The Wheel of Fortune

by Nicholas Mee on November 7, 2017

We never stray far from devices that chop up our days into hours, minutes and seconds. We are now all synchronized and no-one is out of step with the rest of the world. It is difficult to imagine how different life must have been when days came and went and the passage of time was apparent only in the motions of sun, moon and stars.

It seems natural to us that a day is composed of 24 equal hours, but before the invention of the clock the hours of daylight were usually divided into 12 hours, so that hours of summer were longer than hours of winter.

The earliest reasonably accurate timekeepers were clepsydra or water clocks, which were invented at least 2,500 years ago. Clepsydra remained in use in the cathedrals and monasteries of medieval Europe. They were often attached to devices that would strike an alarm bell to call the monks to prayer at appropriate times and this is the origin of the word clock—it derives from the French cloche, meaning bell. Clepsydra were only superseded with the invention of the mechanical clock. Plenty of water is available in England, but it is often not the best place for reading a sundial and this could be one reason why mechanical clocks were first constructed there.

None of the earliest clocks have survived to modern times, but we have a good idea when they were first constructed.

A Holywood Superstar

Diagram showing an eclipse of the moon from De Sphaera Mundi.

John of Holywood was one of the stars of 13th century astronomy. Johannes de Sacrobosco, as he was known to his learned contemporaries, was an Englishman who taught in Paris and wrote the most influential astronomy text of the age De Sphaera Mundi (On the Spherical World).

De Sphaera Mundi is a brief account of the medieval universe summarising all that was known of astronomy. For several centuries it was recommended reading for all university students.  Sacrobosco placed the Earth at the centre of the Cosmos and discussed the motion of the sun and planets, the length of the year, the inclination of the Earth’s axis, the size of the Earth and its division into arctic, temperate and tropical zones, even the reasons for eclipses of the sun and moon.

Robert the Englishman taught at the University of Montpellier in France where he wrote a commentary on De Sphaera Mundi that gives us a clue to when the mechanical clock was invented. Writing in 1271 Robert says:

Nor is it possible for any clock to follow the judgement of Astronomy with complete accuracy. Yet clock makers are trying to make a wheel that will complete one revolution for every one of the equinoctial circle, but they cannot perfect their work.

In other words, clock makers were trying to construct a mechanical device that would rotate in time with the passage of the sun and stars across the sky.

Tick Tock

Robert tells us that in 1271 astronomers were trying (but failing) to construct a mechanical clock. They were missing one crucial component—the escapement. This is a ratchet with interlocking teeth that swings back and forth at a regular pace allowing the gradual release of energy stored in a spring or suspended weight in small uniform steps. It is the escapement that produces the characteristic tick tock of a clock.

Dunstable Priory in the county of Bedfordshire, about 30 miles (50 kilometres) north of London. Credit: Wikimedia – John Armagh.

The problem was soon solved, however, as the earliest reference to the construction of a fully functional mechanical clock is in the Annals of Dunstable Priory for the year 1283. We can, therefore, pin down the invention of the clock almost to within a decade.

The new technology spread rapidly to other important towns and cities in southern England. Within a few years there are reports of clocks in Exeter Cathedral, Old St Paul’s in London, Merton College, Oxford, Norwich Cathedral, Ely Abbey and Canterbury Cathedral, and in subsequent decades they are found in the cathedrals of France and Italy.

Documents from Norwich Cathedral dating to 1322-1325 record the construction of a remarkable astronomical clock by master clockmaker Roger de Stoke. Costing the huge sum of £52 9s 6d, it would have been a mechanical marvel with an elaborate astronomical dial decorated with gilded sun and moon, figures representing the days of the month, and an automaton procession of fifty-nine chorister monks as its crowning glory. Unfortunately, it was destroyed by fire in the 17th century.

The Divine Comedy

The Divine Comedy of Dante Alighieri was written between 1308 and 1320. Dante is shown here with a copy of his epic poem in a fresco by Michelino. Dante’s city Florence appears on the right, while to the left sinners pass downwards to Hell; the seven-terraced Mount Purgatory rises in the background and the spheres of Heaven revolve overhead.

Cantos X and XXIV of Paradise, the third part of the Divine Comedy, contain what may be the earliest literary references to mechanical clocks. In Canto XXIV Dante writes:

So Beatrice; and those elated spirits
Formed themselves in spheres around fixed poles,
Flashing out like comets while they whirled.

And as wheels turn within the works of clocks,
So that the largest seems, to the observer,
To stand still while the smallest seems to fly,

Just so those singing rings, to different measures
Dancing in swift circles and in slow,
Enabled me to judge their wealth of joy.

(trans. James Finn Cotter)

Richard of Wallingford

The astronomer John North made a remarkable discovery in 1965 in the Bodleian Library in Oxford. He found a book written in 1327 describing the design of a mechanical clock—Richard of Wallingford’s Tractatus Horologii Astronomici.

Richard of Wallingford was a blacksmith’s son, born in the year 1292 in the small, but prosperous town of Wallingford. Richard would study at nearby Oxford where he may have been a fellow of Merton College, famous during this period for the Merton School of mathematicians, known also as the Oxford Calculators. Richard constructed various devices for taking astronomical measurements and performing calculations and wrote about astronomy, astrology, trigonometry and his design for a mechanical clock.

In 1327, Richard was elected Abbot of St Albans. He is depicted as a holy geometer with set square and compasses in the 14th century History of the Abbots of St Albans. A close look at Richard’s face shows that it is covered in blemishes. He was described rather uncharitably by his contemporaries as ‘so sorely afflicted with leprosy that he was unable to live the monastic life with others without causing offence’, although he probably suffered from scrofula or king’s evil rather than leprosy.

Richard was a divisive leader who struggled to contain rebellions by disgruntled monks and revolts from local peasants. He believed the abbey needed a sophisticated mechanical clock based on his design, but constructing the clock was very expensive. Even King Edward III was critical when visiting the abbey. Richard told the king there would be monks aplenty to repair the buildings when he was gone, but none could complete his clock.

Not long afterwards, in 1334, the abbot’s bedchamber was struck by lightning and the building burst into flames. This was rather an ominous portent in a superstitious age. Richard’s health declined rapidly following the lightning strike and he was never free from pain again. Having already lost the sight in one eye, as the disease progressed he lost the ability to speak. Two years later, aged 44, he died.

The clock remained incomplete, but Richard’s belief that no-one else could finish his work proved unfounded. Although the next abbot did no further work on the clock, it was completed during the abbacy of Thomas de la Mare who hired the clockmaker Laurence de Stoke to finish the task with the assistance of the monk William Walsham.

The ironwork clock was a mechanical model of the heavens with a face showing the stars of the night sky. The orb of the sun completed one circuit of the face each day, ringing a bell on the hour, and indicating the time on a numbered dial. The moon’s orb was painted half black half white and rotated gradually to model the phases of the moon. The clock also showed the tides at London Bridge, the closest port to St Albans, and may even have predicted eclipses. A revolving wheel of fortune completed the mechanism, which is perhaps appropriate considering the mixed fortunes of Richard’s life.

Unfortunately, the clock no longer exists. It was probably destroyed in the 16th century during Henry VIII’s dissolution of the monasteries.

Rediscovery and Reconstruction

Following his discovery of Richard of Wallingford’s Tractatus Horologii Astronomici in the Bodleian Library, John North translated the manuscript and his interpretation of Richard’s design is the basis for replica clocks including one built in 1988 that is on view today in St Alban’s Cathedral.

Reconstruction of Richard of Wallingford’s clock in St Albans Cathedral.


Further Information

On the Spherical World by John of Holywood:

John North gives his account of Richard of Wallingford’s clock in God’s Clockmaker: Richard of Wallingford and the Invention of Time.


Golden Spacequakes

by Nicholas Mee on October 24, 2017

A reproduction of Zhang Heng’s seismoscope

Long ago in the year 132 AD the Imperial Astronomer Zhang Heng designed an earthquake detector. The History of the Later Han Dynasty reports that his ingenious invention would alert the Chinese emperor to catastrophic seismic events in distant regions of the empire. Zhang Heng’s seismoscope is described as a bronze vessel two metres in diameter with eight dragon heads mounted around its circumference. A reconstruction is shown here. Each dragon clasps a small metal ball in its teeth, while the open mouth of a bronze toad gapes wide below. A faint tremor from a distant earthquake causes a rod within the vessel to overbalance pulling a lever that opens the mouth of the dragon facing towards the earthquake. Its ball is released and falls clanging into the waiting mouth of a toad.

From Earthquakes to Spacequakes

Fast forward almost two thousand years and gravitational wave observatories are routinely detecting spacequakes in far flung regions of the universe. In August the two LIGO detectors in the United States were joined by the newly upgraded VIRGO detector near Pisa in Italy. By determining the arrival time of faint cosmic rumbles at each detector with split second accuracy it is now possible to get a good fix on the direction of the source of the gravitational ripples. This is valuable information as it enables astronomers to seek any visible sign of the catastrophic event that produced the blast of gravitational waves.

On 17 August the three instruments captured an unmistakable signal, quite different to the four previous events detected by LIGO. It was catalogued as GW170817. Just 1.7 seconds later NASA’s Fermi Gamma-ray Space Telescope detected a short gamma ray burst emanating from the same region of sky and telescopes around the world were marshalled to locate the glowing embers of the event that produced the gamma radiation. Within twelve hours the source of the gamma ray burst was tracked down.

Left: Overexposed image of the galaxy NGC 4993 before the kilonova explosion. Right: The arrow indicates the kilonova. Credit: NASA.

For the first time we have an optical counterpart for a gravitational wave event. It is still being studied, but it is already one of the most observed events in the history of astronomy. The gravitational waves and short gamma ray burst were generated by a kilonova 130 million light years away in a galaxy known as NGC 4993. Kilonovae form a new class of stellar explosions intermediate between novae and supernovae. They are around one thousand times brighter than a nova and this is the reason for their name. Nonetheless, they are just one thousandth to one hundredth of the luminosity of a supernova. We now know a kilonova is the spectacular explosion produced when a pair of neutron stars collide and merge.

Neutron Star Collisions

Neutron stars are like gigantic atomic nuclei—the entire mass of a star is compressed to nuclear densities. They are among the strangest objects in the cosmos. Typically, one and a half solar masses is packed into a sphere just 20 kilometres in diameter—the size of a major city. Tiny by cosmic standards, but incredibly dense, the mass of each teaspoonful of neutron star is well over a billion tonnes. Try stirring that into your cup of tea.

Artist’s impression of merging neutron stars. Credit: NASA/AEI/ZIB/M Koppitz and L Rezzolla.

Russell Hulse and Joseph Taylor were the first to discover a binary neutron star system in 1974. There is more about this remarkable system in the post: Pan Galactic Gargle Blaster! The neutron stars whose collision generated the GW170817 event are presumed to have had a similar history. Over the course of millions of years they would have gradually spiralled together as they lost energy due to the emission of gravitational waves. The amplitude of these waves was too small to detect until they came almost within touching distance 100 seconds before their fatal encounter.

Neutron stars are composed of an exotic form of matter consisting largely of neutrons. Such material only exists within the extreme gravitational stranglehold of a neutron star. Any fragment smashed free in a collision would be extremely unstable and undergo immediate radioactive decay with dramatic and violent consequences. Neutrons would transform into protons with the emission of electrons and neutrinos. Neutron-rich heavy nuclei would form and rapidly decay into more stable lighter nuclei in a blaze of gamma radiation. This is the origin of the short gamma ray burst detected by the Fermi satellite. The ongoing radioactive decay of the material emitted in the merger produces the visible afterglow of the kilonova. The neutron stars that merged in the GW170817 event are believed to have undergone the ultimate collapse and formed a black hole.

Artist’s conception of a kilonova. Credit: NASA.

The Birth of Heavy Metal

Neutron star collisions might answer one of the mysteries of the cosmos. How were heavyweight atoms such as platinum and gold created?

Massive stars generate energy through a sequence of nuclear fusion processes that ultimately transform the core of the star into iron and nickel. Eventually, no further energy can be generated by fusion reactions and the core collapses triggering the detonation of the star as a supernova. The exploding core of iron and nickel is bathed in a vast flux of high energy protons and neutrons that was long thought to explain the origin of heavier nuclei all the way up to uranium and plutonium. However, recent computer simulations suggest the extreme conditions necessary for nucleosynthesis may not last long enough for the creation of elements beyond silver and its neighbours in the Periodic Table. This presents us with a conundrum: Where do all the heavy elements come from?

David Eichler, Mario Livio, Tsvi Piran and David Schramms suggested in 1989 that neutron star collisions might provide an alternative process in which heavy elements are synthesised. This attracted little support at the time as it was assumed that such events would be too rare to account for the quantities of gold, uranium and other elements that we find in the galaxy.

Tutankhamun’s mask

Interstellar Goldrush

Computer models of neutron star mergers, such as the one that generated the GW170817 event, suggest that around 20,000 times the mass of the Earth could be ejected in these events. This material would be blasted out at at about one fifth of the speed of light and dispersed far and wide throughout the galaxy. It would be in the form of heavy elements including about ten parts per million of gold nuclei, so the total amount of gold dust created in a kilonova would be about one fifth of the mass of the Earth. Observations of the recent kilonova suggest that the computer models are correct.

But are these events frequent enough to account for the observed amounts of heavy elements?

Tightening the Net

The question is whether heavy elements are produced in relatively small quantities in unusual events—supernovae—or whether they are produced in extremely large quantities in very rare events—neutron star collisions.

Support for the latter possibility comes from a recently discovered dwarf galaxy known as Reticulum II. Discovered in 2015 and located in the obscure southern constellation of Reticulum or the Little Net, this galaxy is a close companion of the Milky Way, just 97,000 light-years away. Most dwarf galaxies contain little, if any, heavy elements. By contrast, there are significant amounts of the heavy elements in the stars and interstellar gas of Reticulum II.

Supernova explosions are unusual events. It is estimated that one occurs in the Milky Way galaxy every 30 years or so, but most are hidden from us by interstellar dust clouds. In even the feeblest dwarf galaxy, we would expect a supernova at least once every 100,000 years, so if the heavy elements are produced in supernovae, over the 13.8 billion year history of the universe the heavy elements would accumulate even in dwarf galaxies. Neutron star collision could be so rare, however, that most dwarf galaxies have never hosted even a single such event. It looks as though the Reticulum II dwarf galaxy is the winner of the neutron star collision lottery. The heavy elements that it contains were probably produced in a single neutron star collision. This provides important evidence that long ago most of the heavy elements in our environment were also produced in this way.

The origin of each element of the Periodic Table. Credit: Wikimedia – based on data by Jennifer Johnson at Ohio State University.

The above chart indicates the origin of each element in the Periodic Table according to modern astrophysics. (The chart is slightly misleading in that it only shows the final process in which a particular nucleus was created. Most nuclei are created following a sequence of possibly very different processes. For instance, boron nuclei are created when cosmic rays hit carbon nuclei and dislodge a proton, but the carbon nucleus would have been created in a star or supernova explosion.)


Further Information

For some spectacular computer simulations of neutron star collisions take a look at:

There is more about LIGO and the detection of gravitational waves in the post: Cosmic Ripples.

There is more about gamma ray bursts in the post: Pan Galactic Gargle Blaster!


The Path to Immortality

October 11, 2017

It is 1697, we enter a dimly lit tavern in one of the less inviting districts of London. Huddled in the shadows we see a man in a loose cloak sitting expectantly with his accomplice at a small table. He has long grey hair, a sharp nose and a determined look in his piercing eyes. […]

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The Googolplex

October 3, 2017

One million is a big number. To really comprehend numbers such as this we need some sort of scale. So, how big is a million? And what about even bigger numbers? Millions, billions, even trillions are thrown around in everyday conversation today without much thought about the differences in size of these huge numbers. Typically there are about […]

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The Harmony of the World

October 3, 2017

Johannes Kepler transformed astronomy in the early years of the 17th century. His revolution was built on accurate observations of the planets compiled over many years by Tycho Brahe. The New Astronomy Kepler published his findings in 1609 in a book called Astronomia Nova (The New Astronomy), which includes two laws describing how planets travel around […]

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Sieving for Numbers

October 1, 2017

Alexander’s general Ptolemy I Soter became the first pharaoh of the Ptolemaic dynasty of Egypt following Alexander’s death in 323 BC. Ptolemy founded the famous Library of Alexandria. Dedicated to the muses, the nine goddesses of the arts, it was the original museum. During the Ptolomaic era Alexandria would replace Athens as the leading cultural centre in […]

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The Oracle

October 1, 2017

Plato believed we have an innate knowledge of geometry and much else besides. While this might be true up to a point, his argument is not totally convincing. Plato presents the idea in his dialogue The Meno, which takes the form of a discussion between the philosopher Socrates and a slave-owning aristocrat called Meno. Socrates demonstrates […]

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The Laws of Thought

September 30, 2017

George Boole was the son of a cobbler. Born in 1815 in Lincoln, he was largely self-taught, with little more than a primary school education. Despite these humble beginnings, Boole would become one of the leading mathematicians of his day. He founded a school in Waddington near Lincoln when just 19. Soon he was exchanging letters […]

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The Alchemists’ Dream

September 23, 2017

The alchemists’ dream was to understand and control the structure of matter and to turn base metal into gold. Modern physicists are equally curious, but hopefully rather less avaricious. Four Forces The 20th century saw the development of machines to delve deep into the structure of matter. John Cockcroft and Ernest Walton constructed the first particle accelerator […]

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Alchemical Furnaces of the Cosmos

September 21, 2017

Arthur Eddington was raised in a Quaker family in northern England. After studying in Manchester, he won a scholarship to Cambridge University and by the 1920s he established himself as the world’s leading astrophysicist. Eddington developed models of the structure and evolution of stars that form the foundations of the subject even today. The key […]

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