Cardano's Consoltation

TRIGGER WARNING: This post mentions Hamlet's To Be or Not To Be soliloquy and the dark themes contained therein. If you are currently feeling life to be a "sea of troubles," you may want to skip this post and find a different one to read. Wishing you well, dear reader!

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

 

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

On the title page of Cardano's Three Books of Consolation English'd is printed the statement, "Of great use in these times." This is the 1683 English translation of the 1542 original, which had also been translated into English in 1573, and which I read in 2026, and I would say it is of great use in all these times.

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Reading this book by Cardano put me in mind of the poem If Still Your Orchards Bear by Edna St. Vincent Millay that ends with the stanza

I think you will have need of tears;

I think they will not flow;

Supposing in ten thousand years

Men ache, as they do now.

Both her poem and this book are testimonie to me that the experience of being human doesn't change - not with decades and not with centuries - no matter the rise and fall of empires or advances in technology. We still feel joy and sorrow, still experience loss and gain, still feel hope and despair. We still wonder about the purpose of life and what, if anything, comes after it.

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

This small volume consists of three "books," each of which is broken up into chapters. At the head of each chapter is a summary of what the chapter is about. For example, in the picture below, we see that in chapter 1 of book 1 we will find: Good discourses a necessary remedy against all misfortunes. Opinion makes many things good or evil.

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Though Cardano does cover many areas of human experience, I'm moving here into a deep diver into his reflections on death - hence the "trigger warning" at the beginning of this post. In chapter 1 of book 2 some potentially familiar sentiments. As you read them, see if they remind you of anything else you've come across elsewhere in literature:

I have felt more grief than pleasure in this world. Seeing then this love of life availeth nothing, nay tho it were desirable, tis better to cast off this burden of cares . . .

 . . . what can Death be better compared to than a Dream?

Death may be fitly compared to a sound sleep.

What is our life by continual toil, perpetually attended with labor, suspicious, and dangers . . .

If what comes to mind is Hamlet's To Be or Not to Be soliloquy, you are not alone. In that soliloquy, Shakespeare speaks through Hamlet of the "sea of troubles" and the "slings and arrows of outrageous fortune" that we experience in life and of the "heartaches and the thousand natural shocks that flesh is heir to." He ponders further: "To die - to sleep; to sleep, perhance to dream."

While there is currently no scholarship providing a direct link between Shakespeare and Cardano's book, this book has been included by some academics in lists of potential influences on Shakespeare - as one of the widely circulating humanist texts that drew on stoic philosophy and belonged to the tradition of books of consolation.

I work hard to keep my posts as factual as possible, but I hope I can be allowed a small, reasonable flight of fancy on occasion - fully acknowledged as such. I like to think that there IS a link here. Here is some of my thinking on the matter:

Girolamo Cardano and John Dee had met - Cardano's writing did circulate widely - Dee was influential in Elizabethan circles - and Shakespeare and Dee (though decades apart in age) both moved in those Elizabethan circles - I, personally, like to think that the book Shakespeare has Hamlet holding in Act 2, Scene 2, when Polonius walks in and asks, "What do you read, my lord?" is Cardano's book. This scene is followed not long after by Act 3, Scene 1 where Hamlet speaks the To Be or Not To Be soliloquy.

The Globe Theatre, London

The Globe Theatre, London

Again, just to be clear, there is no PROOF that this is THE book that Hamlet is holding (though there's no evidence against it either), but when I read or see Hamlet, I think of it being Cardano's book in his hands. Though not proven (and probably not provable), it is certainly plausible.

Here are two further glimpses into Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9). These pages form the closest connection for me between Cardano's thoughts and Hamlet's speech.

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Cardan His Three Books of Consolation English'd (British Library Shelfmark 8405.a.9)

Well, the Hamlet connection became a rather lengthy side-trip from where I began. But I'll end by zooming out a bit once more. Cardano writes of so many things in this book. He touches on how without experiencing illness we cannot appreciate health, and without having experienced troubles, we cannot fully appreciate ease. He puts things in perspective. He addresses our appetites, writing, "whatsoever is profitable or necessary to any creature that is naturally desirable in which desires brute beasts (who are guided only by sense) do not transgress. Whereas man, who has most reason in his understanding has least in his actions, for [man] eats, drinks, and sleeps more than either conveniency or necessity require."

He addresses poverty and riches and our perspectives on them: "Should it come to pass now as it did in the time of Noah that all money, provisions, cattle, and other commodities were carried away in a universal Flood, I believe then no man would think himself injured by poverty. Why then dost thou complain having whereon to live? This plainly evidences 'tis not poverty but envy that molests thee."

I'll close out with some comparisons he makes - the last line of which made me laugh out loud.

“Perhaps thou wilt say I would have Pleasure without Pain: ‘Tis contrary to nature, for Joy is continually attended by Sorrow, Glory with Envy, Wisdom is not gotten without labor, Wealth is not obtain’d without care, Children are kept with trouble, Banqueting is attended by sickness, Ease with poverty, Power with envy, Quiet with weariness. Every man has something to complain of. Some be afflicted with Poverty, others want Children, this man is Sick, that man wants a Wife, and this man would be rid of his.”

Our dear mathematician Cardano had many thoughts on many subjects, and these are but some of them. If interested, and perhaps headed to London, here is a link to this item in the catalogue of the British Library.

Da Vinci and his Math Consultants: MILAN

Sforza Castle, Milan, Italy

Leonardo da Vinci worked for various patrons in various cities over the course of his life. One of these patrons was Ludovico Sforza, and one of these cities was Milan, where Sforza ruled as duke. The pictures above and below are of Sforza Castle.

Sforza Castle, Milan, Italy

Leonardo (1452-1519) first worked in Milan from 1482 to 1499 and then again from 1508 to 1513. And though his patron was Ludovico Sforza, he was free to take commissions from others while there. One of these was the painting The Virgin of the Rocks (the one that is now in the Louvre). 

Madonna of the Rocks, Leonardo da Vinci (Louvre)

Another commission was that of The Last Supper, which he painted for the monastery of Santa Maria della Grazie.

Leonardo da Vinci's Last Supper, Santa Maria della Grazie, Milan

Santa Maria della Grazie, Milan, Italy

Santa Maria della Grazie, Milan, Italy

Before moving on to Leonardo's mathematical consultants, I want to share one more of his works that is in Milan - one I had not heard of before traveling here. This one is found inside the Sforza Castle. It's in a room, or I should say, "IS the room" of Sala della Asse.

Salla della Asse, Castello Sforzezco, Milan, Italy

It's hard to make out, but this fresco on the walls and ceiling are of intertwining plants and trees and is intended to make the room seem to be an outdoor setting rather than an interior room. The intent was for it to look like a grove of mulberry trees. It doesn't help that my pictures were taken over and around barriers blocking the opening to the room which is undergoing renovations. The painting dates to about 1498.

Salla della Asse, Castello Sforzezco, Milan, Italy

Salla della Asse, Castello Sforzezco, Milan, Italy

While in Milan, Leonardo met mathematician Luca Pacioli. Pacioli had been invited to work in Milan by Duke Ludovico Sforza in 1497, but Leonard already know of Pacioli and had purchased his book Summa arithmetica in 1495 - one of the most expensive books in Leonardo's library. Pacioli became a geometry tutor and collaborator to Leonardo. The collaboration was extensive, and though they were forced to leave Milan in 1499 due to war with France, their paths did not separate until 1506.

Portrait of Luca Pacioli (attributed to Jacopo de' Barbara - source: Wikipedia - Public Domain)

Pacioli was born in Sansepolcro in the Republic of Florence in about 1447 (making him 5 years Leonardo's senior). As well as being a mathematician, he was also a Franciscan friar and is considered the father of accounting and bookkeeping. In the mid-1460s, Pacioli lived in Venice where he worked as a mathematics tutor. It was during this time that he wrote his first book, a book of arithmetic for the boys he was tutoring. About 10 years later, he moved to Perugia. He continued to work as a private tutor there until become the first chair of mathematics at the university there. One of Pacioli's books, Divina proportione (Divine proportion) was completed during his time in Milan (1498), and it was illustrated by Leonardo da Vinci. I don't know of any other mathematicians who can claim the honor of having one of their books illustrated by da Vinci!

Illustrations by Leonardo da Vinci, from Luca Pacioli's Divina proportione, 1509 edition (Public Domain - Wikipedia)

First printed illustration of a rhombicuboctahedron, Leonardo da Vinci, published in Divinina proportione (Public Domain - Wikipedia)

Another of Leonardo's mathematical consultants was Fazio Cardano, father of the more famous Girolamo Cardano. Fazio and Leonardo met early in Leonardo's time in Milan, and Fazio may have been Leonardo's first tutor in the sciences. We know that in 1490 Leonardo traveled from Milan to nearby Pavia where Fazio was professor of mathematics.

University of Pavia

Towers just outside the historic University of Pavia buildings

This trip resulted in Leonardo's famous Vitruvian Man, which he completed later back in Milan.

Vitruvian Man by Leonardo da Vinci (Public Domain - retrieved from Wikipedia)

One topic of conversation between Leonardo and Fazio was that of optics and perspective. Fazio had edited the first printed edition of a book the topic of optics, Perspectivo communis by John Peckham (1230-1292), which was the first printed book that included diagrams (beating out even Euclid's Elements for that distinction). Leonardo mentions Fazio Cardano in his notebooks many times, especially in the form of reminders to himself to ask for one or another book on proportions. 

Leonardo da Vinci's Last Supper, Santa Maria della Grazie, Milan

Circling back around to Leonardo's Last Supper, we see his use of perspective as the room in which the supper is being held recedes into the distance. The painting is on the wall of the refectory where the monks of the day would have eaten. The perspective of the painting would make it look as if the monks were joining the disciples in the Last Supper.

Leonardo da Vinci's Last Supper, Santa Maria della Grazie, Milan

Leonardo da Vinci's Last Supper, Santa Maria della Grazie, Milan

Young Girolamo Cardano, who would grow up to be one of the most prominent mathematicians of the 16th century, was used by his father Fazio as a bit of pack mule - having him carry his bags as Fazio went about his business. This included visits to Leonardo. As a teenager, Girolamo Cardano met Leonardo da Vinci and saw the Last Supper. 

Leonardo da Vinci's Last Supper, Santa Maria della Grazie, Milan

In one of my readings on Girolamo Cardano (and sadly, I can't remember which one) he comments that when he visited the Last Supper somewhat later in life that Leonardo's masterpiece was already disintegrating mere decades after he painted it. It is on Girolamo Cardano that my travels in northern Italy are focused, but it's pretty cool that I get to "meet" other folks along the way - other folks such as Pacioli, Fazio, and, not least, Leonardo da Vinci.

Oh, and before concluding, I should mention that a significant portion of Leonardo da Vinci's notes - the Codex Atlanticus - reside in Milan's Biblioteca Ambrosiana. Here you can find a room dedicated to this codex and with pages from it on display.

Biblioteca Ambrosiana, Milan

Biblioteca Ambrosiana, Milan

Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Detail of da Vinci notes from Codex Atlanticus, Biblioteca Ambrosiana, Milan

Just before getting to the room containin the codex, there is a room containing paintings by da Vinci and early copies of da Vinci works. Below are a couple of examples.

Biblioteca Ambrosiana, Milan

Biblioteca Ambrosiana, Milan

Girolamo Cardano: VENICE

In his 20s and early 30s, Girolamo Cardano lived in the Veneto (i.e. near Venice). He finished his medical degree in Padua, having studied first in Pavia until the university there was closed due to French invasion and war. After graduating from Padua with his medical degree (and for prejudicial reasons being denied a license by the College of Physicians in Milan), Cardano moved to the small town Piove di Sacco just east of Padua. He practiced medicine independently there. In his autobiography, he writes of his days in Sacco being the happiest of his life. 

There was at least one one not-so-happy event during this time, however. It involves a run-in with a Venetian senator.

Senate Hall, Doge's Palace, Venice

The ceiling of Senate Hall, Doge's Palace, Venice

Cardano was one of the greatest mathematical minds of his era. He also spent large chunks of his life in poverty and had to turn to gambling to make ends meet. Due to his mathematical skill, he did well at gambling. In fact, he was the first to make a study of probability as something that could be measured. He predated Pascal and Fermat by about 100 years on that, but he left his book in manuscript form and didn't publish. Anyway, back to the story. Cardano was gambling with a Venetian Senator - no one knows the senator's name for sure at this point* - nor where he lived, but senators were wealthy, so let's imagine the pallazo pictured below as representative of the senator's home - very imposing.

Door to Palazzo Van Axel

Palazzo Van Axel

As they played, Cardano was losing money. They continued the next day, and he lost the rest of his money. This was not normal for Cardano, given that he had an understanding of probability that others in his day did not have. Eventually he realize the cards were marked, and he struck out at the senator with a dagger, leaving a gash on his face. Despite having done this and despite the senator having two young bodyservants in the room, they kept on playing. Now that Cardano knew that the cards were marked, he began winning and recovered all the money (his own and that of the senator) - along with clothes and rings that he had lost the previous day. Wanting to make amends for having harmed the senator, he threw some of the money back and then escaped the house - fighting his way through the house-servants who were unable to use weapons. The senator, weighing what he had to gain or lose, having defrauded Cardano, ordered the door opened and Cardano let go.

Of the rest of the evening Cardano writes in his memoirs: 

"On that same day about eight o'clock in the evening, while I was doing my best to escape from the clutches of the police because I had offered violence to a Senator, and keeping meanwhile my weapons beneath my cloak, I suddenly slipped, deceived in the dark, and fell into a canal. I kept my presence of mind even as I plunged, threw out my right arm, and, grasping the gunwale of a passing boat, was rescued by the passengers. When I scrambled aboard the skiff, I discovered in it, to my surprise, the Senator with whom I had just gambled. He had the wounds on his face bound up with a dressing; yet he willingly enough brought me out a suit of garments such as sailors wear. Dressed in these clothes, I traveled with him as far as Padua."**

So, the "not-so-good" situation had a happy ending!

Having walked all around Venice the last 4 days, I can certainly see how he could have slipped. The walkways can be very narrow - or can dead-end unexpectedly into a canal - and some canals are edged in marble, which is very slippery.

In order to "walk in the same footsteps" or "sail the same waters" as Cardano, I took a gondola ride today. I imagine that his experience was much different than mine. For one thing, I wasn't soaking wet. For another, I'm sure the senator had a fancy gondola with an enclosure.

*In his uniquely wonderful novel, The Quantum Astrologer's Handbook, author Michael Brooks gives the Senator's name as Thomas Lezun. I believe this comes from an early biography of Cardano.

**Quote taken from Cardano's The Book of My Life, chapter 30, titled: "Perils, Accidents, and Manifold, Diverse, and Persistent Treacheries." The book is quite the read - very eccentric. It's a biography like what I would want to write about myself!

Girolamo Cardano in London

Frontispiece of Girolamo Cardano in the copy of Libelli Quinque owned by John Dee

Over the two years that I have been planning this math history sabbatical, I have been reading widely and deeply of Girolamo Cardano.  However, because I had to give up my planned time in Italy due to the COVID-19 pandemic, I can really only write this one post about Cardano rather than the 5 to 10 I had been planning on.  His life is SO INTERESTING that I find myself having to hold back very strongly right now from sharing all that I could about him because I yet hope to get to Italy some day and to be able to share about him bit-by-bit accompanied by pictures of locations relating to his life.

Though unable to travel in Italy, I was still able to study Cardano "on location" at least to some degree, as he did spend some time in England and does have a connection with John Dee whose life and work I was able to research to a greater extent during this abbreviated sabbatical.

And so, on to Cardano  .  .  .

Girolamo Cardano was famous throughout Europe as a physician and, in 1552, he was prevailed upon by the ailing Archbishop of St. Andrews, John Hamilton, to make the uncharacteristic move of traveling all the way to Scotland from his beloved Milan.  On his way home from Edinburgh Cardano spent time in London. Cardano was in London as a guest of the court of King Edward VI and was staying with Sir John Cheke in the area of Southwark.  

Southwark Cathedral, London

Southwark Cathedral, London

Courtiers wished Cardano's opinion on the king's health, but even more so wanted to know what Cardano saw in the stars with regard to the king's future, so Cardano was asked to draw up a horoscope of the king (which, as we have seen, can be a dangerous proposition). 

Southwark Cathedral, London

When Cardano was introduced to the king he was told what title to use, but, out of respect for the Pope, Cardano would not address the king as being defender of the faith and head of the church of England.  Because of these scruples Cardano received for his services only 100 pounds rather than the 500 to 1000 pounds he otherwise would have been paid.  Despite this, Cardano's audience with the king went well, both of them being impressed with the other.  The king asked about Cardano's writings and ideas, and Cardano wrote of Edward that he "was a wonderful boy who, I was told, had already learned seven languages.  He was as fluent in French and Latin as in his native tongue.  He was trained in logic and was extremely intelligent.  He was in his fifteenth year when I met him.  He asked me, speaking in Latin as beautifully and fluently as myself, `What new ideas does your book De Rerum Varietate contain?'"  Cardano, in his later writing in a commentary on Ptolemy, also expressed that Edward "was very open and most amiable" and that he was "so cheerful; he brought youth back to his teachers; he played the lute; he was interested in public affairs; and he was a free spirit  .  .  ."

The mid-sixteenth century was quite a time in England.  Edward's father, Henry VIII, had broken with Rome and gone through multiple wives in order to get a son to maintain the Tudor line.  Edward had two older sisters in the wings who could ascend the throne after him -- one Catholic and one Protestant.  Edward was young, only nine years old when he ascended to the throne.  According to his father's will, there was supposed to have been a Regency Council appointed for him, but somehow his uncle, Edward Seymour, became sole Lord Protector of the Realm, while his other uncle Thomas Seymour, who had married the last of Henry VIII's six wives, plotted and schemed in the background.  By the time of Cardano's visit both of these uncles had been beheaded, and the 1st Duke of Northumberland, John Dudley, whose father had been killed by the king's father, was leading the government.

If I were Cardano, I don't think I would have wanted to cast a horoscope of King Edward -- or anyone else at court for that matter!  As requested, however, Cardano did cast a horoscope for the king, and for whatever reason, through error or through expediency, he predicted a virtuous and wise reign along with a reasonably long life for Edward.  Sadly, by the next summer this brilliant and engaging young king was dead.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

But let's back up a bit and talk about other elements of Cardano's London sojourn.  While there Girolamo Cardano met John Dee, a man 26 years his junior.  Despite the age difference this visit isn't surprising given that Cardano was staying with Dee's former tutor, John Cheke, and that Cheke was closely connected with the court. Cheke had been a tutor of Prince Edward and had since been appointed Gentleman of the Privy Chamber and had served for some time as a Member of Parliament and was also, briefly, Secretary of State.  The meeting is also not surprising given Dee's familiarity with and appreciation of Cardano's work.

The pictures above and below are images from Dee's copy of Cardano's work Libelli Quinque.  From all of the marginalia and working and reworking of horoscopes it seems that Dee was using this book to teach himself how to cast horoscopes.  (I would like to have thought that Cardano may have given this book to Dee during their time together in London, but given all the work in it, it seems that Dee had this book four or five years earlier when he was studying in Louvain.)  In the picture above, you see Dee correcting or reworking Cardano's work seemingly in order to train himself, and in the picture below you see Dee doing his own work in the margin and then scratching it out and starting over.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

In the picture below you see a lot less crossing out than is the case two pictures above.  It may be that Dee was correcting a printing error here.  As you can imagine, printers of the time would have had a particularly hard time setting the type for this sort of work.  The placement of the information in each section of the square was important, so it may be that Dee was simply copying over the information to the correct position here.

Dee's copy of Cardano's Libelli Quinque (with thanks to RCP London for permission to post)

Cardano and Dee discussed many things in their time together -- among other topics, they discussed the magical properties of a gem that they were inspecting, and they also talked together of a perpetual motion machine.  Certainly they must have discussed astrology -- perhaps also mathematics.  If there were ever conversations in this world that I would like to have overheard, the conversations between these two men would certainly be near the top of my list!

Historical Plaque at Southwark Cathedral, London

In 1552, when Cardano was in London, the structure that is now Southwark Cathedral was present and had the role of a parish church at that time.  Though certainly there has been tremendous change to all of London in the last 468 years, including renovations or additions to this church, its location and at least some of its features would have been familiar to Cardano and Dee.  It is, after all, the oldest gothic church building in London.  Shakespeare, who was a parishioner here, was a close contemporary of theirs (and Shakespeare may have modeled the magician Prospero in his play The Tempest after John Dee).

Southward Cathedral, London

The pictures above and below were taken from the same spot, just looking in different directions.  Southwark Cathedral, above, is very close to the Thames, below.

Facing away from the cathedral and towards the Thames

The focus of this post is Cardano, but as I fear it will be at least a year before I can continue my travels, I want to point out that the waterfront below contains a quotation from Sir Walter Raleigh, "There are two things scarce matched in the universe, the sun in its heaven and the Thames upon the earth."  Dee was an adviser to the explorers, including Raleigh, under Queen Elizabeth I in the quest for empire, but that is another story for another day (or another year).

The Thames waterfront, with Raleigh quote, as seen from Southwark Cathedral

Just to put it all in context I've taken a short video showing the area in the pictures above.  Thank you for following me in my math travels -- this was as far as I was able to journey, due to the COVID-19 pandemic, but I sure hope to be back with more content in a year!