Gears of the Heavens: Technology and the Representation of the World

Ja‘far ibn Muhammad al-Balkhi (Abu Ma‘shar), Introductorium in astronomiam Albumasaris Abalachi octo continens libros partials (Introduction to astronomy, containing the eight divided books of Abu Ma‘shar Abalachus), 1506, Qatar National Library

No science could develop very far without relying on observational instruments, and no society could function without developing tools, crafts, and mechanical devices that responded to the needs of that society. For example, Islamic astronomy had to develop new instruments in order to carry out the investigations that first subjected the Greek astronomical tradition to factual objective scrutiny. And agriculture, as well as all other aspects of civil life, could not have developed as much as they did if people did not develop surveying tools to allocate lots of land for plantation, and all sorts of instruments for industrial production. Fountains, water clocks as well as water lifting devices for landscaping supplied medieval Islamic society with much of the affluent living for which it was justifiably famed. Remains of some such water clocks are still visible in major cities of the Islamic world and in particular in the city of Fez in Morocco which has the remains of a thirteenth-century water clock still adorning its street across from al-Buʻinaniya Madrasa (school).

Of all the astronomical instruments that were used in early Islamic culture for calculations and observations, the ones that became very popular were the two instruments whose construction theory was very simple: the planispheric astrolabe whose basic construction depended on a single mathematical theorem of stereographic projection, which was well known and described in classical Greek times, and the quadrant, which was constructed just like an astrolabe but by folding the astrolabe twice along its perpendicular diameters. Stereographic projection itself was rather simple. It assumed an observer whose eye was placed at the south pole, for northern astrolabes, and who looked at the universe upward, drawing straight lines from his/her eyesight to points and circles in the starry heaven and marking the intersections of those lines with the plane of the equator. The resulting markings of points, lines, and curves on the plane of the equator constituted one way of translating spherical surfaces onto plane ones. The advantage of stereographic projection is that is preserved the angles, which are formed on a spherical surface into equal angles projected on the plane.

Muhammad ibn Muhammad ibn Ahmad Abu ‘Abd Allah, Badr al-Din (Sibt al-Maridini), al-Risāla al-Fatḥīya fī al-a‘māl al-jaybīya (The introductory epistle on sinusoidal operations), 15th century, National Library and Archives of Egypt

If one projected the constellations on the plane of the equator, made of brass this time, and then perforated that map cutting out the empty spots and leaving only the important stars and constellations one needed, and then projected the major circles of the earth as extended onto the heavenly sphere, like the horizon circle, the equator, and the longitude circles, then one could simulate the apparent motion of the sky around the earth and be able to simulate the angles specific stars would make with the local horizon and specific circles would make with each other. The whole machine would then operate like a slide rule, and in the same way the slide rule used to allow one to perform a set of calculations and read the result off the scale of the ruler, one could in a similar fashion simply read the answers to a host of astronomical and mathematical problems off the edge of an astrolabe. The tenth-century astronomer Sufi, who wrote the most influential book on star constellations, also wrote a book on the making and use of an astrolabe in which he described the manner with which the astrolabe could yield the solution to some 380 astronomical and spherical trigonometric problems.

Muhammad ibn Muhammad Ibn al-Attar, Kashf al-qinā‘ fī rasm al-arbā‘ (The removal of the veil in the description of the quadrants), 1731, Library of Congress

In a real sense, by rotating astrolabe disks, one on top of the other, one could simulate the workings of the heavenly bodies as they were observed from the earth. And in addition one could also solve many earthly surveying problems like determining the heights of mountains and other high inaccessible objects, or width of rivers, etc. Quadrants would yield the same benefits, since they essentially follow the same projection principles, and be more useful observationally as they were usually made of wood, thus lighter to carry, and were three to four times larger than astrolabes, thus increasing their precision for direct observations. In addition, both astrolabes and quadrants were usually executed by very skillful artisans and thus for the most part, when they were well executed, constituted veritable treasures in their own right, and became prime examples of decorative art works. As a result it is no wonder that those two instruments alone constitute the most popular instruments in the collections of most museums of art and science that have anything to do with Islamic civilization.

Three Arabic manuscripts from the Bašagić Collection of Islamic Manuscripts in the University Library of Bratislava

al-Hidāyah fī al-ḍalālah fī ʻarafah al-waqt wa-al-qiblah (Deliverance from error on knowledge of times of day and the direction of prayer), 1683, National Library and Archives of Egypt

Most of the preserved astrolabes that were made during the long history of the Islamic civilization do not only solve problems proscribed by the application of the astronomical and spherical trigonometric problems inherited from the classical Greek tradition. In addition, they also solve newer problems that were generated by the requirements of the ritual practices of the religion of Islam. Every Muslim has to pray five times a day, at times that were astronomically defined by phenomena such as twilights and length of shadows for different days of the year, and perform the prayers in the particular direction of the qibla, that is the direction of the cubic structure of the Kaaba in the city of Mecca in the Arabian Peninsula.

Both the twilight and the shadow lengths require the solution of rather sophisticated mathematical geographical problems, and the determination of the direction of prayer requires the application of several spherical trigonometric laws as well. None of those problems were of any concern to the classical Greeks or to any other ancient civilization upon which Islamic civilization drew, and thus there were no specific techniques developed for their solution. In the case of simple plane trigonometry, the classical Greeks did not even know of such functions as the sine, the cosine, and the tangent. The rudimentary definitions of those functions were only developed in ancient India, and became known to scientists working in the Islamic civilization as a result of the long contacts and exchanges between India and the world of Islam which had already yielded the acquisition of the Indian numerals and the Indian decimal system. And as in the case of the numerals, the wide 

Muhammad ibn Muhammad al-Budayri, Risālah fī al-burūj wa-al-manāzil (A treatise on zodiacal signs and constellations), 1831, Library of Congress 

geographical scope of the Islamic civilization also facilitated the wide spreading of the trigonometric functions, after adding to them some that were developed within that civilization in particular. As a result of this marriage with the ancient Indian civilization, astrolabes, for example, included on the upper left-hand quadrants on their backs graphic representations of both the sine and the cosine functions, and on the lower half of the same back they usually included functions of tangents and cotangents. So in essence an astrolabe was also used as a portable table of trigonometric functions. On the upper right-hand quadrant on the back, astrolabes also included curves that could be used for the determination of the qibla directions for five to six major cities as measured by the height of the sun on various days of the year. That latter feature was totally unknown to earlier Indian and Greek civilizations. In the same quadrant there are usually other curves as well such as those that yield the length of shadows at noon for various latitudes of the earth that could also be helpful for determining the times of the two noon and afternoon prayers. On the face of the astrolabe, and usually on the plate of the local horizon of a specific latitude, which usually ran through several cities located along that latitude, there were also curves that were designed specifically for the determination of the dawn, noon, afternoon, and evening prayers, as could be determined from the direct measurement of the heights of the sun and the various stars for everyday of the year. All these developments made the astrolabe a completely new, sophisticated instrument, which only resembled its ancient Greek ancestor but went far beyond the capabilities of that ancestor.Because of their sophistication as astronomical tools, treatises describing their construction and use were either translated from Arabic into Latin during the Middle Ages or were composed afresh for that same purpose. Famous poets such as Chaucer did in fact compose a treatise on the subject, and the treatise of the ninth century astrologer Mashaʼallah was also translated into Latin.

Ahmad ibn Majid al-Saʻdi, Kitāb al-fawāʼid fī maʻrifat ʻilm al-baḥr wa-al-qawāʻid (The benefits from knowing the basics and rules of seafaring), 1926, Library of Congress

The attraction of the astrolabe to the Latin scientists persisted well into the Renaissance. A prime example of that interest is attested to by a drawing that was made in Florence, sometime during the early part of the sixteenth century, by one of the famous architects of the time, Antonio de Sangallo the Younger (1484–1546‏). Among the papers of this architect, still preserved at the Drawings and Prints Cabinet of the Uffizi Gallery, there is one in particular on which he drew with great details an astrolabe that was made in Baghdad around the year 850 AD. The reason that much is known about the drawing is due to the meticulousness of de Sangallo who also copied the signature of the astrolabe maker which was originally engraved on the back of the astrolabe, a signature that could not have added any astronomical or mathematical components to the astrolabe, and only reflected the clear attention to details by de Sangallo and his obvious esteem for anything that looked like an astronomical instrument coming from the world of Islam.

During the latter half of the sixteenth century, the Arsenius family of astrolabe makers, this time from the far northern European countries, took a keen interest in astrolabes that were made in the Islamic world. In one particular instance, one member of the Arsenius family managed to get hold of an astrolabe that was made by al-Khama'iri of Spain in the year 619 of Hijra, that is 1222/23 AD, and replaced its rete (the uppermost perforated plate representing the map of the stars and constellations) and added one of its local plates so that the astrolabe would work for a city whose latitude was 51 degrees.

Mechanical Devices

And as astrolabes could be seen as physical examples of the workings of the celestial world, mechanical devices were in themselves perceived as examples of two physical principles. On the one hand they demonstrated the workings of such fundamental principles as nature abhorring vacuum, which were exhibited by the workings of a regular siphon which was well understood in ancient Greek times if not before, and on the other they also demonstrated the social utility of such devices both for individual as well as more generalized public purposes. And in this field as well, engineers who worked in the Islamic world did not satisfy themselves with the legacy they inherited from the Greek classical texts, but went far beyond it to incorporate the new developments that were produced in the new civilization. From the first half of the ninth century, we find engineers, like Banu Musa, who were also mathematicians, astronomers, patrons of translations of scientific texts, and diplomats in their own right, producing mechanical devices that embodied such innovations as the conical valve that were unheard of in the classical Greek times. But the same devices also embodied the application of very subtle principles that could awe masters and visitors alike. The historical sources report that those engineers had the ear of one of the caliphs of their time because they produced for him such vessels as pitchers that seemed full of liquid but nothing could be poured out of them or looked empty and yet could fill one cup after another.

The more formidable theoretician of mechanical devices who lived some four centuries after Banu Musa, is an engineer by the name of Abu al-ʻIzz ibn Ismaʻil al-Jazari (died1206), who composed a comprehensive book, which he called Jāmiʻ bayna al-ʻilm wa-al-ʻamal al-nāfiʻ fī al-ṣināʻat al-ḥiyal (A compendium of theory and useful practice in the art of mechanical devices). In it he states explicitly that he saw his function as describing devices that demonstrated how the hidden principles of nature worked, and with those devices he was only enabling principles that exist in potential to materialize in actuality. From such language it becomes evident that his main interlocutor was the great Greek philosopher Aristotle who also was supposed to have devoted a short treatise to mechanical problems. But the idea that principles, or laws of nature, are always there in potential waiting to be revealed or actualized informed the basic assumptions of al-Jazari about the manner in which nature operated. This meant that natural laws could be discovered, and illustrations of the manner in which they operated can be constructed. So in a sense all the devices that he described should be read as samples, as he explicitly says in the introduction to his work, of all types of machines that illustrate the same natural principles. Accordingly it becomes easy to understand why he tended to give several devices under each category as if trying to illustrate the same principle in so many different ways, and to say that nature's laws work in many different areas, and are not restricted to a specific set of circumstances to be revealed.

Of course, this theoretical rendering of the function of mechanical devices does not stop them from being very useful in real life. The clocks he described in his text could be very easily used for public exhibition of time as was indeed done according to the historical sources that described those clocks, or the archaeological remains of such clocks that have been preserved. Water fountains, water lifting devices, various types of drinking devices and locks could all be considered very useful for gardening, agriculture, diversion of rivers, and the like. Similarly, drinking vessels, medical vessels that were used by physicians to measure the amount of blood extracted during blood-letting, or those vessels that assisted their owners with their ablution duties, all fulfilled very useful social functions.

But the most awe-inspiring function those devices could fulfill was their deployment in political circumstances to impress upon a visiting ambassador the richness and awesome knowledge of the potentate, all in a political game of brinksmanship that is usually played among rulers. For example, we are told by the historical sources that when an ambassador was sent to meet with the local potentate, he was taken to a room, which was decorated with an artificial tree with metallic birds attached to its branches. The birds began to chirp when the potentate sat down and stopped when he got up. Needless to say, the ambassador was highly impressed and obviously reported all that technological savvy back to his own country.

The people who constructed those devices belonged to a class in Islamic society that is still poorly studied. This class of artisans who produced the astrolabes, the large observational instruments, the celestial globes, the quadrants as well as the mechanical devices knew a lot about the behavior of materials, and about the crafting of exacting measures that allowed for precise observations, or rendered the solution of very sophisticated mathematical and astronomical problems easy to manipulate. They must have known the properties of alloys like brass, as well as the extent to which metal instruments could be enlarged before they began to collapse under their own weight. The more sophisticated among them could have known about the mathematical principles governing the instruments they were constructing, like knowing the meaning of every curve they were to draw on an astrolabe, which required very sophisticated mathematical training. Those of them who produced a jewel-like map that was based on the projection that preserved the directions and distances to Mecca were obviously very competent astronomers and mathematicians at the same time. And those did not need much instruction as to how to perform their work.

Alchemy, Metalworking, and Other Innovations

Mu‛ayyad al-Din al-Tugra’i, Kitāb mafātīh ar-rahma wa-asrār al-hikma (The keys of mercy and the secrets of wisdom), 18th century, Library of Congress

The artisans who also doubled as alchemists, for their discipline was called "art" ( an'a ) par excellence, must have been also quite knowledgeable about the behavior of metals, and must have had extensive experience in developing sensitive balances for very exacting weights and measures. Some of them must have been employed in the various mint centers that produced the coins of the realm, while others must have also doubled as pharmacists or worked very closely with pharmacists on account of their knowledge of weights and measures. The alchemical treatises that have survived contain linguistic expressions that are indicative of professional jargon that could have been employed by members of guild-like fraternities. And they were the ones who passed on their extensive knowledge of chemical processes like distillation to the Latin west through the translations of their alchemical treatises. Common European words such as alcohol, alembic, etc, owe their origins to the works of such artisans. 

But there were others, who were manually skilled and did know, for example, how to engrave brass, but did not know much about the curves they were drawing. We are told by authors of scientific treatises that they had to re-write their mathematical or astronomical works in a language such artisans could understand. Other mathematicians, like Abu al-Wafa' al-Buzjani (d. 998), wrote a specific treatise on what the artisans would need by way of geometry, and another one on what they would need by way of arithmetic. This can only mean that those two classes of the society did not operate on the same plateau, but that they had cooperated significantly among themselves.

Still there were those artisans who must have learned their craft through apprenticeship and did not leave much writings about the actual material they produced. A case in point is the astrolabist Khalif, whose astrolabe was meticulously copied by de Sangallo, and who was explicitly referred to as the apprentice (student) of ʻAli ibn ʻIsa.

Artisans who produced such industrial products as steel, sugar, ceramics, as well as a whole host of decorative glass and metalworks, for example, did not leave much writings to describe their operations. But we know that although their crafts were probably learned by apprenticeship, their products and their methods of' production were passed on to Europe either during the Middle Ages, as was the case with the production of sugar from sugar cane, or during the Renaissance as the surviving samples of European glass and metalwork that were executed in imitation of their Islamic counterparts and arc still included among the prized possessions of western museums.

And because of the immense geographic span that was occupied by the Islamic civilization, from the borders of China and India, in the east and the southeast, all the way to Spain in the west, Islamic civilization itself also acted as a facilitating medium of dissemination as was done with the Indian numerals that were disseminated to Europe through the agency of the Islamic civilization and are still called "Arabic numerals" in the west on that account. Similarly, industrial and technical innovations like paper making, and the navigating compass, whose origins are to be found in ancient China, were also passed on to Europe by the same Islamic civilization. Of course some of those inventions and techniques were modified in the Islamic civilization before they were passed on. Paper, which was first made in China from mulberry bark, were mainly manufactured from linen and rags in the Islamic world and the practice continued in Europe as well. Arabic fourteenth-century sources already speak of imported paper from such European cities as Venice, but also mention that it was of a much inferior quality to that which was produced in the eastern cities of Egypt and the Levant. Similarly, the sugar cane, which first came to the Islamic civilization from India, very quickly became a common staple in Islamic civilization and was planted specifically to feed the industry of producing sugar and was itself passed to China to the east and to Europe in the west.

Referenced Items

  1. Deliverance from Error on Knowledge of Times of Day and the Direction of Prayer
  2. A Brief Essay on the Quadrant Known as Muqantarat
  3. The "Fatḥīyah" Essay on Using the Mughayyab Quadrant
  4. An Essay on the Tilt of the Mujayyab Quadrant
  5. Introduction to Astronomy, Containing the Eight Divided Books of Abu Ma'shar Abalachus
  6. A Treatise on Zodiacal Signs and Constallations: Unique Jewels on the Benefits of Keeping Time
  7. The Keys of Mercy and the Secrets of Wisdom
  8. The Benefits from Knowing the Basics and Rules of Seafaring