Ptolemy

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The Peacock Clock and the Beauty of Engineering

Introduction

[This entry was posted more than five years ago in “IR HAOSHER” [in Hebrew] and is the beginning of my journey in the footsteps of al-Jazari, this is an updated version]

Modern machines are designed to be functional, reliable, and inexpensive. No one in the Technion (Israel Institute of Technology) ever talked to me about the beauty of Engineering. Sometimes when I look at a machine or its parts, there is something breathtaking as beautiful as art. Can I capture this beauty? What terms should I use? These questions resurface when my friend, Dr. Oved Kedem, retired and I looked for a present for a man who loves science and the history of science.

A water clock or clepsydra (from Greek “to steal water”) is a clock where time is measured by the regulated flow of water into or out from a vessel. Water clocks, along with the sundials, are the oldest instruments for measuring time. It is not known when and where they were invented. There is evidence for the use of water clocks in the Middle East, ancient Egypt around the 16th century BC and evidence of early water clocks also in other regions of the world, including India and China. I was looking for an exciting water clock, and so I went on a journey that started at the Weizmann Institute of Science, Through Kafr Qara (كفر قرع), Istanbul and Washington and is still going. I chose to build the water clock of the peacocks.

The Peacock water clock, Topkapi Manuscript,1206

How does it work?

The technical explanation, as always, will be colored in blue, so anyone who is not interested in a scoop wheel and a tipping bucket can skip those bits

A drawing of the mechanism with my captions

The clock was built in the wall of a pool with a fountain in the center. The main tank is getting water from the pool, at a rate approximately equal to the water flow to the tipping bucket. I wrote about tipping buckets, for example here and I will do a full mathematical analysis in the future. The latter is the heart of the clock, and when it fills up, once every half an hour, the center of gravity changes, and the vessel tilt on its axis and discharges its water on the scoop wheel which drives all the clock’s components.  On the copper ball (see diagram above) a peacock made from copper, his tail raised, revolves. The two peacock chicks in the second miḥrāb (محراب)‎) are moving toward each other like they are quarreling. The peahen in the top miḥrāb moves from right to left. The commotion of the peacocks is happening every half an hour, and the glass roundels are colored in red, or lit in the night, to count the passing hours.

The Beauty of Science and Technology

The mechanical drawings by al-Jazari look like Turkish miniatures. My love M.has a treasure chest where she keeps postcards from our travels worldwide, although we have not sent a postcard in ages. When I showed her the Peacock Clock, she searched her collection and found a postcard from our journey to Istanbul twenty years ago, chosen by its merits as a picture without knowing anything about the book or the author.

Despite the narrative break, we should stop here for a moment to contemplate:

A Hidden claim here is that beauty is beauty is beauty. The beauty of the postcard has nothing to to do with the machine and the way it works; it’s just a beautiful postcard because of its composition, the colors, and other questions for art-lovers. Weizmann Institute “agrees.” In the “Beauty of Science” exhibition, images of experimental results that look beautiful and aesthetic to the eye without any relation to the science behind them. I chose as an example of an image from research by Dr. Einat Vitner. Obviously, the resemblance to Picasso caught the attention of the researcher and the viewers, but I don’t know anything about the scientific significance, or its connection to the elusive concept of beauty in science or engineering.

The Beauty of Science, “Dance of Astrocytes,“ Dr. Einat Vitner, 2011

Is The Peacock Clock beautiful without being a machine?

During my work, I went to Kafr Qara كفر قرع) ) to meet with Dr. Ibrahim Yehia, Director of  TRDC( a Regional Research Center). I wanted to talk to him about his work in the village with active science groups but during the conversation I found, to my surprise, that he got al-Jazari’s book in Arabic, and has a deep interest and knowledge on the subject.  He was a student of Prof. Fuat Sezgin, a professor of History of Science at the Goethe University in Frankfurt, and the founder of both Islam science museums in Frankfurt and Istanbul. The museum exhibits the significant role played by medieval Muslim scientists, inventors, and physicians. Almost all of the items on display are reconstructions of historical instruments and tools that were built by the University of Frankfurt’s Institute of Arabic and Islamic Sciences. Although I am a very rational person with no tendency to mysticism, I thought the way al-Jazari ‘s work permeates into my life is surprising,  a bit strange and attractive. In the same year, I  went to Istanbul to see the Museum. The Museum is located in Gülhane Park which was once part of the garden of Topkapı Palace and is beautiful. It has a beautiful collection of Sextants (navigation) and fascinating maps. Medical instruments from the period in which Islam was at the forefront of science and technology, but the objects designed by al-Jazari seemed like pale folkloristic copies of the book I love:

The elephant clock, right the drawing from the book, left, the model from the Museum.

It can be argued that the Museum artists failed to transfer the two-dimensional beauty of the drawing to a three-dimensional model, but I think there’s a lot more than that. The issue is related to the beauty of machines. Meanwhile, I found out about the exhibition entitled – 1001 Inventions the National Museum in Washington., enter it manually with Sir Ben Kingsley in the role of al-Jazari (a little long ~ 13 min)

The exhibition was launched in 2006 at the Museum of Science and Industry in Manchester and quickly became an international attraction. It was introduced in the British Parliament in London, in the European Parliament in Brussels and the United Nations building in New York. In January 2010 the 1001 Inventions launched at the world-famous London Science Museum to be followed by Istanbul, New York, Dubai, San Francisco and Washington, where I saw it with my son Noah.

The exhibition uses al-Jazari as a role model of technology in the Islamic golden age, with two water clocks: The Elephant water clock and the Scribe water clock. Despite dealing with science and technology, the exhibition is proposing a different narrative: the middle ages are not a dark period in-between the decline of the Roman Empire and the Renaissance, but also the golden age of Islam.  As a result, the items themselves (“elephant clock”, “pumping facility” and so on) are great designs without running water, gears or any working mechanism at all. This is a very decorated but empty shell. Despite the investment, I do not think that none of the objects is even close to original beauty.

I think there is something inside us that identifies and responds to beauty. When it comes to science and engineering, this beauty is related to precision and correctness. In the past seven years, I have taught high school student “computational science,” and it is easy to say a software solution is “beautiful,” and when it is cumbersome and forced. The beauty, in this case, is not purely aesthetic but has to do with simplicity and strength.

Simplicity

To explain the connection between simplicity and beauty, I want to stand on the shoulders of giants. Aristotle believed that the Earth was the center of the universe and the Sun, Moon, planets are attached to transparent, rotating spheres surrounding the Earth. More astronomical observations were difficult to fit in the model and by the time of Ptolemy(2nd century AD),  the model included a system of two spheres per planet: one called its deferent; the other, its epicycle. The final model was so complicated, Alfonso X, king of Castile called the Wise (Spanish: el Sabio) who gained considerable scientific fame based on his deep interest  in astronomy said: “If the Lord Almighty had consulted me before embarking on creation thus, I should have recommended something simpler.”

Picture of the world according to Ptolemy, the most complete and detailed description of the geocentric model following Aristotle

in the evolution of the scientific model of the movement of celestial bodies there are more heroes, Copernicus is perhaps the best known of them all, but I would like jumped straight to Johannes Kepler (1571-1630) who replaced this complicated  system with three simple rules:

  1. Elliptic orbit: The orbit of a planet is an ellipse with the Sun at one of the two foci.
  2. The law of increasing velocity: The planet travels faster when closer to the Sun, and then slower when farther from the Sun. Kepler wrote this law mathematically enabling calculations and predictions.
  3. The harmonic law – The Square of the orbital period (the time it takes for the planet to circle the Sun and we call it “year”) is directly proportional to the cube of the semi-major axis of its orbit.

The summary of Kepler’s laws is maybe too concise, but I think everyone could see the beauty in the ability to explain the complex movement of the night sky using three simple rules that require mathematics of middle school. The simplicity and elegance of Kepler’s model help us to be convinced but do not make it right. Like any scientific or engineering theory, it should be repeatedly tested and verified. Astronomical observations are numerous and contain deviations and mistakes. The regularity is not simple. Kepler spent many years analyzing the data. As the scientific model consists of simple rules, as the rules explain more phenomena, sometimes seemingly unrelated, there is a sense of logical harmony, echoing within us as more beautiful.

Power

From time to time, there is an engineering achievement, such as the telephone or the electric bulb that makes us truly believe in the power of human invention to improve the lives of humanity. What makes an engineering or scientific solution powerful beyond its success? It tried to look at an example:

The wheel is such an old invention that we have no way of knowing who or where it originated. Depictions of a wheeled vehicle appeared between 3500–3350 BCE in the Bronocice clay from southern Poland. The wheel helps to bridge distances and ease the transportation of objects and goods. To my surprise, the benefits of transportation were limited for thousands of years due to a lack of roads and infrastructure.

However the wheel was still used for many purposes, Stone mills powered by water, Distaff and a spinning wheel, pulleys to lift the weight, toothed wheels to change the speed, torque, and direction of a power source which allowed ancient civilizations to create complex machines as al-Jazari demonstrated so gracefully.

The index of power asks how elaborate is the engineering solution and how many layers it includes. I think it’s similar, but different, from the beauty of subtext, when the contents of a book or movie, which was not transferred to us explicitly, becomes understood as the book/movie unfolds. This is not just the complexity, but the integration and the consolidation, The beauty of how the various components fit together; the water fill the tipping bucket carefully designed so that it will tilt every half hour, rotating the scoop wheel, a little bit like our enjoyment of Rube Goldberg’s  machine :

Rube Goldberg self-operating napkin

In this respect, when the machine lost its function and made just a design is losing its power and simplicity, and hence its beauty, even if its shape is intact. With the crew of the workshop of the Clore Science Garden, we built a prototype of the Peacocks Clock:

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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.