The History of China - Supplemental Biopic: The Mathematician Of Heaven

Episode Date: August 11, 2015

This short episode covers the life of one of the great mathematicians, astronomers, and engineers of ancient China: Zu Chongzhi. In his life from 429-500 CE, he will re-create an ancient precursor to the compass that had been lost for centuries, calculate the motions of the celestial objects with a degree of accuracy in excess of 99.9%, design a comprehensive new calendar system, and derive the value of π to a degree of accuracy that would not be surpassed the world over for another millennium. Learn more about your ad choices. Visit megaphone.fm/adchoices

You're listening to an Airwave Media Podcast. Hi everyone, this is Scott. If you want to learn about the world's oldest civilizations, find out how they were rediscovered, follow the story of Mark Antony and Cleopatra's descendants over ten generations, or take a deep dive into the Iron Age or the Hellenistic era, then check out the Ancient World Podcast. Available on all podcasting platforms or go to ancientworldpodcast.com. That's the Ancient World Podcast. Hello, and welcome to the History of China.

Supplemental Biopic, The Mathematician of Heaven Even though we may be on hiatus for a month from my first vacation in some two odd years, and as of now I'm sequestered away from the internet entirely for two weeks in central Minnesota, well, what can I say? I can't help but give you guys some additional details about the period we're in right now. We're not going to be advancing the narrative any in these supplemental mini-episodes, but instead backtracking a fair bit and exploring some of the more overlooked, perhaps less flashy aspects of Chinese culture during these tumultuous decades of the Southern and Northern Period. You know, the sort of stories that just managed to get left out in the pell-mell of dynasties rising and falling and armies clashing violently.

Today, we'll be focusing on one of the famed mathematicians, engineers, and astronomers of the era, Zhu Chongzhe. Zhu Chongzhe was born in the year 429, in the capital of what was first Eastern Jin, and then Liu Song, Nanjing, or again, as it was then known, Jian Kang. Though Chongzhe would spend his entire life south of the Yangtze River, his grandfather had actually been one of the many ethnically Han emigres to the south when he felt he could no longer keep his family safe among the warfare of the northern Qianbei. Once safely south, he'd come to hold the title of Chief Minister of the Palace Buildings, an auspicious post within the imperial

court that his son after him, Chongzhi's father, would likewise come to hold in time. As was common in the pre-modern era, Zhu was a family of mathematicians and astronomers several generations deep. As such, he was exposed to such concepts from an early age, specifically learning from the nine chapters on the mathematic arts and the associated commentary by the mathematician Liu Hui, and showed a particular talent for the discipline. In addition, he showed aptitude for engineering as well as literary style. This multitude of talents, and surely his family connections within the court, earned the young Du Chongzhe a place in the Hualing Student Academy by the personal order of Emperor Xiao Wu in the early

450s, following the Liu Song emperor's violent capture of the capital city and execution of his own brother, the former emperor, as we discussed at length back in episode 62. So while the Liu Song dynasty boiled and began to burn, Zhu Chongzhi had been set on the path to personal success, come what may, for the upper echelons of the imperial household. His stint at the academy bore out what the imperial court had seen in him, and soon enough, Chongzhi had secured a spot within the prestigious roles of the Nanjing Imperial University, where he labored under his instructors as what amounted to a research assistant. Again, he proved more than capable of the tasks set before him, as once he'd completed his coursework at the Capital University,

he was rewarded with an assignment at the office of the governor of the nearby city Nanshu, which bordered the capital, serving, then and now, as a vital linking port between the Yangtze River and the Grand Canal. Later, he'd be recalled to the capital and made an officer in the military, where he'd continue his meticulous studies. Over the course of his various stints in public office, Zhu Chongzhi completed numerous treatises and worked on his professional interests, specifically advanced mathematics and astronomical observations. In the field of pure mathematics, he was well known in his time and as far forward as the 12th century under the Song dynasty for his book the Zui Shu, which can perhaps best be translated as Methods for Interpolation. The work reportedly contained detailed formulas for the volume of a sphere, as well as cubic

equations, both highly advanced for the time. His work was so advanced that it would be adopted into the imperial examination system of the Tang dynasties in the year 656, although it was later dropped from the examinations on account of them being so advanced that none of the prospective imperial officials could adequately wrap their heads around the formulas and proofs within. Later, the book was inducted as one of the ten classical texts in 1084 under the Song dynasty. Unfortunately, it did not survive the turmoil of the late Song dynasty and the Mongolian invasions, and was lost to the ages.

But his most significant contribution to mathematics was his work on calculating the value of pi. The search for pi, of course, far preceded the 5th century of Zhu Chongzhi's time, since at the very least the calculations of Archimedes in the 3rd century BCE. Zhu's initial approximation of pi independently recreated Archimedes' own calculation of the ratio at 22 over 7, but over the course of his work, he refined his equation to the truly remarkable ratio of 355 over 113, known in Chinese as Zhu's fraction, that was accurate to six decimal places, an unprecedented feat that would stand as the world's best rational approximation of pi until the late 16th century in the Netherlands. And this milestone of calculation that would stand as the world's best rational approximation of pi until the late 16th century in the Netherlands.

And this milestone of calculation that would stand for more than a thousand years before being surpassed is even more impressive because of the meager tools Zhu used to arrive at his eponymous proportion. He would use nothing more than simple counting rods, that is to say, sticks, laid out in patterns to infer. He would purportedly arrive at his eponymous fraction by painstakingly laying out 24,576 rods into a 12,288-sided polygon, and then using that shape to approximate a true circle by using extremely lengthy calculations involving hundreds of square roots to arrive at an approximation with nine decimal places of

accuracy. Quite the hobby. According to the history of the Sui dynasty, compiled in the 7th century, quote, Zhu Chongzhi further devised a precise method of calculating, taking a circle of diameter 10 million chang. He found the circumference of this circle to be less than 31,415,927 chang, and greater than 31,415,926 chang. He deduced from these results that the accurate value of the circumference must lie between these two values. Therefore, the precise value of the ratio of the circumference of a circle to its diameter is as 355 to 113, and the approximate value is as 22 to 7." In terms of engineering feats, Zhu was no slouch either, and most famously recreated the famed southern pointing chariot.

What is a southern pointing chariot, you might ask? It acted, in effect, as a non-magnetic compass, a machine that, through a complex set of differential gears, da Vinci himself would have been proud of, operated to maintain a figurine attached to the chariot, pointing due south at all times. Much like the magnetic compass later on, such a machine was highly valued as a battlefield asset for properly moving and aligning armies. Legendarily, the chariot had been almost a gift from the heavens, and had been present since the demigods of Chinese mythological origin tales first merged their tribes into the Han people thousands of years prior. But realistically, the first actual, functioning southern-pointing chariot can be traced back to the late Han dynasty, and is attributed to the engineer Ma Jun

of the early and mid-third century. Using principles similar to what allows the wheels of a modern car to rotate at different speeds but with equal torque when making a turn, Ma Jun had successfully created a chariot that would unerringly point south on its own. Unfortunately, the end of the Han dynasty and the as-yet-ongoing strife in the following Age of Disunity saw the secret of the southern-pointing chariot lost in the chaos. During the early conquests of Emperor Wu of Liu Song, he was briefly excited at the prospect of recovering a functioning prototype of the chariot following his acquisition of the Guanzhong region. However, upon inspection, it proved to be only an empty shell and functioned by having a person sit within and manually turn the figurine whenever the chariot was turned. Suffice it to say, Wu was less than impressed,

and so he turned to Zhu Chongzhi in the year 478, who felt confident that he could recreate the ancient device. According to the Book of Qi, quote, During the reign of Shen Ming, Zhu Chongzhe was commissioned to reconstruct the southern pointing chariot according to the ancient rules. He accordingly made new machinery of bronze, which would turn round without a hitch and indicate the direction with uniformity. Since Ma Jun's time, such a thing had not been. End quote. The final and perhaps most impressive of his disciplines, however,

was his observations and calculations of the skies above. Among his findings, he determined that a year consisted of 365.2428 days, which is about 50 seconds off from our current knowledge of the year being 365.2421 days. He also calculated the orbital period of Jupiter at 11.858 years, 99.96% accurate, or about a day and a half different from our current understanding. In addition, he accurately predicted the number and timing of overlaps between the sun and the moon with 99.99% accuracy, as 27.21223 per year, which in turn allowed him to predict with great accuracy as many as four solar eclipses between 436 and 459,

gaining him wide prestige among the royal court. In fact, Zeus' calculations regarding heavenly motions were so advanced for the time that many of his contemporaries found his conclusions baffling or even profane. He'd spent years developing a new calendar system he called the Daming, or calendar of great brightness. Prior to Zhu's Daming innovation, the Chinese calendar had been based on a cycle of 19 years, each with 12 months consisting of 29 or 30 days. The Daming calendar, however, was based on a cycle of 391 years and was arrived at through Zhu Chongzhe's observations and measurements of the tropical year compared to the sidereal or astrological year. Though far more accurate in its measurements than

the calendar system then in use, his rather stark shift in the measurement of time itself raised more than a few eyebrows at court and drew the condemnation of his fellow minister, Tai Fa Xin, who declared that Zhu's calendar was, quote, distorting the eternal truth of heaven and violating the teachings of the great classics, end quote, a criticism against progress and innovation that would be echoed across time. Why, we've always done it this way. We can't change it now. But Zhu answered his challenger in kind, stating that his Da Ming calendar, Xiaowu was convinced and ordered the implementation of the new calendar in 464. That would be delayed, however, by the untim the implementation of the new calendar in 464. That would be delayed, however, by the untimely death of the Liu Song monarch.

His successor, Emperor Qianfei, sided more with the criticisms of Minister Tai Faxin and canceled the adoption of the Daming calendar. Upon Emperor Xiaowu's death, and knowing that his skills would not be put to great use by the new emperor, Zhu retired from his ministerial position and devoted the rest of his life to purely scientific studies. In fact, Zhu Chongzhe would not live to see his calendar, magnum opus, come into general use. He would die in the year 500 CE, at 71 years old, as a peerless mathematician and astronomer. His life work was taken up, as he had from his father before him, by his son, Zhu Gengzhi, who in fact had assisted his father in writing the Zui Shu. Upon his father's death, Gengzhi became the primary advocate of his father's superior calendar system and began once again lobbying the imperial court of the southern Qi dynasty to take up the

system for general use. His efforts would prove successful in 510, and southern China officially began to utilize Zhu Chongzhi's method of keeping track of time through studious observation of heavenly movements. With Zhu Chongzhi's death, China lost a scientist and mathematician who was literally centuries ahead of his time, a mind so advanced that even the best and brightest Tang China could offer up for its academy examinations more than 150 years later found themselves quite stumped by the sheer complexity of his findings. And with his great book the Zui Shu subsequently destroyed at the end of the Song dynasty, perhaps one of the greatest mathematical tomes in world history was lost forever. Nevertheless, Zhu Chongzhe is remembered for the tremendous mind he was, and his contributions to

the sciences in almost every field he devoted himself to. His name lives on not only in his eponymous formula to approximate pi, but has been given to two astronomical objects as a testament to the study that came to define his life. On the face of the moon, there is a crater that is named after him, as well as the asteroid 1964V01, aka 1888 Zhu Chongzhe. And as perhaps a nod to the formulas he produced being so complex that it took centuries for anyone else to be able to adequately understand them, his name has also been afic to the Zhu Xi stream cipher, an advanced encryption algorithm. And so we come to the conclusion of Zhu Chongzhi's life.

I'm still on holiday for about two more weeks, and I'll be traveling to Washington next, but I'll see if I can get another one of these biopics out in the meantime, before I get back to my home in my real mic at the end of August to pick back up on the end stages of the Southern and Northern Dynasties and the Age of Disunity as a whole. Until then, wishing you all the best, and as always, thank you for listening. 400 years ago, a trio of tiny kingdoms were perched on some damp islands off the coast of Europe. Within three short centuries, these islands would become the centre of an empire which ruled a quarter of the globe and on which the sun never set. I'm Samuel Hume,

a historian of the British Empire, and my podcast Pax Britannica follows the people and events that built that empire into a global superpower. Learn the history of the British Empire by listening to Pax Britannica everywhere you find your podcasts, or go to pod.link slash pax.