Al-Jazari Water pumps and Patents

Introduction

Category V deals with water pumps or in the language of al-Jazari “On machines for raising water from pools and shallow wells which are not deep, and from running streams.”

Al-Jazari is a man of few words, and his introductions are quite minimal, but in this chapter, he dives straight to the point. His opening line is: “I have shown the picture of that (machine for lifting water by an animal who turns a lever) after the text of the next chapter”. There is nothing about the current state of things, what were the pumps available in his time, what drove the need for improvements?  Nor any other introductory remark. However, the first two pumps are an improvement and automation of the Shaduf (شادوف) or in Hebrew קילון (kilon). This is a manual device for raising water, known to man for thousands of years. Al-Jazari design includes three improvements: mechanization, significant efficiency improvement and the use of segmented gear. Nowadays an engineer would write at least three different patents. This would lead us to a discussion of patents and al-Jazari.

Shaduf

The Shaduf is a hand-operated device for lifting water. We do not know who or when was it invented, but it was in use in ancient Egypt and Mesopotamia to irrigate land for thousands of years. Surprisingly enough, it is still used today in India, Egypt, and some other countries

The Shaduf consists of an upright frame on which is suspended a long pole, at one end of this pole hangs a bucket or a ladle. The other end carries a balancing weight which serves as the counterpoise of a lever.

With a relatively small effort the operator lifts the bucket or the ladle and carry water from a body of water (typically, a river or pond) onto the irrigation system. From this point, the water will flow to the crops in the fields due to gravity. The operation of the Shaduf is completely manual, but it’s easier to pull the rope down using the balancing weigh than lift the water. Moreover the Shaduf transport the water to the beginning of the irrigation canal. It is interesting to note that the Shaduf appears in old Hebrew text, The Mishnah “study by repetition” is the first major written collection of the Jewish oral traditions. It was sealed at the beginning of the third century AD. I did not find a translation, so this is my rough translation that does not capture the beauty of the ancient Hebrew:

 

“משקין בית השלהין במועד ובשביעית, בין ממעיין שיצא כתחילה, בין ממעיין שלא יצא כתחילה; אבל אין משקין לא ממי הגשמים, ולא ממי הקילון.” (משנה: מועד קטן, פרק א)

“Water an irrigated field during the festival and sabbatical, both from a newly-emerging spring and from a spring that did not just emerged. But do not water the field with water from rainwater or Shaduf water.”

Shaduf, a photograph from Eygpt, 2001

How does it work?

The first two water pumps of al-Jazari are relatively simple machines comparing to the complexities of the clocks and automata explained in previous posts. A-Jazri dedicated one page each. I placed the two drawings side by side. The technical explanation, as always, will be colored in blue, so anyone who is not interested in segmented gear or runged wheel can skip those bits.

The first two pumps designed by al-Jazari. The left pump has a single ladle. A single page from a dispersed copy, dated to 1315. The right pump includes four ladles. Topkapi copy, 1206.

We shall start with the diagram on the left of the pump that has one ladle. In the top room, a donkey is rotating the main shaft and the toothed wheel connected to it. The later rotates a toothed wheel in 900. Today we would probably use beveled gear for this purpose, but al-Jazari gives no details. My love M. complained that in the drawing you could not see the gears pressed against each other and the segmented gear which I shall explain in the next paragraph are perpendicular to their real direction. All these issues and more are related to the drawing made in the 12th century. In the future, I hope to add animations that will help my current readers to understand the mechanism. On the same axle, there is a segmented gear with the same cogs and spacing. However, only a sector of the circular gear has cogs on the periphery, in this case, a quarter of a circle. This segmented gear fits into a runged wheel which is connected to the axle of the ladle. When the cogs interlock with the stages of the wheel, they rotate the axle, and the ladle lifts about 15 liters of water at a time.  After a quarter of a circle, there are no more cogs, and nothing to prevent the runged wheel to rotate backward dropping the ladle into the water and the process repeats itself. The pump to the right is identical in its mechanism only there are four ladles and four segmented gears. That means that each donkey rotation will result in 60 liters. The efficiency improvement is probably less than 4x because the donkey will be slower because of the heavy load.

Efficiency

This chapter is quite unusual in the book because it deals with the engineering core, improving process efficiency, while most of the chapters are about surprising automata and rotating peacocks. The question of efficiency for most machines of al-Jazari is out of place if not completely from another discipline. The question of efficiency is an essential component in any engineering process. A process is efficient if we increase the amount of work performed while reducing the use of resources (raw materials, labor, fuel, time, etc.) Al-Jazari is an engineer by nature (Hebrew) and when the subject is water pumps he designed a significant efficiency improvement.

Al-Jazari and patents

In our world, the mechanization of the Shaduf justifies a patent, the improved efficiency by approximately 3-4 justifies another patent. There is a question mark about the inventor of the segmented gear. Some claim that segmented gear appeared 1st in the “The Book of Secrets” by Ibn Khalaf al-Muradi other give the invention to al-Jazari. I hope to obtain “The Book of Secrets” and then I’ll be able to formulate my own opinion.  I think that if al-Jazari was aware of this discussion, he was really surprised.

The official history of Patents starts with the Venetian law from 1474:

“Any person in this city who makes any new and ingenious contrivance, not made heretofore in our dominion, shall, as soon as it is perfected so that it can be used and exercised, give notice of the same to our office of Provveditori de Comun [State Judicial Office], it being forbidden up to 10 years for any other person in any territory and place of ours to make a contrivance in the form and resemblance thereof, without the consent and license of the author.”

Although the present patent laws are more complex, the essence practically identical:  The patent system is protecting inventors so that they will have an opportunity to receive proper compensation for their efforts. Why patent law was necessary in Venice in the fifteenth century and was not necessary in Diyarbakir in the twelfth century?

The need originated because of the emerging glass industry. Master Angelo Barovier in mid-fifteenth century invented the method to create clear glass, which was pure like rock crystal called ” cristallo”. This recipe was one of the most closely guarded secrets of the Venetian Republic for centuries.

Of course, if another manufacturer would be allowed to copy the recipe with minimal effort,  the willingness to invest in innovation and development will be diminished. Today patents are a major concern in high tech and pharmaceutical industry, but there was a time when mirror production was in the front of technology.

Venetian Goblet from the 16th century. Louvre Museum collection.

The world of al-Jazari was very different. This is not a sophisticated industrial world where multiple manufacturers were competing for everything including know-how and technology. The question of commercialization of knowledge is not relevant. The world of programming evolved differently. In parallel to proprietary knowledge and patent protection, there is the Free and Open Source Software-FOSS. The cornerstone of the movement is promoting cooperation between people, using computers. You can almost say that al-Jazari is precursory of the open source movement only with pumps and automata. This is not my assessment but facts. The following quote is from the book introduction as translated by Donald R. Hill.  The quote is a little long, but speaks for itself about his motivation of sharing his knowledge:

“I am in the service of the king Salih Nasir aI-DIn Abi al-Fath Mahmiid bin Muhammad bin Qara Arslan bin Dawiid ibn Sukman bin Artuq, the king of Diyarbakir, may God preserve him with those whom He chooses to preserve. That is following my service to his father and his brother, God sanctify their souls, before the kingship passed to him – a [total] period of twenty-five years, the first of them year 577. God, may He be exalted, has singled him out with distinctions of intelligence, high-mindedness, justice and probity, so that he surpasses in justice and probity the kings of the present age, and excels the lords of near and far in beneficence and graciousness…. I never began to construct a device of mine without his anticipating

it [i.e., its purpose] by the subtlety of his perception. He is completed by the refinement of his opinion and his wisdom. I was in his presence one day and had brought him something which he had ordered me to make. He looked at me, and he looked at what I had made and thought about it, without my noticing. He guessed what I had been thinking about, and unveiled unerringly what I had concealed.

He said ‘you have made peerless devices, and through strength have brought them forth as works; so do not lose what you have wearied yourself with and have plainly constructed. I wish you to compose for me a book which assembles what you have created separately, and brings together a selection of individual items and pictures’.”

The Arbiter for a drinking session

Introduction

This is a drinking game for the effervescent parties in Diyarbakır Palace as we met in The automaton who drinks the king’s leaving and A boat placed on a pool during a drinking party (in Hebrew).

The Arbiter is a complicated automaton (a self-operating machine) which includes: A slave (جارِية) pouring wine to a goblet in the lower level. Above her, on a balcony, there are four slave girls who play music on a flute, tambourine and a lute. Above them, there is a half-naked male dancer in a niche, and on top of the dome, there is a horse rider carrying a lance. During the party, the musicians play their instruments, the dancer dances (I swear!) and the horse and the rider rotate slowly. When commotion stops the slave girl tilt the bottle and pours wine to the goblet. A servant (a living person) takes the goblet and serve it to the participant the spear points to his direction. The process repeats itself twenty times, almost seven hours in total. At that time the black doors behind the dancer open and a man emerges out of the door, his hands are in the air, signaling that celebration is over and there is no more wine. Al-Jazari calms the worried reader, saying that the head of the assembly can choose to refill the reservoir. The wild parties in Diyarbakir can raise a lot of questions about the crazy amounts of wine, the half-naked dancer, and more. Maybe I will write about all this in the future. I want to focus on clothes, did observer of the automaton in the 12th century knew she was a slave by her dress?  What can we learn from the text and the illustrations about clothing in the Artuqid palace?

The Arbiter for a drinking session. Topkapi manuscript, 1206.

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in floats, Tipping buckets or camshaft can skip those bits. The illustration below is my modification of the drawing from the book; it will help us to follow the mechanism:

Drawing of the mechanism

In the beginning, a servant lifts the dome (1) and fill the reservoir (2) with filtered wine.  At the bottom of the reservoir, there is a thin pipe, so wine is dripping to the tipping bucket(3). I wrote about tipping buckets before, for example in the fountain of the two tipping buckets (in Hebrew). In the front view, you can see the tipping bucket in action. After twenty minutes the bucket is full of wine, and it becomes overbalanced, and tips down, emptying itself on the scoop wheel (4) which turns the adjacent teeth wheel (5) which turns the 900 teeth wheel(6) which is connected to the rider axle(more clearly seen from the side). This makes the rider rotates, and the “lucky” participant that the spear is pointing in his direction will get to drink the goblet. I used quotation for “lucky” because the goblet contains a liter of wine, more than an entire bottle! I don’t know what the alcohol content in the 12th century was, but it seems like a sure way to get drunk with a severe hangover. I do not want to think about someone who was lucky enough to win two goblets during the seven hours of the party.  The wine from the scoop wheel is collected and falls on the second scoop wheel(7). The rotating wheel rotates the axle and the pegs(8)connected to it, hitting the levers connected to the musician’s arms. This causes the up and down movement, simulating the drummer bit and the playing of the lute. The rods, an early version of camshaft transform the circular motion into linear motion were the rods pattern creates different drumming bit and lute music. The wine flow from the 2nd scoop wheel to the air tank, pushing air in a narrow pipe with a whistle at the end(9). This produces the sound of the flute player. Finally, the wine goes down in a hidden tube (10) through the slave body and fills the bottle. The latter is on an axle, and the weight will cause it to tilt and fill the goblet. For clarity, I skipped two mechanisms. Readers who love to ponder on this kind of gadgets can try to decipher the remaining components and questions will be, as always, appreciated.

Fashion and clothing in the “Book of Knowledge of Ingenious Mechanical Devices.”

The choices of clothing by Muslims reflect their religious and cultural world. We call the veil worn by some Muslim women to cover their hair- hijab (Arabic: حجاب). In the Qur’an and other classical Arabic texts, the term was used to denote a partition, a curtain and it is a generic term for modest attire. During the Hajj (حَجّ), the pilgrimage to Mecca, one of the five pillars of Islam, the men wear a white outfit that was not touched by a needle or thread (how is that even possible?).  What (if anything) can we learn about life in the 12th century in Diyarbakır by looking at the illustration and the few direct references of al-Jazari to clothing details?

Five slaves from the “Book of Knowledge of Ingenious Mechanical Devices” Topkapi manuscript,1206

In the top left illustration, we can see a young black slave (غلام) truncates the candle wick from The candle clock of the swordsman (Hebrew). No explicit description of him in the book but his attire is the simplest, in comparison to all the other slaves and includes a short red dress with stripes on the sleeves. The sleeves’ stripes appear in almost every dress of slaves or free men. I don’t know if this was the fashion in Diyarbakır or the stripes had a meaning or use? If a knowledgeable reader can enlight me, I would love to learn.

The slave girl pouring wine at the center is from the automaton in the present post. She wears a blue dress or gown with decorations that cover her from neck to ankles. She also has two brown stripes on her sleeves. The garment doesn’t look “cheap” or “service uniform” Her black hair can be seen under the cover. Although her dress could have been worn by devout Muslim today her head cover is not acceptable by contemporary moderate standards (hijab) and certainly not by more religious Muslims demanding a niqāb or chador.

We met the slave washing the king’s hands here (in Hebrew). The illustration, in this case, is large and rich with details. The blue dress is very similar, if not identical, to dress of the slave girl. It is particularly interesting. Muslim men are forbidden(حَرَام‎ ḥarām) to wear silk clothes or gold jewelry. This is not from the Quran but a later story told by Ali Ibn Abi Talib, Muhammad cousin and the fourth Caliph accepted by both Sunni and Shia. The restriction is very specific but interpreted as an echo of the biblical verse:

“The woman shall not wear that which pertaineth unto a man, neither shall a man put on a woman’s garment: for all that do so are an abomination unto the Lord thy God.”

(Deuteronomy 22:5 King James Version)

It is possible that his red jacket without sleeves is enough to distinguish between them? He is also wearing a small red hat quite similar to the fez (more correctly ṭarbūsh). It is interesting to note because the ṭarbūsh is usually attributed to the period of Sultan Mahmud II (1808-1839) when it was introduced as part of the Ottoman Empire judges and spread to clerical circles and the educated elite.

The next slave, to the left and below, is from the automaton of a standing slave holding a Fish and A Goblet. In this case, al-Jazari himself provides a relatively detailed description of the dress:

” He is a standing slave, ten years old in appearance, dressed in a short jacket (farajiya) with a robe(qaba) underneath it, and a cap (qalansuwa) on his head.”

The qaba (قابا, I hope I spelled right?) is a type of a robe with sleeves, at mid-calf –between the knee and ankle that has a diagonal fastening of one side over the other. The “Encyclopedia of Islamic Civilization” claimes that in Abbasid times qaba belonged to the military? According to the illustrations in the book, the qaba was widely used among slaves and free men. The hat (qalansuwa  = قلنسوة‎) is written like the Arabic city in the center of Israel; I don’t know if this is the origin of the city name. This hat was quite popular, and Harun al-Rashid was wearing this hat in his nocturnal wanderings through Baghdad in disguise. Unlike the qaba which repeats itself in many illustrations, there is quite a selection of headdress. For example, the slave girl who emerges from a cupboard holding a glass of wine is covered with a colorful scarf with a picturesque ribbon. Quite similar to today hijab. She is also wearing loose red trousers under the qaba. This combination can be found both in the book and outside.

Eight “free” people (in the sense of not slaves) from the “Book of Knowledge of Ingenious Mechanical Devices” Topkapi manuscript,1206.

The top left illustration is the scribe from the elephant water clock. There are three scribes in the book, all three wear green qabas with brown stripes on the sleeves and wear pale blue turbans. I couldn’t find any evidence of “professional clothing” of scribes. You should also note that the scribe has a beard. Allowing the beard to grow (لحية) and trimming the mustache is mandatory in Sunni Islam and is considered to be Fitrah (فطرة‎) or the state of purity and innocence we are all born with including the natural tendency to distinguish between good and evil and to believe in the existence of Allah. As none of the slaves are bearded, they probably weren’t Muslims.

The two Sheikhs are part of the automaton in Category II dedicated to vessels and figures suitable for drink sessions.  Al-Jazari did not write anything about the Sheikhs, but Sheikh (( شيخ is a title given to the leader of the Bedouin or Arab tribes. The meaning of the name in Arabic is old, although the Sheikh is not necessarily old. They are also dressed in qaba and turbans. I don’t see in the illustration a difference between the of Sheik’s qaba and the slaves’  qaba. It is quite possible that there were large differences in the quality of the cloth or decoration which are not captured in the illustrations. However, the turban characterizes only the free people. Before anything else, the turban was practical in protecting the eyes from the sand and providing the face protection from the sun.  On top of this, the turban (عمامة, pronounced amama) was part of Muslim’s traditional attire and their identity. The turbans were a source of pride and a symbol of religious affiliation. Taking a man’s turban was considered a humiliating act, touching someone’s turban was perceived as an insult. It explains well why none of the slaves wear a turban.

The last picture below is from the musical boat(Hebrew). This is the King and his boon companion ( نديم =Nadim) I wrote about it here (Hebrew). Everyone is wearing a qaba, including the King himself. His blood-red qaba has gold trim. On top of the decorations, everybody has, he has additional decorations of the collar, the cufflinks and the fringes of the qaba as well as a golden belt. Red is not necessarily Royal, another member of the party is wearing red, though with fewer decorations.

I’m pretty sure al-Jazari was very surprised from this post, and it didn’t occur to him that the illustrations he prepared to improve the understanding of his machines, and are truly groundbreaking, would become a fashion guide for 12th century Diyarbakir. However eight hundred and twelve years later this is the only window that would allow me to peep into the  Palace in Diyarbakır. At least for me, this was an interesting journey.

Building the Elephant Clock in Lego

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.

 

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.”

The Elephant Clock – Multiculturalism or a Circus?

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:

  • Freshness (something new)
  • Great skills
  • A sense of danger
  • An awe-inspiring images

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.

The Castle Clock

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 upper doors open and a figure comes out and stands as if he had suddenly emerged.
  • The lower door is rotating on its axis, and the text “Allah al-Malik” meaning ” God is The King and Owner of “
  • The Two falcons with outspread wings lean forward and cast a bronze ball into a vase, inside the vase a cymbal is hung, making a sound which can be heard from afar.

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:

  • First, al-Jazari is a man who is familiar with the literature of his time. The opening lines of the Castle clock chapter are: “I followed the method of the excellent Archimedes in distributing the twelve signs of the Zodiac. Al-Jazari is probably referring “On the construction of water clock” – كتاب أرشميدس في عمل البنكامات. This book was attributed to Archimedes, but its source is unclear. This reinforces al-Jazari statement in the introduction:

“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.

  • Secondly, in Diyarbakir in eastern Turkey, there are little more than fourteen hours of daytime in the summer and approximately nine hours of daytime in winter. Al-Jazari made a considerable engineering effort ensuring that there would be twelve hours between sunrise and sunset in summer and winter. This is the purpose of the flow regulator which adjust a short hour in the winter compared to the longer hour in the summertime. Time is not an illusion or a pure man-made concept. The Earth orbited the sun before there were humans around and the sunrise and the sunset, as well as summer and winter, were here before we gave them their name. But the perception of time and its measurement are human inventions. If I would have met al-Jazari and told him that a second that was impossible to measure in his time is the basic unit of time and its scientific definition is approximately 9 billion (for those who want precision 9,192,631,770) cyclic switching between two energy levels of the atom cesium. Not only would that he would not understand a word but also would think me really He did not need such precision that did not fit his daily experience. But I use Waze, a navigation application, and we need accurate atomic clocks at this level of precision to bring me to my destination on time. In today world, the concept of time which varies according to the seasons seems far-fetched, but in the world of al-Jazari who knew sundials and water clocks, it made perfect sense.
  • Thirdly al-Jazari made detailed measurements of the water regulator attributed to Archimedes and found it insufficient. Then he explains in detail how he tries to solve the problem without success through trial and error. It’s ridiculous to compare a modern engineer to al-Jazari, but it is delightful to read the report of a very talented engineer more than eight hundred years ago. It turns out that his concerns are not very different from the concerns of a current engineer. From the text, it turns out he did a “literature review” and theoretical calculations (in this case unsuccessful), and plan and perform the experiments. He was also a skilled man who knows copper, bronze and wood and their processing. When al-Jazari explains, for example, how to prepare the main water reservoir, he’s not satisfied with a drawing and selecting material (copper) but explains how to get a perfect cylinder with a precise wooden disk and how to ensure that the cylinder would have the same diameter all along. For the technical reader, it is easy to sympathize with the difficulties and solutions. There is something appealing in this combination of a man of the books, an engineer, a craft master and an artist who we can meet through the pages and the hundreds of years that passed.

The Beaker Water-Clock

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:

  • The clock face or dial supports solar
  • The slope of the beaker radius requires some understanding of fluid mechanics.

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></iframe>

Two engineering issues need further discussion:

  • The clock face and the variable length of the day.
  • How did al-Jazari find a practical solution to Bernoulli’s equation which he did not know or understood?

    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.

The Scribe Candle clock, on clock face and hands

Introduction

The Scribe candle clock is the second scribe holding a pen out of three scribes that appear in the book. The scribe rotates continuously and passes fifteen degrees every hour, so one degree (one marking) is approximately four minutes. We already met a scribe holding a pen in the elephant water clock (in Hebrew), and soon I hope to write on the beaker water clock that has a different mechanism, but a very similar scribe. The scribe and his pen are used as a hand in a clock. It reminded me “modern” analog clocks and made me go back and examine the development of concepts such as minutes and seconds and the development of the clock dial.

The candle clock of the scribe ” Book of Knowledge of Ingenious Mechanical Devices” Topkapi manuscript, 1206.

How does it work?

Al-Jazari opens this chapter:

“I came upon a clock made by Yunus al-Asturlabi which had the appearance of the clock I described in the first chapter[ meaning the candle clock of the sword men]. A cross-beam which had a hole in its center for the wick replaced the cap which I used to hold the candle down, and I discovered that the wax flowed into the interior of the sheath and over the instruments inside the sheath. .. This gave much trouble; for this reason the design was useless. “

We do not know who Yunus al-Asturlabi was. Eilhard Wiedemann, a German physicist, one of the first researchers of science in Islam, who did much to bring the work of the al-Jazari to the west, suggested the astronomer and mathematician Ibn Yunus. Probably we will never know for sure. Correct identification or not, it is quite interesting because we have no evidence of any sophisticated candle clocks before al-Jazari’s.

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 by the book translator and annotator Donald R. Hill with my captions:

A drawing of the mechanism by Donald Hill with my captions

The candle is placed on a holder inside a brass sheath, and only the wick protrudes through a hole in the cap. A long rod is soldered to the bottom of the holder. The rod runs through the main weight so that the weight is free to move up and down. Two strings are connected to the bottom of the rod and through two pulleys to the main weight. The latter is relatively heavy, slightly more than one kilogram. At nightfall the wick is lit, at that time the candle is in full size, the rod reaches its lowest point and the main weight its highest. As the candle is consumed, the main weight will descend exerting force, through the pulleys, on the holder upward and the holder and rod will go up at a constant rate depending on the rate of the combustion. A string which turns the scribe is attached to the bottom of the weight. Every hour the scribe and his pen will cover 150, so one can tell the time within 4 minutes. The holder pulls the ball’s channel up and every hour the highest ball in the channel has risen until it is level with the hole in the back of the falcon’s head, at which point it rolls out and falls from the falcon beak.

Minutes and their measurement

The globe and the clock face owe their divisions to a numerical system which is four thousand years old. The Babylonians made astronomical calculations using Sexagesimal (base 60) numeral system.  We can only conjecture why people of the ancient Middle East (Assyrians were also Sexagesimal ) adopted the use of base 60. One assumption is that the number 60 was chosen because it is the first number divisible by all the numbers 1 to 6. Alternatively, base 60 was preferred because the lunar year contains three hundred and sixty days. There are more suggestions. Hipparchus of Nicaea already mentioned here(Hebrew), as well as other Greek astronomers, used the tools previously developed by the Babylonians astronomers.  Hipparchus used the geometry of a sphere to find locations on Earth. There were attempts to use grid lines before, but he was the first to apply rigorous mathematical principles to the determination of places on the Earth’s surface, by specifying their longitude and latitude in terms of 3600 running South to North(longitude) and parallel to the equator(latitude).

Claudius Ptolemy considered the most famous astronomer of antiquity. His book the Almagest, from Arabic  (المجسطي) is considered to be one of the most influential scientific texts of all time. Its geocentric model whereby planets revolve around Earth was accepted for more than twelve hundred years until the work of Nicolaus Copernicus in the 16th century. Ptolemy used and expanded the work of Hipparchus by subdivisions of 3600 of longitude and latitude into smaller sections. Each degree was divided into sixty parts called “partes minutae primae” literally “the first small part.” This was later reduced to minutes. The minutes were further divided into sixty “partes minutae secundae” or “second small parts.” Later reduced to seconds.  Interestingly enough the time units in Hebrew “DAKA” and “SHNIYA” reflect the historical names.

Clock still didn’t show minutes and seconds for hundreds of years after the Almagest, partly because of technology limitations and partly because there was no need. In the middle ages, the meaning of an hour as sixty minutes was not understood by most people. Not many mechanical clocks from the fourteenth century are left, but those I could find do not have hands, in most cases, and ring a bell to indicate the hours.

The Salisbury cathedral clock is said to be the oldest working clock in the world. It is dated to 1386 (not certain). It is a large iron-framed clock without a dial and obviously with no hands. There are other clocks competing for this title. None of them has minutes’ hand:

The Salisbury cathedral clock

The Forchtenberg clock tower in a small town in south Germany is one of the oldest surviving mechanical clock towers. In contrast to the controversial dating of the Salisbury cathedral clock, the year 1463 is carved in iron. The only uncertainty; was the clock made at this date? Or could it be older and this is the first repair date? This clock has only an hour hand:

The Forchtenberg clock tower

Who was the first to install the minute hand? It is not clear, but the second hand has a story we know. Jost Bürgi was a Swiss clockmaker, a maker of astronomical instruments and a mathematician. He was employed at the Court William IV, Landgrave of Hesse-Kassel, a mathematician and astronomer by himself. Although now forgotten he was an outstanding astronomer, his observations, particularly those of the fixed stars, were at least as accurate as those by Tycho Brahe. Bürgi was brought to the court to develop scientific instruments, and assist in the observation that could confirm the heliocentric model by Copernicus. He built various instruments. In 14th April 1586, the count wrote to Tycho Brahe about a highly accurate clock which Bürgi had built which, for the first time, had a minute hand, a seconds hand and had an error of less than a minute in 24 hours! Christoph Rothman, another astronomer wrote about the new amazing clock:

“The duration of a second is not very short but resembles the length of the shortest note in a moderately slow song.

This quote commemorates a time when science and technology produce a new reality.

Bürgi precision clock

Epilogue

I read today about a new exhibition of Christian Boltanski in the Israel Museum called “life”. He wrote: [my translation from Hebrew]

“a major part of my job is the fact that each person is special, one-of-a-kind and important, each will finally vanish. Most of us will be forgotten in two generations, with the passing of those close to us. “

It’s certainly not true for al-Jazari but probably true for most of us. The exhibition combines early works of Boltanski alongside new works and includes a digital timer continually counting the seconds from the moment of birth of the artist. I found a photo of a timer installation of Boltanski at the Biennale. I don’t know if the installation in the Israel Museum is identical.

Christian Boltanski, the Venice Art Biennale, 2011.

 

 

The automaton of a slave girl holding a glass of wine and slaves in the Artuqid Palace

Introduction

It is a decorated wooden cupboard by the king’s side during the feast. It has a door with two closed leaves. Every seven and a half minutes the doors would open and reveal an automaton (a mechanical device made in imitation of a human being) of a slave girl holding in her right hand a glass filled with wine and in her left a small towel. The king takes the glass, drinks the wine it contains, puts the glass back in her hand and, if he wishes, wipes his mouth with the towel. Then he closes the door leaves on her.  This process will repeat itself every eighth of an hour.

We met slaves and slave girls here and here(in Hebrew), but a quick search of the” Book of Knowledge of Ingenious Mechanical Devices ” reveals ten different chapters mentioning slaves or slave girls. This seems a lot! I went to study slaves in the Islamic world in the twelfth century and how similar or different it is from al-Jazari’s book. To my surprise, my journey led me to Cairo Geniza.

Automaton of the Slave Girl, Serving a Glass of Wine”, a folio from Syria or Iraq, 1315

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in an inclined plane or a tipping bucket can skip those bits. To understand the mechanism, I use a drawing by the book translator Donald R. Hill with my captions. The slave girl became a boy? I guess Hill or his illustrator did not think that gender was important?

A drawing of the mechanism by Donald Hill with my captions

The cupboard is about 1.6 meter (originally six spans, in Arabic شبر or shabr) and width of approximately 60 cm. There is a wine reservoir above the cupboard which is dripping slowly to the tipping bucket below. I already discussed the tipping bucket here. The tipping bucket fills in seven and a half minutes (eighth of an hour) and discharges all at once into the glass in the slave-girl’s hand. The glass becomes heavy enough to lower the hand of the slave which is on an axis, lifting the extension rod from the docking station.

The slave-girl will roll down the inclined plane and pushes the left leaf with her left hand, which is holding the towel like she is offering the wine glass to the king. The king takes the glass from her hand, drinks its contents, and if he wishes, wipes his mouth with the towel. Then he puts the glass back in her hand, presses it down, and pushes the slave girl gently until she docks. This process will repeat itself every seven and a half minutes as long as there is wine in the reservoir.

Slaves and girl slaves in the “Book of Knowledge of Ingenious Mechanical Devices “

In ten chapters of the “Book of Knowledge of Ingenious Mechanical Devices “ slaves are mentioned:

  1. Category I, chapter seven – The candle clock of the swordsman(Hebrew): An automaton of young black (غلام),  with no beard holding a sword to shorten the candle wick.
  2. Category  II, chapter three – An arbiter for drinking parties: An automaton of a young a slave girl ( (جَارِيَة‎) in Wikipedia also a concubine)  with a  bottle and a glass as well as four slave girls in the balcony.
  3. Category II, chapter four –The musical boat: An automaton of a musical boat with a slave holding a jug and goblet, and four slave girls, flute-player, a harpist and two tambourine-players. I believe that they are “qiyan” – educated girls and women who entertained and entranced the caliphs and aristocrats. I already wrote about them here (in Hebrew)
  4. Category II, chapter seven – A slave holding a Fish and a Goblet: An Automaton of a young slave pouring wine
  5. Category II, chapter eight – A man holding a goblet  and a bottle: An automaton of a slave pouring wine into a goblet
  6. Category II, chapter ten –A slave girl emerges out of a cupboard with a glass of wine: (The current post) Automaton of a slave protruding from a cupboard with a glass of wine.
  7. Category III, second chapter- al-Jazari’s motivation to make the automatic pitcher is written explicitly: ” King Salih, may God double his righteousness, disliked a servant or slave-girl pouring water on to his hands for him to perform his ritual ablutions and he wished me to make [something] for pouring water onto his hands for his ritual ablutions.”
  8. Category III, third chapter – A  slave who pours water over the king’s hands: An automaton of a  slave who pours water over the king’s hands.
  9. Category III, ninth chapter – A basin of the peacock for washing the hands (Hebrew): Automaton for washing, one with soap, the other with a towel
  10. Category III, chapter ten- A basin of the slave for washing the hands: An automaton of a kneeling slave holding a water pitcher in his right hand

Cairo Geniza and slavery in the twelfth century

Do we know who were the slaves and the female slave? How they were enslaved and what kind of life did they have?

Cairo Geniza (storage) is a large collection of Jewish manuscripts and fragments written between the ninth century and the nineteenth century and preserved in the attic of the synagogue in Fustat or old Cairo. Maimonides, while in Cairo, used to pray in this synagogue, and it is therefore also known as the Maimonides synagogue.

In my ignorance, I thought the Geniza was for damaged Bibles and holy books but apparently because the Hebrew language was considered sacred they saved everything: court documents, bills of sale, and the correspondence of the local Jewish community and more. Craig Perry wrote his doctoral thesis: “The Daily Life of Slaves and the Global Reach of Slavery in Medieval Egypt, 969-1250 CE” based on materials from the Cairo Geniza. This is not the story of the slaves in Diyarbakir palace where al-Jazari worked, but we can learn a lot.

In an undated letter from the Cairo Geniza, a local court in the Red Sea port of Aydhāb (today in Sudan). Two slave women appeared before the Qadi (Muslim judge), one of them testified that they were kidnapped when they went to fetch water at a local well and sold into slavery. The Qadi asked if they were Muslims? Because according to Islamic law, Muslims were ineligible for enslavement. One of the two insisted that she was Jewish and therefore the case was transferred to a Jewish court. The writer of the letter asked for advice from Fustat about how to handle the matter. His decision to consult with associates explains how this document came to be preserved in the Genizah. We don’t know what happened to the unfortunate women but this is an example of how women were enslaved, and there is a wealth of information about buying and selling of individual slaves.

The second way I already mentioned (in Hebrew) is diplomatic exchanges: for instance, the Egyptian historian Al-Maqrizidescribes  large processions of male and female slaves arrived in Cairo from regions to the south, the first one at 1023 CE:

“On Tuesday, when eight days remained in the month the gift of Ibn

Makārim b. Abū Yazīd arrived from Muḥdathah in Aswān, and it was:

twenty heads of horses, eighty fine camels, a number of black [slaves], females and males, a cheetah in a cage, Nubian goats, birds, monkeys and elephant tusks. “

Prestige gifts of slaves were not limited to Nubia. The Fatimid Caliph al-Mustanṣir Billah received gifts of Turkish slaves from the Byzantine emperor Michael IV, slaves, and eunuchs from the Amir of Yemen and slaves the ruler of al-andalus(الأندلس), the Muslim kingdom of Iberia.

The near constant warfare at the edges of the Islamic empire produced a steady supply of prisoners-of-war and  “wholesale” slave trade.

We don’t know if the slaves in the Palace in Diyarbakır came as a gift from another ruler, purchased individually, or captured during a war.

The bills of sale contain a wealth of information that is useful for reconstructing the geography of slavery, Allowing Perry to do the statistics on the origin of slave girls, horrifying as it may sound. Perry found a large majority of Nubian slaves along with quite a few slaves from other sources:

It is impossible to know, of course, the origin of the slaves in the Palace in Diyarbakır but the Geniza documents cover slave trade in the entire Middle East, and it is reasonable to assume that that is was not very different.

When I think of slaves, I think of hard work in the cotton fields or the sugar plantations in South America. The Islamic world of the 12th century was not associated with large-scale agricultural production. The use of domestic slaves reflects the relative wealth and urban nature of the Muslim elite. Families of merchants, judges, scholars, and others were able to purchase slaves to help with raising the children and household chores. This is evident from the Geniza and is very similar to the book of al­-Jazari. All the slaves in the book are part of the Palace household, helping with daily tasks or helping during the feast.

Slave women were frequently used as child-bearing concubines by Muslim men. According to Islamic law, children born to a Muslim master and a female slave were free-born Muslims. The Fatimid  Caliph al-Mustanṣir Billah, already mentioned, was the son of Sudanese slave named Rasad. That was not the situation in the Jewish community where the Rabbinical establishment struggled to deal with the phenomenon, but that’s another story. I completely Ignored the topic of slave soldiers. This is essential to the history of the twelfth century but is not part of al-Jazari’s book.

Epilogue

My deep connection to al-Jazari makes me want to apologize on his behalf because of the casual manner in which he relates to slavery. It is more painful due to human rights situation in Israel and the general feeling that human rights are under attack.

This is childish; you can’t throw me and the education I received at home and in  Hashomer Hatzair” (a Socialist-Zionist, secular Jewish youth movement) to the 12th century. While I was searching for information on slavery I found  a text by Benjamin of Tudela  which for me was always just a happy song  (in Hebrew) by “HaGashash HaHiver”, an iconic Israeli comedy trio:

” And from there (Aden) to the region of Aswān is a journey of twenty days through the desert. This is Sebā on the Nile River that descends from the land of Kush. There are some among the Kush who have a king and they call him the sulṭān al-ḥabash. There is a people among them that are like animals that eat the grasses that grow on the bank of the Nile and in the fields. They go about naked and lack the intelligence of human beings. They lie with their sisters and with anyone they wish. (Sebā) is very hot. When the people of Aswān go raiding in their land, they carry with them bread, grain, raisins, and figs. They throw this toward (these people), who come to get it. They obtain many prisoners and sell them in Egypt and all of the kingdoms around them. These are the black slaves, the sons of Ham.”

This is more documentation (?) of capturing slaves in Nubia, but the reference to slaves is chilling and I’m afraid that it tells more about Benjamin of Tudela and his lack of ability to see another human suffering then it tells about the poor enslaved Africans. I would like to conclude with a line from the Universal Declaration of Human Rights:

“All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.”

universal declaration of human rights, December 1948

 

Al Jazari and “Rav-Bariach”(Multi-Lock)

” If I have seen further than others, it is by standing upon the shoulders of giants.” Isaac Newton in a letter to Robert Hooke, 1676

Introduction

From “Rav-Bariach” web page (in Hebrew) I copied the following paragraph:

“In 1972 an upset customer came into the locks shop where Abraham Bachri used to work and requested to install four locks on her door to provide her lost sense of security following a burglary she experienced. This innocent request sparked the imagination of Abraham, who along with his friend Moshe Dolev, developed a multi-lock that was installed in the center of the door, first a wooden door and later with steel core.”

I have no reason to suspect that either man knew the “four bolt” lock designed by al-Jazari, but the lovely similarity made me think about inventions and “reinventions.” The question of who invented the telephone or the light bulb, to name famous cases, generally has legal and economic implications. I am more interested in the human spirit, and this will be the topic of this post.

Drawing of the locking mechanism of the four bolts, Topkapi manuscript, 1206

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in bolts or locking mechanism can skip those bits. There are four bolts made from wood or iron, on the back of a door, in all four directions. One closes to the right, one to the left, another upwards and another downwards. Each bolt is notched with “, triangular teeth “sawtooth”  facing the locking mechanism, in the center, with a key lock:

Drawing of the notched bolt, Topkapi manuscript, 1206.

The locking wheel has teeth match to the bolts, but it only rotates when the key is inserted into the lock, then each bolt locks the door on one of the sides (top, bottom, left and right). The following image compares the original lock “Rav Bariach ” and the reconstruction of the lock of al-Jazari from the Museum of The History of Science and Technology in Islam in Istanbul:

You can see two locks with four bolts on four sides with a central locking system and a single key. This is a short video of the reconstruction of al-Jazari lock

A little bit of trigonometry

During my military service, I met a guy, from a religious Kibbutz, called Yakir Katz. (It was almost 40 years, and I could be confused with the details) He told me, bursting with laughter, that his father, who worked in the Kibbutz workshop, came home full of excitement and said he discovered a relation between the two legs of a right angle triangle depends only on the angle. Yakir explained to his father that this is the tangent (marked as tan or tg), and  it is a basic trigonometric function that every high school student learns:

tan(alpha)=a/b

I remember us arguing vigorously because I thought that the “rediscovery” of the Tangent is not ridiculous at all but really a reason for astonishment and even admiration to a man whose life circumstances allowed him who only limited education (I think eight years) and he had to go to work at a young age.

Trigonometry (from Greek τρίγωνον “triangle” + μέτρον “measurement”) is the study of triangles and the relationships involving lengths and angles of triangles.These relationships are expressed using the trigonometric functions, of which the most used are the Sine, Cosine and the Tangent already mentioned. Hipparchus of Nicaea, astronomer, geographer and Hellenistic mathematician is known as “the father of trigonometry,” was the first to create trigonometry tables. For young people who never saw a trigonometry table this is how we used to find Tangent or Sine values before calculator become available:

Sine values from the trigonometry tables

His other famous achievements in Astronomy include setting the length of the solar year with an error of about 6 min per year, inventing a system of coordinates to position stars and ranked stars according to their brightness further developed by Ptolemy. That system by Ptolemy is effectively still in use today.

Shoulders of giants

The metaphor of dwarfs standing on the shoulders of giants (Latin: Nanos gigantum humeris insidente) is attributed to Bernard of Chartres, a twelve-century French scholar. The metaphor meaning is that science and technology advance based on previous knowledge. Its most familiar expression is by Isaac Newton (the motto of this post) “If I have seen further it is by standing on the shoulders of Giants.”

Newton’s quote appears in a letter to Robert Hooke one of the greatest experimental scientists of the 17th century, a polymath, architect, astronomer, philosopher, and the author of Micrographia the first scientific best-seller. Some people believe that this comment was an insult to Hooke, who was a hunchbacked due to a severe Kyphosis, following the criticism of Hooke on the Newtonian optics and the bitter feud between the two men who accompanied them until the death of Hooke in 1703. But the original letter is three years early to the conflict and Newton write with high esteem to Hooke. From the letter, it seems that the famous quote reflects the genuine perception of Newton of his achievements and science in general. It is interesting to note, in this context, that in various places al-Jazari indicates his debt to giants from the past.

Obviously, I don’t recommend anyone to “reinvent” something, and it is far superior to lean on “the shoulders of giants.” But is there a significant difference between the human achievement of Yakir’s father and Hipparchus of Nicaea? As far as both are concerned trigonometry as a mathematical tool didn’t exist, and both developed what was necessary from scratch.

It’s not really connected, but I couldn’t resist. The picture of dwarfs standing on the shoulders of giants reminded me the story of Orion, son of Poseidon. He was enormous in stature and the most handsome of the earthborn. He courted Merope, daughter of Oenopion. Oenopion was unhappy with the giant lover, gave him wine to drink and stabbed out Orion’s eyes. Orion stumbled to the workshop of Hephaestus. Hephaestus told his servant, Cedalion, to guide Orion to the uttermost East where Helios, the Sun, healed him.

Greek mythology: A manuscript from the 15 century. The blind giant Orion is carrying the boy Cedalion on his shoulders to act as the giant’s eyes.