Domingo é dia de “Domini”

«It is much better to do all things as God intended by capturing the magnetic frequencies from the sun with the paramagnetic soil or round tower antenna. In one sentence, make your soil susceptible (resonate) to the sun, do not, with magnets, try to bring the sun to earth.»

– Philip S. Callahan

 

“A união faz a força”

Killing the Angel in the House

«All I could do was to offer you an opinion upon one minor point — a woman must have money and a room of her own if she is to write fiction (…).  So that when I ask you to earn money and have a room of your own, I am asking you to live in the presence of reality, an invigorating life, it would appear, whether one can impart it or not.»

– Virginia Woolf, “A room of one’s own

 

«The cheapness of writing paper is, of course, the reason why women have succeeded as writers before they have succeeded in the other professions.

But to tell you my story – it is a simple one. You have only got to figure to yourselves a girl in a bedroom with a pen in her hand. She had only to move that pen from left to right–from ten o’clock to one. Then it occurred to her to do what is simple and cheap enough after all–to slip a few of those pages into an envelope, fix a penny stamp in the corner, and drop the envelope into the red box at the corner. It was thus that I became a journalist; and my effort was rewarded on the first day of the following month–a very glorious day it was for me–by a letter from an editor containing a cheque for one pound ten shillings and sixpence.

But to show you how little I deserve to be called a professional woman, how little I know of the struggles and difficulties of such lives, I have to admit that instead of spending that sum upon bread and butter, rent, shoes and stockings, or butcher’s bills, I went out and bought a cat–a beautiful cat, a Persian cat, which very soon involved me in bitter disputes with my neighbours.

What could be easier than to write articles and to buy Persian cats with the profits?

But wait a moment. Articles have to be about something. Mine, I seem to remember, was about a novel by a famous man.

And while I was writing this review, I discovered that if I were going to review books I should need to do battle with a certain phantom. And the phantom was a woman, and when I came to know her better I called her after the heroine of a famous poem, The Angel in the House. It was she who used to come between me and my paper when I was writing reviews. It was she who bothered me and wasted my time and so tormented me that at last I killed her. You who come of a younger and happier generation may not have heard of her–you may not know what I mean by the Angel in the House. I will describe her as shortly as I can.

She was intensely sympathetic. She was immensely charming. She was utterly unselfish. She excelled in the difficult arts of family life. She sacrificed herself daily. If there was chicken, she took the leg; if there was a draught she sat in it–in short she was so constituted that she never had a mind or a wish of her own, but preferred to sympathize always with the minds and wishes of others. Above all–I need not say it—she was pure. Her purity was supposed to be her chief beauty–her blushes, her great grace. In those days–the last of Queen Victoria–every house had its Angel.

And when I came to write I encountered her with the very first words. The shadow of her wings fell on my page; I heard the rustling of her skirts in the room. Directly, that is to say, I took my pen in my hand to review that novel by a famous man, she slipped behind me and whispered: “My dear, you are a young woman. You are writing about a book that has been written by a man. Be sympathetic; be tender; flatter; deceive; use all the arts and wiles of our sex. Never let anybody guess that you have a mind of your own. Above all, be pure.” And she made as if to guide my pen.

I now record the one act for which I take some credit to myself, though the credit rightly belongs to some excellent ancestors of mine who left me a certain sum of money–shall we say five hundred pounds a year?–so that it was not necessary for me to depend solely on charm for my living.

I turned upon her and caught her by the throat. I did my best to kill her. My excuse, if I were to be had up in a court of law, would be that I acted in self-defence. Had I not killed her she would have killed me. She would have plucked the heart out of my writing.

For, as I found, directly I put pen to paper, you cannot review even a novel without having a mind of your own, without expressing what you think to be the truth about human relations, morality, sex. And all these questions, according to the Angel of the House, cannot be dealt with freely and openly by women; they must charm, they must conciliate, they must–to put it bluntly–tell lies if they are to succeed.

Thus, whenever I felt the shadow of her wing or the radiance of her halo upon my page, I took up the inkpot and flung it at her. She died hard. Her fictitious nature was of great assistance to her. It is far harder to kill a phantom than a reality. She was always creeping back when I thought I had despatched her. Though I flatter myself that I killed her in the end, the struggle was severe; it took much time that had better have been spent upon learning Greek grammar; or in roaming the world in search of adventures. But it was a real experience; it was an experience that was bound to befall all women writers at that time. Killing the Angel in the House was part of the occupation of a woman writer.

But to continue my story. The Angel was dead; what then remained?

You may say that what remained was a simple and common object–a young woman in a bedroom with an inkpot. In other words, now that she had rid herself of falsehood, that young woman had only to be herself. Ah, but what is “herself”? I mean, what is a woman? I assure you, I do not know. I do not believe that you know. I do not believe that anybody can know until she has expressed herself in all the arts and professions open to human skill. That indeed is one of the reasons why I have come here out of respect for you, who are in process of showing us by your experiments what a woman is, who are in process of providing us, by your failures and successes, with that extremely important piece of information.

But to continue the story of my professional experiences. I made one pound ten and six by my first review; and I bought a Persian cat with the proceeds. Then I grew ambitious. A Persian cat is all very well, I said; but a Persian cat is not enough. I must have a motor car. And it was thus that I became a novelist–for it is a very strange thing that people will give you a motor car if you will tell them a story. It is a still stranger thing that there is nothing so delightful in the world as telling stories. It is far pleasanter than writing reviews of famous novels.

And yet, if I am to obey your secretary and tell you my professional experiences as a novelist, I must tell you about a very strange experience that befell me as a novelist. And to understand it you must try first to imagine a novelist’s state of mind. I hope I am not giving away professional secrets if I say that a novelist’s chief desire is to be as unconscious as possible. He has to induce in himself a state of perpetual lethargy. He wants life to proceed with the utmost quiet and regularity. He wants to see the same faces, to read the same books, to do the same things day after day, month after month, while he is writing, so that nothing may break the illusion in which he is living–so that nothing may disturb or disquiet the mysterious nosings about, feelings round, darts, dashes and sudden discoveries of that very shy and illusive spirit, the imagination. I suspect that this state is the same both for men and women.

Be that as it may, I want you to imagine me writing a novel in a state of trance. I want you to figure to yourselves a girl sitting with a pen in her hand, which for minutes, and indeed for hours, she never dips into the inkpot. The image that comes to my mind when I think of this girl is the image of a fisherman lying sunk in dreams on the verge of a deep lake with a rod held out over the water. She was letting her imagination sweep unchecked round every rock and cranny of the world that lies submerged in the depths of our unconscious being.

Now came the experience, the experience that I believe to be far commoner with women writers than with men. The line raced through the girl’s fingers. Her imagination had rushed away. It had sought the pools, the depths, the dark places where the largest fish slumber. And then there was a smash. There was an explosion. There was foam and confusion. The imagination had dashed itself against something hard. The girl was roused from her dream. She was indeed in a state of the most acute and difficult distress.

To speak without figure she had thought of something, something about the body, about the passions which it was unfitting for her as a woman to say. Men, her reason told her, would be shocked. The consciousness of–what men will say of a woman who speaks the truth about her passions had roused her from her artist’s state of unconsciousness. She could write no more. The trance was over. Her imagination could work no longer. This I believe to be a very common experience with women writers–they are impeded by the extreme conventionality of the other sex. For though men sensibly allow themselves great freedom in these respects, I doubt that they realize or can control the extreme severity with which they condemn such freedom in women.

These then were two very genuine experiences of my own. These were two of the adventures of my professional life.

The first–killing the Angel in the House–I think I solved. She died.

But the second, telling the truth about my own experiences as a body, I do not think I solved. I doubt that any woman has solved it yet. The obstacles against her are still immensely powerful–and yet they are very difficult to define.

Outwardly, what is simpler than to write books? Outwardly, what obstacles are there for a woman rather than for a man?

Inwardly, I think, the case is very different; she has still many ghosts to fight, many prejudices to overcome.

Indeed it will be a long time still, I think, before a woman can sit down to write a book without finding a phantom to be slain, a rock to be dashed against. And if this is so in literature, the freest of all professions for women, how is it in the new professions which you are now for the first time entering?

Those are the questions that I should like, had I time, to ask you.

And indeed, if I have laid stress upon these professional experiences of mine, it is because I believe that they are, though in different forms, yours also.

Even when the path is nominally open–when there is nothing to prevent a woman from being a doctor, a lawyer, a civil servant–there are many phantoms and obstacles, as I believe, looming in her way. To discuss and define them is I think of great value and importance; for thus only can the labour be shared, the difficulties be solved.

But besides this, it is necessary also to discuss the ends and the aims for which we are fighting, for which we are doing battle with these formidable obstacles. Those aims cannot be taken for granted; they must be perpetually questioned and examined.

The whole position, as I see it–here in this hall surrounded by women practising for the first time in history I know not how many different professions–is one of extraordinary interest and importance. You have won rooms of your own in the house hitherto exclusively owned by men. You are able, though not without great labour and effort, to pay the rent. You are earning your five hundred pounds a year.

But this freedom is only a beginning–the room is your own, but it is still bare. It has to be furnished; it has to be decorated; it has to be shared. How are you going to furnish it, how are you going to decorate it? With whom are you going to share it, and upon what terms? These, I think are questions of the utmost importance and interest. For the first time in history you are able to ask them; for the first time you are able to decide for yourselves what the answers should be. Willingly would I stay and discuss those questions and answers–but not tonight. My time is up; and I must cease.»

– Virginia Woolf, “Professions for Women“, speech delivered on January 21, 1931, before the National Society for Women’s Service, published posthumously in “The Death of the Moth and Other Essays”.

Science for a gracious woman

«A particle of tuition conveys a science to a comprehensive mind: and having reached it, expands of its own impulse. As oil poured on water, as a secret entrusted to the vile, as alms bestowed upon the worthy, however little, so does science infused into a wise mind spread by intrinsic force

– Bhaskara

 

Bhaskaracharya (1114-1185), also known as Bhaskara II, son of a famous astrologer, Mahesvara, was born in Akaria (Vijayapura, India).

Bhaskaracharya contributed for a greater understanding of number systems and advanced methods of equation solving, particularly, the formula of quadratic equation.

His concept of differential calculus predates Newton and Leibniz by half a millennium.

He was able to accurately calculate the sidereal year, the time it takes for the earth to orbit the sun: there is but a scant difference in his figure of 365.2588 days and the modern figure of 365.2596 days.

His main work, “Siddhanta Siromani” (Sanskrit for “Crown Jewel of Accuracy”), written in the year of 1150 A.D., was divided into four sections:
– Lilavati (“Gracious”) – on arithmetics;
– Bijaganita (“Seed counting”) – on algebra;
– Goladhyaya (“Celestial globe”);
– Grahaganita (“Mathematics of the planets”).

Līlāvatī means “gracious woman” (from Sanskrit लीलावती, Līlā = gracious, -vatī = female possessing the quality). 

Many of the arithmetical problems are addressed to Līlāvatī. For example:

«Oh Līlāvatī, intelligent girl, if you understand addition and subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10, and 100, as well as [the remainder of] those when subtracted from 10000.» 

«Fawn-eyed child Līlāvatī, tell me, how much is the number [resulting from] 135 multiplied by 12, if you understand multiplication by separate parts and by separate digits. And tell [me], beautiful one, how much is that product divided by the same multiplier?»

«Whilst making love a necklace broke.
A row of pearls mislaid.
One sixth fell to the floor.
One fifth upon the bed.
The young woman saved one third of them.
One tenth were caught by her lover.
If six pearls remained upon the string
How many pearls were there altogether?» (*)

Bhaskaracharya’s conclusion to “Lilavati” states:

«Joy and happiness is indeed ever increasing in this world for those who have Lilavati clasped to their throats, decorated as the members are with neat reduction of fractions, multiplication and involution, pure and perfect as are the solutions, and tasteful as is the speech which is exemplified.»

 

(*) Resolution:

1/6 x + 1/5 x + 1/3 x + 1/10 x + 6 = x

5/30 x + 6/30 x + 10/30 x + 3/30 x – 30/30 x + 6 = 0

– 6/30 x + 6 = 0

x = 30

Tower of the winds

The Tower of the Winds is an octagonal Pentelic marble clocktower on the Roman agora in Athens.

According to the testimony of Vitruvius and Varro, it was built by Andronicus of Cyrrhus around 50 BC, but according to other sources might have been constructed in the 2nd century BC before the rest of the forum.

The structure features a combination of eight sundials, a water clock driven by water coming down from the Acropolis and a wind vane. The 12-metre-tall structure has a diameter of about 8 metres and was topped in antiquity by a weathervane-like Triton that indicated the wind direction. The considerable height of the tower was motivated by the intention to place the sundials and the wind-vane at a visible height on the Agora, making it effectively an early example of a clock-tower.

Below the frieze, the eight wind deities (“Anemoi”) are depicted: Boreas (N), Kaikias (NE), Eurus (E), Apeliotes (SE), Notus (S), Livas (SW), Zephyrus (W), and Skiron (NW).

The deities equivalent to the Greek Anemoi in Roman mythology were the Venti (in Latin, “winds”). These gods had different names, but were otherwise very similar to their Greek counterparts, borrowing their attributes and being frequently conflated with them.

In Greek mythology, the Anemoi (in Greek, Ἄνεμοι, “winds”) were each ascribed a cardinal direction, from which their respective winds came, and were each associated with various seasons and weather conditions.

They were sometimes represented as mere gusts of wind, at other times were personified as winged men, and at still other times were depicted as horses kept in the stables of the storm god Aeolus, who provided Odysseus with the Anemoi in the Odyssey. Astraeus, the astrological deity sometimes associated with Aeolus, and Eos, the goddess of the dawn, were the parents of the Anemoi, according to the Greek poet Hesiod.

The four chief Anemoi:

Boreas (Greek: Βορέας, Boréas) – was the god of the cold north wind and the bringer of winter. His name meant “North Wind” or “Devouring One”. Boreas is depicted as being very strong, with a violent temper to match. He was frequently shown as a winged old man with shaggy hair and beard, holding a conch shell and wearing a billowing cloak. Pausanias wrote that Boreas had snakes instead of feet, though in art he was usually depicted with winged human feet. Boreas was closely associated with horses. He was said to have fathered twelve colts after taking the form of a stallion, to the mares of Erichthonius, king of Troy. These were said to be able to run across a field of grain without trampling the plants. The Greeks believed that his home was in Thrace, and Herodotus and Pliny both describe a northern land known as Hyperborea (“Beyond the North Wind”), where people lived in complete happiness and had extraordinarily long lifespans. Boreas was also said to have kidnapped Oreithyia, an Athenian princess, from the river Ilissus. Boreas had taken a fancy to Oreithyia, and had initially pleaded for her favours, hoping to persuade her. When this failed, he reverted to his usual temper and abducted her as she danced on the banks of the Ilissus. Boreas wrapped Oreithyia up in a cloud, raped her, and with her, Boreas fathered two sons—the Boreads, Zethes and Calais—and two daughters— Khione, goddess of snow, and Cleopatra. The Roman equivalent of Boreas was Aquilo, or Aquilon. An alternate, rarer name used for the northern wind was Septentrio, a word derived from septem triones (“seven oxen”) referring to the seven prominent stars in the northern constellation Ursa Major. Septentrio is also the source of the word septentrional, a synonym for boreal, meaning “northern”;

Notus (Greek Νότος, Nótos) – was the south wind and bringer of the storms of late summer and autumn. Notus was associated with the desiccating hot wind of the rise of Sirius after midsummer, and was feared as a destroyer of crops. Notus’ equivalent in Roman mythology was Auster, the embodiment of the sirocco wind, who brought heavy cloud cover and fog or humidity;

Zephyrus (in Greek Ζέφυρος, Zéphuros, related to zophos, “gloom, mist”, Zephyrus in Latin, and Zefferus in Old English) – was the west wind and bringer of mild breezes. The gentlest of the winds, Zephyrus is known as the fructifying wind, the messenger of spring. It was thought that Zephyrus lived in a cave in Thrace. He was said to be the husband of his sister Iris, the goddess of the rainbow. He abducted another of his sisters, the goddess Chloris (root of “chlorophile”, equivalent to Roman goddess Flora, from the Latin “flos”, flower), and gave her the domain of flowers. With Chloris, he fathered Ampyx, Mopsus and Carpus (“fruit”). He is said to have vied for Chloris’s love with his brother Boreas, eventually winning her devotion. Additionally, with yet another sister and lover, the harpy Podarge (also known as Celaeno), Zephyrus was said to be the father of Balius and Xanthus, Achilles’ horses. One of the surviving myths in which Zephyrus features most prominently is that of Hyacinth. Hyacinth was a very handsome and athletic Spartan prince. Zephyrus fell in love with him and courted him, and so did Apollo. The two competed for the boy’s love, but he chose Apollo, driving Zephyrus mad with jealousy. Later, catching Apollo and Hyacinth throwing a discus, Zephyrus blew a gust of wind at them, striking the boy in the head with the falling discus. When Hyacinth died, Apollo created the hyacinth flower from his blood. In the story of Cupid and Psyche, Zephyrus served Cupid by transporting Psyche to his cave and then, by his absence, causing the death of Psyche’s two sisters. Zephyrus’ Roman equivalent was Favonius, who held dominion over plants and flowers. The name Favonius, which meant “favorable”, was also a common Roman name. Zephyrus is linked to many love stories, suggesting a possible relation with the Greek word “Zefksis” for “union, conjuction”. According to Boccaccio’s “Genealogia”, “life” or “vita” is the meaning of the Greek “Zephs” from which the West wind’s name derives;

Favonius

Eurus (Greek: Εύρος, Eúros) – the east wind, was not associated with any of the three Greek seasons, and is the only one of these four Anemoi not mentioned in Hesiod’s Theogony or in the Orphic Hymns. He was considered an unlucky wind and was thought to bring warmth and rain. His symbol was an inverted vase, spilling water. His Roman counterpart was Vulturnus (not to be confused with Volturnus, a tribal river-god who later became a Roman deity of the River Tiber).

Additionally, four intermediate winds, the Anemoi Thuellai (Άνεμοι θύελλαι; Greek: “Tempest-Winds”), were sometimes referenced, representing the northeast, southeast, northwest, and southwest winds. Originally, as attested in Hesiod and Homer, these four minor Anemoi were wicked and violent daemons (spirits) created by the monster Typhon, and male counterparts to the harpies, who were also called thuellai. These were the winds held in Aeolus’s stables; the other four, “heavenly” Anemoi, were not kept locked up. However, later writers confused and conflated the two groups of Anemoi, and the distinction was largely forgotten.

The Anemoi Thuellai:

Kaikias – was the Greek deity of the northeast wind. He is shown as a bearded man with a shield full of hail-stones, and his name is cognate to the Latin word caecus “blind”, that is, he was seen as a “dark” wind. The Roman spelling of Kaikias was Caecius.

Apeliotes – sometimes known to the Romans as Apeliotus, was the Greek deity of the southeast wind. As this wind was thought to cause a refreshing rain particularly beneficial to farmers, he is often depicted wearing gumboots and carrying fruit, draped in a light cloth concealing some flowers or grain. He is cleanshaven, with curly hair and a friendly expression. Because Apeliotes was a minor god, he was often synthesized with Eurus, the east wind. Subsolanus, Apeliotes’ Roman counterpart, was also sometimes considered the east wind, in Vulturnus’ place.

Skiron, or Skeiron – was the Greek god of the northwest wind. His name is related to Skirophorion, the last of the three months of spring in the Attic festival calendar. He is depicted as a bearded man tilting a cauldron, representing the onset of winter. His Roman counterpart is Caurus, or Corus. Corus was also one of the oldest Roman wind-deities, and numbered among the di indigetes (“indigenous gods”), a group of abstract and largely minor numinous entities.

Lips – was the Greek deity of the southwest wind, often depicted holding the stern of a ship. His Roman equivalent was Afer ventus (“African wind”), or Africus, due to Africa being to the southwest of Italy. This name is thought to be derived from the name of a North African tribe, the Afri.

Source: http://en.wikipedia.org/wiki/Anemoi

The clepsydra and the final goal of the clockmakers’ art

In Ancient Greece, a water clock was known as “water thief“, clepsydra in Greek (κλέπτειν kleptein, ‘to steal’; ὕδωρ hudor, ‘water’).

It is likely to be the oldest time-measuring instrument, with the only exceptions being the vertical gnomon and the day-counting tally stick. Where and when it was first invented is not known, and given its great antiquity it may never be.

The bowl-shaped outflow is the simplest form of a water clock and is known to have existed in Babylon and in Egypt around the 16th century BC. Other regions of the world, including India and China, also have early evidence of water clocks.

The oldest water clock of which there is physical evidence dates to c. 1417-1379 BC, during the reign of Amenhotep III where it was used in the Temple of Amen-Re at Karnak. The oldest documentation of the water clock is the tomb inscription of the 16th century BC Egyptian court official Amenemhet, which identifies him as its inventor. These water clocks were stone vessels with sloping sides that allowed water to drip at a nearly constant rate from a small hole near the bottom to mark the hours. There were twelve separate columns with consistently spaced markings on the inside to measure the passage of “hours” as the water level reached them. It took about an hour for the water level to sink to each level. The columns were for each of the twelve months to allow for the variations of the seasonal hours. These clocks were used by priests to determine the time at night so that the temple rites and sacrifices could be performed at the correct hour.

A full-size reconstruction may be seen in the New Walk Museum, and illustrates how it could act as a timekeeper independent of the Sun. The vessel is filled with water to a mark near the rim, and then allowed to empty via a narrow jet near the base. With a cylindrical container the rate of flow diminishes as the head of water within the pot decreases, so the water surface drops more slowly with time. The ancient Egyptian designer (Amenhemhet, about 1550 B.C.) has cleverly compensated for this by employing a conical vessel, which chosen angle gave rise to an optimized approximation to a constant descent rate of the water surface.

In Babylon, water clocks were cylindrical in shape. Use of the water clock as an aid to astronomical calculations dates back to the Old Babylonian period (c. 2000 BC–c. 1600 BC). While there are no surviving water clocks from the Mesopotamian region, most evidence of their existence comes from writings on clay tablets. Two collections of tablets, for example, are the Enuma-Anu-Enlil (1600–1200 BC) and the MUL.APIN (7th century BC). In these tablets, water clocks are used in reference to payment of the night and day watches (guards). These clocks measured time “by the weight of water flowing from” it. The volume was measured in capacity units called qaMana (the Greek unit for about one pound) is the weight of water in a water clock. It is important to note that during Babylonian times, time was measured with temporal hours. So, as seasons changed, so did the length of a day. “To define the length of a ‘night watch’ at the summer solstice, one had to pour two mana of water into a cylindrical clepsydra; its emptying indicated the end of the watch. One-sixth of a mana had to be added each succeeding half-month. At equinox, three mana had to be emptied in order to correspond to one watch, and four mana were emptied for each watch of the winter solstitial night.”

In China, as well as throughout eastern Asia, water clocks were very important in the study of astronomy and astrology. The oldest reference dates the use of the water-clock in China to the 6th century BC.

Huan Tan (40 BC – AD 30), a Secretary at the Court in charge of clepsydrae, wrote that he had to compare clepsydrae with sundials because of how temperature and humidity affected their accuracy, demonstrating that the effects of evaporation, as well as of temperature on the speed at which water flows, were known at this time.[17] In 976, Zhang Sixun addressed the problem of the water in clepsydrae freezing in cold weather by using liquid mercury instead. Again, instead of using water, the early Ming Dynasty engineer Zhan Xiyuan (c. 1360-1380) created a sand-driven wheel clock, improved upon by Zhou Shuxue (c. 1530-1558).[19]

In both Greek and Roman times, a commonly used water clock was the simple outflow clepsydra. This small earthenware vessel had a hole in its side near the base.

This type of clepsydra was used in courts, in the manner of a stop-clock, to allocate fixed periods of time to speakers: the greater the crime, the longer the period an advocate could argue his client’s case. For fairly minor offences, the vessel was partially filled with water to last about a 20 minute period of time. In important cases, for instance, when a person’s life was at stake, the vessel was fully filled. These devices gave rise to the expression “Your time has run out”. If proceedings were interrupted for any reason, such as to examine documents, the hole in the clepsydra was stopped with wax until the speaker was able to resume his pleading.

There is an interesting legend presumably about a water clock, involving the Indian mathematician and astrologer Bhaskaracharya (1114-1185) and his daughter Lilavati, after whom was named his book on arithmetic. According to a Persian translation, when Lilavati became of marriageable age, Bhaskaracharya cast her horoscope to determine the most propitious day and hour for her wedding to take place. The signs told him that if she was not married at a particular place at a particular time, the bridegroom would die shortly after the wedding. To prevent this, Bhaskaracharya made a small hole in the bottom of a cup which he then put into a jug of water. He had calculated that the cup would sink to the bottom at the appropriate hour for the wedding. Though he warned his daughter not to disturb this arrangement, Lilavati’s curiosity led her to lean over the device, and in doing so, a pearl fell off her garments and blocked the hole in the cup. The cup never sank and poor Lilavati was not able to be married. Her father wrote for her a Mathematics manual, which was supposed to console her and to keep her occupied as she studied its contents.

In the medieval Islamic world (632-1280), the use of water clocks has its roots from Archimedes during the rise of Alexandria in Egypt and continues on through Byzantium. The first water clocks to employ complex segmental and epicyclic gearing was invented by the Arab engineer Ibn Khalaf al-Muradi in Islamic Iberia circa 1000. His water clocks were driven by water wheels.

The water clocks by Al-Jazari, however, are credited for going “well beyond anything” that had preceded them. The most sophisticated water-powered astronomical clock was Al-Jazari’s castle clock, considered by some to be an early example of a programmable analog computer, in 1206. It was a complex device that was about 11 feet (3.4 m) high, and had multiple functions alongside timekeeping. It included a display of the zodiac and the solar and lunar orbits, and a pointer in the shape of the crescent moon which traveled across the top of a gateway, moved by a hidden cart and causing automatic doors to open, each revealing a mannequin, every hour. It was possible to re-program the length of day and night everyday in order to account for the changing lengths of day and night throughout the year, and it also featured five musician automata who automatically play music when moved by levers operated by a hidden camshaft attached to a water wheel. Other components of the castle clock included a main reservoir with a float, a float chamber and flow regulator, plate and valve trough, two pulleys, crescent disc displaying the zodiac, and two falcon automata dropping balls into vases.

The final goal of the clockmakers’ art was to construct a clock showing the relative movements of the Sun, Moon and stars as accurately as possible. The underlying problem is that Sun (civil) time, lunar (tidal) time and star (sidereal) time are not integrally related to one another, and any small discrepancy in ratio soon builds up into an obvious error. The Moon rises on average some 50 minutes later each day, whilst the starry background appears to complete one turn in about 23 hours 56 minutes.

Adapted from various sources