Note, this book is unpublished, and in the process of being written. Please do not quote from this webpage. Once the book is complete it will be released here free of charge as a pdf file. (Hopefully by the end of 2022) Changes may occur to this material before it is published. This early copy has been placed on this website so that reviewers and editors can read it and reply to it.
5 April 2022 Dan Gibson
We have examined four different Qibla directions in early Islam: the Petra Qibla, the between Qibla, the parallel Qibla, and the Mecca Qibla. According to Gibson’s theory, these four different Qiblas were quite intentional: they reflect the religious and political struggles of the early Muslim world.
The data demands an explanation. The Qibla calculations of the early mosque builders are often shockingly accurate: this despite the absence of the sophisticated astronomical and mathematical calculations which would come later to the Muslim world. So, the accuracy of these early mosques begs the question: how did early mosque builders calculate their Qiblas so accurately?
In order to address this question, we will introduce the ancient navigational tool of the Indian Circle and describe how it was used to calculate early Qiblas.
The Four Cardinal Directions
The first requirement when plotting coordinates over any distance is to establish the cardinal directions. Methods for determining cardinal directions had existed for thousands of years, even when the earliest mosques were built. The Great Pyramid in Egypt is oriented so that the four corners of the monument face north, south, east, and west, with an astonishing error of only 0.067 degrees. (i)
For the past millennium we might simply use a magnetic compass to determine the North Pole. This was not possible when the earliest mosques were being constructed for two reasons. First, the Arab world did not have access to this technology until c. 680 AH (c. 1280 CE), so the builders of the first mosques had to use other, well-established means to find true north. Second, the magnetic North Pole is different from the true North Pole. While sufficient for the casual traveler, this difference would affect the nuanced measurements used for directing the Qibla.
An excellent method for finding the cardinal directions had been available to Arabic caravans navigating the deserts and plains of Arabia and Syria for centuries. This method would later be called the Indian Circle. It was incredibly simple: see the illustrations below. The method was as follows:
- The mosque builder would put a straight pole in the ground and trace the edge of the shadow it cast with small pegs, as the shadow shifted through the day. These pegs would mark out a large arc on the ground.
- The mosque builder would then take a length of cord and draw a circle on the ground around the pole. An East-West line could then be marked where the circle intersected the large arc of pegs.
- Using the string, the mosque builder could measure a point equal distance on the East-West orientation line and then place a small post at these two points. He could then draw two equal circles from these posts.
- The point where the circles intersect would make the north-south line. The mosque builder would then place a pole into the ground where the north-south line and the east-west line intersect This would represent the spot where he stood, and from where he wanted to calculate the Qibla direction. From now on he would measure from this point. (ii)
The Windrose Compass
Once the mosque builder had established the four cardinal directions of the Indian Circle, drawn out on the ground, the next task was to plot coordinates and create a compass. In Arabic, these coordinates were known as akhnām (directions). Today we divide a circle into 360 degrees, but according to the Arab manuscripts, they calculated 224 degrees in the circle. These 224 degrees would be plotted by dividing the circle into 32 sections.
5 To create the compass, the navigator would first measure two equal distance lines at 45 and 90 degrees. Two rods would have been suitable for pre-set measurements.
6 The navigator would then add a small post at the end of each measurement, and from those posts, trace two circles with a string.
7 Where the circles intersected, the navigator would add a new directional line to the compass.
8 This process would be duplicated until the navigator filled the entire compass with 32 lines. These lines were known as Rhumb lines in Arabic.
9 If it was needed, the mosque builder could add smaller units known as zāms. Seven zāms would constitute one akhnām, and 32 akhnām would complete the circle. This would, of course, total in 224 degrees. This chart is often referred to as a compass rose or a windrose.
10 If the builder stood at the post in the center of the circle, and looked along one of the 32 akhnām rhumb lines at night, he would see a place where a particular star rose or set on the horizon. One of these star names could then be used to communicate one of 32 directions quickly and simply.
So far, no mathematical calculations were needed to draw the Arab Windrose. A complete windrose was not necessary if the mosque builder knew the general direction that he wanted to face. However, the next step would require some calculations.
Arab caravan masters had long recognized that the North Star was fairly stable in its position in the sky. As a caravan traveled north, the star appeared to rise higher in the sky. So, Arab merchants began to measure the height of the North Star from the horizon. This measurement was quite reliable due to the often-flat topography of the plains of Arabia.
Initially, measuring the height of the North Star was as simple as measuring the number of finger-widths the star was from the horizon, held at arm’s length. The width of the finger, or iṣba’, was also divided into zāms, or an eighth of a finger width. Eventually, the Arabs began to use small pieces of wood with a string marked with measurements (a kamal) to measure the North Star. This system has been used for millennia and is described in many nautical manuals. (iii) This method is even used today by Arab dhow captains who do not have modern instruments. (iv)
To continue the Qibla calculation:
11 Next, the mosque builder would mark equal measurements north, south, east, and west onto the chart on the ground. The size of these measurements was not important if they were equal in length and would accommodate the number of zāms required for the measurement. The mosque builder would measure the height of the North Star where he wanted to build the mosque and count the zāms at the center post equal to the height of the North Star. For instance, if he measured the North Star as seven zāms high, he would count the zāms starting at number seven at the centre post.
12 The mosque builder would then place another peg onto the Windrose either north or south that represented the Holy City that he wanted to face. For example, if he was measuring for a Qibla to the Holy City of Petra in Jordan, he would mark the 17th zām north and then place a peg on that spot. He would then measure it again farther east or west, and place another peg on those spots. Then he would draw a line between the two. The direction to the Holy City of Petra would be somewhere along that line.
Once the north-south calculation had been made, the mosque builder would need to find the east or west measurement of the city he needed to face (for example, Petra, as above). Obviously, he would know if he was east or west of the Holy City of Petra. But how far? Here the Nabataean Arabs had an advantage over others. Their caravans had been traversing the Middle East for over a thousand years before the founding of Islam. Their caravan masters had perfected a method of charting distance east or west. It was as easy as counting their steps. They knew that if they traveled directly north168,000 steps or 168 km, the pole star would raise one zām. So they used this measurement to calculate their distance east or west.
First century Roman historian Pliny the Elder recorded that the Arab merchants of his time counted their steps as they traveled across the desert. Pliny wrote that a trip from Timna, the capital of the Qataban in Yemen, to Gaza, a port on the Mediterranean Sea, was 2,437,500 steps. (v) This journey required 65 days of travel by camel. (vi)
The suggestion that a caravan could accurately count each step from stop to stop may stretch credulity for a modern reader. But, it was a common trait of Arab caravans to recite poetry as they traveled. (vii) The caravan master would walk, stepping according to the meter of the poetry, and each of these lengthy poems had an established number of steps, according to its meter. Thus, by noting which poems had been recited, a caravan master could count his steps through hours, days, and weeks of travel with reasonable accuracy.
In time, caravan masters had established mental tables of distances between cities all over the known world. Thus, each city had a zām measurement corresponding to the height of the North Star, and other zām measurements corresponding to the distances to other cities. Tables of these city names and measurements were known as zij. At first most zij were memorized, but later they were recorded in books and nautical manuals. Caravan masters could use zij measurements and the Indian Circle method to guide their caravans across the trackless deserts of the Middle East, arriving at destinations that were far over the horizon.
It was especially challenging to make the east-west measurements when building a mosque in a remote location. While the mosque builder would use zij numbers available to him to add up the distances between cities, he would also need to calculate angles using Pythagoras’ theorem. This simple geometrical tool had been established around570-495 BCE and was available to every builder and navigator. (viii) But again, once these distances were confirmed by repeated travel, the builder needed only calculate the distance of the proposed mosque to the nearest known city on the zij table available to him. By the time of the first mosques, centuries of caravan travel would have made this data readily available to mosque builders, which simplified the Qibla process.
Calculating the Qibla
We have argued that Nabataean Arab navigators could establish the cardinal directions with the Indian Circle, fill the windrose compass with 32 directions each associated with a star, assign zām measurements for the North Star, and calculate distance between distant geographic locations. We will finally describe how these skills could be employed to calculate a Qibla direction with remarkable accuracy.
The Syrian astronomer al-Battani, who wrote from Raqqa c. 297 AH (910 CE) described this early method of determining the Qibla. His observations are supported by other writers, such as Iranian astronomer Khwarazm Habash al-Hasib writing c. 209 AH (825 CE). Historian of astronomy David King summarizes al-Batanni this way:
another method [of calculating the Qibla], mentioned by al-Battani, was widely used and remained popular until the nineteenth century. The method could not be simpler. First draw a circle on a horizontal plane and mark the cardinal directions. Then draw a line parallel to the north-south line and at an angular distance - measured on the circle - equal to the longitude difference between Masjid al-Haram and the new locality and another line parallel to the east-west line at an angular distance equal to the latitude difference. Then the line joining the centre of the circle to the intersection of these two lines defines the qibla. (ix)
Al-Battani described the Indian circle. Later astronomers and mathematicians would develop more sophisticated methods of determining the Qibla direction. But, as al-Battani proves, these astronomers acknowledge that in the past the Indian Circle method was used to calculate the Qibla.
To continue our example, in line with al-Battani’s recollection:
13 Once the mosque builder knew how many zāms he was east or west of the Holy City, he would plot this line on his diagram.
14 He would then draw a line from the center post out to where the new line intersected with the North Star line. This was the Qibla direction from the position where he stood. He could then go about building his mosque with amazing accuracy, which only depended on his ability to calculate the east and west distances.
Many early maps use the city of Alexandria as the focal point for their measurements. Alexandria was the ancient centre of study and knowledge; it was the location of the original Alexandrian Library and Museum established c. 250 BCE. For Nabataean merchants, Alexandria was the closest large port city that dealt directly with Rome, and so Alexandria was a suitable and common reference point long before the advent of Islam, and many charts and maps used Alexandria as a starting reference.
The Indian Circle did have flaws. If the east-west calculation was inaccurate, the Qibla would also be inaccurate. Further, the Indian Circle did not take into account the curvature of the earth. The result of this error is that the further east or west the Qibla calculation, the more inaccurate it was. According to our research in consultation with a mathematician, when the calculation was made as far east as India or west as Morocco, the error could be as much as ten degrees. An Indian Circle for a Qibla in Morocco toward Petra would face 10 degrees further south than intended.
The above illustration represents the margin of error when calculating a Petra based Qibla using the Indian Circle. The lighter areas are the most accurate, and the darker regions are the most flawed.
If the mosque builders calculated their coordinates using Ptolemy’s model, which miscalculated the world as 10% smaller than it actually is, the margin of error would still be lesser. Above is an illustration of the margin of error when using the size of the earth suggested by Ptolemy Claudius.
On the Nabataea.net website we have added the Indian Circle calculations to The Qibla Tool. These can be toggled on or off, in order to compare modern calculations with the ancient Indian Circle method. Below are the modern results for the mosque in Anjar, with options to view the results for using the Indian Circle from Petra, Mecca, or the Between location.
The Qibla Tool allows scholars to compare the difference between the old Indian Circle method and modern electronic tools. This data ought to put to rest the superfluous conjecture that the Indian Circle method was wildly inaccurate.
Of course, the Indian Circle did not remain the primary means of making these calculations in the Muslim world. Around 215 AH (830 CE), Abbasid Caliph Ma’mun became concerned with the accuracy of these geographic calculations as the Arabs were switching to Greek measurements for their navigation and astronomy. His primary concern was the accuracy of calculations over great distances. Al-Ma’mun discovered that the Greeks had calculated that the equivalent hissa of one degree was five hundred stades. The hissa was the unit which the Arabs used for measuring distances. Al-Ma’mun found that amongst Arab scholars, there was not sufficient knowledge about the length of a hissa compared to other known units. His resulting experiments are very well attested by lbn Yunus (380 AH), al-Biruni (416 AH), Yahya ibn Akthan, (c. 215 AH), and Habash al-Hasib (c. 215 AH). lbn Yunus recorded:
Ma’mun … asked him to measure the amount of one degree of a great circle on the surface of the earth. He said: “We both set off together for this [purpose]. He ordered Ibn ‘Ali Ibn ‘Isa al-Asṭurlabi and ‘Ali ibn Buhturi to do the same and they went off in a different direction. Sanadibn ‘Ali said: “Khalid ibn ‘Abd al-Malik and I travelled to between W’mah and [Palmyra] and there we measured the amount of a degree of a great circle on the surface of the earth. It was fifty-seven miles [al-mil or Arabic mile]. ‘Ali ibn ‘Isa and ‘Ali ibn al-Buhturi also made measurements and the two of them found the same as this. The two reports from the two directions, the two measurements with the same result arrived at the same time. (x)
A second group of scientists, including Habash al-Hasib, headed east of Baghdad. Al-Biruni reported:
At that time - according to what Habash related, a group of scholars of instrument construction and expert constructors from amongst the carpenters and brass-workers - Al-Ma’mun ordered the construction of instruments and the selection of a place for this survey. There was chosen a location in the desert of Sinjar between the area of Mosul and Samarra, where they were satisfied that the ground was level. They transported the instruments there and they selected a place where they observed the solar altitude at midday. Then two groups set forth (in two different directions). Khalid and a group of surveyors and instrument-makers headed in the direction of the northern pole, and ‘Ali ibn ‘Isa al-Asturlabi and Ahmad ibn al-Buhturi the surveyor with another group towards the south pole. Each of the two groups observed the altitude of the sun at midday until they found that it had changed by one degree, apart from the change that resulted in the solar declination. They measured the track on their way out and set up markers with arrows as they went, and as they returned they investigated the distance for the second time. The two groups met again at the place from which they had set out, and they found that one degree of the terrestrial meridian is equivalent to fifty-six miles. Habash claimed that he had heard Khalid dictating that number to the Qadi Yahya ibn Aktiam. (xi)
Once Greek astronomy and the use of the 360 degree circle became the common practice in Arabia, the use of the old windrose compass with its 224 degrees was ignored by all but Dhow navigators.
We have sought to demonstrate that the Arabs of Muhammad’s time did have the knowledge and tools to accurately determine Qibla direction. As the Muslim armies pressed deeper and deeper into Byzantine Roman territory, the use of Roman roads and milestones slowly replaced the ancient knowledge of the Indian Circle until, it seems, only a handful of specialists were able to accurately chart new mosque Qiblas. Despite the transition toward Western measurements and mathematics, the Indian Circle was a powerful tool in calculating Qibla direction. Its reliability confirms our argument that the early Qiblas of Islam, while problematic and unexpected, were not an accident of incompetence. These Qiblas were directed with intention by competent builders using reliable, testable, ancient knowledge.
i Glen Dash, “Occam’s Egyptian razor: the equinox and the alignment of the pyramids,” in The Journal of Ancient Egyptian Architecture2 (2017): 1-8.
ii Martin Isler, “An Ancient Method of Finding and Extending Direction,” in Journal of the American Research Center in Egypt 26 (1989): 191-206.
iii For example: Aḥmad ibn Mājid al-Najdī, Arab Navigation in the Indian Ocean Before the Coming of the Portuguese, being a translation of Kitab al-Fawa’id di usul al-bahr wa’l-qawa’id, trans. G. R. Tibbetts (London: The Royal Asiatic Society of Great Britain & Ireland, 1971).
iv Hasan Salih Shihab, “Stellar Navigation of the Arabs,” in The Principles of Arab Navigation, ed. Anthony R. Constable and William Facey (Kuwait: Arabian Publishing, 2013), 21.
v Pliny the Elder, The Natural History, trans. John Bostock and H.T. Riley (London: Taylor and Francis, 1855), 12.32, http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D12%3Achapter%3D13
While most translations render the number in this passage in Roman miles, we have confirmed with historian and Latin scholar Bill Thayer that Pliny’s text literally reads 2,437,500 passusor paces. Bill Thayer wrote us of the Roman numerals in the passage: “those are numbers (the bars above them multiply by 1000, the bars to the sides by 100 more): thus (24 * 100,000) + (37 *1000) + 500 = 2,437,500 passus = 2437.5 Roman miles.”
vi Pliny the Elder, The Natural History, 12.32, http://www.perseus.tufts.edu/hopper /text?doc=Perseus%3Atext%3A1999.02.0137%3Abook%3D12%3Achapter%3D32
vii Henry Baerlein, The Singing Caravan: Some echoes of Arabian Poetry, (Godshill: Millersford Books, 1910), 31.
viii Alfred Posamentier, The Pythagorean Theorem: The Story of Its Power and Beauty, (Amherst: Prometheus Books, 2010), 23.
ix David A. King, “Astronomy and Islamic Society: Qibla, Gnomonics and Timekeeping,” in Encyclopedia of the History of Arabic Science1 (1996), 142. The only extant chapters of the Ḥākimī Zīj, Ibn Yūnus by are in two unpublished manuscripts at Leiden and Oxford, comprising about three hundred folios. A manuscript in Paris contains a hundred folios. A manuscript in Paris contains an anonymous abridgment of part of the zij and is a source for some additional chapters up to chapter 57, and chapters 77–81. This translation came from: David A. King, “Too Many Cooks…A New Account of the Earliest Muslim Geodetic Measurements,” Suhayl: International Journal for the History of the Exact Natural Sciences in Islamic Civilisation (2000), 207-241.
xi King, Too Many Cooks, 215