Pump powered by a water wheel

This post is dedicated to Gedalya and Aba Neeman (grandfather and great-grandfather of my love). On their tombstones engraved “Loved the work and manufacturing of water pumps in the land of Israel.”

 introduction

This revolutionary water pump is the fifth  pump in Category V which is dedicated to “machines for raising water from pools, and from wells which are not deep, and from running streams.”

Fifth water pump, Topkapi manuscript,1206

Al-Jazari won his fame mainly because of exotic water clocks full of surprises like the Castle water clock or The water clock of the peacocks(in Hebrew) and wonderful automata like The Arbiter for a drinking session and many more. This pump, like the four pumps in previous chapters, shows that al-Jazari was involved in the real hardship of the people around him. Water pumping is essential to any society, for drinking water, watering crops, for excess water and flood pumping, during fire extinguishing and more.

The common pumps in the world of Islam in the 12th century were the Shaduf (Arabic شادوف) and the Saqiya (Arabic ساقية). Both are ancient irrigation tools for raising water. The Shaduf is fully manual and consists of an upright frame on which suspends a long pole with a bucket at one end a counterweight at the other. The operator pulls the rope until the bucket is full of water. With the help of the balancing weight, he lifts the bucket and pours them into the irrigation canal. The Saqiya is a mechanical device raising a chain of buckets or pots using a donkey or an ox to raise the water.

These two pumps are quite similar to a human using a bucket to raise water, only saving work and effort.  The water wheel pump does not imitate the human action and can be seen as an extension and development of the piston pump of Ctesibius (Κτησίβιος), a Greek inventor and mathematician in the golden period of Alexandria, in Ptolemaic Egypt. He wrote the first treatises on experiments with compressed air which earned him the title of “father of pneumatics”. He invented the first piston pump which was apparently very popular in the Roman Empire. At least twenty five such pumps were found in excavations of Roman sites. You can read more here. None of Ctesibius writing survived, we know of him only because of later writers quoting his work. I don’t know about Ctesibius pumps in the Muslim world, and there is no reference to Ctesibius in al-Jazari’s book. We shall never know what, if any, information about Ctesibius was available to al-Jazari.

How does al-Jazari water wheel pump work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in intake or discharge valves can skip those bits. This is a short YouTube clip from “Technology Science in Islam” explaining the operation of the pump:

The energy source of the pump is the water wheel, turning by water flow. The water wheel is connected through gears to a wheel with an eccentric pin (positioned not in the Center) within a rail inside the crank connected to a fixed point. When the wheel turns the rod moves left, and one piston is pulled, and one piston is pushed. This mechanism is called a slider crank mechanism, and it converts straight-line motion to rotary motion, as in a reciprocating piston engine, or to convert rotary motion to straight-line motion, as in a reciprocating piston pump. This mechanism is essential to modern machinery.

Slider crank mechanism

Two pistons are attached to suction pipes going down to the river. The suction pipes continue upward and come together to a single supply. The suction pipe has two directional one-way valves called the intake valve and discharge valve. This is a modified drawing of the piston and the valves. In al-Jazari original drawing there is no water, and both valves are closed, which is possible only during construction and impossible during pumping. In addition, in the facsimile edition, the drawing is cut:

Piston and valves, modified drawing

When the piston moves backward (as in the drawing), the intake valve opens, and the discharge valve is closed. So the pump is disconnected from the supply line and draws water from the river. When the piston moves forward (pushed) the intake valve closes, and the discharge valve opens, and water is pushed upward in the supply pipe. This mechanism is called double action because when one piston is being pushed the second piston is being pulled, so the water supply is continuous.

There are three major innovations in al-Jazari’s pump in comparison to Ctesibius pump. Each one would justify a separate patent today. In the Web, there are lists of what al-Jazari invented, for example, here or here. The discussion on the right for a patent is foreign to al-Jazari and the 12th century in general. In a future post, I hope to write about the history of patents and the concept of intellectual property in The Book of Knowledge of Ingenious Mechanical Devices.

  1. The piston pump of Ctesibius was a manual pump and requires a person to operate it. Al-Jazari used a water wheel to power the pump. Al-Jazari also writes that the water wheel is like the one used to rotate millstones which were well known at his time. This is a big advantage in pumps for drinking water or irrigation
  2. The use of waterwheel demanded to convert circular motion (water wheel) to linear motion (motion of the cylinders). History of the crank (in various forms) is documented from the 2nd century BC in China. Al-Jazari knew the book by the “Banu Musa” which includes a crankshaft. But the crank-slider mechanism is more efficient and remains in use to this day, without significant changes.
  3. Ctesibius’s pump only works when immersed in water. If the water level decreases, it will cease pumping. The al-Jazari’s pump has suction pipes that allow it to function properly above the river water level. A decrease in water level (up to a point) should not affect it at all.

Was this pump built or is it just an idea?

Occasionally someone wonders if al-Jazari indeed built his machines or were they just fantasy blueprints or suggestions that never materialized? Unfortunately we don’t have any proofs. The Palace in Diyarbakir was only partially excavated and there is no archeological evidence of al-Jazari machine. I don’t know any external evidence, for example, a Muslim traveler visiting the Palace in the 13th century who was able to report one of the exotic machines like the elephant clock. However, I’m convinced that the pump, like the Palace door and Castle clock, described in previous posts, were indeed built. I have two arguments:

  1. The number and level of details make you feel that this pump was built. For example,  a rope wrapped on the copper piston to improve sealing. The very use of the rope is a hint of an improvement cycle. It is hard to assume that this was a part of a design which never came to life. Moreover,  al-Jazari is very specific and requested a rope made from cannabis used at his time by sailors. This rope was selected, probably, due to its resistance to water. Could it be that al-Jazari thought about all these details although the pump was not built? Possible but not very likely.
  2. In 1976 the London Science Museum built an accurate model of the water wheel pump. The only difference was that the pump was powered by electricity and not by the Thames. A picture of the model is below. The model produced a steady stream of water with zero problems. It is possible that al-Jazari was a wonderful designer and the museum team was the first to realize his design that just worked great on the first try. It is more likely to think, and experience quite often proved it, that the shift from the drawing board to a real machine requires iterations and improvements. The Museum staff’s success relies thus on the practical experience of al-Jazari’s pump.

    Pump reconstruction. London Science Museum

    Aba Neeman Pumps Ltd.

    In 1980 I learned Chemistry at Tel Aviv University and I was looking for a summer job for my livelihood. I don’t remember exactly how it was arranged, but I went to work in the factory “Aba Neeman Pumps Ltd”, that was owned and managed by the grandfather of my love, Gedalia’s Neeman. In my first day in the factory, I helped cast impellers in the sand. Quite similar to what al-Jazari did 800 years before me. I don’t want you to have the wrong impression about my technical skills at the time. I got 5 minutes explanation about the task and until the end of the workday I broke with hammer unneeded bronze parts. The offices were tiny and no one needed my knowhow in chemistry or computers. Most of the summer I was an apprentice of the lathe operator. It was wonderful. I enjoyed it so much that I took an evening course in Lathe operation. The factory was built by Aba Neeman in 1900. He was a real autodidact; His formal studies amounted to a “Yeshiva”, a Jewish educational institution that focuses on the study of traditional religious texts. All he knew about machines was learned from his work and experimentation. He worked in the metalwork workshop of Leon Stein, who did all the metal work required for the young Jewish community in Israel: repairing wagons, maintenance of pumps, and a repair of the steam boiler in the winery in Zichron. In the absence of electricity and engines, the lathe was operated by the movement of the legs like old Singer sewing machines. Such a manual lathe was the beginning of the factory. Aba Neeman specialized in water pumps and amazingly, the only difference between the pump made by Aba Neeman and al-Jazari’s pump, explained above, is that Aba Neeman’s pump was powered by a diesel engine and al-Jazari’s pump was powered by a water wheel. The Author and farmer Moshe Smilanski wrote that “the pump of Aba Neeman was working for  44 years with no problems” ( from “Inventor and Efforts” by Saul Avitsur [Hebrew]). This was not eight hundred years ago, only in the last century but  “the farmer and author” and a pump that holds 44 years sound so far away, something to long for, like al-Jazari.

Al-Jazari Combination Lock and the Boxes from Isfahan

“This Ifrit bore me off on my bride night, and put me into a casket and set the casket in a coffer, and to the coffer he affixed seven strong padlocks of steel and deposited me on the deep bottom of the sea that raves…and this wretched Jinni wotteth not [does not know] that destiny may not be averted nor hindered. ”

The Story of King Shahryar and His Brother from The Arabian Nights, translator Sir Richard Burton,1850.

 

In Category six that consists of “dissimilar designs” al-Jazari describes “A lock for locking a chest using 12 letters of the alphabet”.

Locking board in the alphabet lock, Topkapi manuscript, 1206

Description of the Chest by al-Jazari

The technical explanation, as always, will be colored in blue, so anyone who is not interested in cylinders or cotter-tapered pins can skip those bits. This is a chest with four combination locks in the four corners of the cover. Each combination lock uses sixteen out of twenty-eight letters in the Arabic alphabet; it uses the letters without a diacritical mark, a point, or sign added to a letter to distinguish it from another similar letter. For example, the difference between bāʾ ب (comparable to b in English) and nun ن (comparable to n in English) is the location of the point below or above the letters. Al-Jazari doesn’t explain his choice, perhaps to prevent mistakes.

The four dials

Chest reconstruction from HTTP://WWW.JAZARIMACHINES.COM/EN (link is not working anymore)

 

The four dials on the chest cover are relatively complex. Each dial consists of three disks with a triangular notch in its outer perimeter. When all the notches were aligned, the chest could be opened. I attached the original drawing of al-Jazari cross-section of the dial with the modern drawing of Hill and added captions:

Integrated drawing of the lock components, the original drawing by al-Jazari, with the modern drawing by the book translator and annotator, Dr. Donald Hill

Since it still seems complicated to comprehend, I added the drawing of the components before assembly:

The dial component, a drawing by the book translator Donald Hill, with my captions

When you turn each of the three cylinders to their proper letter, all notches are aligned and allow the opening of the lock. It requires the knowledge of twelve letters, three letters per each dial multiplied by four dials. This system is held in place together but allows convenient rotation of its components using a cotter-pin. When you want to change the code, you remove the pin and mechanically rotate the disc so the location of the notch will match the chosen letter.

The Isfahan Boxes

None of the wonderful machines of al-Jazari survived the hundreds of years passed, and all we have are beautiful manuscripts. I fantasize about an extensive archaeological excavation in the Palace in Diyarbakir that would reveal remnants of the castle’s clock or any other monumental work. Until then, both boxes with alphabet locks from Isfahan in Iran dated to the late twelfth century are the closest thing to time travel, to see al-Jazari at his work. In the David Museum in Copenhagen, there is a fragmented brass box inlaid with silver and copper with four alphabet locks. The four dials are in a straight line and not in the four corners of a rectangle, but the similarity to al-Jazari’s chest is evident. Like al-Jazari each dial contains 16 letters. The letters which are used are without a diacritical mark. There is a resemblance to the locking process and the details of the mechanism. The box is simpler, and each dial has just two cylinders. Only eight letters (and not twelve) are required to open the crate. On the box there is the maker signature saying:

“Work of Mohammed b. [Ben] Hamid al Asturlabi

 Al Isfhani in the year

Five hundred and ninety-seven [1200 AD]

And I have tested it[it works]”

Fragments of a box made by Asturlabi, 1200 AD, Museum David Copenhagen

To my astonishment there in another safe from the same period by Asturlabi at the Boston art museum. This box also has four alphabet locks of two cylinders, creating eight-letter code. This time also there is an additional three guards’ façade, probably as symbolic protection from a later period. The signature indicates that the box was prepared by Asturlabi four years earlier (593 to AH or 1197 AD). Although it’s childish, I can’t help feeling a bit left out: why two boxes by Asturlabi from Isfahan have survived and not even one machine by al-Jazari? There is no answer, nor there can be one.

Box by Asturlabi,1197 AD, Isfahan, Boston Arts Museum

Astrolabe

From the name of the maker, it is obvious that his profession and probably the family profession was producing astrolabes. Astrolabe (ٱلأَسْطُرلاب) is a sophisticated device of astronomers and navigators to measure the angle of a star above the horizon. It has many functions but was used primarily for finding latitude when you know the local time or as a clock when you know your position. There is a good explanation and a demo here. Four astrolabes from the 12th century created by Asturlabi family from Isfahan still exist, but I could not find their pictures. There are pictures of astrolabes from Isfahan from the 9th century until the 16th century, and this is one beautiful example:

The 13th-century astrolabe from Isfahan, Muhammad B.AbiBaker, The Museum of the history of science, Oxford.

Surprisingly, perhaps, there is a link between the astrolabe and the combination locks. The lock consists of rotating cylinders with respect to the alphabet circle. In the astrolabe, there is a framework called “Rete” bearing a projection of the ecliptic plane and several pointers indicating the positions of the brightest stars. This frame is free to rotate in respect to the astrolabe disk, called the mater (mother). Both the astrolabe and the alphabet lock are rotating mechanical systems around the center. This is done in both cases by using a cotter pin (a tapered pin) that holds all the components in place and allows rotation around an axis. This pin has the shape of a horse head, hence his name in Arabic فرس (mare). I attach a photo of astrolabe dismantled; you can see exactly the same mechanism and the same cotter pin (red circle) as in the drawing by al-Jazari above.

Astrolabe dismantled for parts. The cotter pin in the red circle

If you really want to go on a historic-scientific journey, you can read the guide that Geoffrey Chaucer wrote for his 10-year-old son Lewis. Chaucer, one of the fathers of the English literature and the author of “The Canterbury Tales” was also an astronomer. This is the first publication in English on this topic as well as a great introduction to the Astronomy in the 14th century. The guide contains more than fourty (!) uses the astrolabe.

Who’s ahead?

Al-Jazari wrote  in the opening paragraph:

“The earlier [workers] in this craft made locks for locking and opening by means of the letters. Among them were [those that] locked by means of  four  a chest and made a lock on its lid as I shall describe”

Al-Jazari, obviously, did not claim primacy. Is it possible that the Isfahan boxes are part of the boxes that al-Jasari mentioned? Could it be that al-Jazari book got to Isfahan and inspired Asturlabi to build his boxes? The answer is probably no to both. The boxes were made in the years 1197-1200. We don’t have an exact date for completion of the book.  Rachel Ward claims that the book was written between 1200 to 1197. It’s a little earlier than Donald Hill who believed that the book was written between 1204-1206. The small gap is due to different sources. Hill was relying mainly on the copy from Oxford University, and Ward is basing her calculation on the earlier copy of Topkapi. Either way, the closeness between the time the book was written and the dates of the production of the boxes in Isfahan almost negates the possibility of mutual influence. Much more likely is both the Isfahan boxes and al-Jazari’s chest are part of the same rich material culture in the Muslim world at the time.

It is interesting to note that the first alphabet lock in Europe is probably the work of Giovanni Fontana, A Venetian engineer from the 15th century, three hundred years after al-Jazari. Fontana was very diverse, including measuring heights with falling stones, water and sand clocks, and trigonometric measurements. He wrote one of the first technology books in the Renaissance: “Bellicorum Instrumentorum Liber.” The book includes siege machines but also fantastic inventions like a bird propelled by a rocket, and an early version of four wheels bicycles and last but not least an alphabet lock:

The alphabet lock of Giovanni Fontana, 1420-1430

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’.”

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.