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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 Gregoriancalendar 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 thetropical 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