The only measurement tool in the book and why al-Jazari is the first engineer

Introduction

Al-Jazari tells that when he mentioned to some people that any(not colinear) three points could be position on the circle they didn’t believe him, so he built the only measurement instrument in the book to find the center-point of three points of unknown position. The device is quite straight forward, but we can learn quite a bit from his choice to solve, what is clearly a mathematical problem, with an “engineering” solution.

An Instrument for finding the center of a circle, Topkapi, 1206

How does it work?

The technical explanation is so short that I decided to make an exception and not color it in blue. I hope you can forgive me. Al-Jazari took a ruler and built a vertical on the center point. He placed his instrument between the two points; found the center point and drew a perpendicular segment. He repeated the process for two more points. The intersection of the perpendicular segments is the center of the circle and the distance to each point is the radius. Besides, similarly to angle measuring instruments, there is an ark, which allows to measure and mark different angles.

Some Math

One can prove that any three points that are not colinear (al-Jazari was aware of this point and specify it explicitly) are on a circle in two approaches:

  • Euclidean geometry
  • Analytic geometry.

In Euclidean geometry, three points which are not colinear form the vertices of a triangle. All triangles can be within a circle. The center of the circle is the intersection of the three perpendicular bisectors. It is relatively easy to prove. If you want to practice your Euclidean geometry, look at the diagram below, build the three radiuses BO AO CO and prove they are identical using triangle congruence theorems. Euclid’s “Elements” was translated into Arabic relatively early in the House of Wisdom in Baghdad (بيت الحكمة )). There is no direct reference in al-Jazari’s book to Euclid, but his device is based on this theorems:

Right side drawing from my Euclidean geometry book, on the left a drawing by al-Jazari.

In a different approach, you can find the center circle with analytic geometry:

Circle equation, Analytic geometry

When:

r is the circle radius

a,b are the coordinates of the center point

Since the triangle has three vertices, we have three equations in three unknowns (a, b, r) and an immediate solution. Analytic geometry has roots in ancient Greece and Persia of the 11th century, but the breakthrough was made by René Descartes, philosopher, scientist and mathematician. We remember Descartes mostly because of the proposition “I think, therefore I am.” Descartes was a remarkable mathematician and the first to offer a system of axes (x, y), as in the diagram above, which is named after him: Cartesian coordinate system. It allows the graphical representation of functions. Generations of mathematics students were, are and will be very grateful. Also, he took advantage of the Cartesian system to connect geometry and algebra, creating analytical geometry. Descartes was an impressive polymath, his contributions to philosophy and mathematics are the pillars of the two disciplines, but he also was a key figure in the Scientific Revolution and made a contribution to optics.

Polymath and al-Jazari, the first engineer

A polymath (Greek: πολυμαθής) literally “having learned much” is an individual whose knowledge spans a significant number of subjects. Both in English and Hebrew we often use the term “Renaissance man” although all the “engineers” before al-Jazari were actually polymath long before the Renaissance:

Archimedes was a gifted mathematician, scientist, and engineer, who invented the “Archimedes Screw” (a pump, still used to this day), he has improved the power and the accuracy of the Catapult, made a giant crane known as “Archimedes Claw” not to mention the myth (?) of burning the Roman fleet using mirrors. All this pales in comparison to his contributions to mathematics and physics. Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals, developed the concept of buoyant force in “On Floating Bodies” and gave the mathematical explanation to the lever.

Hero of Alexandria was an engineer, mathematician, and physicist.  Hero may have been either a Greek or a Hellenized Egyptian. It is almost certain that Hero taught at the famous Library of Alexandria because most of his writings appear as lecture notes. He is known for his research in hydrostatics, but I have already written about Hero concerning his book on automata, he also built the Aeolipile, the first steam engine. In mathematics, Hero described a method for iteratively computing the square root of a number, but his name is most closely associated with Hero’s formula for finding the area of a triangle from its side lengths.

The Banū Mūsā (“Sons of Moses”) were three 9th-century Persian scholars who lived and worked in Baghdad. The Banu Musa wrote almost 20 books, the majority of which are now lost. They are known for their Book of Ingenious Devices on automata and mechanical devices. I wrote about them in the context of the fountains, but in the context of a polymath, we can mention their contribution to mathematics, The most important work of theirs is the Book on the Measurement of Plane and Spherical Figures, a foundational work on geometry that was frequently quoted by both Islamic and European mathematicians.

Al-Jazari is not like that. His contribution to engineering is diverse. I mention already the automata and the use of the camshaft, the significant advances in candle clocks [Hebrew] including the invention of the bayonet connection, the thermal insulation, the double-action pump but he was not involved in science or math or other fields outside engineering.

The concept of the Renaissance man was coined by Leon Battista Alberti ” A man can do all things if he but wills them”, a manifestation of the deep humanism in the roots of the Renaissance. The basic premise is that the infinite human ability to evolve, and we must embrace all knowledge in our way to develop our abilities. The world has expanded so that it is just impossible. Thomas Young, an English polymath in early 19th century, regarded by many as the last man who “knew everything” was skilled in medicine, physics, Linguistics, harmony (music) and even accounting. The web site of the Israeli medical association includes thirty-two different major specialties and more, numerous subspecialties. It is not possible, even theoretically, to complete all medical specialties during one life, let alone in other areas.

We live in a more skeptical and concerned world. We ask our children, already at a young age, “What do you want to be when you grow up? We narrow the field in high school and ask the students to find majors area of study where they excel. We have institutions, counseling centers, and tests to help young people choose their profession. A physics student will get the necessary mathematical background but will not receive academic credit for courses in Assyrian or typography. In second degree studies, we reduce the field of study further, and in Ph.D., we focus on one question only. As a society, we look at people that change profession with concern, maybe as less stable who lack the ability to focus.

Following Donald Hill, The book translator, and annotator and somewhat because of my own training, I thought that using an instrument (instead of a formal proof) indicates a limited background in mathematics. This may be true. My Love M. commented that mathematical proofs are less approachable to most people and lack the magic of the instrument al-Jazari built. Al-Jazari was the first “pure engineer” not because of lack of mathematical background, or ability in math and science, but because of his passion for engineering and his ability to translate abstract and formal issues to instruments.

The Peacock Clock and the Beauty of Engineering

Introduction

[This entry was posted more than five years ago in “IR HAOSHER” [in Hebrew] and is the beginning of my journey in the footsteps of al-Jazari, this is an updated version]

Modern machines are designed to be functional, reliable, and inexpensive. No one in the Technion (Israel Institute of Technology) ever talked to me about the beauty of Engineering. Sometimes when I look at a machine or its parts, there is something breathtaking beautiful as art. Can I capture this beauty? What terms should I use? These questions resurface when my friend, Dr. Oved Kedem, retired and I looked for a present for a man who loves science and history of science.

A water clock or clepsydra (from Greek “to steal water”) is a clock where time is measured by the regulated flow of water into or out from a vessel. Water clocks, along with the sundials, are the oldest instruments for measuring time. It is not known when and where they were invented. There is evidence for the use of water clocks in the Middle East, ancient Egypt around the 16th century BC and evidence of early water clocks also in other regions of the world, including India and China. I was looking for an exciting water clock, and so I went on a journey that started at the Weizmann Institute of Science, Through Kafr Qara (كفر قرع), Istanbul and Washington and is still going. I chose to build the water clock of the peacocks.

The Peacock water clock, Topkapi Manuscript,1206

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in a scoop wheel and a tipping bucket can skip those bits

A drawing of the mechanism with my captions

The clock was built in the wall of a pool with a fountain in the center. The main tank is getting water from the pool, at a rate approximately equal to the water flow to the tipping bucket. I wrote about tipping buckets, for example here and I will do a full mathematical analysis in the future. The latter is the heart of the clock, and when it fills up, once every half an hour, the center of gravity change and the vessel tilt on its axis and discharges its water on the scoop wheel which drives all the clock’s components.  On the copper ball (see diagram above) a peacock made from copper, his tail raised, revolves. The two peacock chicks in the second miḥrāb (محراب)‎) are moving toward each other like they are quarreling. The peahen in the top miḥrāb moves from right to left. The commotion of the peacocks is happening every half an hour, and the glass roundels are colored in red, or lit in the night, to count the passing hours.

The Beauty of Science and Technology

The mechanical drawings by al-Jazari look like Turkish miniatures. My love M.has a treasure chest where she keeps postcards from our travels worldwide, although we have not sent a postcard in ages. When I showed her the Peacock Clock, she searched her collection and found a postcard from our journey to Istanbul twenty years ago, chosen by its merits as a picture without knowing anything about the book or the author.

Despite the narrative break, we should stop here for a moment to contemplate:

A Hidden claim here is that beauty is beauty is beauty. The beauty of the postcard has nothing to to do with the machine and the way it works; it’s just beautiful postcard because of its composition, the colors and other questions for art-lovers. Weizmann Institute “agrees.” In the “Beauty of Science” exhibition, images of experimental results that look beautiful and aesthetic to the eye without any relation to the science behind them. I chose as an example of an image from research by Dr. Einat Vitner. Obviously, the resemblance to Matisse caught the attention of the researcher and the viewers, but I don’t know anything about the scientific significance, or its connection to the elusive concept of beauty in science or engineering.

The Beauty of Science, “Dance of Astrocytes,“ Dr. Einat Vitner, 2011

Is The Peacock Clock beautiful without being a machine?

During my work, I went to Kafr Qara كفر قرع) ) to meet with Dr. Ibrahim Yehia, Director of  TRDC( a Regional Research Center). I wanted to talk to him about his work in the village with active science groups but during the conversation I found, to my surprise, that he got al-Jazari’s book in Arabic, and has a deep interest and knowledge on the subject.  He was a student of Prof. Fuat Sezgin, a professor of History of Science at the Goethe University in Frankfurt, and the founder of both Islam science museums in Frankfurt and Istanbul. The museum exhibits the significant role played by medieval Muslim scientists, inventors, and physicians. Almost all of the items on display are reconstructions of historical instruments and tools that were built by the University of Frankfurt’s Institute of Arabic and Islamic Sciences. Although I am a very rational person with no tendency to mysticism, I thought the way al-Jazari ‘s work permeates into my life is surprising,  a bit strange and attractive. In the same year, I  went to Istanbul to see the Museum. The Museum is located in Gülhane Park which was once part of the garden of Topkapı Palace and is beautiful. It has a beautiful collection of Sextants (navigation) and fascinating maps. Medical instruments from the period in which Islam was at the forefront of science and technology, but the objects designed by al-Jazari seemed like pale folkloristic copies of the book I love:

The elephant clock, right the drawing from the book, left, the model from the Museum.

It can be argued that the Museum artists failed to transfer the two-dimensional beauty of the drawing to a three-dimensional model, but I think there’s a lot more than that. The issue is related to the beauty of machines. Meanwhile, I found out about the exhibition entitled – 1001 Inventions the National Museum in Washington., enter it manually with Sir Ben Kingsley in the role of al-Jazari (a little long ~ 13 min)

The exhibition was launched in 2006 at the Museum of Science and Industry in Manchester and quickly became an international attraction. It was introduced in the British Parliament in London, in the European Parliament in Brussels and the United Nations building in New York. In January 2010 the 1001 Inventions launched at the world-famous London Science Museum to be followed by Istanbul, New York, Dubai, San Francisco and Washington, where I saw it with my son Noah.

The exhibition uses al-Jazari as a role model of technology in the Islamic golden age, with two water clocks: The Elephant water clock and the Scribe water clock. Despite dealing with science and technology, the exhibition is proposing a different narrative: the middle ages are not a dark period in-between the decline of the Roman Empire and the Renaissance, but also the golden age of Islam.  As a result, the items themselves (“elephant clock”, “pumping facility” and so on) are great designs without running water, gears or any working mechanism at all. This is a very decorated but empty shell. Despite the investment, I do not think that none of the objects is even close to original beauty.

I think there is something inside us that identifies and responds to beauty. When it comes to science and engineering, this beauty is related to precision and correctness. In the past seven years, I have taught high school student “computational science,” and it is easy to say a software solution is “beautiful,” and when it is cumbersome and forced. The beauty, in this case, is not purely aesthetic but has to do with simplicity and strength.

Simplicity

To explain the connection between simplicity and beauty, I want to stand on the shoulders of giants. Aristotle believed that the Earth was the center of the universe and the Sun, Moon, planets are attached to transparent, rotating spheres surrounding the Earth. More astronomical observations were difficult to fit in the model and by the time of Ptolemy(2nd century AD),  the model included a system of two spheres per planet: one called its deferent; the other, its epicycle. The final model was so complicated, Alfonso X, king of Castile called the Wise (Spanish: el Sabio) who gained considerable scientific fame based on his deep interest  in astronomy said: “If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler.”

Picture of the world according to Ptolemy, the most complete and detailed description of the geocentric model following Aristotle

in the evolution of the scientific model of the movement of celestial bodies there are more heroes, Copernicus is perhaps the best known of them all, but I would like jumped straight to Johannes Kepler (1571-1630) who replaced this complicated  system with three simple rules:

  1. Elliptic orbit: The orbit of a planet is an ellipse with the Sun at one of the two foci.
  2. The law of increasing velocity: The planet travels faster when closer to the Sun, and then slower when farther from the Sun. Kepler wrote this law mathematically enabling calculations and predictions.
  3. The harmonic law – The Square of the orbital period (the time it takes for the planet to circle the Sun and we call it “year”) is directly proportional to the cube of the semi-major axis of its orbit.

The summary of Kepler laws is maybe too concise, but I think everyone could see the beauty in the ability to explain the complex movement of the night sky using three simple rules that require mathematics of middle school. The simplicity and elegance of Kepler’s model help us to be convinced but do not make it right. Like any scientific or engineering theory, it should be repeatedly tested and verified. Astronomical observations are numerous and contain deviations and mistakes. The regularity is not simple. Kepler spent many years analyzing the data. As the scientific model consists of simple rules, as the rules explain more phenomena, sometimes seemingly unrelated, there is a sense of logical harmony, echoing within us as more beautiful.

Power

From time to time, there is an engineering achievement, such as the telephone or the electric bulb that makes us truly believe in the power of human invention to improve the lives of humanity. What makes an engineering or scientific solution powerful beyond its success? It tried to look at an example:

The wheel is such an old invention that we have no way of knowing who or where it originated. Depictions of a wheeled vehicle appeared between 3500–3350 BCE in the Bronocice clay from southern Poland. The wheel helps to bridge distances and ease transportation of objects and goods. To my surprise, the benefits of transportation were limited for thousands of years due to a lack of roads and infrastructure.

However the wheel was still used for many purposes, Stone mills powered by water, Distaff and a spinning wheel, pulleys to lift the weight, toothed wheels to change the speed, torque, and direction of a power source which allowed ancient civilizations to create complex machines as al-Jazari demonstrated so gracefully.

The index of power asks how elaborate is the engineering solution and how many layers it includes. I think it’s similar, but different, from the beauty of subtext, when the contents of a book or movie, which was not transferred to us explicitly, becomes understood as the book/movie unfolds. This is not just the complexity, but the integration and the consolidation, The beauty of how the various components fit together; the water fill the tipping bucket carefully designed so that it will tilt every half hour, rotating the scoop wheel, a little bit like our enjoyment of Rube Goldberg’s  machine :

Rube Goldberg self-operating napkin

In this respect, when the machine lost its function and made just a design is losing its power and simplicity, and hence its beauty, even if its shape is intact. With the crew of the workshop of the Clore Science Garden, we built a prototype of the Peacocks Clock:

What is so beautiful about this door? (Cast brass door for the Artuqid Palace in Diyarbakir)

Introduction

The sixth and final category in the book contains five dissimilar designs. The first and most grand of all is the Artuqids Palace door in Diyarbakir, Eastern Anatolia. Al-Jazari opens this chapter with some enthusiastic message very unusual for him:

It is the masterpiece; to view it saddles are strapped on. Truly it is the pearl, the orphan, a priceless possession.”

This passionate text surprised me because this door, engineering speaking, is quite simple and doesn’t contain the inventions and surprises included in most of al-Jazari works. The beauty is not in engineering, but in the art and the craft. Donald Hill, translator, and interpreter of the book, Engineer by heart, was interested mainly in the casting technology: “Of particular importance, also, is the first unequivocal description of metal casting in closed mould-boxes with green sand, a method not used in the West until the end of the fifteenth century.” Casting is a manufacturing process in which a liquid metal (al-Jazari used copper, brass, and bronze) is poured into a mold with the desired shape. “Green” sand is used even today. The name is a bit confusing as the sand is not green color at all. Instead, the sand is called “green” because it is “wet” sand, which contains water and organic bonding compounds much like we say “green wood” in carpentry.

I have two very different questions:

  • Sorry, what is so beautiful about this door? Or at least why al-Jazari admired his work?
  • How is it possible that military considerations are not part of the design? What does it say about al-Jazari as an engineer?

Description of the door and its beauty

It is a door with two leaves which rise to the height of about four and a half meters (originally 18 spans ( شِبْر) ) and the width of each leave is a meter and a half.

The Palace door, Topkapi Manuscript, 1206

The Palace door, Topkapi Manuscript, 1206

In the center of each leave, there is a complex geometric pattern that includes Hexagram (Star of David) and Octagram. It is interesting to note that both these shapes belong to the family of Magic stars. A magic star is a star polygon in which numbers are placed at each of the n vertices and n intersections, such that the four numbers on each line sum to the same magic constant: M=4n+2. The solutions I know to magic stars are only from the 20th century, but the use of the two was very common in the Muslim world. Is it possible that al-Jazari sensed mathematical beauty without knowing the math?

Since it is a relatively complicated pattern, I colored the drawing to see Magic Stars:

Islamic art makes frequent use of geometric patterns which were developed over the centuries. There is  “artistic unity” across time and place. I bring three pictures of three doors with different geographical, cultural and historical background, both Shi’ite and Sunni Islam

The left door is a Turkish door from the14th-century. The middle door is a Grand Palace in Fez in Morocco from the 13th-century. The wooden door from Iran on the right is not dated.

The Islamic aesthetic shift toward complex geometric structures is attributed to the prohibition in the Qur’an of figurative images to avoid becoming objects of worship. Geometric structures are abstract, emphasized symmetries, and suggested infinity and therefore reminding Muslims the idea of the infinite nature of Allah. This explanation does not satisfy me since the second commandment :

” Thou shalt not make unto thee any graven image or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth. Thou shalt not bow down thyself to them, nor serve them”

Did not yield a similar tradition in Jewish art. I don’t see anything that would justify the special enthusiasm from the geometric patterns of al-Jazari. However, if any of my readers find some special beauty or a hidden message, please comment as I would love to learn.

The pattern was bounded by brass plates a which carried Kufic((كوفي ) inscriptions and leaf motif decorations. This reads “the dominion is God’s, the One, the Conqueror”

Kufic is the oldest calligraphic form of the various Arabic scripts. Kufic developed around the end of the 7th century in Kufa, Iraq, from which it takes its name, and other centers. Kufic was prevalent in manuscripts from the 7th to 10th centuries. In the late 12th century, when the door was made, it was less used, and I do not know if this choice has a special meaning?

The calligraphy is surrounded by  bronze plates which were decorated with red copper leaves:

The process is relatively complex; firstly, he casted bronze panels. Using a scalpel, he carved the leaf template and poured melted red copper.

In the drawing, there are no brass domes, but in the text, there is a detailed explanation and diagram of a dome. I took the liberty to add this to the original drawing by al-Jazari:

I did not cover every detail, but I cannot ignore the door’s knockers from cast brass in the shape of two connected serpents, their heads facing each other. Their mouths are open as if they wished to devour the lion between them.   The door did not survive (I am convinced it was built, and not just designed, because of the richness and the details in the text). It is interesting to note that very similar Bronze door-knockers from the Great Mosque in Cizre are now in the Museum of Turkish and Islamic Arts in Istanbul. To my surprise, pretty similar versions have found their way to Copenhagen and Berlin museums.

We will never know what caused al-Jazari to be that happy with this door. Maybe he enjoyed his geometric patterns and thought particularly beautiful, Maybe He enjoyed his success in the complex casting or his work with various metals, brass, copper, and silver, maybe he was happy the amount and richness of the details and possibly it was a combination of all.

 

Military engineers and engineering history

Engineering has existed since ancient times, the invention of a pulley, the construction of the Egyptian pyramids or the copper production process are all “Engineering” according to all modern definitions but only in the 14th century was the first use of the term engine’er. The origin of the word is from Latin words “in generare” meaning “to create” but relating to the designing or creating engines of war like the catapult or assault towers. For many years all the engineers were military engineers. Archimedes, a gifted mathematician and scientist had a major role in the Second Punic War. He improved the power and accuracy of the Catapult, He designed a giant claw to destroy Roman ships, and the peak of his inventions was burning the Roman fleet using mirrors.  Leonardo da Vinci engineering career included military chapters as evident from his letter to Ludovico Sforza, ruler of Milan. He wrote:

“I have plans for very light, strong and easily portable bridges with which to pursue and, on some occasions, flee the enemy.. Also, if one cannot, when besieging a terrain, proceed by bombardment either because of the height of the glacis or the strength of its situation and location, I have methods for destroying every fortress.”

The Faculty of engineering at the Technion is still called “civil engineering,” to be separated from military engineering, although the former has become almost a non-issue in the modern world of engineering.

It is somewhat surprising that there is no military engineering chapter al-Jazari’s work and even when he builds the door for the Palace, no considerations of strength or defense capability are mentioned, not even a single word. Two possible explanations:

  1. The principality in Diyarbakir was so peaceful that there was no need for a military engineer.
  2. The expectations from the Court engineer in Diyarbakir were different.

 

A change in Diyarbakir and al-Jazari as an “engineering magician.”

The dynasty was founded by Artuk Bey, a general under the Seljuq emir of Damascus. In 1086 he was appointed the governor of Jerusalem, a surprising twist to a story about a Muslim dynasty which ruled in Diyarbakir Anatolia. We need to remember that the Middle East map in the 11th and 12th centuries is very different from the map we know today. After Artuk death in 1091 his sons, Sökmen and Ilghazi were expelled from Jerusalem by the Fatimid vizier and set themselves up in Diyarbakır and Mardin in Anatolia.

This door was installed at the Artuqid Palace in Diyarbakir where al-Jazari was the court engineer. The Palace was built within the walls of Diyarbakir during the reign of Salih Nasreddin Mahmud (1200-1222) Artuqid king who employed al-Jazari like his father and brother before him. The Palace was excavated in the 1960s, but most of it is still buried under the mound, and I have a fantasy that the site will be excavated a second time and we will find some of the remains of al-Jazari’s work. In the 12th century, there were a few battles with the Crusaders, with Georgia and clashes of within the Muslims. I don’t think a peaceful period is the explanation of the absence of the military aspect in al-Jazari’s work.

The Artuqids are a Turkmen dynasty which started as a warrior tribe, and its original power was military. In the 12th century, they were settling in the old cities of Amida (the previous name Diyarbakir ) and Mardin. These are ancient cities with urban culture since the Assyrians. The population is diverse and includes veteran Christian and newcomer Turkmen population as well as other migrants from Iran and other places that continued through the 13th century. Beyond the monumental Al- Jazari book, there was probably a workshop for copying and illustrating manuscripts. Rachel Ward identified two other illuminated manuscripts that were produced there. There were new architectural designs, Sharon Talmor as part of her graduate work at the University of Tel Aviv found three which mark a new era in Islamic architecture. As a part of the assimilation of a warrior tribe into the urban setting, there was probably a need for a change, and there was a thirst for cultural and artistic activities. I’d love to hear other suggestions too, but this is a possible explanation for the absence of military engineering.

So the circle closes. The question of the beauty of the door is connected to the role of al-Jazari. As we step into the book, I think we will be more convinced of his role as  “a magician of engineering”  the man who harness science and technology to create and beauty and astonishment.