water clock – The Book of Knowledge of Ingenious Mechanical Devices (original) (raw)

Introduction

The device that closes the book is also the simplest of all. In the ancient world, one of the means of measuring time was the submersible float (طرزهار). It’s a buoy with a hole so that the water penetrates and causes it to sink after a given time. This was necessary to monitor the water flow in irrigation canals or for cooking. Al-Jazari feared that the user would nap and miss the sinking of the buoy, so he added a sound effect. It made me search for materials on ancient alarm clocks, which is the subject of this post.

Boat for measuring one hour, Topkapi manuscript, 1205

How does it work?

Sinking buoys don’t require an explanation, so I gave up the traditional blue coloring of the engineering explanations. Obviously, if there is a hole in the buoy, water will penetrate it, and the buoy, or in this case, the boat will sink. The duration of the sinking was achieved by trial and error. Al-Jazari used sinking buoys in the elephant clock and elsewhere. The twist here is the sound alert. I added to al-Jazari’s drawing contours that enclose the airspace and highlights the hole in the bottom:

A drawing by al-Jazari with my additions and captions.

The sailor and boat are made of copper. And they are welded together so that a common airspace is created. At first, the boat sinks slowly, and the trapped air slowly exits under the pressure of the rising water. Due to the slowness of the process, the whistle does not make a sound. There are also five holes for a secondary air exit from the sailor’s hat, which reduce the air output through the whistle and help to silence it. The boat is full of water at the end of the hour, and a rapid sinking begins. The air quickly compresses through the whistle and makes a sound, and helps the sleepy watcher to wake up and do his job.

Early alarm clocks

The earliest alarm clock I have found is associated with Plato, the Greek philosopher. Plato would get up early. In “The Laws,” his last work, he wrote what might explain his need for an alarm clock:

” Asleep, man is useless, he may as well be dead…it a disgrace and unworthy of a gentleman…if he devotes the whole of any night to sleep.”

Plato allegedly designed his own alarm clock. I have reservations because the information comes from Athenaeus of Naucratis, who wrote the “Deipnosophistae” some 200 years later, and there is no other evidence for this alarm clock. It’s an interesting water clock (not based on a sinking buoy), but in terms of sound play, it’s not very different from Al-Jazari. You can see a nice animation:

There is a good variety of antique alarm clocks. Ctesibius built a particularly precise water clock**.** We already encountered Ctesibius in a post about A Pump Powered by a Water Wheel. He was an inventor and mathematician in Alexandria, Ptolemaic Egypt, and is best known as the “father of pneumatics.” Very little is known about his life. He was probably the first director of the Museum of Alexandria. His writings have not survived, but his inventions were documented by Athenaeus, I already mentioned, Philo of Byzantium, Heron of Alexandria, and an exceptionally detailed description of the water clock appears in “De architectura, libri decem,” known today as The Ten Books on Architecture by Marcus Vitruvius, a Roman architect and engineer during the 1st century BC. I will expand on the water clock immediately, but Vitruvius also wrote:

” At Jaffa in Syria and among the Nomads in Arabia, are lakes of enormous size that yield very large masses of asphalt, which are carried off by the inhabitants thereabouts.”

apparently referring to the Dead Sea. The strange combination of Jaffa, Syria, and the Dead Sea sounds like a child confused by various holidays and mixes Christmas and Chanuka, but this whole Levant may seem like one geographical unit from Rome. This is a good animation of the clock:

You can see that Ctesibius was aware of the well-known problem of water clocks, which is the variable flow rate with the vessel’s water level. You can read more here. His solution is a tank always full of water, and the excess spills out. This creates a constant flow rate in the second tank, raising the buoy with the indicator indicating the passing minutes. At the end of an hour, the siphon (an invention attributed to Ctesibius) empties the buoy tank and turns the gear counting the hours. Vitruvius writes that there was an “alarm clock system that dropped gravel stones on a gong and blew the trumpets,” but this part has no technical details, so we can only imagine how it worked. A somewhat strange story is that the clock was installed at court in Alexandria and indicated the amount of time lawyers could speak while the severity of the crime determined the amount of water. Ctesibius’ water clock was considered the most accurate until Dutch physicist Christiaan Huygens invented the pendulum clock.

There are other ancient alarm clocks, but it is amusing to know, and says quite a bit about the importance of patents, that a French inventor named Antoine Redier patented an alarm clock in 1847, more than 2,000 years after Plato, who was astonished in his grave and perhaps expected some of the royalties…

Introduction

The Drummers Clock is a water clock and probably one of the first drum machines and musical robot ancestor. It features five mechanical drummers: two cymbal players, two drummers with a drum slung over their shoulders, and a drummer sitting in front of two kettle drums. Despite significant advances in robotics and AI- Artificial Intelligence, musical robots fall short compared to human musicians; their music lacks subtleties and is “mechanical.” The simplicity of the drum machine, in contrast to a robot violinist, helps to focus on the real issue. This post moves between explanations of the drummers’ clock and thoughts on the difficulties in creating a “musical” musical robot.

The Drummers’ Clock, a dispersed copy, 1315

How does it work?

This is a simple version of the Castle clock with fewer mechanisms to display the time, and those that remained are simpler. The large components: The water tank, float, and flow controller are identical to the Castle clock and the “Time cart” is very similar, a little like a cheap version of a mobile phone. Al-Jazari does not explain them again but refers the reader to the first chapter (the Castle clock). I also turn directly to musicians. Al-Jazari writes:

“When an hour has passed the musicians (نوبة – nūbah, a musical genre found in the North African, it has its origins in Arabo-Andalusian music.) perform with a clamorous sound which is heard from afar.”

The technical explanation, as always, will be colored in blue, so anyone who is not interested in tipping buckets or scoops wheels can skip those bits. The diagram below is the original drawing of al-Jazari with my captions.

The water flows on the scoop wheel once an hour. This is a large clock, and every time about eight liters of water flows. It is turning the scoop wheel on its axle so that the pegs move the rod which is connected by a copper chain to the slave-girls’ hands. The pegs are an early version of a camshaft and convert circular motion to linear movement. The number of pegs and the intervals between them create different patterns of drumming. The copper strip goes through the hollow wooden body of the musician, and when pulled it goes up and later falls to hit the drum. The pegs are organized in a way that is characteristic of the work of al-Jazari, two adjacent pegs, and a third peg apart. The result is two relatively fast beats, and a third after a pause. There are also two trumpet players, but they are only “decor accessories.” The sound of trumpets is produced separately by the water pouring into an air vessel and compressing the air out through the pipe with a whistle. Al-Jazari used this in many devices, including the Perpetual Flute.

Robotics and the student’s disappointment

Robotics is an enjoyable and sometimes exciting way to teach and learn science and technology. This is true for excellent students and students with difficulties in mathematics and science. Most of the students gladly take upon themselves robotics problems, research a topic, and build a robot using original thinking and their ideas. I taught robotics in different settings: in elementary school Gavrieli, in middle school Branco Weiss and at the Davidson Institute of science education. I found it a creative learning experience in all the years I taught. Beyond the programming tools, mechanical engineering, electronics, and sensors, it teaches children to confront and overcome obstacles, builds confidence and self-esteem, and gives inspiration to science and technology. As a part of the introduction, I would present a wide range of robots, including a robot that plays the violin:

In almost every class I taught, students (happy and enthusiastic) were complaining that the robot’s performance is “mechanical” or “robotic” as a weakness. Violin has a wealth of nuances in how the violinist produces the violin sound (Timbre). This results from many choices, such as which string to use, the pressure of the bow, the point of contact, the bowing speed, to use the whole bow or only partially. All these choices reflect the musical understanding of the violinist and will echo emotionally with the listener. The Musical robot in the movie is programmed so that it “knows” to play the notes, but it has no musical understanding at all. The concept of an artistic interpretation is foreign to him. The drum machine is much simpler in comparison to the violin and will facilitate the discussion.

Musical robots and music

The drummer’s choice includes “merely” the question of the drums selection and the beating template. In terms of the drum machine of al-Jazari, this is the arrangement of the pegs for each drum and possibly changing the length to affect the volume. Al-Jazari made these decisions during “programming” or the design phase, but we can easily think of a modern drumming robot with all the parameters free to change in real-time. This will allow changing hand techniques and evolving drum beat patterns but will not progress us even one step toward musical interpretation.

This is a nontrivial challenge for robot builders. Robots in science fiction literature and toward the end of the 20th century are machines that can replicate human action, especially when it is repetitive. When Karel Čapek coined the word “robot” in the play R.U.R (Rossum’s Universal Robots), the idea was to replace humans when the work was tedious, difficult, or even dangerous. Prominent examples are the welding robots in the automotive industry or the Police Bomb Disposal Robot. In recent years, there has been a shift in direction, and a lot of research has been done on Artificial Intelligence (AI). There are exceptional results in various fields, including robotics stock traders, diagnostic medical robots, and precise surgery robots. What was considered thirty years ago insurmountable, like software playing chess or go (a Japanese board game) is a reality. Chess software like Komodo can beat any human grandmaster. The contribution of AI to music (AIM- Artificial Intelligence Music) is more modest and limited, at this time, to conferences and academia, and no robot can be matched to a human musician. People are not jamming to concerts to listen to musical robots. AIM is a broad field and includes many topics, some of which are relatively simple to understand, Like:

Some are more complex, but still approachable:

Some are borderline science fiction:

As someone who likes robots and automatons, maybe like al-Jazari at his time, I’m surprised by the pleasure I get from reading about the difficulties of the AIM community and the human abilities which are so hard to imitate. Despite what I wrote, I would like you to see the film below: I don’t know how it was done and what part is human, and what part is AIM, but it is certainly fun to watch and listen to!

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 as 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 the 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 changes, 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 a 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 Picasso 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’s 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 the 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:

Introduction

The boat clock is a simpler version of the elephant clock. The scribe indicates the minutes passed and one Dragon (two in the elephant clock) swinging on its axis every half an hour. It looks like an early sketch for the elephant clock or a simpler version for beginners. Perhaps, for this reason, nobody wrote, or at least I haven’t found anything nor restorations or animations in contrast to the abundance for the elephant clock. The Dragon appears here in more detail and also has a drawing of his own but the text refers to it as a serpent just with legs and wings, it got me thinking about the biblical serpent and the story of the tree of the knowledge of good and evil. This post is dedicated to the serpent-dragon, and on this occasion, I also explain the balancing process which allows the dragon to go for a marvelous swing and return safely on his legs.

The Boat Clock, Topkapi manuscript, 1206.

How does the dragon make a flip and Lands on his feet?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in submersible floats or torque and center of mass can skip those bits. In the water clock of the boat, like the elephant clock, the main mechanism is a sinking float, a float with a hole which sinks slowly during half an hour. After half an hour the float is full of water and begins to sink quickly and releases a ball that falls into the dragon’s mouth:

Drawing from the book, Topkapi manuscript, I tilted the dragon to visualize the swing and added the lead weights in his tail and the ball.

The dragon is made of a thin brass plate which was rolled to a pipe and hammered to form the shape of a dragon. The dimensions are not very detailed, but the Dragon’s tail forms a circular ring of four fingers, or 8 cm, diameter. The dragon head is hammered separately and soldered to the ring. The Dragon’s legs are holding an axle which is free to rotate. The ball I added does not appear in the original drawing, but is described in the text and weighs 30 dirhams (درهم), almost 100 grams. When it falls into the Dragon’s mouth, it generates a torque causing the dragon to flip. A torque or moment of force is the rotational equivalent of linear force. The torque is given by the cross product of the position vector (distance vector) and the force vector:

Some of the students I taught physics during the years struggle with cross products and especially with the moment of force. But we all know intuitively that it is easier to open the door by pushing it near the handle than push it near the hinges.(larger r =larger torque). Or when we struggle to remove the lug nuts of a flat wheel, we often use a wrench extension for the same reason – to generate a larger torque.

When the dragon’s head is downwards, the ball falls off, and the lead weight in his tail exert torque in the opposite direction and reset the Dragon position. My love M. said that the dragon is like a roly-poly and of course she is correct. This is a round-bottomed toy, usually egg-shaped, that tends to right itself when pushed at an angle, and does this in a seeming contradiction to the force of gravity.

Drawing of a roly-poly

The bottom of the toy is made of a high-density material such as metal, and thus the center of mass is low relative to the height of the toy. This is very similar to the lead weights in the tail of the dragon. The ball falls into the Dragon’s mouth function as the finger pushing the toy over. In both cases, the low center of mass exerts a torque that reinstates the upright orientation.

Interestingly enough al-Jazari calls the lead “black lead” (الرصاص اسود) because in his time they called Tin “white lead”. Maybe in a future post, I will write more about the metallurgy of the 12th century.

A Serpent or a Dragon?

Serpentes (snakes) are an elongated, legless, carnivorous suborder of reptiles. They are characterized by the absence of limbs. Al-Jazari serpent has wings and legs making it a legendary creature or a Dragon. Dragons do not exist (sorry if I offended the fans of dragons) and respectively do not have a rigid biological definition. A dragon is a large, serpent-like mythological creature that appears in the folklore of many cultures around the world. Beliefs about dragons vary significantly by region, so horns wings and the number of legs vary a lot. All dragons have superpowers. We are more aware dragons capable of breathing fire in the western cultures but Bakunawa, a dragon from the Philippines, can swallow the moon, and the Vietnamese dragon can control the weather. It can be argued that the Dragon figure was influenced by various snakes, especially spitting cobras, bats (wings) and giant lizards and in the modern era extinct dinosaurs. In the Wikipedia entry of the “Elephant clock” appears this wonderful quote in the name of al-Jazari signifying his “multicultural mentality”:

“The elephant represents the Indian and African cultures, the two dragons represent Chinese culture, the phoenix represents Persian culture, the water work represents Greek culture, and the turban represents Islamic culture.”

Al-Jazari didn’t write these lines. Such errors are amazing and funny and are one of the risks of a free-content encyclopedia relying on volunteers editors.

In contrast to the threatening figure of the Western Dragon, Chinese Dragon is a symbol of strength, integrity, and wisdom. The Chinese Dragon is depicted as a lizard-like creature without wings and four clawed feet and long tendril appended to each side of the snout. Al-Jazari’s Dragon is not very Chinese. However, at home, we have a facsimile edition of the “Sarajevo Haggadah.” It’s Passover Haggadah written in Barcelona around 1350, and it is considered to be the oldest surviving Haggadah. The Haggadah is displayed at the National Museum of Bosnia and Herzegovina in Sarajevo, and this is the origin of its name. To my surprise, the Haggadah is packed with dragons. On top of this, in the 19th century in Paris, a small book was printed: – L’ornementation des Moyen-âge. This is a collection of illustration from medieval manuscripts and also includes many dragons. The dragons in all three books are very similar, the same general, lizard-like structure, the same animal head which is not completely defined, small wings and legs. If my rationality hadn’t so constrained me, I would be convinced that the three illustrators visited some mysterious zoo and made a drawing of the dragon that was held not far from the reptile room.

Right side dragons from Haggadah Sarajevo, in the center the Dragon of the Boat, Topkapi manuscript and to the left a dragon from L’ornementation des manuscrits au Moyen-âge

All this discussion about snakes with legs took me back to the Bible story, Genesis 2-3. Adam and Eve were in the garden of Eden, where “And out of the ground made the Lord God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil.” God allowed Adam and Eve to enjoy the fruits of the Garden except for the tree of knowledge, “for in the day that thou eatest thereof thou shalt surely die. Now the serpent was more subtil than any beast of the field which the Lord God had made” The Serpent Tempted Eve claiming “then your eyes shall be opened, and ye shall be as gods, knowing good and evil.” Therefore the snake lost its legs and got in trouble with men kind: “And the Lord God said unto the serpent, Because thou hast done this, thou art cursed above all cattle, and above every beast of the field; upon thy belly shalt thou go, and dust shalt thou eat all the days of thy life:

Genesis 2-3 King James Version

But did al-Jazari know the Biblical story about how the ancient serpent lost his feet?

Years ago I visited the Topkapi Museum in Istanbul, and near one of the swords there was a summary of the “The Binding הָעֲקֵידָה Ha-Aqedah” only, Ishmael (and not Isac) is the victim and the hero of the story. First, I thought there was a confusion, but this is of course just my ignorance. Eid al-Adha ( عيد الأضحى‎) ‘Feast of the Sacrifice’ is the second of two Islamic holidays celebrated worldwide each year. The sacrifice celebrated is the sacrifice Ibrahim (Abraham) our father, was asked by God to sacrifice his son Ismail (Ishmael) though the Qur’an does not name the son. In my eyes, both stories are equally heinous, and already as a child, I remember my inner resistance. Like the story of the Binding, the story of the garden of Eden in the Quran is completely different:

“And you, Adam, inhabit the Garden, you and your wife, and eat whatever you wish; but do not approach this tree, lest you become sinners.

But Satan whispered to them, to reveal to them their nakedness, which was invisible to them. He said, “Your Lord has only forbidden you this tree, lest you become angels, or become immortals.”

Quran, Surah 7 elevation, Translated by Talal Itani.

In the Quran, there is no tree of knowledge. The only tree mentioned by name is the Tree of Immortality ( شجرة الخلود Shajarat al-Kholoud ) The Serpent is not the seducer but the devil himself, and he is tempting Adam and Eve with eternal life. In Surah 2, The Heifer, appears Iblis (إبليس), which is another name for the devil in Islam. Eve, as a woman, is the main guilty in the original sin, both in Judaism and Christianity. In Islam Eve is Adams’ partner and clean from sin. It is very unlikely that al-Jazari didn’t know the Serpent from the story of the creation and knew only the Quran version and the source of the legs and wings who can tell?

Introduction

The elephant clock is by far the most popular of all the works by al-Jazari. There have been several modern reconstructions, multiple animations, and it has its own Wikipedia entry, and more. In the previous post, I tried to explain why millions of viewers in the mall in Dubai or the “1001 inventions” were captivated by its magic. The current post is different from anything I’ve written so far and is a record of my journey to reconstruct the elephant clock in Lego, including the difficulties and the learning on the way. The elephant is in the initial stages, and I hope to post an update every week. I’d love to hear your suggestion, ideas, or advice you may have for me.

Elephant clock, Topkapi manuscript, 1206.

Why build?

When I started this journey, I was working at the Davidson Institute of science education. I proposed to Prof. Haim Harari, founding Chairman of Davidson Institute and former President of the Weizmann Institute of science, to build al-Jazari fifty machines in the “Science Garden”, an open-air museum in Weizmann Institute. Haim refused and told me that the Science Garden was rooted in the 17th-century Newtonian physics and he would like to bring it into the 21st century. Instead, my proposal would take us back to the 12th century… This blog is my alternative exhibition.

Beyond the magic of al-Jazari machines and their value to the history of technology, It is important in undermining stereotypes about Islam that exist both in the Jewish and Arabic population in Israel. Arab Labor ( “AVODA ARAVIT”) is a racial slur that is widely used long before the amusing sitcom written by Sayed Kashua. The slur indicates low quality work. On the other hand, Arab society perceives itself as debilitated and with little contribution to the world of science. Arab students come to Weizmann Institute feeling this is the “temple of science” where they do not belong. The wonderful machines of al-Jazari emphasize the scientific achievements of the Islam golden age, which is not taught at schools at all, and offer a different perspective to both Jews and Arabs.

Previous posts included animations. To me, there is no replacement for actually building the machine. The difficulties on the road and resulting learning are priceless.

Why Lego?

Some reconstructions of al-Jazari were made, including the Elephant Clock. These are pictures of three of reconstructions:

Three reconstructions of the Elephant Clock, left Ibn Battuta Mall in Dubai, in the middle Sharjah Museum of Islamic Civilization, right the Istanbul Museum of The History of Science & Technology in Islam.

I have a lot of respect and appreciation for the restorers. Their Elephant clock is possibly more similar to the original than I am assuming. Somehow their beautiful work can’t recreate the beauty of the illustrations in the book and in the process of transferring the 2D illustration to a 3D reconstruction some of the magic is lost. I think they are too realistic. The elephant is a “real” elephant and the canopy is beautiful and very dignified. There is no room left for our imagination. Also, the Elephant Clock is static in Istanbul as well as in the 1001 inventions exhibition, more like a statue demonstrating the beauty of the design rather than a working water clock. In Dubai, I think, the Elephant Clock is powered by electric motors. This reduces the experience, at least in my eyes. The reconstruction should rely on 12-century technology and the ability of al-Jazari to perform complex control scheme before we had electronics and controllers. The magic of al-Jazari is contemporary (strange but true).

I have no reason to assume that I know something the restores did not know. The move to LEGO simplifies the aesthetic choices and offers playfulness and sense of contemporary at the same time. No LEGO work is a part of the Turkish tradition of miniature art. However, Lego is free to correspond with this art. Lego has its own design language, and even adults works in Lego and Hyper-technology Lego works are fun and playful, also this is a great excuse for me to build in Lego…

Previous al-Jazari machines in Lego

I know only one of al-Jazari machine made in LEGO. Interestingly enough, it is the Elephant Clock. You can see it here:

I Think the design is charming and the use of LEGO is both clever and quite sophisticated. There’s breathing space in the Lego elephant, and I like the human figures, which are an entertaining use of LEGO components. But although the design follows al-Jazari, its operation is based on the “smart brick” (a programmable, lego controller which serves as the brain of LEGO robots) and electric motors. This, in my mind, defies the point. Or at least the challenge I am hoping to meet: reconstruct, and on the way test and learn,al-Jazari engineering from the 12th century.

Where am I

I made a plan to build a LEGO elephant, 60 bricks high(about 60 cm). There is no precise measurement in the Book of Knowledge, but this is roughly 2:1 scale in relation to the book. The giant elephant you see in the Dubai restoration, for example, is elephant real size (~3.5 m) rather than the dimensions extracted from the original work. I used Tinker Cad, I found it very user-friendly. I inserted a 3D a model of an Asian elephant and filled it with LEGO bricks:

At this point, I did not insert to the model the other components of the clock, such as the canopy, Mahout, the dragons, etc. l will see as I go if I prefer hands-on experimentation or the use the CAD software.

I ordered 5420 dark gray Lego bricks of various sizes from eight different suppliers, from Denmark to Croatia, from the U.S. to France. Thank you bricklink (Internet market for LEGO) I wouldn’t manage without you. The reason for so many suppliers is simple. No one supplier had so many gray parts. Last week I began to build. It looks like this:

About one-third of my LEGO elephant. The trunk rests in our cereal Bowl. Otherwise, it would fall. I began experimenting with the buoy and the mechanism of the scribe, but this will be in my next post.

Introduction

The elephant clock is by far the most popular of all al-Jazari’s works. There are a few modern reconstructions of it: some in different exhibitions and museums, but also one in the Dubai Mall. The clock has a variety of animations in 2D and in 3D, and it even has its own Wikipedia page. Due to the complexity of the mechanism, I divided this post into two; in the first part, I will explain what the viewer sees and try to explore the sources of the magic. The second part will be more engineering-oriented, and I will explain how the mechanisms work in the backstage, and what is so unique about this clock.

The Elephant clock, manuscript from 1315, Syria

What does the viewer see?

An elephant, approximately one meter and twenty centimeters long, who is carrying on its back a canopy with four pillars and a castle. On top of the castle’s dome, is a bird. Inside the elephant, is a hidden water reservoir and a sinking float (a float with a hole that sinks slowly) during half an hour. More details in the next post. In the canopy sits a scribe holding a pen pointing at a semi-circle with tick marks. During this half hour, the scribe rotates and his pen indicates the minutes that have passed. At the end of every half hour, the scribe returns to its original position. At the same time, there will be quite an impressive show. Between the elephant’s shoulders, rides a mahout (the elephant keeper and driver). In his right hand, is an ax and a mallet in his left. Every half hour the mahout strikes the copper elephant, first, with the ax and then with the mallet. In the castle balcony sits a man. His hands are on the heads of two falcons which he keeps them from opening their beaks. Once every half hour, he raises one of his hand, and the corresponding falcon shoots out a ball. The ball falls into the dragon’s maw, making the dragon swing on its axis and then lay the ball on the cymbal in a jar. During this time, the bird on the dome is also spinning. Above the head of the falconer is a semi-circle with fifteen black holes. Every full hour one hole turns so that the sum of white indicates the number of hours passed since sunrise.

You can see a short video demonstrating the elephant clock and explaining the mechanism:

A fuller explanation will also come in the next post.

Why an elephant?

The Elephant water clock **entry **in Wikipedia reads:

“The elephant represents the Indian and African cultures, the two dragons represents ancient Chinese culture, the phoenix represents Persian culture, the water work represents ancient Greek culture, and the turban represents Islamic culture signifying the multicultural mentality of the intellectual al-Jazari. “

The quote certainly is not by al-Jazari, but whoever wrote it explained the wealth of the clock. Nonetheless, it made me think. I am afraid that the whole concept of multiculturalism is completely foreign to the 12th century and al-Jazari. What is a possible explanation for the elephant?

The Middle Ages and strange elephants

The trade routes in the middle ages were spread over Europe, the Middle East, India, China, and Africa. On the east coast of Africa, they traded ivory, gold, ebony, and slaves. China exported silk and porcelain, India spices and drugs. Rumors about elephants, giraffes, and other exotic animals reached Europe but the artists who drew the manuscripts had never seen an actual elephant. They drew them based on their imagination. There is an entire site dedicated to the weird drawings of elephants. I give just two examples:

Thomas of Cantimpré, Liber de natura rerum, France 1290

A hoofed wooly elephant “Livre des simples médecines” a manuscript from the 15 century.

The original manuscript by al-Jazari was unfortunately lost, but the manuscript from Topkapi is from 1206, I wrote about it here. This is the year al-Jazari died, so it is probably a copy of the original. You can see that the elephant looks like an Asian elephant and the mahout and the canopy are located correctly. Al-Jazari’s familiarity with elephants is not necessarily surprising, although I couldn’t find any evidence for elephants in Diyarbakir. Arab rulers had menageries or collections of exotic animals. In addition to the curiosity and pleasure they provided, they demonstrated the ruler’s wealth and power as well as the impact of the sovereign from India to Africa. Offerings of rare animals were part of the diplomatic process and sometimes part of the tax system. Until the 13th century, the agreement between the Nubian Kingdom and the Muslim rulers of Egypt demanded that the Nubian people provide Egypt with three hundred and sixty slaves annually, in addition to providing some wildlife. It This was the primary source for giraffes in the Sultan of Cairo’s menagerie.

Book of the animals, Syria, 15th Century.

The use of animals as a diplomatic gesture is well documented. For example, Baybars, the Mameluke Sultan of Egypt and Syria in the 13th century gave elephants, giraffes, and zebras to the king of Spain, Emperor of Byzantium and the Mongol Khan. In the 10th century, Cordoba sent a giraffe to Tunisia and a story I particularly like about the elephant, Abul-Abbas. Harun al-Rashid, the Abbasid caliph in Baghdad, sent an Asian elephant to Aachen, Germany to the Carolingian emperor Charlemagne. It happened in the 9th century, and surprisingly enough, there’s a Jewish angle to this story. The elephant was brought by Yitzhak the Jew. There is a historical novel “The travels of Isaac the Jew and Abu Alabas the elephant”(in Hebrew). It is interesting to note that other presents including an elaborate water clock made of brass, described in the Royal Frankish Annals were sent with the elephant. The water clock marked the 12 hours with balls of brass falling on a plate every hour, and also had twelve horsemen who appeared in turn at each hour. Perhaps al-Jazari knew the story as part of his extensive knowledge of water clocks?

The Elephant Clock and the Circus

The diplomatic delegations and the royal gifts indicate that the elephant was a symbol of power and wisdom, but in the context of the elephant clock, I think more about the circus and exotic acts. The elephant is made of copper and is just a stage for the show, but the swinging dragons, the Mahout with his fearsome tools, the Falcons and the spinning bird form a great circus number. An exciting circus act has, in my opinion, four components, not in binding order, not always all of them, and certainly not of the same significance or importance:

I looked at several iconic circus shows and Jules Léotard’s act is a good point of comparison. Léotard was a French acrobatic performer who made history as the first man ever to perform the aerial act on a trapeze. It most certainly meets the requirement for freshness. Likewise, the elephant clock is also the first of its kind; no clock ever, before or after, is similar, and everyone who watches it, even today, is amazed.

Secondly, great skills: Léotard practiced his acrobatic stunts over his parents’ pool before he revealed them in 1859 in Cirque Napoleon in Paris. Then he appeared in London before an audience that went crazy because of his aerial flips between five trapezes with only a pile of mattresses to protect him. The elephant clock also demonstrates such high proficiency and skills both to the innocent and to the skilled observer, considering the control of the timing using the sinking float, the complex movement of the three characters(the mahout, the scribe, and the man in the balcony), and the virtuoso swing of the dragons. All are innovative engineering tricks demonstrating al-Jazari’s skills in water clocks and automatons.

Regarding the sense of danger, the crowd in the circus was afraid for Léotard’s life and this element intensified the experience; however, automatons by definition lack this aspect.

Jules Léotard, a French acrobat, 19 century

Last but not least, the awe-inspiring image. Léotard, like all circus performers, could be dressed in a sports suit, but as you can see in the picture he’s wearing theatrical shorts, bracelets emphasize his wrists, and the collar of his shirt reminds us of a royal necklace. All this help to imprint his image in our mind. The picture that al-Jazari created is a lot more than the sum of its components and is intriguing audiences till this very day.

Introduction

Al-Jazari opened _“The Book Of Knowledge Of Ingenious Mechanical Devices_” with a monumental clock, perhaps the most complex of all ten water clocks and candle clocks explained in the book: The Castle Clock.

Sometimes you know you read a wonderful book the second you read the first paragraph:

“Call me Ishmael. Some years ago – never mind how long precisely – having little or no money in my purse, and nothing particular to interest me on shore, I thought I would sail about a little and see the watery part of the world. It is a way I have of driving off the spleen and regulating the circulation.”

Moby Dick by Herman Melville

In the right hands, the beginning of a novel can make you feel like you were abducted from reality and you are drifting down a river which will take you to other worlds. Not only engineers who open al-Jazari’s book are captured immediately by its magic of the machines he designed eight hundred years ago. We will never know if al-Jazari wanted a powerful opening to demonstrate his ability at its best, or he positioned machines at random order and was surprised by the very question? This post hopes to explain the Castel Clock as well as discuss what we can about al-Jazari from the text.

How does it work?

The Castle Clock had a complicated movement throughout the day, and it is on the boundary between a clock and an automaton(a machine that performs a function according to a predetermined set of instructions). There is something theatrical in many automata. Sometimes it is by design, like the automata in Greek theater used for “Deus ex machina”, literally “god from the machine”. Sometimes there are other objectives like the lion automaton built by Leonardo da Vinci for François Ier, king of France. When the King tapped the lion with his sword, its body opened and presented lilies, a symbol associated with the French royalty. The clock by al-Jazari is also very theatrical.

The Castle Clock from a dispersed copy, 1315.

At the beginning of the day all twenty-four doors, in two rows, are closed and the Golden Crescent, which is a little hard to see in the picture, is positioned to the left. During the day, the half-moon is moving right, and every hour three things are happening:

The picture of the falcon is taken from a dream or myth. Horus is one of the most significant ancient Egyptian deities. He was most often depicted as a falcon. Horus had many battles with Seth, the god of the desert, in which he lost his left eye, then a new eye was created for him called “the eye of the Moon” or “the diamond” and symbolizes an endless vision. I have no reason to assume that al-Jazari was familiar with Egyptian mythology, but who knows?

Above the upper row of doors, we can see the Zodiac sphere. At the beginning of the day, the sun will be on the eastern horizon, about to rise. The sun climbs until noon, then descends until nightfall and the six signs that have been visible will disappear, and the six that have been hidden will appear. At noon the drummers drum, the trumpeters blow, and the cymbalist plays his cymbals for a while.

Al-Jazari does not write anything about the reason for multiple mechanisms to display the time. The crescent actually functions as a modern analog clock hand, and the rest are just “decoration” and maybe a resonance box. In the world of modern engineering, it could be considered excessive and even wasteful, but there is magic that passes through centuries of the Falcons even if there is no additional information.

Erich Kästner, the wonderful author of Pünktchen und Anton(Dot and Anton in English), was concerned: ” By the children who would prefer to eat porridge for three days than deal with such complex issues as his reflections [my translation from Hebrew]. He came up with a different font “so if you see something like that you can skip it altogether…” It seems to me this even more needed for technical explanations of engineers that will be in blue.

The Castle Clock is a sophisticated version of the classical water clock or clepsydra where time is measured by the regulated flow of out a vessel where the amount is then measured. The difficulty is that the water flow rate is not uniform and depends on pressure (altitude) of the water in the vessel. To overcome this problem, al-Jazari used a conical plug and the float chamber.

Conical plug, the Castle clock, Topkapi, 1206

The main reservoir is feeding the float chamber through a conical plug thus whenever the water level drops the valve (a float that is a plug in a cone shape) goes down with the water level allowing the chamber to be refilled. Every time the chamber is full of water, the conical plug will seal the chamber isolating it from the main reservoir. In this way, the float chamber is always full of water and therefore the water flow at a constant rate and does not depend on the height of the water in the main reservoir.

A drawing of the clock mechanism, Topkapı manuscript, 1206, my captions

At Sunrise a servant makes sure that all doors are closed and the time cart is on the right side (looking from the back). During the day water will flow at a rate determined by the flow regulator and the main float would drop with the water level at the main reservoir. The main float is made of copper, and it is quite heavy. When it drops, it pulls the rope, which through the pulley would turn the main disk and pull the time cart attached to the golden crescent which would move to the left at a constant velocity indicating the time passed from sunrise. Every hour the cart will progress one door, and a smart mechanism would open the doors while dropping down two bronze balls. The balls would roll down and reach an opening above the heads of the Falcons. The curving claws of the Falcons are welded to a copper tube that can rotate on its axis. The falcon stands upright because of a balancing weight. When the bronze ball drops down, it changes the balance, and the falcon would lean forward, and the falcon wings, attached to a body on a hinge will spread open, and the ball will fall on the cymbal hidden in the vase. Now that the falcon head is light again, the balancing weight will bring him to its original position. The clock is packed with similar invention and “patents”.

A drawing of the falcon mechanism, Topkapi manuscript, 1206

The book contains almost 50 pages explaining the various mechanisms with detailed construction instructions. Readers who are interested in the details can learn them here and see the simulation here

What did I learn about Al-Jazari?

We have no information about al-Jazari except what is in the text itself. We can “pick” the book to learn about al-Jazari and his world. Consider the adjustable flow regulator intended to ensure that the clock movement fits the changing length of the day. This controller is a small engineering marvel itself, but I am interested in it because of the triple encounter it offers with al-Jazari and his world:

“I have studied the books of the earlier [scholars] and the works of the later [craftsmen] –masters of ingenious devices with movements like pneumatic [movements], and water machines … I considered the treatment of this craft for a period of time and I progressed, by practicing it, from the stage of book learning to that of witnessing, and I have taken the view on this matter of some of the ancients and those more recent [scholars]. “

The question of openness or seclusion to the world for people of faith is a relevant question even today for Jews or Muslims. Maimonides, Rabbi Moshe Ben Maimon, the most important rabbinical arbiters in Jewish history, and polymath, scientist, and physician lived almost in the same time frame in Cordoba, far away from Diyarbakir in Anatolia but he was a part of the same Muslim world. During his medical studies, he was introduced to the writings of Aristotle in natural science and did not feel any threat to his faith. He even wrote:

” Consequently he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics.” Guide for the Perplexed

It’s amazing to read when today Orthodox Jewish children are forbidden to learn mathematics or natural sciences. Al-Jazari, more engineer than a philosopher, does not deal with matters of faith directly, but his faith is embedded in the text. This doesn’t bother him at all to read and learn from pagan scholars.

Introduction

Al-Jazari himself wrote the introduction to this chapter, and It makes sense to bring his opening remarks:

“The king, Salih. Abu al-Fath. Mahmud, may God assist Islam by prolonging his life, proposed that I should make for him an instrument having no chains, balances or balls, not liable to rapid change or decay, from which could be told the passage of the hours and the divisions of the hours without inconvenience. It should be of handsome design and suitable for journeys or for settled residence. I considered the matter and made, according to his suggestion, what I shall now describe. “

What follows is the water clock of the scribe (in Arabic ورّاق). The clock design required two computational parts:

This post is relatively heavy in mathematics, and the “blue” parts (the technical explanation) are larger than usual. I Hope you can prevail them well.

The water clock of the beaker. Probably a dispersed manuscript from Cairo, 1354

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in pulleys or balancing weight can skip those bits. The drawing below is the Beaker water clock mechanism with my captions:

This is a copper beaker divided into two parts, upper beaker and a base are connected by an onyx with a very fine hole. The beaker is filled with water at the beginning of the day. The float is raised to its maximum height, and the weight is hanging down as far as possible. During the day the water would discharge slowly through the onyx to the base. As a result, the float would sink, and the weight would rise, causing the large pulley to rotates with the scribe and his pen. The water is sufficient for 14 hours and 30 minutes for the longest day of the year. At sunset, the water is returned to the beaker from the base, and the process repeats itself.

You can watch this short YouTube video from Technology & Science In Islam” showing the beaker clock :

iframe width=”854″ height=”480″ src=”https://www.youtube.com/embed/LNpDtxpBWes” frameborder=”0″ allow=”autoplay; encrypted-media” allowfullscreen>

Two engineering issues need further discussion:

The clock face and the variable length of the day

In summer the days are long and the nights are short and vice versa in the winter. We’re moving the clock one hour forward at the beginning of the summer (“DST” – Daylight Saving Time), and at the fall we set the clock back. The Idea of the “DST” is attributed to Benjamin Franklin, and the rationale is energy saving, but it was suggested that daylight saving time improves quality of sleep, as we sleep longer during the darkness that allows deeper sleep and we know that a lack of sunlight can cause Seasonal Affective Disorder. Al-Jazari also dealt with the variable length of the day. Below is a screenshot from the YouTube clip. I added some captions.

The clock face, “Technology & Science In Islam” with my caption.
The clock face is divided into eighteen bands, and each band is divided into twelve equal solar hours. The outer band covers 3600; it is designed for ten days from June 21 (the summer solstice). The solar hour will be 300, but in Diyarbakır, there are about 14.5 hours of daytime so that the solar hour will be longer by~ 12 minutes in comparison to the constant hour. The eighteenth band(innermost) is intended for the last ten days of December. Diyarbakir has only 9.5 hours light, and therefore the band was shortened:
9.5/14.5* 360 = 2360
Every hour will be slightly less than 200 so the hour is only 46 minutes!
The concept of solar hours seems very strange in the 21st century and complicates everything. Just to think that programmers will be forced to change program timings with the calendar.
Our notion of time rests on the celestial bodies movement. The years were counted based on the Sun or the Moon and the day, hour, minutes, and seconds were all derive from it. In fact, until 1967 the second was defined as 1/86,400 of a mean solar day. Only with the development of the Atomic clock, the definition was detached from the Earth’s rotation cycle, and the second is defined to be exactly 9,192, 631,770 cycles of a Cesium atomic clock. As weird as it may sound, atomic clocks and their ridicules precision are part of our daily life, and we cannot use Waze, or any navigation software, without them. In the world of the 12th-century solar hours made perfect sense and were more connected to nature and the movement of the celestial bodies.

Bernoulli’s equation and the “solution” of al-Jazari

A difficult problem in any water clock is that the water flow is not constant but depends on the water level in the tank. The following diagram illustrates the problem. For simplicity the beaker is cylindrical, and the onyx was inlarge for clarity:

It is clear that at the beginning of the day when the beaker is full of water the water flow will be much stronger in comparison to the water flow after ten hours when the water level in the tank has dropped. How can we calculate the water flow and what can be done?

The mathematical solution to the problem was given by Daniel Bernoulli, a Swiss mathematician of the 18th century and a winner of the French Academy Award ten times. The first, to my surprise, was for a clepsydra (water clock) to measure time at sea. (I’m looking for specs of the clock and any assistance would be welcomed.) The many awards were not always a source of happiness. In 1734 he won the Academy Award with his father, Johann Bernoulli, a mathematician in his own right. The father couldn’t bear the shame of being equivalent to his son and banned Daniel from his house and did not reconcile with him until his death. I doubt that Joseph Cedar (Israeli movie director) was aware of the Bernoulli’s story, but the similarity to the movie “Footnote” is striking. The most important work of Daniel Bernoulli is hydrodynamics released in 1738:

Despite extensive research (I found six different studies!) that indicates that students of Physics and Engineering have conceptual difficulties to understand Bernoulli’s equation, I will challenge my readers with the solution of the water clock problem.

Bernoulli equation states:

Where :

P is the pressure.

rho is the water density.

g is the gravitational acceleration~ 9.8 m/s2

h is the water height above a reference plane.

v is the water velocity.

He/she who wants to go deeper can go here and there are four lessons which I recommend at khan academy. Our problem looks like this:

We can write the Bernoulli equation:

Where P1 is the pressure in the beaker, h1 is the height of the water in the beaker and v1 is the water flow velocity in the beaker. Respectively the pressure in the onyx is P2, h2 is the water height in the onyx, and v2 is water flow velocity in the onyx. However, the beaker and the onyx are both open to the atmosphere. Thus P1 = P2 = 1 atm and can be removed. The water level in the beaker is h(t) and depends on time because when the water flows through the onyx to the base, h will be reduced. However, the onyx water height was determined as the reference plane and hence h2 = 0. Rearranging:

Since the onyx is very narrow in comparison with the beaker, we can assume that the flow in the onyx is much faster relative to the water velocity in the beaker and can be neglected for the calculation of the water velocity in the onyx:

If this looks somewhat familiar, it is because this is Torricelli law and I used to run some very nice experiments with my middle school students at Beit Hashmonai:

Torricelli law, three identical holes at different heights

The amount of water through the onyx must be equal to the amount of water lost by the beaker:

Where A2 is the cross-section of the onyx and A1 is the cross-section of the beaker:

Where r2 is the radius of the onyx. However, A1 is a function of time since the radius of the beaker is not constant but gets narrower at the bottom:

The velocity v1 is the change in the beaker water height:

We combine the last five equations:

Rearrange and make sure that the rate is constant (This is the reason for the whole exercise!) or:

For dh**/**dt to be constant, the radius of the beaker must be equal to the fourth root of the water height.

These mathematical tools were not available to al-Jazari. There is no evidence in the “Book of Knowledge of Ingenious Mechanical Devices” to the extensive mathematical knowledge that was available in the Muslim world of the 12th century. I suspect that the mathematical education of al-Jazari was rather limited. This is a different topic and I hope to write a separate post in the future.

However al-Jazari was very resourceful, he developed a practical technique that allowed him to overcome the lack of mathematical tools. While preparing the beaker, he filled it with water and observed the outflow of the water with a reliable clock. If the float sank to the second mark, then the beaker radius is correct else al-Jazari hammered the beaker to widen it or make it narrower. Then the water is emptied from the beaker. The process was repeated for each mark. It is a pity that we do not have the beaker al-Jazari hammered to compare it to the theoretical calculation. One must admire the practicality of al-Jazari solution.