Monday, March 30, 2020

John Dee - Walking a Fine Line

Dee's copy of Cardano's Libelli Quinque (thanks to RCP London for permission to post)
There were many fine lines that "my" three mathematicians (Cardano, Napier, and Dee) had to walk, due to the fact that the 16th century was a time of religious upheaval as well as a time when science and magic were not well-distinguished.  Astrology especially seemed to be valued or censured depending on the whim of a given magistrate or ruler on any given day.  And it is John Dee and his astrology that I will focus on in this post, though I could address the situations of all three here and also pull in religion, alchemy, and mathematics alongside astrology.

The book in the photo above was written by Cardano and owned by Dee, and it seems that Dee had this book as early as 1547 or 1548 when he was studying in Louvain in the Low Countries.  Dee worked through this book so diligently that there is almost no page that is unmarked.  Given what seem to be reworkings and corrections it may very well be that he was using this book to teach himself to do genitures (the horoscopes in the square format that you see in the image above).

Dee's father had worked hard at moving up in society both financially and in proximity to the court so that he could provide his son with an education and with connections.  The elder Dee's fortunes fell spectacularly in 1553 and left John without the inheritance he should have had to sustain him, but his reputation as a scholar and his connections did hold up and provide him with patronage from the monarch (at times).  A short recap from a previous post: King Henry VIII appointed John Dee as a Junior Founding Fellow of Trinity College, Cambridge.  Dee's tutor, John Cheke, from his time as a student at St. John's College had also been tutor to Prince Edward, and once Edward became king, Cheke was a close aide to the king.  Cheke brought John Dee into the upper echelons of the court where he was presented to the king.  Dee made a gift to the king of two astronomical works that he had written while in Louvain, and the king provided Dee a (small) patronage.
Looking from the Royal Observatory at Greenwich in 2016 to where Greenwich Palace would have stood in the 1500s.
Sadly, King Edward VI died in 1553 at the age of 15.  His older sister Mary (aka "Bloody Mary") ascended the throne.  Under her, in 1555, Dee was arrested for casting horoscopes of Mary, of her husband Philip, and of  her sister Princess Elizabeth.  He was charged with "calculating, conjuring, and witch-craft."  He was initially imprisoned at Hampton Court Palace (portions of which that date to the Tudor era are shown in the five pictures below).
Hampton Court Palace (2016)
Hampton Court Palace (2016)
Hampton Court Palace (2016)
Hampton Court Palace

Hampton Court Palace (2016)
The charge against Dee was increased to that of treason, and he was then sent on to the Tower of London for trial by the Privy Council.  Though I haven't been able to find details of exactly where he was held in Hampton Court or in the Tower or how he was transported, it makes sense that he could have been taken by boat down the Thames from Hampton Court to the Tower, perhaps even through Traitor's Gate.  Travel then was by river as much as possible, which was far easier and far safer than overland travel.
The Thames passing Hampton Court Palace (2016)

Traitor's Gate, Tower of London

Traitor's Gate, Tower of London

Traitor's Gate, Tower of London

Traitor's Gate, Tower of London

Tower of London
Dee eventually confessed  to whatever the Privy Council wanted to hear and was cleared of charges of treason, but he was then turned over the "Bloody" Edmund Bonner, Bishop of London to be tried to for his religious beliefs.  He was now imprisoned at Bonner's palace, which was located among the buttresses of the southwest side of St. Paul's Cathedral in London.  He may have been held in the palace's coal house.  Dee had been connected with Edward VI's protestant court, and to have been handed over to Bonner for religious questioning was a very dire situation indeed.  It was later written of Bonner by protestant author John Foxe:

"This cannibal in three years space three hundred martyrs slew
They were his food, he loved so blood, he spared none he knew."

St. Paul's Cathedral - different structure than in Dee's day but the same site
We don't know details of his questioning, what we do know is that Dee not only survived but, quite surprisingly, became closely attached to Bonner.  The next we know of Dee is that he has become ordained into the Catholic clergy and was then a chaplain at St. Paul's under Bonner, in a position to interrogate others and closely attached to Bonner's household.  Dee called Bonner his "singular friend" and remained committed to him even after Elizabeth had taken the throne and England was once again a Protestant nation, a time at which Bonner was stripped of his honors and held in Marshalsea Prison where he died. This association was to impact Dee the rest of his life and keep him from gaining appointments he might otherwise have had.

During his time of imprisonment, one book that Dee had with him was the Mathemalogium of Andreas Alexander.  Dee worked through this book meticulously, and obviously had time to do so, as his handwriting is much neater and easier to read than his writing in other books he owned.  At the end of the book he writes the date and mentions Reverend Father Edmund Bonner, Bishop of London as "my singular friend." (My thanks to the Royal College of Physicians in London for permission to post the following three pictures.)
Dee's Marginalia in Alexander's Mathemalogium - note "manicule" (pointing hand) on the left.
Last page of Dee's copy of Mathemalogium - with Bonner note
"singularis amici mei"
Despite having taken holy orders in the Catholic Church under Bonner, and despite having been arrested by Queen Mary for his astrological work, John Dee was appointed by Robert Dudley to use his astrological knowledge in order to select an auspicious date for Protestant Elizabeth's coronation.  (So what's up here?!  Is astrology OK or not? Is it science or is it sorcery?  You may be requested by the court to use it, or you may be arrested, perhaps executed for doing so!)  John Dee took on the task and set the date of January 15, 1559.  On that date, chosen astrologically by Dee, Elizabeth was crowned queen at Westminster Abbey.  Given her long and glorious reign, perhaps he was able to read the stars aright.
Westminster Abbey

Westminster Abbey

Westminster Abbey

Westminster Abbey
Dee was an adviser to Queen Elizabeth I.  He is credited with having coined the phrase "British Empire," and he was high in Elizabeth's favor.  But he never received an official position at court, which he was obviously holding out for, having been offered positions at the court of the French king and at the court of Holy Roman Emperor, Charles V.  She had promised to double the pension that her brother Edward had provided to Dee, but this never happened.  They were close enough that she visited him at his house at Mortlake (though never went inside) and that she called on him in questions of empire, navigation, alchemy, and signs in the heavens, and he may have done some spying for her during some of his travels on the continent.

One example of their interactions dates to 1577 when he was called upon to go to Windsor Castle in order to give advice about navigation and at which time he made the astonishing proposal that England should challenged Spain's claims to the New World.  One element of this is that Dee believed that King Arthur had had colonies in the New World, and therefore Elizabeth had a right to reclaim this lost British Empire.
Windsor Castle

Windsor Castle

Windsor Castle -  ER standing for Elizabeth Regina

Windsor Castle -  ER standing for Elizabeth Regina

Windsor Castle
But I need to bring this back around to his astrological work.  While in Windsor he was also expected to elucidate the meaning of a comet that was causing hysteria throughout Europe.  Those at court feared it might be an ill omen for the queen.   Elizabeth herself asked Dee to speak to her of it.  Though his words are not recorded, it is evident that he reassured her and encouraged her not to fear it.  After this conversation, though Elizabeth's courtiers warned her to look away from the comet, she looked directly at it, saying, "Iacta est alea" or "The die is cast."  It may be that Dee had not only told her that the comet did not bode harm to her but rather was an omen of her rise among the rulers of Europe.

Though Queen Elizabeth I provided gifts to Dee from time to time, she never did appoint him to an official position at court nor provide him the pension she had promised.  Despite the fact that astrology and alchemy were standard practices at the time, and despite the fact that Elizabeth herself dabbled in alchemy and requested astrologically-based advice from Dee, it seems Dee ended up a bit too far to the "occult" side of the fine line he was walking - especially once he began to practice "angel magic" and took on as his scryer Edward Kelley.  Because of his increasingly dark reputation in later life (whether deserved or not) Elizabeth found it necessary to distance herself from Dee, and this great scholar, once renowned not only in England but throughout Europe, ended up dying in poverty and obscurity.

Saturday, March 28, 2020

Modern Day Math

I'm going to take a quick jump out of the 16th century and into the 21st century for this math history blog post.  While in London to study John Dee, I had a landmark in mind that I really wanted to see that has nothing to do with Dee (although now that I'm writing this I realize there may be a tie in, but more on that later).  The landmark I was interested in is 20 Fenchurch Street, also known as the Walkie-Talkie Building, which is the sky-scraper to the right on the pictures above and below.
I became interested in this building while doing a teaching observation in the classroom one of my colleagues.  The topic being introduced that day related to foci of conic sections.  Being the great teacher that she is, she began the class by sharing some engaging real-life examples with her students - one of them being this building and it's properties.  So  .  .  .  other than the fact that it's pretty cool looking, what's so interesting about this building?  And what does it have to do with math?
A curved glass surface can reflect the sun's rays in such a way that they are focused on a point and thus concentrated.  And that is what happened with this building.  The focus was at or near ground level at a nearby street, and the concentrated rays resulted in temperatures at that spot of up to 205 degrees Fahrenheit.  Before the parking areas were blocked off with orange cones, a Jaguar was damaged: its side-view mirror being melted by the heat, and a van was damaged: the plastic of the dashboard becoming melted, as well as a bottle that was inside ending up basically baked.  Tiles on a storefront in that area were baked to the point of cracking off, and a carpet inside a nearby store started to burn and smoke.  As news of this "heat-ray" spread, people turned up with frying pans and were able to fry eggs out on the sidewalk here.
As far as I know, this building doesn't have the shape of a specific conic section that is studied in the classroom.  If it had -- for instance, it if were a paraboloid -- the heat intensity at the focus would have been even higher.
I say I've jumped to the 21st century out of my 16th-century posts, but such properties of curved glass or mirrors were actually known even in ancient times.  Archimedes used this idea to create his famous "burning mirrors" as a weapon of war to protect Syracuse from the invading Roman troops.  Leonardo da Vinci (whom Girolamo Cardano knew) sketched such mirrors as well.  And one of "my mathematicians," John Napier wrote of plans for creating such a device at a time when a second Spanish Aramada attack on England and Scotland was feared.
If this has been known about for so long, why did the architect design the building in such a way?  Was he not aware of the implications?  Well, actually he was aware of this, but he also knew that the sun would only be in the proper position for such concentrations of its rays to take place for 2 to 3 weeks of the year and then only for a couple of hours per day during those weeks.  From what I understand, he was also counting on London's notoriously cloudy, foggy, rainy weather to keep this from being an issue.  (I've heard he's blaming global warming, but that may just be a rumor.)   Responsibility for the issues I've mentioned above has been taken, and those whose vehicles were damaged were reimbursed for repairs.
If you are reading this and have a great deal of familiarity with the building you may have noticed something about the pictures I've posted above that is bothering you.  I went on this photo-jaunt not long after arriving in London, and I was not yet oriented to directions here that early on in my trip.  As some of you may have noticed, I actually ended up on the wrong side, the north side, which is where all of the pictures above (except the first two) are taken.  In my defense, I think my mistake is understandable, not only because of my lack of orientation to the city but because if you look at the two pictures at the top of this post, this building seems to be concave in only one direction.  Because what I could see of the building showed it to be concave on the side I was on I thought I was in the right place.  But then I walked a bit further and noticed that it is actually concave on both sides.  It is more concave to the south, and, of course the south is the side where the sun is going to be more of a problem.  The four pictures below show the south side of the building.  If the glass looks a bit different it's because they have now fixed the issue by installing aluminum (or, as the British would say, "aluminium") fins.  Problem solved!

These two pictures (just above and just below) were taken from the Tower of London.  This city has quite a mix of the old and the new, which I find very enjoyable.
I've included two YouTube videos on this topic below.  The first is just under 2 minutes long, and the second is just over 4 minutes long.  I wanted to share visuals of some of the damage that was done, along with some additional explanation.

Wednesday, March 25, 2020

John Dee - Early Life

Tower of London
John Dee was born in the Tower Ward of London on July 13, 1527 to Roland Dee and Jane Wilde Dee.  John's father Roland was in the textile business, and his mother had an inheritance from her father, William Wilde of Milton-next-Gravesend in Kent.  John was born into a world that was being shaken by unprecedented change:

1492 Christopher Columbus discovers the "New World"
1514 Copernicus drafts (though doesn't yet publish) his heliocentric model of the universe
1517 Martin Luther's 95 Theses set in motion the Protestant Reformation
1519-1522 First circumnavigation of the globe (Magellan-Elcano Expedition)
1527 King Henry VIII begins to seek annulment from Katherine of Aragon, leading eventually to England's break with Rome.

All of these events shaped the world into which John Dee was born and hence the course of his life.
The White Tower, built by William the Conqueror in the early 1080s
John Dee was baptized into the Roman Catholic faith at the church of St. Dunstan's in the East, which at the time would have been an imposing parish church, richly decorated by the members of the wealthy guilds in that area of London.  Now it is a ruin, but it has been preserved by the city of London and now serves as a park, as shown in the five pictures below.
The namesake of the church, St. Dunstan, lived from 909 to 988 and was an abbot of Glastonbury, a bishop of London, and an archbishop of Canterbury.  He was later canonized and was considered a patron saint of goldsmiths and, thus, alchemists.  Given Dee's later associations with Arthurian lore (which involves Glastonbury) and with alchemy, it seems somehow appropriate that the church in which he was baptized and raised was named for this particular saint.
 The area of London in which John Dee grew up was a busy center of commerce.  The quays near the Billingsgate Docks bustled with ships bringing goods into the capital city.  Nearby streets were Cheapside, the thoroughfare for London's main market, known as a "cheap," and Lombard Street named for the northern Italian merchants who had settled there in the twelfth century.   Dee's father was a mercer, and the family was of middling income, but Roland worked hard to improve his lot in order to be able to provide connections and an education for his son.  Eventually Roland Dee became a "gentleman sewer" to the king (which doesn't necessarily mean he sewed the king's clothing, but he was probably involved with buying and maintaining fabrics for the king's palaces and garments).  This put Roland into contact with the king, and thus in position for reward for good services.  In 1544, King Henry VIII appointed Roland Dee to the position of "Packer to the Strangers" - a position in which he assessed customs on exports by foreigners and charged fees for packing them.  By 1541, Roland Dee was one of the wealthiest merchants in St. Dunstan's.  The rise in the Dee fortunes allowed Roland to provide his son John with an education.  After his grammar school training, John Dee entered St. John's College, Cambridge in 1542.
The pictures above and below are of St. John's College as it looked in 2016 on my first sabbatical.  It would have looked different in Dee's time.  It was a small college then and had only been founded 30 years previously.  Dee was tutored by John Cheke, one of the foremost teachers of the day and the first Regius Professor of Greek at Cambridge.  Cheke was also a tutor to Prince Edward and Princess Elizabeth, both future monarchs.
Dee was very serious about his education.  He claims to have studied 18 hours a day, allowing 4 hours for sleep and 2 hours for meals.  Dee showed aptitude for mathematics at an early age.  Certainly, he had learned 'vulgar' numbers of trade in his growing-up years due to his father's business.  Dee was drawn to the geometry of Euclid, but this was not looked on favorably at Cambridge.  In fact, a fellow of the college just before Dee's time there had, in his lectures on mathematics, dismissed such manual studies as geometry as being unfit for gentlemen and unable to provide them the judgement and eloquence that could be gained by literary studies. But Dee remained devoted to geometry, eventually writing the preface to the first English edition of Euclid (1570); this preface has now become famous in its own right.
First English Edition of Euclid's Elements as displayed at RCP London 2016
Dee learned something else at Cambridge that we today might not look favorably on.  It was something that was not part of the curriculum, and this was his occult work, particularly in alchemy which seems to have been a natural outgrowth of Aristotelian philosophy.  This study served him well in his later life consulting for Queen Elizabeth I who herself was a practitioner of alchemy.
De humani corporis fabrica libri septem by Vesalius (RCP London)
 For the reasons stated at the beginning of this post, the world had turned on its head just before the time of Dee's birth, and the changes just kept coming.  It was during Dee's student days at Cambridge that two of the most important books in the scientific revolution were published a book on human anatomy by Andreas Vesalius, De humani corporis fabrica libri septem, and the book on the cosmos that Copernicus had drafted so many years before (but wisely waited to have published after his death), De revolutionibus orbium coelestium.  The book of Vesalius opened up the inner spaces of the human body for study, and the book of Copernicus opened up the outer spaces of the cosmos for study.  These were both published in 1543, and a foundational book on algebra, Girolamo Cardano's Ars Magna was published two years later in 1545.
De humani corporis fabrica libri septem by Vesalius (RCP London)
John Dee's serious approach to his studies paid off, and in 1546 King Henry VIII appointed him as a Junior Founding Fellow of the newly opened Trinity College, Cambridge.  There Dee was a Reader in Greek and also taught logic and sophistry.
Above the Great Gate is Trinity's founder, Henry VIII, with a rather interesting scepter.

Trinity College, Cambridge, Great Court (2016)
The college, of course, looks different now than it would have in Dee's day.  For example, the chapel, which is the building containing the clock, was not finished until 1567, which is during Dee's lifetime but after his time as a fellow there.  The fountain in the center was built in the early years of the 17th century.  A building that Dee would have been familiar with is that of the chapel of King's College, Cambridge, which was built between 1446 and 1515.  King's College is just to the south of Trinity, and St. John's is just to the north.  The chapel was begun by Henry VI of the House of Lancaster, but there is much in the details of the chapel that relate to the Tudor Dynasty that Dee is closely associated with.

Do you see the intertwined H and A in the picture below?  This was carved at the time of Henry VIII's wedding to Anne Boleyn and is part of the ceiling just below the organ.
The Tudor Rose also makes and appearance in many places inside and outside the chapel.

And so, with some digressions and tangents, I give you the early life of John Dee and the world that he was born into.  Future posts will trace more of the course of his life.