Measuring time and space. Generations 451-454, 1000-1080

Towards the end of this period a metalsmith in Toledo devised a universal astrolabe. His name was al-Zarqali, known later in the west as Arzachel.

earliest surviving astrolabe

Astrolabes were made of brass and were things of beauty. This one is from Iran, a century earlier. (Image from UC Santa Barbara) 

The astrolabe was a glorified protractor, but much more sophisticated. It allowed a person to measure the positions of the stars and planets, thereby enabling them to determine local time. It had been devised by the ancient Greeks, but had a drawback: each one was valid only for a given latitude. Al-Zarqali’s astrolabe had the advantage that it could be set for any latitude and so was much more useful. Over the following centuries it became known in northern Europe as a Saphaea. Abelard and Heloise, in Paris in the following century, named their son Astrolabe. Chaucer describes the use of one in the Canterbury Tales a couple of centuries later still. Astrolabes were leading-edge technology until the development of the telescope in the 1500’s.

Astrolabes were also used to measure the heights of buildings.

measuring height with an astrolabe

Here is a much later image, from the 16th century, demonstrating its use. (Image courtesy of the Whipple Library, University of Cambridge)

The muslim world stretched from Toledo across North Africa, through the middle east to what is now Afghanistan. The use of the astrolabe demonstrates a new departure in thinking that was taking place across this world. It used mathematical principles (straight lines, perfect numbers) to describe the observed world where lines are never straight and numbers never quite add up. For the ancient Greeks the two were irreconcilably separate. But islamic scholars demonstrated that precise mathematical principles could be used to describe the fuzzy physical world.

One of the greatest scholars lived at the eastern end of this world, between the Caspian Sea and Afghanistan. Al-Biruni was so influential that some have described the first half of the eleventh century as ‘the age of Al-Biruni’. Because the caliphs in Baghdad 1500 miles or 2500 km away were retreating behind the protection of their Mamluk guards, this region was left to fend for itself, and so al-Biruni lived in a time of political turmoil. Depending on who was ruling at any time he moved from one town to another, always continuing his wide-ranging researches.

He wrote a history of India, based on reports from captured Indian scholars brought back from the campaigns of one of his rulers. This was the first known dispassionate study of another culture, a heathen one at that, not one of a people of the Book. Here is an extract:

“With regard to God, the Hindus believe that he is one, eternal, without beginning and end, acting by free will, almighty, all-wise, living, giving life, ruling, and preserving; one who is unique in his sovereignty, beyond all likeness and unlikeness, and neither resembling anything nor having anything resemble him. In order to illustrate this, we shall produce some extracts from the Hindu literature, lest the reader should think that our account is nothing but hearsay.”

He wrote a book on pharmacology in which he listed each plant in five languages. And using the astrolabe and islamic advances in trigonometry, he developed a method to measure the circumference of the Earth.The previous best attempt had been in Egypt, and involved placing a stake in the ground in Cairo, pacing the distance north to Alexandria, and then measuring the angle of the sun’s shadow at each place. Al-Biruni introduced his method with the following sentences: ‘Here is another method for the determination of the circumference of the Earth. It does not require walking in deserts.’ (quoted in ‘Pathfinders’ by Jim Al-Khalili, Puffin Books)

Travelling on his patron’s military campaigns in Pakistan, he saw a mountain surrounded by a plain near the fort of Nandana, which was just what he needed to apply his new method. In a two-stage process, he first calculated the height of the mountain from the plain. Then he climbed to the top of the mountain and measured the angle to the horizon.This gave him the first triangle ABH in the diagram.Then by calculating the distance to the horizon he could project a second, larger triangle with the same angles between the mountaintop, the horizon and the centre of the Earth, triangle ACS.


I don’t understand the maths myself, but I can see that the angle marked θ has the same value at the centre of the Earth, at ground level and between the top of the mountain and the horizon line, that another angle is a right angle and so the third must also be equal.

How ingenious! The calculations presupposed that the Earth was a perfect sphere and scientists now tell us it isn’t quite, but his work displays a confidence in the human ability to make sense of the world around us. The age of al-Biruni indeed.


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