The Mechanics of Banu Musa in the Light of Modern System and Control Engineering

This article is a review of the book published recently by Professor Attila Bir (Istanbul Technical University, Faculty of Electrical and Electronics Engineering, Istanbul) on Banu Musa's book of mechanics studied in the framework of modern system and control engineering.

Atilla Bir, “Kitâb al-Hiyal” of Banû Mûsâ bin Shâkir Interpreted in Sense of Modern System and Control Engineering. Preface and edition by Ekmeleddin Ihsanoglu (Studies and Sources on the History of Science, 4.) 227 pp., figs., tables, bibl. Istanbul: Research Centre for Islamic History, Art, and Culture IRCICA, 1990. ISBN 92-9063-355-0.

1. Banu Musa: scholars and patrons of science

The three brothers Banū Mūsā, sons of Mūsā ibn Shākir al-Munajjim, are scholars from the 9th-century Baghdad, at that time the capital of the Abbasid dynasty that ruled the Muslim Empire for several centuries. Their names, in order of seniority, were Muhammad, Ahmad, and al-Hasan. Their works in different scientific areas are attributed to them jointly, although we do know that they had their own areas of expertise. Muhammad was mainly a specialist in geometry and astronomy, while Ahmad worked mainly on mechanics and al-Hasan excelled mainly in geometry.

Their father, Musa ibn Shakir, was a close friend of al-Ma’mun, the son of the Caliph Harun al-Rashid. When Musa ibn Shakir died, al-Ma’mun became the guardian of the three brothers. They were given a good education in Baghdad, studying geometry, mechanics, music, mathematics and astronomy. During the al-Ma’mun caliphate between 813 and 833, they carried on a successful career in science, engineering and patronage. After him, they continued their work under al-Mu’tasim (r. 833 – 842), al-Wathiq (r. 842-847) and al-Mutawakkil (r. 847-861). Muhammad and Ahmad Banū Mūsā were obviously in favour with al-Mutawakkil who employed them in engineering works related to the construction of canals of al-Dja’fariyya, a new city he founded near Baghdad.

Besides their proper scientific work, Banū Mūsā were also patrons of translation of Greek scientific works and they funded the work of scientists, such as Thābit ibn Qurra (d. 901). They used a significant part of their wealth in fostering the intense intellectual activity that was an important feature of life in Baghdad at this time.

The Banū Mūsā brothers were among the first group of mathematicians who faced the hard task to carry forward the mathematical developments in Islamic civilisation in the first half of the 9th century. Their most famous treatise is Kitāb ma’rifat masāhat al-ashkāl al-basīta wa ‘l-kuriya (The Book of the Measurement of Plane and Spherical Figures) in which they made important mathematical contributions. This work became well known through the translation into Latin by Gherard of Cremona entitled Liber trium fratum de geometria.

Figure 1: The cover page of the book Kitāb al-hiyal.

In astronomy, the Banū Mūsā made observations and measurements, but it seems they did not document their research in a conserved writing. Under the request of the Caliph al-Ma’mun, they measured a degree of latitude of the Earth. For this purpose, they organised an expedition to Northern Mesopotamia, in a desert region, where they made precise measurements. They also made many observations of the sun and the moon from Baghdad. Muhammad and Ahmad measured the length of the year, obtaining the value of 365 days and 6 hours and observed the star Regulus in Baghdad in 255 H (840-41), 232 H (847-48), and 235 H (850-51).

The three brothers are most known by their achievements in mechanics. Their book Kitāb al-hiyal (The Book of Ingenious Devices) is an outstanding contribution in the field of mechanical sciences. Although it is ascribed to them jointly, certain testimonies ascribe it to Ahmad ibn Mūsā, who seems to be the mechanician of the group. This treatise, in the form of a catalogue of machines, is a large illustrated work on mechanical devices including automata. The book described a total of 100 devices and how to use them. It was based partly on the work of Heron of Alexandria and Philon of Byzantium, other ancient texts and contained original work by the brothers. Some of these inventions include: valve, float valve, feedback controller, automatic flute player, a programmable machine, trick devices, and self-trimming lamp. The work was first partly translated and interpreted into German by Eilhard Wiedemann and Friedrich Hauser. It was translated and annotated in English by Donald R. Hill, and its Arabic original text was edited by Ahmad Y. al-Hassan.

A total of 100 devices are taken up and explained in great detail in the book. 73 of these are related to trick vessels and the others consist of 15 automatic control systems, 7 water jets, 3 oil lamps, one bellow and one lifting mechanism system. Their application is generally based on aerostatic and hydrostatic pressure principles. The systems are more advanced than earlier ancient ones in that they can even satisfy contemporary technologic requirements. The book provides the first examples of various mechanic elements, technical drawings, logic and command systems and especially automatically controlled systems.

About eighty of the devices are trick vessels; the remainder include lamps, alternating fountains, and a clamshell grab, identical in design to its modern counterpart. The trick vessels display a bewildering variety of effects: for example, a pitcher into which liquids of three different colours are poured in succession -when the tap is opened they discharge in the order in which they were poured; or a basin that is replenished when small amounts of liquid are extracted from it, but is not replenished if a larger amount is taken. These effects, and many others, are obtained by switching mechanisms operated by small variations in aerostatic and hydraulic pressures, and by the use of automatically activated conical valves. The purpose of these devices was partly didactic and partly to amuse. They appear trivial to us, but the Banū Mūsā’s mastery of delicate controls was unsurpassed until fairly recent times.

Figure 2: An oil lamp in which the wick is automatically regulated and the oil level automatically controlled.

2. Making the past live again: Modern reconstruction of Banū Mūsā’s machines

In his study of Kitāb al-hiyal, Atilla Bir examines Banu Musa’s inventions and devices, analyzing each one as a system incorporating various mechanisms. Then, basing his analysis on various logical relationships and linear and non-linear blocks, he obtains the corresponding block diagrams. This method of establishing the workings of the systems and explaining their behaviour is very much in accordance with the principles of modern systems analysis and as such will be fully understood only by those who are familiar with modern control engineering. While this may seem to be an anachronistic approach, the only interpretative method fully explains how all these devices worked. Also, it does justice to the extraordinary ingenuity and inventiveness of the Banū Mūsā. In his appreciation of Professor Bir’s book, the late Donald R. Hill, specialist of Muslim technology, stated that this modern mechanical analysis of Kitāb al-hiyal by Banū Mūsā should appeal to historians of technology to become aware of the present work, and “appreciate the implications of Dr. Bir’s methodology” (see also the review published by D. R. Hill of the book in Isis, vol. 83, 1992: p. 480.)

To characterise the procedure followed by the author and his method in accounting for the original work, we reproduce hereinafter extracts from chapter 2 (pp. 9-10):

“In the sense of system engineering, the models in the work Kitab al-hiyal are formed by the combination of a limited number of motifs. To understand the working principles and to derive the models of these systems, first, the basic motif has to be examined. One observes that certain motifs are frequently reused in different models and others are rarely used or developed to be used only for one determined system.

Figure 3: A1 is a fountain operated by an ‘elevation tank’; A2 is a construction with two outlets which, changing mutually and periodically, pours out hot and cold waters.

“To study the motifs separately, one has to determine the physical principles that each motif is based on. By means of dynamic equations approximate mathematical models are derived, in agreement with the physical principles, specific simplifications and possible assumptions. Thus the entire model of the system is obtained by combining the individual models of the motifs. The mathematical models are expressed by block diagrams in accordance with the terminology of system engineering. In the block diagrams the linear or linearized functions are expressed through transfer functions. In system engineering, the transfer function of a linear system is defined as the Laplace transformed ratio of the output variable to the input variable. This ratio is formed when all the initial conditions are taken as zero. The transfer function concept is equivalent to the Laplace transformed impulse response of the system.

“The unlinearized elements, or elements that effect the system with their nonlinear characteristics, are shown in the models through non-linear blocks. These nonlinear blocks are drawn double-framed in the models. In these blocks the input-output relation is drawn in cartesian coordinates, the input variable taken on the apsis and the output variable on the ordinate.

“Aside from the linear and non-linear blocks, logic and memory elements are also used in the system models. Logic elements are given through conventional symbols. For valves and taps, the symbol of a switch is used. Special symbols are also derived as in the model of the turbine motif. In evaluating different properties it is possible to give different models of a given system. For the realization, the most suitable model is chosen and it is kept unchanged throughout the work as far as possible, although difficulties come up especially in deriving the model of the ?balanced valve with two or three positions’ [Motif 6]”.

Figure 4: Example: Model 88-A Fountain from which the waters spurts out in the shape of a lily, or in the shape of a shield.

As an example, we present hereinafter the description of the author of the model 88-A describing a fountain from which the water spurts out in the shape of a lily, or in the shape of a shield (or spear) (fig. 4) (p. 188):

“The water flows from the tank d to the fountain body through the pipe d-b. The body in the form of a bud is divided in two sections by the partition z-e. If the water should shoot out in the shape of a lily (Figure 88-b), a reversed funnel is fixed over the partition z-e. The connection between the upper and lower sections is achieved by five pipes h which are slightly inclined and attached to the funnel wand. The water entering from b into the lower section goes through the pipes h to the upper section. Under pressure the water in the upper section throws out revolving first tangent to the funnel and then to the upper end k of the bud. At the same time, the water which goes from the lower section into the funnel squirts out from the a end of the funnel and falls back in the fountain in form of drops. The water which throws out as a thin round leaf from the end k and the water which squirts out like a string from the end a of the fountain form together an elegant lily.

“If the water which throws out from the pipes h attached to the funnel is pressed down by a cover a at the end k of the bud (Figure 88-c), the water squirts out as a thin rotating membrane and appears like a shield.

“At last if the water is spurted out under full pressure only from the end a, it heightens a while in thickness of an arm and falls back in drops appearing like a spear (Figure 88-d)”.

For a certain time, ancient and medieval mechanics was handled with the tools of modern science and engineering. Thus machines were reconstructed and redrawn, sometimes with computer assisted simulation of their functions. This questioning of the past with the tools of modern technology attained now Islamic mechanics. Several important contributions of Muslim mechanicians were reconstructed and their functioning explained in a modern way. It is in this context that the book under review should be viewed as an important step towards the understanding of Banū Mūsā’s machines with the modern scientific knowledge and the tools of symbolic language of nowadays mathematics.

Figure 5: Last page of the manuscript copy of Kitāb al-hiyal kept in the Library of Topkapi Palace Museum A 3474.

Works dealing with technical and mechanical subjects are few in Islamic science. This new book highlights one of the outstanding Muslim contributions of the past in the field of mechanical sciences. In this work, the author interprets and analyses Kitāb al-hiyal from the point of view of modern systems and control engineering. The book includes descriptions and modern explanations of various machines, including magic cups, automatic control mechanisms, oil lamps, fountains, etc. In dealing with these machines in this way, the book reflects a new approach and methodology in the history of science, linking ancient medieval Islamic science with modern scientific approaches and tools.

With this new approach, the book represents a very good attempt to revive the interest in Islamic technology, not only among professional historians, but also in the circles of engineers and the public who are interested in the achievements of Islamic civilisation.

Further reading:

Banū Mūsā 1979. The Book of Ingenious Devices (Kitāb al-Hiyal) by the Banū (sons of) Mūsā ibn Shākir. Translated and annotated by Donald R. Hill. Dordrecht etc.: D. Reidel. Reprinted in Islamabad, 1989.

Banū Mūsā 1981. Kitāb al-hiyal. Critical edition of the Arabic text and introduction by Ahmad Y. al-Hassan. Aleppo: Publications of the Institute for the History of Arabic Science.

[Banû Mûsâ: Studies] 2001. Banû Mûsâ ibn Shâkir (9th Century). Texts and Studies. Collected and reprinted by F. Sezgin et al. (Natural Sciences in Islam, 40). Frankfurt: Institut für Geschichte der Arabisch-Islamischen Wissenschaften.

Al-Dabbagh, D., “Banu Musa”, Dictionary of Scientific Biography (New York 1970-1990).

Hassan, al-, Ahmad Y. & Hill, Donald R. 1986. Islamic Technology. An Illustrated History. Paris/Cambridge: UNESCO/ Cambridge University Press.

Hassan, al-, Ahmad Y. & Iskandar, Yusuf & Zaki, Albert & Maqbul, Ahmad (editors) 2001. The Different Aspects of Islamic Culture. Vol. IV: Science and Technology in Islam, Parts I-II. Paris: UNESCO.

Hill, Donald R. 1977. “The Banû Mûsâ and the Book of Ingenious Devices. ” History of Technology vol. 2: pp. 39-76.

Hill, D. R. 1978. “Technology and Mechanics (hiyal).” In: The Genius of Arab Civilization: Source of Renaissance. Edited by John Hayes. Cambridge (Mass.): The MIT Press (paperback 1984), pp. 203-217.

Hill, D. R. 1984. History of Engineering in Classical and Medieval Times. London: Croom Helm.

Hill, D. R. 1991. “Arabic Mechanical Engineering: Survey of the Historical Sources.” AS&P vol. 1: pp. 167-186.

Hill, D. R. 1993. Islamic Science and Engineering. Edinburgh: Edinburgh University Press. Arabic translation: Kuwait, 2004.

Hill, D. R. 1993. “Science and Technology in Ninth-Century Baghdad.” In: Science in Western and Eastern Civilization in Carolingian Times. Edited by P. L. Butzer et D. Lohrmann. Bâle: Birkhäuser Verlag, pp. 486-502.

Hill, D.R. 1996. “Engineering”, Encyclopaedia of the History of Arabic Science. Edited by Roshdi Rashed with the collaboration of Régis Morelon. London/New York: Routledge, vol. 3, pp. 751-795.

Hill, D.R. 1998. Studies in Medieval Islamic Technology: From Philo to al-Jazarî-From Alexandria to Diyâr Bakr. Edité par David A. King. (Variorum Collected Studies Series). Aldershot, Eng. /Brookfield, Vt.: Ashgate.

O’Connor, J. J. and Robertson, E. F. 1999. “Banu Musa Brothers”, in MacTutor History of Mathematics (November 1999): link.

Rashed, Roshdi 1996. “Archimedean Learning in the Middle Ages: the Banū Mūsā”, Historia Scientiarum vol. 2: pp. 1-16.

Rashed, R. 1996. Les Mathématiques infinitésimales du IXe au XIe siècle. Vol. I : Fondateurs et commentateurs: Banū Mūsā, Thābit ibn Qurra, Ibn Sinān, al-Khāzin, al-Qūhī, Ibn al-Samh, Ibn Hūd. London: al-Furqan Islamic Heritage Foundation.

Shams, al-, Mâjid ‘Abdallâh 1977. Muqaddima li-‘ilm al-mîkânîk fî al-hadhâra al-‘arabiya (Introduction to mechanics in the Arabian Islamic). Baghdad: Markaz ‘ihyâ’ al-turâth al-‘ilmî al-‘arabî.

Shawqî, Jalâl 1973. Turâth al-‘arab fî ‘l-mîkanîk (The heritage of the Arabs in mechanics). Beirut: ‘Âlam al-kutub.

Shawqî, J. 1995. ‘Usûl al-hiyal al-handasiya fî ‘l-tarjamât al-‘arabiya (Sources of mechanics in Arabic translations). Kuwait: Mu’assasat al-Kuwait li-‘l-taqaddum al-‘ilmî.

Shawqî, J. 1995. Al-‘ulûm wa-‘l-ma’ârif al-handasiya fî ‘l-hadhâra al-islâmiya (Mechanical sciences in Islamic civilisation). Kuwait: Mu’assasat al-Kuwait li-‘l-taqaddum al-‘ilmî.