Clocks

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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 that will take you to other worlds. Not only are engineers who open al-Jazari’s book captured immediately by the magic of the machines he designed eight hundred years ago. We will never know whether al-Jazari intended a powerful opening to demonstrate his ability at its best, or whether he positioned the machines in random order and was surprised by the very question. This post aims to explain the Castel Clock and discuss what we can learn 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, such as 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, revealing lilies, a symbol associated with 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 or Owner of Dominion”
  • The two falcons with outstretched wings lean forward and cast a bronze ball into a vase; inside the vase, a cymbal is hung, producing a sound that 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,” which 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 explain the reason for the multiple mechanisms used 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 has passed through the centuries of the Falcons, even without 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 that this is even more needed for technical explanations of engineers who will be in blue.

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

Conical plug, the Castle clock, Topkapi, 1206

The main reservoir feeds the float chamber through a conical plug; thus, whenever the water level drops, the valve (a float that is a conical plug) goes down with the water level, allowing the chamber to be refilled. Every time the chamber is filled with water, the conical plug seals it, isolating it from the main reservoir. In this way, the float chamber is always full of water, and therefore the water flow is 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 all doors are closed and that 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 will 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, turns the main disk and pulls the time cart attached to the golden crescent, which moves to the left at a constant velocity, indicating the time passed since sunrise. Every hour, the cart will progress one door, and a smart mechanism will 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’s wings, attached to the body on a hinge, will spread open, and the ball will fall on the cymbal hidden in the vase. Now that the falcon’s head is light again, the balancing weight will bring it to its original position. The clock is packed with similar inventions 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 by itself, but I am interested in it because of the triple encounter it offers with al-Jazari and his world:

  • First, al-Jazari 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’s 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 a polymath, scientist, and physician, lived in the same time frame in Cordoba, far from Diyarbakir in Anatolia, yet he was part of the same Muslim world. During his medical studies, he was introduced to Aristotle’s writings on natural science and felt no 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 that today Orthodox Jewish children are forbidden to learn mathematics or natural sciences. Al-Jazari is more of an engineer than a philosopher; he does not directly address matters of faith, 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, eastern Turkey, there are approximately 14.5 hours of daylight in the summer and 9 hours in the winter. Al-Jazari made considerable engineering efforts to ensure that there would be twelve hours between sunrise and sunset in summer and winter. This is the purpose of the flow regulator, which adjusts the short hours in the winter compared to the longer hours in the summer. 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 names. But the perception of time and its measurement are human inventions. If I had met al-Jazari and told him that a second, which was impossible to measure in his time, is the basic unit of time, and that its scientific definition is approximately 9 billion (for those who want precision, 9,192,631,770) cycles of the cesium atom between two energy levels. Not only would he would not understand a word, but he would also think me really weird. 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’s world, the concept of time, which varies with the seasons, seems far-fetched, but in al-Jazari’s world, 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 his concerns are not very different from those of a current engineer. From the text, it turns out he did a “literature review” and theoretical calculations (in this case, unsuccessful), and planned and performed the experiments. He was also a skilled man who knew 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 the selection of material (copper); he also explains how to make a perfect cylinder using a precise wooden disk and how to ensure that the cylinder will have the same diameter throughout. 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.
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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&#8221; 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.

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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.