Banu Musa

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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.

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The fountain that changes its shape and the controversy with the Banu Musa

“Allah has promised the believing men and believing women gardens beneath which rivers flow, wherein they abide eternally.”

Qur’an 9:72

The fountain with two tipping buckets, Topkapi manuscript, 1206

Introduction

The Muslim paradise is called Jannah ( جنّة), literally “garden.”  Every time heaven is mentioned in the holy book of Qur’an, there is a description of flowing water and fruit-bearing trees. This is not surprising because Islam came from the desert, hot and arid lands. I would like to ignore the other attributes of al-Jannah such as houris; splendid companions of equal age, lovely eyed and virgins, who will accompany the faithful. My only focus is on the scenery. Like Garden of Eden in the Bible, there are four rivers in Jannah, the Euphrates flows according to both books, but the other rivers are different, and they have a common source named Salsabil (سلسبيل).

Gardens were significant to Islam from its inception. The garden landscaping has a spiritual meaning which exceeds the human need for shade and water. They are perceived as a place of rest and contemplation, an earthly equivalent to life in heaven. This metaphor reached its peak in Chahar-bagh, (چهارباغ), in which the garden was divided into four parts by water channels; the four water channels being the four rivers of paradise with a fountain in the center of a pool, representing Salsabil. I think that al-Jazari’s deep interest in fountains is related to the importance of gardens in Islam. 

A miniature of paradise from the 16th century

How does the fountain work?

The fountain of al-Jazari is installed in a pool. For an hour the fountain shoots up from the main orifice and then for one hour it emits six curving jets from six nozzles, and the process repeats itself. Today it is a trivial task for any engineer, but in the 12th century, with no electronics or electric valves, it was almost a miracle. The technical explanation, as always, will be colored in blue, so anyone who is not interested in early control systems can skip those bits.

At some distance from the pool, al-Jazari built a high house into which the water flowed. This section does not appear in the drawing. The water from the high house flew into the copper bowl welded to a pipe with four openings. This is the same drawing as above, but with my captions.

At the bottom of the titling pipe, al-Jazari welded a ring which is seated on an axle so that the pipe is like a kids seesaw. The right side is slightly heavier, and therefore it tilts to the right, and the water comes from both openings on the right. The main opening fills the tank and the narrow pipe which shoots the water up in the air. The secondary opening is much smaller, and it slowly fills the tipping bucket (in red). In the drawing, the tipping bucket is almost full. After one hour, the weight of the water at the front-end is heavy enough to make the tipping bucket swing, and the black rod will push the tilting pipe upward so the seesaw would tilt to the left and water fill the other tank, the wide pipe around the narrow pipe and comes out in six jets. The process repeats itself.

Banū Mūsā

Al-Jazari opens the fourth Category “On fountains which change their shapes at known intervals and on perpetual flutes” with a brief statement:

“I did not follow the system of the Banū Mūsā, may God have mercy upon them, who in earlier times distinguished themselves in the matters covered by these subjects.”

The Banū Mūsā brothers are the predecessors of al-Jazari and are important to understanding his work. Banū Mūsā, the sons of Moses, is the name shared by three scholars, brothers from the ninth-century, sons of Mūsā ibn Shākir, a Persian astronomer. At a young age, they join the famous House of Wisdom, a library and a translation center in Baghdad. It is known that the brothers wrote together more than 20 books, but most have been lost over the years. Their most famous book and only two copies survived is The Book of Ingenious Devices (كتاب الحيل Kitab al-Hiyal( which al-Jazari is referring. The book was commissioned by the Abbasid Caliph of Baghdad, Abu Jafar al-Ma’mun ibn Harun (786–833), who instructed the Banu Musa to acquire all of the Hellenistic texts that had been preserved during the decline and fall of Roman civilization. This rescue operation has cultural importance, which exceeds by far the current post. Some of the devices described in their Book were inspired by the works of Hero of Alexandria and Philo of Byzantium, as well as ancient Persian, Chinese, and Indian engineering. However, many of the other devices described in the book were original inventions by the Banu Musa brothers. Donald Hill, who translated this book, as well as al-Jazari’s book, wrote:

“The Banu Musa went “well beyond anything achieved by Hero or Philo.” Their preoccupation with automatic controls distinguishes them from their Greek predecessors, including the “use of self-operating valves, timing devices, delay systems, and other concepts of great ingenuity.”

The book describes the construction of 100 devices, including seven automatic fountains.

What is the Controversy?

Al-Jazari did not specify which fountain he is referring to, but he did write:

“They made the alternation [fountain water shapes] with vanes turned by wind or by water so that the fountains were changed at every rotation, but this is too short an interval for the change to appear [to the full effect]. Then in two designs they used a pipe like an almost horizontal balance arm. The water flowed through it …”

It is clear that this is the fountain he is referring to:

A fountain that alternates water shapes by use of a balance from
The Self Changing Fountain of Banu Musa bin Shakir by Prof. Salim T S Al-Hassani

He concludes: ” I do not know whence this confusion [came], from the original or from the copy.”

For those who really want to dive into the details, you can see here the fountains the Banu Musa. There could be no argument that al-Jazari borrowed key concepts from the Banu Musa, including the placement of a narrow pipe within a wide pipe, the concept of two water tanks and variable feeding with time. His main disagreement is over the control method. In his opinion, the intervals were too short, and the result could be erratic. He’s probably right. Al-Jazari explains what’s wrong with the design, but the details are of little importance. The technology changed so dramatically that the historical techniques to control the timing are only an odd puzzle of how we can control timing before we had, electronics and electric valves. However, curiosity and skepticism are the best guides for every engineer today, just like eight centuries ago.

Curiosity and Doubts

Anybody who taught high school or Bachelor’s degree in science or technology knows that academic success is no guarantee for curiosity, healthy doubts, or critical thinking in general. Excellent students can answer the questions in the exam but find it difficult to ask questions about a scientific paper or engineering presentation, to test if the assumptions are robust and can stand rigorous evaluation, if there is an alternative explanation or if there can be another model. Many excellent and feel uncomfortable with the new requirements so different from their previous experience in school. In parenthesis, as an educator, I have to say that this is not a decree of fate and schools can do a lot, but that’s another discussion. My encounter with al–Jazari is limited to his book, but beyond is high of engineering capabilities, it is clear he was curious and had a healthy measure of inquisitiveness and skepticism. He checked the water regulator attributed to Archimedes and found it insufficient, he read the Banu Musa and had his doubts regarding the control method. Beyond the benefit of the healthy engineering skepticism, as he adds question marks, I like him more.

 

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The Magic Pitcher, a Walnut and the Art of Motorcycle Maintenance

Introduction

Al-Jazari describes a handsome pitcher of beautiful workmanship.  The slave brings it at the end of the meal and pours over a diner’s hands moderately warm water. To the surprised spectators, he serves a second,  miserable diner with water, too hot for bathing and too cold water for a third. Finally, he tilts the pitcher, and no water comes out. To the delight of the company, he continued his round and selects the “winners” who would receive proper bathing and the other who would get the party laugh. We are used getting cold or hot water by will, in the twelve century this was a technology miracle. To the best of my knowledge, this is the earliest Thermos, an insulating storage vessel for cold\hot drinks.

Water Pitcher, variable temperature, 1206 Topkapi manuscript.

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in heat transfer or patents to insert and take out water can skip those bits. Al-Jazari took a brass pitcher and removed the bottom and welded two parallel plates with a finger wide air gap in-between them.  Al-Jazari wrote that he tried to use a single brass plate as a spacer, but the cold water was heated, and the hot water got cold as expected. The copper is an excellent heat conductor, while the air trapped between the plates is an excellent heat insulator. Donald R. Hill,  the book translator, wrote:

“Although al-Jazari describes these devices at considerable length, the designs show little advance on those described by the Banu Musa [you can read more here] Indeed the latter are in several ways more sophisticated.”

However, to my knowledge, this is the first use of double walls and air insulation, and like a lot of al-Jazari work was obtained by trial and error. The drawings of al-Jazari are usually exceptional, but in this case, he chose a section that makes it more difficult, at least for me, to understand. I attach a contemporary drawing made by Donald R. Hill, The book translator, and annotator, showing two cross section. I added captions.

A drawing made by Donald R. Hill, The book translator, and annotator, showing two cross section of the pitcher.

On the right side, we look at the pitcher, perpendicular to both the copper plates dividing it into two tanks; one for hot water and one for cold water. The distance between the plates was enlarged for clarity. In reality, it was “a finger” about 2 inches. In the upper third of the pitcher, two funnels were installed, leading the hot water to its tank and the cold water to its half of the pitcher. To fill the pitcher, al-Jazari used a deflector on an axle. You can see it in both sections. The plate had a heavier side, towards the cold water so that one would fill the cold water first. When the cold water tank was full, the float pushed the deflector plate which tilts toward the hot water tank and enables us to fill the other half. A second buoy (al-Jazari used a walnut) with a gauge marked that this tank was also full. The Pitcher had a hollow handle with two holes for air entry. The holes were connected to two pipes, one leading to the half pitcher with cold water and the other to the half of the hot water.  When the slave leaves the two holes open, air enters to both sides of the pitcher, and mixed water, in a comfortable temperature, comes out of the nozzle. When the slave covers one of the holes, water comes out only from the side of the pitcher that has an air inlet, hot or cold depending on the hole he sealed. If the slave sealed both holes, no water would come out at all.

spirit of silliness

Al –Jazari  wrote:

“It is a pitcher of handsome workmanship with a handle and a spout. The slave brings it on a tray at the end of the meal and places it in front of the diner [al-makhdum -lit. the one being served]. He lifts the pitcher from the tray and pours over the diner’s hands moderately warm water, with which he completes his ritual ablutions (wudu) or the washing of his hands. Then on the hands of the person whom he is putting to the test he pours hot water unbearable to the touch, so he cannot wash his hands. Then on the hands of the person whom he is putting to the test he pours very cold water, unbearable to the touch. Then he tilts the pitcher over [the hands of] the person whom he is putting to the test and nothing comes out of the pitcher. He pours out [warm water] to whomsoever he wishes in the company, and refuses it to whomsoever he wishes.”

This description fits better the court jester than a slave servant. Assuming he survived the night, it is also a testimony about a folly in the court in Diyarbakır. Court jester was a medieval profession responsible for fun and entertainment in the courts. Most of us know the Western version with colorful clown clothes, jester hat and a wand. But there are also court jesters in the Islamist courts. A Persian version called the DALQAK is somewhat similar, In the book  “Fools Are Everywhere: The Court Jester Around the World” there is a list of the jesters in the Abbasid Caliphate. The most famous one Abū Nuwās who was a poet and a jester in the court of Harun al-Rashid and appears several times in The Book of “One Thousand and One Nights.”

Jesters, musicians, and dancers in a Turkish miniature, Topkapi Palace

The role of the Court fool in medieval times was to speak honestly, sometimes even mocking the King or his noblemen without suffering the consequences. For example in the Book “Of Fools at Court “ by Clemens Amelunxen when a powerful nobleman complained that a fool was walking on his right, the jester hopped over to the left and answered in sarcasm: “well, I don’t mind a fool walking on my right!”. It is possible that the pitcher stunt was part of the leeway that was possible for the court fool. Either way, this is a little surprising glimpse to the court culture of the Artuqid.

Zen and the Art of Motorcycle Maintenance

I read the book “Zen and the Art of Motorcycle Maintenance”  by Robert m. Pirsig, few years before I had my own BSA Motorcycle that needed everything I know about bike maintenance and challenged the mechanics in Chlenov street garage when I was not sufficient. I found this book in a used Bookstore and even if I did not immerse in the roots of the debate between Sophists and Socrates, I was deeply moved by the book and three or four stories are part of me ever since.

Robert m. Pirsig

The book is the story of a journey of Pirsig and his son on a motorcycle across the United States. This is partially autobiographical, weaving the journey in the United States back roads with a complicated internal search (he underwent a mental breakdown and hospitalization) and deep philosophical discussions.

Pirsig and his son ride with his close friends John and Sylvia. They have an expensive BMW motorcycle and John, like most of us, wants to enjoy driving it without getting into maintenance and technological problems.  The handlebars of John’s BMA started slipping, and Pirsig is offering to shim them with a can of beer. He writes:

“I thought this was pretty clever myself. Save him a trip to God knows where to get shim stock. Save him time. Save him money. But to my surprise, he didn’t see the cleverness of this at all…. As far as I know, those handlebars are still loose. And I believe now that he was actually offended at the time. I had had the nerve to propose repair of his new eighteen-hundred dollar BMW, the pride of a half-century of German mechanical finesse, with a piece of old beer can!….What emerged in vague form at first and then in sharper outline was the explanation that…I was going at it in terms of underlying form. He was going at it in terms of immediate appearance. I was seeing what the shim meant. He was seeing what the shim was… Who likes to think of a beautiful precision machine fixed with an old hunk of junk?”

Should you ask how this story is connected to al-Jazari?  Without any discussions or explanations, he used a Walnut as a buoy. To me, this is identical to using a beer can as a shim, i.e., looking at things in terms of the underlying form. I would like to finish in a quote from Pirsig on the essence and form. If I replaced steel with copper, Al-Jazari (in my opinion) would agree with every word:

” I’ve noticed that people who have never worked with steel have trouble seeing this—that the motorcycle is primarily a mental phenomenon. They associate metal with given shapes—pipes, rods, girders, tools, parts—all of them fixed and inviolable, and think of it as primarily physical. But a person who does machining or foundry work or forger work or welding sees “steel” as having no shape at all. Steel can be any shape you want if you are skilled enough, and any shape but the one you want if you are not.”