Hero of Alexandria

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A boat which is an alarm clock

Introduction

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

Boat for measuring one hour, Topkapi manuscript, 1205

How does it work?

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

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

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

Early alarm clocks

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

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

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

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

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

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

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

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

 

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The only measurement tool in the book and why al-Jazari is the first engineer

Introduction

Al-Jazari tells that when he mentioned to some people that any(not colinear) three points could be position on the circle they didn’t believe him, so he built the only measurement instrument in the book to find the center-point of three points of unknown position. The device is quite straight forward, but we can learn quite a bit from his choice to solve, what is clearly a mathematical problem, with an “engineering” solution.

An Instrument for finding the center of a circle, Topkapi, 1206

How does it work?

The technical explanation is so short that I decided to make an exception and not color it in blue. I hope you can forgive me. Al-Jazari took a ruler and built a vertical on the center point. He placed his instrument between the two points; found the center point and drew a perpendicular segment. He repeated the process for two more points. The intersection of the perpendicular segments is the center of the circle and the distance to each point is the radius. Besides, similarly to angle measuring instruments, there is an ark, which allows to measure and mark different angles.

Some Math

One can prove that any three points that are not colinear (al-Jazari was aware of this point and specify it explicitly) are on a circle in two approaches:

  • Euclidean geometry
  • Analytic geometry.

In Euclidean geometry, three points which are not colinear form the vertices of a triangle. All triangles can be within a circle. The center of the circle is the intersection of the three perpendicular bisectors. It is relatively easy to prove. If you want to practice your Euclidean geometry, look at the diagram below, build the three radiuses BO AO CO and prove they are identical using triangle congruence theorems. Euclid’s “Elements” was translated into Arabic relatively early in the House of Wisdom in Baghdad (بيت الحكمة )). There is no direct reference in al-Jazari’s book to Euclid, but his device is based on this theorems:

Right side drawing from my Euclidean geometry book, on the left a drawing by al-Jazari.

In a different approach, you can find the center circle with analytic geometry:

Circle equation, Analytic geometry

When:

r is the circle radius

a,b are the coordinates of the center point

Since the triangle has three vertices, we have three equations in three unknowns (a, b, r) and an immediate solution. Analytic geometry has roots in ancient Greece and Persia of the 11th century, but the breakthrough was made by René Descartes, philosopher, scientist and mathematician. We remember Descartes mostly because of the proposition “I think, therefore I am.” Descartes was a remarkable mathematician and the first to offer a system of axes (x, y), as in the diagram above, which is named after him: Cartesian coordinate system. It allows the graphical representation of functions. Generations of mathematics students were, are and will be very grateful. Also, he took advantage of the Cartesian system to connect geometry and algebra, creating analytical geometry. Descartes was an impressive polymath, his contributions to philosophy and mathematics are the pillars of the two disciplines, but he also was a key figure in the Scientific Revolution and made a contribution to optics.

Polymath and al-Jazari, the first engineer

A polymath (Greek: πολυμαθής) literally “having learned much” is an individual whose knowledge spans a significant number of subjects. Both in English and Hebrew we often use the term “Renaissance man” although all the “engineers” before al-Jazari were actually polymath long before the Renaissance:

Archimedes was a gifted mathematician, scientist, and engineer, who invented the “Archimedes Screw” (a pump, still used to this day), he has improved the power and the accuracy of the Catapult, made a giant crane known as “Archimedes Claw” not to mention the myth (?) of burning the Roman fleet using mirrors. All this pales in comparison to his contributions to mathematics and physics. Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals, developed the concept of buoyant force in “On Floating Bodies” and gave the mathematical explanation to the lever.

Hero of Alexandria was an engineer, mathematician, and physicist.  Hero may have been either a Greek or a Hellenized Egyptian. It is almost certain that Hero taught at the famous Library of Alexandria because most of his writings appear as lecture notes. He is known for his research in hydrostatics, but I have already written about Hero concerning his book on automata, he also built the Aeolipile, the first steam engine. In mathematics, Hero described a method for iteratively computing the square root of a number, but his name is most closely associated with Hero’s formula for finding the area of a triangle from its side lengths.

The Banū Mūsā (“Sons of Moses”) were three 9th-century Persian scholars who lived and worked in Baghdad. The Banu Musa wrote almost 20 books, the majority of which are now lost. They are known for their Book of Ingenious Devices on automata and mechanical devices. I wrote about them in the context of the fountains, but in the context of a polymath, we can mention their contribution to mathematics, The most important work of theirs is the Book on the Measurement of Plane and Spherical Figures, a foundational work on geometry that was frequently quoted by both Islamic and European mathematicians.

Al-Jazari is not like that. His contribution to engineering is diverse. I mention already the automata and the use of the camshaft, the significant advances in candle clocks [Hebrew] including the invention of the bayonet connection, the thermal insulation, the double-action pump but he was not involved in science or math or other fields outside engineering.

The concept of the Renaissance man was coined by Leon Battista Alberti ” A man can do all things if he but wills them”, a manifestation of the deep humanism in the roots of the Renaissance. The basic premise is that the infinite human ability to evolve, and we must embrace all knowledge in our way to develop our abilities. The world has expanded so that it is just impossible. Thomas Young, an English polymath in early 19th century, regarded by many as the last man who “knew everything” was skilled in medicine, physics, Linguistics, harmony (music) and even accounting. The web site of the Israeli medical association includes thirty-two different major specialties and more, numerous subspecialties. It is not possible, even theoretically, to complete all medical specialties during one life, let alone in other areas.

We live in a more skeptical and concerned world. We ask our children, already at a young age, “What do you want to be when you grow up? We narrow the field in high school and ask the students to find majors area of study where they excel. We have institutions, counseling centers, and tests to help young people choose their profession. A physics student will get the necessary mathematical background but will not receive academic credit for courses in Assyrian or typography. In second degree studies, we reduce the field of study further, and in Ph.D., we focus on one question only. As a society, we look at people that change profession with concern, maybe as less stable who lack the ability to focus.

Following Donald Hill, The book translator, and annotator and somewhat because of my own training, I thought that using an instrument (instead of a formal proof) indicates a limited background in mathematics. This may be true. My Love M. commented that mathematical proofs are less approachable to most people and lack the magic of the instrument al-Jazari built. Al-Jazari was the first “pure engineer” not because of lack of mathematical background, or ability in math and science, but because of his passion for engineering and his ability to translate abstract and formal issues to instruments.

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The basin of the Peacock and the magic of automata

Introduction

The basin of the peacock is an automatic basin for the ritual ablution- Wuḍū (وضوء). A servant brings the basin and positions it so that the beak of the peacock is facing the master. The servant pulls a hidden lever in the tail of the peacock, and water begins to flow. Then the left door opens, and mechanical slave emerges holding soap. Toward the end of the washing, the right door opens, and another mechanical slave emerges, this time, holding a towel, to dry the master’s hands. The automata are important to the history of technology. Methods invented to refine automata laid the basis for modern technology, but I hope in this post to talk about the source of the magic of automata.

Basin of the peacock, Topkapi manuscript, 1206

How Does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in siphons or automaton mechanism can skip those bits.

The hollow Peacock is made of copper, large enough to contain the water needed for the purification ceremony. The arched neck is a siphon. A siphon is a tube in an inverted ‘U’ shape, which causes a liquid to flow upward, above the surface of a reservoir, with no pump, but powered by the pull of gravity. The siphon will work while the water in the peacock’s body would rise above the bend in the peacock neck. The peacock’s tail, which is spread out, is divided into two volumes. The bottom part is connected to the body of the peacock. The top is separated with a conical plug. This plug is connected by a curved lever which reaches the cover of the tail. At first, the servant fills the water when the plug is open, thus filling the body of the peacock and the lower half of the tail then he pushes the plug. At this stage, the water level is below the bend in the peacock’s, so nothing happens. With the plug in place, he fills the top half of the peacock’s tail and brings the basin to the king. Now the servant pulls the plug and connects all the Peacock parts. The water came down and rise over the bend of the Peacock neck, and the ritual ablution begins.

Al-Jazari and  Donald Hill settled for a side drawing, but my love M. insisted that it’s hard to understand the operation of the automaton without a frontal drawing. So I expanded the drawing:

When pouring water into the basin, the water flows through a hole in the floor into the lower chamber, and the float goes up until it pushes the mechanical slave holding the soap, causing him to move forward and open the left door and thus “offer” the soap to the king. The float doesn’t continue to rise because its movement is limited by the ceiling of the lower chamber. The water continues to rise to the upper chamber, so the second float begins to rise. His rod is shorter and triggers the second mechanical slave just before the water end. When the second slave moves forward, it opens the right door and offers a towel.

 

Automaton  (self-operating machine) magic

Automaton (plural automata) were not invented by al-Jazari. We know of automata in ancient Greece (Greek: αὐτόματον “acting of one’s own will”). The automata were used in temples and as accessories in the Greek theatre.  The first engineering text that I am aware of is by Hero of Alexandria, a mathematician, engineer, and scientist from the 1st century AD. “Automatopoietica” (αυτoματoπoιητικ ‘ ης) usually translated “on making automatons.” It is reasonable to assume that Hero knew of Aristotle’s “Poetics,” the earliest surviving work focusing on literary theory, in which Aristotle examine the principles behind epic poetry, comedy, and mainly tragedy. We can expand (?)  Poetics as the artistic elements which compose any art form and in our case, the art of automata. Today when we say poetic, we mean an emotional, leary style of expression. I don’t know if this was true in Alexandria, the book is a description of machines that perform “magic” with mechanics or pneumatics, such as automatic door opening in the shrine or statues that pours wine.

Al-Jazari developed and perfected the world of automata. He was the first to employ the camshaft as part of his automata, see the Castel Water Clock or the  Musical Boat [in Hebrew]. He also expanded the use of water flow, smart use of gears, buoys and balancing weights built a long list of automatons, some I already covered, and some I would translate from Hebrew in the near future.

The 18th century was the golden age of automatons. Most of them rely on the camshaft quite similar to the work by al-Jazari. It’s hard to choose between the many exotic examples. I can’t ignore the “Digesting Duck”  (Canard Digérateur) built by Jacques de Vaucanson. The Duck was the size of a living duck and was covered in perforated gold-plated copper to allow a view of the inside workings. It moved like a duck, wiggling its beak in the water, quacking, and most famously though, it could eat pellets offered to it, and then poop them. De Vaucanson claimed that duck contained a small “chemical laboratory” capable of breaking down the wheat grain. In the 19th century, it was found that Vaucanson had faked the mechanism, and the Duck’s poop consisted of pre-prepared breadcrumb pellets, dyed green.

An American artist’s (mistaken) drawing of the Digesting Duck.

I particularly like the automaton of Maillardet, also known (by error) as “Maelzel’s Juvenile Artist.” This is an automaton that can draw four different drawings and write in calligraphy three poems which, among other things, revealed the true creator, Maillardet, in contrast to its wrong reference to Maelzel. The full story appears in this video:

It is impossible to ignore that the eighteenth century is the age Romanticism (also known as the Romantic era), an artistic, literary, musical and intellectual movement originated in Europe. For example in a Hoffman story “The Nutcracker and the Mouse King” Mr. Drosselmeyer, who is a clockmaker and inventor, made a splendid gift for the children: a clockwork castle with mechanical people moving about. Also Olympia, in Der Sandmann (The Sand-man), the life-size mechanical doll with which Nathanael falls disastrously in love. Nili Mirsky in the epilog to “The Golden Pot and other stories “writes about chronic dualism: In the day a strict Prussian judge and in the night a romantic poet or the tension between the occult world and what is exposed in his stories. I suggest adding the tension between the mechanical doll and living humans.

The methods invented to refine mechanical dolls laid the basis for modern technologies, not only for robotics. For example, Edmund Cartwright patented the power loom in 1784, key development in the industrialization of weaving after a visit to “The Turk,” a mechanical doll who played chess and then proved to be a hoax. The mechanical part was real, but there was a concealed man who computed the chess moves. Cartwright wrote: “it is more difficult to construct a machine that shall weave than one which shall make all the variety of moves required in that complicated game?”. Thomas Edison incorporated the camshaft of al-Jazari or Maillardet with the music box and created the phonograph, the first device that allowed recording of music or voices. In general, there are many more examples of a drift of the technology from the “useless” world of automatons to the “practical” world, but I want to talk about the source of the magic.

The automaton is a mechanical doll who moves around and does things that are reserved only to living beings. I don’t think the automata maker confused themselves with the all-mighty creator. There is no mysticism or black magic in mechanical dolls, but there is small magic or amazement in the gap between the mechanical system and human behavior.  Allegedly this magic should disappear in the modern world. Drawing and writing poems are relatively simple tasks for a LEGO robot, which is only a toy. At MIT-Laboratory researcher investigate energy-efficiency in legged robots and created a mechanical “Cheetah” that goes far beyond any dream of makers in previous centuries. I am the last person who wants to reduce the wonder from the Cheetah but the kids watching the contemporary robot do not have the amazed face of the kids watching  “Maelzel’s Juvenile Artist.”  was the charm preserved? Why? I think magic is different. The observer in the thirteenth century and the eighteenth-century lived-in a world with a lot less technology and understood the world around him in a way that we lost. We live in a world saturated with technology and used to not understand most of it, even if we have a technological education. The cell phone in our hands is a powerful computer. Hundreds of engineers from various disciplines, electrical engineer, material engineers, chemists, and a solid-state physicist were needed to produce the microprocessor alone. I doubt that there is one person in Apple or Samsung that knows all the details of the microprocessor, and this is before we even discuss the touch screen or the antenna. We live (well!) with our lack of understanding and content with using it without knowing “the details.” In the 18th century, and before, the automaton was a demonstration of the strength of technology. It allowed René Descartes, the famous French philosopher, mathematician, and scientist to think (fantasize?) that one day the scientific principles at the base of Humans and animals would be revealed, just like we can understand the mechanism of the automaton. This was a challenge to religion and a song of praise to science and its powers. Not every innocent observer is Descartes, but this is the root of our amazement. When we live in a technological world we don’t understand, the astonishment question is very different. Why be astonished more (or less?) by a robot or a cell phone or a game of virtual reality? The magic of the old mechanical dolls is precisely the fact that we can see the technology does its wonders, you can see the gears fit, and the reader (pushrod) moves over the camshaft. We, the eighteenth-century observer and al-Jazari, are, for one moment, in the same place of admiration.