Arab Science - A Journey of Innovation Qatar Foundation

Mathematics and astronomy

Arab star knowledge had both sacred and practical applications

A mediaeval Arab depiction of Aristotle teaching astronomy to other Greek scholars

Caliph Harun al Rashid, shown bathing, was a major Abbasid patron of science

The ornate qibla in all mosques marks the direction of Mecca for daily prayer, accurately calculated using astronomy and sophisticated mathematics



Early Arab astronomy and mathematics each drove the development of the other. The same thinkers who worked with one, worked with both.

The birth of modern astronomy and higher mathematics was the result of the requirements of the new religion of Islam, and of a state and an economy that extended for thousands of miles across the Earth.

Just as today, early Arabs and their Muslim partners were challenged with several religious requirements. They needed to pray five times a day at precise times, and they needed to face Mecca when doing so. They also needed to construct a calendar that was accurate and universal, so they could know the precise times and dates that the four sacred months, including Ramadan, would begin and end. They needed to know when the sacred days fell, and how to apportion inheritances in conformity with religious teaching.

But as their territories increased and their economies grew, they also needed to know how to assess taxes, how to divide properties, how to keep track of vast revenues and expenses, and how to compensate investors. They needed to know how to navigate from Syria to Spain and from Basra to Jeddah.

The calendar issue alone was daunting. Mankind had been struggling with creating an accurate calendar for thousands of years, with limited success. The best (though still imperfect) calendars required periodic addition of a 13th month every 19 years to balance out the errors in the calculation of days in the year.

Another challenge was posed by the fact that the Muslim calendar was lunar, while most others were solar. The lunar year is 11 days shorter than the solar year. And to compound the complexity of the new Muslim calendar, each month started not with the new moon or the full moon, but the first sighting of the crescent moon.

But the time issue did not stop there. Like the rest of mankind, early Arabs did not know exactly how long the day was. How could you make accurate calculations about the month and the year, if you couldn't measure a single day? This was made especially daunting by the shifting seasonal lengths of day and night, compounded by geographic location.

Arab thinkers concluded that the answers would reside in numbers and the heavens. They already had, or were acquiring through a process of translation, the various mathematical discoveries of ancient mathematicians like Euclid, Pythagoras, and Ptolemy. The core of these ancient writings was Greek geometry, literally 'measuring the Earth'.

As had the Greeks before them, the Arabs began to apply geometry to questions beyond the Earth, but to a more intense degree than their predecessors. Eventually, they would depart the physical world altogether as they developed purely abstract mathematics like algebra, trigonometry, and calculus.

But those tools were not yet available in the early 9th century. Early Arabs and their partners were still working with the tools of Greek geometry. Yet as they dealt with issues of time and space, they came to focus more and more on spherical rather than plane geometry.

This shift in focus was based on the implicit assumption that the Earth was a sphere, a very radical breakthrough when for centuries later, Europe would still believe the Earth was flat.

And it was through geometry that it would gradually occur to the great Arab-Muslim thinkers that to calculate the correct time of day, they would need to imagine a triangle whose three points or vertices were the sun's position, the zenith of the sky, and the north celestial pole. The known quantities were the sun's position and the north celestial pole. The correct time, they theorised, was the angle at the intersection of two arcs: one through the arc of the zenith and the pole, the other through the arc of the sun and the pole.

Another question was locating Mecca, no matter where one was in the far flung caliphate, so one could pray in the right direction. And another was calculating when the crescent moon would appear, rather than depend on physical sighting alone.

Spherical geometry and its derivatives again provided the answers.

The first major Abbasid patron of serious scientific and mathematical research was the legendary Caliph Harun Al Rashid, ruling at the end of the 8th century in Baghdad. When he formalised his research process at a Baghdad centre called the Dar Al Hikmat or House of Wisdom, Harun set in motion not only a process of original discovery and invention but a determined effort to recapture all the scientific breakthroughs that had come before, in particular in Greece, Rome, Persia, and India.

He acquired works by Ptolemy, Aristotle, and the 7th century Indian mathematician-astronomer Brahmagupta, including his Brahma Sphuta Siddhanta, or Opening of the Universe, and he brought the Indian mathematician Kanka to his court. He also hired an army of translators to begin to render these documents into Arabic.

Adding to the simmering process of discovery was a prominent family of mathematician-astronomers, the Thabits, originally from the region around Harran in Iraq.

Another invaluable resource for Arab astronomers and mathematicians of the 800s was a fabled book about stars and numbers written around 150 CE by Ptolemy the Greek in Alexandria. This book was known as the Almagest in Latinised Arabic, roughly translating as The Great Book.

The book's brilliance lay in how the Almagest sought to explain, through mathematics, the changing positions of the sun, moon, stars and planets. It depended heavily on spherical geometry and even an early version of spherical trigonometry, created by Hipparchus in Greece long before Ptolemy. Aside from providing complicated mathematical formulae for explaining the movements of sun and stars, Ptolemy catalogued more than 1,000 individual stars in the Almagest.

The book's flaw was that Ptolemy situated the Earth at the centre of the solar system and the universe, postulating that the planets and sun and everything else revolved around the Earth. Ptolemy's error meant that his various mathematical models of the universe were built on a mistaken premise, and so in some cases required complicated formulae and tortured explanations to explain the discrepancy.

Despite the Almagest's central flaw, its geocentric view of the solar system prevailed in both Arab and European astronomy for 1,400 years after it was written.

According to some accounts, it was first translated into Arabic in the 8th century by the Jewish translator Sahl Ibn Tabbari. Later Arabic translations were done, and three centuries later, Catholic and Jewish scholars in Al Andalus and elsewhere translated these Arabic versions into Latin, beginning the slow transformation of European scientific thinking.

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