In order for the barbarians to follow the way of heaven, they would first need to find their way to the wellspring of Confucian virtue, the Middle Kingdom. Such a journey would require both maps and the ability to establish position at sea. Thus the provision of accurate charts and a viable system of navigation was of paramount importance—not only to facilitate the safe passage of Zheng He and his fleets but also to encourage the barbarians to return tribute to the new emperor.

Zhu Di and his father, Hong Wu, had encouraged the development of every aspect of navigation. A handbook titled Notebook on Sea Bottom Currents, found in Quanzhou, states that, after announcing the ascension of the Yongle emperor (Zhu Di) to the throne, Zheng He and his admirals were instructed to search for navigation charts, collecting all the information about currents, islands, mountains, straits, and the positions of stars. They used this data to revise their navigation charts, including compass points and the cross-references of stars.

The Chinese cultivated Arab navigators and astronomers, especially during the Yuan dynasty (1279–1368). According to Gong Zhen, in 1403, two years before the first formal expedition, Zheng He, Jang Min, and Li Qi were sent by Zhu Di to visit countries of the western oceans. Their mission included recruiting foreign navigators capable of deep-sea navigation. For this and much other information in chapters 3 5, and 6, I am indebted to Tai Peng Wang’s research.1

The writer Yan Congjian stated in Shuyu Zhouzi Lu (Compiled information about the remotest foreign countries):

In the first year of the reign of the Emperor Hong Wu of the Ming dynasty (1368) the Emperor converted the Bureau of History into the Bureau of Astronomy. He also established the Bureau of the Chinese Islamic Astronomy. In the second year (1369) the Hong Wu Emperor summoned eleven Chinese Muslims including Zheng Ah Li, the Chinese Muslim Astronomical Officer, to the capital, Nanjing, “on a mission to improve on the Islamic calendars and to observe the astronomical-phenomena. They were each conferred upon with gifts and official titles accordingly.

In 1382 the emperor summoned a group of scholars, including the Islamic observatory official Hai Da Er and a master of Islam named Ma Sa Yi Hei, to choose the best astronomy books among several hundred volumes of Xiyu Shu (Books from the western regions) at the Yuan court in Beijing. The next year, a Chinese translation of the selected books, Tian Wen Shu (Works of astronomy), was published.

According to the Ming translator Ma Ha, the Tian Wen Shu was originally written by Abu Hassan Koshiya (A.D. 971–1029), a Yuan mathematician who played a dominant role in the development of spherical trigonometry. Ma Ha praises Koshiya as “one of the greatest scholars of all times who explained the ultimate theories of astronomy in all its great profundity and simplicity.”

The Tian Wen Shu explained the Islamic concepts of longitude and latitude. So it is clear that early Chinese concepts of latitude, longitude, and a round earth go back at least to this Ming translation of Islamic geography books. In about 1270 the Arab astrologist Jamal ad-Din had made a terrestrial globe of the earth that correctly depicted the proportions of land (30 percent) and sea (70 percent). He gave the globe to Guo Shoujing, as will be described in later chapters.

A reliance on Islamic navigators continued in Zheng He’s era. Zheng He himself was a Muslim, and given the advanced state of navigation and astronomy in the Islamic world, it’s no wonder he recruited other Muslims to his fleets. According to Chen Shuiyuan, a Taiwanese historian, many were located in Quanzhou, one of the most cosmopolitan cities in the world and home to special graveyards reserved for Muslim sailors. Zheng He and his team also searched the provinces of Fujian, Guangdong, and Zhejiang for superior navigators.

Foreign navigators and astronomers who voyaged on Chinese ships were given Chinese names, such as Wang Gui, Wu Zheng, and Ma Zheng. When they returned after a successful mission, they were rewarded. In 1407, for example, foreigners returning to Quanzhou received notes equivalent to fifty taeles of silver as well as rolls of embroidered silk. In 1430, when a foreign Muslim named Sheban returned from the final expedition, the Xuan De Emperor promoted him to deputy battalion commander.

In a paper titled “Instruments and Observation at the Imperial Astronomical Bureau During the Ming Dynasty,” Professor Thatcher E. Deane states:

As with the development of the calendric systems…were most evident at the beginning of a dynasty, less so at the beginning of an individual emperor’s reign, and almost never at any other time when such expenditures were not direct investments in legitimising state and ruler. Hong Wu had an urgent need to improve the calendrical system because he was the first of the dynasty; Zhu Di was accused of usurping the throne so he also had a very strong need.

Gifts for Foreign Rulers

This obsessive focus on improving navigational techniques enabled Zheng He’s fleets to reach foreign countries, where, after presenting their credentials, the Chinese ambassadors would supply maps and astronomical tables to the rulers. The gift of knowledge was intended to make it possible for them to return tribute to the Middle Kingdom.

We know from recent excavations at the Jingdezhen kilns (where the bulk of the ceramics carried in Zheng He’s fleets were fired) and from excavations in Cairo beside the Red Sea Canal, as well as from collections in Europe, that Chinese delegations offered personal gifts to foreign leaders. Ceramic copies of Mamluk candlesticks were given to the Mamluk sultans, along with blue and white flasks, ewers, porcelain cups, and pen boxes. A ewer cover decorated with an armillary sphere in cobalt was fired for the king of Portugal, as were ceramic tiles for Ottoman sultans.

Gifts for more ordinary folk made the journey as well. Playing cards, chess, and mah-jongg sets were given to merchants. Children’s whirligig toys, kites, and hot-air balloons were dispensed.

The saddest cargo of the great fleets were women. Traditionally, foreign rulers were each presented with one hundred slave girls. When the fleets returned, the Xuan De emperor observed: “Ten thousand countries are our guests.” The number of concubines and slave girls embarked must have been staggering. In a subsequent chapter, we’ll show how, after the Chinese squadron reached Venice, female slaves and their offspring made a significant impact on the domestic life and population of Venice, Florence, and Tuscany.

Finally, a word about the most valuable part of the fleet—the sailors.

Like their modern counterparts, their most prized possessions were mementoes of their loved ones at home—drawings, locks of a wife’s or children’s hair, little presents, perhaps a pet dog, a tub of roses, or a tame, flightless bird or pet duck. Chinese sailors were avid gamblers; playing cards and dice were part of everyday life, as was mah-jongg.

Like today’s sailors, they would have been keen to better themselves. As the voyage progressed and boredom set in, they would have put aside novels for progressively more serious reading. By Zheng He’s era, printed popular books were widely available and all kinds of pocket encyclopedias were sold. Reference books ( jih yung lei shu) with illustrations and descriptions covered all manner of practical subjects: agriculture; salt and sugar manufacture; collecting ceramics and bronzes; ship and cart making; coal and fuel use; paper making and printing; welding technology; alcohol fermentation; pearl and jade collecting.

The Nung Shu, a popular encyclopedia first published in 1313, provided descriptions and illustrations of agricultural machinery, including tilt and trip hammers; rotary grinding mills; winnowing fans; bellows powered by piston rods, connecting rods, and horizontal water wheels; flour-sifting machinery drawn by a water wheel; vertical water wheels for driving textile machinery; winders or windlasses with cranks for cranes, wells, and mine shafts; salt mills; pearl-diving apparatus; scoop wheels; pallet chain pumps driven by animals; chain pumps powered by horizontal water wheels; chain pumps operated solely by the current; rotary grinding mills operated by horizontal windmills; double-edged runner mills operated by horizontal water wheels; roller mills; cotton gins; and mills for grinding rice or corn. (See examples on pages in later chapters.)

Doubtless these descriptions of how to make a wide variety of useful farm machinery would have had value to farmers in other countries. Once the Chinese sailors were ashore, they could have supplemented their wages by selling these books, just as sailors in my time would sell cigarette rations to the locals or give their rum tots to pretty girls.

Another pocket encyclopedia, the Wu-ching Tsung-yao, a collection of the most important military techniques, gave detailed accounts of the construction and functions of a vast array of military machines. Here is Professor Joseph Needham’s translation of the text next to an eleventh-century description of how to make a flamethrower:

On the right is the naphtha flame thrower ( fang meng huo yu). The tank is made of brass and supported on four legs. From its upper surface arise four vertical tubes attached to a horizontal cylinder above. They are all connected with the tank. The head and tail of the cylinder are large, (the middle) of narrow diameter. In the tail is a small opening the size of a millet grain. The head end has two round openings.

The description continues for another six lines before instructions are given for loading the machine:

Before use the tank is filled with rather more than three catties of the oil with a spoon through a filter (sha lo). At the same time gunpowder (huo yao) is placed in the ignition chamber at the head. When the fire is to be started one applies a heated branding-iron (to the ignition chamber) and the piston rod is forced fully into the cylinder.2

Subsequent instructions describe how to cope with misfiring or breakdown.

There are equally detailed descriptions of other military hardware in this remarkable book. The most formidable weapon described is a water-wheeled battleship dating from the Song dynasty (A.D. 960–1279). It details a twenty-two-wheeled ship commanded by rebels and an even bigger one owned by the government. “Against the paddle wheel fighting ship of Yang Yao, the government force used live bombs thrown from trebuchet catapults. For these they used pottery containers with very thin walls, within which were placed poisonous drugs, lime and fragments of scrap iron. When these were hurled onto the rebel ships during engagements, the lime filled the air like smoke or fog so that sailors could not open their eyes.”3

What is extraordinary is that this military information seems to have been unclassified—it could have been acquired by anyone. It must have been of considerable value to realms that lacked sophisticated gunpowder weapons in the 1430s, including Venice and Florence. Perhaps Chinese officers supplemented their incomes by selling these military pocket encyclopedias.

We can be confident that Zheng He’s fleets had every weapon then known to the Chinese: sea-skimming rockets, machine guns, mines, mortars, bombards for use against shore batteries, cannons, flame-throwers, grenades, and much more. His fleets were powerfully armed and well supplied by water tankers and grain and horse ships, which enabled them to stay at sea for months on end. In addition, the ships were repositories of great wealth—both material and intellectual.

Of equal importance were the calendars carried by the fleets. Given the order to inform distant lands of the commencement of the new reign of Xuan De, an era when “everything should begin anew,” a calendar was essential to Zheng He’s mission.

Today, calendars are little more than holiday presents—Pirelli Tire calendars, featuring beautiful women, gardening calendars awash with color, others that remind us of bank holidays, when to celebrate Easter and file our tax returns. In the 1430s, Europeans had no unified calendar, for they had not yet agreed how to measure time. The Gregorian calendar did not come into use until a century later. To Islamic people, however, a unified calendar was essential. The Muslim calendar was based on lunar months rather than the solar year. Each month had a different purpose, such as the month to make the hajj, the pilgrimage to Mecca, which began on the first day of the new moon. The Muslim calendar also provided the times of the five daily prayers.

The calendar was likewise of great political and economic importance to the Chinese, who for thousands of years had led the world in calendar making. In Ancient Chinese Inventions, Deng Yinke describes their meticulous approach.

In 1276 Kublai Khan, the first emperor of the Yuan dynasty, assigned the task of compiling a new calendar to astronomer Guo Shou Jing so that his new empire would have a unified calendar from north to south and the errors in previous calendars could be corrected. Guo was a scientist with an exceptional talent and dedication. On taking over the task, Guo said “a good calendar must be based on observations and observations depend upon good devices.” He went on to examine the Hun Yi (armillary sphere), the only instrument in the observatory of the capital Dadu (Beijing), and found that the North Star of it was set at 35° which was at the latitude of Kaifeng where the Hun Yi was made. This meant that the instrument had not been adjusted when it was transported to Dadu from Kaifeng…. Guo thus made it a priority to develop new devices. Within three years of strenuous efforts he worked out twelve astronomical devices which were far better in function and accuracy than previous ones. He also made a number of portable instruments for use in field studies outside Dadu.

As part of the calendar project, Guo presided over a nationwide programme of astronomical observations. He selected twenty-seven sites for astronomical observation throughout the country, which covered a wide area from latitude 15° N to 65° N and longitude 128° E to longitude 102° E. The items of observation included the length of the shadow of the gnomon, the angle of the North Star from the ground surface, and the beginning times of day and night on the vernal equinox and the autumnal equinox…. Guo also examined nearly nine hundred years of astronomical records from 462 to 1278 and selected six figures from the records for calculating the duration of the tropical year. Guo’s result was 365.2425 days, which was the same as that of the Gregorian calendar, the calendar now widely used across the world….

Guo Shou Jing and the other astronomers worked for four years and completed the calendar in 1280. They made numerous calculations converting the data of the ecliptic coordinate and the equatorial coordinate systems, and used twice interpolations to solve the variations in the speed of the sun’s movement, which affected the accuracy of the calendar. The calendar was unprecedented in accuracy. It adopted the winter solstice of the year 1280, the ninth year of the Yuan dynasty, as the epoch, the point of reference for the calendar, and established the duration of a tropical year of 365.2425 days and that of a lunar month 29.530593 days. The error between the duration of its tropical year and that of the revolution of the earth around the sun was only 26 seconds. The calendar was named the Shoushi, meaning “measuring time for the public.”

Issuing calendars was the prerogative of the emperor alone. Accuracy was necessary to enable astronomers to predict eclipses and comets—a sign that the emperor enjoyed heaven’s mandate. If predictions proved incorrect, the astronomer responsible was severely punished, often with death.

The Shoushi calendar produced by Guo Shoujing was officially adopted by the Ming Bureau of Astronomy in 1384. This is the calendar that Zhu Di and the Xuan De emperor would have ordered Zheng He to present to foreign heads of state (discussed in detail in later chapters).

The Shoushi calendar can be viewed in the Yuan shi-lu, the official history of the Yuan dynasty. However, copies also came into the possession of Europeans, notably the diarist Samuel Pepys and the famous scientists Robert Boyle and Robert Hooke. The Japanese and Koreans also copied the calendar, and translations from those languages can be viewed on our website.

The calendar contained the length of a solar day at the latitude of Beijing. This is the duration from the time when the sun is at its maximum height (altitude) in the sky from one day to the next. We tend to think of this as twenty-four hours. It is not. The earth rotates around its own axis every twenty-three hours and fifty-six minutes while also traveling round the sun. The combination of the two movements means that the earth’s position relative to the sun, compared with its position relative to the stars, varies by about four minutes each day. Moreover, the earth’s trajectory around the sun is not a circle but an ellipse. The sun is not at the center of this ellipse, so that as the earth nears the sun it accelerates. As the earth recedes from the sun, on the longer leg of the ellipse, it decelerates. Its rotation also speeds up approaching the sun and slows down receding from the sun.

Thus, the length of the solar day varies throughout the year. The difference of this length is called the equation of time of the sun. To predict the length of the year at 365.2425 days, which is accurate to within ten seconds a year, Guo Shoujing had to take into account four of these movements. In order to accomplish that, he must have known how the solar system worked, including the facts that the earth travels around the sun in an ellipse and is not at the center of the universe and that the earth is attracted to the sun’s much bigger mass.


A diagram showing how the earth travels in an ellipse around the sun.

Guo Shoujing’s calculations for the lunar month of 29.530593 days were even more impressive, requiring a more complex trigonometry. The moon travels around the earth as the earth is moving in an ellipse around the sun. This means that as the earth approaches the sun, the moon’s attraction to the sun’s mass increases, so the speed at which the moon travels around the earth accelerates. Then, as the earth recedes from the sun on its elliptical path, the moon decelerates. Hence, to make his extraordinarily accurate calculations, Guo had to be aware not only that the earth travels around the sun in an ellipse but also that the moon circles the earth. He had to have understood spherical trigonometry and to have employed calculus and have had an accurate idea of the respective masses of earth, sun, and moon.

However, there are further ramifications to Guo Shoujing’s achievements. The earth’s trajectory around the sun is not constant: it changes over the years. Guo knew of these changes, which he had gathered from Chinese observations stretching back eight hundred years. The great French astronomer Pierre-Simon Laplace credited Guo Shoujing with knowledge of what Laplace called the “diminution of the ecliptic”—essentially, the fact that the earth’s ecliptic path around the sun had grown flatter over the centuries.

Even further refinements were taken into account by Guo Shoujing. The earth is not a perfect sphere but an oblate spheroid with flattened poles. Its center of gravity is somewhat below the center of its volume. This means the earth has a slight wobble, which can be deduced by the apparent position of the stars—in particular by Polaris, the Pole Star, which apparently moves over a 26,000-year period. This movement had been compensated for by the Chinese before Guo Shoujing’s era. Templates had been made to adjust for the apparent movement of Polaris.

Finally, Guo Shoujing knew of the planets’ orbits around the sun, and even of Jupiter’s rotation and its circling moons. The American writer Rosa Mui and colleagues Paul Dong and Zhou Xin Yan have kindly informed me of the work of Professor Xi Zezong, a Chinese astronomer based in Beijing, who has found that Jupiter’s satellites or moons were first discovered two thousand years before Galileo by the Chinese astronomer Gan De.

Since A.D. 85, Chinese astronomers have made accurate observations of the period of planetary revolutions around the sun (synodic intervals). They are correct to within a few hours—Mercury 115 days, Venus 584 days, Mars 779 days, Jupiter 398 days, Saturn 378 days. (In later chapters, we provide evidence that Copernicus, Galileo, Kepler, Hooke, and Newton were aware of the Chinese astronomers’ work.)

In their published paper entitled “Calendars, Interpolation, Gnomons and Armillary Spheres in the Works of Guo Shoujing (1231–1314),” Ng Say Tiong and Professor Helmer Aslaksen of the Department of Mathematics, National University of Singapore, note that the inconsistent motions of the moon and sun were discovered in the Eastern Han period (A.D. 25–200), and during the North and South dynasty (A.D. 386–589), respectively. The method of interpolation employed by A.D. 554–610 was the equal interval second difference method. (Please refer to our 1434 website for further explanation.) Guo Shoujing improved on this by using a third difference method of interpolation, which enabled him to determine the equation of time of the sun and moon and hence to predict their positions. Guo Shoujing had developed the forward distance method of interpolation subsequently further developed by Newton into calculus.

The Shoushi calendar, which Zheng He’s fleets presented to heads of state, based upon Guo Shoujing’s pioneering work, contained a mass of astronomical data running to thousands of observations. It enabled comets and eclipses to be predicted for years ahead, as well as times of sunrise and sunset, moonrise and moonset. The positions of the sun and moon relative to the stars and to each other were included, as were the positions of the planets relative to the stars, sun, and moon. Adjustments enabled sunrise and sunset, and moonrise and moonset, to be calculated for different places on earth for every day of the year. As described in detail in chapter 4, the calendar enabled longitude to be calculated by using the slip between solar and sidereal time, by eclipses of the moon, or by the angular distance between the moon and selected stars or planets. Please refer to the 1434 website and to the endnotes for further explanation.

Tai Peng Wang has found the specific stars by which Zheng He’s fleet navigated. We can set these up on the “Starry Night” computer program for the dates when Zheng He’s fleet was transiting the Indian Ocean en route for the Malabar Coast of India and Cairo. We can also compare these stars with those included in Zheng He’s navigational tables and the almanac for the year 1408, now in the Pepys Library at Cambridge. (The 1408 tables contain similar astronomical information as that contained in the Shoushi calendar.)

Thus Zheng He was able to provide Europeans with maps, navigational tools, and an astronomical calendar beyond anything they had yet been able to produce on their own. Supplied with this revolutionary knowledge, the barbarians would be able to make their way to the Middle Kingdom, appropriately “with deference.”

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