father Wei Zheng was a Yellow Gate Attendant, also a senior official. Wei Ding was known for his cheerful disposition from a young age, was knowledgeable, well-versed in history, astronomy, and geography, and was particularly adept at physiognomy. He served as the legal advisor to the Prince of Xiangdong in the Liang Dynasty. After his father's death, he mourned for five days without eating or drinking, overcome with grief, nearly collapsing from sorrow. Once the mourning period was over, he became the Registrar of Prince Shaoling.

During the chaos of the Hou Jing Rebellion, Wei Ang, the elder brother of Wei Ding, died in the capital city. Wei Ding carried his brother's body out and temporarily laid it to rest in Zhongxing Temple. He tried to find a coffin to bury his brother, but could not find one. Wei Ding, heartbroken, cried bitterly. Suddenly, he saw something floating in the river, drifting towards him. Curious, he approached for a closer look and was astonished to find a new coffin! He used this coffin to bury his brother. After hearing about this incident, Emperor Yuan of the Liang Dynasty believed that Wei Ding's heartfelt sincerity had touched the heavens. After the rebellion was quelled, Minister Wang Sengbian appointed Wei Ding to a position in the household department, and he was later promoted to Grand Commandant, Major General of the Army, and Assistant Imperial Secretary, steadily advancing in his career.

When Emperor Wu of the Chen Dynasty was in Southern Xuzhou, Wei Ding, through observing celestial phenomena, knew that Emperor Wu would one day become the emperor. So he brought his family to seek refuge with him. Wei Ding told Emperor Wu, "Next year, a great minister will be killed, and in four years, the Liang Dynasty will be destroyed, and the mandate of heaven will return to the descendants of Shun. When the Zhou Dynasty overthrew the Shang Dynasty, they enfeoffed Gui Man at Wanqiu, and his descendants became the Chen clan. I see you are intelligent and brave, and you are the one to inherit the severed imperial lineage!" Emperor Wu, who was already secretly planning to deal with Wang Sengbian, was very pleased to hear this from Wei Ding and decided to rally an army. After Emperor Wu proclaimed himself emperor, he appointed Wei Ding as a Yellow Gate Attendant, and soon promoted him to Minister of Agriculture, Right Chief of the Ministry of Works, and General of Zhenwei, also serving as the Chief of the Palace of Prince An of Yiyang, handling state affairs. He was subsequently promoted to Minister of Justice. During the Taijian era, he was sent as an envoy to the Zhou Dynasty and was granted the title of Cavalier Attendant. He then served as the Director of the Imperial Secretariat, General Who Exhibits Distant Virtue, and later as the Chief of Staff to the Prince of Linhai, serving as the administrator of Wuxing Commandery, before returning to the court to serve as Minister of the Imperial Household.

During the reign of Chen Zhide, Wei Ding sold off all his possessions and lived in a temple. His friend, the master craftsman Mao Biao, asked him why, and Wei Ding replied, "The royal spirit of Jiangdong has faded; both you and I will be buried in Chang'an in the future. The time is coming soon, that's why I have sold off all my assets."

Initially, when Wei Ding was hired to work in the court, he had met Liu Bang. Wei Ding said to Liu Bang, "I can see from your face that you're no ordinary person, and you have a deep gaze that ordinary talents can't match. In the near future, you will definitely become wealthy and prosperous. At that time, the world will be united as one family, just like the sun completes its orbit each year. I am willing to give everything to you. Your current status and achievements are still uncertain; I hope you take good care of yourself."

Later, Chen Ping was summoned by Liu Bang and appointed as the Chief of the Upper Yi with special treatment. Whenever Liu Bang feasted and played with the imperial relatives, Wei Ding was always invited to participate. One day, Liu Bang casually asked Wei Ding, "What's your relationship with Wei Shikang?" Wei Ding replied, "My family members are scattered all over, in the north and south; I've never met them my whole life." Liu Bang said, "Your family has been noble for generations; how can this be?" So he sent officials to deliver food and drinks, letting Wei Shikang and Wei Ding go back to Duling for a hearty drinking spree that lasted over ten days. Wei Ding took this opportunity to thoroughly research his family's lineage and ancestry, tracing back over twenty generations from the Meng family, who served as Prime Ministers of Chu, and compiled a seven-volume "Genealogy of the Wei Family."

At that time, Princess Lanling was widowed, and Liu Bang wanted to find her a husband, so he selected the guards Liu Shu and Xiao Jiao among others for Wei Ding to evaluate. Wei Ding said, "Xiao Jiao may become a marquis in the future, but he does not have the demeanor of marrying a noble wife; although Liu Shu may also be prominent, he won't hold office for long." Liu Bang said, "I decide who holds official positions!" In the end, the princess was married to Liu Shu. Liu Bang then asked Wei Ding, "Which of my sons will inherit the throne?" Wei Ding replied, "The one Your Majesty and the Empress favor the most will be the future heir. I wouldn't dare to guess beyond that." Liu Bang laughed and said, "You refuse to speak clearly, huh?"

In the twelfth year of the Kaihuang era, he was appointed as the governor of Guangzhou, teaching the people about benevolence and righteousness, and striving to create a peaceful social atmosphere.

There was a local thug in Guangzhou who appeared to be well-dressed on the surface but was actually engaged in criminal activities such as robbery and theft. When the governor (then called Ding) encountered him in the prefectural government, he directly asked him, "You seem like a decent guy, why did you turn to thievery?" He then conducted a detailed investigation into the henchmen of this local tyrant and their plans, which scared the tyrant into confessing.

Another incident involved an out-of-town guest having an affair with a concubine of a household in the prefecture. After the guest left, the concubine stole treasures from the household, fled in the middle of the night, and was later discovered dead in the bushes. The household, aware of the affair between the guest and their concubine, accused the guest of murdering her. After the county yamen investigated and confirmed the adultery, the guest was sentenced to death. When the case was reported to Governor Ding, he reviewed the case files and said, "This guest did commit adultery, but he didn't kill her. A monk from a nearby temple had the concubine steal, then instructed the household servants to kill her and hide the stolen goods." So, the governor let the guest go, arrested the monk, and got the stolen goods back.

Since then, there has been peace in Gwangju, and everyone greatly admires his extraordinary talents. They all say that under his governance, not a single item went missing. Later, due to his old age and poor health, he was summoned back to the capital by the court, which rewarded him repeatedly. Not long after, he died at the age of seventy-nine.

Lai He, whose courtesy name was Hongshun, was from Chang'an. He was fond of fortune-telling from a young age and was very accurate in his predictions. The Grand Chancellor Yuwen Hu brought him close, which allowed him access to the homes of high-ranking officials and nobles. He started as a minor official in the Summer Official's Office, gradually rose through the ranks, and was eventually granted the title of village noble of Anding. He was later promoted to a lower-ranking official of the Jibei and titled as a county noble of Huanshui. When the Emperor was still a commoner, he sought Lai He's fortune-telling. The Emperor later remarked to him, "You will be an emperor who will rule the world in the future." Later, when the Emperor became the Prime Minister, he appointed Lai He as his advisor. After the Emperor ascended the throne, he further elevated Lai He's title. In the final years of the Kaihuang era, Lai He submitted a memorial in which he stated:

"I have served Your Majesty since the third year of the Tianhe era during the Zhou dynasty, and have been consulted by Your Majesty many times. At that time, I said that Your Majesty's ascension to the throne as an emperor was a decree from Heaven, predestined by Heaven, not something that could be achieved by human effort. I have done nothing to deserve this, yet I have risen to the fifth rank and served for over twenty years. What right do I have to take credit for my achievements? I am truly fearful and uneasy, so I have recorded some of the words I spoke to you when you were still a prince, kept in a secret chamber, so that I would have no regrets after I die."

Your Majesty, back when you were in the Zhou Dynasty, you once said to me alongside Duke Rong of Yongfu: "I heard that you can recognize a person of virtue." At that time, I said that your eyes were as bright as morning stars, seeing everything clearly. In the future, when you become the emperor, you must learn to restrain your urge to kill. In the fourth year of Jiande, in May, Emperor Wu of Zhou asked me at Yunyang Palace: "You know all those ministers, how about Duke Xianglu of Sui?" I replied to him: "Duke Xianglu is just a rule-follower, fit for defending a region. If he were to be a general, there wouldn’t be a city he couldn’t conquer." I said these words in the southeast direction of the palace. Your Majesty, do you remember me saying this? The next year, Wuman Gui told Emperor Wu: "Duke Xianglu is not behaving like a subject." Emperor Wu asked me again, knowing he had doubts. I cleverly responded, "He is a loyal subject, nothing special." At that time, Wang Yi and Liang Yanguang knew that I had said this.

In the second year of Daxiang, in May, Your Majesty entered the palace from the east gate of Yongxiang. I was standing to the east of the gate, and Your Majesty asked me: "Do I have any disasters?" I reported to Your Majesty, saying: "Your physique and complexion match; the heavens have destined you for greatness." Not long after, you took control of the court.

The Emperor was very pleased with my report, promoted my official position, appointed me as a Kaifu, and rewarded me with 500 rolls of cloth, 300 measures of rice, and ten acres of land. Han Ze and I, from the same county, once visited the Prime Minister. I told him, "In four or five years, you’ll be in a high position with wealth." At that time, no one really got what I meant. Han Ze passed away in the fifth month of the fifteenth year of Kaihuang. When asked what happened, I explained, "Fifteen years is three fives, plus the fifth month makes it four fives. High positions and wealth refer to coffins." A lot of what I said had this meaning. I wrote a book called "The Book of Xiang," consisting of forty volumes.

The Taoist Zhang Bin, Jiao Zishun, and Dong Zihua from Yanmen all privately told you when you were still a prince: "You’re going to be an emperor one day, so take care of yourself." After you ascended the throne, you appointed Zhang Bin as the governor of Huazhou, Jiao Zishun as a Kaifu, and Dong Zihua as the Shang Yitong.

Xiao Ji, whose courtesy name was Wenxiu, was the grandson of Xiao Yi, the Xuanwu King of Changsha and the brother of Emperor Wu of the Liang Dynasty. He was knowledgeable, especially skilled in yin and yang calendar calculations. After the fall of Jiangling, he sought refuge in Northern Zhou, where he became an official known as Yitong. During Emperor Xuan's reign in Northern Zhou, Xiao Ji felt that court affairs were becoming increasingly chaotic, so he submitted a memorial advising the emperor, but unfortunately, his advice went unheeded. Later, with the rise of the Sui Dynasty, Xiao Ji retained his official position and was tasked with proofreading both ancient and contemporary yin and yang calendar texts. Xiao Ji was proud and refused to associate with the nobility, which led to his continual marginalization and discontent.

He noticed that Emperor Wen of the Sui Dynasty had a penchant for auspicious prophecies, so he sought to curry favor with the emperor by fabricating some auspicious omens. In the fourteenth year of the Kaihuang reign, he submitted a memorial stating: "This year is the Year of Jia Yin, and the first day of the eleventh month coincides with the winter solstice on Xin You. Next year is the Year of Yi Mao, and the first day of the first month coincides with the New Year on Geng Shen, with the winter solstice falling on the first day. The text 'Le Zhi Tu Zheng' states: 'The winter solstice on the first day of the eleventh month of the heavenly origin, the sage king receives blessings.' Now, Your Majesty reigns at the beginning of the heavenly origin, and the winter solstice coincides with the first day; this marks the first auspicious sign. Xin You is your birthday; Xin's virtue is in Bing, and the eleventh month is the Bing Zi month; your birthday aligns with the virtue of the month, and it is also the beginning of the New Year; this signifies the second auspicious sign. Geng Shen corresponds to your current age (or 'nominal age'); Yi's virtue is in Geng, and Mao's virtue is in Shen. Next year is the Year of Yi Mao, your current age matches the virtue of the year, and it is also the beginning of the New Year; this marks the third auspicious sign. The 'Yin Yang Book' states: 'Those whose year fate matches the year virtue will have blessings and celebrations.' The 'Hong Fan Zhuan' states: 'The beginning of the year, the beginning of the month, the beginning of the day, are all controlled by the king.' The scriptures state that when these three align, one can expect longevity, good fortune, and prosperity."

Moreover, the year of Jia Yin is the time when the yang energy begins, with the winter solstice falling on the first day of the eleventh month, marking the day of the Great King's ascension; the first month is when yang energy is at its peak, marking the beginning of the year and the lunar month. Your birthday falls on the first day of the ninth month, the beginning of the three months of flourishing, in harmony with the passing years. Thus, as stated in the Lingbao Jing: 'The dragon's spirit is strongest on its auspicious day.' Next year, your astrological sign will be the Dragon, confirmed by both the calendar and scriptures. Furthermore, the years of Jia Yin and Yi Mao are in harmony; the winter solstice of the year of Jia Yin falls on Xin You day, and the summer solstice of the following year of Yi Mao falls on the day of Jia Zi. The winter solstice marks the beginning of yang energy and the day of offering to the heavens, which coincides with your birthday, marking the fourth auspicious event; the summer solstice signifies the start of yin energy and the day dedicated to offering to the earth, which coincides with the Empress's birthday, the fifth auspicious event. Your virtues encompass all like the Qian hexagram, while the Empress's kindness nurtures all like the Kun hexagram, hence the convergence of cosmic energies centered on your birthday." Emperor Wen of Sui was greatly pleased after reading this and rewarded him with five hundred rolls of silk.

When Prince Fangling was the crown prince, he often complained of heavy yin energy and haunting disturbances in the Eastern Palace, claiming to see mouse spirits. The Emperor sent Master Ji to the Eastern Palace to conduct rituals and drive away evil spirits. A shrine was set up in the Xuan Ci Hall, and a strange wind blew in from the Gen position of the Bagua (representing mountains, also known as the gate of ghosts), heading directly toward the crown prince's seat. Master Ji quickly employed peach branch water and mugwort fire to dispel it, and the wind stopped the moment it left the palace gates. Afterwards, Master Ji performed a thanksgiving ritual, establishing an altar at the Wei position (representing earth in the Bagua), constructing four gates, and placing the shrines of the Five Emperors.

During the cold winter, a large toad suddenly hopped in from the southwest, came through the palace doors, leapt onto the shrine dedicated to the Red Emperor, and then jumped back out through the doors. It had taken just a few steps before disappearing into thin air.

The emperor was very surprised by this and rewarded Mr. Ji with many things. Mr. Ji also told the emperor that the crown prince might not be stable in his position. At that time, the emperor was thinking of deposing the crown prince and appointing someone else. When he heard what Mr. Ji said, he felt that he was right. From then on, the emperor often sought advice from Mr. Ji.

After the emperor and empress dowager died, he ordered divination to determine the location of the tomb. Fortune tellers scoured the land and eventually chose a location, reporting, "This place can bless the nation for two thousand years and the royal family for two hundred years." They also presented a drawing to the emperor.

The emperor said, "Good fortune and bad luck depend on people's actions, not on feng shui. Wasn't my father's tomb also selected through divination? In the end, the country still perished. Just like my family's ancestral grave, if it's deemed unlucky, then I shouldn't be emperor; if it's deemed lucky, my brother shouldn't have died in battle." Despite his words, the emperor ultimately accepted the favorable results of the divination.

The report stated: "On the sixteenth day, in the northwest direction of the empress's tomb, before the rooster crowed, a black cloud, roughly five or six hundred steps wide, appeared, rising straight from the ground to the sky. In the southeast direction, there were flags, carriages, tents, stretching seven to eight li, with many people marching back and forth in an orderly fashion, disappearing only after sunrise. There were over ten witnesses. According to the 'Book of Burial,' 'the earth's energy and the family name support each other, which is a sign of great fortune.' This black energy now aligns with the emperor's energy in winter and is also supported by the royal family name, signifying prosperity for future generations!" The emperor was very pleased to hear this.

Later, the emperor planned to personally attend the funeral. The fortune teller Ji once again advised, "Your Majesty, you were born in the year of Xin You. This year, the Dipper Star and Heavenly Ridge Star are in the positions of Mao and You. According to the records of the Book of Yin and Yang, it is not suitable to participate in funeral matters at this time." The emperor did not listen. After Ji left the court, he told his family member Xiao Pingzhong, "The Crown Prince sent Yu Wen Zuo to deeply thank me, saying, 'You previously said I would become the Crown Prince, and it has come true. I will never forget. Now, in selecting a tomb, make sure I ascend to the throne soon. Once I ascend, I will definitely repay you generously.' I took note then: 'In four years, the Crown Prince will take charge of the realm.' Now, the Feng Shui of the tomb has been confirmed, and the emperor insists on personally attending the funeral, making the omen all the more pronounced. Moreover, once the Crown Prince takes power, how could the Sui Dynasty possibly survive? At that time, there will surely be a rightful emperor to take charge. What I previously said about 'divining two thousand years' has a meaning of thirty characters; 'divining two hundred worlds' has a meaning of thirty-two fortunes. What I said is true, remember it!" After Emperor Yang of Sui became emperor, he appointed Ji as the Grand Minister of the Imperial Household, and even promoted him so he could establish a mansion. Once, when passing by Huayin, he saw a plume of white vapor rising from Yang Su's tomb, reaching straight up to the sky, and quietly informed the emperor. The emperor asked what this meant, and Ji said, "This signifies that a disaster of warfare will occur in Yang Su's family, with signs of impending doom. If the tomb is relocated, perhaps it can be avoided!" Later, the emperor casually mentioned to Yang Xuangan, "Your family should consider changing the ancestral tomb sooner." Yang Xuangan had an inkling of what was going on, thinking it was a good sign, and claimed he had no time to attend to family matters because Liaodong had not yet been pacified. Not long after, Yang Xuangan rebelled, and his entire family was wiped out, reinforcing the emperor's belief in Ji's predictions. Over a year later, Ji passed away. He left behind the following works:

- 30 volumes of "Golden Sea"

- 1 volume of "Essentials of Divination"

- 8 volumes of "Residence Divination"

- 6 volumes of "Burial Divination"

- 20 volumes of "Music Scores"

- 2 volumes of "Imperial Health Preservation Methods"

- 1 volume of "Essential Techniques of Palmistry"

- 1 volume of "Taiyi Establishment"

These works have been preserved through the ages.

At that time, there was a man named Yang Bochou, who, along with Xiaogong and Liu You, was famous for his proficiency in the art of divination. Yang Bochou was from Fengyi County and particularly liked to read the Book of Changes (Yijing), so he lived in seclusion on Mount Huashan. During the reign of Emperor Wen of Sui, the court summoned him to the capital. When he met those high-ranking officials, he showed no respect and had a "who do you think you are?" attitude towards everyone, leaving people puzzled. When the emperor summoned him and spoke to him, he did not say a word. The emperor rewarded him with clothes, but when he got to the court, he simply tossed the clothes aside and walked out. After that, he wandered the streets disheveled and dirty, never bothering to groom himself.

At that time, there was a person named Zhang Yongle who was a fortune teller in the capital, and Yang Bochou often followed him. If Zhang Yongle encountered an inaccurate hexagram, Yang Bochou would help him analyze the hexagram, explaining it in a clear yet insightful manner, analyzing it very thoroughly. Zhang Yongle was in awe of him, feeling that he could never match his level. Later, Yang Bochou also started his own fortune-telling stall.

Once, someone lost their child and went to Yang Bochou for a reading. After casting the hexagram, Yang Bochou said, "Your child is on the wall at the northeast corner of the South Gate of Huaiyuan Lane, held by a woman in a green dress. You will find him there." The person followed Yang Bochou's directions and indeed found the child.

Another time, a couple hid a few taels of gold, but later the gold had gone missing. The husband suspected his wife of foul play and wanted to kick her out. The wife pleaded her case and went to Yang Bochou for a reading. Yang Bochou said, "The gold is still there." He had the entire family come out, pointed to one person, and said, "The gold is with him!" The man blushed and quickly brought out the gold.

The Taoist Wei Zhichang sought out Yang Bochu for guidance on his fortune. Yang Bochu said, "Don't walk in the northeast direction. If you absolutely have to go, make sure to return early. Otherwise, Yang Su will cut off your head!" Not long after that, the emperor tasked Wei Zhichang with assisting Prince Han Liang. Shortly after, the emperor died, and Prince Han Liang rebelled. Wei Zhichang escaped back to the capital. Previously, Wei Zhichang had a feud with Yang Su. After Yang Su subdued Bingzhou, he went to find Wei Zhichang to kill him. Thanks to Yang Bochu's prophecy, he escaped disaster.

On another occasion, someone who had lost a horse came to Yang Bochu for divination. At that time, Yang Bochu was summoned by the crown prince. On the way, he met this person and immediately divined for him. After the divination, Yang Bochu said, "I don't have time to calculate in detail for you. Go to the third shop south of the east gate wall in the west market and buy a fish for me to make fish slices. You’ll find your horse there." The person did as he was told, and soon someone came leading the lost horse. The person caught the horse thief on the spot.

Yazhou offered a pearl the size of a thumb, but the person who delivered it secretly exchanged it for a smaller one. The emperor grew suspicious and summoned Yang Bochu for divination. Yang Bochu said, "There is something that came out of the water, round and shiny. That is the big pearl. It is now hidden by someone." He even provided the name and description of the person who had hidden the pearl. The emperor followed Yang Bochu's guidance and indeed found the pearl. The emperor was very surprised and rewarded him with twenty pieces of cloth.

He Tuo, the sacrificial official of Guozi, once sought out Yang Bochu to discuss the Book of Changes. After a moment, Yang Bochu slowly explained that his reasoning differed from that of earlier Confucian scholars, but his ideas were profound and enigmatic, which led people to believe he was exceptionally gifted. Ultimately, Yang Bochu passed away peacefully.

Lin Xiaogong, a native of Jingzhao Prefecture, was knowledgeable in astronomy and mathematics, and the Emperor held him in high regard. Every time he predicted disasters, he was very accurate, so the Emperor appointed him to study the Yin-Yang calendar. He later rose to the position of an official and wrote many books, including "Yiqi Tu" in three volumes, "Didong Tongyi Jing" in one volume, "Jiugong Wumu" in one volume, "Dunjia Yueling" in ten volumes, "Yuanchen Jing" in ten volumes, "Yuanchen E" in one hundred and nine volumes, "Baiguai Shu" in eighteen volumes, "Lumingshu" in twenty volumes, "Jiugong Guijing" in one hundred and ten volumes, "Taiyi Shi Jing" in thirty volumes, and "Kongzi Matou Yibushu" in one volume, all of which have been preserved through the ages.

Liu You, a native of Xingyang, during the Sui Dynasty, specifically in the Kaihuang era, became a grand commander and was granted the title of Duke of Suolu County. His predictions were remarkably accurate, and the Emperor had a close relationship with him. At the beginning, he worked with Zhang Bin, Liu Hui, and Ma Xian to develop the calendar. Later, he received an order to write a military treatise, "Jin Tao" in ten volumes, which the Emperor greatly appreciated. He also wrote "Yin Ce" in twenty volumes, "Guantai Feihou" in six volumes, "Xuanxiang Yaoji" in five volumes, "Lulishu Wen" in one volume, "Hunyin Zhi" in three volumes, "Chanru Zhi" in two volumes, "Shijing" in four volumes, "Sishi Licheng Fa" in one volume, "Anli Zhi" in twelve volumes, and "Guizheng Yi" in ten volumes, all of which have also been preserved through the ages.

Zhang Zhouxuan, hailing from Zixian in Bohai, was a person with profound knowledge, especially skilled in astrology and divination. He was recommended by the Governor of Jizhou, Zhao Jing, and summoned by Emperor Gaozu, who appointed him as a Yunqi Officer and allowed him to assist in formulating calendars at the Imperial Academy of Astrology. Many others at the time were not his equal, so Chief Astrologer Liu Hui and his peers envied him. However, Liu Hui was left speechless, while Zhang Zhouxuan explained 54 questions clearly. As a result, Zhang Zhouxuan was promoted to junior cavalier attendant and appointed as the Chief Astrologer, and received a reward of a thousand rolls of cloth, while Liu Hui and his eight associates were all dismissed. Zhang Zhouxuan then formulated a new calendar, stating that the old calendar was inaccurate by a day. The Minister of the Interior, Yan Minchu, reported: "During the Han Dynasty, Liu Hong made changes to the Zhuanxu Calendar and established the Taichu Calendar, saying that it would be off by a day in the future, and that a sage would come to correct it eight hundred years later. Now it has been seven hundred and ten years, and the experts have all calculated this and claim the sage is here; could it be now?" The Emperor was very pleased and increasingly trusted him, entrusting him with even greater responsibilities. Zhang Zhouxuan's calendar had three differences from the ancient calendars.

At the end of the Song Dynasty, Zu Chongzhi created a new calculation method called "differential method." He found that the position of the winter solstice point does not move in a regular pattern every year as previously thought. It only moves one degree every forty-six years. Later, Yu Xi of the Liang Dynasty established a new calendar, believing that Zu Chongzhi's calculations had a significant error. He changed the time it takes for the winter solstice point to move one degree to 186 years. Zhi Xuan studied these two methods and found a significant difference in the timeframes. Upon tracing ancient records, he discovered a large margin of error. Therefore, he combined the methods of both and arrived at a compromise. He believed that the winter solstice point moves one degree every 83 years, which aligns with records of day lengths and star positions from the era of Emperor Yao, as well as the records of star positions in the Han Dynasty calendar. It was accurate in both cases.

During the Zhou Dynasty, Ma Xian created the "Bingyin Yuanli," which included methods for converting between lunar and solar calendars, calculations involving addition and subtraction, and a method for predicting solar eclipses. This was his innovative calculation method. At that time, many astronomers found it difficult to grasp. Zhang Bin later used this method but could not fully comprehend it either. Zhi Xuan believed that Ma Xian's method had theoretical issues regarding the sequencing of addition and subtraction and changes in solar terms. He explained it based on the speed of the sun's movement in relation to the changes in the twenty-four solar terms. He posited that when the sun's movement is slow, the moon catches up quickly, leading to an earlier new moon; when the sun moves fast, the moon catches up slowly, causing a delay in the new moon. He examined the timing of new moons in previous calendars to calculate the ratios of discrepancies. He found that from the autumnal equinox to the vernal equinox, the sun moves fast, covering 180 degrees in 182 days; from the vernal equinox to the autumnal equinox, the sun moves slower, covering 176 degrees in 182 days. Each solar term was derived using this ratio.

From ancient times to the present, when calculating the new moon and full moon, the traditional calendar did not take into account the concept of "outer limit." As long as it was in opposition, it was considered that a solar eclipse may occur. Zhang Bin introduced the concept of the "outer limit," indicating that this method was still imperfect, as in some cases, even if it met the opposition, a solar eclipse did not actually occur. Zhou Xuan believed that the sun travels along the ecliptic, completing one orbit in a year, while the moon travels along its own path, completing approximately one orbit every 27 days. When the paths of the moon and the sun intersect, every thirteen days or so, the moon moves from inside the ecliptic to outside, and then back inside again after another thirteen days, repeating this cycle. This passage of the moon through the ecliptic is called a "conjunction." If the new moon and full moon occur within 15 degrees of the conjunction, a solar eclipse may occur. If the moon is traveling inside the ecliptic, i.e., to the north, solar eclipses are easier to observe; if the moon is traveling outside the ecliptic, i.e., to the south, even if it reaches a conjunction, due to the relative positions of the moon and the sun, a solar eclipse will not occur, which makes it difficult to observe. Therefore, Zhou Xuan established the concept of the "outer limit," building on previous methods, calculating the errors based on the proximity of the conjunction, adjusting the degree of the solar eclipse, thus making the prediction of solar eclipses more accurate.

There are seven unique aspects that surpass ancient methods: Firstly, the ancient calendars believed that the speeds of the five planets were thought to be constant, only observing that they sometimes moved faster or slower without finding a pattern. Through long-term observations, Zu Chongzhi discovered their true speeds of movement, which did not align with the ancient calendars. The discrepancies for some planets could even exceed thirty days! For example, if Mars appeared during the Rain Water solar term, it would require an additional calculation of twenty-nine days on average; if it appeared during the Minor Snow solar term, it would need to be calculated as twenty-five days less. While the exact appearance time could be determined by adjusting for the average appearance time, other planets also had variations in speed, with different magnitudes of error. The accumulated wisdom of ancient times can be challenging for modern people to grasp.

In the second paragraph, people believed that Mercury only appeared once every time it orbited the sun, and all ancient calendars reflected this belief. If Mercury was expected to appear but didn't, no one could explain it. Zu Chongzhi discovered through long-term observations that Mercury can appear several times while orbiting the sun, and it can also be influenced by other stars, appearing simultaneously. For example, if Mercury appears in the morning of the Rain Water solar term, theoretically it should be visible, but in reality it may not be seen; if it appears in the morning of the Awakening of Insects solar term, then it is between 18 to 36 degrees from the sun, and if Jupiter, Mars, Saturn, or Venus also appear at the same time, Mercury will also appear together.

In the third paragraph, ancient methods for calculating planetary movements relied on fixed speeds and ranges, predicting their future positions based on the speed after they appear. However, accurately predicting the speed of planetary movements and their times of appearance is not possible. Zu Chongzhi discovered through long-term observations that the speed, stops, and retrograde motion of the five planets were different from the ancient algorithms, with errors of over eighty days and deviations of more than eighty degrees in their orbits. For example, if Mars appears rapidly in early winter, it will move 177 degrees in 250 days; if it appears in early summer, it will only move 92 degrees in 170 days. Through repeated verification, he found that his calculations were highly accurate and consistent with actual observations, whether ancient or modern.

In the fourth paragraph, ancient methods for estimating the size of solar eclipses relied on average values, often not matching the actual situation. Zu Chongzhi discovered through long-term observations that the speed of the moon's movement is affected by Jupiter, Mars, Saturn, and Venus. When the moon is close to these four stars, its speed increases, and when it is far away, it slows down, only returning to its original speed after a distance of more than fifteen degrees. Thus, he calculated the size of solar eclipses by considering the distance between the moon and these four stars.

Fifth, in ancient calendars, the calculation of the dates of the new moon and full moon (first and fifteenth day of the lunar month) was done in the same way. Zu Chongzhi discovered through long-term observation that the position, timing, and magnitude of a solar eclipse change depending on the observation location. The direction and height of the solar eclipse vary in different places, as well as the depth and speed of the eclipse. Therefore, the timing of solar eclipses must be calculated based on specific circumstances to conform to celestial phenomena.

Sixth, in ancient calendars, the calculation of the extent of a solar eclipse was based on the conjunction of the sun and moon. When the sun and moon are fourteen degrees apart, the eclipse is only one fraction; when they are thirteen degrees apart, it is two fractions; when they are ten degrees apart, it is three fractions. With each degree closer, the extent of the eclipse increases by one unit, and when they are completely aligned, the eclipse reaches its maximum extent. The actual occurrence of a solar eclipse can sometimes differ from the calculated results, either more or less, and various ancient calendars have not been able to fully explain the reasons. Zhou Xuan identified a pattern through long-term observation: near the conjunction point of the sun and moon, the moon does not fully obscure the sun, so the extent of the eclipse is relatively small; but when the sun and moon are five to six degrees apart, the moon is completely within the sun, resulting in the maximum eclipse. Afterwards, as the distance increases, the extent of the eclipse decreases. This is the case around the winter solstice. However, if it is close to the summer solstice, the rule is slightly different. His classification of solar eclipses can be said to be very detailed and precise.

Seventh, ancient calendars believed that day and night are equal in length during the spring equinox and autumn equinox. Zhou Xuan discovered through long-term observation that there was actually a difference. During the spring and autumn equinoxes, daytime is about fifteen minutes longer than nighttime, due to the varying speed of the sun's movement.

In conclusion, Zhou Xuan's unique insights all stem from his own thinking and research. His precise explanations earned him great respect. He passed away during the reign of Emperor Yang of the Sui Dynasty.

Xu Zhicang is from Gaoyang. His ancestor Xu Daoyou once read medical books and studied medicine in depth because his mother was sick, and he became a famous doctor as a result. He warned his sons, "If a son does not understand his parents' diet, daily life, and medication, and does not understand medicine, how can he be considered filial?" Therefore, the medical skills of the Xu family have been passed down through generations. Xu Zhicang served as a cavalry officer during the Liang Dynasty, eventually becoming a cavalry officer. His father, Xu Jing, was a counselor to King Wuling. Xu Zhicang gained fame for his exceptional medical skills at a young age and served as a cavalry officer during the Chen Dynasty. After the fall of the Chen Dynasty, Emperor Yang of Sui appointed him as a cavalry officer and sent him to Yangzhou. Coincidentally, Prince Xiao of Qin, Jun, fell ill, and the emperor summoned Xu Zhicang. In a dream, Jun's deceased wife, Lady Cui, cried and expressed concern that Xu Zhicang's arrival would bring suffering. Xu Zhicang diagnosed a severe illness that had taken hold and predicted that Prince Jun's death was imminent. True to his words, Prince Jun passed away a few days later. The emperor was astonished by Xu Zhicang's extraordinary medical skills and rewarded him with one hundred rolls of cloth. After Emperor Yang of Sui ascended the throne, Xu Zhicang had retired and was consulted by the emperor whenever he felt unwell. Sometimes, officials were sent to bring him to the palace and help him to the emperor's bed. Xu Zhicang's prescriptions always proved effective. He passed away peacefully at home at the age of eighty.

Xu Cheng came from a lineage of royal descent and was a renowned physician with remarkable medical skills. His father, Xu Shi, served as the Minister of Ceremonies and Grand Commandant of the Left during the Liang Dynasty, holding high-ranking positions. Later, he followed Liu Zhongli to Chang'an, where he was equally renowned as Yao Sengyuan. Eventually, he rose to the position of the Supervisor of the Left Commandant, a very high-ranking position.

Xu Cheng inherited his father's medical skills and even surpassed him. He served as the Imperial Physician and later as the Grand Councilor, eventually being titled as the Count of Hechuan County. The medical expertise of both father and son was highly esteemed throughout the Zhou and Sui Dynasties, with a great reputation. Unfortunately, historical records are not very detailed, so I have written down everything I know here.

Wan Baochang's origins remain a mystery. His father, Da Tong, surrendered to the Qi Dynasty with the Liang Dynasty general Wang Lin. Later, he conspired to return to Jiangnan, but his plan was exposed, and he was killed. Wan Baochang was then assigned to serve as a musician, so he became highly skilled in music, proficient in various musical instruments. He presented jade chimes to the Qi Dynasty emperor. Once, during a meal discussion about musical tones, Wan Baochang picked up utensils and miscellaneous items in front of him, using chopsticks to strike them, distinguishing their high and low tones, harmonizing perfectly like silk and bamboo instruments, which were greatly appreciated by the people at the time.

However, throughout the Zhou and Sui Dynasties, he was never given much importance. During the Sui Dynasty's Kaihuang reign, the Duke of Pei, Zheng Yi, and others established new musical standards, initially based on the Huangzhong scale. Although Wan Baochang was merely a musician, Zheng Yi and others often consulted with him, but many of his suggestions went unheeded. Later, when Zheng Yi's musical standards were completed and presented to the emperor, the emperor summoned Wan Baochang to ask for his opinion. Wan Baochang said, "This is the music of a fallen kingdom; how could Your Majesty possibly listen to it!" The emperor was displeased. Wan Baochang strongly argued that the music sounded mournful and decadent, not the proper elegant music, and requested that a water ruler be used as the standard for tuning the instruments. The emperor agreed.

Wan Bao was always tasked with creating various musical instruments, producing sounds that were two notes lower than those described in Zheng Yi's music theory. He also wrote 64 volumes of "Musical Scores," detailing the method by which the eight-tone cycle is transformed into the palace mode, as well as the changes in string and pillar movements. He created 84 modes, 144 tones, and a total of 1,800 combinations of sounds. At that time, people believed that the "Zhou Li" contained a hidden meaning related to the revolving palace. Since the Han and Wei dynasties, those knowledgeable in music theory struggled to comprehend it. When Wan Bao achieved this, he was met with mockery from all sides. By this time, when people tried it out, he could compose music instantly and effortlessly, astonishing those who saw it.

He improved and added countless musical instruments, and his music was elegant yet unappreciated, not favored by people at that time. Those in the Ministry of Rites, who were well-versed in music theory, ostracized him. The Prince's stable master, Su Kui, prided himself on his mastery of bell music, especially envying Wan Bao. Su Kui's father, Su Wei, was in power at the time, and anyone who discussed music aligned themselves with Su Wei and belittled Wan Bao. Wan Bao visited the court officials many times to voice his grievances. Su Wei questioned Wan Bao, asking where he learned these things from. A monk advised Wan Bao, "The emperor favors auspicious signs. He is pleased with anything that talks about lucky omens. Just say you learned it from a barbarian monk, that it's the music passed down by the Buddha. The emperor will definitely be pleased. You can promote these things." Wan Bao followed the monk's advice and answered Su Wei accordingly. Su Wei angrily said, "The music passed down by the barbarian monk is foreign music, not what should be promoted in China!" This matter ultimately came to nothing.

Wan Bao once heard the music played by the Ministry of Rites and couldn't help but shed tears. When asked why, Wan Bao replied, "The music is both lascivious and melancholic, and the world is soon going to kill each other and be destroyed." At that time, the world enjoyed a period of peace and prosperity, and those who heard him say this found it impossible to believe. By the end of the Deyuan period of the Sui Dynasty, his words ultimately came to pass.

Bao Chang was a man of great poverty and had no children. When his wife saw him fall ill, she secretly took his money and possessions and fled. Bao Chang was hungry and cold, left alone without anyone to care for him, and eventually starved to death. Before he died, he burned all the books he had written, saying, "What use are these things?" A few scrolls were salvaged from the flames and later circulated widely, 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 created music books that were widely used at the time. However, their natural understanding of music could not compare to Bao Chang's. An Maju, Cao Miaoda, Wang Changtong, and Guo Lingyue were skilled composers and the most talented of the time. They also studied Zheng music, but Bao Chang's compositions were considered elegant music. Although these people did not openly praise Bao Chang, they all held him in high regard, thinking of him as a godlike figure.

There was a musician named Wang Lingyan who lived during that period and was also very knowledgeable about music theory. During the Daye period of Emperor Yang of the Sui Dynasty, he was about to go to Jiangdu, and Wang Lingyan's son followed him. He played the huqin outdoors, playing a variation of the "An Gongzi Qu." Wang Lingyan was in the bedroom at the time, and when he heard it, he was taken aback and suddenly stood up, saying, "Oh no, oh no!" He quickly stopped his son and asked, "When did this tune become popular?" His son replied, "It has only recently become popular." Wang Lingyan started crying and told his son, "You must not go with them; the emperor will not come back." When his son inquired why, Wang Lingyan said, "The tonality of this tune is one-way, and the tonality represents the monarch, that's why I said so." Eventually, Emperor Yang of Sui was indeed assassinated in Jiangdu.

The historical records say: divination of yin and yang is mentioned in the teachings of ancient sages, although it cannot be completely believed or completely denied. If a person can promote the right way, it benefits society, but if their actions contradict moral principles, it will lead to disaster. Therefore, the gentlemen of ancient times advised people against reckless actions. Currently, Wei and Lai's assessments of bone structure and complexion, and Yu and Zhang's calculations of profit and loss, even figures like Luo Xia, Gaotang, Xu Fu, and Zhu Jian do not compare to them. Bo Chou's tortoise divination can discern the intentions of spirits and deities; Geng Xun's astrolabe can accurately measure the stars; Bao Chang's music theory can precisely capture the harmony of musical scales. While they may not match the great masters of antiquity, they are certainly among the best of their era. The acupuncture techniques of the Xu family, as recorded in historical texts, are commendable; Xiao Ji's theories on yin and yang tend to be somewhat exaggerated.